Estimation problems in wireless sensor networks (WSNs) typically involve collecting and processing data from distributed sensors at the fusion center to infer the state of an environment. However, not all measurements contribute equally to estimation accuracy. In this work, we incorporate the concept of ordered transmission into sequential estimation to select the most informative measurements from different sensors, while ensuring the desired estimation quality. We analyze a general estimation problem with different estimator choices and derive stopping rules for collecting measurements. Then, we derive the expected number of transmissions required for our ordered transmission-based sequential estimation scheme and compare it with that of a conventional sequential estimation scheme with unordered transmissions. To validate the proposed protocol, we apply it to a radar-based WSN for target localization and velocity estimation, designing an ordered transmission strategy and a sequential stopping rule. Simulation results show that our protocol requires fewer transmissions compared to conventional sequential estimation while maintaining similar estimation accuracy in general WSNs. In a radar-based WSN, the proposed protocol achieves reliable estimation with reduced communication overhead and improved response time.

Occupancy grid mapping is a common approach to support automotive driving perception capabilities. We present an occupancy grid estimation algorithm using sensor point-cloud measurements aided by side information from other sensing modalities like cameras. This prior side information is in the form of an erroneous occupancy map estimate, referred to as prior support information. Specifically, we extract a prior map using you only look once (YOLO) object detection on camera images. A sparse Bayesian learning-based mapping algorithm is designed with a modified hierarchical model to incorporate this prior. Experiments done on public real-world driving datasets, nuScenes and RADIATE, demonstrate that our approach achieves better target detection and scatter noise reduction than the state-of-the-art methods. Furthermore, our method seamlessly works on the two datasets although we train YOLO only using camera images from nuScenes.

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.

An occupancy grid map (OGM) is used in automotive driving applications to model the vehicle surroundings using data from sensors on vehicles like light detection and ranging (LiDAR), radar, or their fusion. In stateof- the-art work, pattern-coupled sparse Bayesian learning (PCSBL) was used to estimate the OGM by leveraging spatial dependencies in the map when either a single sensor modality was used or when fusion of multiple sensor modalities was employed. The PCSBL method, however, has high computational complexity, making real-time implementation challenging for large-sized grid maps. To address this limitation, we propose several methods to improve the computational efficiency of PCSBL while maintaining mapping accuracy. First, we utilize a precomputed lookup table to accelerate selection matrix construction. Second, we implement adaptive resolution reduction based on sensor measurements, lowering problem dimensionality where coarse resolution suffices. Third, we develop two novel methods that exploit the narrow angular interactions between measurements and the map regions to enhance computational efficiency. The first method partitions measurements into spatially disjoint submaps that enable parallel processing. The second method exploits the angular structure to impose a block structure on the selection matrix, reducing the computational overhead of matrix operations. Experiments on the nuScenes and RADIATE public datasets show that the presented methods reduce runtime by at least an order of magnitude compared with the benchmark PCSBL and fusion-based PCSBL methods while preserving detection accuracy.

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.

This survey paper examines recent advancements in low-resolution signal processing, emphasizing quantized compressed sensing. Rising costs and power demands of high-sampling-rate data acquisition drive the interest in quantized signal processing, particularly in wireless communication systems and Internet of Things sensor networks, as 6G aims to integrate sensing and communication within cost-effective hardware. Motivated by this urgency, this paper covers novel signal processing algorithms designed to address practical challenges arising from quantization and modulo operations, as well as their impact on system performance. We begin by introducing the framework of one-bit compressed sensing and discuss relevant theories and algorithms. We explore the application of quantized compressed sensing algorithms to sensor networks, radar, cognitive radio, and wireless channel estimation. We highlight how generic methods can be tailored to an application using specific examples from wireless channel estimation. Additionally, we review other low-resolution techniques beyond one-bit compressed sensing along with their applications. We also provide a brief overview of the emerging concept of unlimited sampling. While this paper does not aim to be exhaustive, it selectively highlights results to inspire readers to appreciate the diverse algorithmic tools (convex optimization, greedy methods, and Bayesian approaches) and sampling techniques (task-based quantization and unlimited sampling).

This work studies the problem of jointly estimating unknown parameters from Kronecker-structured multidimensional signals, which arises in applications like intelligent reflecting surface (IRS)-aided channel estimation. Exploiting the Kronecker structure, we decompose the estimation problem into smaller, independent subproblems across each dimension. Each subproblem is posed as a sparse recovery problem using basis expansion and solved using a novel off-grid sparse Bayesian learning (SBL)-based algorithm. Additionally, we derive probabilistic error bounds for the decomposition, quantify its denoising effect, and provide convergence analysis for off-grid SBL. Our simulations show that applying the algorithm to IRS-aided channel estimation improves accuracy and runtime compared to state-of-the-art methods through the low-complexity and denoising benefits of the decomposition step and the high-resolution estimation capabilities of off-grid SBL.

