Navigating a nonholonomic robot in a cluttered, unknown environment requires accurate perception and precise motion control for real-time collision avoidance. This article presents neural proximal alternating-minimization network (NeuPAN): a real-time, highly accurate, map-free, easy-to-deploy, and environment-invariant robot motion planner. Leveraging a tightly coupled perception-to-control framework, NeuPAN has two key innovations compared to existing approaches: first, it directly maps raw point cloud data to a latent distance feature space for collision-free motion generation, avoiding error propagation from the perception to control pipeline; second, it is interpretable from an end-to-end model-based learning perspective. The crux of NeuPAN is solving an end-to-end mathematical model with numerous point-level constraints using a plug-and-play proximal alternating-minimization network, incorporating neurons in the loop. This allows NeuPAN to generate real-time, physically interpretable motions. It seamlessly integrates data and knowledge engines, and its network parameters can be fine-tuned via back propagation. We evaluate NeuPAN on a ground mobile robot, a wheel-legged robot, and an autonomous vehicle, in extensive simulated and real-world environments. Results demonstrate that NeuPAN outperforms existing baselines in terms of accuracy, efficiency, robustness, and generalization capabilities across various environments, including the cluttered sandbox, office, corridor, and parking lot. We show that NeuPAN works well in unknown and unstructured environments with arbitrarily shaped objects, transforming impassable paths into passable ones.

We study sparse principal component analysis in the high-dimensional, sample-limited regime, aiming to recover a leading component supported on a few coordinates. Despite extensive progress, most methods and analyses are tailored to the flat-spike case, offering little guidance when spike energy is unevenly distributed across the support. Motivated by this, we propose Spectral Energy Pursuit (SEP), an effective iterative scheme that repeatedly screens and reselects coordinates, with a sample complexity that adapts to the energy profile. We develop our framework around a structure function \(s(p)\) that quantifies how spike energy accumulates over its top \(p\) entries. To our knowledge, SEP is the first polynomial-time SPCA method with a sample-complexity guarantee governed by the full energy profile: it succeeds with \(m\gtrsim \max_{1\le p\le k} p\,s^2(p)\,\log n\) samples, recovering the classical \(k^2\log n\) rate for flat spikes and improving to \(k\log n\) for sufficiently concentrated profiles. As a lightweight post-processing, a single truncated power iteration is proven to enable the final estimator to attain a uniform statistical error bound. Empirical simulations using a flat profile and offset-regularized decaying profiles validate that SEP adapts to profile structure without profile-specific tuning and outperforms existing algorithms.

In 6G networks, integrated sensing and communication (ISAC) is envisioned as a key technology that enables wireless systems to perform joint sensing and communication using shared hardware, antenna(s) and spectrum. ISAC designs facilitate emerging applications such as digital twins, smart cities and autonomous driving. Such applications also demand ultra-reliable and low-latency communication (URLLC), a feature that was first introduced in 5G and is expected to be further enhanced in 6G. Thus, an ISAC-enabled URLLC system can prioritize critical and time-sensitive targets and ensure information delivery under strict latency and reliability constraints. We propose a bi-static multiple-input multiple-output (MIMO) ISAC system to detect the arrival of URLLC messages and prioritize their delivery. In this system, a dual-function base station (BS) communicates with a user equipment (UE) and a sensing receiver (SR) is deployed to collect echo signals reflected from a target of interest. The BS regularly transmits messages of enhanced mobile broadband (eMBB) services to the UE. During each eMBB transmission, if the SR senses the presence of a target of interest, it immediately triggers the transmission of an additional URLLC message. To reinforce URLLC transmissions, we propose a dirty-paper coding (DPC)-based technique that mitigates the interference of both eMBB and sensing signals. To decode the eMBB message, we consider two approaches for handling the URLLC interference: treating interference as noise (TIN) and successive interference cancellation (SIC). For this system, we formulate the rate-reliability-detection trade-off in the finite blocklength (FBL) regime by evaluating the communication rate of the eMBB transmissions, the reliability of the URLLC transmissions and the probability of the target detection. Our numerical analysis show that our proposed DPC-based ISAC scheme significantly outperforms power-sharing based ISAC and traditional time-sharing schemes. In particular, it achieves higher eMBB transmission rate while satisfying both URLLC and sensing constraints.

Collaborative perception allows each agent to enhance its perceptual abilities by exchanging messages with others. It inherently results in a trade-off between perception ability and communication costs. Previous works transmit complete full-frame high-dimensional feature maps among agents, resulting in substantial communication costs. To promote communication efficiency, we propose only transmitting the information needed for the collaborator's downstream task. This pragmatic communication strategy focuses on three key aspects: i) pragmatic message selection, which selects task-critical parts from the complete data, resulting in spatially and temporally sparse feature vectors; ii) pragmatic message representation, which achieves pragmatic approximation of high-dimensional feature vectors with a task-adaptive dictionary, enabling communicating with integer indices; iii) pragmatic collaborator selection, which identifies beneficial collaborators, pruning unnecessary communication links. Following this strategy, we first formulate a mathematical optimization framework for the perception-communication trade-off and then propose PragComm, a multi-agent collaborative perception system with two key components: i) single-agent detection and tracking and ii) pragmatic collaboration. The proposed PragComm promotes pragmatic communication and adapts to a wide range of communication conditions. We evaluate PragComm for both collaborative 3D object detection and tracking tasks in both real-world, V2V4Real, and simulation datasets, OPV2V and V2X-SIM2.0. PragComm consistently outperforms previous methods with more than 32.7 K× lower communication volume on OPV2V.

In this paper, we investigate channel estimation for reconfigurable intelligent surface (RIS) empowered millimeter-wave (mmWave) multi-user single-input multiple-output communication systems using low-resolution quantization. Due to the high cost and power consumption of analog-to-digital converters (ADCs) in large antenna arrays and for wide signal bandwidths, designing mmWave systems with low-resolution ADCs is beneficial. To tackle this issue, we propose a channel estimation design using task-based quantization that considers the underlying hybrid analog and digital architecture in order to improve the system performance under finite bit-resolution constraints. Our goal is to accomplish a channel estimation task that minimizes the mean squared error distortion between the true and estimated channel. We develop two types of channel estimators: a cascaded channel estimator for an RIS with purely passive elements, and an estimator for the separate RIS-related channels that leverages additional information from a few semi-passive elements at the RIS capable of processing the received signals with radio frequency chains. Numerical results demonstrate that the proposed channel estimation designs exploiting task-based quantization outperform purely digital methods and can effectively approach the performance of a system with unlimited resolution ADCs. Furthermore, the proposed channel estimators are shown to be superior to baselines with small training overhead.

Combining wireless sensing and edge intelligence, edge perception networks enable intelligent data collection and processing at the network edge. However, traditional sample partition based horizontal federated edge learning (HFEEL) struggles to effectively fuse complementary multi-view information from distributed devices. To address this limitation, we propose a vertical federated edge learning (VFEEL) framework tailored for feature-partitioned sensing data. In this paper, we consider an integrated sensing, communication, and computation (ISCC)-enabled edge perception network, where multiple edge devices utilize wireless signals to sense environmental information for updating their local models, and the edge server aggregates feature embeddings via over-the-air computation (AirComp) for global model training. First, we analyze the convergence behavior of the ISCC-enabled VFEEL in terms of the loss function degradation in the presence of wireless sensing noise and aggregation distortions during AirComp. Then, to accelerate convergence, we aim to optimize the batch size, sensing power, and transmission power control at edge devices as well as the denoising factors at the edge server under limited network constraints on overall energy consumption and per-round latency. Due to the tight coupling of variables, the problem is non-convex. To address this problem, we design an alternating optimization-based algorithm to efficiently obtain a high-quality solution. Numerical results are conducted based on a human motion recognition task to verify that the proposed ISCC-enabled VFEEL algorithm achieves higher accuracy compared with other benchmarking schemes including ISCC-enabled HFEEL approach.

With rising cardiovascular and respiratory disorders and an aging population, healthcare systems require efficient non-contact vital sign monitoring (NCVSM) solutions. This study introduces a robust framework for multi-person localization and vital signs monitoring using multiple-input-multiple-output (MIMO) frequency-modulated continuous wave (FMCW) radar in cluttered environments. First, we developed a hardware phantom that simulates multi-person NCVSM scenarios using recorded thoracic impedance signals to replicate cardiopulmonary dynamics, enabling repeatable validation under diverse conditions. Second, we designed a robust algorithm for multi-person localization leveraging sparse signal processing with physiological characteristics, alongside dictionary-based vital signs estimation that handles interfering respiration harmonics. An adaptive signal refinement procedure enhances continuous NCVSM accuracy by leveraging estimate continuity. Performance was validated through 12 phantom trials and 12 human trials in single- and multi-person scenarios, demonstrating superior performance. In multi-person human trials, our method achieved respiration rate accuracies of$94.14\%$,$98.12\%$, and$98.69\%$within error thresholds of 2, 3, and 4 breaths per minute, respectively, and heart rate accuracies of$87.10\%$,$94.12\%$, and$95.54\%$within the same thresholds, highlighting the framework's potential for reliable healthcare and IoT applications.

In this article, we introduce a deep unfolding framework for Tail-iterative soft thresholding algorithm (ISTA) and Tail-fast ISTA (FISTA), extending classical sparse recovery algorithms into learned architectures and improving upon existing unfolding techniques. By combining the interpretability of iterative solvers with the adaptability of model-based networks, our approach achieves efficient and robust recovery of sparse signals. Tail-based methods incorporate an iterative support estimation step, where the support and target estimations are refined alternately, providing a key advantage over traditional approaches. We integrate this into our architecture, enhancing both recovery performance and noise robustness. We compare the proposed methods against classical solvers, including FISTA and Tail-FISTA, as well as deep unfolding techniques, LISTA and DU-FISTA, across various sparsity levels, dynamic ranges (DRs), and both noiseless and noisy conditions. In noiseless cases, our methods achieve slightly lower performance than classical solvers but with significantly reduced computational costs. Under heavy noise and a high number of nonzero elements, where classical methods struggle, our learned approaches remain resilient and achieve improved recovery rates. To evaluate generalization, we also tested our methods on data generated with a perturbed sensing matrix. In this case, under noisy scenarios, our proposed methods outperform classical sparse recovery algorithms. The proposed framework is general and applies to any linear sparse recovery task in compressed sensing (CS), offering computational efficiency, robustness to noise, and adaptability to real-world data, showcasing the advantages of deep unfolding techniques with iterative support estimation.

Future wireless systems are envisioned to utilize the large spectra available at THz bands for wireless communications. Extremely massive multiple-input multiple-output (MIMO) antennas can be costly and power inefficient for wideband THz communications. An alternative antenna technology, which can achieve low-cost and power-efficient THz signaling, is based on leaky wave antennas (LWAs). In this paper, we explore the usage of the LWAs for wideband downlink multi-user THz communications. We propose a model for LWA-aided communication systems that faithfully captures the antenna operations. We show that LWAs yield frequency-dependent beams, where the equivalent wideband channel induces a dependence between angle, frequency, and spectral lobe width. We identify the LWA’s inherent frequency-selective beamsteering capabilities as motivating multi-band THz communications, in which subbands are allocated among users based on their relative angles. Then, we propose an alternating optimization algorithm for jointly optimizing the LWA configuration along with the spectral division and power allocation to maximize the achievable sum rate performance. Our numerical results show that a single LWA can generate diverse beampatterns, exhibiting performance comparable to costly MIMO architectures in wideband THz multi-user systems.

Infrastructure-mounted sensors can capture rich environmental information to enhance communications and facilitate beamforming in millimeter-wave systems. This work presents an efficient sensing-assisted long-term beam tracking framework that selects optimal beams from a codebook for current and multiple future time slots. We first design a large attention-enhanced neural network (NN) to fully exploit past visual observations for beam tracking. A convolutional NN extracts compact image features, while gated recurrent units with attention capture the temporal dependencies within sequences. The large NN then acts as the teacher to guide the training of a lightweight student NN via knowledge distillation. The student requires shorter input sequences yet preserves long-term beam prediction ability. Numerical results demonstrate that the teacher achieves Top-5 accuracies exceeding 93% for current and six future time slots, approaching state-of-the-art performance with a 90% reduction of model parameters. The student closely matches the teacher's performance while reducing the number of model parameters by over 1670% and cutting complexity by over 450%, despite operating with 60% shorter input sequences. This improvement significantly enhances data efficiency, reduces latency, and reduces power consumption in sensing and processing.

Typical reconfigurable intelligent surface (RIS) implementations include metasurfaces with almost passive unit elements capable of reflecting their incident waves in controllable ways, enhancing wireless communications in a cost-effective manner. In this paper, we advance the concept of intelligent metasurfaces by introducing a flexible array geometry, termed flexible intelligent metasurface (FIM), which supports both element movement (EM) and passive beamforming (PBF). In particular, based on the single-input single-output (SISO) system setup, we first compare three modes of FIM, namely, EM-only, PBF-only, and EM-PBF, in terms of received signal power under different FIM and channel setups. The PBF-only mode, which only adjusts the reflecting phase, shows less effective than the EM-only mode in enhancing received signal strength. The EM-PBF mode, which optimizes both element positions and phases, further enhances performance. Additionally, we investigate the channel estimation problem for FIM systems by designing a protocol that gathers EM and PBF measurements, enabling the formulation of a compressive sensing problem for joint cascaded and direct channel estimation. We then propose a sparse recovery algorithm called clustering mean-field variational sparse Bayesian learning, which enhances estimation performance while maintaining low complexity.

This paper presents a polarization-aware movable antenna (PAMA) framework that integrates polarization effects into the design and optimization of movable antennas (MAs). While MAs have proven effective at boosting wireless communication performance, existing studies primarily focus on phase variations caused by different propagation paths and leverage antenna movements to maximize channel gains. This narrow focus limits the full potential of MAs. In this work, we introduce a polarization-aware channel model rooted in electromagnetic theory, unveiling a defining advantage of MAs over other wireless technologies such as precoding: the ability to optimize polarization matching. This new understanding enables PAMA to extend the applicability of MAs beyond radio-frequency, multipath-rich scenarios to higher-frequency bands, such as mmWave, even with a single line-of-sight (LOS) path. Our findings demonstrate that incorporating polarization considerations into MAs significantly enhances efficiency, link reliability, and data throughput, paving the way for more robust and efficient future wireless networks.

In 6G and future communication systems, the adoption of large scale antenna arrays and high frequency bands is an inevitable trend. This leads to most users operating in the near-field region, where higher angular resolution and sensitivity to distance changes make user mobility effects fundamentally different from those in the far-field. In this work, a systematic study of near-field channel dynamics under user mobility is investigated. We begin by analyzing the Doppler characteristics associated with both line of sight (LoS) and multipath components, and demonstrate that notable Doppler shifts can occur even at low user velocities. In particular, the LoS component exhibits antenna dependent Doppler shifts, highlighting the spatially non-uniform nature of Doppler effects in near-field scenarios. Based on this, we derive a closed form expression for the coherence time in scattering-free environments, which reveals its dependence on antenna aperture, wavelength, user motion, etc. Unlike far-field LoS channels where Doppler effects can be compensated by a phase rotation, the near-field counterpart exhibits antenna dependent Doppler shifts, resulting in a finite coherence time even without scattering. For multipath scenarios, where the near-field channel is inherently sparse, we establish upper and lower bounds for the temporal correlation function. Furthermore, to track time-varying channels, we propose an array segmentation strategy and formulate a state-space model of the near-field channel in the dictionary domain. The proposed estimation framework comprises an expectation maximization (EM) stage using Kalman filtering with Rauch-Tung-Striebel smoothing (KF-RTSS) for virtual channel statistics and a fixed-point iteration for parameter refinement, followed by a Kalman filtering stage for channel prediction. A detailed complexity analysis is also provided. Finally, extensive simulations validate our theoretical analysis and show that the proposed method accurately captures near-field channel dynamics, offering robust performance across different angles, distances, and signal to noise ratios.

This paper considers an intelligent reflecting surface (IRS)-assisted bi-static localization architecture for the sixth-generation (6G) integrated sensing and communication (ISAC) network. The system consists of a transmit user, a receive base station (BS), an IRS, and multiple passive targets in either the far-field or near-field region of the IRS. In particular, we focus on the challenging scenario where the line-of-sight (LOS) paths between targets and the BS are blocked, such that the emitted orthogonal frequency division multiplexing (OFDM) signals from the user reach the BS merely via the user-target-IRS-BS path. Our objective is to localize the targets by estimating their relative positions to the IRS from the received signal at the BS, instead of the BS. We show that subspace-based methods, such as the multiple signal classification (MUSIC) algorithm, can be applied to estimate the relative states from the targets to the IRS, while the spectrum ambiguity exhibits caused by the low-rank IRS-BS channel. To overcome this issue, we propose a novel spatiotemporal IRS phase profile and create a virtual signal model by concatenating the temporal signals over multiple OFDM symbols. Furthermore, we rigorously prove that the spectrum ambiguity issue can be resolved almost surely, if the MUSIC algorithm is applied to our properly constructed temporal-domain signals. Numerical results verify the effectiveness and efficiency of our proposed IRS-assisted localization scheme over the other localization counterparts. Our paper demonstrates the potential of employing passive anchors, i.e., IRSs, to improve the sensing coverage of the active anchors, i.e., BSs.

This paper introduces a deep unfolding-based approach for Full Waveform Inversion (FWI) in quantitative ultrasound imaging. Our technique leverages trained deep neural networks to perform an optimized gradient step that achieves superior results and significantly reduces the number of iterations required for convergence—a crucial advantage for real-world applications. While a recently proposed deep unfolding approach, MB-QRUS, demonstrated higher efficiency than traditional FWI, our experiments on both the training dataset and out-of-distribution examples show that our method significantly outperforms classical FWI and MB-QRUS in reconstruction quality under noisy conditions, while maintaining a high level of efficiency. This work enhances the potential for real-time quantitative ultrasound imaging in clinical settings and suggests broader applicability of FWI across various domains.

The rising demand for multi-person non-contact vital signs monitoring (NCVSM) in healthcare highlights the potential of radar technology, especially in cluttered environments. Single-input multiple-output frequency-modulated continuous- wave (FMCW) radars enable multi-object localization, which is crucial for multi-person NCVSM. However, detecting and positioning humans in crowded scenarios is challenging due to resolution limitations. This work first proposes an iterative method for multi-human localization exploiting joint sparsity and cardiopulmonary properties. Then, the method is unfolded into a neural network that preserves the data’s unique features to further enhance accuracy and reduce computational cost. Simulations containing real-world data show the network’s superior performance in detecting and positioning multiple adjacent humans, outperforming existing techniques via key metrics. This approach can be integrated into advanced NCVSM systems where accuracy and computational efficiency are paramount.

We consider the problem of causal filtering of a model-free process from (noisy) nonlinear measurements. The ‘model-free process’ means that we do not have a state-space model (SSM) of the process dynamics, limiting the use of traditional model-driven filters, such as unscented Kalman filter (UKF) and particle filter (PF). To address the problem we propose a particle-based data-driven nonlinear state estimation (pDANSE) method. In pDANSE, a recurrent neural network (RNN) provides the statistical parameters of a Gaussian prior of the underlying state, and particles are then drawn from the prior to compute the posterior moments. pDANSE is typically trained in a semi-supervised fashion. For our experiments we study the use of half-wave rectification as a nonlinear transformation of measurements. We first show that an unsupervised learning-based method under-performs, and subsequently the semi-supervised learning-based pDANSE performs satisfactorily. Using Lorenz-63 system as benchmark, pDANSE is found to be competitive against a model-driven PF that knows the exact SSM.

Sampling signals with a high dynamic range (DR) poses significant challenges in analog-to-digital conversion (ADC), where the DR of the ADC must exceed that of the input signal to prevent information loss. Modulo sampling offers a promising solution to this problem by reducing the DR of the signal prior to sampling. In this paper, we address the modulo recovery problem in scenarios where the folding parameter is unknown and potentially time-varying, motivated by practical hardware limitations that make it difficult to maintain a constant and precise folding parameter. We provide a theoretical guarantee for the unique recovery of band-limited (BL) signals from modulo samples without requiring knowledge of the folding parameter. Additionally, we develop a robust recovery algorithm specifically for scenarios with a constant but unknown folding parameter. The algorithm’s performance is evaluated through simulations under various conditions, including different oversampling rates and noise levels. The results demonstrate that our method achieves high accuracy in signal recovery, even in challenging environments.

Occlusion is a key factor leading to detection failures. This paper proposes a motion-assisted detection (MAD) method that actively plans an executable path, for the robot to observe the target at a new viewpoint with potentially reduced occlusion. In contrast to existing MAD approaches that may fail in cluttered environments, the proposed framework is robust in such scenarios, therefore termed clutter resilient occlusion avoidance (CROA). The crux to CROA is to minimize the occlusion probability under polyhedron-based collision avoidance constraints via the convex-concave procedure and duality-based bilevel optimization. The system supports lidar-based MAD with intertwined execution of learning-based detection and optimization-based planning. Experiments show that CROA outperforms various MAD schemes under a sparse convolutional neural network detector, in terms of point density, occlusion ratio, and detection error, in a multi-lane urban driving scenario.

This paper presents a polarization-aware movable antenna (PAMA) framework that integrates polarization effects into the design and optimization of movable antennas (MAs). While MAs have proven effective at boosting wireless communication performance, existing studies primarily focus on phase variations caused by different propagation paths and leverage antenna movements to maximize channel gains. This narrow focus limits the full potential of MAs. In this work, we introduce a polarizationaware channel model rooted in electromagnetic theory, unveiling a defining advantage of MAs over other wireless technologies such as precoding: the ability to optimize polarization matching. This new understanding enables PAMA to extend the applicability of MAs beyond radio-frequency, multipath-rich scenarios to higherfrequency bands, such as mmWave, even with a single line-of-sight (LOS) path. Our findings demonstrate that incorporating polarization considerations into MAs significantly enhances efficiency, link reliability, and data throughput, paving the way for more robust and efficient future wireless networks.

In this paper, we propose a bi-static multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system to detect the arrival of ultra-reliable and low-latency communication (URLLC) messages and prioritize their delivery. In this system, a dual-function base station (BS) communicates with a user equipment (UE) and a sensing receiver (SR) is deployed to collect echo signals reflected from a target of interest. The BS regularly transmits messages of enhanced mobile broadband (eMBB) services to the UE. During each eMBB transmission, if the SR senses the presence of a target of interest, it immediately triggers the transmission of an additional URLLC message. To reinforce URLLC transmissions, we propose a dirty-paper coding (DPC)-based technique that mitigates the interference of both eMBB and sensing signals. For this system, we formulate the rate-reliability-detection trade-off in the finite blocklength regime by evaluating the communication rate of the eMBB transmissions, the reliability of the URLLC transmissions and the probability of the target detection. Our numerical analysis show that our proposed DPC-based ISAC scheme significantly outperforms power-sharing based ISAC and traditional time-sharing schemes. In particular, it achieves higher eMBB transmission rate while satisfying both URLLC and sensing constraints.

Integrated sensing and communication (ISAC) in the near-field regime offers the potential to jointly support high-rate downlink transmission and high-resolution multi-target detection by exploiting the spherical-wave nature of electromagnetic propagation. In this paper, we propose a unified beamforming framework for a multi-user multi-target near-field ISAC system. In this system, a multi-antenna base station simultaneously serves multiple single-antenna users and senses multiple point-targets without prior knowledge of their radar cross sections. By optimizing the transmit covariance matrix, our design maximizes the minimum weighted transmit beampattern gain across all targets to ensure accurate sensing while strictly limiting inter-target cross-correlations and guaranteeing per-user communication rate. We extend classical far-field beam-pattern and cross-correlation measures to the near-field by incorporating both angle and range dependencies, enabling discrimination of targets along the same direction but at different distances. The resulting non-convex program is efficiently relaxed to a semidefinite program via rank-one lifting. We then develop a closed-form reconstruction to recover optimal rank-one beamformers. Numerical simulations demonstrate that our near-field ISAC design can simultaneously resolve and serve users/targets along the same direction but at different distances, achieving significant gains over far-field and single-target benchmarks.

Radio frequency wireless power transfer enables charging low-power mobile devices without relying on wired infrastructures. Current existing wireless power transfer systems are typically designed assuming far-field propagation, where the radiated energy is steered to towards given angles, resulting in limited efficiency and possible radiation in undesired locations. An emerging technology for wireless signaling is based on dynamic metasurface antennas (DMAs), which efficiently realize electrically large arrays. When such arrays are employed at high frequencies, wireless power transfer might take place in the radiating near-field (Fresnel) region, where spherical wave propagation holds, providing more degrees-of-freedom and improved performance. In this article, we study wireless power transfer systems charging multiple devices in the Fresnel region, where the energy transmitter is equipped with a DMA, exploring how the antenna configuration can exploit the spherical wavefront to generate focused energy beams. In particular, after presenting a mathematical model for DMA-based radiating near-field wireless power transfer systems, we characterize the weighted sum-harvested energy maximization problem of the considered system, and we propose an efficient solution to jointly design the DMA weights and digital precoding vector. Then, by accounting for hardware constraints, we further extend our study to encompass practical scenarios with discrete phase shifts in DMA elements. Simulation results show that our design generates focused energy beams capable of improving energy transfer efficiency in the radiating near-field with minimal energy pollution.

This article presents a new optical integrated sensing and communication (O-ISAC) framework tailored for cost-effective light-emitting diode (LED) for enhanced Internet of Things (IoT) applications. Unlike prior research on ISAC, which predominantly focused on radio frequency (RF) band, O-ISAC capitalizes on the inherent advantages of the optical spectrum, including the ultrawide license-free bandwidth, immunity to RF interference, and energy efficiency—attributes crucial for IoT communications. The communication and sensing in our O-ISAC system unfold in two phases: 1) directionless O-ISAC and 2) directional O-ISAC. In the first phase, distributed optical access points emit nondirectional light for communication and leverage small-aperture imaging principles for sensing. In the second phase, we put forth the concept of optical beamforming, using collimating lenses to concentrate light, resulting in substantial performance enhancements in both communication and sensing. Numerical and simulation results demonstrate the feasibility and impressive performance of O-ISAC benchmarked against optical separate communication and sensing systems.

Super-resolution (SR) has garnered significant attention within the computer vision community, driven by advances in deep learning (DL) techniques and the growing demand for high-quality visual applications. With the expansion of this field, numerous surveys have emerged. Most existing surveys focus on specific domains, lacking a comprehensive overview of this field. Here, we present an in-depth review of diverse SR methods, encompassing single-image SR (SISR), video SR (VSR), stereo SR (SSR), and light field SR (LFSR). We extensively cover over 150 SISR methods, nearly 70 VSR approaches, and approximately 30 techniques for SSR and LFSR. We analyze methodologies, datasets, evaluation protocols, empirical results, and complexity. In addition, we conducted a taxonomy based on each backbone structure according to the diverse purposes. We also explore valuable yet understudied open issues in the field. We believe that this work will serve as a valuable resource and offer guidance to researchers in this domain. To facilitate access to related work, we created a dedicated repository available at https://github.com/AVC2-UESTC/Holistic-Super-Resolution-Review

Channel estimation poses significant challenges in millimeter-wave massive multiple-input multiple-output systems, especially when the base station has fewer radio-frequency chains than antennas. To address this challenge, one promising solution exploits the beamspace channel sparsity to reconstruct full-dimensional channels from incomplete measurements. This paper presents a model-based deep learning method to reconstruct sparse, as well as approximately sparse, vectors fast and accurately. To implement this method, we propose a trimmed-ridge regression that transforms the sparse-reconstruction problem into a least-squares problem regularized by a nonconvex penalty term, and then derive an iterative solution. We then unfold the iterations into a deep network that can be implemented in online applications to realize real-time computations. To this end, an unfolded trimmed-ridge regression model is constructed using a structural configuration to reduce computational complexity and a model ensemble strategy to improve accuracy. Compared with other state-of-the-art deep learning models, the proposed learning scheme achieves better accuracy and supports higher downlink sum rates.

Due to the utilization of large antenna arrays at base stations (BSs) and the operations of wireless communications in high frequency bands, mobile terminals often find themselves in the near-field of the array aperture. In this work, we address the signal processing challenges of integrated near-field localization and communication in uplink transmission of an integrated sensing and communication (ISAC) system, where the BS performs joint near-field localization and signal detection (JNFLSD). We show that JNFLSD can be formulated as a matrix factorization (MF) problem with proper structures imposed on the factor matrices. Then, leveraging the variational inference (VI) and unitary approximate message passing (UAMP), we develop a low complexity Bayesian approach to MF, called UAMP-MF, to handle a generic MF problem. We then apply the UAMP-MF algorithm to solve the JNFLSD problem, where the factor matrix structures are fully exploited. Extensive simulation results are provided to demonstrate the superior performance of the proposed method.

Motivated by progress in data-driven supervised learning, semantic communication has witnessed remarkable advancements in improving the efficiency of data transmission under various channel conditions. These advancements typically require a substantial amount of training data for offline training, which is challenging in practical systems. Therefore, in this work, we propose O2SC, a one-shot online-learning framework for semantic communication to achieve adaptive transmission under different channel conditions. Since semantic communication relies on acquired channel state information (CSI), we jointly design the channel estimation and semantic communication processes. Specifically, we introduce a denoising module based on one-shot self-supervised learning, allowing semantic communication systems to adapt to new channel conditions without the need to collect extensive training data. The denoising module is utilized to eliminate noise in the received data samples, using only the data samples themselves. Following this, we further exploit meta-learning to allow the system to quickly adapt to diverse channel conditions, by finding an appropriate initialization for each data sample in a timely way. Simulation results demonstrate that the proposed method achieves performance close to that of supervised learning-based approaches while also providing improved generalizability across different channel conditions.

We propose a robust transceiver design for a covert integrated sensing and communications (ISAC) system with imperfect channel state information (CSI). Considering both bounded and probabilistic CSI error models, we formulate worst-case and outage-constrained robust optimization problems of joint transceiver beamforming and radar waveform design to balance the radar performance of multiple targets while ensuring the communications performance and covertness of the system. The optimization problems are challenging due to the non-convexity arising from the semi-infinite constraints (SICs) and the coupled transceiver variables. In an effort to tackle the former difficulty, S-procedure and Bernstein-type inequality are introduced for converting the SICs into finite convex linear matrix inequalities (LMIs) and second-order cone constraints. A robust alternating optimization framework referred to alternating double-checking is developed for decoupling the transceiver design problem into feasibility-checking transmitter- and receiver-side subproblems, transforming the rank-one constraints into a set of LMIs, and verifying the feasibility of beamforming by invoking the matrix-lifting scheme. Numerical results are provided to demonstrate the effectiveness and robustness of the proposed algorithm in improving the performance of covert ISAC systems.

Distributed over-the-air computation (AirComp) is a promising technology for fast data aggregation in wireless networks by leveraging multiple access channel to achieve communication and computation simultaneously. However, device-to-device (D2D) links applied are vulnerable to obstacles, and the performance of distributed AirComp is restricted by the device with the worst channel condition. To tackle these issues, we introduce a multi-functional reconfigurable intelligent surface (MF-RIS) to reconstruct the wireless propagation environment, where the MF-RIS can achieve signal reflection, refraction, and amplification simultaneously. Specifically, we propose an MF-RIS-aided distributed AirComp framework, where MF-RIS receives the aggregated data from all devices and then transmits it to each device for post-processing. We formulate a mean-squared error (MSE) minimization problem by jointly optimizing transmit scalar, receive scalar, and MF-RIS coefficients. To address this non-convex problem, we employ an alternating optimization (AO) technique to decompose it into three subproblems, where semi-closed form or closed form solutions are obtained. Then, we extend the single-input single-output (SISO) system into multiple-input multiple-output (MIMO) one. Next, we derive the asymptotic MSE performance for SISO and MIMO cases when the number of RIS elements and that of transmit/receive antennas are very large. Numerical results demonstrate the superiority of MF-RIS in improving MSE performance compared to the baseline without RIS. Additionally, the MF-RIS outperforms its passive counterparts, which reveals the advantages of deploying MF-RIS in distributed AirComp systems to reduce data aggregation error.

This paper puts forth a new metric, dubbed channel cycle time (CCT), to measure the short-term fairness of communication networks. CCT characterizes the average duration between two consecutive successful transmissions of a user, during which all other users successfully accessed the channel at least once. In contrast to existing short-term fairness measures, CCT provides more comprehensive insight into the transient dynamics of communication networks, with a particular focus on users’ delays and jitter. To validate the efficacy of our approach, we analytically characterize the CCTs for two classical communication protocols: slotted Aloha and CSMA/CA. The analysis demonstrates that CSMA/CA exhibits superior short-term fairness over slotted Aloha. Beyond its role as a measurement metric, CCT has broader implications as a guiding principle for the design of future communication networks by emphasizing factors like fairness, delay, and jitter in short-term behaviors.

Navigating a nonholonomic robot in a cluttered, unknown environment requires accurate perception and precise motion control for real-time collision avoidance. This article presents neural proximal alternating-minimization network (NeuPAN): a real-time, highly accurate, map-free, easy-to-deploy, and environment-invariant robot motion planner. Leveraging a tightly coupled perception-to-control framework, NeuPAN has two key innovations compared to existing approaches: first, it directly maps raw point cloud data to a latent distance feature space for collision-free motion generation, avoiding error propagation from the perception to control pipeline; second, it is interpretable from an end-to-end model-based learning perspective. The crux of NeuPAN is solving an end-to-end mathematical model with numerous point-level constraints using a plug-and-play proximal alternating-minimization network, incorporating neurons in the loop. This allows NeuPAN to generate real-time, physically interpretable motions. It seamlessly integrates data and knowledge engines, and its network parameters can be fine-tuned via backpropagation. We evaluate NeuPAN on a ground mobile robot, a wheel-legged robot, and an autonomous vehicle, in extensive simulated and real-world environments. Results demonstrate that NeuPAN outperforms existing baselines in terms of accuracy, efficiency, robustness, and generalization capabilities across various environments, including the cluttered sandbox, office, corridor, and parking lot. We show that NeuPAN works well in unknown and unstructured environments with arbitrarily shaped objects, transforming impassable paths into passable ones.

Most near-field (NF) localization algorithms cannot deal with the underdetermined case, while those which can are computationally expensive due to employment of fourth-order cumulants. In this work, a low-complexity solution is provided for underdetermined three-dimensional (3-D) NF localization, by employing second-order statistics with a tailored array configuration named two parallel centrally symmetric unfold coprime (TPSC) array. Its implementation can be divided into three stages. Firstly, the proposed algorithm constructs two cross-correlation matrices based on the received array data, which eliminates the non-linear range-related information of NF signals. Secondly, covariance and vectorization operations are applied to these two cross-correlation matrices to form a virtual array with extended aperture. Finally, the two-dimensional (2-D) angle parameters are estimated by the sparse and parametric approach (SPA) and a phase retrieval operation, and then the one-dimensional (1-D) range parameter is achieved by the multiple signal classification (MUSIC) algorithm. One specific feature is that the estimated angle and range parameters are matched automatically. An analysis of the properties of the TPSC array is provided, and an optimal parameter configuration is derived, given that the total number of array elements is fixed. Simulation results demonstrate that the designed TPSC array can achieve underdetermined 3-D NF localization, and deliver enhanced estimation capabilities, surpassing those of established algorithms.

Communication and energy efficiencies are two crucial objectives in the pursuit of edge intelligence in 6G networks, and become increasingly important given the prevalence of large model training. Existing designs typically focus on either communication efficiency or energy efficiency due to the fact that improving one objective generally comes at the expense of the other. Over-the-air federated learning (OTA-FL) has recently emerged as a promising approach to enhance both efficiencies through an integrated communication and computation design. Nevertheless, most previous studies on OTA-FL only consider scenarios where the dataset for the entire FL procedure is collected and available prior to training. In real-world applications, devices continuously collect new data in an online manner. This underscores the significance of sample collection through sensing in a practical FL pipeline. We propose to integrate sensing with communication and computation into a joint design to further boost the communication-and-energy efficiencies of OTA-FL. Specifically, we consider a training latency and energy consumption minimization problem with performance guarantees. To this end, we first derive an average training error (ATE) metric to quantify convergence performance. Then, a joint sensing, communication and computation resource allocation strategy is developed based on a deep reinforcement learning (DRL) algorithm that nests convex optimization with a deep Q-network. Extensive experiments are conducted to validate our theoretical analysis, and demonstrate the effectiveness of the proposed design for communication-and-energy efficient FL.

Maneuvering target tracking is an important service of future wireless networks to assist innovative applications such as intelligent transportation. However, tracking maneuvering targets by cellular networks faces many challenges. In particular, the dense network and high-speed targets make the selection of the sensing nodes (SNs) and the associated power allocation very challenging. Existing methods demonstrated engaging performance, but with high computational complexity. In this paper, we propose a model-driven deep learning (DL)-based approach for SN selection. To this end, we first propose an iterative SN selection method by jointly exploiting the majorization-minimization (MM) framework and the alternating direction method of multipliers (ADMM). Then, we unfold the iterative algorithm as a deep neural network and prove its convergence. The proposed method achieves lower computational complexity, as the number of layers is less than the number of iterations required by the original algorithm, and each layer only involves simple matrix-vector additions/multiplications. Finally, we propose an efficient power allocation method based on fixed point (FP) water filling and solve the joint SN selection and power allocation problem under the alternative optimization framework. Simulation results show that the proposed method achieves better performance than conventional optimization-based algorithms with much lower computational complexity.

Reconfigurable holographic surfaces (RHSs) have been suggested as an energy-efficient solution for extremely large-scale arrays. By controlling the amplitude of RHS elements, high-gain directional holographic patterns can be achieved. However, the complexity of acquiring real-time channel state information (CSI) for beamforming is exceedingly high, particularly in large-scale RHS-assisted communications, where users may be distributed in the near-field region of RHS. This paper proposes a one-shot multi-user beam training scheme in large-scale RHS-assisted systems applicable to both near and far fields. The proposed beam training scheme comprises two phases: angle search and distance search, both conducted simultaneously for all users. For the angle search, an RHS angular codebook is designed based on holographic principles so that each codeword covers multiple angles in both near-field and far-field regions, enabling simultaneous angular search for all users. For the distance search, we construct the distance-adaptive codewords covering all candidate angles of users in a real-time way by leveraging the additivity of holographic patterns, which is different from the traditional phase array case. Simulation results demonstrate that the proposed scheme achieves higher system throughput compared to traditional beam training schemes. The beam training accuracy approaches the upper bound of exhaustive search at a significantly reduced overhead.

Gold nanoparticles (GNPs) hold promise to improve the detection and treatment of diseases such as cancer and Alzheimer's. However, detecting GNPs in the body remains an unmet technological challenge. This work introduces a new methodology for remotely localizing and tracking GNPs in various therapeutic settings, including through biological tissues, using a compact millimeter-wave radar system. By modeling GNP detection as a sparse recovery problem, we propose a method that localizes GNPs in cluttered environments as well as detects changes in concentrations that relate to changes in the intensity of the reflected signals. Our approach paves the way to a first-ever noninvasive, non-ionizing, simple approach for bioimaging and tracking GNPs inside the body.

