Md Kowsher, Tara Esmaeilbeig, Chun-Nam Yu, Chen Chen, Mojtaba Soltanalian, Niloofar Yousefi. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2025.

Md Kowsher, Nusrat Jahan Prottasha, Prakash Bhat, Chun-Nam Yu, Mojtaba Soltanalian, Ivan Garibay, Ozlem Garibay, Chen Chen, Niloofar Yousefi. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2025.

This paper investigates the effects of coarse quantization with mixed precision on measurements obtained from sparse linear arrays, synthesized by a collaborative automotive radar sensing strategy. The mixed quantization precision significantly reduces the data amount that needs to be shared from radar nodes to the fusion center for coherent processing. We utilize the low-rank properties inherent in the constructed Hankel matrix of the mixed-precision array, to recover azimuth angles from quantized measurements. Our proposed approach addresses the challenge of mixed-quantized Hankel matrix completion, allowing for accurate estimation of the azimuth angles of interest. To evaluate the recovery performance of the proposed scheme, we establish a quasi-isometric embedding with a high probability for mixed-precision quantization. The effectiveness of our proposed scheme is demonstrated through numerical results, highlighting successful reconstruction.

Recently, one-bit modulo sampling, also known as unlimited one-bit (UNO), has been proposed as a bridge between modulo sampling and coarse quantization. This approach successfully combines the benefits of both techniques by providing efficient, low-cost quantization for modulo sampling while also offering a natural method for designing dithers that are uniformly distributed across the signal’s dynamic range (DR). However, the scheme faces challenges due to the need for multiple dithering sequences, which complicates their generation and implementation. In this paper, we address this issue by applying quantization to the discrete cosine transform (DCT) coefficients of the modulo samples rather than to the samples themselves. This allows us to achieve successful signal reconstruction using only a single dithering sequence, as demonstrated through numerical results.

Parameter-Efficient Fine-Tuning (PEFT) is a popular class of techniques that strive to adapt large models in a scalable and resource-efficient manner. Yet, the mechanisms underlying their training performance and generalization remain underexplored. In this paper, we provide several insights into such fine-tuning through the lens of linearization. Fine-tuned models are often implicitly encouraged to remain close to the pretrained model. By making this explicit, using an $\ell_2$-distance inductive bias in parameter space, we show that fine-tuning dynamics become equivalent to learning with the positive-definite neural tangent kernel (NTK). We specifically analyze how close the fully linear and the linearized fine-tuning optimizations are, based on the strength of the regularization. This allows us to be pragmatic about how good a model linearization is when fine-tuning large language models (LLMs). When linearization is a good model, our findings reveal a strong correlation between the eigenvalue spectrum of the NTK and the performance of model adaptation. Motivated by this, we give spectral perturbation bounds on the NTK induced by the choice of layers selected for fine-tuning. We empirically validate our theory on Low Rank Adaptation (LoRA) on LLMs. These insights not only characterize fine-tuning but also have the potential to enhance PEFT techniques, paving the way to better informed and more nimble adaptation in LLMs.

Reconfigurable intelligent surfaces (RIS) offer unprecedented flexibility for smart wireless channels. Recent research shows that RIS platforms enhance signal quality, coverage, and link capacity in integrated sensing and communication (ISAC) systems. This paper explores the use of fully-connected beyond diagonal RIS (BD-RIS) in ISAC. BD-RIS provides additional degrees of freedom by allowing non-zero off-diagonal elements in the scattering matrix, enhancing functionality and performance. We aim to maximize the weighted sum of the signal-to-noise ratio (SNR) at both the radar receiver and communication users using BD-RIS. Numerical results demonstrate the advantages of BD-RIS in ISAC, significantly improving SNR for both radar and communication users.

In this study, we develop a holistic framework for space-time adaptive processing (STAP) in connected and automated vehicle (CAV) radar systems. We investigate a CAV system consisting of multiple vehicles that transmit frequency-modulated continuous-waveforms (FMCW), thereby functioning as a multistatic radar. Direct application of STAP in a network of radar systems such as in a CAV may lead to excess interference. We exploit time division multiplexing (TDM) to perform transmitter scheduling over FMCW pulses to achieve high detection performance. The TDM design problem is formulated as a quadratic assignment problem which is tackled by power method-like iterations and applying the Hungarian algorithm for linear assignment in each iteration. Numerical experiments confirm that the optimized TDM is successful in enhancing the target detection performance.