We address the problem of estimating a binary occupancy grid map by fusing point cloud data from radar and LiDAR sensors for automotive driving perception. To achieve this, we introduce two measurement models for fusion and formulate occupancy mapping as sparse vector reconstruction from the set of radar and LiDAR measurements. The first model, called common sparse fusion, jointly estimates a common map from all sensor measurements. The second model, called common innovative sparse fusion, assumes a shared map and an innovation component (error collector) for each sensor modality’s measurements. This approach enhances the robustness of occupancy map estimation against potential sensor mismatch and calibration errors, and inconsistencies between the two modalities. We use the pattern-coupled sparse Bayesian learning (PCSBL) algorithm to recover maps, leveraging the inherent sparsity and spatial dependencies in automotive occupancy maps. Numerical experiments on the public RADIATE dataset show that our feature-level fusion models outperform single-modality mapping and decision-level fusion models in detecting drivable areas and targets. Furthermore, statistical results with corrupted LiDAR data establish that our common innovative sparse fusion model is robust against unreliable sensor data

Sparsity constraints on the control inputs of a linear dynamical system naturally arise in several practical applications such as networked control, computer vision, seismic signal processing, and cyber-physical systems. In this work, we consider the problem of jointly estimating the states and sparse inputs of such systems from low-dimensional (compressive) measurements. Due to the low-dimensional measurements, conventional Kalman filtering and smoothing algorithms fail to accurately estimate the states and inputs. We present a Bayesian approach that exploits the input sparsity to significantly improve estimation accuracy. Sparsity in the input estimates is promoted by using different prior distributions on the input. We investigate two main approaches: regularizer-based maximum a posteriori estimation and Bayesian learning-based estimation. We also extend the approaches to handle control inputs with common support and analyze the time and memory complexities of the presented algorithms. Finally, using numerical simulations, we show that our algorithms outperform the state-of-the-art methods in terms of accuracy and time/memory complexities, especially in the low-dimensional measurement regime.

We study the sparse recovery problem with an underdetermined linear system characterized by a Kronecker-structured dictionary and a Kronecker-supported sparse vector. We cast this problem into the sparse Bayesian learning (SBL) framework and rely on the expectation-maximization method for a solution. To this end, we model the Kronecker-structured support with a hierarchical Gaussian prior distribution parameterized by a Kronecker-structured hyperparameter, leading to a non-convex optimization problem. The optimization problem is solved using the alternating minimization (AM) method and a singular value decomposition (SVD)-based method, resulting in two algorithms. Further, we analytically guarantee that the AM-based method converges to the stationary point of the SBL cost function. The SVD-based method, though it adopts approximations, is empirically shown to be more efficient and accurate. We then apply our algorithm to estimate the uplink wireless channel in an intelligent reflecting surface-aided MIMO system and extend the AM-based algorithm to address block sparsity in the channel. We also study the SBL cost to show that the minima of the cost function are achieved at sparse solutions and that incorporating the Kronecker structure reduces the number of local minima of the SBL cost function. Our numerical results demonstrate the effectiveness of our algorithms compared to the state-of-the-art.

Digital radars with low-resolution analog-to-digital converters (ADCs) can reduce digital processing complexity and power consumption but suffer from limited dynamic range. The poor dynamic range causes high radar cross-section (RCS) targets to mask low-RCS ones. To mitigate this issue, we propose operating the ADC at a high resolution during the initial slowtime slot of each radar frame. The high-resolution measurements are used to estimate the range and RCS of dominant targets, which, along with their known Doppler statistics, are used to construct a dither signal. This dither signal is then employed to acquire low-resolution ADC measurements in the subsequent slow-time slots. With the proposed receiver architecture, our method suppresses strong target returns in the low-resolution measurements, effectively unmasking weak targets. Simulations demonstrate significant improvements in target detection and reduced normalized mean square error in radar channel estimation compared to existing benchmarks.

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.

Digital radars with low-resolution analog-to-digital converters (ADCs) have attracted attention as a solution to reducing the high digital processing complexity and power consumption at the receiver. Radars employing low-resolution ADCs, however, have a limited dynamic range, due to which high-radar cross section (RCS) targets mask low-RCS targets. The masking occurs because the quantized output is primarily determined by returns from high-RCS targets. To enhance the dynamic range of such radars, we propose to operate the ADC at a high resolution in the initial slow-time slot of each radar frame. The resulting high-resolution measurements are used together with the known Doppler statistics of dominant targets to construct a dither signal, which is used as a quantization threshold to acquire low-resolution ADC measurements in the subsequent slow-time slots. By incorporating situation awareness in the form of Doppler statistics, our dither signal can suppress returns from strong targets, effectively unmasking weak targets with low-resolution measurements. We analyze system performance in terms of the probability of detection and show that the proposed approach outperforms existing methods in enhancing the detection of weak targets. The simulations demonstrate that our method significantly improves target detection and reduces the normalized mean square error (NMSE) in the estimated radar channel over comparable 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 timedomain 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 spacetime codes achieve higher detection rates than designs that do not rely on prior information from occupancy maps.