THz communications are expected to play a profound role in future wireless systems. The current trend of the extremely massive multiple-input multiple-output (MIMO) antenna architectures tends to be costly and power inefficient when implementing wideband THz communications. An emerging THz antenna technology is leaky wave antenna (LWA), which can realize frequency selective beamforming with a single radiating element. In this work, we explore the usage of LWAs technology for wideband multi-user THz communications. We propose a model for the LWA signal processing that is physically compliant facilitating studying LWA-aided communication systems. Focusing on downlink systems, we propose an alternating optimization algorithm for jointly optimizing the LWA configuration along with the signal spectral power allocation to maximize the sum-rate performance. Our numerical results show that a single LWA can generate diverse beampatterns at THz exhibiting performance comparable to costly fully digital MIMO arrays.

Task-oriented communication exploits the task to improve communication efficiency. Most existing works on task-oriented communication transmit analog signals without quantization, which limits its application in digital communication systems. This paper studies digital task-oriented communication systems with hardware-limited scalar quantization (TOC-SQ) for computation-limited scenarios such as the Internet of Things, where the source data is encoded by a source encoder and then quantized by hardware-limited quantizers for digital transmission. Accordingly, the receiver contains a source decoder to decode the received signal. Our goal is to minimize the mean squared error (MSE) between the transmitted and received task-relevant signals to achieve optimal task performance under a certain bit budget. In particular, we first establish a theoretical analysis framework for TOC-SQ. Then, the closed-form expressions of the source encoder and decoder are derived for linear tasks. Finally, the lower bound of the MSE between the transmitted and received task-relevant information is analyzed to evaluate the task performance. Simulation results verify that the proposed TOC-SQ achieves 6.9 dB MSE gains in frequency-selective channels compared with analog TOC systems.

The recovery of high dynamic range shift-invariant (SI) signals presents a significant challenge in the realm of analog-to-digital converters (ADCs). A critical aspect in this context is that the dynamic range of the ADC, needs to surpass that of the input analog signal in order to prevent any loss of information. Modulo sampling, a technique recently studied primarily for bandlimited (BL) signals, has proven effective in mitigating dynamic range limitations. Here we extend recent results to more general SI signals. Our suggested method involves applying a low-pass filter (LPF) to obtain a BL signal, which can then be uniquely reconstructed from its modulo samples when sampled above the Nyquist rate. Subsequently, the original SI signal is successfully recovered from the reconstructed BL signal via appropriate filtering. The system’s performance under various noise levels is demonstrated. This method opens new possibilities for efficiently recovering SI signals using modulo sampling, extending its applicability beyond BL signals and leveraging a slightly higher sampling rate than the Nyquist rate.

Compressive sensing (CS) techniques for estimating the direction-of-arrival (DoA) stand apart from traditional approaches due to their ability to derive DoA information from just a single snapshot, eliminating the need for a large number of snapshots. This research addresses the challenge of adaptively choosing sensors for each snapshot during DoA tracking. We have devised a greedy algorithm for sensor selection, incorporating a submodular cost function based on our proposed deterministic prior models for DoA. Notably, we show that this selection algorithm is equally efficient compared to the conventional greedy method that relies on exact knowledge of the DOAs. We also introduce a modified version of a conventional CS-reconstruction algorithm that takes advantage of prior information to reduce the required number of measurements and computational time. We demonstrate that the tracking accuracy is improved when using the deterministic priors for sensor selection and subsequent reconstruction.

Recovering a sparse target vector with reduced sparsity from a given observation vector is a major challenge in many applications. The well-known tail-minimization approaches tackle this challenge by minimizing the tail part of the target vector. Building upon this, recent development, the tail fast iterative soft thresholding algorithm (Tail-FISTA) formulates the tail-minimization problem as an unconstrained l1-minimization problem and solves it with the FISTA method. Motivated by Tail-FISTA and the tail-minimization approaches, in this paper, we propose a sparse signal recovery algorithm called the recursive-tail-FISTA (R-Tail-FISTA). We employ a two-step procedure for R-Tail-FISTA: 1. We consider the tail-minimization problem and formulate it as an unconstrained l1-minimization problem. 2. We solve it by using the Tail-FISTA approach. We demonstrate that the R-Tail-FISTA method performs better in terms of sparse signal recovery compared to state-of-the-art algorithms. Additionally, we demonstrate the superiority of R-Tail-FISTA by recursively applying the tail-minimization technique to the tail part of the target vector twice. Furthermore, we numerically show that the convergence rate is better for R-Tail-FISTA than that of Tail-FISTA.

In this work, we consider a multi-server federated learning (FL) framework, referred to as Confederated Learning (CFL), in order to accommodate a larger number of users. To reduce the communication overhead of the CFL system, we propose a linearly convergent stochastic gradient method. The proposed algorithm incorporates a conditionally-triggered user selection (CTUS) mechanism as the central component. Simulation results show that it achieves advantageous communication efficiency over GT-SAGA.

We consider matrix factorization (MF) with certain constraints, which finds wide applications in various areas. Leveraging variational inference (VI) and unitary approximate message passing (UAMP), we develop a Bayesian approach to MF with an efficient message passing implementation, called UAMP-MF. With proper priors imposed on the factor matrices, UAMP-MF can be used to solve a range of problems formulated as MF, such as dictionary learning, compressive sensing with matrix uncertainty, robust principal component analysis, etc. Numerical examples are provided to show that UAMP-MF significantly outperforms state-of-the-art algorithms in terms of computational complexity, recovery accuracy and robustness.

The employment of extremely large antenna arrays and high-frequency signaling makes future communication systems likely to operate in the near-field region, where the conventional planar wave assumption is invalid. Instead, a spherical wave assumption which provides both the user angle and distance information is more accurate. Spherical wave-based channel representation and estimation is still under investigation. In this work, we propose a distance-parameterized angular-domain sparse model to represent the near-field channel, followed by a joint dictionary learning and sparse recovery based channel estimation algorithm. The proposed sparse representation model overcomes challenges such as the storage burden and high dictionary coherence that arise in the existing polar-domain method. Simulations in multi-user communication scenarios support the superiority of the proposed near-field channel sparse representation and estimation over the polar-domain method in channel estimation error and pave the way to efficient and accurate modeling in the near-field regime.

In task-based quantization, a multivariate analog signal is transformed into a digital signal using a limited number of low-resolution analog-to-digital converters (ADCs). This process aims to minimize a fidelity criterion, which is assessed against an unobserved task variable that is correlated with the analog signal. The scenario models various applications of interest such as channel estimation, medical imaging applications, and object localization. This work explores the integration of analog processing components-such as analog delay elements, polynomial operators, and envelope detectors-prior to ADC quantization. Specifically, four scenarios, involving different collections of analog processing operators are considered: (i) arbitrary polynomial operators with analog delay elements, (ii) limited-degree polynomial operators, excluding delay elements, (iii) sequences of envelope detectors, and (iv) a combination of analog delay elements and linear combiners. For each scenario, the minimum achievable distortion is quantified through derivation of computable expressions in various statistical settings. It is shown that analog processing can significantly reduce the distortion in task reconstruction. Numerical simulations in a Gaussian example are provided to give further insights into the aforementioned analog processing gains.

In this work, we investigate the relationship between the dynamic range and quantization noise power in modulo analog-to-digital converters (ADCs). An algorithm to recover the original signal from quantized modulo observations with 1-bit side information is analyzed. We prove that an oversampling factor of OF$> 3$and a quantizer resolution of$b > 3$are sufficient for the modulo ADC to have better quantization noise suppression than a standard ADC without the modulo operator. Under this setting, the mean squared error (MSE) of a modulo ADC is$\mathcal{O}\left(\frac{1}{\text{OF}^{3}}\right)$whereas that of a standard ADC is only$\mathcal{O}\left(\frac{1}{\text{OF}}\right)$. Numerical results are presented to validate the derived performance guarantees.

Much of Bayesian inference centers around the design of estimators for inverse problems which are optimal assuming the data comes from a known prior. But what do these optimality guarantees mean if the prior is unknown? In recent years, algorithm unrolling has emerged as deep learning's answer to this age-old question: design a neural network whose layers can in principle simulate iterations of inference algorithms and train on data generated by the unknown prior. Despite its empirical success, however, it has remained unclear whether this method can provably recover the performance of its optimal, prior-aware counterparts. In this work, we prove the first rigorous learning guarantees for neural networks based on unrolling approximate message passing (AMP). For compressed sensing, we prove that when trained on data drawn from a product prior, the layers of the network approximately converge to the same denoisers used in Bayes AMP. We also provide extensive numerical experiments for compressed sensing and rank-one matrix estimation demonstrating the advantages of our unrolled architecture \--- in addition to being able to obliviously adapt to general priors, it exhibits improvements over Bayes AMP in more general settings of low dimensions, non-Gaussian designs, and non-product priors.

This paper puts forth a new metric, dubbed channel cycle time (CCT), to measure the short-term fairness of Communication networks. CCT characterizes the average duration between two consecutive successful transmissions of a user, during which all other users successfully accessed the channel at least once. In contrast to existing short-term fairness measures, CCT provides more comprehensive insight into the transient dynamics of communication networks, with a particular focus on users' delays and jitter. To validate the efficacy of our approach, we analytically characterize the CCTs for two classical commu-nication protocols: slotted Aloha and CSMA/CA. The analysis demonstrates that CSMA/CA exhibits superior short-term fairness over slotted Aloha. Beyond its role as a measurement metric, CCT has broader implications as a guiding principle for the design of future communication networks by emphasizing factors like fairness, delay, and jitter in short-term behaviors.

Maneuvering target tracking will be one of the es-sential applications for future perceptive mobile networks, where multiple sensing nodes (SNs) collaboratively track the same tar-get. However, the associated SN selection is a substantial challenge due to stringent latency requirements of sensing applications. In this paper, we propose a model-driven approach by unfolding conventional optimization-based methods to tackle this problem. To this end, we first propose an iterative selection method based on the majorization-minimization (MM) framework and the alternating direction method of multipliers (ADMM). Then, we unfold the MM-ADMM approach as a deep neural network (DNN) to reduce the computational complexity and improve the performance, by leveraging an enhanced surrogate function. Simulation results demonstrate that the unfolded DNN outper-forms conventional methods with much lower computational complexity.

It is a fundamental problem to analyze the performance bound of multiple‐input multiple‐output dual‐functional radar‐communication systems. To this end, we derive a performance bound on the communication function under a constraint on radar performance. To facilitate the analysis, in this paper, we consider a simplified situation where there is only one downlink user and one radar target. We analyze the properties of the performance bound and the corresponding waveform design strategy to achieve the bound. When the downlink user and the radar target meet certain conditions, we obtain analytical expressions for the bound and the corresponding waveform design strategy. The results reveal a tradeoff between communication and radar performance, which is essentially caused by the energy sharing and allocation between radar and communication functions of the system.

Federated learning (FL) has been envisioned to enable many Internet of Things (IoT) devices to perform large-scale machine learning without sharing raw data, resulting in significant privacy improvements. In a wireless IoT system, FL helps clients to secure their confidential information and achieve improved learning performance. However, the conventional FL architecture is vulnerable to Byzantine workers, possessing the potential to send malicious updates that compromise the accuracy of the global model. Previous studies have proposed various secure aggregation rules and attacker detection techniques to address this issue. However, these techniques exhibit limited effectiveness and may lead to a decrease in accuracy. To overcome these limitations, we propose a Byzantine client detection algorithm called FedXPro by combining the PC/BC-DIM neural network and Geometric Median (GM). Predictive coding (PC) is the core of the PC/BC-DIM architecture, which can perform Bayesian inference by fusing priors and likelihoods to determine posterior distributions. The GM is employed to determine the prior knowledge of legitimate clients to execute the PC/BC-DIM algorithm. During training, the framework calculates the probability distribution for a set of valid clients chosen from the GM. In testing, it attempts to reconstruct the same distribution from other clients concerning prior knowledge, and ultimately, the reconstruction power is utilized to filter the malicious clients. Our extensive simulations demonstrate the superiority of our FedXPro approach over other state-of-the-art methods in terms of accuracy, a guaranteed faster convergence rate, and attack detection under different network settings.

Many wearable Internet of Medical Things (IoMT) devices have limited computing power and small storage space. Additionally, the healthcare data sensed by a single IoMT device is not enough to train a sophisticated deep learning model. To address these challenges, we propose a federated split learning (FedSL) framework that allows for collaborative healthcare analytics on multiple IoMT devices with limited resources. Compared to centralized learning, FedSL can protect user privacy by not sending raw data over wireless networks. Furthermore, FedSL offers more flexibility than other federated learning methods. It enables even low-end IoMT devices to participate in model training and result inference. Experimental results show that our FedSL performs well on medical imaging tasks with different data distributions.

Integrated sensing and communications (ISAC) has received considerable attention from both industry and academia. By sharing the spectrum and hardware platform, ISAC significantly reduces costs and improves spectral, energy, and hardware efficiencies. To support the large number of communication users (CUs) and sensing targets (STs), the design of multiple access (MA) is a fundamental issue in ISAC. MA techniques in ISAC are expected to avoid mutual interference between sensing and communicating functions under the critical constraints of both functions. In this article, we present an overview on approaches of MA for ISAC, from orthogonal transmission strategies to nonorthogonal ones, realized in time, frequency, code, spatial, delay-Doppler, power, and/or multiple domains. We discuss their individual implementation schemes and corresponding resource allocation strategies, as well as highlight future research opportunities.

The employment of extremely large antenna arrays and high-frequency signaling makes future 6G wireless communications likely to operate in the near-field region. In this case, the spherical wave assumption which takes into account both the user angle and distance is more accurate than the conventional planar one that is only related to the user angle. Therefore, the conventional planar wave based far-field channel model as well as its associated estimation algorithms need to be reconsidered. Here we first propose a distance-parameterized angular-domain sparse model to represent the near-field channel. In this model, the user distance is included in the dictionary as an unknown parameter, so that the number of dictionary columns depends only on the angular space division. This is different from the existing polar-domain near-field channel model where the dictionary is constructed on an angle-distance two-dimensional (2D) space. Next, using this model, joint dictionary learning and sparse recovery based channel estimation methods are proposed for both line of sight (LoS) and multi-path settings. To further demonstrate the effectiveness of the suggested algorithms, recovery conditions and computational complexity are studied. Our analysis shows that with the decrease of distance estimation error in the dictionary, the support set of the angular-domain sparse vector can be exactly recovered under certain Restricted Isometry Property (RIP) based conditions. The high storage burden and dictionary coherence issues that arise in the polar-domain 2D representation are also well addressed. Finally, simulations in multi-user communication scenarios support the superiority of the proposed near-field channel sparse representation and estimation over the existing polar-domain method in channel estimation error.

We present two deep unfolding neural networks for the simultaneous tasks of background subtraction and foreground detection in video. Unlike conventional neural networks based on deep feature extraction, we incorporate domain-knowledge models by considering a masked variation of the robust principal component analysis problem (RPCA). With this approach, we separate video clips into low-rank and sparse components, respectively corresponding to the backgrounds and foreground masks indicating the presence of moving objects. Our models, coined ROMAN-S and ROMAN-R, map the iterations of two alternating direction of multipliers methods (ADMM) to trainable convolutional layers, and the proximal operators are mapped to non-linear activation functions with trainable thresholds. This approach leads to lightweight networks with enhanced interpretability that can be trained on limited data. In ROMAN-S, the correlation in time of successive binary masks is controlled with side-information based on$\ell _{1}$-$\ell _{1}$minimization. ROMAN-R enhances the foreground detection by learning a dictionary of atoms to represent the moving foreground in a high-dimensional feature space and by using reweighted-$\ell _{1}$-$\ell _{1}$minimization. Experiments are conducted on both synthetic and real video datasets, for which we also include an analysis of the generalization to unseen clips. Comparisons are made with existing deep unfolding RPCA neural networks, which do not use a mask formulation for the foreground, and with a 3D U-Net baseline. Results show that our proposed models outperform other deep unfolding networks, as well as the untrained optimization algorithms. ROMAN-R, in particular, is competitive with the U-Net baseline for foreground detection, with the additional advantage of providing video backgrounds and requiring substantially fewer training parameters and smaller training sets.

This paper proposes a framework for designing robust precoders for a multi-input single-output (MISO) system that performs integrated sensing and communication (ISAC) across multiple cells and users. We use Cramer-Rao-Bound (CRB) to measure the sensing performance and derive its expressions for two multi-cell scenarios, namely coordinated beamforming (CBF) and coordinated multi-point (CoMP). In the CBF scheme, a BS shares channel state information (CSI) and estimates target parameters using monostatic sensing. In contrast, a BS in the CoMP scheme shares the CSI and data, allowing bistatic sensing through inter-cell reflection. We consider both block-level (BL) and symbol-level (SL) precoding schemes for both the multi-cell scenarios that are robust to channel state estimation errors. The formulated optimization problems to minimize the CRB in estimating the parameters of a target and maximize the minimum communication signal-to-interference-plus-noise-ratio (SINR) while satisfying a given total transmit power budget are non-convex. We tackle the non-convexity using a combination of semidefinite relaxation (SDR) and alternating optimization (AO) techniques. Simulations suggest that neglecting the inter-cell reflection and communication links degrades the performance of an ISAC system. The CoMP scenario employing SL precoding performs the best, whereas the BL precoding applied in the CBF scenario produces relatively high estimation error for a given minimum SINR value.

Index modulation (IM) schemes for reconfigurable intelligent surfaces (RIS)-assisted systems are envisioned as promising technologies for fifth-generation-advanced and sixth-generation (6G) wireless communication systems to enhance various system capabilities such as coverage area and network capacity. In this paper, we consider a receive diversity RIS-assisted wireless communication system employing IM schemes, namely, space-shift keying (SSK) with binary modulation and spatial modulation (SM) with M-ary modulation for data transmission. The RIS lies in close proximity to the transmitter, and the transmitted data is subjected to a fading environment with a prominent line-of-sight component statistically modeled by a Rician distribution. A receiver structure based on a greedy detection rule is employed to select the receive diversity branch with the highest received signal energy for demodulation. The performance of the considered system is evaluated by obtaining a series-form expression for the probability of erroneous index detection (PED) of the considered target antenna using a characteristic function approach. In addition, closed-form and asymptotic expressions at high and low signal-to-noise ratios (SNRs) for the bit error rate (BER) of the SSK-based system, and the SM-based system employing M-ary phase-shift keying and M-ary quadrature amplitude modulation schemes are derived. The dependencies of the system performance on various parameters are corroborated via numerical results. The asymptotic expressions and results of PED and BER at high and low SNR values lead to the observation of a performance saturation and the presence of an SNR value as a point of inflection, which is attributed to the greedy detector.

We investigate signal detection in multiple-input-multiple-output (MIMO) communication systems with hardware impairments, such as power amplifier nonlinearity and in-phase/quadrature imbalance. To deal with the complex combined effects of hardware imperfections, neural network (NN) techniques, in particular deep neural networks (DNNs), have been studied to directly compensate for the impact of hardware impairments. However, it is difficult to train a DNN with limited pilot signals, hindering its practical application. In this work, we investigate how to achieve efficient Bayesian signal detection in MIMO systems with hardware imperfections. Characterizing combined hardware imperfections often leads to complicated signal models, making Bayesian signal detection challenging. To address this issue, we first train an NN to ‘model’ the MIMO system with hardware imperfections and then perform Bayesian inference based on the trained NN. Modelling the MIMO system with NN enables the design of NN architectures based on the signal flow of the MIMO system, minimizing the number of NN layers and parameters, which is crucial to achieving efficient training with limited pilot signals. We then represent the trained NN with a factor graph, and design an efficient message passing based Bayesian signal detector, leveraging the unitary approximate message passing (UAMP) algorithm. The implementation of a turbo receiver with the proposed Bayesian detector is also investigated. Extensive simulation results demonstrate that the proposed technique delivers remarkably better performance than state-of-the-art methods.

We consider transmit beamforming and reflection pattern design in reconfigurable intelligent surface (RIS)-assisted integrated sensing and communication (ISAC) systems to jointly precode communication symbols and radar waveforms. We treat two settings of multiple users and targets. In the first, we use a single RIS to enhance the communication performance of the ISAC system and design beams with good cross-correlation properties to match a desired beampattern while guaranteeing a desired signal-to-interference-plus-noise ratio (SINR) for each user. In the second setting, we use two dedicated RISs to aid the ISAC system, wherein the beams are designed to maximize the worst-case target illumination power while guaranteeing a desired SINR for each user. We propose solvers based on alternating optimization as the design problems in both cases are non-convex optimization problems. Through numerical simulations, we demonstrate the advantages of RIS-assisted ISAC systems. In particular, we show that the proposed single-RIS assisted ISAC system improves the minimum user SINR while suffering from a moderate loss in radar target illumination power. On the other hand, the dual-RIS assisted ISAC system improves both minimum user SINR as well as worst-case target illumination power at the targets, especially when the users and targets are not directly visible to the ISAC transmitter.

Federated Learning(FL) is a widely embraced paradigm for distilling artificial intelligence from distributed mobile data. However, the deployment of FL in mobile networks can be compromised by exposure to interference from neighboring cells or jammers. Existing interference mitigation techniques require multi-cell cooperation or at least interference channel state information, which is expensive in practice. On the other hand, power control that treats interference as noise may not be effective due to limited power budgets, and also that this mechanism can trigger countermeasures by interference sources. As a practical approach for protecting FL against interference, we proposeSpectrum Breathing, which cascades stochastic-gradient pruning and spread spectrum to suppress interference without bandwidth expansion. The cost is higher learning latency by exploiting the graceful degradation of learning speed due to pruning. We synchronize the two operations such that their levels are controlled by the same parameter,Breathing Depth. To optimally control the parameter, we develop a martingale-based approach to convergence analysis of Over-the-Air FL with spectrum breathing, termed AirBreathing FL. We show a performance tradeoff between gradient-pruning and interference-induced error as regulated by the breathing depth. Given receive SIR and model size, the optimization of the tradeoff yields two schemes for controlling the breathing depth that can be either fixed or adaptive to channels and the learning process. As shown by experiments, in scenarios where traditional Over-the-Air FL fails to converge in the presence of strong interference, AirBreahing FL with either fixed or adaptive breathing depth can ensure convergence where the adaptive scheme achieves close-to-ideal performance.

In this paper, we propose and study a multi-functional reconfigurable intelligent surface (MF-RIS) architecture. In contrast to conventional single-functional RIS (SF-RIS) that only reflects signals, the proposed MF-RIS simultaneously supports multiple functions with one surface, including reflection, refraction, amplification, and energy harvesting of wireless signals. As such, the proposed MF-RIS is capable of significantly enhancing RIS signal coverage by amplifying the signal reflected/refracted by the RIS with the energy harvested. We present the signal model of the proposed MF-RIS, and formulate an optimization problem to maximize the sum-rate of multiple users in an MF-RIS-aided non-orthogonal multiple access network. We jointly optimize the transmit beamforming, power allocations as well as the operating modes and parameters for different elements of the MF-RIS and its deployment location, via an efficient iterative algorithm. Simulation results are provided which show significant performance gains of the MF-RIS over SF-RISs with only some of its functions available. Moreover, we demonstrate that there exists a fundamental trade-off between sum-rate maximization and harvested energy maximization. In contrast to SF-RISs which can be deployed near either the transmitter or receiver, the proposed MF-RIS should be deployed closer to the transmitter for maximizing its communication throughput with more energy harvested.

This paper studies a new multi-device edge artificial-intelligent (AI) system, which jointly exploits the AI model split inference and integrated sensing and communication (ISAC) to enable low-latency intelligent services at the network edge. In this system, multiple ISAC devices perform radar sensing to obtain multi-view data, and then offload the quantized version of extracted features to a centralized edge server, which conducts model inference based on the cascaded feature vectors. Under this setup and by considering classification tasks, we measure the inference accuracy by adopting an approximate but tractable metric, namely discriminant gain, which is defined as the distance of two classes in the Euclidean feature space under normalized covariance. To maximize the discriminant gain, we first quantify the influence of the sensing, computation, and communication processes on it with a derived closed-form expression. Then, an end-to-end task-oriented resource management approach is developed by integrating the three processes into a joint design. This integrated sensing, computation, and communication (ISCC) design approach, however, leads to a challenging non-convex optimization problem, due to the complicated form of discriminant gain and the device heterogeneity in terms of channel gain, quantization level, and generated feature subsets. Remarkably, the considered non-convex problem can be optimally solved based on the sum-of-ratios method. This gives the optimal ISCC scheme, that jointly determines the transmit power and time allocation at multiple devices for sensing and communication, as well as their quantization bits allocation for computation distortion control. By using human motions recognition as a concrete AI inference task, extensive experiments are conducted to verify the performance of our derived optimal ISCC scheme.

Holographic MIMO communications, enabled by large-scale antenna arrays with quasi-continuous apertures, are potential technology for spectrum efficiency improvement. However, the increased antenna aperture size extends the range of the Fresnel region, leading to a hybrid near-far field communication mode. The users and scatterers randomly lie in near-field and far-field zones, and thus, conventional far-field-only and near-field-only channel estimation methods may not work. To tackle this challenge, we demonstrate the existence of the power diffusion (PD) effect, which leads to a mismatch between the hybrid-field channel and existing channel estimation methods. Specifically, in far-field and near-field transform domains, the power of one channel path may diffuse to other positions, thus generating fake paths. This renders the conventional techniques unable to detect those real paths. We propose a PD-aware orthogonal matching pursuit (PD-OMP) algorithm to eliminate the influence of the PD effect by identifying the PD range, within which the path power diffuses to other positions. PD-OMP fits a general case without prior knowledge of respective numbers of near-field and far-field paths and the user’s location. Simulation results show that PD-OMP can accurately estimate the channel when antenna spacing is below half wavelength and outperform current state-of-the-art hybrid-field channel estimation methods.

Grant-free random access is an effective technology for enabling low-overhead and low-latency massive access, where joint activity detection and channel estimation (JADCE) is a critical issue. Although existing compressed sensing algorithms can be applied for JADCE, they usually fail to simultaneously harvest the following properties: effective sparsity inducing, fast convergence, robust to different pilot sequences, and adaptive to time-varying networks. To this end, we propose an unfolding framework for JADCE based on the proximal gradient method. Specifically, we formulate the JADCE problem as a group-row-sparse matrix recovery problem and leverage a minimax concave penalty rather than the widely-used$\ell _{1}$-norm to induce sparsity. We then develop a proximal gradient-based unfolding neural network that parameterizes the algorithmic iterations. To improve convergence rate, we incorporate momentum into the unfolding neural network, and prove the accelerated convergence theoretically. Based on the convergence analysis, we further develop an adaptive-tuning algorithm, which adjusts its parameters to different signal-to-noise ratio settings. Simulations show that the proposed unfolding neural network achieves better recovery performance, convergence rate, and adaptivity than current baselines.

Federated Learning (FL) is a widely embraced paradigm for distilling artificial intelligence from distributed mobile data. However, the deployment of FL in mobile networks is compromised due to the exposure to interference from neighboring cells, besides a communication bottleneck caused by the uploading of high-dimensional model updates. Existing interference mitigation techniques require multi-cell cooperation or at least interference Channel State Information (CSI), which is expensive in practice. To address these challenges, we propose Spectrum Breathing, which cascades stochastic-gradient pruning and spread spectrum to suppress interference without bandwidth expansion. The cost is higher learning latency by exploiting the graceful degradation of learning speed due to pruning. We synchronize the two operations using a common parameter, Breathing Depth, and develop a martingale-based approach to convergence analysis of the Over-the-Air FL with Spectrum Breathing (AirBreathing FL). Given the receive SIR and model size, the optimization of the tradeoff between pruning and interference-induced error yields the scheme for controlling the breathing depth that can be adaptive to channels and learning process. Experiments show that AirBreathing FL with adaptive breathing depth can obtain close-to-ideal performance in scenarios where traditional over-the-air FL fails to converge in the presence of strong interference.

In this paper, we explore robust transceiver design for an integrated sensing and communications system with bounded channel estimation error. To maximize the minimum sensing performance of multiple targets while satisfying communications requirements, we study the worst-case robust op-timization problem by jointly optimizing the transmitter and receiver variables. The formulated problem is challenging due to the non-convexity arising from the semi-infinite constraints (SICs) and coupled variables. To overcome these difficulties, we adopt the S-procedure to convert the SICs into finite convex linear matrix inequalities (LMIs). Using the alternating opti-mization technique, we decouple the robust transceiver design problem into feasibility-checking subproblems. By exploiting matrix lifting, we transform the rank-one constraints into a set of LMIs, which is leveraged to further check the feasibility of the obtained beamforming scheme. Numerical results are provided to demonstrate the robustness and effectiveness of the proposed algorithm in combating channel errors and improving the performance of ISAC systems.

Hardware-limited task-based quantization is a new design paradigm for data acquisition systems equipped with scalar analog-to-digital converters using a small number of bits. By taking into account the system task, task-based quantizers can efficiently recover the desired parameters from the low-bit quantized observation. Current design and analysis frameworks for hardware-limited task-based quantization are only applicable to inputs with bounded support and uniform quantizers with non-subtractive dithering. In this paper, we propose a new framework based on generalized Bussgang decomposition that enables the design and analysis of hardware-limited task-based quantizers equipped with non-uniform scalar quantizers or have inputs with unbounded support. We consider the scenario in which the task is linear. Under this scenario, we derive new pre-quantization and post-quantization mappings for task-based quantizers with mean squared error (MSE) that closely matches the theoretical MSE.

Non-contact vital signs monitoring (NCVSM) of multiple people is becoming a necessity in healthcare due to increasing morbidity and manpower shortage. In meeting these requirements, frequency modulated continuous wave (FMCW) radars have shown great potential. However, current techniques present difficulties in locating and monitoring humans in noisy environments containing multiple objects. In this work, we first develop a model for NCVSM of multiple people via FMCW radar, based on a single-input-multiple-output setup. By considering the sparse nature of the modeled signals along with human-typical cardiopulmonary characteristics, we provide a joint-sparse recovery mechanism to accurately localize targets in a clutter-rich scenario where existing techniques struggle. Then, we present a robust method for NCVSM of the found individuals, with improved performance results when compared to current NCVSM techniques using several statistical metrics. Our approach offers excellent performance in a medical application where high accuracy is required.

In this paper, we investigate the beamforming design for an integrated sensing and communication (ISAC) system involved full-duplex (FD) communications. Specifically, an FD ISAC base station (BS) performs target detection and communicates with multiple downlink users and uplink users reusing the same time and frequency resources. We jointly optimize the downlink dual-functional transmit signal and the uplink receive beamformers at the BS and the transmit power at the uplink users. The problem is formulated to minimize the total transmit power of the system while ensuring the communication and sensing requirements. The downlink and uplink transmissions are tightly coupled, making the joint optimization challenging. To solve this intractable problem, we first determine the receive beamformers in closed forms with respect to the BS transmit beamforming and the user transmit power and then suggest an iterative solution to the remaining problem. We demonstrate via numerical results that the optimized FD communication-based ISAC leads to power efficiency improvement compared to conventional ISAC with HD communication.

Dynamic metasurface antennas (DMAs) provide a new paradigm to realize large-scale antenna arrays for future wireless systems. In this paper, we study the downlink millimeter wave (mmWave) DMA systems with limited number of radio frequency (RF) chains. By using the specific DMA structure, an equivalent mmWave channel model with hybrid beamforming is first explicitly characterized. Based on that, we propose an effective joint microstrip selection and beamforming scheme to accommodate for the limited number of RF chains. A low-complexity digital beamforming solution with channel gain-based microstrip selection is developed, while the analog beamformer is obtained via a coordinate ascent method. The proposed scheme is numerically shown to approach the performance of DMAs without RF chain reduction, verifying the effectiveness of the proposed schemes.

Ultrasound imaging is an attractive imaging modality due to its low-cost and real-time feedback, although it often falls short in image quality compared to MRI and CT imaging. Conventional ultrasound image reconstruction, such as Delay-and-Sum beamforming, is derived from maximum-likelihood estimation. As such, no prior information is exploited in the image formation process, which limits potential image quality. Maximum-a-posteriori (MAP) beamforming aims to overcome this issue, but often relies on rough approximations of the underlying signal statistics. Deep learning based reconstruction methods have demonstrated impressive results over the past years, but often lack interpretability and require vast amounts of data.In this work we present a neural MAP beamforming technique, which efficiently combines deep learning in the MAP beamforming framework. We show that this model-based deep learning approach can achieve high-quality imaging, improving over the state-of-the-art, without compromising the real-time abilities of ultrasound imaging.

Modulo folding can be used to sample high-dynamic range signals without increasing the dynamic range of the sampler. Specifically, folding is used prior to sampling and then the folded signal is sampled. After sampling, unfolding algorithms are used to compute the true samples (up to a constant factor) from the folded ones. In this work, we consider a modulo sampling framework for finite rate of innovation (FRI) signals which are used to model signals in time of flight imaging. We suggest compactly supported sum-of-sincs filter as a sampling kernel prior to modulo folding and sampling. We derive conditions on the sampling rate and filter coefficients which lead to unfolding of the samples up to an unknown constant. We then propose a modified annihilating filter approach that can uniquely determine the FRI parameters from the unfolded samples with a constant unknown offset. We show that the proposed framework outperforms existing techniques in the presence of noise.

Hybrid beamforming (HBF) is a key enabler for millimeter-wave (mmWave) communications systems, but HBF optimizations are often non-convex and of large dimension. In this paper, we propose an efficient deep unfolding-based HBF scheme, referred to as ManNet-HBF, that approximately maximizes the system spectral efficiency (SE). It first factorizes the optimal digital beamformer into analog and digital terms, and then reformulates the resultant matrix factorization problem as an equivalent maximum-likelihood problem, whose analog beamforming solution is vectorized and estimated efficiently with ManNet, a lightweight deep neural network. Numerical results verify that the proposed ManNet-HBF approach has near-optimal performance comparable to or better than conventional model-based counterparts, with very low complexity and a fast run time. For example, in a simulation with 128 transmit antennas, it attains 98.62% the SE of the Riemannian manifold scheme but 13250 times faster.

In this paper, we propose a semi-federated learning (SemiFL) framework that allows computing-limited clients to collaboratively train a shared model with resource-abundant clients. Specifically, by supporting the coexistence of model-updating and data-offloading, the SemiFL framework enables both centralized and federated learning in a hybrid fashion. Due to the decoding error, we consider the practical case with residual interference. To improve uplink throughput for centralized learning while reducing aggregation distortion for federated learning, we formulate a non-convex optimization problem to jointly optimize the transmit power and receive strategy. Then, we propose an efficient algorithm to solve the challenging problem by using successive convex approximation. Simulation results demonstrate the effectiveness of our SemiFL framework for heterogeneous networks, and reveal the impact of imperfect signal decoding on communication rates.

In practice, Analog-to-Digital Converter (ADC) is used to perform sampling. A practical bottleneck of ADC is its lower dynamic range, leading to loss of information. To address this issue, researchers suggested folding operation on the signal using a modulo operator before passing it as an input to ADC. Though this process preserves the signal information, an unfolding algorithm is required to get the true samples from the folded samples. Noise robustness and computational time are two key parameters of an unfolding algorithm. In this paper, we propose a fast and robust algorithm for unfolding. Specifically, we first show that the first-order difference of the residual samples (the difference between the folded and true samples) is sparse by deriving an upper bound on its sparsity, and can be recovered from its partial Fourier measurements by formulating a sparse recovery problem. We demonstrate that the proposed algorithm is robust to noise and computationally efficient compared to the existing methods.

In this paper, we propose a new multi-functional reconfigurable intelligent surface (MF-RIS) architecture. Different from conventional RIS that only reflects signals, MF-RIS supports multiple functionalities on one surface, including reflection, transmission, amplification, and energy harvesting. As such, MF-RIS is capable of overcoming the double-fading attenuation and achieving full-space coverage by harvesting energy from the base station (BS). The physical implementation and the signal model of MF-RIS are introduced from the perspective of wireless communications. Then, we formulate a sum rate (SR) maximization problem in an MF-RIS-aided non-orthogonal multiple access network. By jointly optimizing the transmit strategy of the BS and the coefficient of the MF-RIS, we design an iterative algorithm to solve the formulated non-convex problem efficiently. Simulation results show that: i) MF-RIS provides up to 98.8% higher SR gain than self-sustainable RIS. ii) There exists a non-trivial trade-off between throughput improvement and self-sustainability, due to the limited number of RIS elements.

Deep unfolding models are designed by unrolling an optimization algorithm into a deep learning network. These models have shown faster convergence and higher performance compared to the original optimization algorithms. Additionally, by incorporating domain knowledge from the optimization algorithm, they need much less training data to learn efficient representations. Current deep unfolding networks for sequential sparse recovery consist of recurrent neural networks (RNNs), which leverage the similarity between consecutive signals. We redesign the optimization problem to use correlations across the whole sequence, which unfolds into a Transformer architecture. Our model is used for the task of video frame reconstruction from low-dimensional measurements and is shown to outperform state-of-the-art deep unfolding RNN and Transformer models, as well as a traditional Vision Transformer on several video datasets.

Sixth generation (6G) cellular communications are expected to support enhanced wireless localization capabilities. The widespread deployment of large arrays and high-frequency bandwidths give rise to new considerations for localization applications. Emerging antenna architectures, such as dynamic metasurface antennas (DMAs), are expected to be frequently utilized thanks to the achievable high angular resolution and low hardware complexity. Further, wireless localization is likely to take place in the radiating near-field (Fresnel) region, which provides new degrees of freedom, because of the adoption of arrays with large apertures. While current studies mostly focus on the use of costly fully-digital antenna arrays, in this paper we investigate how DMAs can be applied for near-field localization of a single user. We use a direct positioning estimation method based on curvature-of-arrival of the impinging wavefront to obtain the user location, and characterize the effects of DMA tuning on the estimation accuracy. Next, we propose an algorithm for configuring the DMA to optimize near-field localization, by first tuning the adjustable DMA coefficients to minimize the estimation error using postulated knowledge of the actual user position. Finally, we propose a sub-optimal iterative algorithm that does not rely on such knowledge. Simulation results show that the DMA-based near-field localization accuracy could approach that of fully-digital arrays at lower cost.

This paper studies a new multi-device edge artificial-intelligent (AI) system, which jointly exploits the AI model split inference and integrated sensing and communication (ISAC) to enable low-latency intelligent services at the network edge. In this system, multiple ISAC devices perform radar sensing to obtain multi-view data, and then offload the quantized version of extracted features to a centralized edge server, which conducts model inference based on the cascaded feature vectors. Under this setup and by considering classification tasks, we measure the inference accuracy by adopting an approximate but tractable metric, namely discriminant gain, which is defined as the distance of two classes in the Euclidean feature space under normalized covariance. To maximize the discriminant gain, we first quantify the influence of the sensing, computation, and communication processes on it with a derived closed-form expression. Then, an end-to-end task-oriented resource management approach is developed by designing an optimal integrated sensing, computation, and communication (ISCC) scheme. By using human motions recognition as a concrete AI inference task, extensive experiments are conducted to verify the performance of the proposed scheme.

