This letter considers the design of sparse actuator schedules for linear time-invariant systems. An actuator schedule selects, for each time instant, which control inputs act on the system in that instant. We address the optimal scheduling of control inputs under a hard constraint on the number of inputs that can be used at each time. For a sparsely controllable system, we characterize sparse actuator schedules that make the system controllable, and then devise a greedy selection algorithm that guarantees controllability while heuristically providing low control effort. We further show how to enhance our greedy algorithm via Markov chain Monte Carlo-based randomized optimization.

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Occupancy grid maps provide information about obstacles and available free space in the environment and are crucial in automotive driving applications. An occupancy map is constructed using point cloud data from sensor modalities such as light detection and ranging (LiDAR) and radar used for automotive perception. In this article, we formulate the problem of estimating the occupancy grid map using sensor point cloud data as a sparse binary occupancy value reconstruction problem. Our proposed occupancy grid estimation method, based on pattern-coupled sparse Bayesian learning (PC-SBL), leverages the sparsity and spatial dependencies inherent in occupancy maps typically encountered in automotive scenarios. The proposed method shows enhanced detection capabilities compared to two benchmark methods based on performance evaluation with scenes from the nuScenes and RADIal public datasets.

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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.@en

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.@en

This monograph presents some exciting and new results on the analysis and design of control of discrete-time linear dynamical systems using sparse actuator control. Sparsity constraints arise naturally in the inputs of several linear systems due to limited resources or the underlying physics. The monograph deals with two types of sparsity constraints: time-varying and time-invariant supported sparse control inputs. It first provides a detailed theoretical discussion on controllability under sparsity constraints, including algebraic necessary and sufficient conditions for ensuring controllability. Several related formulations, covering stabilizability, output controllability, and nonnegative controllability under sparsity constraints, are also presented. Further, for sparsely controllable systems, the monograph describes two efficient, systematic, and rigorous approaches to designing sparse control inputs: compressed sensing algorithms and spare actuator scheduling algorithms. Overall, the concepts covered in the monograph provide various sparsity models, algorithms, and analysis tools that are readily accessible to systems and control, signal processing, and applied mathematics readers.@en

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.

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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.@en

We address the problem of sequentially selecting and observing processes from a given set to find the anomalies among them. The decision-maker observes a subset of the processes at any given time instant and obtains a noisy binary indicator of whether or not the corresponding process is anomalous. We develop an anomaly detection algorithm that chooses the processes to be observed at a given time instant, decides when to stop taking observations, and declares the decision on anomalous processes. The objective of the detection algorithm is to identify the anomalies with an accuracy exceeding the desired value while minimizing the delay in decision making. We devise a centralized algorithm where the processes are jointly selected by a common agent as well as a decentralized algorithm where the decision of whether to select a process is made independently for each process. Our algorithms rely on a Markov decision process defined using the marginal probability of each process being normal or anomalous, conditioned on the observations. We implement the detection algorithms using the deep actor-critic reinforcement learning framework. Unlike prior work on this topic that has exponential complexity in the number of processes, our algorithms have computational and memory requirements that are both polynomial in the number of processes. We demonstrate the efficacy of these algorithms using numerical experiments by comparing them with state-of-the-art methods.@en

In this article, we study the conditions to be satisfied by a discrete-time linear system to ensure output controllability using sparse control inputs. A set of necessary and sufficient conditions can be directly obtained by extending the Kalman rank test for output controllability. However, the verification of these conditions is computationally heavy due to their combinatorial nature. Therefore, we derive noncombinatorial conditions for output sparse controllability that can be verified with polynomial time complexity. Our results also provide bounds on the minimum sparsity level required to ensure output controllability of the system. This additional insight is useful for designing sparse control input that drives the system to any desired output.

