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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.

This short communication addresses the problem of elliptic localization with outlier measurements. Outliers are prevalent in various location-enabled applications, and can significantly compromise the positioning performance if not adequately handled. Instead of following the common trend of using $M$-estimation or adjusting the conventional least squares formulation by integrating extra error variables, we take a different path. Specifically, we explore 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 a feasible set, which is defined by the available bistatic ranges with bounded measurement errors. For a practical approach to the associated min-max problem, we convert it into the 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.

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., Comment: This paper has been submitted to IEEE journal for possible publication

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.

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

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.

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.

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.

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., Comment: The paper has been submitted to IEEE journal for possible publication

Spectrum sensing in cognitive radio necessitates effective monitoring of wide bandwidths, which requires high-rate sampling. Traditional spectrum sensing methods employing high-precision analog-to-digital converters (ADCs) result in increased power consumption and expensive hardware costs. In this paper, we explore blind spectrum sensing utilizing one-bit ADCs. We derive a closed-form detector based on Rao's test and demonstrate its equivalence with the second-order eigenvalue-moment-ratio test. Furthermore, a near-exact distribution based on the moment-based method, and an approximate distribution in the low signal-to-noise ratio (SNR) regime with the use of the central limit theorem, are obtained. Theoretical analysis is then performed and our results show that the performance loss of the proposed detector is approximately $2$ dB ($\pi/2$) compared to detectors employing $\infty$-bit ADCs when SNR is low. This loss can be compensated for by using approximately $2.47$ ($\pi^2/4$) times more samples. In addition, we unveil that the efficiency of incoherent accumulation in one-bit detection is the square root of that of coherent accumulation. Simulation results corroborate the correctness of our theoretical calculations.

This article considers the problem of source localization (SL) using possibly unreliable time-of-arrival (TOA) based range measurements. Adopting the strategy of statistical robustification, we formulate TOA SL as minimization of a versatile loss that possesses resistance against the occurrence of outliers. We then present an alternating direction method of multipliers (ADMM) to tackle the nonconvex optimization problem in a computationally attractive iterative manner. Moreover, we prove that the solution obtained by the proposed ADMM will correspond to a Karush-Kuhn-Tucker point of the formulation when the algorithm converges, and discuss reasonable assumptions about the robust loss function under which the approach can be theoretically guaranteed to be convergent. Numerical investigations demonstrate the superiority of our method over many existing TOA SL schemes in terms of positioning accuracy and computational simplicity. In particular, the proposed ADMM achieves estimation results with mean square error performance closer to the Cram\'{e}r-Rao lower bound than its competitors in our simulations of impulsive noise environments., Comment: Should you have any questions regarding this contribution, please don't hesitate to reach out to me via email at w.x.xiong@outlook.com

Covariance matrix reconstruction is a topic of great significance in the field of one-bit signal processing and has numerous practical applications. Despite its importance, the conventional arcsine law with zero threshold is incapable of recovering the diagonal elements of the covariance matrix. To address this limitation, recent studies have proposed the use of non-zero clipping thresholds. However, the relationship between the estimation error and the sampling threshold is not yet known. In this paper, we undertake an analysis of the mean squared error by computing the Fisher information matrix for a given threshold. Our results reveal that the optimal threshold can vary considerably, depending on the variances and correlation coefficients. As a result, it is inappropriate to use a constant threshold to encompass parameters that vary widely. To mitigate this issue, we present a recovery scheme that incorporates time-varying thresholds. Our approach differs from existing methods in that it utilizes the exact values of the threshold, rather than its statistical properties, to enhance the estimation performance. Our simulations, including the direction-of-arrival estimation problem, demonstrate the efficacy of the developed scheme, especially in complex scenarios where the covariance elements are widely separated.

We investigate the problem of high frequency (HF) source localization using the time-difference-of-arrival (TDOA) observations of ionosphere-refracted radio rays based on quasi-parabolic (QP) modeling. An unresolved but pertinent issue in such a field is that the existing gradient-type scheme can easily get trapped in local optima for practical use. This will lead to the difficulty in initializing the algorithm and finally degraded positioning performance if the starting point is inappropriately selected. In this paper, we develop a collaborative gradient projection (GP) algorithm in order to globally solve the highly nonconvex QP-based TDOA HF localization problem. The metaheuristic of particle swarm optimization (PSO) is exploited for information sharing among multiple GP models, each of which is guaranteed to work out a critical point solution to the simplified maximum likelihood formulation. Random mutations are incorporated to avoid the early convergence of PSO. Rather than treating the geolocation of HF transmitter as a pure optimization problem, we further provide workarounds for addressing the possible impairments and challenges when the proposed technique is applied in practice. Numerical results demonstrate the effectiveness of our PSO-assisted re-initialization strategy in achieving the global optimality, and the superiority of our method over its competitor in terms of positioning accuracy., Comment: This is the accepted version. The final version of this paper has been published in the IEEE Transactions on Aerospace and Electronic Systems. The copyright is with IEEE. This version prevails, as there are unfortunately uncorrected editing mistakes in the final one