In recent years, algorithm unrolling has emerged as a powerful technique for designing interpretable neural networks based on iterative algorithms. Imaging inverse problems have particularly benefited from unrolling based deep network design since many traditional model-based approaches rely on iterative optimization. Despite exciting progress, typical unrolling approaches heuristically design layer-specific convolution weights to improve performance. Crucially, convergence properties of the underlying iterative algorithm are lost once layer specific parameters are learned from training data. In this paper, we propose a neural network architecture that breaks the trade-off between retaining algorithm properties while simultaneously enhancing performance. We focus on non-blind image deblurring problem and unroll the widely-applied Half-Quadratic Splitting (HQS) algorithm. We develop a new parameterization scheme that enforces the layer-specific parameters to asymptotically approach certain fixed points, a new result that we analytically establish. Experimental results show that our approach outperforms many state of the art non-blind deblurring techniques on benchmark datasets, while enabling convergence and interpretability.

In conventional supervised deep learning based channel estimation algorithms, a large number of training samples are required for offline training. However, in practical communication systems, it is difficult to obtain channel samples for every signal-to-noise ratio (SNR). Furthermore, the generalization ability of these deep neural networks (DNN) is typically poor. In this work, we propose a one-shot self-supervised learning framework for channel estimation in multi-input multi-output (MIMO) systems. The required number of samples for offline training is small and our approach can be directly deployed to adapt to variable channels. Our framework consists of a traditional channel estimation module and a denoising module. The denoising module is designed based on the one-shot learning method Self2Self and employs Bernoulli sampling to generate training labels. Besides,we further utilize a blind spot strategy and dropout technique to avoid overfitting. Simulation results show that the performance of the proposed one-shot self-supervised learning method is very close to the supervised learning approach while obtaining improved generalization ability for different channel environments.

MOTIVATION: Imaging Spatial Transcriptomics techniques characterize gene expression in cells in their native context by imaging barcoded probes for mRNA with single molecule resolution. However, the need to acquire many rounds of high-magnification imaging data limits the throughput and impact of existing methods. RESULTS: We describe the Joint Sparse method for Imaging Transcriptomics, an algorithm for decoding lower magnification Imaging Spatial Transcriptomics data than that used in standard experimental workflows. Joint Sparse method for Imaging Transcriptomics incorporates codebook knowledge and sparsity assumptions into an optimization problem, which is less reliant on well separated optical signals than current pipelines. Using experimental data obtained by performing Multiplexed Error-Robust Fluorescence in situ Hybridization on tissue from mouse brain, we demonstrate that Joint Sparse method for Imaging Transcriptomics enables improved throughput and recovery performance over standard decoding methods. AVAILABILITY AND IMPLEMENTATION: Software implementation of JSIT, together with example files, is available at https://github.com/jpbryan13/JSIT.

Distributed machine learning is envisioned as the bedrock of future intelligent networks, where agents exchange information with each other to train models collaboratively without uploading data to a central processor. Despite its broad applicability, a downside of distributed learning is the need for iterative information exchange between agents, which may lead to high communication overhead unaffordable in many practical systems with limited communication resources. To resolve this communication bottleneck, we need to devise communication-efficient distributed learning algorithms and protocols that can reduce the communication cost and simultaneously achieve satisfactory learning/optimization performance. Accomplishing this goal necessitates synergistic techniques from a diverse set of fields, including optimization, machine learning, wireless communications, game theory, and network/graph theory. This Special Issue is dedicated to communication-efficient distributed learning from multiple perspectives, including fundamental theories, algorithm design and analysis, and practical considerations.

Distributed learning is envisioned as the bedrock of next-generation intelligent networks, where intelligent agents, such as mobile devices, robots, and sensors, exchange information with each other or a parameter server to train machine learning models collaboratively without uploading raw data to a central entity for centralized processing. By utilizing the computation/communication capability of individual agents, the distributed learning paradigm can mitigate the burden at central processors and help preserve data privacy of users. Despite its promising applications, a downside of distributed learning is its need for iterative information exchange over wireless channels, which may lead to high communication overhead unaffordable in many practical systems with limited radio resources such as energy and bandwidth. To overcome this communication bottleneck, there is an urgent need for the development of communication-efficient distributed learning algorithms capable of reducing the communication cost and achieving satisfactory learning/optimization performance simultaneously. In this paper, we present a comprehensive survey of prevailing methodologies for communication-efficient distributed learning, including reduction of the number of communications, compression and quantization of the exchanged information, radio resource management for efficient learning, and game-theoretic mechanisms incentivizing user participation. We also point out potential directions for future research to further enhance the communication efficiency of distributed learning in various scenarios.

Beamforming design has been widely investigated for integrated sensing and communication (ISAC) systems with full-duplex (FD) sensing and half-duplex (HD) communication, where the base station (BS) transmits and receives radar sensing signals simultaneously while the integrated communication operates in either downlink or uplink. To achieve higher spectral efficiency, in this paper, we extend existing ISAC beamforming design to a general case by considering the FD capability for both radar and communication. Specifically, we consider an FD ISAC system, where the BS performs target detection and communicates with multiple downlink users and uplink users reusing the same time and frequency resources. We jointly optimize the downlink dual-functional transmit signal and the uplink receive beamformers at the BS and the transmit power at the uplink users. The problems are formulated under two criteria: power consumption minimization and sum rate maximization. The downlink and uplink transmissions are tightly coupled due to both the desired target echo and the undesired interference received at the BS, making the problems challenging. To handle these issues in both cases, we first determine the optimal receive beamformers in closed forms with respect to the BS transmit beamforming and the user transmit power. Subsequently, we invoke these results to obtain equivalent optimization problems and propose iterative algorithms to solve them. In addition, we consider a special case under the power minimization criterion and propose an alternative low complexity design. Numerical results demonstrate that the optimized FD communication-based ISAC brings tremendous improvements in terms of both power efficiency and spectral efficiency compared to the conventional ISAC with HD communication.

Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information, and additional domain knowledge. Simple classical models are useful but sensitive to inaccuracies and may lead to poor performance when real systems display complex or dynamic behavior. On the other hand, purely data-driven approaches that are model-agnostic are becoming increasingly popular as datasets become abundant and the power of modern deep learning pipelines increases. Deep neural networks (DNNs) use generic architectures that learn to operate from data and demonstrate excellent performance, especially for supervised problems. However, DNNs typically require massive amounts of data and immense computational resources, limiting their applicability for some scenarios. In this article, we present the leading approaches for studying and designing model-based deep learning systems. These are methods that combine principled mathematical models with data-driven systems to benefit from the advantages of both approaches. Such model-based deep learning methods exploit both partial domain knowledge, via mathematical structures designed for specific problems, and learning from limited data. Among the applications detailed in our examples for model-based deep learning are compressed sensing, digital communications, and tracking in state-space models. Our aim is to facilitate the design and study of future systems at the intersection of signal processing and machine learning that incorporate the advantages of both domains.

Reconfigurable Intelligent Surfaces (RISs) are envisioned to play a key role in future wireless communications, enabling programmable radio propagation environments. They are usually considered as almost passive planar structures that operate as adjustable reflectors, giving rise to a multitude of implementation challenges, including the inherent difficulty in estimating the underlying wireless channels. In this paper, we focus on the recently conceived concept of Hybrid Reconfigurable Intelligent Surfaces (HRISs), which do not solely reflect the impinging waveform in a controllable fashion, but are also capable of sensing and processing an adjustable portion of it. We first present implementation details for this metasurface architecture and propose a convenient mathematical model for characterizing its dual operation. As an indicative application of HRISs in wireless communications, we formulate the individual channel estimation problem for the uplink of a multi-user HRIS-empowered communication system. Considering first a noise-free setting, we theoretically quantify the advantage of HRISs in notably reducing the amount of pilots needed for channel estimation, as compared to the case of purely reflective RISs. We then present closed-form expressions for the Mean-Squared Error (MSE) performance in estimating the individual channels at the HRISs and the base station for the noisy model. Based on these derivations, we propose an automatic differentiation-based first-order optimization approach to efficiently determine the HRIS phase and power splitting configurations for minimizing the weighted sum-MSE performance. Our numerical evaluations demonstrate that HRISs do not only enable the estimation of the individual channels in HRIS-empowered communication systems, but also improve the ability to recover the cascaded channel, as compared to existing methods using passive and reflective RISs.

We consider Quantized Tensor Robust Principal Component Analysis (Q-TRPCA), which aims to recover a low-rank tensor and a sparse tensor from noisy, quantized, and sparsely corrupted measurements. A nonconvex constrained maximum likelihood (ML) estimation method is proposed for Q-TRPCA. We provide an upper bound on the Frobenius norm of tensor estimation error under this method. Making use of tools in information theory, we derive a theoretical lower bound on the best achievable estimation error from unquantized measurements. Compared with the lower bound, the upper bound on the estimation error is nearly order-optimal. We further develop an efficient convex ML estimation scheme for Q-TRPCA based on the tensor nuclear norm (TNN) constraint. This method is more robust to sparse noises than the latter nonconvex ML estimation approach. Conducting experiments on both synthetic data and real-world data, we show the effectiveness of the proposed methods.

Non-contact technology for monitoring the vital signs of multiple individuals, such as respiration and heartbeat, has been investigated in recent years due to the rising cardiopulmonary morbidity, the risk of disease transmission, and the heavy burden on medical staff. Frequency-modulated continuous wave (FMCW) radars have shown great promise in meeting these needs, even using a single-input-single-output (SISO) setup. However, contemporary techniques for non-contact vital signs monitoring (NCVSM) via SISO FMCW radar, are based on simplistic models and present difficulties in coping with noisy environments containing multiple objects. In this work, we first develop an extended model for multi-person NCVSM via SISO FMCW radar. Then, by utilizing the sparse nature of the modeled signals in conjunction with human-typical cardiopulmonary features, we present accurate localization and NCVSM of multiple individuals in a cluttered scenario, even with only a single channel. Specifically, we provide a joint-sparse recovery mechanism to localize people and develop a robust method for NCVSM called Vital Signs-based Dictionary Recovery (VSDR), which uses a dictionary-based approach to search for the rates of respiration and heartbeat over high-resolution grids corresponding to human cardiopulmonary activity. The advantages of our method are illustrated through examples that combine the proposed model with in-vivo data of 30 individuals. We demonstrate accurate human localization in a noisy scenario that includes both static and vibrating objects and show that our VSDR approach outperforms existing NCVSM techniques based on several statistical metrics. The findings support the widespread use of FMCW radars with the proposed algorithms in healthcare.

Recent years have witnessed growing interest in the application of deep neural networks (DNNs) for receiver design, which can potentially be applied in complex environments without relying on knowledge of the channel model. However, the dynamic nature of communication channels often leads to rapid distribution shifts, which may require periodically retraining. This paper formulates a data-efficient two-stage training method that facilitates rapid online adaptation. Our training mechanism uses a predictive meta-learning scheme to train rapidly from data corresponding to both current and past channel realizations. Our method is applicable to any deep neural network (DNN)-based receiver, and does not require transmission of new pilot data for training. To illustrate the proposed approach, we study DNN-aided receivers that utilize an interpretable model-based architecture, and introduce a modular training strategy based on predictive meta-learning. We demonstrate our techniques in simulations on a synthetic linear channel, a synthetic non-linear channel, and a COST 2100 channel. Our results demonstrate that the proposed online training scheme allows receivers to outperform previous techniques based on self-supervision and joint-learning by a margin of up to 2.5 dB in coded bit error rate in rapidly-varying scenarios.

Two important attributes of analog to digital converters (ADCs) are its sampling rate and dynamic range. The sampling rate should be greater than or equal to the Nyquist rate for bandlimited signals with bounded energy. It is also desired that the signals’ dynamic range should be within that of the ADC’s; otherwise, the signal will be clipped. A modulo operator has been recently suggested prior to sampling to restrict the dynamic range. Due to the nonlinearity of the modulo operation, the samples are distorted. Existing recovery algorithms to recover the signal from its modulo samples operate at a high sampling rate and are not robust in the presence of noise. In this paper, we propose a robust algorithm to recover the signal from the modulo samples which operates at lower sampling rate compared to existing techniques. We also show that our method has lower error compared to existing approaches for a given sampling rate, noise level, and dynamic range of the ADC. Our results lead to less constrained hardware design to address dynamic range issues while operating at the lowest rate possible.

The ongoing pandemic and the necessity of frequent testing have spurred a growing interest in pooled testing. Conventional recovery methods from pooled tests are based on group testing or compressed sensing tools which rely on simplistic modeling of the pooling process, and may not be reliable in the presence of complex and noisy measurement procedures and highly infected populations. In this work, we propose a strategy for pooled testing designed for noisy settings, which bypasses the need for a tractable acquisition model. This is achieved by combining deep learning, for implicitly learning the measurement relationship from data, with factor graph inference, which exploits the structured known pooling pattern. Learned factor graphs provide a quantitative readout corresponding to the infection severity, as opposed to group testing which only detects the presence of infection. The proposed scheme is shown to achieve improved robustness to noise compared with previous approaches and to reliably estimate in highly infected populations.

Intravascular UltraSound (IVUS) is a key tool in guiding the treatment and diagnosis of various coronary heart diseases. However, due to its nature IVUS is a very challenging modality to interpret, and suffers from a severely restricted data transfer rate. This forces a trade-off between temporal and spatial resolution. Here, we propose a model-based deep learning solution that aims to reconstruct images from data that has been beamformed by under-sampling the number of channels by a factor of 4. By exploiting the physics based measurement model, we achieve better performance and consistency in our predictions when compared to benchmark models. This lowers the computational load on existing hardware and enables in exploring our ability to run multiple visualisation modalities simultaneously, without a loss of temporal resolution.

Providing a metric of uncertainty alongside a state estimate is often crucial when tracking a dynamical system. Classic state estimators, such as the Kalman filter (KF), provide a time-dependent uncertainty measure from knowledge of the underlying statistics; however, deep learning based tracking systems struggle to reliably characterize uncertainty. In this paper, we investigate the ability of KalmanNet, a recently proposed; hybrid; model-based; deep state tracking algorithm, to estimate an uncertainty measure. By exploiting the interpretable nature of KalmanNet, we show that the error covariance matrix can be computed based on its internal features, as an uncertainty measure. We demonstrate that when the system dynamics are known, KalmanNet—which learns its mapping from data without access to the statistics—provides uncertainty similar to that provided by the KF; and while in the presence of evolution model-mismatch, KalmanNet provides a more accurate error estimation.

In this paper, we consider the design of a multiple-input multiple-output (MIMO) transmitter which simultaneously functions as a MIMO radar and a base station for downlink multiuser communications. In contrast to the previous designs which guarantee communication performance, we require the covariance of the transmit waveform to be equal to a given optimal covariance for MIMO radar, to guarantee the radar performance. With this constraint, we formulate and solve the signal-to-interference-plus-noise ratio (SINR) balancing problem for multiuser transmit beamforming via convex optimization. By numerical simulations, we first demonstrate the radar performance loss caused by previous designs, and then show the communication performance for our proposed design in terms of balanced SINR versus transmit signal-to-noise ratio.

Finite-rate-of-innovation (FRI) signals are ubiquitous in radar, ultrasound, and time of flight imaging applications. In this paper, we propose a model-based deep learning approach to jointly design the subsampling and reconstruction of FRI signals. Specifically, our framework is a combination of a greedy subsampling algorithm and a learning-based sparse recovery method. Unlike existing learning-based techniques, the proposed algorithm can flexibly handle changes in the sampling rate and does not suffer from differentiability issues during training. Moreover, exact knowledge of the FRI pulse is not required. Numerical results show that the proposed joint design leads to lower reconstruction error for FRI signals compared with existing benchmark methods for a given number of samples. The method can easily adapt to other sparse recovery problems.

In this work, we consider the acquisition of stationary signals using uniform analog-to-digital converters (ADCs), i.e., employing uniform sampling and scalar uniform quantization. We jointly optimize the pre-sampling and reconstruction filters to minimize the time-averaged mean-squared error (TMSE) in recovering the continuous-time input signal for a fixed sampling rate and quantizer resolution and obtain closed-form expressions for the minimal achievable TMSE. We show that the TMSE-minimizing pre-sampling filter omits aliasing and discards weak frequency components to resolve the remaining ones with higher resolution when the rate budget is small. In our numerical study, we validate our results and show that sub-Nyquist sampling often minimizes the TMSE under tight rate budgets at the output of the ADC.

The smoothing task is the core of many signal processing applications. It deals with the recovery of a sequence of hidden state variables from a sequence of noisy observations in a one-shot manner. In this work we propose RTSNet, a highly efficient model-based and data-driven smoothing algorithm. RTSNet integrates dedicated trainable models into the flow of the classical Rauch-Tung-Striebel (RTS) smoother, and is able to outperform it when operating under model mismatch and non-linearities while retaining its efficiency and interpretability. Our numerical study demonstrates that although RTSNet is based on more compact neural networks, which leads to faster training and inference times, it outperforms the state-of-the-art, data-driven smoother in a non-linear use case.

Recently, unfolding techniques have been widely utilized to solve the inverse problems in various applications. In this paper, we study optimization guarantees for two popular unfolded networks, i.e., unfolded networks derived from iterative soft thresholding algorithms (ISTA) and derived from Alternating Direction Method of Multipliers (ADMM). Our guarantees–leveraging the Polyak-Lojasiewicz* (PL*) condition–state that the training (empirical) loss decreases to zero with the increase in the number of gradient descent epochs provided that the number of training samples is less than some threshold that depends on various quantities underlying the desired information processing task. Our guarantees also show that this threshold is larger for unfolded ISTA in comparison to unfolded ADMM, suggesting that there are certain regimes of number of training samples where the training error of unfolded ADMM does not converge to zero whereas the training error of unfolded ISTA does. A number of numerical results are provided backing up our theoretical findings.

Many application domains, spanning from low-level computer vision to medical imaging, require high-fidelity images from noisy measurements. State-of-the-art methods for solving denoising problems combine deep learning with iterative model-based solvers, a concept known as deep algorithm unfolding or unrolling. By combining a-priori knowledge of the forward measurement model with learned proximal image-to-image mappings based on deep networks, these methods yield solutions that are both physically feasible (data-consistent) and perceptually plausible (consistent with prior belief). However, current proximal mappings based on (predominantly convolutional) neural networks only implicitly learn such image priors. In this paper, we propose to make these image priors fully explicit by embedding deep generative models in the form of normalizing flows within the unfolded proximal gradient algorithm, and training the entire algorithm in an end-to-end fashion. We demonstrate that the proposed method outperforms competitive baselines on image denoising.

Multiple-input multiple-output (MIMO) systems utilize multiple antennas and signal acquisition chains, facilitating multi-user communications with increased spectral efficiency and better coverage via beamforming. MIMO systems are typically costly to implement and consume high power. A commonly used method to reduce the cost of MIMO receivers is to design hybrid analog/digital beamforming (HBF), which reduces the number of RF chains. However, the added analog circuitry involves active components whose consumed power may surpass that saved in RF chain reduction. An additional method to realize power-efficient MIMO systems is to use low-resolution analog-to-digital converters (ADCs), however, compromising signal recovery accuracy. In this work, we propose a power-efficient hybrid MIMO receiver with dedicated beamforming to mitigate spatial interferers in congested environments, utilizing low-quantization rate ADCs, jointly optimizing the analog and digital processing using task-specific quantization techniques. We present an efficient analog pre-processing hardware architecture utilizing sparse low-resolution vector modulators to reduce analog processing power while maintaining recovery accuracy. Supported by numerical simulations and power analysis, our power-efficient MIMO receiver achieves comparable signal recovery performance to power-hungry fully-digital MIMO receivers using high-resolution ADCs. Furthermore, our receiver outperforms the task-agnostic HBF receivers with low-quantization rate ADCs in recovery accuracy at lower power.

This paper proposes a novel semi-federated learning (SemiFL) paradigm, which integrates centralized learning (CL) and over-the-air federated learning (AirFL) into a unified framework, with the aid of a simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS). In particular, this SemiFL framework allows computing-scarce users to participant in the learning process by using non-orthogonal multiple access (NOMA) to transmit their local dataset to the base station for model computation on behalf of them. During the uplink communication, scarce spectrum resources are shared among AirFL users and NOMA-based CL users, using a STAR-RIS for interference management and coverage enhancement. To analyze the learning behavior of SemiFL, closed-form expressions are derived to quantify the impact of learning rates and noisy fading channels. Our analysis shows that SemiFL can achieve a lower error floor than the CL or AirFL schemes with partial users. Simulation results show that SemiFL significantly reduces communication overhead and latency compared to CL, while achieving better learning performance than AirFL.

We propose a greedy algorithm to select$N$important features among$P$input features for a non-linear prediction problem. The features are selected one by one sequentially, in an iterative loss minimization procedure. We use neural networks as predictors in the algorithm to compute the loss and hence, we refer to our method as neural greedy pursuit (NGP). NGP is efficient in selecting$N$features when$N\ll P$, and it provides a notion of feature importance in a descending order following the sequential selection procedure. We experimentally show that NGP provides better performance than several feature selection methods such as DeepLIFT and Drop-one-out loss. In addition, we experimentally show a phase transition behavior in which perfect selection of all$N$features without false positives is possible when the training data size exceeds a threshold.

Deep fading represents the typical error event when communicating over wireless channels. We show that deep fading is particularly detrimental for federated learning (FL) over wireless communications. In particular, the celebrated FEDAVG and several of its variants break down for FL tasks when deep fading exists in the communication phase. The main contribution of this paper is an optimal global model aggregation method at the parameter server, which allocates different weights to different clients based on not only their learning characteristics but also the instantaneous channel state information at the receiver (CSIR). This is accomplished by first deriving an upper bound on the parallel stochastic gradient descent (SGD) convergence over fading channels, and then solving an optimization problem for the server aggregation weights that minimizes this upper bound. The derived optimal aggregation solution is closed-form, and achieves the well-known O(1/t) convergence rate for strongly-convex loss functions under arbitrary fading and decaying learning rates. We validate our approach using several real-world FL tasks.

In this paper, we study the problem of sampling finite-rate-of-innovation (FRI) signals by using an integrate-and-fire time encoding machine. We consider a Fourier-domain reconstruction approach and design a robust sampling kernel that has a frequency-domain alias cancellation condition and excludes the zero frequency. In the absence of noise, we present theoretical recovery guarantees for FRI signals with arbitrary pulse shapes using our approach. We show that the minimum firing rate is proportional to the rate of innovation of the FRI signal. In the presence of noise, our technique results in 2−10 dB lower error while estimating the FRI parameters compared to existing methods for the same number of measurements.

Ill-posed inverse problems appear in many image processing applications, such as deblurring and super-resolution. In recent years, solutions that are based on deep Convolutional Neural Networks (CNNs) have shown great promise. Yet, most of these techniques, which train CNNs using external data, are restricted to the observation models that have been used in the training phase. A recent alternative that does not have this drawback relies on learning the target image using internal learning. One such prominent example is the Deep Image Prior (DIP) technique that trains a network directly on the input image with the least-squares loss. In this paper, we propose a new image restoration framework that is based on minimizing a loss function that includes a "projected-version" of the Generalized Stein Unbiased Risk Estimator (GSURE) and parameterization of the latent image by a CNN. We propose two ways to use our framework. In the first one, where no explicit prior is used, we show that the proposed approach outperforms other internal learning methods, such as DIP. In the second one, we show that our GSURE-based loss leads to improved performance when used within a plug-and-play priors scheme.

This article integrates nonorthogonal multiple access (NOMA) and over-the-air federated learning (AirFL) into a unified framework using one simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS). The STAR-RIS plays an important role in adjusting the decoding order of hybrid users for efficient interference mitigation and omnidirectional coverage extension. To capture the impact of nonideal wireless channels on AirFL, a closed-form expression for the optimality gap (also known as the convergence upper bound) between the actual loss and the optimal loss is derived. This analysis reveals that the learning performance is significantly affected by the active and passive beamforming schemes, as well as wireless noise. Furthermore, when the learning rate diminishes as the training proceeds, the optimality gap is explicitly shown to converge with a linear rate. To accelerate convergence while satisfying quality-of-service requirements, a mixed-integer nonlinear programming (MINLP) problem is formulated by jointly designing the transmit power at users and the configuration mode of STAR-RIS. Next, a trust-region-based successive convex approximation method and a penalty-based semidefinite relaxation approach are proposed to handle the decoupled nonconvex subproblems iteratively. An alternating optimization algorithm is then developed to find a suboptimal solution for the original MINLP problem. Extensive simulation results show that: 1) the proposed framework can efficiently support NOMA and AirFL users via concurrent uplink communications; 2) our algorithms achieve a faster convergence rate on independent and identically distributed (IID) and non-IID settings compared to the existing baselines; and 3) both the spectrum efficiency and learning performance are significantly improved with the aid of the well-tuned STAR-RIS.

In this paper, we propose an end-to-end deep learning-based joint transceiver design algorithm for millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, which consists of deep neural network (DNN)-aided pilot training, channel feedback, and hybrid analog-digital (HAD) precoding. Specifically, we develop a DNN architecture that maps the received pilots into feedback bits at the receiver, and then further maps the feedback bits into the hybrid precoder at the transmitter. To reduce the signaling overhead and channel state information (CSI) mismatch caused by the transmission delay, a two-timescale DNN composed of a long-term DNN and a short-term DNN is developed. The analog precoders are designed by the long-term DNN based on the CSI statistics and updated once in a frame consisting of a number of time slots. In contrast, the digital precoders are optimized by the short-term DNN at each time slot based on the estimated low-dimensional equivalent CSI matrices. A two-timescale training method is also developed for the proposed DNN with a binary layer. We then analyze the generalization ability and signaling overhead for the proposed DNN based algorithm. Simulation results show that our proposed technique significantly outperforms conventional schemes in terms of bit-error rate performance with reduced signaling overhead and shorter pilot sequences.

In massive multiple-input multiple-output (MIMO) systems, hybrid analog-digital beamforming is an essential technique for exploiting the potential array gain without using a dedicated radio frequency chain for each antenna. However, due to the large number of antennas, the conventional channel estimation and hybrid beamforming algorithms generally require high computational complexity and signaling overhead. In this work, we propose an end-to-end deep-unfolding neural network (NN) joint channel estimation and hybrid beamforming (JCEHB) algorithm to maximize the system sum rate in time-division duplex (TDD) massive MIMO. Specifically, the recursive least-squares (RLS) algorithm and stochastic successive convex approximation (SSCA) algorithm are unfolded for channel estimation and hybrid beamforming, respectively. In order to reduce the signaling overhead, we consider a mixed-timescale hybrid beamforming scheme, where the analog beamforming matrices are optimized based on the channel state information (CSI) statistics offline, while the digital beamforming matrices are designed at each time slot based on the estimated low-dimensional equivalent CSI matrices. We jointly train the analog beamformers together with the trainable parameters of the RLS and SSCA induced deep-unfolding NNs based on the CSI statistics offline. During data transmission, we estimate the low-dimensional equivalent CSI by the RLS induced deep-unfolding NN and update the digital beamformers. In addition, we propose a mixed-timescale deep-unfolding NN where the analog beamformers are optimized online, and extend the framework to frequency-division duplex (FDD) systems where channel feedback is considered. Simulation results show that the proposed algorithm can significantly outperform conventional algorithms with reduced computational complexity and signaling overhead.

As the standardization of 5G solidifies, researchers are speculating what 6G will be. The integration of sensing functionality is emerging as a key feature of the 6G Radio Access Network (RAN), allowing for the exploitation of dense cell infrastructures to construct a perceptive network. In this IEEE Journal on Selected Areas in Communications (JSAC) Special Issue overview, we provide a comprehensive review on the background, range of key applications and state-of-the-art approaches of Integrated Sensing and Communications (ISAC). We commence by discussing the interplay between sensing and communications (S&C) from a historical point of view, and then consider the multiple facets of ISAC and the resulting performance gains. By introducing both ongoing and potential use cases, we shed light on the industrial progress and standardization activities related to ISAC. We analyze a number of performance tradeoffs between S&C, spanning from information theoretical limits to physical layer performance tradeoffs, and the cross-layer design tradeoffs. Next, we discuss the signal processing aspects of ISAC, namely ISAC waveform design and receive signal processing. As a step further, we provide our vision on the deeper integration between S&C within the framework of perceptive networks, where the two functionalities are expected to mutually assist each other, i.e., via communication-assisted sensing and sensing-assisted communications. Finally, we identify the potential integration of ISAC with other emerging communication technologies, and their positive impacts on the future of wireless networks.

Driving a gradual integration of the physical and digital worlds is perceived to become a reality in the 6G era, from vehicles to drones, from surveillance facilities in cities to agricultural tools in the countryside. Jointly motivated by recent advances in communication and signal processing, radio sensing functionality can be integrated into a 6G radio access network (RAN) in a low-cost and fast manner. That is, future networks have the ability to “see” the physical world through imaging and measuring the surrounding environment, which enables advanced location-aware services, ranging from the physical to application layers. In essence, a radio emission could simultaneously convey communication data from the transmitter to the receiver and deliver environmental information from the scattered echoes. Therefore, sensing and communication (S&C) functionalities are possible to be co-designed to utilize resources efficiently and to assist each other for mutual benefits. This type of research is typically referred to as integrated sensing and communication (ISAC).

This is Part II of the double-part Special Issue (SI) on Integrated Sensing and Communication (ISAC). This SI aims at bringing together contributions from both academia and industry to highlight the recent progress of ISAC, where sensing and communication (S$\$ $C) functionalities are jointly designed to utilize wireless/hardware resources efficiently and to assist each other for mutual benefits. The 32 accepted articles of this SI are arranged into six groups, namely, 1) Fundamental Performance Bounds and Optimization, 2) Time-Frequency Signal Processing, 3) Spatial Signal Processing, 4) Networking and Resource Allocation, 5) ISAC With Emerging Communications Technologies, and 6) ISAC Applications. We kindly refer readers to Part I of this SI for a comprehensive overview written by the Guest Editorial Team, which provides both a bird’s eye view and technical details regarding state-of-the-art ISAC innovations. The contributions made by the papers in Part II are summarized as follows, which correspond to paper groups 4), 5), and 6).

The use of 1-bit analog-to-digital converters (ADCs) is seen as a promising approach to significantly reduce the power consumption and hardware cost of multiple-input multiple-output (MIMO) receivers. However, the nonlinear distortion due to 1-bit quantization fundamentally changes the optimal communication strategy and also imposes a capacity penalty to the system. In this paper, the capacity of a Gaussian MIMO channel in which the antenna outputs are processed by an analog linear combiner and then quantized by a set of zero threshold ADCs is studied. A new capacity upper bound for the zero threshold case is established that is tighter than the bounds available in the literature. In addition, we propose an achievability scheme which configures the analog combiner to create parallel Gaussian channels with phase quantization at the output. Under this class of analog combiners, an algorithm is presented that identifies the analog combiner and input distribution that maximize the achievable rate. Numerical results are provided showing that the rate of the achievability scheme is tight in the low signal-to-noise ratio (SNR) regime. Finally, a new 1-bit MIMO receiver architecture which employs analog temporal and spatial processing is proposed. The proposed receiver attains the capacity in the high SNR regime.

High resolution analog to digital converters (ADCs) are conventionally used at the receiver terminals to store an accurate digital representation of the received signal, thereby allowing for reliable decoding of transmitted messages. However, in a wide range of applications, such as communication over millimeter wave and massive multiple-input multiple-output (MIMO) systems, the use of high resolution ADCs is not feasible due to power budget limitations. In the conventional fully digital receiver design, where each receiver antenna is connected to a distinct ADC, reducing the ADC resolution leads to performance loss in terms of achievable rates. One proposed method to mitigate the rate-loss is to use analog linear combiners leading to design of hybrid receivers. Here, the hybrid framework is augmented by the addition of delay elements to allow for temporal analog processing. Two new classes of receivers consisting of delay elements, analog linear combiners, and one-bit ADCs are proposed. The fundamental limits of communication in single and multi-user (uplink and downlink) MIMO systems employing the proposed receivers are investigated. In the high signal to noise ratio regime, it is shown that the proposed receivers achieve the maximum achievable rates among all receivers with the same number of one-bit ADCs.

Background foreground separation (BFS) is a popular computer vision problem where dynamic foreground objects are separated from the static background of a scene. Typically, this is performed using consumer cameras because of their low cost, human interpretability, and high resolution. Yet, cameras and the BFS algorithms that process their data have common failure modes due to lighting changes, highly reflective surfaces, and occlusion. One solution is to incorporate an additional sensor modality that provides robustness to such failure modes. In this paper, we explore the ability of a cost-effective radar system to augment the popular Robust PCA technique for BFS. We apply the emerging technique of algorithm unrolling to yield real-time computation, feedforward inference, and strong generalization in comparison with traditional deep learning methods. We benchmark on the RaDICaL dataset to demonstrate both quantitative improvements of incorporating radar data and qualitative improvements that confirm robustness to common failure modes of image-based methods.

Lung ultrasound (LUS) is a cheap, safe and non-invasive imaging modality that can be performed at patient bed-side. However, to date LUS is not widely adopted due to lack of trained personnel required for interpreting the acquired LUS frames. In this work we propose a framework for training deep artificial neural networks for interpreting LUS, which may promote broader use of LUS. When using LUS to evaluate a patient's condition, both anatomical phenomena (e.g., the pleural line, presence of consolidations), as well as sonographic artifacts (such as A- and B-lines) are of importance. In our framework, we integrate domain knowledge into deep neural networks by inputting anatomical features and LUS artifacts in the form of additional channels containing pleural and vertical artifacts masks along with the raw LUS frames. By explicitly supplying this domain knowledge, standard off-the-shelf neural networks can be rapidly and efficiently finetuned to accomplish various tasks on LUS data, such as frame classification or semantic segmentation. Our framework allows for a unified treatment of LUS frames captured by either convex or linear probes. We evaluated our proposed framework on the task of COVID-19 severity assessment using the ICLUS dataset. In particular, we finetuned simple image classification models to predict per-frame COVID-19 severity score. We also trained a semantic segmentation model to predict per-pixel COVID-19 severity annotations. Using the combined raw LUS frames and the detected lines for both tasks, our off-the-shelf models performed better than complicated models specifically designed for these tasks, exemplifying the efficacy of our framework.

Large antenna arrays and high-frequency bands are two key features of future wireless communication systems. The combination of large-scale antennas with high transmission frequencies often results in the communicating devices operating in the near-field (Fresnel) region. In this paper, we study the potential of beam focusing, feasible in near-field operation, in facilitating high-rate multi-user downlink multiple-input multiple-output (MIMO) systems. As the ability to achieve beam focusing is dictated by the transmit antenna, we study near-field signalling considering different antenna structures, including fully-digital architectures, hybrid phase shifter-based precoders, and the emerging dynamic metasurface antenna (DMA) architecture for massive MIMO arrays. We first provide a mathematical model to characterize near-field wireless channels as well as the transmission pattern for the considered antenna architectures. Then, we formulate the beam focusing problem for the goal of maximizing the achievable sum-rate in multi-user networks. We propose efficient solutions based on the sum-rate maximization task for fully-digital, (phase shifters based-) hybrid and DMA architectures. Simulation results show the feasibility of the proposed beam focusing scheme for both single- and multi-user scenarios. In particular, the designed focused beams provide a new degree of freedom to mitigate interference in both angle and distance domains, which is not achievable using conventional far-field beam steering, allowing reliable communications for uses even residing at the same angular direction.

Estimating the 3D motion of points in a scene, known as scene flow, is a core problem in computer vision. Traditional learning-based methods designed to learn end-to-end 3D flow often suffer from poor generalization. Here we present a recurrent architecture that learns a single step of an unrolled iterative alignment procedure for refining scene flow predictions. Inspired by classical algorithms, we demonstrate iterative convergence toward the solution using strong regularization. The proposed method can handle sizeable temporal deformations and suggests a slimmer architecture than competitive all-to-all correlation approaches. Trained on FlyingThings3D synthetic data only, our network successfully generalizes to real scans, outperforming all existing methods by a large margin on the KITTI self-supervised benchmark.1

This paper proposes a new, compatible, unified framework which integrates non-orthogonal multiple access (NOMA) and over-the-air federated learning (AirFL) via concurrent communication. In particular, a simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) is leveraged to adjust the signal processing order for efficient interference mitigation and omni-directional coverage extension. With the aim of investigating the impact of non-ideal wireless communication on AirFL, we provide a closed-form expression for the optimality gap over a given number of communication rounds. This result reveals that the learning performance is significantly affected by the resource allocation scheme and channel noise. To minimize the derived optimality gap, a mixed-integer non-linear programming (MINLP) problem is formulated by jointly designing the transmit power at users and configuration mode at the STAR-RIS. Through developing an alternating optimization algorithm, a suboptimal solution for the original MINLP problem is obtained. Simulation results show that the learning performance in terms of training loss and test accuracy can be effectively improved with the aid of the STAR-RIS.

We propose an interpretable graph neural network framework to denoise single or multiple noisy graph signals. The proposed graph unrolling networks expand algorithm unrolling to the graph domain and provide an interpretation of the architecture design from a signal processing perspective. We unroll an iterative denoising algorithm by mapping each iteration into a single network layer where the feed-forward process is equivalent to iteratively denoising graph signals. We train the graph unrolling networks through unsupervised learning, where the input noisy graph signals are used to supervise the networks. By leveraging the learning ability of neural networks, we adaptively capture appropriate priors from input noisy graph signals, instead of manually choosing signal priors. To validate the proposed methods, we conduct extensive experiments on both real-world datasets and simulated datasets, and demonstrate that our methods have smaller denoising errors than conventional denoising algorithms and state-of-the-art graph neural networks. For denoising a single smooth graph signal, the normalized mean square error of the proposed networks is around 40% and 60% lower than that of graph Laplacian denoising and graph wavelets, respectively.

We propose an interpretable graph neural network based on algorithm unrolling to reconstruct a time-varying graph signal from partial measurements. The proposed graph unrolling networks expand algorithm unrolling to the graph-time domain and provide an interpretation of the architecture design from a signal processing perspective. We unroll an iterative inpainting algorithm by mapping each iteration to a single network layer. The feed-forward process is thus equivalent to iteratively reconstructing a time-varying graph signal. We train this network through unsupervised learning, where the input time-varying graph signal is used to supervise the training. By leveraging the learning ability of neural networks, we adaptively capture appropriate priors from input data, instead of manually choosing signal priors. To validate the proposed methods, we conduct experiments on three real-world datasets and demonstrate that our networks achieve smaller reconstruction errors than conventional inpainting algorithms and state-of-the-art graph neural networks.

One of the main challenges in containing the Coronoavirus disease 2019 (COVID-19) pandemic stems from the difficulty in carrying out efficient mass diagnosis over large populations. The leading method to test for COVID-19 infection utilizes qualitative polymerase chain reaction, implemented using dedicated machinery which can simultaneously process a limited amount of samples. A candidate method to increase the test throughput is to examine pooled samples comprised of a mixture of samples from different patients. In this work we study pooling-based COVID-19 tests. We identify the specific requirements of COVID-19 testing, including the need to characterize the infection level and to operate in a one-shot fashion, which limit the application of traditional group-testing (GT) methods. We then propose a multi-level GT scheme, designed specifically to meet the unique requirements of COVID-19 tests, while exploiting the strength of GT theory to enable accurate recovery using much fewer tests than patients. Our numerical results demonstrate that multi-level GT reliably and efficiently detects the infection levels, while achieving improved accuracy over previously proposed one-shot COVID-19 pooled-testing methods.

