One-Bit Target Detection in Collocated MIMO Radar with Colored Background Noise

One-bit sampling has emerged as a promising technique in multiple-input multiple-output (MIMO) radar systems due to its ability to significantly reduce data volume and processing requirements. Nevertheless, current detection methods have not adequately addressed the impact of colored noise, which is frequently encountered in real scenarios. In this paper, we present a novel detection method that accounts for colored noise in MIMO radar systems. Specifically, we derive Rao's test by computing the derivative of the likelihood function with respect to the target reflectivity parameter and the Fisher information matrix, resulting in a detector that takes the form of a weighted matched filter. To ensure the constant false alarm rate (CFAR) property, we also consider noise covariance uncertainty and examine its effect on the probability of false alarm. The detection probability is also studied analytically. Simulation results demonstrate that the proposed detector provides considerable performance gains in the presence of colored noise.

A semidefinite programming approach for robust elliptic localization

This short communication addresses the problem of elliptic localization with outlier measurements, whose occurrences are prevalent in various location-enabled applications and can significantly compromise the positioning performance if not adequately handled. In contrast to the reliance on $M$-estimation adopted in the majority of existing solutions, we take a different path, specifically exploring the worst-case robust approximation criterion, to bolster resistance of the elliptic location estimator against outliers. From a geometric standpoint, our method boils down to pinpointing the Chebyshev center of the feasible set determined by the available bistatic ranges with bounded measurement errors. For a practical approach to the associated min-max problem, we convert it into the well-established convex optimization framework of semidefinite programming (SDP). Numerical simulations confirm that our SDP-based technique can outperform a number of existing elliptic localization schemes in terms of positioning accuracy in Gaussian mixture noise, a common type of impulsive interference in the context of range-based localization.

Sparse array design for MIMO radar in multipath scenarios

Sparse array designs have focused mostly on angular resolution, peak sidelobe level and directivity factor of virtual arrays for multiple-input multiple-output (MIMO) radar. The notion of the MIMO radar virtual array is based on the direct path assumption in that the direction-of-departure (DOD) and direction-of-arrival (DOA) of the targets are equal. However, the DOD and DOA of targets in multipath scenarios are likely to be very different. The identification of multipath targets requires DOD-DOA imaging using the the transmit and receive arrays, not the virtual array. To improve the imaging of both direct path and multipath targets, we introduce several new criteria for MIMO radar sparse linear array (SLA) designs for multipath scenarios. Under the new criteria, we adopt a cyclic optimization strategy under a coordinate descent framework to design the MIMO SLAs. We present several numerical examples to demonstrate the effectiveness of the proposed approaches.

3D Multi-Target Localization Via Intelligent Reflecting Surface: Protocol and Analysis

With the emerging environment-aware applications, ubiquitous sensing is expected to play a key role in future networks. In this paper, we study a 3-dimensional (3D) multi-target localization system where multiple intelligent reflecting surfaces (IRSs) are applied to create virtual line-of-sight (LoS) links that bypass the base station (BS) and targets. To fully unveil the fundamental limit of IRS for sensing, we first study a single-target-single-IRS case and propose a novel \textit{two-stage localization protocol} by controlling the on/off state of IRS. To be specific, in the IRS-off stage, we derive the Cram\'{e}r-Rao bound (CRB) of the azimuth/elevation direction-of-arrival (DoA) of the BS-target link and design a DoA estimator based on the MUSIC algorithm. In the IRS-on stage, the CRB of the azimuth/elevation DoA of the IRS-target link is derived and a simple DoA estimator based on the on-grid IRS beam scanning method is proposed. Particularly, the impact of echo signals reflected by IRS from different paths on sensing performance is analyzed. Moreover, we prove that the single-beam of the IRS is not capable of sensing, but it can be achieved with \textit{multi-beam}. Based on the two obtained DoAs, the 3D single-target location is constructed. We then extend to the multi-target-multi-IRS case and propose an \textit{IRS-adaptive sensing protocol} by controlling the on/off state of multiple IRSs, and a multi-target localization algorithm is developed. Simulation results demonstrate the effectiveness of our scheme and show that sub-meter-level positioning accuracy can be achieved.

Low-Rank Tensor Completion via Novel Sparsity-Inducing Regularizers

To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the thresholding functions of these nonconvex regularizers may not have closed-form expressions and thus iterations are needed, which increases the computational loads. To solve this issue, we devise a framework to generate sparsity-inducing regularizers with closed-form thresholding functions. These regularizers are applied to low-tubal-rank tensor completion, and efficient algorithms based on the alternating direction method of multipliers are developed. Furthermore, convergence of our methods is analyzed and it is proved that the generated sequences are bounded and any limit point is a stationary point. Experimental results using synthetic and real-world datasets show that the proposed algorithms outperform the state-of-the-art methods in terms of restoration performance.