The recently published paper by Gupta and Agrawal [1] exploited the sum-difference co-array (SDCA) to enhance the virtual aperture of sparse arrays. We argue that the key SDCA property established in [1] requires a critical necessary and sufficient condition that is valid for a very rare case only., Comment: 2 pages, 1 figure

In this paper, we devise a sparse array design algorithm for adaptive beamforming. Our strategy is based on finding a sparse beamformer weight to maximize the output signal-to-interference-plus-noise ratio (SINR). The proposed method utilizes the alternating direction method of multipliers (ADMM), and admits closed-form solutions at each ADMM iteration. The algorithm convergence properties are analyzed by showing the monotonicity and boundedness of the augmented Lagrangian function. In addition, we prove that the proposed algorithm converges to the set of Karush-Kuhn-Tucker stationary points. Numerical results exhibit its excellent performance, which is comparable to that of the exhaustive search approach, slightly better than those of the state-of-the-art solvers, including the semidefinite relaxation (SDR), its variant (SDR-V), and the successive convex approximation (SCA) approaches, and significantly outperforms several other sparse array design strategies, in terms of output SINR. Moreover, the proposed ADMM algorithm outperforms the SDR, SDR-V, and SCA methods, in terms of computational complexity., Comment: Updated Appendix D. Accepted by IEEE Transactions on Signal Processing

We analyze the convergence properties of the consensus-alternating direction method of multipliers (ADMM) for solving general quadratically constrained quadratic programs. We prove that the augmented Lagrangian function value is monotonically non-increasing as long as the augmented Lagrangian parameter is chosen to be sufficiently large. Simulation results show that the augmented Lagrangian function is bounded from below when the matrix in the quadratic term of the objective function is positive definite. In such a case, the consensus-ADMM is convergent., Comment: 5 figures. This work has been accepted for publication in Signal Processing (Elsevier)

The study of generalising the central difference for integer order Laplacian to fractional order is discussed in this paper. Analysis shows that, in contrary to the conclusion of a previous study, difference stencils evaluated through fast Fourier transform prevents the convergence of the solution of fractional Laplacian. We propose a composite quadrature rule in order to efficiently evaluate the stencil coefficients with the required convergence rate in order to guarantee convergence of the solution. Furthermore, we propose the use of generalised higher order lattice Boltzmann method to generate stencils which can approximate fractional Laplacian with higher order convergence speed and error isotropy. We also review the formulation of the lattice Boltzmann method and discuss the explicit sparse solution formulated using Smolyak's algorithm, as well as the method for the evaluation of the Hermite polynomials for efficient generation of the higher order stencils. Numerical experiments are carried out to verify the error analysis and formulations.

Distorted sensors could occur randomly and may lead to the breakdown of a sensor array system. We consider an array model within which a small number of sensors are distorted by unknown sensor gain and phase errors. With such an array model, the problem of joint direction-of-arrival (DOA) estimation and distorted sensor detection is investigated and the problem is formulated under the framework of low-rank and row-sparse decomposition. We derive an iteratively reweighted least squares (IRLS) algorithm to solve the resulting problem in both noiseless and noisy cases. The convergence property of the IRLS algorithm is analyzed by means of the monotonicity and boundedness of the objective function. Extensive simulations are conducted regarding parameter selection, convergence speed, computational complexity, and performances of DOA estimation as well as distorted sensor detection. Even though the IRLS algorithm is slightly worse than the alternating direction method of multipliers in detecting the distorted sensors, the results show that our approach outperforms several state-of-the-art techniques in terms of convergence speed, computational cost, and DOA estimation performance., Comment: This work has been submitted to the IEEE for possible publication