Sub-Nyquist sampling is used in modern high-resolution pulse-Doppler radar systems to reduce system resources and improve resolution. Xampling with Doppler focusing is utilized to implement these sub-Nyquist radar systems. Signal recovery involves iterative optimization requiring large computational time that may be prohibitive in real applications. In this paper, we propose Deep Unfolded Radar Sensing (DURAS), a model-based deep learning architecture to address this problem. We utilize the recently introduced complex LISTA (C-LISTA) with recurrent neural network units and complex soft-thresholding to handle the complex-valued measurement signals. We propose a partial Doppler focusing (PDF) framework with ensembling of multiple PDF measurement vectors via a convolutional neural network (CNN). This CNN followed by a complex cardioid activation function is added to the front end of the C-LISTA architecture. Thus, DURAS is a hybrid architecture of partial Doppler focusing, CNN, and C-LISTA that provides considerably improved performance compared to existing methods on target detection in radar systems.

Communication of model updates between client nodes and the central aggregating server is a major bottleneck in federated learning, especially in bandwidth-limited settings and high-dimensional models. Gradient quantization is an effective way of reducing the number of bits required to communicate each model update, albeit at the cost of having a higher error floor due to the higher variance of the stochastic gradients. In this work, we propose an adaptive quantization strategy called AdaQuantFL that aims to achieve communication efficiency as well as a low error floor by changing the number of quantization levels during the course of training. Experiments on training deep neural networks show that our method can converge in much fewer communicated bits as compared to fixed quantization level setups, with little or no impact on training and test accuracy.

Graph signals arise in various applications, ranging from sensor networks to social media data. The high-dimensional nature of these signals implies that they often need to be compressed in order to be stored and conveyed. The common framework for graph signal compression is based on sampling, resulting in a set of continuous-amplitude samples, which in turn have to be quantized into a finite bit representation. In this work we study the joint design of graph signal sampling along with the quantization of these samples, for graph signal compression. We focus on bandlimited graph signals, and show that the compression problem can be represented as a task-based quantization setup, in which the task is to recover the spectrum of the signal. Based on this equivalence, we propose a joint design of the sampling and recovery mechanisms for a fixed quantization mapping, and present an iterative algorithm for dividing the available bit budget among the discretized samples. Our numerical evaluations demonstrate that the proposed scheme achieves reconstruction accuracy within a small gap of that achievable with infinite resolution quantizers, while compressing high-dimensional graph signals into finite bit streams.

We propose a new formulation for the joint phase retrieval and dictionary learning problem with a reduced number of regularization parameters to be tuned. A parallel algorithm based on the block successive convex approximation framework is developed for the proposed formulation. The performance of the algorithm is evaluated when applied to sparse channel estimation in a multi-antenna random access network. Simulation results on synthetic data show the efficiency of the proposed technique compared to the state-of-the-art method.

Dual function radar and communications (DFRC) systems are the focus of growing research attention. The common DFRC setup considers simultaneous probing and information transmission to a remote receiver, typically involving complex radar-oriented waveforms, whose detection can induce a notable burden on the receiver. In many DFRC applications, the communication receivers are devices which are limited in terms of hardware, power, and memory resources. These receivers are required to extract the desired information from the received dual-function waveform, while operating with a given bit budget. In this paper, we design bit constrained communication receivers in dual-function systems, by considering hybrid analog/digital architectures and treating their operation as task-based quantization. We study two forms of analog processing in these hybrid receivers, allowing to combine inputs in different time instances and antennas or only in different antennas at the same time instance. Simulation results demonstrate that the proposed task-based quantization strategy outperforms receivers operating only in the digital domain with the same total number of quantization bits.

We consider a continuous-time sparse multichannel blind deconvolution problem. The signal at each channel is expressed as the convolution of a common source signal and its impulse response given as a sparse filter. The objective is to identify these sparse filters from sub-Nyquist samples of channel outputs by leveraging the correlation across channels. We present necessary and sufficient conditions for the unique identification. In particular, the sparse filters should not share a common sparse convolution factor and it is necessary to have 2L or more samples per channel from at least two distinct channels. We also show that L-sparse filters are uniquely identifiable from two channels provided that there are 2L2Fourier measurements per channel, which can be computed from sub-Nyquist samples. Additionally, in the asymptotic of the number of channels, 2L Fourier measurements per channel are sufficient. The results are applicable to the design of multi-receiver, low-rate, sensors in applications such as radar, sonar, ultrasound, and seismic exploration.

In this paper, we propose a deep algorithm unrolling (DAU) based on a variant of the alternating direction method of multiplier (ADMM) called Plug-and-Play ADMM (PnP-ADMM) for denoising of signals on graphs. DAU is a trainable deep architecture realized by unrolling iterations of an existing optimization algorithm which contains trainable parameters at each layer. We also propose a nested-structured DAU: Its submodules in the unrolled iterations are also designed by DAU. Several experiments for graph signal denoising are performed on synthetic signals on a community graph and U.S. temperature data to validate the proposed approach. Our proposed method outperforms alternative optimization- and deep learning-based approaches.

We consider compressive sensing problems with model mismatch where one wishes to recover a sparse high-dimensional vector from low-dimensional observations subject to uncertainty in the measurement operator. In particular, we design a new robust deep neural network architecture by applying algorithm unfolding techniques to a robust version of the underlying recovery problem. Our proposed network –named Robust lErned Shrinkage-Thresholding (REST) –exhibits additional features including enlarged number of parameters and normalization processing compared to state-of-the-art deep architecture Learned Iterative Shrinkage-Thresholding Algorithm (LISTA), leading to the reliable recovery of the signal under sample-wise varying model mismatch. Our proposed network is also shown to outperform LISTA in compressive sensing problems under sample-wise varying model mismatch.

The Kalman filter (KF) is a celebrated signal processing algorithm, implementing optimal state estimation of dynamical systems that are well represented by a linear Gaussian state-space model. The KF is model-based, and therefore relies on full and accurate knowledge of the underlying model. We present KalmanNet, a hybrid data-driven/model-based filter that does not require full knowledge of the underlying model parameters. KalmanNet is inspired by the classical KF flow and implemented by integrating a dedicated and compact neural network for the Kalman gain computation. We present an offline training method, and numerically illustrate that KalmanNet can achieve optimal performance without full knowledge of the model parameters. We demonstrate that when facing inaccurate parameters KalmanNet learns to achieve notably improved performance compared to KF.

The success of deep neural networks (DNNs) as an enabler of artificial intelligence (AI) is heavily dependent on high computational resources. The increasing demands for accessible and personalized AI give rise to the need to operate DNNs on edge devices such as smartphones, sensors, and autonomous cars, whose computational powers are limited. Here we propose a framework for facilitating the application of DNNs on the edge in a manner which allows multiple users to collaborate during inference in order to improve their prediction accuracy. Our mechanism, referred to as edge ensembles, is based on having diverse predictors at each device, which can form a deep ensemble during inference. We analyze the latency induced in this collaborative inference approach, showing that the ability to improve performance via collaboration comes at the cost of a minor additional delay. Our experimental results demonstrate that collaborative inference via edge ensembles equipped with compact DNNs substantially improves the accuracy over having each user infer locally, and can outperform using a single centralized DNN larger than all the networks in the ensemble together.

We propose a learned-structured unfolding neural network for the problem of compressive sparse multichannel blind-deconvolution. In this problem, each channel’s measurements are given as convolution of a common source signal and sparse filter. Unlike prior works where the compression is achieved either through random projections or by applying a fixed structured compression matrix, this paper proposes to learn the compression matrix from data. Given the full measurements, the proposed network is trained in an unsupervised fashion to learn the source and estimate sparse filters. Then, given the estimated source, we learn a structured compression operator while optimizing for signal reconstruction and sparse filter recovery. The efficient structure of the compression allows its practical hardware implementation. The proposed neural network is an autoencoder constructed based on an unfolding approach: upon training, the encoder maps the compressed measurements into an estimate of sparse filters using the compression operator and the source, and the linear convolutional decoder reconstructs the full measurements. We demonstrate that our method is superior to classical structured compressive sparse multichannel blind-deconvolution methods in terms of accuracy and speed of sparse filter recovery.

While deep learning (DL) architectures like convolutional neural networks (CNNs) have enabled effective solutions in image denoising, in general their implementations overly rely on training data, lack interpretability, and require tuning of a large parameter set. In this paper, we combine classical graph signal filtering with deep feature learning into a competitive hybrid design—one that utilizes interpretable analytical low-pass graph filters and employs 80% fewer network parameters than state-of-the-art DL denoising scheme DnCNN. Specifically, to construct a suitable similarity graph for graph spectral filtering, we first adopt a CNN to learn feature representations per pixel, and then compute feature distances to establish edge weights. Given a constructed graph, we next formulate a convex optimization problem for denoising using a graph total variation (GTV) prior. Via a l1graph Laplacian reformulation, we interpret its solution in an iterative procedure as a graph low-pass filter and derive its frequency response. For fast filter implementation, we realize this response using a Lanczos approximation. Experimental results show that in the case of statistical mistmatch, our algorithm outperformed DnCNN by up to 3dB in PSNR.

Multiple-input multiple-output (MIMO) radar is known to achieve high performance by probing with multiple orthogonal wave-forms. However, implementing a low cost low power MIMO radar is challenging. In this work we study reduced cost MIMO radar receivers restricted to operate with low resolution ADCs. A hybrid analog-digital architecture, referred to as bit-limited MIMO radar (BiLiMO) receivers, which are capable of accurately recovering their targets while operating under strict resolution constraints is designed. This is achieved by applying an additional analog filter to the acquired waveforms, and designing the overall hybrid analog-digital system to facilitate target identification using task-based quantization methods. Our numerical results demonstrate that the proposed BiLiMO receiver operating with strict bit budget achieves target recovery performance which approaches that of costly MIMO radars operating with unlimited resolution ADCs.

Early detection of COVID-19 is key in containing the pandemic. Disease detection and evaluation based on imaging is fast and cheap and therefore plays an important role in COVID-19 handling. COVID-19 is easier to detect in chest CT, however, it is expensive, non-portable, and difficult to dis-infect, making it unfit as a point-of-care (POC) modality. On the other hand, chest X-ray (CXR) and lung ultrasound (LUS) are widely used, yet, COVID-19 findings in these modalities are not always very clear. Here we train deep neural networks to significantly enhance the capability to detect, grade and monitor COVID-19 patients using CXRs and LUS. Collaborating with several hospitals in Israel we collect a large dataset of CXRs and use this dataset to train a neural network obtaining above 90% detection rate for COVID-19. In addition, in collaboration with ULTRa (Ultrasound Laboratory Trento, Italy) and hospitals in Italy we obtained POC ultrasound data with annotations of the severity of disease and trained a deep network for automatic severity grading.

Recently, dynamic metasurface antennas (DMAs) have emerged as a promising technology for realizing massive multiple-input multiple-output (MIMO) wireless systems. The usage of large arrays, jointly with higher transmitted frequencies, often results in the communicating devices operating in the near-field (Fresnel) region, thus requiring different considerations compared to traditional systems, assumed to operate in the far-field regime. In this paper, we study the potential of beam focusing, feasible in near-field operation, for multi-user MIMO systems, where the base station is equipped with a DMA. We introduce a mathematical model for DMA-based near-field MIMO communications. Then, we characterize the sum-rate maximization problem of the considered system, and propose an efficient solution to jointly design the DMA weights and digital precoding vector. Simulation results show that our design generates focused beams such that users residing at the same angular direction can communicate reliably without interfering, which is not achievable using conventional far-field beam steering.

We consider the problem of convergence time minimization for federated learning (FL) implemented in wireless systems. In such setups, each wireless edge device transmits its local FL model parameters to a base station (BS). The BS then uses the received FL parameters to generate a common FL model and broadcasts it to all edge devices. Since the FL parameters must be transmitted over wireless links, the convergence time depends not only on the number of training steps, but also on the FL parameter transmission delay at each training step, which can be substantial when conveying a large number of parameters. In addition, due to limited wireless resources such as spectrum, only a subset of edge devices can participate in each FL training step, which can further increase convergence time. Our goal therefore is to optimize wireless resource management and user selection for FL, as well as limit the volume of transmitted FL parameters. In this paper, three schemes for facilitating communication efficient FL are introduced: First, a probabilistic device selection scheme is designed such that the devices that can significantly improve the convergence speed and training loss have high probabilities for FL parameter transmission. Then, given the subset of participating devices, an efficient wireless resource allocation scheme is developed. Finally, a quantization method is proposed to reduce the data size. Simulation results demonstrate that the proposed FL method can improve handwritten digit identification accuracy and convergence delay by up to 3% and 90% compared to the conventional FL.

The use of photo-activated fluorescent molecules to create long sequences of low-density, diffraction-limited images gives us the ability to achieve highly-precise molecule localizations. However, this methodology requires lengthy imaging times, resulting in poor temporal resolution. This is particularly problematic when dynamic interactions of live cells on short time scales are of interest. We consider the problem of shortening dramatically the acquisition times in super-resolution microscopy down to seconds, in order to image the cellular dynamics during T-cell activation. For this purpose, we apply our newly developed method for super-resolution microscopy, SPARCOM, to real-time imaging of the immune response initiation. Despite the small number of frames used for reconstruction, we are able to achieve high-quality imaging that shows how T-cell receptors re-organize during the activation events, with respect to the cell’s surface. Thus, our work demonstrates the use of SPARCOM for imaging dynamic cellular processes well below the diffraction limit.

Multi-modal distributions are commonly used to model clustered data in statistical learning tasks. In this paper, we consider the Mixed Linear Regression (MLR) problem. We propose an optimal transport-based framework for MLR problems, Wasserstein Mixed Linear Regression (WMLR), which minimizes the Wasserstein distance between the learned and target mixture regression models. Through a model-based duality analysis, WMLR reduces the underlying MLR task to a nonconvex-concave minimax optimization problem, which can be provably solved to find a minimax stationary point by the Gradient Descent Ascent (GDA) algorithm. In the special case of mixtures of two linear regression models, we show that WMLR enjoys global convergence and generalization guarantees. We prove that WMLR’s sample complexity grows linearly with the dimension of data. Finally, we discuss the application of WMLR to the federated learning task where the training samples are collected by multiple agents in a network. Unlike the Expectation-Maximization algorithm, WMLR directly extends to the distributed, federated learning setting. We support our theoretical results through several numerical experiments, which highlight our framework’s ability to handle the federated learning setting with mixture models.

We present extended Cantor arrays based on fourth- order difference co-arrays (E-FO-Cantor). These arrays result from extending the recently proposed fractal arrays to fourth- order difference co-arrays, and lead to fourth-order difference co-arrays that are hole-free. The set of sensor positions of the E-FO-Cantor is expressed in a simple and recursive form. The proposed Cantor arrays lead to O(N2log23) ≈ O(N3.17) degrees of freedom compared to O(N2) that can be achieved by existing sparse arrays with the hole-free property. Compared with other sparse arrays with the hole-free property in their fourth-order co-arrays, the proposed Cantor arrays provide a longer uniform linear array with more virtual sensors, leading to better DOA estimation performance.

The need to recover high-dimensional signals from their noisy low-resolution quantized measurements is widely encountered in communications and sensing. In this paper, we focus on the extreme case of one-bit quantizers, and propose a deep detector network, called LoRD-Net, for signal recovering from one-bit measurements. Our approach relies on a model-aware data-driven architecture, based on a deep unfolding of first-order optimization iterations. LoRD-Net has a task-based architecture dedicated to recovering the underlying signal of interest from the one-bit noisy measurements without requiring prior knowledge of the channel matrix through which the one-bit measurements are obtained. The proposed deep detector has much fewer parameters compared to black-box deep networks due to the incorporation of domain-knowledge in the design of its architecture, allowing it to operate in a data-driven fashion while benefiting from the flexibility, versatility, and reliability of model-based optimization methods. We numerically evaluate the proposed receiver architecture for one-bit signal recovery in wireless communications and demonstrate that the proposed hybrid methodology outperforms both data-driven and model-based state-of-the-art methods, while utilizing small datasets, on the order of merely ~ 500 samples, for training.

The combination of orthogonal frequency modulation (OFDM) and multiple-input multiple-output (MIMO) techniques plays an important role in modern communication systems. In order to meet the growing throughput demands, future MIMO-OFDM receivers are expected to utilize a massive number of antennas, operate in dynamic environments, and explore high frequency bands, while satisfying strict constraints in terms of cost, power, and size. An emerging technology to realize massive MIMO receivers of reduced cost and power consumption is based on dynamic metasurface antennas (DMAs), which inherently implement controllable compression in acquisition. In this work we study the application of DMAs for MIMO-OFDM receivers operating with bit-constrained analog-to-digital converters (ADCs). We present a model for DMAs which accounts for the configurable frequency selective profile of its metamaterial elements, resulting in a spectrally flexible hybrid structure. We then exploit previous results in task-based quantization to show characterized the achievable OFDM recovery accuracy for a given DMA configuration in the presence of bit-constrained ADCs, and propose methods for adjusting the DMA parameters based on channel state information. Our numerical results demonstrate that by properly exploiting the spectral diversity of DMAs, notable performance gains are obtained over existing designs of conventional hybrid architectures, demonstrating the potential of DMAs for realizing high performance massive antenna arrays of reduced cost and power consumption.

Ultrasound localization microscopy has enabled super-resolution vascular imaging through precise localization of individual ultrasound contrast agents (microbubbles) across numerous imaging frames. However, analysis of high-density regions with significant overlaps among the microbubble point spread responses yields high localization errors, constraining the technique to low-concentration conditions. As such, long acquisition times are required to sufficiently cover the vascular bed. In this work, we present a fast and precise method for obtaining super-resolution vascular images from high-density contrast-enhanced ultrasound imaging data. This method, which we term Deep Ultrasound Localization Microscopy (Deep-ULM), exploits modern deep learning strategies and employs a convolutional neural network to perform localization microscopy in dense scenarios, learning the nonlinear image-domain implications of overlapping RF signals originating from such sets of closely spaced microbubbles. Deep-ULM is trained effectively using realistic on-line synthesized data, enabling robust inference in-vivo under a wide variety of imaging conditions. We show that deep learning attains super-resolution with challenging contrast-agent densities, both in-silico as well as in-vivo. Deep-ULM is suitable for real-time applications, resolving about 70 high-resolution patches ( 128×128 pixels) per second on a standard PC. Exploiting GPU computation, this number increases to 1250 patches per second.

Digital receivers are required to recover the transmitted symbols from their observed channel output. In multiuser multiple-input multiple-output (MIMO) setups, where multiple symbols are simultaneously transmitted, accurate symbol detection is challenging. A family of algorithms capable of reliably recovering multiple symbols is based on interference cancellation. However, these methods assume that the channel is linear, a model which does not reflect many relevant channels, as well as require accurate channel state information (CSI), which may not be available. In this work we propose a multiuser MIMO receiver which learns to jointly detect in a data-driven fashion, without assuming a specific channel model or requiring CSI. In particular, we propose a data-driven implementation of the iterative soft interference cancellation (SIC) algorithm which we refer to as DeepSIC. The resulting symbol detector is based on integrating dedicated machine-learning methods into the iterative SIC algorithm. DeepSIC learns to carry out joint detection from a limited set of training samples without requiring the channel to be linear and its parameters to be known. Our numerical evaluations demonstrate that for linear channels with full CSI, DeepSIC approaches the performance of iterative SIC, which is comparable to the optimal performance, and outperforms previously proposed learning-based MIMO receivers. Furthermore, in the presence of CSI uncertainty, DeepSIC significantly outperforms model-based approaches. Finally, we show that DeepSIC accurately detects symbols in non-linear channels, where conventional iterative SIC fails even when accurate CSI is available.

Federated learning (FL) is a framework for distributed learning of centralized models. In FL, a set of edge devices train a model using their local data, while repeatedly exchanging their trained model with a central server, allowing to tune a global model without having the users share their possibly private data. A major challenge in FL is to reduce the bandwidth and energy consumption due to the repeated transmissions of large volumes of data by a large number of users over the wireless channel. Recently, over-the-air (OTA) FL has been suggested to achieve this goal. In this setting, all users transmit their data signal simultaneously over a Multiple Access Channel (MAC), and the computation is done over the wireless channel. In this paper, we develop a novel convergent OTA FL (COTAF) algorithm, which induces precoding and scaling upon transmissions to gradually mitigate the effect of the noisy channel, thus facilitating FL convergence. We analyze the convergence of COTAF to the loss minimizing model theoretically, showing its ability to achieve a convergence rate similar to that achievable over error-free channels. Our simulations demonstrate the improved convergence of COTAF for training using non-synthetic datasets.

Analog signals processed in digital hardware are quantized into a discrete bit-constrained representation. Quantization is typically carried out using analog-to-digital converters (ADCs), operating in a serial scalar manner. In some applications, a set of analog signals are acquired individually and processed jointly. Such setups are referred to as distributed quantization. In this work we propose a distributed quantization scheme for representing a set of sparse time sequences acquired using conventional scalar ADCs. Our approach utilizes tools from secure group testing theory to exploit the sparse nature of the acquired analog signals, obtaining a compact and accurate representation while operating in a distributed fashion. We then show how our technique can be implemented when the quantized signals are transmitted over a multihop communication network providing a low-complexity network policy for routing and signal recovery. Our numerical evaluations demonstrate that the proposed scheme notably outperforms conventional methods based on the combination of quantization and compressed sensing tools.

We consider generalized sampling for stochastic graph signals. The generalized graph sampling framework allows recovery of graph signals beyond the bandlimited setting by placing a correction filter between the sampling and reconstruction operators and assuming an appropriate prior. In this paper, we assume the graph signals are modeled by graph wide sense stationarity (GWSS), which is an extension of WSS for standard time domain signals. Furthermore, sampling is performed in the graph frequency domain along with the assumption that the graph signals lie in a periodic graph spectrum subspace. The correction filter is designed by minimizing the mean-squared error (MSE). The graph spectral response of the correction filter parallels that in generalized sampling for WSS signals. The effectiveness of our approach is validated via experiments by comparing the MSE with existing approaches.

Dual-function radar communication (DFRC) systems implement both sensing and communication using the same hardware. An emerging DFRC strategy embeds transmission of digital messages into agility-based radar schemes in the form of index modulation (IM). This approach provides the ability to communicate without entailing degradation in radar performance, at the cost of increased decoding complexity at the receiver side. In this work we propose schemes for reducing the decoding complexity associated with IM-based DFRC systems. We first focus on the receiver side, developing a sub-optimal low complexity scheme for recovering IM symbols embedded in radar waveforms. Then, we propose a method to modify the radar waveform to facilitate the recovery of the communicated bits with minimal effect on the radar performance. Our numerical results demonstrate that the proposed techniques allow the receiver to reliably recover the transmitted symbols with an affordable computational burden.

Modern radar systems are expected to operate reliably in congested environments under cost and power constraints. A recent technology for realizing such systems is frequency agile radar (FAR), which transmits narrowband pulses in a frequency hopping manner. To enhance the target recovery performance of FAR in complex electromagnetic environments, and particularly, its range-Doppler recovery performance, multi-Carrier AgilE phaSed Array Radar (CAESAR) was proposed. CAESAR extends FAR to multi-carrier waveforms while introducing the notion of spatial agility. In this paper, we theoretically analyze the range-Doppler recovery capabilities of CAESAR. Particularly, we derive conditions which guarantee accurate reconstruction of these range-Doppler parameters. These conditions indicate that by increasing the number of frequencies transmitted in each pulse, CAESAR improves performance over conventional FAR, especially in complex environments where some radar measurements are severely corrupted by interference.

Use of low resolution analog to digital converters (ADCs) is an effective way to reduce the high power consumption of millimeter wave (mmWave) receivers. In this paper, a receiver with low resolution ADCs based on adaptive thresholds is considered in downlink mmWave communications in which the channel state information is not known a-priori and acquired through channel estimation. A performance comparison of low-complexity algorithms for power and ADC allocation among transmit and receive terminals, respectively, is provided. Through simulation of practical mmWave cellular networks, it is shown that the use of low resolution ADCs does not significantly degrade the system throughput (as compared to a conventional fully digital high resolution receiver) when using the adaptive threshold receiver in conjunction with simple power and ADC allocation strategies.

Wireless ultrasound systems can make the imaging process much more efficient, affordable and accessible for users. The standard technique to create B-mode images is to rely on delay and sum (DAS) beamforming, in which the signals at each transducer element are sampled and processed by introducing appropriate delays. However, the sampling rates required to perform digital beamforming are typically high, resulting in high power requirements and a considerable amount of data which cannot be transferred over standard WiFi channels. In this paper we combine recently proposed methods for reducing sampling rate in each channel, and spatial reduction in the number of channels using sparse arrays, in order to implement beamforming at a low data rate without impacting image quality. We refer to our approach as sparse Fourier domain convolutional beamforming, and demonstrate that it can generate B-mode images at rates that are 33 times lower than standard DAS implementations.

Traditional deep learning models are trained on centralized servers using labeled sample data collected from edge devices. This data often includes private information, which the users may not be willing to share. Federated learning (FL) is an emerging approach to train such learning models without requiring the users to share their possibly private labeled data. In FL, each user trains its copy of the learning model locally. The server then collects the individual updates and aggregates them into a global model. A major challenge that arises in this method is the need of each user to efficiently transmit its learned model over the throughput limited uplink channel. In this work, we tackle this challenge using tools from quantization theory. In particular, we identify the unique characteristics associated with conveying trained models over rate-constrained channels, and characterize a suitable quantization scheme for such setups. We show that combining universal vector quantization methods with FL yields a decentralized training system, which is both efficient and feasible. We also derive theoretical performance guarantees of the system. Our numerical results illustrate the substantial performance gains of our scheme over FL with previously proposed quantization approaches.

Accurate symbol detection in multiuser multiple-input multiple-output (MIMO) setups, where multiple symbols are simultaneously transmitted, is a challenging task. A family of algorithms capable of reliably recovering multiple symbols is based on interference cancellation. However, these methods assume that the channel is linear, a model which does not reflect many relevant channels, as well as require accurate channel state information (CSI), which may not be available. In this work we propose a multiuser MIMO receiver which learns to jointly detect in a data-driven fashion, without assuming a specific channel model or requiring CSI. In particular, we propose a data-driven implementation of the iterative soft interference cancellation (SIC) algorithm. The resulting detector, referred to as DeepSIC, is based on integrating dedicated machine-learning (ML) methods into the iterative SIC scheme, and learns to carry out joint detection from a limited set of training samples without requiring the channel to be linear and its parameters to be known. Our numerical evaluations demonstrate that for linear channels with full CSI, DeepSIC approaches the performance of iterative SIC, which is comparable to the optimal performance, while being notably more robust to CSI uncertainty. Finally, we show that DeepSIC accurately detects symbols in non-linear channels, where conventional iterative SIC fails even when accurate CSI is available.

Analog-to-digital conversion allows physical signals to be processed using digital hardware. This conversion consists of two stages: Sampling, which maps a continuous-time signal into discrete-time, and quantization, i.e., representing the continuous-amplitude quantities using a finite number of bits. This conversion is typically carried out using generic uniform mappings that are ignorant of the task for which the signal is acquired, and can be costly when operating in high rates and fine resolutions. In this work we design task-oriented analog-to-digital converters (ADCs) which operate in a data-driven manner, namely they learn how to map an analog signal into a sampled digital representation such that the system task can be efficiently carried out. We propose a model for sampling and quantization which both faithfully represents these operations while allowing the system to learn non-uniform mappings from training data. We focus on the task of symbol detection in multiple-input multiple-output (MIMO) digital receivers, where multiple analog signals are simultaneously acquired in order to recover a set of discrete information symbols. Our numerical results demonstrate that the proposed approach achieves performance which is comparable to operating without quantization constraints, while achieving more accurate digital representation compared to utilizing conventional uniform ADCs.

Recently, there have been several works on unsupervised learning for training deep learning based denoisers without clean images. Approaches based on Stein's unbiased risk estimator (SURE) have shown promising results for training Gaussian deep denoisers. However, their performance is sensitive to hyper-parameter selection in approximating the divergence term in the SURE expression. In this work, we briefly study the computational efficiency of Monte-Carlo (MC) divergence approximation over recently available exact divergence computation using backpropagation. Then, we investigate the relationship between smoothness of nonlinear activation functions in deep denoisers and robust divergence term approximations. Lastly, we propose a new divergence term that does not contain hyper-parameters. Both unsupervised training methods yield comparable performance to supervised training methods with ground truth for denoising on various datasets. While the former method still requires roughly tuned hyper parameter selection, the latter method removes the necessity of choosing one.

Complex-field signal recovery problems from noisy linear/nonlinear measurements appear in many areas of signal processing and wireless communications. In this paper, we propose a trainable iterative signal recovery algorithm named complex-field TISTA (C-TISTA) which treats complex-field nonlinear inverse problems. C-TISTA is based on the concept of deep unfolding and consists of a gradient descent step with the Wirtinger derivatives followed by a shrinkage step with a trainable complex-valued shrinkage function. Importantly, it contains a small number of trainable parameters so that its training process can be executed efficiently. Numerical results indicate that C-TISTA shows remarkable signal recovery performance compared with existing algorithms.

The combination of orthogonal frequency modulation (OFDM) and multiple-input multiple-output (MIMO) systems plays an important role in modern communication systems. In order to meet the growing throughput demands, future MIMO-OFDM receivers are expected to utilize a massive number of antennas, operate in dynamic environments, and explore high frequency bands, while satisfying strict constraints in terms of cost, power, and size. An emerging technology to realize massive MIMO receivers of reduced cost and power consumption is based on dynamic metasurface antennas (DMAs), which inherently implement controllable compression in acquisition. In this work we study the application of DMAs for MIMO-OFDM receivers operating with bit-constrained analog-to-digital converters (ADCs). We exploit previous results in task-based quantization to show how DMAs can be configured to improve recovery in the presence of constrained ADCs, and propose an algorithm for adjusting the DMA parameters based on channel state information. Our numerical results demonstrate that the DMA-based receiver is capable of accurately recovering OFDM signals, and that its performance is comparable to receivers operating without bit limitations, while being significantly less costly and more power efficient.

We consider the problem of detecting one of M signals corrupted with white Gaussian noise. Conventionally, to minimize the probability of error, one uses matched filters to obtain a set of M sufficient statistics. In practice, M may be prohibitively large; this motivates the design and analysis of a reduced set of statistics which we term approximate sufficient statistics. By considering a sequence of sensing matrices that possesses suitable coherence and orthogonality properties, we bound the error exponent of the approximate sufficient statistics and compare it to that of the sufficient statistics. Additionally, we show that lower bound on the error exponent increases linearly for small compression rates.

Many important schemes in signal processing and communications, ranging from the BCJR algorithm to the Kalman filter, are instances of factor graph methods. This family of algorithms is based on recursive message passing-based computations carried out over graphical models, representing a factorization of the underlying statistics. In order to implement these algorithms, one must have accurate knowledge of the statistical model of the underlying signals. In this work we implement factor graph methods in a data-driven manner when the statistics are unknown. In particular, we propose using machine learning (ML) tools to learn the factor graph, instead of the overall system task, which in turn is used for inference by message passing over the learned graph. We apply the proposed approach to learn the factor graph representing a finite-memory channel, demonstrating the resulting ability to implement BCJR detection in a data-driven fashion. We demonstrate that the proposed system, referred to as BCJRNet, learns to implement the BCJR algorithm from a small training set, and that the resulting receiver exhibits improved robustness to inaccurate training compared to the conventional channel-model-based receiver operating under the same level of uncertainty. Our results indicate that by utilizing ML tools to learn factor graphs from labeled data, one can implement a broad range of model-based algorithms, which traditionally require full knowledge of the underlying statistics, in a data-driven fashion.

Federated learning (FL) refers to the adaptation of a central model based on data sets available at multiple remote users. Two of the common challenges encountered in FL are the fact that training sets obtained by different users are commonly heterogeneous, i.e., arise from different sample distributions, and the need to communicate large amounts of data between the users and the central server over the typically expensive up-link channel. In this work we formulate the problem of FL in which different clusters of users observe labeled samples drawn from different distributions, while operating under constraints on the communication overhead. For such settings, we identify that the combination of statistical heterogeneity and communication constraints induces a tradeoff between the ability of the users of each cluster to learn a proper model and the accuracy in aggregating these models into a global inference rule. We propose an algorithm based on multi-source adaptation methods for such communication-aware clustered FL scenarios which allows to balance these performance measures, and demonstrate its ability to achieve improved inference over conventional federated averaging without inducing additional communication overhead.

We study the sample complexity of estimating the covariance matrix T of a distribution over d-dimensional vectors, under the assumption that T is Toeplitz. This assumption arises in many signal processing problems, where the covariance between any two measurements only depends on the time or distance between those measurements. We are interested in estimation strategies that may choose to view only a subset of entries in each vector sample x ∼ , which often equates to reducing hardware and communication requirements in applications ranging from wireless signal processing to advanced imaging. Our goal is to minimize both 1) the number of vector samples drawn from and 2) the number of entries accessed in each sample. We provide some of the first non-asymptotic bounds on these sample complexity measures that exploit T's Toeplitz structure, and by doing so, significantly improve on results for generic covariance matrices. These bounds follow from a novel analysis of classical and widely used estimation algorithms (along with new variants), including methods based on selecting entries from each vector sample according to a so-called sparse ruler. In addition to results that hold for any Toeplitz T, we further study the important setting when T is close to low-rank, which is often the case in practice. We show that methods based on sparse rulers perform even better in this setting, with sample complexity scaling sublinearly in d. Motivated by this, we develop a new estimation strategy that further improves on existing methods in the low-rank case: when T is rank-k or nearly rank-k, it achieves sample complexity depending polynomially on k and only logarithmically on d. Our results utilize tools from random matrix sketching, leverage score based sampling techniques for continuous time signals, and sparse Fourier transform methods. In many cases, we pair our upper bounds with matching or nearly matching lower bounds.

In this article, we consider deep learning strategies in ultrasound systems, from the front end to advanced applications. Our goal is to provide the reader with a broad understanding of the possible impact of deep learning methodologies on many aspects of ultrasound imaging. In particular, we discuss methods that lie at the interface of signal acquisition and machine learning, exploiting both data structure (e.g., sparsity in some domain) and data dimensionality (big data) already at the raw radio-frequency channel stage. As some examples, we outline efficient and effective deep learning solutions for adaptive beamforming and adaptive spectral Doppler through artificial agents, learn compressive encodings for the color Doppler, and provide a framework for structured signal recovery by learning fast approximations of iterative minimization problems, with applications to clutter suppression and super-resolution ultrasound. These emerging technologies may have a considerable impact on ultrasound imaging, showing promise across key components in the receive processing chain.

Massive multiple-input multiple-output (MIMO) communication is a promising technology for increasing spectral efficiency in wireless networks. Two of the main challenges massive MIMO systems face are degraded channel estimation accuracy due to pilot contamination and increase in computational load and hardware complexity due to the massive number of antennas. In this paper, we focus on the problem of channel estimation in massive MIMO systems, while addressing these two challenges: We jointly design the pilot sequences to mitigate the effect of pilot contamination and propose an analog combiner which maps the high number of sensors to a low number of RF chains, thus reducing the computational and hardware cost. We consider a statistical model in which the channel covariance obeys a Kronecker structure, and treat two special cases, corresponding to fully- and partially-separable correlations. We prove that under these models, the analog combiner design can be performed independently of the pilot sequences. Given the resulting combiner, we derive a closed-form expression for the optimal pilot sequences in the fully-separable case and suggest a greedy sum of ratio traces maximization (GSRTM) method for designing sub-optimal pilots in the partially-separable scenario. We demonstrate via simulations that our pilot design framework achieves lower mean squared error than the common pilot allocation framework previously considered for pilot contamination mitigation.

Pilot contamination is a limiting factor in multicell massive multiple-input multiple-output (MIMO) systems because it can severely impair channel estimation. Prior works have suggested coordinating pilot design across cells in order to reduce the channel estimation error caused by pilot contamination. In this paper, we propose a method for coordinated pilot design using fractional programming to minimize the weighted mean squared-error (MSE) in channel estimation. In particular, we apply the recently proposed quadratic transform to the MSE expression which allows the effect of pilot contamination to be decoupled. The resulting problem reformulation enables the pilots to be optimized in closed form if they can be designed arbitrarily. When the pilots are restricted to a given set of orthogonal sequences, pilot optimization reduces to an assignment problem which can be solved by weighted bipartite matching. Furthermore, we consider the max-min fairness of data rates with orthogonal pilots and obtain an extension of the proposed method to correlated Rayleigh fading. Finally, simulations demonstrate the advantage of the proposed (orthogonal and nonorthogonal) pilot designs as compared with state-of-the-art methods in combating pilot contamination.

Non-orthogonal communications play an important role in future digital communication architectures. In such scenarios, the received signal is corrupted by an interfering communications signal, which is much stronger than the thermal noise, and is often modeled as a cyclostationary process in continuous-time. To facilitate digital processing, the receiver typically samples the received signal synchronously with the symbol rate of the information signal. If the period of the statistics of the interference is synchronized with that of the information signal, then the sampled interference is modeled as a discrete-time (DT) cyclostationary random process. However, in the common interference scenario, the period of the statistics of the interference is not necessarily synchronized with that of the information signal. In such cases, the DT interference may be modeled as an almost cyclostationary random process. In this work we characterize the capacity of DT memoryless additive noise channels in which the noise arises from a sampled cyclostationary Gaussian process. For the case of synchronous sampling, capacity can be obtained in closed form. When sampling is not synchronized with the symbol rate of the interference, the resulting channel is not information stable, thus classic information-theoretic tools are not applicable. Using information spectrum methods, we prove that capacity can be obtained as the limit of a sequence of capacities of channels with additive cyclostationary Gaussian noise. Our results allow to characterize the effects of changes in the sampling rate and sampling time offset on the capacity of the resulting DT channel. In particular, it is demonstrated that minor variations in the sampling period, such that the resulting noise switches from being synchronously-sampled to being asynchronously-sampled, can substantially change the capacity.

The problem of recovering a pair of signals from their blind phaseless short-time Fourier transform measurements arises in several important phase retrieval applications, including ptychography and ultra-short pulse characterization. In this paper, we prove that in order to determine a pair of generic signals uniquely, up to trivial ambiguities, the number of phaseless measurements one needs to collect is, at most, five times the number of parameters required to describe the signals. This result improves significantly upon previous papers, which required the number of measurements to be quadratic in the number of parameters rather than linear. In addition, we consider the simpler problem of recovering a pair of generic signals from their blind short-time Fourier transform, when the phases are known. In this setting, which can be understood as a special case of the blind deconvolution problem, we show that the number of measurements required to determine the two signals, up to trivial ambiguities, equals exactly the number of parameters to be recovered. As a side result, we study the classical phase retrieval problem-that is, recovering a signal from its Fourier magnitudes-when some entries of the signal are known a priori. We derive a bound on the number of required measurements as a function of the size of the set of known entries. Specifically, we show that if most of the signal's entries are known, then only a few Fourier magnitudes are necessary to determine a signal uniquely.