In this article, we develop a communication-control co-design framework in a wireless networked control system with multiple geographically separated controllers and controlled systems, modeled via a Poisson point process. Each controlled system consists of an actuator, plant, and sensor. Controllers receive state estimates from sensors and design control inputs, which are sent to actuators over a shared wireless channel, causing interference. Our co-design includes control strategies at the controller based on sensor measurements and transmission acknowledgments from the actuators for both rested and restless systems - systems with and without state feedback, respectively. In the restless system, controllability depends on consecutive successful transmissions, while in the rested system, it depends on total successful transmissions. We use both classical and block ALOHA protocols for channel access, optimizing access based on sensor data and acknowledgments. A statistical analysis of control performance is followed by a Thompson sampling-based algorithm to optimize the ALOHA parameter, achieving sublinear regret. We show how the ALOHA parameter influences control performance and transmission success.

Occupancy maps are used in automotive driving applications to understand the scene around the vehicle using sensor data like LiDAR measurements. State-of-the-art work relies on pattern-coupled sparse Bayesian learning (PCSBL) to estimate the occupancy map from LiDAR point cloud data by leveraging spatial dependencies across grids in the map. However, PCSBL has high computational complexity, posing challenges for real-time implementation on large-sized grid maps. In this work, we propose two methods to improve the computational efficiency of PCSBL for occupancy grid mapping by exploiting the narrow angular interactions of sensor measurements with the map. The first method partitions the measurements into spatially disjoint submaps that can be processed in parallel. The second method exploits the angular structure to impose a block structure on the measurement matrix, allowing more efficient matrix computations to accelerate the algorithm. Experiments on the nuScenes public dataset show that the presented methods reduce computational runtime compared to the benchmark PCSBL method while preserving detection accuracy.

Kronecker compressed sensing refers to using Kronecker product matrices as sparsifying bases and measurement matrices in compressed sensing. This work focuses on the Kronecker compressed sensing problem, encompassing three sparsity structures: (i) a standard sparsity model with arbitrarily positioned nonzero entries, (ii) a hierarchical sparsity model where nonzero entries are concentrated in a few blocks, each with only a subset of nonzero entries, and (iii) a Kronecker-supported sparsity model where the support vector is a Kronecker product of smaller vectors. We present a hierarchal view of Kronecker compressed sensing that explicitly reveals a multiple-level sparsity pattern. This framework allows us to utilize the Kronecker structure of dictionaries and design a two-stage sparse recovery algorithm for different sparsity models. Further, we analyze the restricted isometry property of Kronecker-structured matrices under different sparsity models. Simulations show that our algorithm offers comparable recovery performance to state-of-the-art methods while significantly reducing runtime.

We tackle the anomaly detection problem within a given set of binary processes through a learning-based controlled sensing approach. This problem is particularly pertinent to applications related to the Internet of Things (IoT) that monitor multiple related processes. Each process is defined by a binary random variable indicating its anomalous status. To pinpoint anomalies, a decision-making agent observes a subset of processes at each time point, with each observation incurring an associated cost. We formulate a sequential selection policy that dynamically determines which processes to observe at each moment, aiming to minimize both decision delay and sensing cost. The conventional solution using model-based active hypothesis testing algorithms overlooks the joint statistics of the processes and fails to consider unequal sensing costs or errors in observations. To solve this problem, we, for the first time, pose it as a sequential hypothesis testing problem within the framework of Markov decision processes (MDPs), leveraging both a Bayesian log-likelihood ratio-based reward and an entropy-based reward. We address this problem through two approaches: 1) a deep reinforcement learning-based method involving the design of both deep Q-learning (DQN) and policy gradient actor-critic (AC) algorithms and 2) a deep active inference (AI)-based approach. Our model-based posterior updates to tackle the uncertainties in the observations, combined with the data-driven neural networks to handle the underlying statistical dependence between the processes, strike a balance between the model-based and the data-driven approaches. Our numerical experiments showcase the effectiveness of our algorithms, illustrating their capability to adapt to any unknown statistical dependence among the processes.

We tackle the problem of estimating a binary occupancy grid map by fusing point cloud data from LiDAR and radar sensors for automotive driving perception. To this end, we introduce two sparsity measurement models for fusion, formulating occupancy mapping as a sparse binary vector reconstruction problem. The first model jointly estimates a common map from all measurements, while the second assumes a shared map and an innovation component for each modality's measurements. We use the pattern-coupled sparse Bayesian learning algorithm to recover maps, leveraging the inherent sparsity and spatial dependencies in automotive occupancy maps. Numerical experiments on the RADIATE public dataset show that our fusion-based approach improves mapping accuracy compared to single-modality and high-level fusion mapping algorithms.

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.