The problem of off-grid direction-of-arrival (DOA) estimation is investigated. We develop a grid-based method to jointly estimate the closest spatial frequency (the sine of DOA) grids, and the gaps between the estimated grids and the corresponding frequencies. By using a second-order Taylor approximation, the data model under the framework of joint-sparse representation is formulated. We point out an important property of the signals of interest in the model, namely the proportionality relationship, which is empirically demonstrated to be useful in the sense that it increases the probability of the mixing matrix satisfying the block restricted isometry property. Simulation examples demonstrate the effectiveness and superiority of the proposed method against several state-of-the-art grid-based approaches., Comment: 20 pages, 9 figures, accepted for publication in Signal Processing (Elsevier)

The state-of-the-art deep neural networks (DNNs) have been widely applied for various real-world applications, and achieved significant performance for cognitive problems. However, the increment of DNNs' width and depth in architecture results in a huge amount of parameters to challenge the storage and memory cost, limiting to the usage of DNNs on resource-constrained platforms, such as portable devices. By converting redundant models into compact ones, compression technique appears to be a practical solution to reducing the storage and memory consumption. In this paper, we develop a nonlinear tensor ring network (NTRN) in which both fullyconnected and convolutional layers are compressed via tensor ring decomposition. Furthermore, to mitigate the accuracy loss caused by compression, a nonlinear activation function is embedded into the tensor contraction and convolution operations inside the compressed layer. Experimental results demonstrate the effectiveness and superiority of the proposed NTRN for image classification using two basic neural networks, LeNet-5 and VGG-11 on three datasets, viz. MNIST, Fashion MNIST and Cifar-10.

We propose a novel method to compute a finite difference stencil for Riesz derivative for artibitrary speed of convergence. This method is based on applying a pre-filter to the Gr\"unwald-Letnikov type central difference stencil. The filter is obtained by solving for the inverse of a symmetric Vandemonde matrix and exploiting the relationship between the Taylor's series coefficients and fast Fourier transform. The filter costs O\left(N^{2}\right) operations to evaluate for O\left(h^{N}\right) of convergence, where h is the sampling distance. The higher convergence speed should more than offset the overhead with the requirement of the number of nodal points for a desired error tolerance significantly reduced. The benefit of progressive generation of the stencil coefficients for adaptive grid size for dynamic problems with the Gr\"unwald-Letnikov type difference scheme is also kept because of the application of filtering. The higher convergence rate is verified through numerical experiments., Comment: 14 pages, 2 figures

In this paper, we exploit the maximum correntropy criterion (MCC) to robustify the traditional time-difference-of-arrival (TDOA) location estimator in the presence of non-line-of-sight (NLOS) propagation conditions. For the sake of statistical efficiency, the correntropy-based robust loss is imposed on the underlying time-of-arrival composition via joint estimation of the source position and onset time, instead of the TDOA counterpart generated in the postprocessing of sensor-collected timestamps. We then employ a neurodynamic optimization approach to tackle the highly nonconvex MCC formulation. Furthermore, we examine the local stability of equilibrium for the corresponding projection-type neural network model. Simulation investigations in representative NLOS propagation scenarios demonstrate that our neurodynamic robust TDOA localization solution is capable of outperforming several existing schemes in terms of positioning accuracy., Comment: Submitted to DSP

We investigate the problem of time-of-arrival (TOA) based localization under possible non-line-of-sight (NLOS) propagation conditions. To robustify the squared-range-based location estimator, we follow the maximum correntropy criterion, essentially the Welsch $M$-estimator with a redescending influence function which behaves like $\ell_0$-minimization towards the grossly biased measurements, to derive the formulation. The half-quadratic technique is then applied to settle the resulting optimization problem in an alternating maximization (AM) manner. By construction, the major computational challenge at each AM iteration boils down to handling an easily solvable generalized trust region subproblem. It is worth noting that the implementation of our localization method requires nothing but merely the TOA-based range measurements and sensor positions as prior information. Simulation and experimental results demonstrate the competence of the presented scheme in outperforming several state-of-the-art approaches in terms of positioning accuracy, especially in scenarios where the percentage of NLOS paths is not large enough., Comment: Published in CSSP