We explore the impact of coarse quantization on low-rank matrix sensing in the extreme scenario of dithered one-bit sampling, where the high-resolution measurements are compared with random time-varying threshold levels. To recover the low-rank matrix of interest from the highly-quantized collected data, we offer an enhanced randomized Kaczmarz algorithm that efficiently solves the emerging highly-overdetermined feasibility problem. Additionally, we provide theoretical guarantees in terms of the convergence and sample size requirements. Our numerical results demonstrate the effectiveness of the proposed methodology.

One-bit quantization with time-varying sampling thresholds (also known as random dithering) has recently found significant utilization potential in statistical signal processing applications due to its relatively low power consumption and low implementation cost. In addition to such advantages, an attractive feature of one-bit analog-to-digital converters (ADCs) is their superior sampling rates as compared to their conventional multi-bit counterparts. This characteristic endows one-bit signal processing frameworks with what one may refer to assample abundance. We show that sample abundance plays a pivotal role in many signal recovery and optimization problems that are formulated as (possibly non-convex) quadratic programs with linear feasibility constraints. Of particular interest to our work are low-rank matrix recovery and compressed sensing applications that take advantage of one-bit quantization. We demonstrate that the sample abundance paradigm allows for the transformation of such problems to merely linear feasibility problems by forming large-scale overdetermined linear systems—thus removing the need for handling costly optimization constraints and objectives. To make the proposed computational cost savings achievable, we offer enhanced randomized Kaczmarz algorithms to solve these highly overdetermined feasibility problems and provide theoretical guarantees in terms of their convergence, sample size requirements, and overall performance. Several numerical results are presented to illustrate the effectiveness of the proposed methodologies.

To facilitate target localization, active radar signals or sequences are designed to have low auto-correlation. This goal is typically achieved by the minimization of the auto-correlation integrated side-lobe level (ISL) metric, or the weighted more general version of ISL, known as the WISL metric. In this work, we propose an efficient approach to WISL minimization for unimodular sequence design that takes advantage of the low-cost and easily implementable power method-like iterations. Several numerical results are presented to illustrate the effectiveness of the proposed method.

Intelligent reflecting surface (IRS) technology has recently attracted a significant interest in non-light-of-sight radar remote sensing. Prior works have largely focused on designing single IRS beamformers for this problem. For the first time in the literature, this paper considers multi-IRS-aided multiple-input multiple-output (MIMO) radar and jointly designs the transmit unimodular waveforms and optimal IRS beamformers. To this end, we derive the Cramér-Rao lower bound (CRLB) of target direction-of-arrival (DoA) as a performance metric. Unimodular transmit sequences are the preferred waveforms from a hardware perspective. We show that, through suitable transformations, the joint design problem can be reformulated as two uni-modular quadratic programs (UQP). To deal with the NP-hard nature of both UQPs, we propose unimodular waveform and beamforming design for multi-IRS radar (UBeR) algorithm that takes advantage of the low-cost power method-like iterations. Numerical experiments illustrate that the MIMO waveforms and phase shifts obtained from our UBeR algorithm are effective in improving the CRLB of DoA estimation.

One-bit quantization with time-varying sampling thresholds has recently found significant utilization potential in statistical signal processing applications due to its relatively low power consumption and low implementation cost. In addition to such advantages, an attractive feature of one-bit analog-to-digital converters (ADCs) is their superior sampling rates as compared to their conventional multi-bit counterparts. This characteristic endows one-bit signal processing frameworks with what we refer to as sample abundance. On the other hand, many signal recovery and optimization problems are formulated as (possibly non-convex) quadratic programs with linear feasibility constraints in the one-bit sampling regime. We demonstrate, with a particular focus on quadratic compressed sensing, that the sample abundance paradigm allows for the transformation of such quadratic problems to merely a linear feasibility problem by forming a large-scale overdetermined linear system; thus removing the need for costly optimization constraints and objectives. To efficiently tackle the emerging overdetermined linear feasibility problem, we further propose an enhanced randomized Kaczmarz algorithm, called Block SKM. Several numerical results are presented to illustrate the effectiveness of the proposed methodologies.