We study the convolutional phase retrieval problem, of recovering an unknown signal x ∈ Cnfrom m measurements consisting of the magnitude of its cyclic convolution with a given kernel a ∈ Cm. This model is motivated by applications such as channel estimation, optics, and underwater acoustic communication, where the signal of interest is acted on by a given channel/filter, and phase information is difficult or impossible to acquire. We show that when a is random and the number of observations m is sufficiently large, with high probability x can be efficiently recovered up to a global phase shift using a combination of spectral initialization and generalized gradient descent. The main challenge is coping with dependencies in the measurement operator. We overcome this challenge by using ideas from decoupling theory, suprema of chaos processes and the restricted isometry property of random circulant matrices, and recent analysis of alternating minimization methods.

Biomedical imaging is unequivocally dependent on the ability to reconstruct interpretable and high-quality images from acquired sensor data. This reconstruction process is pivotal across many applications, spanning from magnetic resonance imaging to ultrasound imaging. While advanced data-adaptive reconstruction methods can recover much higher image quality than traditional approaches, their implementation often poses a high computational burden. In ultrasound imaging, this burden is significant, especially when striving for low-cost systems, and has motivated the development of high-resolution and high-contrast adaptive beamforming methods. Here we show that deep neural networks, that adopt the algorithmic structure and constraints of adaptive signal processing techniques, can efficiently learn to perform fast high-quality ultrasound beamforming using very little training data. We apply our technique to two distinct ultrasound acquisition strategies (plane wave, and synthetic aperture), and demonstrate that high image quality can be maintained when measuring at low data-rates, using undersampled array designs. Beyond biomedical imaging, we expect that the proposed deep learning based adaptive processing framework can benefit a variety of array and signal processing applications, in particular when data-efficiency and robustness are of importance.

Contrast enhanced ultrasound is a radiation-free imaging modality which uses encapsulated gas microbubbles for improved visualization of the vascular bed deep within the tissue. It has recently been used to enable imaging with unprecedented subwavelength spatial resolution by relying on super-resolution techniques. A typical preprocessing step in super-resolution ultrasound is to separate the microbubble signal from the cluttering tissue signal. This step has a crucial impact on the final image quality. Here, we propose a new approach to clutter removal based on robust principle component analysis (PCA) and deep learning. We begin by modeling the acquired contrast enhanced ultrasound signal as a combination of low rank and sparse components. This model is used in robust PCA and was previously suggested in the context of ultrasound Doppler processing and dynamic magnetic resonance imaging. We then illustrate that an iterative algorithm based on this model exhibits improved separation of microbubble signal from the tissue signal over commonly practiced methods. Next, we apply the concept of deep unfolding to suggest a deep network architecture tailored to our clutter filtering problem which exhibits improved convergence speed and accuracy with respect to its iterative counterpart. We compare the performance of the suggested deep network on both simulations and in-vivo rat brain scans, with a commonly practiced deep-network architecture and with the fast iterative shrinkage algorithm. We show that our architecture exhibits better image quality and contrast.

Magnetic resonance (MR) imaging tasks often involve multiple contrasts, such as T1-weighted, T2-weighted and fluid-attenuated inversion recovery (FLAIR) data. These contrasts capture information associated with the same underlying anatomy and thus exhibit similarities in either structure level or gray level. In this paper, we propose a coupled dictionary learning based multi-contrast MRI reconstruction (CDLMRI) approach to leverage the dependency correlation between different contrasts for guided or joint reconstruction from their under-sampled k -space data. Our approach iterates between three stages: coupled dictionary learning, coupled sparse denoising, and enforcing k -space consistency. The first stage learns a set of dictionaries that not only are adaptive to the contrasts, but also capture correlations among multiple contrasts in a sparse transform domain. By capitalizing on the learned dictionaries, the second stage performs coupled sparse coding to remove the aliasing and noise in the corrupted contrasts. The third stage enforces consistency between the denoised contrasts and the measurements in the k -space domain. Numerical experiments, consisting of retrospective under-sampling of various MRI contrasts with a variety of sampling schemes, demonstrate that CDLMRI is capable of capturing structural dependencies between different contrasts. The learned priors indicate notable advantages in multi-contrast MR imaging and promising applications in quantitative MR imaging such as MR fingerprinting.

Symbol detection plays an important role in the implementation of digital receivers. In this work, we propose ViterbiNet, which is a data-driven symbol detector that does not require channel state information (CSI). ViterbiNet is obtained by integrating deep neural networks (DNNs) into the Viterbi algorithm. We identify the specific parts of the Viterbi algorithm that depend on the channel model, and design a DNN to implement only those computations, leaving the rest of the algorithm structure intact. We then propose a meta-learning based approach to train ViterbiNet online based on recent decisions, allowing the receiver to track dynamic channel conditions without requiring new training samples for every coherence block. Our numerical evaluations demonstrate that the performance of ViterbiNet, which is ignorant of the CSI, approaches that of the CSI-based Viterbi algorithm, and is capable of tracking time-varying channels without needing instantaneous CSI or additional training data. Moreover, unlike conventional Viterbi detection, ViterbiNet is robust to CSI uncertainty, and it can be reliably implemented in complex channel models with constrained computational burden. More broadly, our results demonstrate the conceptual benefit of designing communication systems that integrate DNNs into established algorithms.

This paper proposes to use a deep neural network (DNN)- based symbol detector for mmWave systems such that channel state information (CSI) acquisition can be bypassed. In particular, we consider a sliding bidirectional recurrent neural network (BRNN) architecture that is suitable for the long memory length of typical mmWave channels. The performance of the DNN detector is evaluated in comparison to that of the Viterbi detector. The results show that the performance of the DNN detector is close to that of the optimal Viterbi detector with perfect CSI, and that it outperforms the Viterbi algorithm with CSI estimation error. Further experiments show that the DNN detector is robust to a wide range of noise levels and varying channel conditions, and that a pretrained detector can be reliably applied to different mmWave channel realizations with minimal overhead.

In this paper, we study the sparse phase retrieval problem, that is, to estimate a sparse signal from a small number of noisy magnitude-only measurements. We propose an iterative soft-thresholding with exact line search algorithm (STELA). It is a parallel coordinate descent algorithm, which has several attractive features: i) fast convergence, as the approximate problem solved at each iteration exploits the original problem structure, ii) low complexity, as all variable updates have a closed-form expression, iii) easy implementation, as no hyperparameters are involved, and iv) guaranteed convergence to a stationary point for general measurements. These advantages are also demonstrated by numerical tests.

Sparse modeling seeks to represent signals as a linear combination of a small number of atoms from an overparametrized dictionary. Despite the success of these linear models, they can be too restrictive for applications involving nonlinear measurements. Using nonlinear atoms, however, poses an additional obstacle to the sparse recovery problem, since it remains non-convex even after relaxing the sparsity objective (e.g., using atomic norms). We address this issue in the context of continuous dictionaries by posing nonlinear sparse recovery as a sparse functional program that explicitly minimizes the functional equivalent of the "ℓ0-norm," i.e., the function support measure. By proving that strong duality holds for these optimization problems, we show that nonlinear sparse recovery over continuous dictionaries precludes relaxations since it may be solved efficiently using duality. This result is non-parametric, in that it does not assume the data follows the measurement model, and does not require incoherence assumptions, such as the restricted isometry/eigenvalue property. We also use strong duality to derive a relation between minimizing the support of a function and minimizing its L1-norm, although this does not imply that the latter leads to sparse solutions. We illustrate this new approach in a nonlinear line spectrum estimation problem.

Sparse arrays are of great interest since they can identify O(N2) uncorrelated sources with N physical sensors. This stems from their large difference coarray, defined as the differences between sensor locations. In a recent study, desired array properties such as closed-form expression for sensor locations, symmetry and large hole-free difference coarray were considered and it was shown that most existing sparse arrays do not exhibit these characteristics simultaneously. Standard Cantor arrays were shown to satisfy all the criteria above, however, their difference coarrays are of size O(Nlog2 3) which is smaller than that obtained with minimum redundancy arrays and nested arrays. In this paper, we introduce a fractal array design where a generator array is extended in a simple recursive fashion. In contrast to previous work, the generator is assumed to be a sparse array with a hole-free difference coarray. We study the resulting arrays and prove they inherit their properties from the generator. Thus, this approach can be used to extend any known sparse configuration to an arbitrarily large array. A small-scale array, which meets all design criteria, can be created and then expanded to generate a symmetric fractal array with a difference coarray of size O(N2), unlike Cantor arrays.

Sparse and low-rank decomposition, also known as robust principle component analysis, has been applied successfully in numerous applications. Typically, this approach leads to a minimization problem which is solved using iterative algorithms. Drawing inspiration from recurrent networks, in recent years deep-learning strategies have been extended to mimic the behavior of iterative algorithms, with reduced complexity. In this work, we propose an extension of these deep architectures to robust principle component analysis in which fully-connected layers are replaced with convolutional ones. This strategy offers spatial invariance and significant reduction in the number of learned parameters. We then apply the proposed method to contrast-enhanced ultrasound, in which low-rank tissue signal needs to be removed in order to visualize blood vessels. We demonstrate the effectiveness of our approach on simulations and in-vivo rat brain scans. The resulting images exhibit improved visual quality and contrast compared with images obtained by commonly practiced methods.

Machine learning, and more specifically deep learning, have shown remarkable performance in sensing, communications, and inference. In this paper, we consider the application of the deep unfolding technique in the problem of signal reconstruction from its one-bit noisy measurements. Namely, we propose a model-based machine learning method and unfold the iterations of an inference optimization algorithm into the layers of a deep neural network for one-bit signal recovery. The resulting network, which we refer to as DeepRec, can efficiently handle the recovery of high-dimensional signals from acquired one-bit noisy measurements. The proposed method results in an improvement in accuracy and computational efficiency with respect to the original framework as shown through numerical analysis.

While neural networks have achieved vastly enhanced performance over traditional iterative methods in many cases, they are generally empirically designed and the underlying structures are difficult to interpret. The algorithm unrolling approach has helped connect iterative algorithms to neural network architectures. However, such connections have not been made yet for blind image deblurring. In this paper, we propose a neural network architecture that advances this idea. We first present an iterative algorithm that may be considered a generalization of the traditional total-variation regularization method on the gradient domain, and subsequently unroll the half-quadratic splitting algorithm to construct a neural network. Our proposed deep network achieves significant practical performance gains while enjoying interpretability at the same time. Experimental results show that our approach outperforms many state-of-the-art methods.

The real-time nature that makes diagnostic ultrasonography so appealing to clinicians imposes strong constraints on the computational complexity of image reconstruction algorithms. As such, these typically rely on traditional delay-and-sum beamforming, a low-complexity approach that unfortunately comes at the cost of reduced image quality as compared to more advanced and content-adaptive beamformers. Here, we propose a model-aware deep learning strategy to ultrasound image reconstruction, which leverages knowledge of minimum variance beamforming while exploiting the efficiency of deep neural networks. Our approach yields high quality images with strong contrast at real-time reconstruction rates. The neural network is trained using in vivo and simulated radio frequency channel data of a single plane wave transmit, and corresponding high-quality minimum-variance beamformed reconstructions. Performance is benchmarked using simulated acquisitions from the PICMUS [1] dataset, demonstrating the convincing generalizability and image quality of the proposed beamformer.

Pilot contamination is a main limiting factor in multi-cell massive multiple-input multiple-output (MIMO) systems due to the non-orthogonality of pilot sequences which can seriously impair the channel measurement. Recent work has suggested coordinating pilot sequence design across multiple cells by choosing the sequences to minimize the channel estimation error. This paper further investigates this approach using a new optimization framework. Specifically, we reformulate the weighted minimum mean-squared error (MMSE) measure as a sum-of-functions-of-matrix-ratio program that can be efficiently solved via a matrix fractional programming approach. The proposed algorithm provides fast convergence to a stationary-point solution of the MMSE problem. Simulations demonstrate the advantage of the proposed method over alternative approaches in enhancing channel estimation accuracy.

Massive multiple-input multiple-output (MIMO) communications are the focus of considerable interest in recent years. While theoretical gains of such massive MIMO have been established, implementing MIMO systems with large-scale antenna arrays in practice is challenging. Among the practical difficulties associated with massive MIMO implementations are increased cost, power consumption, and physical size. In this work we study the implementation of massive MIMO antenna arrays using dynamic metasurface antennas (DMAs), an emerging technology which inherently handles the aforementioned challenges. DMAs realize planar large-scale arrays of tunable antenna elements, and can adaptively incorporate compression and analog combining in the physical antenna structure, thus reducing cost and power consumption. We first propose a mathematical model for massive MIMO systems with DMAs and discuss their constraints compared to ideal antenna arrays. Then, we characterize the fundamental limits of the resulting systems, and propose an algorithm for designing practical DMAs to approach these limits. Our numerical results indicate that the performance of practical DMA-based massive MIMO systems is comparable with ideal antenna arrays.

Massive multiple-input multiple-output (MIMO) systems have been drawing considerable interest. In the uplink, massive MIMO systems are commonly studied assuming that each base station (BS) decodes the signals of its user terminals separately and linearly while treating all interference as noise. Although this approach provides improved spectral efficiency (SE) in favorable channel conditions, it is generally sub-optimal from an information-theoretic perspective. In this work we characterize the SE of massive MIMO when the BSs are allowed to jointly decode the received signals. We consider two schemes for handling the interference, and derive their SEs for both finite and asymptotic number of antennas. Simulation tests of the proposed methods illustrate their gains in SE compared to standard separate linear decoding, and show that the standard approach fails to capture the actual achievable rates of massive MIMO systems, particularly when the interference is dominant.

Massive multiple-input multiple-output (MIMO) systems are the focus of increasing research attention. In such setups, there is an urgent need to utilize simple low-resolution quantizers, due to power and memory constraints. In this work we study massive MIMO channel estimation with quantized measurements, when the quantization system is designed to minimize the channel estimation error, as opposed to the quantization distortion. We first consider vector quantization, and characterize the minimal error achievable. Next, we focus on practical systems utilizing scalar uniform quantizers, and design the analog and digital processing as well as the quantization dynamic range to optimize the channel estimation accuracy. Our results demonstrate that the resulting massive MIMO system which utilizes low-resolution scalar quantizers can approach the minimal estimation error dictated by rate-distortion theory, achievable using vector quantizers.

Quantizers play a critical role in digital signal processing systems. In practice, quantizers are typically implemented using scalar analog-to-digital converters (ADCs), commonly utilizing a fixed uniform quantization rule which is ignorant of the task of the system. Recent works have shown that the performance of quantization systems utilizing scalar ADCs can be significantly improved by properly processing the analog signal prior to quantization. However, the implementation of such systems requires complete knowledge of the underlying model, which may not be available in practice. In this work we design task-oriented quantization systems with scalar ADCs using deep learning, focusing on the task of multiple-input multiple-output (MIMO) channel estimation. By utilizing deep learning, we construct a task-based quantization system, overcoming the need to explicitly recover the system model and to find the proper quantization rule for it. Our results indicate that the proposed method results in practical MIMO systems with scalar ADCs which are capable of approaching the optimal performance limits dictated by indirect rate-distortion theory, achievable using vector quantizers and requiring complete knowledge of the underlying statistical model.

Based on the intravascular infusion of gas microbubbles, which act as ultrasound contrast agents, ultrasound localization microscopy has enabled super resolution vascular imaging through precise detection of individual microbubbles across numerous imaging frames. However, analysis of high-density regions with significant overlaps among the microbubble point spread functions typically yields high localization errors, constraining the technique to low-concentration conditions. As such, long acquisition times are required for sufficient coverage of the vascular bed. Algorithms based on sparse recovery have been developed specifically to cope with the overlapping point-spread-functions of multiple microbubbles. While successful localization of densely-spaced emitters has been demonstrated, even highly optimized fast sparse recovery techniques involve a time-consuming iterative procedure. In this work, we used deep learning to improve upon standard ultrasound localization microscopy (Deep-ULM), and obtain super-resolution vascular images from high-density contrast-enhanced ultrasound data. Deep-ULM is suitable for real-time applications, resolving about 1250 high-resolution patches (128×128 pixels) per second using GPU acceleration.

Ultrasound localization microscopy offers new radiation-free diagnostic tools for vascular imaging deep within the tissue. Despite its high spatial resolution, low microbubble concentrations dictate the acquisition of tens of thousands of images, over the course of several seconds to tens of seconds, to produce a single super-resolved image. To address this limitation, sparsity-based approaches have recently been proposed to significantly reduce the total acquisition time, by resolving the vasculature in settings with considerable microbubble overlap. Here, we report on initial results of improving the spatial resolution and visual vascular reconstruction quality of sparsity-based super-resolution ultrasound imaging from low frame-rate acquisitions, by exploiting the inherent kinematics of microbubbles' flow. Our method relies on simultaneous tracking and sparsity-based detection of individual microbubbles.

Conventional dictionary matching based MR Fingerprinting (MRF) reconstruction approaches suffer from time-consuming operations that map temporal MRF signals to quantitative tissue parameters. In this paper, we design a 1-D residual convolutional neural network to perform the signature-to-parameter mapping in order to improve inference speed and accuracy. In particular, a 1-D convolutional neural network with shortcuts, a.k.a skip connections, for residual learning is developed using a TensorFlow platform. To avoid the requirement for a large amount of MRF data, the designed network is trained on synthesized MRF data simulated with the Bloch equations and fast imaging with steady state precession (FISP) sequences. The proposed approach was validated on both synthetic data and phantom data generated from a healthy subject. The reconstruction performance demonstrates a significantly improved speed - only 1.6s for reconstructing a pair of T1/T2 maps of size 128 × 128 - 50× faster than the original dictionary matching based method. The better performance was also confirmed by improved signal to noise ratio (SNR) and reduced root mean square error (RMSE). Furthermore, it is more compact to store a network instead of a large dictionary.

Many recent works on inference of graph structure assume that the graph signals are fully observable. For large graphs with thousands or millions of nodes, this entails high complexity on the data collection and processing steps. Here, we study a community inference problem on partially observed (sub-sampled) graph signals which sidesteps topology inference, while revealing the coarse structure of the graph directly. Two variants of the inference task are studied: (i) a blind method that infers the communities that the observable nodes belong to; and (ii) a semi-blind method that infers the communities of all nodes using, in addition, side information about the sub-graph between observable and hidden nodes. These techniques for community inference are shown to be efficient and suitable for large graphs analytically and empirically.

Analog-to-digital converters (ADCs) are a major contributor to the power consumption of multiple-input multiple-output (MIMO) communication systems with large number of antennas. Use of low resolution ADCs has been proposed as a means to decrease power consumption in MIMO receivers. However, reducing the ADC resolution leads to performance loss in terms of achievable transmission rates. In order to mitigate the rate-loss, the receiver can perform analog processing of the received signals before quantization. Prior works consider one-shot analog processing where at each channel-use, analog linear combinations of the received signals are fed to a set of one-bit threshold ADCs. In this paper, a receiver architecture is proposed which uses a sequence of delay elements to allow for blockwise linear combining of the received analog signals. In the high signal to noise ratio regime, it is shown that the proposed architecture achieves the maximum achievable transmission rate given a fixed number of one-bit ADCs. Furthermore, a tradeoff between transmission rate and the number of delay elements is identified which quantifies the increase in maximum achievable rate as the number of delay elements is increased.

The fundamental limits of communication over multiple-input multiple-output (MIMO) networks are considered when a limited number of one-bit analog to digital converters (ADC) are used at the receiver terminals. Prior works have mainly focused on point-to-point communications, where receiver architectures consisting of a concatenation of an analog processing module, a limited number of one-bit ADCs with non-adaptive thresholds, and a digital processing module are considered. In this work, a new receiver architecture is proposed which utilizes adaptive threshold one-bit ADCs - where the ADC thresholds at each channel-use are dependent on the channel outputs in the previous channel-uses - to mitigate the quantization rate-loss. Coding schemes are proposed for communication over the point-to-point and broadcast channels, and achievable rate regions are derived. In the high SNR regime, it is shown that using the proposed architectures and coding schemes leads to the largest achievable rate regions among all receiver architectures with the same number of one-bit ADCs.

Quantization allows physical signals to be processed using digital devices. Quantizers are commonly implemented using analog-to-digital converters (ADCs), which operate in a serial and scalar manner and are designed to yield an accurate digital representation of the observed signal. However, in many practical scenarios quantization is part of a system whose task is not to recover the observed signal, but some function of it. Recent works have shown that properly designed task-based quantizers, which include pre-quantization analog combining as well as digital processing, can achieve notable gains in recovering linear functions of the observations. In this work we focus on quantization for the task of recovering quadratic functions. Our analysis is based on principal inertia components (PICs), which form a basis for decomposing the statistical dependence between random quantities. Using PICs, we identify a practical structure of the pre-quantization mapping for recovering quadratic functions, which allows us to design a task-based quantization system capable of accurately estimating these functions. Our numerical study demonstrates that, when using scalar ADCs, notable performance gains that can be achieved using the proposed design over intuitive approaches such as quantizing the quadratic function directly as well as task-ignorant quantization.

Interference-limited communications plays an important role in future digital communication architectures. In such scenarios, the received signal is corrupted by an interfering communications signal, which is typically modeled as a cyclostationary process in continuous-time. To facilitate digital processing, the receiver typically samples the received signal synchronously with the symbol rate of the information signal. The sampled received signal thus contains an interference component which is either cyclostationary or almost cyclostationary in discrete-time (DT), depending on whether the symbol rate of the interference is synchronized with the sampling rate, or it is not. In this work we characterize the capacity of DT interference-limited communications channels, in which the interference is modeled as an additive sampled cyclostationary Gaussian noise. For the case of synchronous sampling, capacity can be obtained in closed form as a direct application of our previous work. When sampling is asynchronous, the resulting channel is not information stable, thus classic information-theoretic tools are not applicable. Using information spectrum methods, we prove that capacity can be obtained as the limit of a sequence of capacities of DT channels with additive cyclostationary noise. Our results facilitate the characterization of the impact of variations in the sampling rate and sampling time offset on the capacity of the resulting DT channel. In particular, it is demonstrated that minor variations in the sampling period can have a notable effect on capacity.

Sampling enables physical signals to be processed using digital hardware. When multiple signals are sampled, the spatial correlation between them may be utilized to reduce the overall reconstruction error. In this work we study joint sampling and reconstruction of multiple correlated stochastic sources, exploiting their correlation to improve recovery. We derive the achievable reconstruction error and the corresponding sampling system for arbitrary sampling rates and spectral structures. The proposed system minimizes the error when sampling below the Nyquist rate by preserving only the most dominant spatial eigenmodes aliased to each frequency. Using this characterization, we obtain sufficient conditions for error free recovery. We also discuss a distributed sampling setting, where each signal is acquired separately, while reconstruction is performed jointly. We characterize conditions under which distributed sampling performs as well as joint sampling. Our numerical results illustrate that joint sampling can achieve negligible reconstruction error using low sampling rates when the signals exhibit notable spatial correlation, and demonstrate that properly exploiting this correlation can dramatically improve reconstruction accuracy.

In traditional optical imaging systems, the spatial resolution is limited by the physics of diffraction, which acts as a low-pass filter. The information on subwavelength features is carried by evanescent waves, never reaching the camera, thereby posing a hard limit on resolution: the so-called diffraction limit. Modern microscopic methods enable super-resolution, by employing fluorescence techniques. State-of-the-art localization based fluorescence subwavelength imaging techniques such as PALM and STORM achieve subdiffraction spatial resolution of several tens of nanometers. However, they require tens of thousands of exposures, which limits their temporal resolution. We have recently proposed sparsity based super-resolution correlation microscopy (SPARCOM), which exploits the sparse nature of the fluorophore distribution, alongside a statistical prior of uncorrelated emissions, and showed that SPARCOM achieves spatial resolution comparable to PALM/STORM, while capturing the data hundreds of times faster. Here, we provide a detailed mathematical formulation of SPARCOM, which in turn leads to an efficient numerical implementation, suitable for large-scale problems. We further extend our method to a general framework for sparsity based super-resolution imaging, in which sparsity can be assumed in other domains such as wavelet or discrete-cosine, leading to improved reconstructions in a variety of physical settings.

We propose tensor-based four-dimensional sub-Nyquist radar that samples in spectral, spatial, Doppler, and temporal domains at sub-Nyquist rates while simultaneously recovering the target's direction, Doppler velocity, and range without loss of native resolutions. We formulate the radar signal model wherein the received echo samples are represented by a partial third-order tensor. We then apply compressed sensing in the tensor domain and use our tensor-orthogonal matching pursuit (OMP) and tensor completion algorithms for signal recovery. Our numerical experiments demonstrate joint estimation of all three target parameters at the same native resolutions as a conventional radar but with reduced measurements. Furthermore, tensor completion methods show enhanced performance in off-grid target recovery with respect to tensor-OMP.

Massive multiple-input-multiple-output (MIMO) communications are the focus of considerable interest in recent years. While the theoretical gains of massive MIMO have been established, implementing MIMO systems with large-scale antenna arrays in practice is challenging. Among the practical challenges associated with massive MIMO systems are increased cost, power consumption, and physical size. In this paper, we study the implementation of massive MIMO antenna arrays using dynamic metasurface antennas (DMAs), an emerging technology which inherently handles the aforementioned challenges. Specifically, DMAs realize large-scale planar antenna arrays and can adaptively incorporate signal processing methods such as compression and analog combining in the physical antenna structure, thus reducing the cost and power consumption. First, we propose a mathematical model for massive MIMO systems with DMAs and discuss their constraints compared to ideal antenna arrays. Then, we characterize the fundamental limits of uplink communications with the resulting systems and propose two algorithms for designing practical DMAs for approaching these limits. Our numerical results indicate that the proposed approaches result in practical massive MIMO systems whose performance is comparable to that achievable with ideal antenna arrays.

Massive multiple-input multiple-output (MIMO) systems have been drawing considerable interest due to the growing throughput demands on wireless networks. In the uplink, massive MIMO systems are commonly studied assuming that each base station (BS) decodes the signals of its user terminals separately and linearly while treating all interference as noise. Although this approach provides improved spectral efficiency which scales with the number of BS antennas in favorable channel conditions, it is generally sub-optimal from an information-theoretic perspective. In this paper, we characterize the spectral efficiency of massive MIMO when the BSs are allowed to jointly decode the received signals. In particular, we consider four schemes for treating the interference, and derive the achievable average ergodic rates for both finite and asymptotic number of antennas for each scheme. Simulation tests of the proposed methods illustrate their gains in spectral efficiency compared with the standard approach of separate linear decoding, and show that the standard approach fails to capture the actual achievable rates of massive MIMO systems, particularly when the interference is dominant.

Ground-penetrating radar (GPR) target detection and classification is a challenging task. Here, we consider online dictionary learning (DL) methods to obtain sparse representations (SR) of the GPR data to enhance feature extraction for target classification via support vector machines. Online methods are preferred because traditional batch DL like K-times singular value decomposition (K-SVD) is not scalable to high-dimensional training sets and infeasible for real-time operation. We also develop Drop-Off MINi-batch Online Dictionary Learning (DOMINODL), which exploits the fact that a lot of the training data may be correlated. The DOMINODL algorithm iteratively considers elements of the training set in small batches and drops off samples which become less relevant. For the case of abandoned anti-personnel landmines classification, we compare the performance of K-SVD with three online algorithms: classical online dictionary learning (ODL), its correlation-based variant, and DOMINODL. Our experiments with real data from L-band GPR show that online DL methods reduce learning time by 36%-93% and increase mine detection by 4%-28% over K-SVD. Our DOMINODL is the fastest and retains similar classification performance as the other two online DL approaches. We use a Kolmogorov-Smirnoff test distance and the Dvoretzky-Kiefer-Wolfowitz inequality for the selection of DL input parameters leading to enhanced classification results. To further compare with the state-of-the-art classification approaches, we evaluate a convolutional neural network (CNN) classifier, which performs worse than the proposed approach. Moreover, when the acquired samples are randomly reduced by 25%, 50%, and 75%, sparse decomposition-based classification with DL remains robust while the CNN accuracy is drastically compromised.

We consider the recovery of a continuous-time Wiener process from a quantized or a lossy compressed version of its uniform samples under limited bitrate and sampling rate. We derive a closed-form expression for the optimal tradeoff among sampling rate, bitrate, and quadratic distortion in this setting. This expression is given in terms of a reverse waterfilling formula over the asymptotic spectral distribution of a sequence of finite-rank operators associated with the optimal estimator of the Wiener process from its samples. We show that the ratio between this expression and the standard distortion rate function of the Wiener process, describing the optimal tradeoff between bitrate and distortion without a sampling constraint, is only a function of the number of bits per sample. We also consider a sub-optimal lossy compression scheme in which the continuous-time process is estimated from the output of an encoder that is optimal with respect to the discrete-time samples. We show that the latter is strictly greater than the distortion under optimal encoding but only by at most 3%. We, therefore, conclude that near optimal performance is attained even if the encoder is unaware of the continuous-time origin of the samples.

The use of multichannel data in line spectral estimation (or frequency estimation) is common for improving the estimation accuracy in array processing, structural health monitoring, wireless communications, and more. Recently proposed atomic norm methods have attracted considerable attention due to their provable superiority in accuracy, flexibility, and robustness compared with conventional approaches. In this paper, we analyze atomic norm minimization for multichannel frequency estimation from noiseless compressive data, showing that the sample size per channel that ensures exact estimation decreases with the increase of the number of channels under mild conditions. In particular, given L channels, order K (log K) (1 + L/1 log N) samples per channel, selected randomly from N equispaced samples, suffice to ensure with high probability exact estimation of K frequencies that are normalized and mutually separated by at least 4/N. Numerical results are provided corroborating our analysis.

We investigate the worst-case robust beamforming for simultaneous wireless information and power transfer in a multiuser beamspace massive multiple-input multiple-output (MIMO) system. The objective is to minimize the transmit power of the base station subject to the individual signal-to-interference-plus-noise ratio and the energy-harvesting constraints under imperfect channel state information. Instead of directly resorting to semi-definite relaxation, we convert the initial non-convex optimization to a power allocation problem, which greatly reduces the computational complexity. The beamforming vectors are proven to be scaled versions of the estimated channels. The optimal scaling factors are then derived in closed-form. The simulations demonstrate that the proposed robust beamforming method achieves the globally optimal point for the initial design when the channel estimation errors are small while leads to satisfactory performance when the channel estimation errors are large.

Recently, ambient backscatter that utilizes surrounding radio frequency (RF) signals for both power and communications, has attracted vast interest since it can free sensors and tags from batteries and has extensive applications in Internet of Things (IoT), Existing studies about ambient backscatter often assume single antenna for each tag. Actually, as we show in this paper, equipping tags with multiple antennas can enlarge communication distance, enhance detection performance, and thus be practically useful. One key challenge of using multiple-antenna tags is the signal detection at the reader because the tag may have limited power and can transmit few training symbols. Therefore, in this paper, we design a blind detector based on F-test for the reader to recover tag signals without any knowledge of RF signals power, noise variance and all channel state information (CSI). Furthermore, we derive the lower and upper bounds of detection probabilities, and its exact expression in a special case. The optimal antenna selection scheme is also proposed to maximize the detection probability. Finally, simulation results are provided to corroborate our theoretical studies.

The problem of recovering a signal from its power spectrum is called phase retrieval. This problem appears in a variety of scientific applications, such as ultra-short laser pulse characterization and diffraction imaging. However, the problem for one-dimensional signals is ill-posed as there is no one-to-one mapping between a one-dimensional signal and its power spectrum. In the field of ultra-short laser pulse characterization, it is common to overcome this ill-posedness by using a technique called Frequency-Resolved Optical Gating (FROG). In FROG, the measured data, referred to as FROG trace, is the Fourier magnitude of the product of the underlying signal with several translated versions of itself. Therefore, in order to recover a signal from its FROG trace, one needs to invert a system of phaseless quartic equations. In this paper, we explore the symmetries and uniqueness of the FROG mapping. Our main result states that a signal bandlimited to B is determined uniquely, up to symmetries, by only 3B FROG measurements.

Signal processing is rich in inherently continuous applications, such as radar, MRI, and source localization, in which sparsity priors play a key role in obtaining state-of-the-art results. To cope with the infinite dimensionality and non-convexity of these estimation problems, they are typically discretized and solved by means of convex relaxations, e.g., using atomic norms. Although successful, this approach is not without issues. Discretization often leads to high dimensional, potentially ill-conditioned optimization problems. Moreover, due to grid mismatch and other coherence issues, a sparse signal in the continuous domain may no longer be sparse when discretized. Finally, performance guarantees for atomic norm relaxations hold under assumptions that may be hard to meet in practice. We address these issues by directly tackling the continuous problem cast as a sparse functional optimization program. We prove that these problems have no duality gap and show that they can be solved efficiently using duality and a stochastic gradient ascent-type algorithm. We illustrate the performance of this new approach on a line spectral estimation problem.

In this paper the focus is on sampling and reconstruction of signals supported on nodes of arbitrary graphs or arbitrary signals that may be represented using graphs, where we extend concepts from generalized sampling theory to the graph setting. To recover such signals from a given set of samples, we develop algorithms that incorporate prior knowledge on the original signal when available such as smoothness or subspace priors related to the underlying graph. For reconstructing arbitrary signals, we constrain the reconstruction to the graph, and provide a consistent reconstruction method, in which both the reconstructed signal and the input yield exactly the same measurements. Given a set of graph frequency domain samples, the sampling and interpolation operations may be efficiently implemented using linear shift-invariant graph filters.

The number of elements of a uniform linear array (ULA) is the main bottleneck in many applications in array processing in terms of cost and power consumption. This motivates the use of sparse arrays where some of the elements are removed. However, designing a sparse array configuration with the smallest number of elements that preserves the full array beam pattern is generally NP hard. In this paper we adopt work in multiple-input-multiple-output (MIMO) radar to study a sparse array composed of two sub apertures. We derive the minimal number of elements required using this design, showing that in general there are two optimal solutions. Next, we present an extension of this approach beyond two sub apertures. By optimizing the number of sub apertures, we prove that the optimal array configuration is related to the notion of prime factorization. This allows to achieve a significant reduction in the number of elements.

Accelerating iterative algorithms for solving inverse problems using neural networks have become a very popular strategy in the recent years. In this work, we propose a theoretical analysis that may provide an explanation for its success. Our theory relies on the usage of inexact projections with the projected gradient descent (PGD) method. It is demonstrated in various problems including image super-resolution.

In this paper we introduce a computationally efficient solution to the problem of graph signal interpolation. Our solution is derived using the Nyström extension and is due to the properties of the Markov matrix which we use as our graph shift operator, inspired by diffusion maps. We focus on graph signals that are smooth over the graph. This assumption cements the relationship between the graph and the graph signal. We experimentally verify our suggested framework on the MNIST data set of handwritten digits.

The iterative linear expansion of threshold framework, or iLET, offers a new approach for solving image restoration problems under sparsity assumptions. Instead of estimating the reconstructed image directly, the iLET paradigm parametrizes the reconstruction process as a linear combination of elementary thresholding functions and optimizes over their coefficients. Here, we rely on the fast and accurate convergence of iLET, and propose an extension of this framework, under the assumption that the reconstructed object is approximately piece-wise constant. This assumption leads to a new total-variation framework of iLET. We demonstrate the applicability of our technique to bio-medical imaging problems, such as computerized tomography reconstruction. Our technique surpasses state-of-the-art reconstructions in terms of PSNR and SSIM, while offering an automatic way for tuning its regularization parameter.

Medical imaging tasks often involve multiple contrasts, such as T1-and T2-weighted magnetic resonance imaging (MRI) data. These contrasts capture information associated with the same underlying anatomy and thus exhibit similarities. In this paper, we propose a Coupled Dictionary Learning based multi-contrast MRI reconstruction (CDLMRI) approach to leverage an available guidance contrast to restore the target contrast. Our approach consists of three stages: coupled dictionary learning, coupled sparse denoising, and k-space consistency enforcing. The first stage learns a group of dictionaries that capture correlations among multiple contrasts. By capitalizing on the learned adaptive dictionaries, the second stage performs joint sparse coding to denoise the corrupted target image with the aid of a guidance contrast. The third stage enforces consistency between the denoised image and the measurements in the k-space domain. Numerical experiments on the retrospective under-sampling of clinical MR images demonstrate that incorporating additional guidance contrast via our design improves MRI reconstruction, compared to state-of-the-art approaches.

The capacity of a Multiple-Input Multiple-Output (MIMO) channel in which the antenna outputs are processed by an analog linear combining network and quantized by a set of threshold quantizers is studied. The linear combining weights and quantization thresholds are selected from a set of possible configurations as a function of the channel matrix. The possible configurations of the combining network model specific analog receiver architectures, such as single antenna selection, sign quantization of the antenna outputs or linear processing of the outputs. An interesting connection between the capacity of this channel and a constrained sphere packing problem in which unit spheres are packed in a hyperplane arrangement is shown. From a high-level perspective, this follows from the fact that each threshold quantizer can be viewed as a hyperplane partitioning the transmitter signal space. Accordingly, the output of the set of quantizers corresponds to the possible regions induced by the hyperplane arrangement corresponding to the channel realization and receiver configuration. This connection provides a number of important insights into the design of quantization architectures for MIMO receivers; for instance, it shows that for a given number of quantizers, choosing configurations which induce a larger number of partitions can lead to higher rates1.

Theoretical and experimental results have shown that compressed sensing with quantization can perform well if the signal is very sparse, the noise is very low, and the bitrate is sufficiently large. However, a precise characterization of the fundamental tradeoffs between these quantities has remained elusive. In our previous work, we considered a quantization scheme that first computes the conditional expectation of the signal. In this paper, we focus on a different approach in which the measurements are encoded directly using Gaussian codebooks. We show that that mean-square error (MSE) distortion of this approach can be analyzed by studying a degraded measurement model without any bitrate constraints. Building upon ideas from statistical physics and random matrix theory, we then provide single-letter formulas for the reconstruction error associated with optimal decoding. These formulas provide an explicit characterization of the mean-squared error (MSE) as a function of: (1) the average quantization bitrate, (2) the prior distribution of the signal, and (3) the spectral distribution of the sensing matrix. These formulas provide upper bounds on the fundamental limits of compressed sensing with quantization. Interestingly, it is shown that in some problem regimes, this method achieves the best known performance, even though the encoding stage does not use any information about the signal distribution other than its mean and variance.

The problem of recovering a one-dimensional signal from its Fourier transform magnitude, called Fourier phase retrieval, is ill-posed in most cases. We consider the closely-related problem of recovering a signal from its phaseless short-time Fourier transform (STFT) measurements. This problem arises naturally in several applications, such as ultra-short laser pulse characterization and ptychography. The redundancy offered by the STFT enables unique recovery under mild conditions. We show that in some cases the unique solution can be obtained by the principal eigenvector of a matrix, constructed as the solution of a simple least-squares problem. When these conditions are not met, we suggest using the principal eigenvector of this matrix to initialize non-convex local optimization algorithms and propose two such methods. The first is based on minimizing the empirical risk loss function, while the second maximizes a quadratic function on the manifold of phases. We prove that under appropriate conditions, the proposed initialization is close to the underlying signal. We then analyze the geometry of the empirical risk loss function and show numerically that both gradient algorithms converge to the underlying signal even with small redundancy in the measurements. In addition, the algorithms are robust to noise.