A framework to generate sparsity-inducing regularizers for enhanced low-rank matrix completion

Applying half-quadratic optimization to loss functions can yield the corresponding regularizers, while these regularizers are usually not sparsity-inducing regularizers (SIRs). To solve this problem, we devise a framework to generate an SIR with closed-form proximity operator. Besides, we specify our framework using several commonly-used loss functions, and produce the corresponding SIRs, which are then adopted as nonconvex rank surrogates for low-rank matrix completion. Furthermore, algorithms based on the alternating direction method of multipliers are developed. Extensive numerical results show the effectiveness of our methods in terms of recovery performance and runtime.

Robust matrix completion via Novel M-estimator Functions

M-estmators including the Welsch and Cauchy have been widely adopted for robustness against outliers, but they also down-weigh the uncontaminated data. To address this issue, we devise a framework to generate a class of nonconvex functions which only down-weigh outlier-corrupted observations. Our framework is then applied to the Welsch, Cauchy and $\ell_p$-norm functions to produce the corresponding robust loss functions. Targeting on the application of robust matrix completion, efficient algorithms based on these functions are developed and their convergence is analyzed. Finally, extensive numerical results demonstrate that the proposed methods are superior to the competitors in terms of recovery accuracy and runtime.

Robust Low-Rank Matrix Completion via a New Sparsity-Inducing Regularizer

This paper presents a novel loss function referred to as hybrid ordinary-Welsch (HOW) and a new sparsity-inducing regularizer associated with HOW. We theoretically show that the regularizer is quasiconvex and that the corresponding Moreau envelope is convex. Moreover, the closed-form solution to its Moreau envelope, namely, the proximity operator, is derived. Compared with nonconvex regularizers like the lp-norm with 0<p<1 that requires iterations to find the corresponding proximity operator, the developed regularizer has a closed-form proximity operator. We apply our regularizer to the robust matrix completion problem, and develop an efficient algorithm based on the alternating direction method of multipliers. The convergence of the suggested method is analyzed and we prove that any generated accumulation point is a stationary point. Finally, experimental results based on synthetic and real-world datasets demonstrate that our algorithm is superior to the state-of-the-art methods in terms of restoration performance.

Network Topology Inference with Sparsity and Laplacian Constraints

We tackle the network topology inference problem by utilizing Laplacian constrained Gaussian graphical models, which recast the task as estimating a precision matrix in the form of a graph Laplacian. Recent research \cite{ying2020nonconvex} has uncovered the limitations of the widely used $\ell_1$-norm in learning sparse graphs under this model: empirically, the number of nonzero entries in the solution grows with the regularization parameter of the $\ell_1$-norm; theoretically, a large regularization parameter leads to a fully connected (densest) graph. To overcome these challenges, we propose a graph Laplacian estimation method incorporating the $\ell_0$-norm constraint. An efficient gradient projection algorithm is developed to solve the resulting optimization problem, characterized by sparsity and Laplacian constraints. Through numerical experiments with synthetic and financial time-series datasets, we demonstrate the effectiveness of the proposed method in network topology inference.

Intelligent Reflecting Surface Assisted Localization: Performance Analysis and Algorithm Design

The target sensing/localization performance is fundamentally limited by the line-of-sight link and severe signal attenuation over long distances. This paper considers a challenging scenario where the direct link between the base station (BS) and the target is blocked due to the surrounding blockages and leverages the intelligent reflecting surface (IRS) with some active sensors, termed as \textit{semi-passive IRS}, for localization. To be specific, the active sensors receive echo signals reflected by the target and apply signal processing techniques to estimate the target location. We consider the joint time-of-arrival (ToA) and direction-of-arrival (DoA) estimation for localization and derive the corresponding Cram\'{e}r-Rao bound (CRB), and then a simple ToA/DoA estimator without iteration is proposed. In particular, the relationships of the CRB for ToA/DoA with the number of frames for IRS beam adjustments, number of IRS reflecting elements, and number of sensors are theoretically analyzed and demystified. Simulation results show that the proposed semi-passive IRS architecture provides sub-meter level positioning accuracy even over a long localization range from the BS to the target and also demonstrate a significant localization accuracy improvement compared to the fully passive IRS architecture.