In this work, we study a deep learning-based initialization approach for unimodular quadratic programs (UQPs), that are concerned with the maximization of a quadratic form over a set of complex unimodular vectors. UQPs have shown prevalent presence in many signal processing and design problems such as in wireless communications and active sensing. Stemming from their NP-hard nature, prior works on UQPs have focused on proposing approximate solutions that generally traded-off speed for obtaining theoretically sound approximations. With the aim of improving the computational efficiency of existing UQP solvers and equipped with highly-scalable deep learning frameworks as a backbone, we propose a novel hybrid solver, which we refer to as Deep-INIT. The proposed data-driven initialization approach makes use of deep learning to automatically learn "good" initializations for an underlying model-based solver called MERIT, that provides strong optimality guarantees for UQP solutions; thereby, speeding up an existing optimality-certificate producing solver for UQPs. In fact, apart from achieving a significant speed-up over the underlying UQP solver, a fundamental characteristic of Deep-INIT is that it preserves the guarantees that emerge from the model-based solver. Our numerical results reaffirm the speedup potential that Deep-INIT offers.

A longstanding problem in statistics pertains to the estimation of probability density functions of continuous random variables from a finite set of their samples. In this paper, we propose a new parametric probability density function estimator based on convex programming. Our formulation decomposes the unknown distribution as a Gaussian penalty function plus an error function, which is then expanded by multi-scale wavelet functions (specifically frames) such as B-Spline and Mexican Hat wavelets. To recover the wavelet coefficients in the error function, a convex quadratic program is formulated which takes into account the positivity of the probability density function-through a linear constraint. The proposed decomposition model is shown to facilitate an accurate estimation of the probability density functions of interest.

Understanding the mathematics and the innate machinery of sparsity measures is instrumental in the proper usage of such information measures in various application arenas, ranging from information collection and sensing, to communications and signal processing. In this paper, the structure of sparsity measures is investigated. Specifically, it is shown that sparsity measures satisfying proper sparsity axioms may only be constructed by vector norms. Moreover, the asymptotic behavior of sparsity measures is studied. Owing to their mathematical structure, our numerical results illustrate a convergence of sparsity measures, as the number of input samples grows large.

Intelligent reflecting surface (IRS) is a rapidly emerging paradigm to enable non-line-of-sight (NLoS) wireless transmission. In this paper, we focus on IRS-aided radar estimation performance of a moving hidden or NLoS target. Unlike prior works that employ a single IRS, we investigate this problem using multiple IRS platforms and assess the estimation performance by deriving the associated Cramér-Rao lower bound (CRLB). We then design Doppler-aware IRS phase shifts by minimizing the scalar A-optimality measure of the joint parameter CRLB matrix. The resulting optimization problem is non-convex, and is thus tackled via an alternating optimization framework. Numerical results demonstrate that the deployment of multiple IRS platforms with our proposed optimized phase shifts leads to a higher estimation accuracy compared to non-IRS and single-IRS alternatives.

One-bit compressive sensing is concerned with the accurate recovery of an underlying sparse signal of interest from its one-bit noisy measurements. The conventional signal recovery approaches for this problem are mainly developed based on the assumption that an exact knowledge of the sensing matrix is available. In this work, however, we present a novel data-driven and model-based methodology that achievesblindrecovery; i.e., signal recovery without requiring the knowledge of the sensing matrix. To this end, we make use of the deep unfolding technique and develop a model-driven deep neural architecture which is designed for this specific task. The proposed deep architecture is able to learn an alternative sensing matrix by taking advantage of the underlying unfolded algorithm such that the resultinglearnedrecovery algorithm can accurately and quickly (in terms of the number of iterations) recover the underlying compressed signal of interest from its one-bit noisy measurements. In addition, due to the incorporation of the domain knowledge and the mathematical model of the system into the proposed deep architecture, the resulting network benefits from enhanced interpretability, has a very small number of trainable parameters, and requires very small number of training samples, as compared to the commonly used black-box deep neural network alternatives for the problem at hand.