Representing a continuous-time signal by a set of samples is a classical problem in signal processing. We study this problem under the additional constraint that the samples are quantized or compressed in a lossy manner under a limited bitrate budget. To this end, we consider a combined sampling and source coding problem in which an analog stationary Gaussian signal is reconstructed from its encoded samples. These samples are obtained by a set of bounded linear functionals of the continuous-time path, with a limitation on the average number of samples per unit time given in this setting. We provide a full characterization of the minimal distortion in terms of the sampling frequency, the bitrate, and the signal's spectrum. Assuming that the signal's energy is not uniformly distributed over its spectral support, we show that for each compression bitrate there exists a critical sampling frequency smaller than the Nyquist rate, such that the distortion in signal reconstruction when sampling at this frequency is minimal. Our results can be seen as an extension of the classical sampling theorem for bandlimited random processes in the sense that they describe the minimal amount of excess distortion in the reconstruction due to lossy compression of the samples and provide the minimal sampling frequency required in order to achieve this distortion. Finally, we compare the fundamental limits in the combined source coding and sampling problem to the performance of pulse code modulation, where each sample is quantized by a scalar quantizer using a fixed number of bits.

A general expression for the quadratic distortion rate function (DRF) of cyclostationary Gaussian processes in terms of their spectral properties is derived. This expression can be seen as the result of orthogonalization over the different components in the polyphase decomposition of the process. We use this expression to derive, in a closed form, the DRF of several cyclostationary processes arising in practice. We first consider the DRF of a combined sampling and source coding problem. It is known that the optimal coding strategy for this problem involves source coding applied to a signal with the same structure as one resulting from pulse amplitude modulation (PAM). Since a PAM-modulated signal is cyclostationary, our DRF expression can be used to solve for the minimal distortion in the combined sampling and source coding problem. We also analyze in more detail the DRF of a source with the same structure as a PAM-modulated signal, and show that it is obtained by reverse waterfilling over an expression that depends on the energy of the pulse and the baseband process modulated to obtain the PAM signal. This result is then used to explore the effect of the symbol rate in PAM on the DRF of its output. In addition, we also study the DRF of sources with an amplitude-modulation structure, and show that the DRF of a narrow-band Gaussian stationary process modulated by either a deterministic or a random phase sine-wave equals the DRF of the baseband process.

This paper presents a new algorithm, termed truncated amplitude flow (TAF), to recover an unknown vector x from a system of quadratic equations of the form yi= |〈ai, x〉|2, where ai's are given random measurement vectors. This problem is known to be NP-hard in general. We prove that as soon as the number of equations is on the order of the number of unknowns, TAF recovers the solution exactly (up to a global unimodular constant) with high probability and complexity growing linearly with both the number of unknowns and the number of equations. Our TAF approach adapts the amplitude based empirical loss function and proceeds in two stages. In the first stage, we introduce an orthogonality-promoting initialization that can be obtained with a few power iterations. Stage two refines the initial estimate by successive updates of scalable truncated generalized gradient iterations, which are able to handle the rather challenging nonconvex and nonsmooth amplitude based objective function. In particular, when vectors x and ai's are real valued, our gradient truncation rule provably eliminates erroneously estimated signs with high probability to markedly improve upon its untruncated version. Numerical tests using synthetic data and real images demonstrate that our initialization returns more accurate and robust estimates relative to spectral initializations. Furthermore, even under the same initialization, the proposed amplitude-based refinement outperforms existing Wirtinger flow variants, corroborating the superior performance of TAF over state-of-the-art algorithms.

The problem of recovering a signal from its phaseless short-time Fourier transform (STFT) measurements arises in several applications, such as ultra-short pulse measurements and ptychography. The redundancy offered by the STFT enables unique recovery under mild conditions. We show that in some cases, the principle eigenvector of a designed matrix recovers the underlying signal. This matrix is constructed as the solution of a simple least-squares problem. When these conditions are not met, we suggest to use this principle eigenvector to initialize a gradient algorithm, minimizing a non-convex loss function. We prove that under appropriate conditions, this initialization results in a good estimate of the underlying signal. We further analyze the geometry of the loss function and show empirically that the gradient algorithm is robust to noise. Our method is both efficient and enjoys theoretical guarantees.

Pulse Doppler multiple input multiple output (MIMO) radar allows to simultaneously detect targets' range, azimuth and velocity. Achieving high resolution requires a large number of transmit and receive antennas, as well as high sampling rates leading to a torrent of samples. Overcoming the rate bottleneck, sub-Nyquist sampling methods have been proposed that break the link between single antenna radar signal bandwidth and range resolution. In this work, we present a sub-Nyquist MIMO radar (SUMMeR) system that extends these methods to a multiple antenna setting. We apply the Xampling framework both in time and space, thus reducing both the number of deployed antennas and samples per receiver, without degrading time and spatial resolution, as illustrated in the simulations.

Cognitive Radio requires both efficient and reliable spectrum sensing of wideband signals. In order to cope with the sampling rate bottleneck when dealing with such signals, sub-Nyquist methods have been proposed. However, these techniques decrease the signal to noise ratio (SNR) due to aliasing effects. Cyclostationary detection, which exploits the periodic property of communication signal statistics, absent in stationary noise, is a natural candidate for this setting. In this work, we consider cyclic spectrum recovery from sub-Nyquist samples, in order to achieve both efficiency and robustness to noise. We show how the cyclic spectrum can be recovered directly from the low rate samples, even for non sparse signals, and derive a lower bound on the sampling rate required for perfect cyclic spectrum recovery in the presence of stationary noise. Simulations show that cyclostationary detection outperforms energy detection in low SNRs in the sub-Nyquist regime.

We present a composite suite of technologies for spectral coexistence of existing communication and radar systems using the Xampling framework. For a stand-alone communication system, we consider a cognitive radio (CRo) that receives multiband signals with unknown carrier frequencies and directions of arrival, and demonstrate joint spectrum sensing via CompreSsed CArrier and Direction-ofarrival Estimation (CaSCADE) with an L-shaped configuration of two uniform linear arrays. For radars operating in bands with widespread spectral interference, we present an X-band prototype of cognitive sub-Nyquist multiple input multiple output (MIMO) radar (SUMMeR). The prototype allows sampling in both spatial and spectral domains at sub-Nyquist rates and cognitively transmits over multiple narrow subbands. Finally, we demonstrate Spectral Coexistence via Xampling (SpeCX) technology that shows joint operation of both - cognitive radio and cognitive monostatic radar - over a common spectrum. Our solutions to individual and joint operation of communication and radar systems supersede existing spectrum sharing technologies that require a compromise over performance of one of the systems.

A cognitive radar adapts the transmit waveform in response to changes in the radar and target environment. In this work, we analyze the recently proposed sub-Nyquist cognitive radar wherein the total transmit power in a multi-band cognitive waveform remains the same as its full-band conventional counterpart. For such a system, we derive lower bounds on the mean-squared-error (MSE) of a single-target time delay estimate. We formulate a procedure to select the optimal bands, and recommend distribution of the total power in different bands to enhance the accuracy of delay estimation. In particular, using Cramér-Rao bounds, we show that equi-width subbands in cognitive radar always have better delay estimation than the conventional radar. Further analysis using Ziv-Zakai bound reveals that cognitive radar performs well in low signal-to-noise (SNR) regions.

We study the problem of recovering a low-rank matrix, X, from phaseless measurements of random linear projections of its columns. We develop a novel solution approach, called AltMinTrunc, that consists of a two-step truncated spectral initialization step, followed by a three-step alternating minimization algorithm. We obtain sample complexity bounds for the AltMinTrunc initialization to provide a good approximation of the true X. When the rank of X is low enough, these are significantly smaller than what existing single vector phase retrieval algorithms need. Via extensive experiments, we demonstrate the same for the entire algorithm.

We consider the problem of estimating the covariance matrix and the transition matrix of vector autoregressive (VAR) processes from partial measurements. This model encompasses settings where there are limitations in the data acquisition of the underlying measurement systems so that data is lost or corrupted by noise. An estimator for the covariance matrix of the observations is first presented. More refined estimators, factoring in structural constraints on the covariance matrix such as sparsity, bandedness, sparsity of the inverse and low-rankness are then introduced that are particularly useful in the high-dimensional regime. These estimates are then used to perform system identification by estimating the state transition matrix with or without further structural assumptions. Non-asymptotic guarantees are presented for all estimators.

We consider problems where one wishes to represent a parameter associated with a signal source - subject to a certain rate and distortion - based on the observation of a number of realizations of the source signal. By reducing these indirect vector quantization problems to a standard vector quantization one, we provide a bound to the fundamental interplay between the rate and distortion in the large-rate setting. We specialize this characterization to two particular quantization scenarios: i) the representation of the mean of a multivariate Gaussian source; and ii) the representation of the eigen-spectrum of a multivariate Gaussian source. Numerical results compare our quantization approach to an approach where one recovers the parameters from the representation of the source signals itself: in addition to revealing that the characterization is sharp in the large-rate setting, the results also show that our approach offers considerable gains.

Traditionally, spatial resolution in optical imaging is limited by diffraction. Although sub-wavelength information is absent in the measurements, state-of-the-art fluorescence based localization techniques such as PALM and STORM manage to achieve spatial resolution of tens of nano-meters, but with limited temporal resolution. A more recent technique super-resolution optical fluctuation imaging (SOFI) exploits the temporal statistical behavior of uncorrelated fluorescence emissions to practically improve the spatial resolution by a factor of two over the diffraction limit, but with considerably faster image capturing. Here we propose to exploit the sparse nature of the fluorophores distribution, combined with a statistical prior of uncorrelated emissions such as in SOFI to achieve spatial resolution comparable to PALM/STORM, while retaining the temporal resolution of SOFI. We demonstrate our method on simulations and show improved results over STORM and SOFI. Our method may facilitate super-resolution imaging and capturing of intra-cellular dynamics within living cells.

Sparse decomposition of ground penetration radar (GPR) signals facilitates the use of compressed sensing techniques for faster data acquisition and enhanced feature extraction for target classification. In this paper, we investigate use of an online dictionary learning (ODL) technique in the context of GPR to bring down the learning time as well as improve identification of abandoned anti-personnel landmines. Our experimental results using real data from an L-band GPR for PMN/PMA2, ERA and T72 mines show that ODL reduces learning time by 94% and increases clutter detection by 10% over the classical K-SVD algorithm. Moreover, our methods could be helpful in cognitive operation of the GPR where the system adapts the range sampling based on the learned dictionary.

We consider the problem of recovering a sparse vector from a quantized or a lossy compressed version of its noisy random linear projections. We characterize the minimal distortion in this recovery as a function of the sampling ratio, the sparsity rate, the noise intensity and the total number of bits in the quantized representation. We first derive a singe-letter expression that can be seen as the indirect distortion-rate function of the sparse source observed through a Gaussian channel whose signal-to-noise ratio is derived from these parameters. Under the replica symmetry postulation, we prove that there exists a quantization scheme that attains this expression in the asymptotic regime of large system dimensions. In addition, we prove a converse demonstrating that the MMSE in estimating any fixed sub-block of the source from the quantized measurements at a fixed number of bits does not exceed this expression as the system dimensions go to infinity. Thus, under these conditions, the expression we derive describes the excess distortion incurred in encoding the source vector from its noisy random linear projections in lieu of the full source information.

We consider the problem of estimating the parameters of a vector autoregressive (VAR) process from low-dimensional random projections of the observations. This setting covers the cases where we take compressive measurements of the observations or have limits in the data acquisition process associated with the measurement system and are only able to subsample. We first present fundamental bounds on the convergence of any estimator for the covariance or state-transition matrices with and without considering structural constraints of sparsity and low-rankness. We then construct an estimator for these matrices or the parameters of the VAR process and show that it is order optimal.

In the phase retrieval problem, the observations consist of the magnitude of a linear transformation of the signal of interest (SOI) with additive noise, where the linear transformation is typically referred to as measurement matrix. The objective is then to reconstruct the SOI from the observations up to an inherent phase ambiguity. Many works on phase retrieval assume that the measurement matrix is a random Gaussian matrix, which in the noiseless scenario with sufficiently many measurements guarantees uniqueness of the mapping between the SOI and the observations. However, in many applications, e.g., optical imaging, the measurement matrix corresponds to the underlying physical setup, and is therefore a deterministic matrix with structure constraints. In this work we study the design of deterministic measurement matrices, aimed at maximizing the mutual information between the SOI and the observations. We characterize necessary conditions for the optimal measurement matrix, and propose a practical design method for measurement matrices corresponding to masked Fourier measurements. Simulation tests of the proposed method show that it achieves the same performance as random Gaussian matrices for various phase recovery algorithms.

The capacity of a discrete-time, multi-input multi-output (MIMO) channel with output quantization is investigated for different receiver architectures. A general framework for low-resolution quantization is proposed in which the antenna outputs are processed by analog combiners and sign quantizers are used for analog-to-digital conversion. The configuration of the analog combiners is chosen as a function of the channel realization so that the transmission rate can be maximized over the set of available configurations. To exemplify the proposed approach, four analog receiver architectures are considered: (a) sign quantization of the antenna outputs, (b) single antenna selection, (c) multiple antenna selection, and (d) linear processing of the antenna outputs. In each scenario, capacity is investigated as a function of the transmit power, the number of transmit/receive antennas and sign quantizers. In particular, it is shown that architecture (a) is sufficient to approach the optimal high signal-to-noise ratio (SNR) performance for a MIMO receiver in which the number of receive antennas is larger than the number of sign quantizers. Numerical evaluations of the average performance are presented for the case in which the channel gains are i.i.d. Gaussian distributed.

We study the convolutional phase retrieval problem, which asks us to recover an unknown signal ${\mathbf x} $ of length $n$ from $m$ measurements consisting of the magnitude of its cyclic convolution with a known kernel $\mathbf a$ of length $m$. This model is motivated by applications to channel estimation, optics, and underwater acoustic communication, where the signal of interest is acted on by a given channel/filter, and phase information is difficult or impossible to acquire. We show that when $\mathbf a$ is random and $m \geq \Omega(\frac{ \| \mathbf C_{\mathbf x}\|^2}{ \|\mathbf x\|^2 } n \mathrm{poly} \log n)$, $\mathbf x$ can be efficiently recovered up to a global phase using a combination of spectral initialization and generalized gradient descent. The main challenge is coping with dependencies in the measurement operator; we overcome this challenge by using ideas from decoupling theory, suprema of chaos processes and the restricted isometry property of random circulant matrices, and recent analysis for alternating minimizing methods.

Automated driving has become increasingly viable through the deployment of a number of sensing technologies on vehicles. These intelligent transportation systems (ITS) employ sensors such as radar, camera and lidars for collision avoidance and vehicle-to-everything (V2X) communication links for active environment sensing. Since the available spectrum for vehicular systems is limited, spectrum sharing in ITS sensors is a subject of active investigation. This paper presents a spectrum sharing technology that enables interference-free operation of an automotive radar and a V2X communication system within a common spectrum. Both systems dynamically share information with each other and optimize their spectral resources to the changing RF environment. The V2X system is a cognitive radio that is capable of blind sensing its spectrum using very low sampling and processing rates. The radar system is also modeled as a cognitive system that employs a Xampling-based sub-Nyquist receiver and transmits in several narrow bands that occupy a fraction of the conventional radar bandwidth. We present a hardware realization of this vehicular spectrum sharing technology and demonstrate spectral coexistence through real-time experiments.

The problem of recovering a signal from its power spectrum, called phase retrieval, arises in many scientific fields. One of many examples is ultrashort laser pulse characterization, in which the electromagnetic field is oscillating with ~1015 Hz and phase information cannot be measured directly due to limitations of the electronic sensors. Phase retrieval is ill-posed in most of the cases, as there are many different signals with the same Fourier transform magnitude. To overcome this fundamental ill-posedness, several measurement techniques are used in practice. One of the most popular methods for complete characterization of ultrashort laser pulses is the frequency-resolved optical gating (FROG). In FROG, the acquired data are the power spectrum of the product of the unknown pulse with its delayed replica. Therefore, the measured signal is a quartic function of the unknown pulse. A generalized version of FROG, where the delayed replica is replaced by a second unknown pulse, is called blind FROG. In this case, the measured signal is quadratic with respect to both pulses. In this letter, we introduce and formulate FROG-type techniques. We then show that almost all band-limited signals are determined uniquely, up to trivial ambiguities, by blind FROG measurements (and thus also by FROG), if in addition we have access to the signals power spectrum.

Conventional synthetic aperture radar (SAR) systems are limited in their ability to satisfy the increasing requirement for improved spatial resolution and wider coverage. The demand for high resolution requires high sampling rates, while coverage is limited by the pulse repetition frequency. Consequently, sampling rate reduction is of high practical value in SAR imaging. In this paper, we introduce a new algorithm, equivalent to the well-known range-Doppler method, to process SAR data using the Fourier series coefficients of the raw signals. We then demonstrate how to exploit the algorithm features to reduce sampling rate in both range and azimuth axes and process the signals at sub-Nyquist rates, by using compressive sensing (CS) tools. In particular, we demonstrate recovery of an image using only a portion of the received signal's bandwidth and also while dropping a large percentage of the transmitted pulses. The complementary pulses may be used to capture other scenes within the same coherent processing interval. In addition, we propose exploiting the ability to reconstruct the image from narrow bands in order to dynamically adapt the transmitted waveform energy to vacant spectral bands, paving the way to cognitive SAR. The proposed recovery algorithms form a new CS-SAR imaging method that can be applied to high-resolution SAR data acquired at sub-Nyquist rates in range and azimuth. The performance of our method is assessed using simulated and real data sets. Finally, our approach is implemented in hardware using a previously suggested Xampling radar prototype.

This paper investigates the information rate loss in analog channels, when the sampler is designed to operate independent of the instantaneous channel occupancy. Specifically, a multiband linear time-invariant Gaussian channel under universal sub-Nyquist sampling is considered. The entire channel bandwidth is divided into n subbands of equal bandwidth. At each time, only k constant-gain subbands are active, where the instantaneous subband occupancy is not known at the receiver and the sampler. We study the information loss through an information , that is, the gap of achievable rates caused by the lack of instantaneous subband occupancy information. We characterize the minimax information rate loss for the sub-Nyquist regime, provided that the number n of subbands and the SNR are both large. The minimax limits depend almost solely on the band sparsity factor and the undersampling factor, modulo some residual terms that vanish as n and SNR grow. Our results highlight the power of randomized sampling methods (i.e., the samplers that consist of random periodic modulation and low-pass filters), which are able to approach the minimax information rate loss with exponentially high probability.

Ultrasound super-localization microscopy techniques presented in the last few years enable non-invasive imaging of vascular structures at the capillary level by tracking the flow of ultrasound contrast agents (gas microbubbles). However, these techniques are currently limited by low temporal resolution and long acquisition times. Super-resolution optical fluctuation imaging (SOFI) is a fluorescence microscopy technique enabling sub-diffraction limit imaging with high temporal resolution by calculating high order statistics of the fluctuating optical signal. The aim of this work is to achieve fast acoustic imaging with enhanced resolution by applying the tools used in SOFI to contrast-enhance ultrasound (CEUS) plane-wave scans. The proposed method was tested using numerical simulations and evaluated using two in-vivo rabbit models: scans of healthy kidneys and VX-2 tumor xenografts. Improved spatial resolution was observed with a reduction of up to 50% in the full width half max of the point spread function. In addition, substantial reduction in the background level was achieved compared to standard mean amplitude persistence images, revealing small vascular structures within tumors. The scan duration of the proposed method is less than a second while current super-localization techniques require acquisition duration of several minutes. As a result, the proposed technique may be used to obtain scans with enhanced spatial resolution and high temporal resolution, facilitating flow-dynamics monitoring. Our method can also be applied during a breath-hold, reducing the sensitivity to motion artifacts.

We present an algorithm for resampling a function from its values on a non-Cartesian grid onto a Cartesian grid. This problem arises in many applications such as MRI, CT, radio astronomy and geophysics. Our algorithm, termed SParse Uniform ReSampling (SPURS), employs methods from modern sampling theory to achieve a small approximation error while maintaining low computational cost. The given non-Cartesian samples are projected onto a selected intermediate subspace, spanned by integer translations of a compactly supported kernel function. This produces a sparse system of equations describing the relation between the nonuniformly spaced samples and a vector of coefficients representing the projection of the signal onto the chosen subspace. This sparse system of equations can be solved efficiently using available sparse equation solvers. The result is then projected onto the subspace in which the sampled signal is known to reside. The second projection is implemented efficiently using a digital linear shift invariant (LSI) filter and produces uniformly spaced values of the signal on a Cartesian grid. The method can be iterated to improve the reconstruction results. We then apply SPURS to reconstruction of MRI data from nonuniformly spaced k-space samples. Simulations demonstrate that SPURS outperforms other reconstruction methods while maintaining a similar computational complexity over a range of sampling densities and trajectories as well as various input SNR levels.

Finite-Rate-of-Innovation (FRI) sampling theory prescribes a procedure for exact recovery of Dirac impulses from linear measurements in the form of orthogonal projections of streams of Dirac impulses onto the subspace of Fourier—bandlimited functions. This enables recovery of a continuous time sparse signals at sub-Nyquist rates. In many cases, the transform domain of interest may be more general than the Fourier domain. Recent work has extended FRI sampling theory to the spherical Fourier Transform, fractional Fourier Transform and the Laplace Transform. In this paper, we develop a broad FRI framework applicable to a general class of transformations that includes Fourier, Laplace, Fresnel, fractional Fourier, Bargmann and Gauss—Weierstrass transforms, among others. For this purpose, we consider the Special Affine Fourier Transform (SAFT) which parametrically generalizes a number of well known unitary transforms linked with signal processing and optics. We first derive a version of Shannon's sampling theory based on the convolution structure tailored for the SAFT domain. Having identified the subspace of SAFT—bandlimited functions, we apply FRI sampling theory to the SAFT and study recovery of sparse signals, thus providing a unified view of FRI sampling theory for a large class of disparately studied operations.

We propose fast algorithms that speed up or improve the performance of recovering spectrally sparse signals from un-derdetermined measurements. Our algorithms are based on a non-convex approach of using alternating projected gradient descent for structured matrix recovery. We apply this approach to two formulations of structured matrix recovery: Hankel and Toeplitz mosaic structured matrix, and Hankel structured matrix. Our methods provide better recovery performance, and faster signal recovery than existing algorithms, including atomic norm minimization.

Communication signals are often cyclostationary, that is they have statistical characteristics that vary periodically in time. The cyclic spectrum, a characteristic function of such signals, exhibits spectral peaks at certain locations, called cyclic frequencies. These locations as well as the cyclic spectrum support are defined by the signal parameters, in particular carrier frequency, bandwidth and symbol rate. In this paper, we propose an estimation algorithm that extracts these from the signal cyclic spectrum. This algorithm can be applied to multiband signals, namely signals composed of more than one transmission. Prior to parameter estimation, the number of signals is first estimated. Exploiting the cyclostationarity of communication signals improves the robustness to noise of the parameter estimation. In particular, the proposed algorithm can be used for Cognitive Radios, which traditionally deal with low signal to noise ratios multiband signals, for spectrum sensing purposes by estimating the carrier frequencies and bandwidths. Simulations demonstrate estimation from synthesized and RF Nyquist samples as well as sub-Nyquist samples.

This paper considers phase retrieval from the magnitude of 1-D oversampled Fourier measurements. We first revisit the well-known lack of identifiability in this case, and point out that there always exists a solution that is minimum phase, even though the desired signal is not. Next, we explain how the least-squares formulation of this problem can be optimally solved via PhaseLift followed by spectral factorization, and this solution is always minimum phase. A simple approach is then proposed to circumvent non-identifiability: adding an impulse to an arbitrary complex signal (offset to the Fourier transform) before taking the quadratic measurements, so that a minimum phase signal is constructed and thus can be uniquely estimated. Simulations with synthetic data show the effectiveness of the proposed method.

Phaseless super-resolution is the problem of reconstructing a signal from its low-frequency Fourier magnitude measurements. It is the combination of two classic signal processing problems: phase retrieval and super-resolution. Due to the absence of phase and high-frequency measurements, additional information is required in order to be able to uniquely reconstruct the signal of interest. In this work, we use masks to introduce redundancy in the phaseless measurements. We develop an analysis framework for this setup, and use it to show that any super-resolution algorithm can be seamlessly extended to solve phaseless superresolution (up to a global phase), when measurements are obtained using a certain set of masks. In particular, we focus our attention on a robust semidefinite relaxation-based algorithm, and provide reconstruction guarantees. Numerical simulations complement our theoretical analysis.

We consider the problem of hypothesis testing for detection of a signal in Gaussian noise. We assume that the vector of measurements is unobserved, and that our observations consist of phaseless inner products with a set of known measurement vectors. This is typical of the phase retrieval problem, where the goal is to recover the vector of measurements. We provide a simple estimator for the test statistic that does not necessitate a phaseless recovery method to reconstruct the measurements. Our analysis shows that for random measurement vectors, we can reconstruct the test statistic for any signal from a sufficient number of observations, quadratic in the signal length, using a simple least-squares approach. The primary advantage of this method its simplicity and computational efficiency, which comes at the expense of requiring many more measurements. We show that for Fourier measurements vectors, our approach works only when the signal is also a Fourier vector.

Modern imaging systems use single-carrier short pulses for transducer excitation. The usage of coded signals allowing for pulse compression is known to improve signal-to-noise ratio (SNR), for example in radar and communication. One of the main challenges in applying coded excitation (CE) to medical imaging is frequency dependent attenuation in biological tissues. Previous work overcame this challenge and verified significant improvement in SNR and imaging depth by using an array of transducer elements and applying pulse compression at each element. However, this approach results in a large computational load. A common way of reducing the cost is to apply pulse compression after beamforming, which reduces image quality. In this work we propose a high-quality low cost method for CE imaging by integrating pulse compression into the recently developed frequency domain beamforming framework. This approach yields a 26-fold reduction in computational complexity without compromising image quality. This reduction enables efficient implementation of CE in array imaging paving the way to enhanced SNR, improved imaging depth and higher frame-rate.

We address the problem of reference-based compressed sensing: reconstruct a sparse signal from few linear measurements using as prior information a reference signal, a signal similar to the signal we want to reconstruct. Access to reference signals arises in applications such as medical imaging, e.g., through prior images of the same patient, and compressive video, where previously reconstructed frames can be used as reference. Our goal is to use the reference signal to reduce the number of required measurements for reconstruction. We achieve this via a reweighted ℓ1-ℓ1minimization scheme that updates its weights based on a sample complexity bound. The scheme is simple, intuitive and, as our experiments show, outperforms prior algorithms, including reweighted ℓ1minimization, ℓ1-ℓ1minimization, and modified CS.

We propose a new algorithm to learn a dictionary along with sparse representations from signal measurements without phase. Specifically, we consider the task of reconstructing a two-dimensional image from squared-magnitude measurements of a complex-valued linear transformation of the original image. Several recent phase retrieval algorithms exploit underlying sparsity of the unknown signal in order to improve recovery performance. In this work, we consider sparse phase retrieval when the sparsifying dictionary is not known in advance, and we learn a dictionary such that each patch of the reconstructed image can be sparsely represented. Our numerical experiments demonstrate that our proposed scheme can obtain significantly better reconstructions for noisy phase retrieval problems than methods that cannot exploit such "hidden" sparsity.

We study parameter estimation for sparse nonlinear regression. More specifically, we assume the data are given by y = f( \bf x^T \bf β^* ) + ε, where f is nonlinear. To recover \bf βs, we propose an \ell_1-regularized least-squares estimator. Unlike classical linear regression, the corresponding optimization problem is nonconvex because of the nonlinearity of f. In spite of the nonconvexity, we prove that under mild conditions, every stationary point of the objective enjoys an optimal statistical rate of convergence. Detailed numerical results are provided to back up our theory.

The minimal distortion attainable in recovering the waveform of a continuous-time Wiener process from an encoded version of its uniform samples is considered. We first introduce a combined sampling and source coding problem and prove an associated source coding theorem. We then derive an upper bound on the minimal distortion attainable under any sampling rate and a prescribed number of bits to encode the samples. We show that this bound is accurate to within a second order term in the sampling rate, and converges to the true distortion-rate function of the Wiener process as the sampling rate goes to infinity. For example, this bound implies that by providing a single bit per sample it is possible to achieve the optimal distortion-rate performance of the Wiener process, given by its distortion-rate function, to within a factor of 1.5. We conclude the distortion-rate function of the Wiener process is strictly smaller than the indirect distortion-rate function from its uniform samples obtained at any finite sampling rate. This is in contrast to stationary infinite bandwidth processes.

The goal of subspace learning is to find a $k$-dimensional subspace of $\mathbb{R}^d$, such that the expected squared distance between instance vectors and the subspace is as small as possible. In this paper we study subspace learning in a partial information setting, in which the learner can only observe $r \le d$ attributes from each instance vector. We propose several efficient algorithms for this task, and analyze their sample complexity.

We consider the problem of learning a dictionary matrix from a number of observed signals, which are assumed to be generated via a linear model with a common underlying dictionary. In particular, we derive lower bounds on the minimum achievable worst case mean squared error (MSE), regardless of computational complexity of the dictionary learning (DL) schemes. By casting DL as a classical (or frequentist) estimation problem, the lower bounds on the worst case MSE are derived following an established information-theoretic approach to minimax estimation. The main contribution of this paper is the adaption of these information-theoretic tools to the DL problem in order to derive lower bounds on the worst case MSE of any DL algorithm. We derive three different lower bounds applying to different generative models for the observed signals. The first bound only requires the existence of a covariance matrix of the (unknown) underlying coefficient vector. By specializing this bound to the case of sparse coefficient distributions and assuming the true dictionary satisfies the restricted isometry property, we obtain a lower bound on the worst case MSE of DL methods in terms of the signal-to-noise ratio (SNR). The third bound applies to a more restrictive subclass of coefficient distributions by requiring the non-zero coefficients to be Gaussian. Although the applicability of this bound is the most limited, it is the tightest of the three bounds in the low SNR regime. A particular use of our lower bounds is the derivation of necessary conditions on the required number of observations (sample size), such that DL is feasible, i.e., accurate DL schemes might exist. By comparing these necessary conditions with sufficient conditions on the sample size such that a particular DL technique is successful, we are able to characterize the regimes, where those algorithms are optimal in terms of required sample size.

The amount of information lost in sub-Nyquist sampling of a continuous-time Gaussian stationary process is quantified. We consider a combined source coding and sub-Nyquist reconstruction problem in which the input to the encoder is a noisy sub-Nyquist sampled version of the analog source. We first derive an expression for the mean squared error in the reconstruction of the process from a noisy and information rate-limited version of its samples. This expression is a function of the sampling frequency and the average number of bits describing each sample. It is given as the sum of two terms: minimum mean square error in estimating the source from its noisy but otherwise fully observed sub-Nyquist samples, and a second term obtained by reverse waterfilling over an average of spectral densities associated with the polyphase components of the source. We extend this result to multi-branch uniform sampling, where the samples are available through a set of parallel channels with a uniform sampler and a pre-sampling filter in each branch. Further optimization to reduce distortion is then performed over the pre-sampling filters, and an optimal set of pre-sampling filters associated with the statistics of the input signal and the sampling frequency is found. This results in an expression for the minimal possible distortion achievable under any analog-to-digital conversion scheme involving uniform sampling and linear filtering. These results thus unify the Shannon-Whittaker-Kotelnikov sampling theorem and Shannon rate-distortion theory for Gaussian sources.

With the emergence of Cognitive Radios (CRs), that aim at solving the spectrum scarcity issue, the traditional task of spectrum sensing has recently been revisited. Blind sub-Nyquist sampling and reconstruction methods of multiband signals have been proposed, alleviating the burden of both the analog and digital sides. In this work, we propose a new sub-Nyquist sampling system composed of sensors lying in a uniform linear array (ULA) that adopts some of the concepts of the Modulated Wideband Converter (MWC). Our system overcomes two practical issues of the MWC: the challenging choice of mixing functions which intentionally aliases the signal, and the introduction of the same sensor noise to all of the system channels. We provide two carrier frequencies recovery algorithms, and show how the signal can be reconstructed once these are estimated. We derive bounds for the minimal number of sensors and minimal sampling rate required for perfect signal reconstruction. Simulations show that for an equal number of channels or sensors and an identical sampling rate, our system outperforms the traditional MWC in terms of reconstruction performance.

This work considers the problem of super-resolution. The goal is to resolve a Dirac distribution from knowledge of its discrete, low-pass, Fourier measurements. Classically, such problems have been dealt with parameter estimation methods. Recently, it has been shown that convex-optimization based formulations facilitate a continuous time solution to the super-resolution problem. Here we treat super-resolution from low-pass measurements in Phase Space. The Phase Space transformation parametrically generalizes a number of well known unitary mappings such as the Fractional Fourier, Fresnel, Laplace and Fourier transforms. Consequently, our work provides a general super-resolution strategy which is backward compatible with the usual Fourier domain result. We consider low-pass measurements of Dirac distributions in Phase Space and show that the super-resolution problem can be cast as Total Variation minimization. Remarkably, even though are setting is quite general, the bounds on the minimum separation distance of Dirac distributions is comparable to existing methods.

Signals consisting of short pulses are present in many applications including ultrawideband communication, object detection and navigation (radar, sonar) and medical imaging. The structure of such signals, effectively captured within the finite rate of innovation (FRI) framework, allows for significant reduction in sampling rates, required for perfect reconstruction. In this work we consider ultrasound imaging, where the FRI signal structure allows to reduce both sampling and processing rates. We show that beamforming, a crucial processing step in image generation that generally requires oversampling, can be implemented directly on reduced rate samples. This is obtained by replacing the standard time-domain processing by a frequency domain approach and relying on FRI sampling techniques in frequency. Using this approach we achieve significant rate reduction while retaining adequate image quality for both 2D and 3D imaging setups using data obtained by commercial imaging system.

Covariance estimation from compressive samples has become particularly attractive for two main reasons. First, many applications do not require the signal itself, and second-order statistics are oftentimes sufficient. The resulting requirement on the sampling rate of the original signal can therefore be reduced. Second, signal recovery from compressive samples leads to underdetermined systems which require additional constraints, such as the popular sparsity assumption. In contrast, covariance estimation can yield overdetermined problems, even from compressive samples, so that the additional constraints on the signal can be dropped. In this paper, we provide a unified framework for deriving lower bounds on the sampling rate required for covariance estimation of stationary signals, by deriving the lower Beurling density of the difference set associated with the original sampling set. A general sampling scheme is first considered, followed by the analysis of multicoset sampling. We prove that, in both cases, the sampling rate can be arbitrarily low, as was remarked extensively in the literature.

In this paper, we suggest a modified distributed compressed sensing (CS) approach based on the iterative hard thresholding (IHT) algorithm, namely, distributed IHT (DIHT). Our technique improves upon a recently proposed DIHT algorithm in two ways. First, for sensing matrices with i.i.d. Gaussian entries, we suggest an efficient and tight method for computing the step size μ in IHT based on random matrix theory. Second, we improve upon the global computation (GC) step of DIHT by adapting this step to allow for complex data, and reducing the communication cost. The new GC operation involves solving a Top-K problem and is therefore referred to as GC.K. The GC.K-based DIHT has exactly the same recovery results as the centralized IHT given the same step size μ. Numerical results show that our approach significantly outperforms the modified thresholding algorithm (MTA), another GC algorithm for DIHT proposed in previous work. Our simulations also verify that the proposed method of computing μ renders the performance of DIHT close to the oracle-aided approach with a given “optimal” μ.

The problem of recovering signals from the Short-Time Fourier Transform (STFT) magnitude is of paramount importance in many areas of engineering and physics. This problem has received a lot of attention over the last few decades, but not much is known about conditions under which the STFT magnitude is a unique signal representation. Also, the recovery techniques proposed by researchers are mostly heuristic in nature. In this work, we first show that almost all signals can be uniquely identified by their STFT magnitude under mild conditions. Then, we consider a semidefinite relaxation-based algorithm and provide the first theoretical guarantees for the same. Numerical simulations complement our theoretical analysis and provide many directions for future work.

Ultrasound imagers suffer from a large data rate between their analog to digital converter (ADC) front-end and digital beamforming backend. This becomes a limiting factor when the number of elements is increased, such as in modern 2D transducers. To address this issue, prior work considered sub-Nyquist sampling techniques that exploit the disparity between the signal's physical bandwidth and innovation rate. In this work, we extend this framework using an analog-domain subarray beamforming technique that is feasible due to the narrowband nature of the sub-Nyquist signal acquisition. When applied to waveforms taken from a commercial ultrasound machine, this method reduces both the low-rate ADC count by a factor of eight and the total data rate by a factor of 54 with minimal image degradation.

Cognitive Radio (CR) challenges the traditional task of spectrum sensing with requirements of reliability, efficiency and real-time. Sub-Nyquist sampling has been considered for this task in order to cope with the sampling rate bottleneck of the wideband signals a CR usually deals with, by exploiting their multiband structure. However, communication signals suffer from fading and shadowing effects that affect a single CR's performance. In this paper, we consider collaborative spectrum sensing by a network of CRs, each sharing an observation matrix derived from sub-Nyquist samples of their respective received signal with a fusion center. Exploiting the fact that all received signals share a joint support, equal to that of the transmitted signal, the fusion center recovers it by combining the measurements of the different CRs. We present two joint reconstruction algorithms, Block Sparse Simultaneous Orthogonal Matching Pursuit (BSOMP) and Block Sparse Simultaneous Iterative Hard Thresholding (BSIHT), that adapt the original OMP and IHT to both block sparse and matrix (simultaneous) inputs. Simulations show that our algorithms outperform a collaborative scheme based on hard decisions, namely the union of the supports recovered by each CR individually, demonstrating that cooperation between CRs via measurement fusion improve their performance.

Signal recovery from the magnitude of the Fourier transform, or equivalently, from the autocorrelation, is a classical problem known as phase retrieval. Due to the absence of phase information, some form of additional information is required in order to be able to uniquely identify the underlying signal. In this work, we consider the problem of phase retrieval using masks. Due to our interest in developing robust algorithms with theoretical guarantees, we explore a convex optimization-based framework. In this work, we show that two specific masks (each mask provides 2n Fourier magnitude measurements) or five specific masks (each mask provides n Fourier magnitude measurements) are sufficient for a convex relaxation of the phase retrieval problem to provably recover almost all signals (up to global phase). We also show that the recovery is stable in the presence of measurement noise. This is a significant improvement over the existing results, which require O(log2n) random masks (each mask provides n Fourier magnitude measurements) in order to guarantee unique recovery (up to global phase). Numerical experiments complement our theoretical analysis and show interesting trends, which we hope to explain in a future publication.

