Millimeter wave (mmWave) systems, currently employed in 5G and IEEE 802.11ad/ay devices, enable high data rates through wide bandwidths and directional communication. However, high carrier frequencies used in these systems result in a higher phase noise than lower frequency systems. This paper investigates the problem of spatial channel estimation in the presence of severe phase noise, which manifests as partially coherent phase perturbations in the observed channel measurements. In this model, phase noise remains relatively constant within a packet but varies substantially across packets. Under such partially coherent phase noise, we first develop two computationally efficient on-grid algorithms to estimate narrowband mmWave channels: Partially Coherent Matching Pursuit (PCMP) and Enhanced Partially Coherent Matching Pursuit (EPCMP), assuming a known channel sparsity. Both algorithms exploit the sparse structure in mmWave channels, enabling a significant reduction in training overhead while achieving good estimation performance. The main difference between PCMP and EPCMP is how the sparse channel support is identified. The EPCMP algorithm can achieve better estimation performance at the cost of increased computational complexity compared to the PCMP algorithm. We then relax the known-sparsity assumption, adapt the proposed algorithms accordingly, and further extend them to the wideband case for an unknown sparsity. Additionally, we derive sufficient conditions to recover a support element with proposed algorithms. Simulation results demonstrate the advantages of our methods over comparable channel estimation benchmarks.

Radar is a key technology in automotive driving for target detection and perception. In this work, we leverage prior environmental information in the form of occupancy maps to design space-time codes for a fully digital MIMO radar. We transform this design problem into the optimization of spatial beamforming gains and time-domain codes. The beamforming gains are optimized to enhance the strength of returns from cells associated with a higher uncertainty of occupancy. The time-domain codes are optimized to minimize the correlation between returns of targets within the drivable space. We validate our method on the nuScenes dataset to show that the designed space-time codes achieve higher detection rates than designs that do not rely on prior information from occupancy maps.

We study the recovery of a sparse vector with a Kronecker structure from an underdetermined linear system with a Kronecker-structured dictionary. This problem arises in several applications, such as the channel estimation of an intelligent reflecting surface-aided wireless system. Existing work only exploits the Kronecker structure in support of the sparse vector and solves the entire linear system jointly with high complexity. Instead, we decompose the original sparse recovery problem into multiple independent subproblems and solve them individually. We obtain the sparse vector as the Kronecker product of individual solutions, retaining its Kronecker structure. Besides, the subproblems exhibit reduced effective measurement noise. Our simulations demonstrate that our method has superior estimation accuracy and runtime compared to the existing work. We attribute the low complexity to the reduced dimensionality of the subproblems and improved accuracy to the denoising effect of the decomposition step.

In this work, we study the restricted isometry property (RIP) of Kronecker-structured matrices, formed by the Kronecker product of two factor matrices. Previously, only upper and lower bounds on the restricted isometry constant (RIC) in terms of the RICs of the factor matrices were known. We derive a probabilistic measurement bound for the sth-order RIC. We show that the Kronecker product of two sub-Gaussian matrices satisfies RIP with high probability if the minimum number of rows among two matrices is $\mathcal{O}\left( {s\ln \max \left\{ {{N_1},{N_2}} \right\}} \right)$. Here, s is the sparsity level, and N1and N2are the number of columns in the matrices. We also present improved measurement bounds for the recovery of Kronecker-structured sparse vectors using Kronecker-structured measurement matrices. Finally, our analysis is further extended to the Kronecker product of more than two matrices.

In this paper, we investigate the use of modulo-ADCs in compressed sensing to handle the issue of the limited dynamic range of standard ADCs. The current state-of-the-art algorithm for modulo-compressed sensing uses an ℓ1-norm-based approximation of the sparsity constraint, resulting in a computationally demanding mixed-integer linear optimization. Handling noisy measurements further complicates the problem, requiring mixed-integer quadratic programming, a problem known to be NP-hard. We present an alternative iterative hard-thresholding approach to address this issue. Our solution is computationally simpler and capable of handling noisy measurements. Additionally, we provide theoretical guarantees that the algorithm can successfully recover sparse vectors if the sampling operator satisfies the integer augmented-restricted isometry property, which holds when the number of measurements is sufficiently large.

Estimation problems in wireless sensor networks typically involve gathering and processing data from distributed sensors to infer the state of an environment at the fusion center. However, not all measurements contribute significantly to improving estimation accuracy. The ordered transmission protocol, a promising approach for enhancing energy efficiency in wireless networks, allows for the selection of measurements from different sensors to ensure the desired estimation quality. In this work, we use the idea of ordered transmission to reduce the number of transmissions required for sequential estimation within a network, thereby achieving energy-efficient estimation. We derive a new stopping rule that minimizes the number of transmissions while maintaining estimation accuracy similar to general sequential estimation with unordered transmissions. Moreover, we derive the expected number of transmissions required for both general sequential estimation with unordered transmissions and proposed sequential estimation with ordered transmissions and make a comparison between the two systems. Simulation results indicate that our proposed scheme can efficiently reduce transmissions while still ensuring the quality of estimation.