The earlier works in the context of low-rank-sparse-decomposition (LRSD)-driven stationary synthetic aperture radar (SAR) imaging have shown significant improvement in the reconstruction–decomposition process. Neither of the proposed frameworks, however, can achieve satisfactory performance when facing a platform residual phase error (PRPE) arising from the instability of airborne platforms. More importantly, in spite of the significance of real-time processing requirements in remote sensing applications, these prior works have only focused on enhancing the quality of the formed image, not reducing the computational burden. To address these two concerns, this article presents a fast and unified joint SAR imaging framework where the dominant sparse objects and low-rank features of the image background are decomposed and enhanced through a robust LRSD. In particular, our unified algorithm circumvents the tedious task of computing the inverse of large matrices for image formation and takes advantage of the recent advances in constrained quadratic programming to handle the unimodular constraint imposed due to the PRPE. Furthermore, we extend our approach to ISAR autofocusing and imaging. Specifically, due to the intrinsic sparsity of ISAR images, the LRSD framework is essentially tasked with the recovery of a sparse image. Several experiments based on synthetic and real data are presented to validate the superiority of the proposed method in terms of imaging quality and computational cost compared to the state-of-the-art methods.

One-bit quantization has attracted considerable attention in signal processing for communications and sensing. The arcsine law is a useful relation often used to estimate the normalized covariance matrix of zero-mean stationary input signals when they are sampled by one-bit analog-to-digital converters (ADCs)—practically comparing the signals with a given threshold level. This relation, however, only considers a zero threshold which can cause a remarkable information loss. For the first time in the literature, this paper introduces an approach to extending the arcsine law to the case where one-bit ADCs apply time-varying thresholds. In particular, the proposed method is shown to accurately recover the variance and autocorrelation of the stationary signals of interest.

Co-array-based Direction of Arrival (DoA) estimation using Sparse Linear Arrays (SLAs) has recently gained considerable attention in array processing thanks to its capability of providing enhanced degrees of freedom for DoAs that can be resolved. Additionally, deployment of one-bit Analog-to-Digital Converters (ADCs) has become an important topic in array processing, as it offers both a low-cost and a low-complexity implementation. Although the problem of DoA estimation form one-bit SLA measurements has been studied in some prior works, its analytical performance has not yet been investigated and characterized. In this paper, to provide valuable insights into the performance of DoA estimation from one-bit SLA measurements, we derive an asymptotic closed-form expression for the performance of One-Bit Co-Array-Based MUSIC (OBCAB-MUSIC). Further, numerical simulations are provided to validate the asymptotic closed-form expression for the performance of OBCAB-MUSIC and to show an interesting use case of it in evaluating the resolution of OBCAB-MUSIC.

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.

This letter studies the problem of Direction of Arrival (DoA) estimation from low-resolution few-bit quantized data collected by Sparse Linear Array (SLA). In such cases, contrary to the one-bit quantization case, the well known arcsine law cannot be employed to estimate the covaraince matrix of unquantized array data. Instead, we develop a novel optimization-based framework for retrieving the covaraince matrix of unquantized array data from low-resolution few-bit measurements. The MUSIC algorithm is then applied to an augmented version of the recovered covariance matrix to find the source DoAs. The simulation results show that increasing the sampling resolution to 2 or 4 bits per samples could significantly increase the DoA estimation performance compared to the one-bit sampling regime while the power consumption and implementation costs is still much lower in comparison to the high-resolution sampling implementations.

Parameter estimation from noisy and one-bit quantized data has become an important topic in signal processing, as it offers low cost and low complexity in the implementation. On the other hand, Direction-of-Arrival (DoA) estimation using Sparse Linear Arrays (SLAs) has recently gained considerable interest in array processing due to their attractive capability of providing enhanced degrees of freedom. In this paper, the problem of DoA estimation from one-bit measurements received by an SLA is considered and a novel framework for solving this problem is proposed. The proposed approach first provides an estimate of the received signal covariance matrix through minimization of a constrained weighted least-squares criterion. Then, MUSIC is applied to the spatially smoothed version of the estimated covariance matrix to find the DoAs of interest. Several numerical results are provided to demonstrate the superiority of the proposed approach over its counterpart already propounded in the literature.

The lack of interpretability in current deep learning models causes serious concerns as they are extensively used for various life-critical applications. Hence, it is of paramount importance to develop interpretable deep learning models. In this paper, we consider the problem of blind deconvolution and propose a novel model-aware deep architecture that allows for the recovery of both the blur kernel and the sharp image from the blurred image. In particular, we propose the Deep Unfolded Richardson-Lucy (Deep-URL) framework - an interpretable deep-learning architecture that can be seen as an amalgamation of classical estimation technique and deep neural network, and consequently leads to improved performance. Our numerical investigations demonstrate significant improvement compared to state-of-the-art algorithms.

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.