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The problem of estimating occupancy grids to support automotive driving applications using LiDAR sensor point clouds is considered. We formulate the problem as a sparse binary occupancy value reconstruction problem. Our proposed occupancy grid estimation method is based on pattern-coupled sparse Bayesian learning and exploits the inherent sparsity and spatial occupancy dependencies in LiDAR sensor measurements. The proposed method demonstrates enhanced detection capabilities compared to commonly used benchmark methods, as observed through testing on scenes from the nuScenes dataset.@en

The stabilizability of a linear dynamical system (LDS) refers to the existence of control inputs that drive the system state to zero. In this article, we analyze both the theoretical and algorithmic aspects of the stabilizability of an LDS using sparse control inputs with potentially time-varying supports. We show that an LDS is stabilizable using sparse control inputs if and only if it is stabilizable (using unconstrained inputs). For a stabilizable LDS, we present an algorithm to determine the sparse control inputs that steer the system state to zero. We show that all stabilizable LDSs are also sparse mean square stabilizable when the process noise has zero mean and bounded second moment. For such an LDS, we devise a method to sequentially estimate the sparse control inputs to stabilize the LDS in the mean square sense. We prove that a detectable and stabilizable LDS is sparse stabilizable through output feedback and develop an algorithm for finding the corresponding sparse control inputs. Finally, we analyze the stabilizability of an LDS using sparse control inputs with common support. Our results shed light on the conditions under which a given LDS is stabilizable using sparse control inputs and the design of the corresponding control inputs.

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The emergence of compressive sensing and the associated ℓ₁ recovery algorithms and theory have generated considerable excitement and interest in their applications. This chapter will examine recent developments and a complementary set of tools based on a Bayesian framework to address the general problem of sparse signal recovery and the challenges associated with it. Bayesian methods offer superior performance compared to convex optimization-based methods and are parameter tuning-free. They also have the flexibility necessary to deal with a diverse range of measurement modalities and structured sparsity in signals than hitherto possible. Parsimonious signal representation using overcomplete dictionaries for compression, estimation of sparse communication channels with large delay spread as in underwater acoustics, low-dimensional representation of MIMO wireless channels, brain imaging techniques, such as MEG and EEG, are a few examples. We provide a mathematically rigorous and in-depth overview of this fascinating area within sparse signal recovery. We highlight the generality and flexibility of Bayesian approaches and show how it greatly facilitates their deployment in communications-related applications, even though they generally lead to nonconvex optimization problems. Further, we show that, by reinterpreting the Bayesian cost function as a technique to perform covariance matching, one can develop new, ultrafast Bayesian algorithms for sparse signal recovery. As an example application, we discuss the utility of these algorithms in the context of 5G communications with several case studies including wideband time-varying channel estimation and low-resolution analog-to-digital conversion-based signal recovery.

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In this paper, we consider the problem of estimating the states of a linear dynamical system whose inputs are jointly sparse and outputs at a few unknown time instants are missing. We model the missing data mechanism using a Markov chain with two states representing the missing and non-missing data. This mechanism with memory governed by the Markov chain models intermittent outages due to communication channels and occlusions corresponding to moving objects. We rely on the sparse Bayesian learning framework to derive an estimation algorithm that uses Kalman smoothing to handle temporal correlation and the Viterbi algorithm to handle missing data. Further, we demonstrate the utility of our algorithm by applying it to the frequency division duplexed multiple input multiple output downlink channel estimation problem.

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Phased arrays in near-field communication allow the transmitter to focus wireless signals in a small region around the receiver. Proper focusing is achieved by carefully tuning the phase shifts and the polarization of the signals transmitted from the phased array. In this paper, we study the impact of polarization on near-field focusing and investigate the use of dynamic polar-ization control (DPC) phased arrays in this context. Our studies indicate that the optimal polarization configuration for near-field focusing varies spatially across the antenna array. Such a spatial variation motivates the need for DPC phased arrays which allow independent polarization control across different antennas. We show using simulations that DPC phased arrays in the near-field achieve a higher received signal-to-noise ratio than conventional switched- or dual-polarization phased arrays.@en