We consider the problem of jointly estimating the states and sparse inputs of a linear dynamical system using noisy low-dimensional observations. We exploit the underlying sparsity in the inputs using fictitious sparsity-promoting Gaussian priors with unknown variances (as hyperparameters). We develop two Bayesian learning-based techniques to estimate states and inputs: sparse Bayesian learning and variational Bayesian inference. Through numerical simulations, we illustrate that our algorithms outperform the conventional Kalman filtering based algorithm and other state-of-the-art sparsity-driven algorithms, especially in the low-dimensional measurement regime.

Millimeter-wave radar is a common sensor modality used in automotive driving for target detection and perception. These radars can benefit from side information on the environment being sensed, such as lane topologies or data from other sensors. Existing radars do not leverage this information to adapt waveforms or perform prior-aware inference. In this paper, we model the side information as an occupancy map and design transmit beamformers that are customized to the map. Our method maximizes the probability of detection in regions with a higher uncertainty on the presence of a target. Simulation results on the nuScenes dataset show that the designed beamformer achieves substantially higher detection rates than a conventional omnidirectional beamformer for the same transmitted power.

This paper develops a channel estimation technique for millimeter wave (mmWave) communication systems. Our method exploits the sparse structure in mmWave channels for low training overhead and accounts for the phase errors in the channel measurements due to phase noise at the oscillator. Specifically, in IEEE 802.11ad/ay-based mmWave systems, the phase errors within a beam refinement protocol packet are almost the same, while the errors across different packets are substantially different. Consequently, standard sparsity-aware algorithms, which ignore phase errors, fail when channel measurements are acquired over multiple beam refinement protocol packets. We present a novel algorithm called partially coherent matching pursuit for sparse channel estimation under practical phase noise perturbations. Our method iteratively detects the support of sparse signal and employs alternating minimization to jointly estimate the signal and the phase errors. We numerically show that our algorithm can reconstruct the channel accurately at a lower complexity than the benchmarks.

The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters comprise both discrete and continuous variables, making the convergence analysis nontrivial. This paper introduces a set of conditions that ensure the convergence of a specific class of EM algorithms that estimate a mixture of discrete and continuous parameters. Our results offer a new analysis technique for iterative algorithms that solve mixed-integer non-linear optimization problems. As a concrete example, we prove the convergence of an existing EM-based sparse Bayesian learning algorithm that estimates the state of a linear dynamical system with jointly sparse inputs and bursty missing observations. Our results establish that the algorithm converges to the set of stationary points of the maximum likelihood cost with respect to the continuous optimization variables.

This paper presents novel cascaded channel estimation techniques for an intelligent reflecting surface-aided multiple-input multiple-output system. Motivated by the channel angular sparsity at higher frequency bands, the channel estimation problem is formulated as a sparse vector recovery problem with an inherent Kronecker structure. We solve the problem using the sparse Bayesian learning framework which leads to a non-convex optimization problem. We offer two solution techniques to the problem based on alternating minimization and singular value decomposition. Our simulation results illustrate the superior performance of our methods in terms of accuracy and run time compared with the existing works.

We consider a set of data samples such that a fraction of the samples are arbitrary outliers, and the rest are the output samples of a single-layer neural network with rectified linear unit (ReLU) activation. Our goal is to estimate the parameters (weight matrix and bias vector) of the neural network, assuming the bias vector to be non-negative. We estimate the network parameters using the gradient descent algorithm combined with either the median- or trimmed mean-based filters to mitigate the effect of the arbitrary outliers. We then prove that $\tilde{O}\left( \frac{1}{p^2}+\frac{1}{\epsilon^2p}\right)$ samples and $\tilde{O}\left( \frac{d^2}{p^2}+ \frac{d^2}{\epsilon^2p}\right)$ time are sufficient for our algorithm to estimate the neural network parameters within an error of $\epsilon$ when the outlier probability is $1-p$, where $2/3 DOI 10.52202/068431-0796

We address the problem of monitoring a set of binary stochastic processes and generating an alert when the number of anomalies among them exceeds a threshold. For this, the decision-maker selects and probes a subset of the processes to obtain noisy estimates of their states (normal or anomalous). Based on the received observations, the decision-maker first determines whether to declare that the number of anomalies has exceeded the threshold or to continue taking observations. When the decision is to continue, it then decides whether to collect observations at the next time instant or defer it to a later time. If it chooses to collect observations, it further determines the subset of processes to be probed. To devise this three-step sequential decision-making process, we use a Bayesian formulation wherein we learn the posterior probability on the states of the processes. Using the posterior probability, we construct a Markov decision process and solve it using deep actor-critic reinforcement learning. Via numerical experiments, we demonstrate the superior performance of our algorithm compared to the traditional model-based algorithms.