In this paper, the receive spatial modulation (RSM) scheme is studied in the downlink of the multi-cell multi-user systems, assuming that the base station (BS) is equipped with a large number of antennas and serves a large number of multi-antenna users, while the user-antenna ratio is bounded. The system model is practical and applicable in a comprehensive manner, accounting for channel estimation, spatially correlated channels, pilot contamination, and path loss. Combining the concepts of RSM and massive multiple-input multiple-output (MIMO), the spectral efficiency of linear preprocessing zero-forcing (ZF) and regularized ZF (RZF) methods is studied by approximating the probability of antenna detection and deriving a lower bound for the spatial-domain mutual information. With the aid of the large-system analysis, the deterministic equivalent expressions are provided for the achievable rates that are asymptotically exact. The Monte Carlo simulations validate this claim and show that for limited dimensions, the proposed deterministic equivalents yield accurate approximations, even for strongly correlated channels. The results further show that in comparison with the conventional massive MIMO systems with single-antenna users, equipping each user with multiple antennas and applying the RSM scheme enhances the spectral efficiency when each cell is not heavily loaded.

In this paper, we study the problem of low-rank matrix recovery based on the information obtained by comparing matrix entries (where each comparison is represented by one-bit) and not the entries themselves. This is highly relevant in the context of recommendation systems, due to the fact that users (particularly those less familiar with the rating system) are more comfortable with comparing products than giving exact ratings. We investigate when and how a low-rank matrix (such as a rating matrix in the recommendation system) can be efficiently recovered using one-bit data, particularly by establishing the limitations of such a recovery. We devise a computational approach based on matrix factorization to accomplish the reconstruction task. The numerical examples exhibit the significant potential of the proposed approach in low-rank matrix recovery from one-bit comparison information.

Sequences with good correlation and distribution properties play a central role in various areas of signal processing. In this paper, we propose an efficient computational framework for designing sequences with two key properties: (i) an impulse-like auto-correlation, and (ii) a probability distribution of sequence entries which is uniform in nature; although the results can be easily extended to an arbitrary distribution. The proposed method is based on utilizing the Fast Fourier Transform (FFT) operations, and thus can generate very long sequences in small time frames. Several numerical examples are provided to exhibit the performance of the suggested construction framework.

In this paper, we present a consensus-based framework for decentralized estimation of deterministic parameters in wireless sensor networks (WSNs). In particular, we propose an optimization algorithm to design (possibly complex) sensor gains in order to achieve an estimate of the parameter of interest that is as accurate as possible. The proposed design algorithm employs a cyclic approach capable of handling various sensor gain constraints. In addition, each iteration of the proposed design framework is comprised of the Gram-Schmidt process and power-method like iterations, and as a result, enjoys a low-computational cost.

Big data analysis is a fundamental research topic with extensive technical obstacles yet to be overcome. Graph clustering has shown promise in addressing big data challenges by categorizing otherwise unlabeled data-thus giving them meaning. In this paper, we propose a set of non-convex programs, generally referred to as Hard and Soft Clustering programs, that rely on matrix factorization formulations for enhanced computational performance. Based on such formulations, we devise clustering algorithms that allow for large data analysis in a more efficient manner than traditional convex clustering techniques. Numerical results confirm the usefulness of the proposed algorithms for clustering purposes and reveal their potential for usage in big data applications.

Restoration of shredded signals remains a relevant and significant challenge in archaeological and forensic efforts. In this work, we present a novel approach for reconstruction of shredded signals (including text documents and images) within a context of general multidimensional sparse signals. To this end, we present a generic efficient non-convex optimization method that employs iterative sparsity enhancement of the observed signal. A key component of the design follows from the observation that most natural signals are sparse in a given representation domain. Computational results portrait the potential of our suggested method in several practical cases of signal reconstruction.

In this paper, we propose a new approach to the design of training sequences that can be used for an accurate estimation of multi-input multi-output channels. The proposed method is particularly instrumental in training sequence designs that deal with three key challenges: 1) arbitrary channel and noise statistics that do not follow specific models, 2) limitations on the properties of the transmit signals, including total power, per-antenna power, having a constant-modulus, discrete-phase, or low peak-to-average-power ratio, and 3) signal design for large-scale or massive antenna arrays. Several numerical examples are provided to examine the proposed method.