The minimal sampling frequency required to achieve the rate-distortion function of a Gaussian stationary process is analyzed. Although the Nyquist rate is the minimal sampling frequency that allows perfect reconstruction of a bandlimited signal from its samples, relaxing perfect reconstruction to a prescribed distortion may allow a lower sampling frequency to achieve the optimal rate-distortion trade-off. We consider a combined sampling and source coding problem in which an analog Gaussian source is reconstructed from its rate-limited sub-Nyquist samples. We show that each point on the distortion-rate curve of the source corresponds to a sampling frequency fDRsmaller than the Nyquist rate, such that this point can be achieved by sampling at frequency fDRor above. This can be seen as an extension of the sampling theorem in the sense that it describes the minimal amount of excess distortion in the reconstruction due to lossy compression of the samples, and provides the minimal sampling frequency required in order to achieve that distortion.

This letter considers the problem of recovering a positive stream of Diracs on a sphere from its projection onto the space of low-degree spherical harmonics, namely, from its low-resolution version. We suggest recovering the Diracs via a tractable convex optimization problem. The resulting recovery error is proportional to the noise level and depends on the density of the Diracs. We validate the theory by numerical experiments.

Recently, a new approach to sub-Nyquist sampling and processing in pulse-Doppler radar was introduced, based on the Xampling approach to reduced-rate sampling combined with Doppler focusing performed on the low-rate samples. This method imposes no restrictions on the transmitter, reduces both the sampling and processing rates and exhibits linear signal-to-noise ratio improvement with the number of pulses. Here we extend previous work on sub-Nyquist pulse-Doppler radar by incorporating a clutter removal algorithm operating on the sub-Nyquist samples, allowing to reject clutter modeled as a colored Gaussian random process. In particular, we show how to adapt standard clutter rejection techniques to work directly on the sub-Nyquist samples, allowing to preserve high detection rates even in the presence of strong clutter, while avoiding the need to first interpolate the samples to the Nyquist grid.

We consider the classical 1D phase retrieval problem. In order to overcome the difficulties associated with phase retrieval from measurements of the Fourier magnitude, we treat recovery from the magnitude of the short-time Fourier transform (STFT). We first show that the redundancy offered by the STFT enables unique recovery for arbitrary nonvanishing inputs, under mild conditions. An efficient algorithm for recovery of a sparse input from the STFT magnitude is then suggested, based on an adaptation of the recently proposed GESPAR algorithm. We demonstrate through simulations that using the STFT leads to improved performance over recovery from the oversampled Fourier magnitude with the same number of measurements.

We consider the classical Direction of arrival (DOA) estimation problem in the presence of random sensor phase errors are present at each sensor. To eliminate the effect of these phase errors, we propose a DOA recovery technique that relies only on magnitude measurements. This approach is inspired by phase retrieval for applications in other fields. Ambiguities typically associated with phase retrieval methods are resolved by introducing reference targets with known DOA. The DOA estimation problem is formulated as a nonlinear optimization in a sparse framework, and is solved by the recently proposed GESPAR algorithm modified to accommodate multiple snapshots. Numerical results demonstrate good DOA estimation performance. For example, the probability of error in locating a single target within 2 degrees is less than 0.1 for SNR ≥ 15 dB and one snapshot, and negligible for SNR ≥ 10 dB and five snapshots.

We study the problem of sparse recovery in an overcomplete dictionary. This problem has attracted considerable attention in signal processing, statistics, and computer science, and a variety of algorithms have been developed to recover the sparse vector. We propose a new method based on the computationally efficient Viterbi algorithm which is shown to achieve better performance than competing algorithms such as Orthogonal Matching Pursuit (OMP), Orthogonal Least-Squares (OLS), Multi-Branch Matching Pursuit (MBMP), Iterative Hard Thresholding (IHT), and l1 minimization. We also explore the relationship of the Viterbi-based approach with OLS.

The performance analysis of random vector channels, particularly multiple-input-multiple-output (MIMO) channels, has largely been established in the asymptotic regime of large channel dimensions, due to the analytical intractability of characterizing the exact distribution of the objective performance metrics. This paper exposes a new nonasymptotic framework that allows the characterization of many canonical MIMO system performance metrics to within a narrow interval under finite channel dimensionality, provided that these metrics can be expressed as a separable function of the singular values of the matrix. The effectiveness of our framework is illustrated through two canonical examples. In particular, we characterize the mutual information and power offset of random MIMO channels, as well as the minimum mean squared estimation error of MIMO channel inputs from the channel outputs. Our results lead to simple, informative, and reasonably accurate control of various performance metrics in the finite-dimensional regime, as corroborated by the numerical simulations. Our analysis framework is established via the concentration of spectral measure phenomenon for random matrices uncovered by Guionnet and Zeitouni, which arises in a variety of random matrix ensembles irrespective of the precise distributions of the matrix entries.

Recovering structured models (e.g., sparse or group-sparse vectors, low-rank matrices) given a few linear observations have been well-studied recently. In various applications in signal processing and machine learning, the model of interest is structured in several ways, for example, a matrix that is simultaneously sparse and low rank. Often norms that promote the individual structures are known, and allow for recovery using an order-wise optimal number of measurements (e.g., 11 norm for sparsity, nuclear norm for matrix rank). Hence, it is reasonable to minimize a combination of such norms. We show that, surprisingly, using multiobjective optimization with these norms can do no better, orderwise, than exploiting only one of the structures, thus revealing a fundamental limitation in sample complexity. This result suggests that to fully exploit the multiple structures, we need an entirely new convex relaxation. Further, specializing our results to the case of sparse and low-rank matrices, we show that a nonconvex formulation recovers the model from very few measurements (on the order of the degrees of freedom), whereas the convex problem combining the 11 and nuclear norms requires many more measurements, illustrating a gap between the performance of the convex and nonconvex recovery problems. Our framework applies to arbitrary structure-inducing norms as well as to a wide range of measurement ensembles. This allows us to give sample complexity bounds for problems such as sparse phase retrieval and low-rank tensor completion.

Lower dimensional signal representation schemes frequently assume that the signal of interest lies in a single vector space. In the context of the recently developed theory of compressive sensing, it is often assumed that the signal of interest is sparse in an orthonormal basis. However, in many practical applications, this requirement may be too restrictive. A generalization of the standard sparsity assumption is that the signal lies in a union of subspaces. Recovery of such signals from a small number of samples has been studied recently in several works. Here, we consider the problem of only subspace recovery in which our goal is to identify the subspace (from the union) in which the signal lies using a small number of samples, in the presence of noise. More specifically, we derive performance bounds and conditions under which reliable subspace recovery is guaranteed using maximum likelihood (ML) estimation. We begin by treating general unions and then obtain the results for the special case in which the subspaces have structure leading to block sparsity. In our analysis, we treat both general sampling operators and random sampling matrices. With general unions, we show that under certain conditions, the number of measurements required for reliable subspace recovery in the presence of noise via ML is less than that implied using the restricted isometry property, which guarantees complete signal recovery. In the special case of block sparse signals, we quantify the gain achievable over standard sparsity in subspace recovery. Our results also strengthen existing results on sparse support recovery in the presence of noise under the standard sparsity model.

Communication signals are often cyclostationary, that is they have statistical characteristics that vary periodically in time. In the frequency domain, this translates into correlation between spectral components of the signal. As a result, the cyclic spectrum, a characteristic function of the second-order moment of such signals, exhibits spectral peaks at certain locations, called cyclic frequencies. Exploiting the cyclostationarity of communication signals allows to better model them and describe their properties. Moreover, it improves robustness to noise when processing such signals. The traditional signal processing task of spectrum sensing has been recently challenged by Cognitive Radios (CRs) into dealing with wideband signals in an efficient and reliable way. CR receivers deal with signals with high Nyquist rates and low Signal to Noise Ratios (SNRs). On the one hand, sub-Nyquist sampling of such signals alleviates the burden both on the analog and the digital side. On the other hand, it increases the sensitivity to noise due to its aliasing. In this paper, we derive a method to reconstruct the cyclic spectrum of cyclostationary signals from sub-Nyquist samples rather than their spectrum or power spectrum, in order to better deal with noise. Any processing such as signal detection can then be performed on the reconstructed cyclic spectrum.

In the context of Cognitive Radio (CR), opportunistic transmissions can exploit temporarily vacant spectral bands. Efficient and reliable spectrum sensing is key in the CR process. CR receivers traditionally deal with wideband signals with high Nyquist rates and low Signal to Noise Ratios (SNRs). Sub-Nyquist sampling of such signals has been proposed for efficient sampling in CRs. The modulated wideband converter (MWC) is an example of such a sampling scheme. It is composed of an analog front-end, that aliases the signal intentionally before sampling it at a low rate. The signal can then be digitally reconstructed from the low rate samples, using the known relation between the samples and the original signal. Unfortunately, in real hardware implementation, this relation becomes unknown. Physical effects have a considerable impact on the sampling process, and as a consequence, the signal cannot be reliably recovered. In this paper, we present an efficient automated calibration algorithm that builds the actual transfer function of the system, without any prior knowledge. We then present a new, MWC based, CR prototype, on which the calibration algorithm was tested. Experiments on our hardware prototype, based on an embedded proprietary card, show that our calibrated transfer function leads to signal reconstruction whereas the theoretical one fails. Our specification complies with CR requirements of the IEEE standard 802.22 and was experimentally verified with different modulations. It vastly improves a previous prototype in terms of bandwidth, higher maximal frequency and coping with lower SNR.

Contemporary sonography is performed by digitally beamforming signals sampled by several transducer elements placed upon an array. High-resolution digital beamforming introduces the demand for a sampling rate significantly higher than the signal's Nyquist rate, which greatly increases the volume of data that must be processed. In 3D ultrasound imaging, 2D transducer arrays rather than 1D arrays are used, and more scan-lines are needed for volumetric imaging. This implies that the amount of sampled data is vastly increased with respect to 2D imaging. In this work we show that a considerable reduction both in sampling rate and processing time can be achieved by applying the ideas of Xampling and frequency domain beamforming, leading to a sub-Nyquist sampling rate. We extend previous work on frequency domain beamforming for 2D ultrasound imaging to the geometry imposed by 3D tissues and a grid of transducer elements. This method uses only a portion of the bandwidth of the ultrasound signals to reconstruct the image. We demonstrate our results by imaging a phantom comprised of fishing wires, and show that by performing 3D beamforming in the frequency domain, a sub-Nyquist sampling rate and a low processing rate are obtained, while keeping adequate image quality.

We explore a fundamental problem of super-resolving a signal of interest from a few measurements of its low-pass magnitudes. We propose a 2-stage tractable algorithm that, in the absence of noise, admits perfect super-resolution of an r-sparse signal from 2r2-2r + 2 low-pass magnitude measurements. The spike locations of the signal can assume any value over a continuous disk, without increasing the required sample size. The proposed algorithm first employs a conventional super-resolution algorithm (e.g. the matrix pencil approach) to recover unlabeled sets of signal correlation coefficients, and then applies a simple sorting algorithm to disentangle and retrieve the true parameters in a deterministic manner. Our approach can be adapted to multi-dimensional spike models and random Fourier sampling by replacing its first step with other harmonic retrieval algorithms.

We consider sub-Nyquist sampling and Compressed Sensing (CS) for channel estimation in Ultra Wideband (UWB) communication systems, by exploiting the sparse nature of the channel impulse response. Receiver hardware schemes are presented that directly sample the analog channel output at rates far below Nyquist and allow access to a predefined subset of channel Fourier coefficients. CS methods are then applied to these coefficients in order to estimate the unknown channel. Simulations on Channel Model (CM) 1 of the IEEE 802.15.4a standard show that estimation is possible from low rate samples with little performance degradation paving the way to sub-Nyquist UWB channel sounding.

The phase retrieval problem has a long history and is an important problem in many areas of optics. Theoretical understanding of phase retrieval is still limited and fundamental questions such as uniqueness and stability of the recovered solution are not yet fully understood. This paper provides several additions to the theoretical understanding of sparse phase retrieval. In particular we show that if the measurement ensemble can be chosen freely, as few as 4k - 1 phaseless measurements suffice to guarantee uniqueness of a k-sparse M-dimensional real solution. We also prove that 2(k2- k + 1) Fourier magnitude measurements are sufficient under rather general conditions.

We investigate sampling and detection of orthogonal frequency-division multiplexing (OFDM) signals with unknown carriers at sub-Nyquist rates. Efficient acquisition and processing of such broadcast signals is a challenge but constitutes a crucial part of enabling cognitive radios. In order to alleviate both the analog and digital burden when treating wideband signals, we adapt the modulated wideband converter (MWC), a recently proposed sub-Nyquist sampling system, to fit OFDM signals. In particular, after detecting the active bands using the MWC, we use several different equalization methods in order to improve the bit-error rate (BER). We then show how to process the real sub-Nyquist samples in each band in order to recover the complex OFDM signal. A standard digital OFDM receiver is then used to detect the input symbols. To evaluate the performance of our system, we derive an analytical bound on the BER as a function of the received signal to noise ratio. Simulations validate the proposed system.

We propose a reconstruction method for the phase retrieval problem prevalent in optics, crystallography, and other imaging applications. Our approach uses signal sparsity to provide robust reconstruction, even in the presence of outliers. Our method is multi-layered, involving multiple random initial conditions, convex majorization, variable splitting, and alternating directions method of multipliers (ADMM)-based implementation. Monte Carlo simulations demonstrate that our algorithm can correctly and robustly detect sparse signals from full and undersampled sets of squared-magnitude-only measurements, corrupted by additive noise or outliers.

We propose a new approach for the low-rate identification of memory polynomials (MPs), which are frequently used to model RF power amplifiers (PAs). Based on ideas from the finite rate of innovation framework, we find the coefficients of the MP in the frequency domain, which requires a relatively small number of measurements (samples), commensurate with the degrees of freedom in the model. By choosing a random set of frequency components, the stability of the identification is ensured. We show that the method can be used directly for special input signals, such as one used for orthogonal frequency division multiplexing, and extend the idea for arbitrary inputs. Experiments using measured data from a class-AB PA demonstrate the effectiveness of the approach. The sampling rate for identifying this PA is reduced by a factor of 1024 (from 107.52MHz to 105 kHz).

This paper investigates the effect of sub-Nyquist sampling upon the capacity of an analog channel. The channel is assumed to be a linear time-invariant Gaussian channel, where perfect channel knowledge is available at both the transmitter and the receiver. We consider a general class of right-invertible time-preserving sampling methods which includes irregular nonuniform sampling, and characterize in closed form the channel capacity achievable by this class of sampling methods, under a sampling rate and power constraint. Our results indicate that the optimal sampling structures extract out the set of frequencies that exhibits the highest signal-to-noise ratio among all spectral sets of measure equal to the sampling rate. This can be attained through filterbank sampling with uniform sampling grid employed at each branch with possibly different rates, or through a single branch of modulation and filtering followed by uniform sampling. These results reveal that for a large class of channels, employing irregular nonuniform sampling sets, while are typically complicated to realize in practice, does not provide capacity gain over uniform sampling sets with appropriate preprocessing. Our findings demonstrate that aliasing or scrambling of spectral components does not provide capacity gain in this scenario, which is in contrast to the benefits obtained from random mixing in spectrum-blind compressive sampling schemes.

We consider minimum variance estimation within the sparse linear Gaussian model (SLGM). A sparse vector is to be estimated from a linearly transformed version embedded in Gaussian noise. Our analysis is based on the theory of reproducing kernel Hilbert spaces (RKHS). After a characterization of the RKHS associated with the SLGM, we derive a lower bound on the minimum variance achievable by estimators with a prescribed bias function, including the important special case of unbiased estimation. This bound is obtained via an orthogonal projection of the prescribed mean function onto a subspace of the RKHS associated with the SLGM. It provides an approximation to the minimum achievable variance (Barankin bound) that is tighter than any known bound. Our bound holds for an arbitrary system matrix, including the overdetermined and underdetermined cases. We specialize it to compressed sensing measurement matrices and express it in terms of the restricted isometry constant. For the special case of the SLGM given by the sparse signal in noise model, we derive closed-form expressions of the Barankin bound and of the corresponding locally minimum variance estimator. Finally, we compare our bound with the variance of several well-known estimators, namely, the maximum-likelihood estimator, the hard-thresholding estimator, and compressive reconstruction using orthogonal matching pursuit and approximate message passing.

We investigate the problem of a monostatic radar transceiver trying to detect a sparse target scene. Several past works employ compressed sensing (CS) algorithms to this type of problem, but either do not address sample rate reduction, impose constraints on the radar transmitter, or propose CS recovery methods with prohibitive dictionary size. Here, using the Xampling framework, we describe a sub-Nyquist sampling approach which overcomes the shortcomings of previous methods. Xampling allows reducing the number of samples needed to accurately represent the signal, directly in the analog-to-digital conversion process. After sampling, the entire digital recovery process is performed on the low rate samples without having to return to the Nyquist rate. With our recovery method we are able to obtain good detection performance even at SNRs as low as -25dB.

We treat the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and coordinate-wise optimality. These conditions are then used to derive three numerical algorithms aimed at finding points satisfying the resulting optimality criteria: the iterative hard thresholding method and the greedy and partial sparse-simplex methods. The theoretical convergence of these methods and their relations to the derived optimality conditions are studied.

Sonography techniques use multiple transducer elements for tissue visualization. Signals detected at each element are sampled prior to digital beamforming. The required sampling rates are up to 4 times the Nyquist rate of the signal and result in considerable amount of data, that needs to be stored and processed. A developed technique, based on the finite rate of innovation model, compressed sensing (CS) and Xampling ideas, allows to reduce the number of samples needed to reconstruct an image comprised of strong reflectors. A significant drawback of this method is its inability to treat speckle, which is of significant importance in medical imaging. Here we build on previous work and show explicitly how to perform beamforming in the Fourier domain. Beamforming in frequency exploits the low bandwidth of the beamformed signal and allows to bypass the oversampling dictated by digital implementation of beamforming in time. We show that this allows to obtain the same beamformed image as in standard beamforming but from far fewer samples. Finally, we present an analysis based CS-technique that allows for further reduction in sampling rate, using only a portion of the beamformed signal's bandwidth, namely, sampling the signal at sub-Nyquist rates. We demonstrate our methods on in vivo cardiac ultrasound data and show that reductions up to 1/25 over standard beamforming rates are possible.

The classical shift retrieval problem considers two signals in vector form that are related by a cyclic shift. In this paper, we develop a compressive variant where the measurement of the signals is undersampled. While the standard procedure to shift retrieval is to maximize the real part of their dot product, we show that the shift can be exactly recovered from the corresponding compressed measurements if the sensing matrix satisfies certain conditions. A special case is the partial Fourier matrix. In this setting we show that the true shift can be found by as low as two measurements. We further show that the shift can often be recovered when the measurements are perturbed by noise.

We propose a distributed algorithm for sparse signal recovery in sensor networks based on Iterative Hard Thresholding (IHT). Every agent has a set of measurements of a signal x, and the objective is for the agents to recover x from their collective measurements at a minimal communication cost and with low computational complexity. A naïve distributed implementation of IHT would require global communication of every agent's full state in each iteration. We find that we can dramatically reduce this communication cost by leveraging solutions to the distributed top-K problem in the database literature. Evaluations show that our algorithm requires up to three orders of magnitude less total bandwidth than the best-known distributed basis pursuit method.

We study compressive sensing in the spatial domain for target localization in terms of direction of arrival (DOA), using multiple-input multiple-output (MIMO) radar. A sparse localization framework is proposed for a MIMO array in which transmit/receive elements are placed at random. This allows to dramatically reduce the number of elements, while still attaining performance comparable to that of a filled (Nyquist) array. Leveraging properties of a (structured) random measurement matrix, we develop a novel bound on the coherence of the measurement matrix, and we obtain conditions under which the measurement matrix satisfies the so-called isotropy property. The coherence and isotropy concepts are used to establish respectively uniform and non-uniform recovery guarantees for target localization using spatial compressive sensing. In particular, nonuniform recovery is guaranteed if the number of degrees of freedom (the product of the number of transmit and receive elements MN) scales with K(log G)2, where K is the number of targets, and G is proportional to the array aperture and determines the angle resolution. The significance of the logarithmic dependence in G is that the proposed framework enables high resolution with a small number of MIMO radar elements. This is in contrast with a filled virtualMIMO array where the product MN scales linearly with G.

We consider the problem of estimating two deterministic vectors in a linear Gaussian model where one of the unknown vectors is subject to a sparsity constraint. We derive the maximum likelihood estimator for this problem and develop the Projected Orthogonal Matching Pursuit (POMP) algorithm for its practical implementation. The corresponding constrained Cramér-Rao bound (CCRB) on the mean-square-error is developed under the sparsity constraint. We then show that estimation in linear dynamical systems with a sparse control can be formulated as a special case of this problem.

This paper considers the capacity of sub-sampled analog channels when the sampler is designed to operate independent of the instantaneous channel realization, and investigates sampling methods that minimize the worst-case (minimax) sampled capacity loss due to channel-independent (universal) sampling design. Specifically, a compound multiband channel with unknown subband occupancy is considered, when perfect channel side information is available to both the receiver and the transmitter. We restrict our attention to a general class of periodic sub-Nyquist samplers, which subsumes as special cases sampling with modulation and filter banks. Our results demonstrate that under both Landau-rate and super-Landau-rate sampling, the minimax sampled capacity loss due to universal design depends only on the band sparsity ratio and the undersampling factor, modulo a residual term that vanishes at high signal-to-noise ratio. We quantify the capacity loss under sampling with periodic modulation and low-pass filters, when the Fourier coefficients of the modulation waveforms are randomly generated (called random sampling). Our results highlight the power of random sampling methods, which achieve minimax sampled capacity loss uniformly across all channel realizations and are thus optimal in a universal design sense.

This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging, and many other applications. Our approach, called PhaseLift, combines multiple structured illuminations together with ideas from convex programming to recover the phase from intensity measurements, typically from the modulus of the diffracted wave. We demonstrate empirically that a complex-valued object can be recovered from the knowledge of the magnitude of just a few diffracted patterns by solving a simple convex optimization problem inspired by the recent literature on matrix completion. More importantly, we also demonstrate that our noise-aware algorithms are stable in the sense that the reconstruction degrades gracefully as the signal-to-noise ratio decreases. Finally, we introduce some theory showing that one can design very simple structured illumination patterns such that three diffracted figures uniquely determine the phase of the object we wish to recover.

We explore two fundamental questions at the intersection of sampling theory and information theory: how channel capacity is affected by sampling below the channel's Nyquist rate, and what sub-Nyquist sampling strategy should be employed to maximize capacity. In particular, we derive the capacity of sampled analog channels for three prevalent sampling strategies: sampling with filtering, sampling with filter banks, and sampling with modulation and filter banks. These sampling mechanisms subsume most nonuniform sampling techniques applied in practice. Our analyses illuminate interesting connections between undersampled channels and multiple-input multiple-output channels. The optimal sampling structures are shown to extract out the frequencies with the highest SNR from each aliased frequency set, while suppressing aliasing and out-of-band noise. We also highlight connections between undersampled channel capacity and minimum mean-squared error (MSE) estimation from sampled data. In particular, we show that the filters maximizing capacity and the ones minimizing MSE are equivalent under both filtering and filter-bank sampling strategies. These results demonstrate the effect upon channel capacity of sub-Nyquist sampling techniques, and characterize the tradeoff between information rate and sampling rate.

We present a reduced-dimension multiuser detector (RD-MUD) structure for synchronous systems that significantly decreases the number of required correlation branches at the receiver front end, while still achieving performance similar to that of the conventional matched-filter (MF) bank. RD-MUD exploits the fact that, in some wireless systems, the number of active users may be small relative to the total number of users in the system. Hence, the ideas of analog compressed sensing may be used to reduce the number of correlators. The correlating signals used by each correlator are chosen as an appropriate linear combination of the users' spreading waveforms. We derive the probability of symbol error when using two methods for recovery of active users and their transmitted symbols: the reduced-dimension decorrelating (RDD) detector, which combines subspace projection and thresholding to determine active users and sign detection for data recovery, and the reduced-dimension decision-feedback (RDDF) detector, which combines decision-feedback matching pursuit for active user detection and sign detection for data recovery. We derive probability of error bounds for both detectors, and show that the number of correlators needed to achieve a small probability of symbol error is on the order of the logarithm of the number of users in the system. The theoretical performance results are validated via numerical simulations.

In this paper, we investigate the extension of previous work on compressed sampling receivers from mathematical abstractions and proof of concept work into a system that directly competes with more traditional receivers in standard CMOS integrated circuit technology. As developed in the literature, the Modulated Wideband Converter shows great promise as a compressed sampling receiver due to its flexibility and inherent spectral agility. We propose several modifications to the system that improve its usability and performance in real-world scenarios. Then, using standard LTE receivers as a basis for comparison, we propose a set of target specifications for the Modulated Wideband Converter, discuss the associated circuit challenges, and evaluate potential solutions that build upon prior work in integrated circuit and system design.

We consider the problem of reconstructing a data stream from a small subset of its entries, where the data stream is assumed to lie in a low-dimensional linear subspace, possibly corrupted by noise. It is also important to track the change of underlying subspace for many applications. This problem can be viewed as a sequential low-rank matrix completion problem in which the subspace is learned in an online fashion. The proposed algorithm, called Parallel Estimation and Tracking by REcursive Least Squares (PETRELS), identifies the underlying low-dimensional subspace via a recursive procedure for each row of the subspace matrix in parallel, and then reconstructs the missing entries via least-squares estimation if required. PETRELS outperforms previous approaches by discounting observations in order to capture long-term behavior of the data stream and be able to adapt to it. Numerical examples are provided for direction-of-arrival estimation and matrix completion, comparing PETRELS with state of the art batch algorithms.

A sensitive receiver operation in multi-access reception is to detect the presence of training signals and identify sources from which the signals are sent, with a certain physical delay and center frequency. This is typically a sequential search, where the receiver tests the presence of specific signals and then acquires synchronization parameters (delays, Dopplers), for each component. In this paper, we develop an optimal compressive multichannel sampling (CMS) architecture, the output samples of which are fed to the proposed Sparsity Regularized (SR) Generalized Likelihood Ratio Test (GLRT). It is shown that SR-GLRT using the optimal sampling scheme exhibits better performance than conventional compressed sensing structure, and furthermore effectively scales down the storage requirement and complexity with greater flexibility than conventional architectures.

We address the problem of recovering signals from samples taken at their rate of innovation. Our only assumption is that the sampling system is such that the parameters defining the signal can be stably determined from the samples. As such, our analysis subsumes previously studied nonlinear acquisition devices and nonlinear signal classes. Our strategy relies on minimizing a least-squares (LS) objective, which is generally non-convex and might possess many local minima. We show, though, that under the stability hypothesis, any optimization method designed to trap a stationary point necessarily converges to the true solution. We demonstrate the usefulness of our approach in recovering finite-duration and periodic pulse streams.

We address the problems of multi-domain and single-domain regression based on distinct labeled training sets for each of the domains and a large unlabeled training set from all domains. We formulate these problems as ones of Bayesian estimation with partial knowledge of statistical relations. We propose a worst-case design strategy and study the resulting estimators. Our analysis explicitly accounts for the cardinality of the labeled sets and includes the special cases in which one of the labeled sets is very large or, in the other extreme, completely missing. We demonstrate our estimators in the context of audio-visual word recognition and provide comparisons to several recently proposed multi-modal learning algorithms.

Massively broadband® RF channel sounding is severely constrained by the sampling rates required for analog to digital conversion. Analog compressed sensing (CS) techniques based on Xampling have demonstrated the ability to lower sampling rates far below the Nyquist rate. Here, we show attributes of the multipath channel sounding problem appear to be well suited to CS approaches for reducing measurement acquisition time while simultaneously estimating time delays, multipath amplitudes, and angles of arrival. This paper presents results of the fusion of CS with modern channel sounding. We show measured propagation data from 60 GHz field trials and note the channel sparsity in time and space. We then propose an architecture for the first massively broadband CS channel sounder based on the Xampling framework (which we call the Channel Sounding Xampler) to exploit the sparsity, and we use field measurements to explore tradeoffs between analog and digital signal processing to perform channel impulse response (CIR) parameter estimation in real time. We also offer conceptual approaches for the Channel Sounding Xampler designed to trade off analog and digital components with the goal of improving CIR acquisition at sub-THz frequencies.

Recent developments in medical treatment put challenging demands on ultrasound imaging systems. These demands typically imply increasing the number of transducer elements involved in each imaging cycle. Confined to traditional sampling methods, the inevitable result is a significant growth in the amount of raw data that needs to be transmitted from the system front end, and then processed by the processing unit, effecting machinery size and power consumption. In this paper, we derive a scheme which reduces the amount of transmitted data, by applying Compressed Sensing (CS) techniques to analog ultrasound signals detected in the transducer elements. We follow the spirit of Xampling, which combines classic methods from sampling theory with recent developments in CS, aimed at sampling analog signals far below the Nyquist rate. Our scheme enhances SNR, by integrating low-rate samples extracted from multiple transducer elements. We refer to this process as “beamforming in the compressed domain”, or “compressed beamforming”.

We explore several reduced-dimension multiuser detection (RD-MUD) structures that significantly decrease the number of required correlation branches at the receiver front-end, while still achieving performance similar to that of the conventional matched-filter (MF) bank. RD-MUD exploits the fact that the number of active users is typically small relative to the total number of users in the system and relies on ideas of analog compressed sensing to reduce the number of correlators. We first develop a general framework for both linear and nonlinear RD-MUD structures. We then present theoretical performance analysis for two specific detectors: the linear reduced-dimension decorrelating (RDD) detector, which combines subspace projection and thresholding to determine active users and sign detection for data recovery, and the nonlinear reduced-dimension decision-feedback (RDDF) detector, which combines decision-feedback orthogonal matching pursuit for active user detection and sign detection for data recovery. The theoretical performance results for both detectors are validated via numerical simulations.

This paper develops the fundamental capacity limits of a sampled analog channel under a sub-Nyquist sampling rate constraint. In particular, we derive the capacity of sampled analog channels over a general class of time-preserving sampling methods including irregular nonuniform sampling. Our results indicate that the optimal sampling structures extract out the set of frequencies that exhibits the highest SNR among all spectral sets of support size equal to the sampling rate. The capacity under sub-Nyquist sampling can be attained through filter-bank sampling, or through a single branch of modulation and filtering followed by uniform sampling. The capacity under sub-Nyquist sampling is a monotone function of the sampling rate. These results indicate that the optimal sampling schemes suppress aliasing, and that employing irregular nonuniform sampling does not provide capacity gain over uniform sampling sets with appropriate preprocessing for a large class of channels.

In this paper, we consider the problem of estimating finite rate of innovation (FRI) signals from noisy measurements, and specifically analyze the interaction between FRI techniques and the underlying sampling methods. We first obtain a fundamental limit on the estimation accuracy attainable regardless of the sampling method. Next, we provide a bound on the performance achievable using any specific sampling approach. Essential differences between the noisy and noise-free cases arise from this analysis. In particular, we identify settings in which noise-free recovery techniques deteriorate substantially under slight noise levels, thus quantifying the numerical instability inherent in such methods. This instability, which is only present in some families of FRI signals, is shown to be related to a specific type of structure, which can be characterized by viewing the signal model as a union of subspaces. Finally, we develop a methodology for choosing the optimal sampling kernels for linear reconstruction, based on a generalization of the Karhunen-Loève transform. The results are illustrated for several types of time-delay estimation problems.

This paper revisits the sparse multiple measurement vector (MMV) problem, where the aim is to recover a set of jointly sparse multichannel vectors from incomplete measurements. This problem is an extension of single channel sparse recovery, which lies at the heart of compressed sensing. Inspired by the links to array signal processing, a new family of MMV algorithms is considered that highlight the role of rank in determining the difficulty of the MMV recovery problem. The simplest such method is a discrete version of MUSIC which is guaranteed to recover the sparse vectors in the full rank MMV setting, under mild conditions. This idea is extended to a rank aware pursuit algorithm that naturally reduces to Order Recursive Matching Pursuit (ORMP) in the single measurement case while also providing guaranteed recovery in the full rank setting. In contrast, popular MMV methods such as Simultaneous Orthogonal Matching Pursuit (SOMP) and mixed norm minimization techniques are shown to be rank blind in terms of worst case analysis. Numerical simulations demonstrate that the rank aware techniques are significantly better than existing methods in dealing with multiple measurements.

Identification of time-varying linear systems, which introduce both time-shifts (delays) and frequency-shifts (Doppler-shifts), is a central task in many engineering applications. This paper studies the problem of identification of underspread linear systems (ULSs), de fined as time-varying linear systems whose responses lie within a unit-area region in the delay-Doppler space, by probing them with a known input signal. The main contribution of the paper is that it characterizes conditions on the bandwidth and temporal support of the input signal that ensure identification of ULSs described by a finite set of delays and Doppler-shifts, and referred to as parametric ULSs, from single observations. In particular, the paper establishes that sufficiently-underspread parametric linear systems are identifiable as long as the time-bandwidth product of the input signal is proportional to the square of the total number of delay-Doppler pairs in the system. In addition, the paper describes a procedure that enables identification of parametric ULSs from an input train of pulses in polynomial time by exploiting recent results on sub-Nyquist sampling for time delay estimation and classical results on recovery of frequencies from a sum of complex exponentials.

We explore several fundamental questions at the intersection of sampling theory and information theory. In particular, we study how capacity is affected by a given sampling mechanism below the channel's Nyquist rate, and what sampling strategy should be employed to maximize capacity. Two classes of sampling mechanisms are investigated: uniform sampling with filtering and uniform sampling with a filter bank. Optimal filters that maximize capacity are identified for both cases. We also highlight connections between capacity and minimum mean squared error (MMSE) estimation from sampled data. Our results indicate that maximizing capacity of sampled analog channels is a joint optimization problem over both the trans mission strategy and the sampling technique.

We address the problem of denoising for image patches. The approach taken is based on Bayesian modeling of sparse representations, which takes into account dependencies between the dictionary atoms. Following recent work, we use a Boltzman machine to model the sparsity pattern. In this work we focus on the special case of a unitary dictionary and obtain the exact MAP estimate for the sparse representation using an efficient message passing algorithm. We present an adaptive model-based scheme for sparse signal recovery, which is based on sparse coding via message passing and on learning the model parameters from the data. This adaptive approach is applied on noisy image patches in order to recover their sparse representations over a fixed unitary dictionary. We compare the denoising performance to that of previous sparse recovery methods, which do not exploit the statistical dependencies, and show the effectiveness of our approach.

We develop sub-Nyquist sampling systems for analog signals comprised of several, possibly overlapping, finite duration pulses with unknown shapes and time positions. To the best of our knowledge, stable and low-rate sampling strategies for a superposition of unknown pulses without knowledge of the pulse locations have not been derived. We propose a multichannel scheme based on Gabor frames that exploits the sparsity of signals in time and enables sampling multipulse signals at sub-Nyquist rates. Our approach is based on modulating the input signal in each channel with a properly chosen waveform, followed by an integrator. As we show, the resulting scheme is flexible and exhibits good noise robustness.

Causal processing of a signal's samples is crucial in on-line applications such as audio rate conversion, compression, tracking and more. This paper addresses the problem of causally reconstructing continuous-time signals from their samples. We treat a rich variety of sampling mechanisms encountered in practice, namely in which each sampling function is obtained by applying a unitary operator on its predecessor. Examples include pointwise sampling at the output of an anti-aliasing filter and magnetic resonance imaging, which correspond respectively to the translation and modulation operators. Such sequences of functions were studied extensively in the context of stationary random processes. We thus utilize powerful tools from this discipline, to derive a causal interpolation method that best approximates the commonly used non-causal reconstruction formula.

This paper studies conditions under which a signal can be reconstructed from partial frequency content. We focus on signals in shift-invariant spaces generated by multiple generators. For these signals, we derive a lower bound on the necessary signal bandwidth as well as sufficient conditions on the generators such that signal recovery is possible. When the available frequency content is not sufficient to recover the signal, we propose appropriate pre-processing that can improve the reconstruction ability.

We propose a demonstration of sub-Nyquist sampling and reconstruction in real-time, based on prototype hardware and embedded FPGA.

Generic acquisition hardware promotes a unified treatment of various signal classes. In modern applications involving wide input bandwidths, uniform sampling, the common practice for generic digitization, leads to prohibitively large sampling and processing rates due to the wide Nyquist bandwidth of the input. In this paper, we present the X-ADC system which narrows down the input bandwidth by analog preprocessing prior to sampling at rates substantially lower than Nyquist. As we show, the X-ADC strategy is generic in the sense that multitude radio and medical imaging applications with structured signals can utilize the same architecture for low rate acquisition. A recently published sub-Nyquist hardware, which was designed according to the proposed X-ADC scheme, provides a concrete reference for the present study. We complement the generic acquisition by reporting on a real-time embedded implementation of a sub-Nyquist reconstruction algorithm. The embedded design enables, for example, fast spectrum sensing which is essential to real-time cognitive radio applications.

We explore the capacity of sub-Nyquist sampled analog channels based on modulation and filter bank sampling techniques. In particular, we derive the capacity of sampled analog channels under sampling via modulation banks and filter banks. A connection between these sampling mechanisms and MIMO Gaussian channels is illuminated. For sampling with a single branch of modulation and filtering, we identify the modulation sequence that optimizes capacity. These results illustrate the importance of the sampling technique on the capacity of sampled analog channels for a broad class of nonuniform sampling structures.

The literature on compressed sensing has focused almost entirely on settings where the signal is noiseless and the measurements are contaminated by noise. In practice, however, the signal itself is often subject to random noise prior to measurement. We briefly study this setting and show that, for the vast majority of measurement schemes employed in compressed sensing, the two models are equivalent with the important difference that the signal-to-noise ratio (SNR) is divided by a factor proportional to p/n, where p is the dimension of the signal and n is the number of observations. Since p/n is often large, this leads to noise folding which can have a severe impact on the SNR.

The fundamental principle underlying compressed sensing is that a signal, which is sparse under some basis representation, can be recovered from a small number of linear measurements. However, prior knowledge of the sparsity basis is essential for the recovery process. This work introduces the concept of blind compressed sensing, which avoids the need to know the sparsity basis in both the sampling and the recovery process. We suggest three possible constraints on the sparsity basis that can be added to the problem in order to guarantee a unique solution. For each constraint, we prove conditions for uniqueness, and suggest a simple method to retrieve the solution. We demonstrate through simulations that our methods can achieve results similar to those of standard compressed sensing, which rely on prior knowledge of the sparsity basis, as long as the signals are sparse enough. This offers a general sampling and reconstruction system that fits all sparse signals, regardless of the sparsity basis, under the conditions and constraints presented in this work.

The problem studied in this paper is unbiased estimation of a sparse nonrandom vector corrupted by additive white Gaussian noise. It is shown that while there are infinitely many unbiased estimators for this problem, none of them has uniformly minimum variance. Therefore, the focus is placed on locally minimum variance unbiased (LMVU) estimators. Simple closed-form lower and upper bounds on the variance of LMVU estimators or, equivalently, on the Barankin bound (BB) are derived. These bounds allow an estimation of the threshold region separating the low-signal-to-noise ratio (SNR) and high-SNR regimes, and they indicate the asymptotic behavior of the BB at high SNR. In addition, numerical lower and upper bounds are derived; these are tighter than the closed-form bounds and thus characterize the BB more accurately. Numerical studies compare the proposed characterizations of the BB with established biased estimation schemes, and demonstrate that while unbiased estimators perform poorly at low SNR, they may perform better than biased estimators at high SNR. An interesting conclusion of this analysis is that the high-SNR behavior of the BB depends solely on the value of the smallest nonzero entry of the sparse vector, and that this type of dependence is also exhibited by the performance of certain practical estimators.