In this paper, we address the problem of one-bit compressed sensing using the data-driven deep learning approach. Our approach uses an untrained neural network to reconstruct sparse vectors from their one-bit measurements. We define a new cost function using the untrained network, which maximizes the consistency between one-bit measurements and the corresponding linear measurements. The resulting optimization problem is solved using the projected gradient descent scheme and the backpropagation method. Our algorithm offers superior empirical performance compared to the existing model-based algorithms. Also, unlike the other deep learning-based algorithms that use learned generative priors, our algorithm does not require a large training set. Further, we empirically show that the proposed algorithm exhibits performance that is comparable to the learned generative network-based method.

In this paper, we address the anomaly detection problem where the objective is to find the anomalous processes among a given set of processes. To this end, the decision-making agent probes a subset of processes at every time instant and obtains a potentially erroneous estimate of the binary variable which indicates whether or not the corresponding process is anomalous. The agent continues to probe the processes until it obtains a sufficient number of measurements to reliably identify the anomalous processes. In this context, we develop a sequential selection algorithm that decides which processes to be probed at every instant to detect the anomalies with an accuracy exceeding a desired value while minimizing the delay in making the decision and the total number of measurements taken. Our algorithm is based on active inference which is a general framework to make sequential decisions in order to maximize the notion of free energy. We define the free energy using the objectives of the selection policy and implement the active inference framework using a deep neural network approximation. Using numerical experiments, we compare our algorithm with the state-of-the-art method based on deep actor-critic reinforcement learning and demonstrate the superior performance of our algorithm.

In this paper, we address the classical problem of one-bit compressed sensing. We present a deep learning based reconstruction algorithm that relies on a generative model. The generator which is a neural network, learns a mapping from a low dimensional space to a higher dimensional set comprising of sparse vectors. This pre-trained generator is used to reconstruct sparse vectors from their one-bit measurements by searching over the range of the generator. Hence, the algorithm presented in this paper provides excellent reconstruction accuracy by accounting for any other possible structure in the signal apart from sparsity. Further, we provide theoretical guarantees on the reconstruction accuracy of the presented algorithm. Using numerical results, we also demonstrate the efficacy of our algorithm compared to other existing algorithms.

In this work, we consider control of linear dynamical systems using sparse inputs. We provide an algorithm for determining a sequence of sparse inputs that will take the system from any given initial state to a desired final state, and stay in that state thereafter. We formulate this as a sparse vector recovery problem and obtain conditions on the sparse recovery algorithm that will enable the state of the system to be within an ε-ball of the desired state. Further, we also give a computationally efficient test that checks whether it is possible to remain in a given desired state using only sparse inputs.

This paper presents a new tomography-based anomaly mapping algorithm for composite structures. The system consists of an array of piezoelectric transducers which sequentially excites the structure and collects the resulting waveform at the remaining transducers. Anomaly indices computed from the sensor waveforms are fed as input to the mapping algorithm. The output of the algorithm is a color map indicating the outline of damage on the structure when present. Unlike prior work on this topic, the algorithm of this paper explicitly accounts for both sparsity and cluster pattern structures that are typical of structural anomalies. Hence, the algorithm of this paper provides excellent reconstruction accuracy by incorporating the available prior information on the anomaly map. Experimental results on a unidirectional composite plate confirms that the algorithm of this paper outperforms two competing methods in terms of reconstruction accuracy.

In this letter, we address the problem of observability of a linear dynamical system from compressive measurements and the knowledge of its external inputs. Observability of a high dimensional system state may require a large number of measurements in general, but we show that if the initial state vector admits a sparse representation, the number of measurements can be significantly reduced by using random projections for obtaining the measurements. We derive guarantees for the observability of the system using tools from probability theory and compressed sensing. Our analysis uses properties of the transfer matrix and random measurement matrices to derive concentration of measure bounds, which lead to sufficient conditions for the restricted isometry property of the observability matrix to hold. Hence, under the derived conditions, the initial state can be recovered by solving a computationally tractable convex optimization problem.

We consider the problem of estimating the intensity map of a spatially random phenomenon over a geographical area observed by a sensor network. The spatial phenomenon of interest is modeled using a Gaussian random field specified by its nonlinear mean and covariance functions. Our proposed algorithm includes two stages: a novel greedy sparse recovery algorithm to estimate the parameters of the mean function, and a spatial interpolation stage using an algorithm called simple kriging. Further, we study the application of the proposed algorithm to radio spectrum cartography, and show that it offers a significant advantage in terms of accuracy of map reconstruction compared to existing methods.

This work addresses the problem of sequential recovery of temporally correlated sparse vectors with common support from noisy under-determined linear measurements. The Kalman sparse Bayesian learning (SBL) algorithm is an efficient tool for solving the problem when the temporal correlation is modeled using a first order autoregressive model. However, this method processes the input data in a batch mode, which results in high latency. We propose two online SBL algorithms which operate on the observations in a serial fashion. They are sequential expectation maximization (EM) schemes, implemented using fixed lag smoothing and sawtooth lag smoothing. The online algorithms require significantly lower computational and memory resources compared to their offline counterparts. Also, estimates of the sparse vectors become available after a fixed delay from the time observations arrive. Using Monte Carlo simulations, we illustrate that the mean square error and support recovery performance of the proposed algorithms is very close to the offline Kalman SBL algorithm.