In this work, a directional modulation-based technique is devised to enhance the security of a multi-antenna wireless communication system employing M-PSK modulation to convey information. The directional modulation method operates by steering the array beam in such a way that the phase of the received signal at the receiver matches that of the intended M-PSK symbol. Due to the difference between the channels of the legitimate receiver and the eavesdropper, the signals received by the eavesdropper generally encompass a phase component different than the actual symbols. As a result, the transceiver which employs directional modulation can impose a high symbol error rate on the eavesdropper without requiring to know the eavesdropper's channel. The optimal directional modulation beamformer is designed to minimize the consumed power subject to satisfying a specific resulting phase and minimal signal amplitude at each antenna of the legitimate receiver. The simulation results show that the directional modulation results in a much higher symbol error rate at the eavesdropper compared to the conventional benchmark scheme, i.e., zero-forcing precoding at the transmitter.

We consider the problem of sum-rate maximization in massive MIMO two-way relay networks with multiple (communication) operators employing the amplify-and-forward (AF) protocol. The aim is to design the relay amplification matrix (i.e., the relay beamformer) to maximize the achievable communication sum-rate through the relay. The design problem for the case of single-antenna users can be cast as a non-convex optimization problem, which in general, belongs to a class of NP-hard problems. We devise a method based on the minorization-maximization technique to obtain quality solutions to the problem. Each iteration of the proposed method consists of solving a strictly convex unconstrained quadratic program; this task can be done quite efficiently such that the suggested algorithm can handle the beamformer design for relays with up to ∼ 70 antennas within a few minutes on an ordinary PC. Such a performance lays the ground for the proposed method to be employed in massive MIMO scenarios.

In this paper, we present an optimization framework for designing precoding (a.k.a. beamforming) signals that are instrumental in achieving a fair user performance through the networks. The precoding design problem in such scenarios can typically be formulated as a non-convex max-min fractional quadratic program. Using a penalized version of the original design problem, we derive a simplified quadratic reformulation of the problem in terms of the signal (to be designed). Each iteration of the proposed design framework consists of a combination of power method-like iterations and the Gram-Schmidt process, and as a result, enjoys a low computational cost. Moreover, the suggested approach can handle various types of signal constraints such as total-power, per-antenna power, unimodularity, or discrete-phase requirements - an advantage which is not shared by other existing approaches in the literature.

In this paper, we consider the cognitive satellite uplink where satellite terminals reuse frequency bands of Fixed-Service (FS) terrestrial microwave links which are the incumbent users in the Ka 27.5–29.5 GHz band. In this scenario, the transmitted power of the cognitive satellite terminals has to be controlled so as to satisfy the interference constraints imposed by the incumbent FS receivers. We investigate and analyze a set of optimization frameworks for the power and rate allocation problem in the considered cognitive satellite scenario. The main objective is to shed some light on this rather unexplored scenario and demonstrate feasibility of the terrestrial-satellite co-existence. In particular, we formulate a multi-objective optimization problem where the rates of the satellite terminals form the objective vector and derive a general iterative framework which provides a Pareto-optimal solution. Next, we transform the multi-objective optimization problem into different single-objective optimization problems, focusing on popular figures of merit such as the sum-rate or the rate fairness. Supporting results based on numerical simulations are provided which compare the different proposed approaches.

We consider the problem of sum-rate maximization in multiple-input multiple-output (MIMO) amplify-and-forward relay networks with multi-operator. The aim is to design the MIMO relay amplification matrix (i.e., the relay beamformer) to maximize the achievable communication sum rate through the relay. The design problem for the case of single-antenna users can be cast as a non-convex optimization problem, which, in general, belongs to a class of NP-hard problems. We devise a method based on the minorization–maximization technique to obtain quality solutions to the problem. Each iteration of the proposed method consists of solving a strictly convex unconstrained quadratic program. This task can be done quite efficiently, such that the suggested algorithm can handle the beamformer design for relays with up to$\sim 70$antennas within a few minutes on an ordinary personal computer. Such a performance lays the ground for the proposed method to be employed in medium-scale (or lower regime massive) MIMO scenarios.