We introduce Xampling, a design methodology for analog compressed sensing in which we sample analog bandlimited signals at rates far lower than Nyquist, without loss of information. This allows compression together with the sampling stage. The main principles underlying this framework are the ability to capture a broad signal model, low sampling rate, efficient analog and digital implementation and lowrate baseband processing. In order to break through the Nyquist barrier so as to compress the signals in the sampling process, one has to combine classic methods from sampling theory together with recent developments in compressed sensing. We show that previous attempts at sub-Nyquist sampling suffer from analog implementation issues, large computational loads, and have no baseband processing capabilities. We then introduce the modulated wideband converter which can satisfy all the Xampling desiderata. We also demonstrate a board implementation of our converter which exhibits sub-Nyquist sampling in practice.

We address the problem of worst-case robust downlink beamforming for a multi-antenna secondary network (SN) in a cognitive radio framework. An important issue is the interference leaked to the primary users (PUs) resulting from the transmission between the SN base station and the secondary users (SUs). Our aim is to provide the SUs with a minimum acceptable quality-of-service (QoS), while keeping the interference to the PUs below a given threshold. Previous solutions for this scenario involve several coarse approximations. Here we avoid these approximations and obtain an exact reformulation of the worst-case problem using Lagrange duality. Finally, we use semidefinite relaxation (SDR) to convert the resulting problem to a convex form. Computer simulations show that the SDR step does not involve any approximation as the resulting solution is always rank-one.

We consider the problem of estimating a deterministic sparse vector x0from underdetermined measurements Ax0+ w, where w represents white Gaussian noise and A is a given deterministic dictionary. We analyze the performance of three sparse estimation algorithms: basis pursuit denoising, orthogonal matching pursuit, and thresholding. These approaches are shown to achieve near-oracle performance with high probability, assuming that x0is sufficiently sparse. Our results are non-asymptotic and are based only on the coherence of A, so that they are applicable to arbitrary dictionaries.

We investigate the impact of using non-ideal lowpass filters in the modulated wideband (MWC) converter, which is a recent sub-Nyquist sampling system for sparse wideband analog signals. We begin by deriving a perfect reconstruction condition for general lowpass filters, which coincides with the well-known Nyquist inter-symbol interference (ISI) criterion in communication theory. Then, we propose to compensate for the non-ideal lowpass filters using a digital FIR correction scheme. The proposed solution is validated by experimental results.

Sampling theorems for signals that lie in a union of subspaces have been receiving growing interest. A recent model that describes analog signals over a union is that of a union of shift-invariant (SI) subspaces. Until now, sampling and recovery algorithms have been developed only for a finite union of SI subspaces. Here we extend this paradigm to a special case of an infinite union, in which the SI subspaces are generated by pulses with unknown delays, taken from a continuous interval. We develop a unified approach to time delay recovery of the pulses, from low rate samples of the signal taken at the lowest possible rate. In particular, we derive sufficient conditions on the pulses and the sampling filters in order to ensure perfect recovery of the signal. We then show that by properly manipulating the low-rate samples, the time delays can be recovered using the well-known ESPRIT algorithm.

We consider the estimation of a sparse parameter vector from measurements corrupted by white Gaussian noise. Our focus is on unbiased estimation as a setting under which the difficulty of the problem can be quantified analytically. We show that there are infinitely many unbiased estimators but none of them has uniformly minimum mean-squared error. We then provide lower and upper bounds on the Barankin bound, which describes the performance achievable by unbiased estimators. These bounds are used to predict the threshold region of practical estimators.

We address the problem of Bayesian estimation where the statistical relation between the signal and measurements is only partially known. We propose modeling partial Baysian knowledge by using an auxiliary random vector called instrument. The joint probability distributions of the instrument and the signal, and of the instrument and the measurements, are known. However, the joint probability function of the signal and measurements is unknown. Our model generalizes that underlying the method of instrumental variables from statistics, in that the instrument does not have to satisfy any requirements and no parametric form for the optimal regressor needs to be available. We begin by deriving an estimator for this scenario, via a worst-case design strategy. We then propose a non-parametric method for learning this estimator from a set of examples. Finally, we demonstrate our approach in the context of enhancement of facial images that have undergone an unknown degradation.

Sub-Nyquist systems capture the signal information in a different fashion than uniform high-rate samples. Consequently, digital processing, which is the prime reason for leaving the analog domain, becomes challenging. We propose a digital algorithm that translates samples obtained by the modulated wideband converter, a recent sub-Nyquist system, to the standard format of existing software packages. Our algorithm works in baseband, that is without the need to interpolate the samples to the Nyquist grid. Related methods such as nonuniform sampling or the random demodulator are shown to lack the baseband processing option.

We revisit the problem of recovering a continuous-time signal lying within a known shift-invariant subspace from nonlinear and nonideal samples. Recently, an iterative algorithm for perfect recovery of such signals was proposed. This method requires operations which are not linear time-invariant (LTI), rendering it impractical due to its polynomial dependency on the data length. We describe an alternative iterative algorithm for recovering the signal, which involves only LTI operations. In the revised method, each iteration is much faster and implementation is simpler. Furthermore, the overall running time of our approach depends linearly on the number of samples.

This paper considers recovery of jointly sparse multichannel signals from incomplete measurements. Several approaches have been developed to recover the unknown sparse vectors from the given observations, including thresholding, simultaneous orthogonal matching pursuit (SOMP), and convex relaxation based on a mixed matrix norm. Typically, worst case analysis is carried out in order to analyze conditions under which the algorithms are able to recover any jointly sparse set of vectors. However, such an approach is not able to provide insights into why joint sparse recovery is superior to applying standard sparse reconstruction methods to each channel individually. Previous work considered an average case analysis of thresholding and SOMP by imposing a probability model on the measured signals. Here, the main focus is on analysis of convex relaxation techniques. In particular, the mixedl2,1approach to multichannel recovery is investigated. Under a very mild condition on the sparsity and on the dictionary characteristics, measured for example by the coherence, it is shown that the probability of recovery failure decays exponentially in the number of channels. This demonstrates that most of the time, multichannel sparse recovery is indeed superior to single channel methods. The probability bounds are valid and meaningful even for a small number of signals. Using the tools developed to analyze the convex relaxation technique, also previous bounds for thresholding and SOMP recovery are tightened.

A traditional assumption underlying most data converters is that the signal should be sampled at a rate exceeding twice the highest frequency. Practical signals often posses a sparse structure so that a large part of the bandwidth is not exploited. In this paper, we consider a framework for utilizing this sparsity in order to sample such analog signals at a low rate. By relying on results developed in the context of compressed sensing (CS) of finite-length vectors, we develop a general framework for low-rate sampling of signals in shift-invariant spaces. In contrast to the problems treated in the context of CS, here we explicitly consider sampling of analog signals for which no underlying finite-dimensional model exists.

We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. Based on an uncertainty relation for block-sparse signals, we define a block-coherence measure and show that a block-version of the orthogonal matching pursuit algorithm recovers block k-sparse signals in no more than k steps if the block-coherence is sufficiently small. The same condition on block-sparsity is shown to guarantee successful recovery through a mixed lscr2/lscr1optimization approach. The significance of the results lies in the fact that making explicit use of block-sparsity can yield better reconstruction properties than treating the signal as being sparse in the conventional sense, thereby ignoring the additional structure in the problem.

This paper addresses source separation from a linear mixture under two assumptions: source sparsity and orthogonality of the mixing matrix. We propose efficient sparse separation via a two-stage process. In the first stage we attempt to recover the sparsity pattern of the sources by exploiting the orthogonality prior. In the second stage, the support is used to reformulate the recovery task as an optimization problem. We then suggest a solution based on alternating minimization. Random simulations are performed to analyze the behavior of the resulting algorithm. The simulations demonstrate convergence of our approach as well as superior recovery rate in comparison with alternative source separation methods and K-SVD, a leading algorithm in dictionary learning.

The problem of multiuser downlink beamforming is studied under the assumption that the transmitter has erroneous covariance-based channel state information (CSI). The goal is to minimize the transmit power under the worst-case quality-of-service (QoS) constraints. Previous convex optimization-based solutions to this problem involve several coarse approximations of the original problem. In our proposed solution, such coarse approximations are avoided and an exact representation of the worst-case solution is obtained using Lagrange duality. The so-obtained problem is then converted to a convex form using semidefinite relaxation (SDR). Computer simulations show that the SDR step does not involve any approximation as the resulting solution is always rank-one. Simulation results demonstrate substantial performance improvements over earlier worst-case optimization-based downlink beamforming techniques.

A key requirement facing organisms acting in uncertain dynamic environments is the real-time estimation and prediction of environmental states, based on which effective actions can be selected. While it is becoming evident that organisms employ exact or approximate Bayesian statistical calculations for these purposes, it is far less clear how these putative computations are implemented by neural networks in a strictly dynamic setting. In this work, we make use of rigorous mathematical results from the theory of continuous time point process filtering and show how optimal real-time state estimation and prediction may be implemented in a general setting using simple recurrent neural networks. The framework is applicable to many situations of common interest, including noisy observations, non-Poisson spike trains (incorporating adaptation), multisensory integration, and state prediction. The optimal network properties are shown to relate to the statistical structure of the environment, and the benefits of adaptation are studied and explicitly demonstrated. Finally, we recover several existing results as appropriate limits of our general setting.

The problem considered in this letter is to bound the performance of estimators of a deterministic parameter which satisfies given constraints. Specifically, previous work on the constrained Cramer-Rao bound (CRB) is generalized to include singular Fisher information matrices and biased estimators. A necessary and sufficient condition for the existence of a finite CRB is obtained. A closed form for an estimator achieving the CRB, if one exists, is also provided, as well as a necessary and sufficient condition for the existence of such an estimator. It is shown that biased estimators achieving the CRB can be constructed in situations for which no unbiased technique exists.

We address a sampling problem in which the goal is to approximate a signal from its nonideal (generalized) samples. The reconstruction is constrained to lie in a subspace, and to be consistent with the measured samples. It is well known how to obtain a consistent approximation, if the sampling and reconstruction spaces satisfy a certain direct sum condition. Here we show when consistency can be achieved without the need for this condition. The proposed solution provides geometrical insight into the structure of the problem and extends previous treatments by finding a consistent and simultaneously robust approximation of the signal from its samples.

A lower bound on the minimum mean-squared error (MSE) in a Bayesian estimation problem is proposed in this paper. This bound utilizes a well-known connection to the deterministic estimation setting. Using the prior distribution, the bias function which minimizes the Cramer-Rao bound can be determined, resulting in a lower bound on the Bayesian MSE. The bound is developed for the general case of a vector parameter with an arbitrary probability distribution, and is shown to be asymptotically tight in both the high and low signal-to-noise ratio (SNR) regimes. A numerical study demonstrates several cases in which the proposed technique is both simpler to compute and tighter than alternative methods.

The past several years have witnessed a surge of research investigating various aspects of sparse representations and compressed sensing. Most of this work has focused on the finite-dimensional setting in which the goal is to decompose a finite-length vector into a given finite dictionary. Underlying many of these results is the conceptual notion of an uncertainty principle: a signal cannot be sparsely represented in two different bases. Here, we extend these ideas and results to the analog, infinite-dimensional setting by considering signals that lie in a finitely generated shift-invariant (SI) space. This class of signals is rich enough to include many interesting special cases such as multiband signals and splines. By adapting the notion of coherence defined for finite dictionaries to infinite SI representations, we develop an uncertainty principle similar in spirit to its finite counterpart. We demonstrate tightness of our bound by considering a bandlimited lowpass train that achieves the uncertainty principle. Building upon these results and similar work in the finite setting, we show how to find a sparse decomposition in an overcomplete dictionary by solving a convex optimization problem. The distinguishing feature of our approach is the fact that even though the problem is defined over an infinite domain with infinitely many variables and constraints, under certain conditions on the dictionary spectrum our algorithm can find the sparsest representation by solving a finite-dimensional problem.

Traditional sampling theories consider the problem of reconstructing an unknown signalxfrom a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is thatxlies in a known subspace. Recently, there has been growing interest in nonlinear but structured signal models, in whichxlies in a union of subspaces. In this paper, we develop a general framework for robust and efficient recovery of such signals from a given set of samples. More specifically, we treat the case in whichxlies in a sum ofksubspaces, chosen from a larger set ofmpossibilities. The samples are modeled as inner products with an arbitrary set of sampling functions. To derive an efficient and robust recovery algorithm, we show that our problem can be formulated as that of recovering a block-sparse vector whose nonzero elements appear in fixed blocks. We then propose a mixed lscr2/lscr1program for block sparse recovery. Our main result is an equivalence condition under which the proposed convex algorithm is guaranteed to recover the original signal. This result relies on the notion of block restricted isometry property (RIP), which is a generalization of the standard RIP used extensively in the context of compressed sensing. Based on RIP, we also prove stability of our approach in the presence of noise and modeling errors. A special case of our framework is that of recovering multiple measurement vectors (MMV) that share a joint sparsity pattern. Adapting our results to this context leads to new MMV recovery methods as well as equivalence conditions under which the entire set can be determined efficiently.

We treat the linear regression problem of estimating thetas from noisy observations where the norm of thetas is bounded. Instead of using the constrained least-squares approach which minimizes the data error over bounded norm vectors, we explore the use of the Chebyshev-center estimate (CC), that is aimed at minimizing the worst-case squared-error over all bounded-norm vectors thetas and bounded noise. We derive an explicit expression for the CC estimate and explore some of its statistical properties. In particular, we show that it can be viewed as a generalized Bayesian estimate where both the parameter vector and the noise have hierarchial Gaussian priors.

We address the problem of minimum mean-squared error (MMSE) estimation where the estimator is constrained to belong to a pre-defined set of functions. We derive a simple closed form formula that reveals the structure of the restricted estimator for a wide class of constraints. Using this formula we study various types of constrained estimation problems that arise commonly in the fields of signal processing and communication.

We develop a perfect reconstruction scheme from point-wise sub-Nyquist rate samples for multi-band signals. Our approach is blind, namely the knowledge of the band locations is not used in the design of either the sampling or the reconstruction stage. This is in contrast to previous approaches to reconstruct this class of signals, which required information about the spectral support at least in the reconstruction stage. Our scheme guarantees exact recovery for a wide class of multi-band signals without the use of heuristics or discretization methods.

The Weiss-Weinstein bound (WWB) provides a lower limit on the mean-squared error (MSE) achievable by an estimator of an unknown random parameter. In this correspondence, it is shown that some previously proposed simplified versions of the bound do not always hold for constrained parameters, i.e., parameters whose distribution has finite support. These simplifications can produce results which are no longer lower bounds on the MSE. Sufficient conditions are provided for the reductions to be valid.

The seminal work of Stein in the 1950's ignited a large body of research devoted to improving the total mean-squared error (MSE) of the least-squares (LS) estimator. A drawback of these methods is that they improve the total MSE at the expense of increasing the MSE of some of the individual signal components. Here we consider a framework for developing linear estimators that outperform LS over bounded norm signals, under all weighted MSE measures. We first derive an easily verifiable condition on a linear method that ensures LS domination for every weighted MSE. We then suggest a minimax estimator that minimizes the worst-case MSE over all weighting matrices and bounded norm signals subject to the universal weighted MSE domination constraint.

We address the problem of minimum mean-squared error (MMSE) estimation under convex constraints. The familiar orthogonality principle, developed for linear constraints, is generalized to include convex restrictions. Using the extended principle, we study two types of convex constraints: constraints on the estimated vector (e.g. bounded norm), and constraints on the structure of the estimator (e.g. filter with bounded coefficients). It is shown that in both cases there exists a simple closed form expression for the constrained MMSE estimator. As an application of our approach, we develop Wiener type filters under certain restrictions, which allow for practical implementations.

Wyner's wiretap channel is generalized to the case when the sender, the receiver and the eavesdropper have multiple antennas. We consider two cases: the deterministic case and the fading case. In the deterministic case, the channel matrices of the intended receiver and the eavesdropper are fixed and known to all the nodes. In the fading case, the channel matrices experience block fading and the sender has only the intended receiver's channel state information (CSI) and statistical knowledge of the eavesdropper's channel. For the deterministic case, a scheme based on the generalized-singular-value-decomposition (GSVD) of the channel matrices is proposed and shown to achieve the secrecy capacity in the high signal-to-noise-ratio (SNR) limit. When the intended receiver has only one antenna (MISO case) the secrecy-capacity is characterized for any SNR. Next, a suboptimal "artificial noise" based scheme is considered. Its performance is characterized and observed to be nearly optimal in the high SNR regime for the MISO case. This scheme extends naturally to the fading case and results are reported for the MISO case. For the independent Rayleigh fading distribution as we simultaneously increase the number of antennas at the sender and the eavesdropper, the secrecy capacity approaches zero if and only if the ratio of the number of eavesdropper antennas to transmitter antennas is at least two.

It is becoming increasingly evident that organisms acting in uncertain dynamical environments often employ exact or approximate Bayesian statistical calculations in order to continuously estimate the environmental state, integrate information from multiple sensory modalities, form predictions and choose actions. What is less clear is how these putative computations are implemented by cortical neural networks. An additional level of complexity is introduced because these networks observe the world through spike trains received from primary sensory afferents, rather than directly. A recent line of research has described mechanisms by which such computations can be implemented using a network of neurons whose activ- ity directly represents a probability distribution across the possible “world states”. Much of this work, however, uses various approximations, which severely re- strict the domain of applicability of these implementations. Here we make use of rigorous mathematical results from the theory of continuous time point process filtering, and show how optimal real-time state estimation and prediction may be implemented in a general setting using linear neural networks. We demonstrate the applicability of the approach with several examples, and relate the required network properties to the statistical nature of the environment, thereby quantify- ing the compatibility of a given network with its environment.

We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze blind minimax estimators (BMEs), which consist of a bounded parameter set minimax estimator, whose parameter set is itself estimated from measurements. Thus, our approach does not require any prior assumption or knowledge, and the proposed estimator can be applied to any linear regression problem. We demonstrate analytically that the BMEs strictly dominate the least-squares (LS) estimator, i.e., they achieve lower mean-squared error (MSE) for any value of the parameter vector. Both Stein's estimator and its positive-part correction can be derived within the blind minimax framework. Furthermore, our approach can be readily extended to a wider class of estimation problems than Stein's estimator, which is defined only for white noise and nontransformed measurements. We show through simulations that the BMEs generally outperform previous extensions of Stein's technique.

We investigate optimal encoding and retrieval of digital data, when the storage/communication medium is described by quantum mechanics. We assume an m-ary alphabet with arbitrary prior distribution, and an n-dimensional quantum system. Under these constraints, we seek an encoding-retrieval setup, comprised of code-states and a quantum measurement, which maximizes the probability of correct detection. In our development, we consider two cases. In the first, the measurement is predefined and we seek the optimal code-states. In the second, optimization is performed on both the code-states and the measurement. We show that one cannot outperform "pseudo-classical transmission," in which we transmit n symbols with orthogonal code-states, and discard the remaining symbols. However, such pseudo-classical transmission is not the only optimum. We fully characterize the collection of optimal setups, and briefly discuss the links between our findings and applications such as quantum key distribution and quantum computing

In this paper, we consider the optimization of the compound capacity in a rank one Ricean multiple input multiple output channel using partial channel state information at the transmitter side. We model the channel as a deterministic matrix within a known ellipsoid, and address the compound capacity defined as the maximum worst case mutual information in the set. We find that the optimal transmit strategy is always beamforming, and can be found using a simple one dimensional search. Similar results are derived for the worst case sum-rate of a multiple access channel with individual power constraints and a total power constraint. In this multiuser setting we assume equal array response at the receiver for all users. These results motivate the growing use of systems using simple beamforming transmit strategies

Many sources of information are of analogue or continuous-time nature. However, digital signal processing applications rely on discrete data. We consider the problem of approximating L2inner products, i.e., representation coefficients of a continuous-time signal, while having the possibly non-ideal signal samples, as the only available data. By adopting a generalized sampling scheme, a minimax solution is suggested. We then compare our approach with the piecewise-constant approximation method, commonly used for this problem

We treat the problem of evaluating the performance of estimators for estimating a deterministic parameter vector x, with the mean-squared error (MSE) as the performance measure. Since the MSE depends on the unknown vector x, direct comparison between estimators is a difficult problem. Here we consider a framework for examining the MSE of different approaches based on the concepts of admissible and dominating estimators. Using a saddle-point framework we reduce these abstract concepts to a concrete convex optimization problem, which can then by analyzed by utilizing the machinery of convex optimization. Our development considers both the case of linear estimation in linear models as well as more general nonlinear models

This paper addresses the problem of designing linear-phase finite impulse response digital filters using an L1optimality criterion. An efficient procedure for the design of such filters is proposed and it is shown that the resulting filter has several desirable properties. Specifically, the L1filter possesses flat passbands and stopbands while keeping the transition band comparable to that of the leastsquares filters. A comparison with existing methods is made, and it is shown that our method is as efficient as the celebrated Remez exchange algorithm.

We consider the problem of estimating an unknown deterministic parameter vector in a linear model with a Gaussian model matrix. The matrix has a known mean and independent rows of equal covariance matrix. Our problem formulation also allows for some known columns within this model matrix. We derive the maximum likelihood (ML) estimator associated with this problem and show that it can be found using a simple line-search over a unimodal function which can be efficiently evaluated. We then analyze its asymptotic performance using the Cramer Rao bound. Finally, we discuss the similarity between the ML, total least squares (TLS), and regularized TLS estimators

We treat the problem of beamforming for signal estimation in the presence of steering vector uncertainties, where the goal is to estimate a signal amplitude from a set of array observations. Conventional beamforming methods typically aim at maximizing the signal-to-interference-plus-noise ratio (SINR). Recently, a maximum likelihood (ML) approach was introduced that leads to an iterative beamformer. Here we suggest an expected least-squares (LS) strategy that results in a simple linear beamformer. We then demonstrate through simulations that the LS beamformer often performs similarly to the ML method in terms of mean-squared error and outperforms conventional SINR-based approaches.

We consider the problem of estimating an unknown deterministic parameter vector in a linear model with a Gaussian model matrix. We derive the maximum likelihood (ML) estimator for this problem and show that it can be found using a simple line-search over a unimodal function that can be efficiently evaluated. We then discuss the similarity between the ML, the total least squares (TLS), the regularized TLS, and the expected least squares estimators.

Robust estimation of a random vector in a linear model in the presence of model uncertainties has been studied in several recent works. While previous methods considered the case in which the uncertainty is in the signal covariance, and possibly the model matrix, but the noise covariance is assumed to be completely specified, here we extend the results to the case where the noise statistics may also be subjected to uncertainties. We propose several different approaches to robust estimation, which differ in their assumptions on the given statistics. In the first method, we assume that the model matrix and both the signal and the noise covariance matrices are uncertain, and develop a minimax mean-squared error (MSE) estimator that minimizes the worst case MSE in the region of uncertainty. The second strategy assumes that the model matrix is given and tries to uniformly approach the performance of the linear minimum MSE estimator that knows the signal and noise covariances by minimizing a worst case regret measure. The regret is defined as the difference or ratio between the MSE attainable using a linear estimator, ignorant of the signal and noise covariances, and the minimum MSE possible when the statistics are known. As we show, earlier solutions follow directly from our more general results. However, the approach taken here in developing the robust estimators is considerably simpler than previous methods

We consider the problem of multichannel estimation, in which we seek to estimate multiple input vectors that are observed through a set of linear transformations and corrupted by additive noise. The input vectors x/sub k/ are known to satisfy a weighted norm constraint. We discuss both the case where the linear transformations are fixed (certain) and the case where they are only known to reside in some deterministic uncertainty set. We seek the linear estimator that minimizes the worst-case mean-squared error (MSE) across all possible values of the linear transformations and possible values of x/sub k/. We show that for an arbitrary choice of weighting matrix, the minimax MSE estimator can be formulated as a solution to a semidefinite programming problem (SDP). In the case in which the linear transformations are fixed and the norms are unweighed, the minimax MSE multichannel estimator has an explicit closed from solution. Finally, we demonstrate through examples, that the minimax MSE estimator can significantly increase the performance over conventional least-squares based methods.

We present several analytical and numerical results demonstrating the superiority of minimax estimators over least-squares (LS) estimation. We show that, for any bounded parameter set, a linear minimax estimator achieves lower mean-squared error than the LS estimator, over the entire parameter set. When a parameter set is unknown, we propose to estimate the parameter set from the data, and show that in many cases, the obtained blind minimax estimator still dominates the LS estimator. The results are related to and compared with other LS-dominating estimators, such as the James-Stein estimator.

We treat the problem of reconstructing a signal, x, that lies in a subspace, W, from its noisy samples. The samples are modelled as the inner products of x with a set of sampling vectors that span a subspace, S, not necessarily equal to W. We consider two approaches to reconstructing x from the noisy samples, a least-squares (LS) method and a minimax mean-squared error (MSE) strategy. We show that if the elements of x are finite, then the minimax MSE approach results in a smaller MSE than the LS approach for all values of x. We then generalize the results to the problem of minimizing an inner-product MSE.

We develop a computationally efficient approximation of the maximum likelihood (ML) detector for 16 quadrature amplitude modulation (16-QAM) in multiple-input multiple-output (MIMO) systems. The detector is based on a convex relaxation of the ML problem. The resulting optimization is a semidefinite program that can be solved in polynomial time with respect to the number of inputs in the system. Simulation results in a random MIMO system show that the proposed algorithm outperforms the conventional decorrelator detector by about 2.5 dB at high signal-to-noise ratios.

We consider the problem of designing an estimation filter to recover a signal x[n] convolved with a linear time-invariant (LTI) filter h[n] and corrupted by additive noise. Our development treats the case in which the signal x[n] is deterministic and the case in which it is a stationary random process. Both formulations take advantage of some a priori knowledge on the class of underlying signals. In the deterministic setting, the signal is assumed to have bounded (weighted) energy; in the stochastic setting, the power spectra of the signal and noise are bounded at each frequency. The difficulty encountered in these estimation problems is that the mean-squared error (MSE) at the output of the estimation filter depends on the problem unknowns and therefore cannot be minimized. Beginning with the deterministic setting, we develop a minimax MSE estimation filter that minimizes the worst case point-wise MSE between the true signal x[n] and the estimated signal, over the class of bounded-norm inputs. We then establish that the MSE at the output of the minimax MSE filter is smaller than the MSE at the output of the conventional inverse filter, for all admissible signals. Next we treat the stochastic scenario, for which we propose a minimax regret estimation filter to deal with the power spectrum uncertainties. This filter is designed to minimize the worst case difference between the MSE in the presence of power spectrum uncertainties, and the MSE of the Wiener filter that knows the correct power spectra. The minimax regret filter takes the entire uncertainty interval into account, and as demonstrated through an example, can often lead to improved performance over traditional minimax MSE approaches for this problem

In the above titled paper (ibid., vol. 49. no.9, pp. 2309-2313, Sep 03), several equations were printed incorrectly. The corrections are presented.

A new class of linear multiuser receivers, referred to as the covariance shaping multiuser (CSMU) receiver, is proposed, for suppression of interference in multiuser wireless communication systems. This class of receivers is based on the recently proposed covariance shaping least-squares estimator, and is designed to minimize the total variance of the weighted error between the receiver output and the observed signal, subject to the constraint that the covariance of the noise component in the receiver output is proportional to a given covariance matrix, so that we control the dynamic range and spectral shape of the output noise. Some of the well-known linear multiuser receivers are shown to be special cases of the CSMU receiver. This allows us to interpret these receivers as the receivers that minimize the total error variance in the observations, among all linear receivers with the same output noise covariance, and to analyze their performance in a unified way. We derive exact and approximate expressions for the probability of bit error, as well as the asymptotic signal-to-interference+noise ratio in the large system limit. We also characterize the spectral efficiency versus energy-per-information bit of the CSMU receiver in the wideband regime. Finally, we consider a special case of the CSMU receiver, equivalent to a mismatched minimum mean-squared error (MMSE) receiver, in which the channel signal-to-noise ratio (SNR) is not known precisely. Using our general performance analysis results, we characterize the performance of the mismatched MMSE receiver. We then treat the case in which the SNR is known to lie in a given uncertainty range, and develop a robust mismatched MMSE receiver whose performance is very close to that of the MMSE receiver over the entire uncertainty range.

We develop a new linear estimator for estimating an unknown vector x in a linear model, in the presence of bounded data uncertainties. The estimator is designed to minimize the worst-case regret across all bounded data vectors, namely the worst-case difference between the MSE attainable using a linear estimator that does not know the true parameters x, and the optimal MSE attained using a linear estimator that knows x. We demonstrate through several examples that the minimax regret estimator can significantly increase the performance over the conventional least-squares estimator, as well as several other least-squares alternatives.

We consider the problem of interpolating a continuous-time signal from a set of uniformly spaced discrete-time samples. One of the prime methods of interpolation is based on the use of uniform B-splines. We introduce a new interpolation approach using nonuniform B-splines as interpolation kernels. We show, both theoretically and through simulation results, that using nonuniform B-splines for interpolation of a signal from uniform samples can result in a higher quality of interpolation with respect to uniform B-splines, at the same computational cost.

We consider the problem of designing a robust linear equalizer under channel uncertainties. Specifically, we propose a robust peak distortion (RPD) equalizer, in which we minimize the error probability of the worst-case sequence and the worst-case channel, in the uncertainty region. We show that the RPD equalizer can be found efficiently using standard convex optimization packages. We then demonstrate through simulations that under channel uncertainty the RPD equalizer outperforms traditional equalizers, and previously proposed robust equalizers.

We consider the problem of designing linear multiple input multiple output (MIMO) precoders for fixed receivers. We first derive a precoder that minimizes the average power subject to signal to interference plus noise ratio (SINR) constraints, and then derive a precoder that maximizes the worst case SINR subject to an average power constraint. We show that both problems can be solved using standard optimization packages. In addition, a more efficient solution based on Karush-Kuhn-Tucker (KKT) optimality conditions is presented which gives more insight into the problem. Our design promises equal SINR and fairness among the multiple outputs. Simulation results in a multiuser system show that the proposed precoders can significantly outperform existing linear precoders.

We develop a sufficient condition for the least-squares measurement (LSM), or the square-root measurement, to minimize the probability of a detection error when distinguishing between a collection of mixed quantum states. Using this condition we derive the optimal measurement for state sets with a broad class of symmetries. We first consider geometrically uniform (GU) state sets with a possibly non-Abelian generating group, and show that if the generator satisfies a weighted norm constraint, then the LSM is optimal. In particular, for pure-state GU ensembles, the LSM is shown to be optimal. For arbitrary GU state sets we show that the optimal measurement operators are GU with generator that can be computed very efficiently in polynomial time, within any desired accuracy. We then consider compound GU (CGU) state sets which consist of subsets that are GU. When the generators satisfy a certain constraint, the LSM is again optimal. For arbitrary CGU state sets, the optimal measurement operators are shown to be CGU with generators that can be computed efficiently in polynomial time.

The paper develops and explores applications of a linear shaping transformation that minimizes the mean squared error (MSE) between the original and shaped data, i.e., that results in an output vector with the desired covariance that is as close as possible to the input, in an MSE sense. Three applications of minimum MSE shaping are considered, specifically matched filter detection, multiuser detection and linear least-squares parameter estimation.

This paper introduces a general framework for constructing signals with prescribed properties that can be described as inner products of the signal with a set of vectors, with almost arbitrary construction and constraint spaces. We first derive a procedure for constructing a signal in a given construction space, with prescribed properties in a given constraint space. Building upon these results, we develop a procedure for constructing a signal with prescribed properties in two disjoint constraint spaces.

We consider the problem of unambiguous discrimination between a set of linearly independent pure quantum states. We show that the design of the optimal measurement that minimizes the probability of an inconclusive result can be formulated as a semidefinite programming problem. Based on this formulation, we develop a set of necessary and sufficient conditions for an optimal quantum measurement. We show that the optimal measurement can be computed very efficiently in polynomial time by exploiting the many well-known algorithms for solving semidefinite programs, which are guaranteed to converge to the global optimum. Using the general conditions for optimality, we derive necessary and sufficient conditions so that the measurement that results in an equal probability of an inconclusive result for each one of the quantum states is optimal. We refer to this measurement as the equal-probability measurement (EPM). We then show that for any state set, the prior probabilities of the states can be chosen such that the EPM is optimal. Finally, we consider state sets with strong symmetry properties and equal prior probabilities for which the EPM is optimal. We first consider geometrically uniform (GU) state sets that are defined over a group of unitary matrices and are generated by a single generating vector. We then consider compound GU state sets which are generated by a group of unitary matrices using multiple generating vectors, where the generating vectors satisfy a certain (weighted) norm constraint.

We introduce a new class of finite-dimensional frames with strong symmetry properties, called geometrically uniform (GU) frames, that are defined over a finite Abelian group of unitary matrices and are generated by a single generating vector. The notion of GU frames is then extended to compound GU (CGU) frames which are generated by a finite Abelian group of unitary matrices using multiple generating vectors. The dual frame vectors and canonical tight frame vectors associated with GU frames are shown to be GU and, therefore, also generated by a single generating vector, which can be computed very efficiently using a Fourier transform (FT) defined over the generating group of the frame. Similarly, the dual frame vectors and canonical tight frame vectors associated with CGU frames are shown to be CGU. The impact of removing single or multiple elements from a GU frame is considered. A systematic method for constructing optimal GU frames from a given set of frame vectors that are not GU is also developed. Finally, the Euclidean distance properties of GU frames are discussed and conditions are derived on the Abelian group of unitary matrices to yield GU frames with strictly positive distance spectrum irrespective of the generating vector.

We propose a new linear multiuser receiver for synchronous code-division multiple-access (CDMA) systems, referred to as the orthogonal multiuser (OMU) receiver. Unlike the linear minimum mean-squared error (MMSE) receiver, the OMU receiver depends only on the signature vectors and does not require knowledge of the received amplitudes or the channel signal-to-noise ratio (SNR). Several equivalent representations of the receiver are developed with different implications in terms of implementation. In the first, the receiver consists of a decorrelator demodulator followed by an optimal whitening transformation on a space formed by the signatures. In the second, the receiver consists of a bank of correlators with correlating vectors that are projections of a set of orthogonal vectors, and are closest in a least squares sense to the decorrelator vectors and also closest in a least squares sense to the signature vectors. In the third, the receiver consists of a single-user matched filter (MF) followed by an optimal whitening transformation on a space formed by the signatures. We derive exact and approximate expressions for the probability of bit error, as well as the asymptotic signal-to-interference+noise ratio (SINR) in the large system limit. The analysis suggests that over a wide range of channel parameters the OMU receiver can outperform both the decorrelator and the single-user MF and perform similarly to the linear MMSE receiver, despite not knowing the channel parameters.

We derive the asymptotic signal-to-interference ratio (SIR) of the decorrelator in the large system limit, both for the case in which the number of users exceeds the spreading gain and for the case in which the number of users is less than the spreading gain. We show that, contrary to what is claimed by Tse and Hardy (see ibid., vol.45, p.641-57, Mar. 1999) and by Tse and Zeitouni (see ibid., vol.46, p.171-188, Jan. 2000) when the number of users exceeds the spreading gain and the decorrelator is defined in terms of the Moore-Penrose pseudoinverse, the SIR does not converge to zero.

We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing among a collection of quantum states, represented by a set of density operators. We show that the design of the optimal detector can be formulated as a semidefinite programming problem. Based on this formulation, we derive a set of necessary and sufficient conditions for an optimal quantum measurement. We then show that the optimal measurement can be found by solving a standard (convex) semidefinite program. By exploiting the many well-known algorithms for solving semidefinite programs, which are guaranteed to converge to the global optimum, the optimal measurement can be computed very efficiently in polynomial time within any desired accuracy. Using the semidefinite programming formulation, we also show that the rank of each optimal measurement operator is no larger than the rank of the corresponding density operator. In particular, if the quantum state ensemble is a pure-state ensemble consisting of (not necessarily independent) rank-one density operators, then we show that the optimal measurement is a pure-state measurement consisting of rank-one measurement operators.

This correspondence develops a linear whitening transformation that minimizes the mean-squared error (MSE) between the original and whitened data, i.e.,one that results in a white output that is as close as possible to the input, in an MSE sense. When the covariance matrix of the data is not invertible, the whitening transformation is designed to optimally whiten the data on a subspace in which it is contained. The optimal whitening transformation is developed both for the case of finite-length data vectors and infinite-length signals.

Tight frames and rank-one quantum measurements are shown to be intimately related. In fact, the family of normalized tight frames for the space in which a quantum-mechanical system lies is precisely the family of rank-one generalized quantum measurements on that space. Using this relationship, frame-theoretical analogs of various quantum-mechanical concepts and results are developed. The analog of a least-squares quantum measurement is a tight frame that is closest in a least-squares sense to a given set of vectors. The least-squares tight frame is found for both the case in which the scaling of the frame is specified (constrained least-squares frame (CLSF)) and the case in which the scaling is chosen to minimize the least-squares error (unconstrained least-squares frame (ULSF)). The well-known canonical frame is shown to be proportional to the ULSF and to coincide with the CLSF with a certain scaling.

We consider the generic problem of detecting a transmitted signal when one of M known signals is transmitted. Instead of using a classical matched filter (MF) detector, matched to the transmitted signals, we propose using an orthogonal matched filter (OMF) detector, which is matched to a set of orthogonal signals that are closest in a least-squares sense to the transmitted signals. We show that this approach is equivalent to optimally whitening the output of the MF demodulator, and then basing the detection on the whitened output. We provide simulation results which suggest that, in many cases, the OMF detector outperforms the MF detector.

We consider the problem of constructing measurements optimized to distinguish between a collection of possibly nonorthogonal quantum states. We consider a collection of pure states and seek a positive operator-valued measure (POVM) consisting of rank-one operators with measurement vectors closest in squared norm to the given states. We compare our results to previous measurements suggested by Peres and Wootters (1991) and Hausladen et al. (1996), where we refer to the latter as the square-root measurement (SRM). We obtain a new characterization of the SRM, and prove that it is optimal in a least-squares sense. In addition, we show that for a geometrically uniform state set the SRM minimizes the probability of a detection error. This generalizes a similar result of Ban et al. (see Int. J. Theor. Phys., vol.36, p.1269-88, 1997).

This paper introduces a filter bank interpretation of various sampling strategies, which leads to efficient interpolation and reconstruction methods. An identity, referred to as the interpolation identity, is used to obtain particularly efficient discrete-time systems for interpolation to uniform Nyquist samples, either for further processing in that form or for conversion to continuous-time. The interpolation identity also leads to a new class of sampling theorems including an extension of Papoulis' (1997) generalized sampling expansion.