This paper revisits the problem of locating a signal-emitting source from time-difference-of-arrival (TDOA) measurements under non-line-of-sight (NLOS) propagation. Many currently fashionable methods for NLOS mitigation in TDOA-based localization tend to solve their optimization problems by means of convex relaxation and, thus, are computationally inefficient. Besides, previous studies show that manipulating directly on the TDOA metric usually gives rise to intricate estimators. Aiming at bypassing these challenges, we turn to retrieve the underlying time-of-arrival framework by treating the unknown source onset time as an optimization variable and imposing certain inequality constraints on it, mitigate the NLOS errors through the $\ell_1$-norm robustification, and finally apply a hardware realizable neurodynamic model based on the redefined augmented Lagrangian and projection theorem to solve the resultant nonconvex optimization problem with inequality constraints. It is validated through extensive simulations that the proposed scheme can strike a nice balance between localization accuracy, computational complexity, and prior knowledge requirement., Comment: This paper has been accepted for publication by Signal Processing

A foremost task in frequency diverse array multiple-input multiple-output (FDA-MIMO) radar is to efficiently obtain the target signal in the presence of interferences. In this paper, we employ a novel "low-rank + low-rank + sparse" decomposition model to extract the low-rank desired signal and suppress the jamming signals from both barrage and burst jammers. In the literature, the barrage jamming signals, which are intentionally interfered by enemy jammer radar, are usually assumed Gaussian distributed. However, such assumption is oversimplified to hold in practice as the interferences often exhibit non-Gaussian properties. Those non-Gaussian jamming signals, known as impulsive noise or burst jamming, are involuntarily deviated from friendly radar or other working radio equipment including amplifier saturation and sensor failures, thunderstorms and man-made noise. The estimation performance of the existing estimators, relied crucially on the Gaussian noise assumption, may degrade substantially since the probability density function (PDF) of burst jamming has heavier tails that exceed a few standard deviations than the Gaussian distribution. To capture a more general signal model with burst jamming in practice, both barrage jamming and burst jamming are included and a two-step "Go Decomposition" (GoDec) method via alternating minimization is devised for such mixed jamming signal model, where the $a$ $priori$ rank information is exploited to suppress two kinds of jammers and estimate the desired target. Simulation results verify the robust performance of the devised scheme.

With the wide deployment of digital image capturing equipment, the need of denoising to produce a crystal clear image from noisy capture environment has become indispensable. This work presents a novel image denoising method that can tackle both impulsive noise, such as salt and pepper noise (SAPN), and additive white Gaussian noise (AWGN), such as hot carrier noise from CMOS sensor, at the same time. We propose to use low-rank matrix approximation to form the basic denoising framework, as it has the advantage of preserving the spatial integrity of the image. To mitigate the SAPN, the original noise corrupted image is randomly sampled to produce sampled image sets. Low-rank matrix factorization method (LRMF) via alternating minimization denoising method is applied to all sampled images, and the resultant images are fused together via a wavelet fusion with hard threshold denoising. Since the sampled image sets have independent but identical noise property, the wavelet fusion serves as the effective mean to remove the AWGN, while the LRMF method suppress the SAPN. Simulation results are presented which vividly show the denoised images obtained by the proposed method can achieve crystal clear image with strong structural integrity and showing good performance in both subjective and objective metrics.

This study addresses the problem of discrete signal reconstruction from the perspective of sparse Bayesian learning (SBL). Generally, it is intractable to perform the Bayesian inference with the ideal discretization prior under the SBL framework. To overcome this challenge, we introduce a novel discretization enforcing prior to exploit the knowledge of the discrete nature of the signal-of-interest. By integrating the discretization enforcing prior into the SBL framework and applying the variational Bayesian inference (VBI) methodology, we devise an alternating optimization algorithm to jointly characterize the finite-alphabet feature and reconstruct the unknown signal. When the measurement matrix is i.i.d. Gaussian per component, we further embed the generalized approximate message passing (GAMP) into the VBI-based method, so as to directly adopt the ideal prior and significantly reduce the computational burden. Simulation results demonstrate substantial performance improvement of the two proposed methods over existing schemes. Moreover, the GAMP-based variant outperforms the VBI-based method with i.i.d. Gaussian measurement matrices but it fails to work for non i.i.d. Gaussian matrices., Comment: 35 pages, 8 figures

Matrix completion (MC) is a promising technique which is able to recover an intact matrix with low-rank property from sub-sampled/incomplete data. Its application varies from computer vision, signal processing to wireless network, and thereby receives much attention in the past several years. There are plenty of works addressing the behaviors and applications of MC methodologies. This work provides a comprehensive review for MC approaches from the perspective of signal processing. In particular, the MC problem is first grouped into six optimization problems to help readers understand MC algorithms. Next, four representative types of optimization algorithms solving the MC problem are reviewed. Ultimately, three different application fields of MC are described and evaluated., Comment: 12 pages, 9 figures