As a widely used tool in tackling general quadratic optimization problems, semidefinite relaxation (SDR) promises both a polynomial-time complexity and an a priori known sub-optimality guarantee for its approximate solutions. While attempts at improving the guarantees of SDR in a general sense have proven largely unsuccessful, it has been widely observed that the quality of solutions obtained by SDR is usually considerably better than the provided guarantees. In this paper, we propose a novel methodology that paves the way for obtaining improved data-dependent guarantees in a computational way. The derivations are dedicated to a specific quadratic optimization problem (called m-QP) which lies at the core of many communication and active sensing schemes; however, the ideas may be generalized to other quadratic optimization problems. The new guarantees are particularly useful in accuracy sensitive applications, including decision-making scenarios.

Visual motion perception in biological vision systems is typically modeled via a set of elementary motion detectors (EMDs) forming a spatially distributed network. This paper addresses the problem of estimating the weights of such an EMD construct from a linear combination of their output signals. This challenge arises in e.g. mathematical modeling of animal motion perception. In particular, the spatial excitation properties of sinusoidal gratings are important since these basis signals are typically utilized as visual stimuli in biology. It is demonstrated that one cannot uniquely estimate the weights of more than three contributing EMDs with a single frequency sinusoidal grating as the visual stimulus. However, a higher spatial excitation order can be obtained with multi-frequency sinusoidal grating stimuli. Two approaches to the design of stimuli with a given spatial excitation order are presented. Several numerical examples are provided to examine the performance of the proposed stimuli design methods.

In this paper, we study the problem of unimodular code design to improve the detection performance of statistical multiple-input multiple-output (MIMO) radar systems. To this end, we consider a system transmitting arbitrary unimodular signals and a discrete-time formulation of the problem. Due to the complicated form of the performance metric of the optimal detector, we resort to the Bhattacharyya distance for code design. We devise a novel method based on the majorization of matrix functions to obtain solutions to the constrained design problem. Simulation results show the effectiveness of the proposed method.

In this paper, we study the joint design of Doppler robust transmit sequence and receive filter to improve the performance of an active sensing system dealing with signal-dependent interference. The signal-to-interference-plus-noise ratio (SINR) of the filter output is considered as the performance measure of the system. The design problem is cast as a max-min optimization problem to robustify the system SINR with respect to the unknown Doppler shifts of the targets. To tackle the design problem, we devise a novel method to obtain optimized pairs of transmit sequence and receive filter sharing the desired robustness property.

In this paper, we study the problem of approaching peak periodic or aperiodic correlation bounds for complex-valued sets of sequences. In particular, novel algorithms based on alternating projections are devised to approach a given peak periodic or aperiodic correlation bound. Several numerical examples are presented to assess the tightness of the known correlation bounds as well as to illustrate the effectiveness of the proposed methods for meeting these bounds.

The NP-hard problem of optimizing a quadratic form over the unimodular vector set arises in radar code design scenarios as well as other active sensing and communication applications. To tackle this problem, a monotonically error-bound improving technique (MERIT) is proposed to obtain the global optimum or a local optimum of UQP with good sub-optimality guarantees. The provided sub-optimality guarantees are case-dependent and may outperform the π/4 approximation guarantee of semi-definite relaxation.

The Randomized Kaczmarz Algorithm is a randomized method which aims at solving a consistent system of over determined linear equations. This letter discusses how to find an optimized randomization scheme for this algorithm, which is related to the question raised by . Illustrative experiments are conducted to support the findings.

Due to its long-standing importance, the problem of designing the receive filter and transmit sequence for clutter/interference rejection in active sensing has been studied widely in the last decades. In this letter, we propose a cyclic optimization of the transmit sequence and the receive filter. The proposed approach can handle arbitrary peak-to-average-power ratio (PAR) constraints on the transmit sequence, and can be used for large dimension designs (with ~ 103variables) even on an ordinary PC.

In this paper, Perfect Root-of-Unity Codes (PRUCs) with entries in αp= {x ∈ C | xp= 1} where p is a prime are studied. A lower bound on the number of distinct phases in PRUCs over αpis derived. We show that PRUCs of length L ≥ p(p - 1) must use all phases in αp. It is also shown that if there exists a PRUC of length L over αpthen p divides L. We derive equations (which we call principal equations) that give possible lengths of a PRUC over αptogether with their phase distribution. Using these equations, we prove for example that the length of a 3-phase perfect code must be of the form L = 1/4 (9h12+ 3h22) for (h1, h2) ∈ Z2and we also give the exact number of occurrences of each element from α3in the code. Finally, all possible lengths (≤100) of PRUCs over α5and α7together with their phase distributions are provided.