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In this letter, we revisit the recently proposed cell outlier-resistant method cellMCD (minimum covariance determinant) and derive a version of it called cellMCD+ that has better performance. We illustrate the performance gain of cellMCD+ via numerical simulations in the case of estimating low-rank structured covariance matrices.

This paper investigates the transmit beamforming design for multiple-input multiple-output systems to support both multi-target localization and multi-user communications. To enhance the target localization performance, we derive the asymptotic Cramér-Rao bound (CRB) for target angle estimation by assuming that the receive array is linear and uniform. Then we formulate a beamforming design problem based on minimizing an upper bound on the asymptotic CRB (which is shown to be equivalent to maximizing the harmonic mean of the weighted beampattern responses at the target directions). Moreover, we impose a constraint on the SINR of each received communication signal to guarantee reliable communication performance. Two iterative algorithms are derived to tackle the non-convex design problem: one is based on the alternating direction method of multipliers, and the other uses the majorization-minimization technique to solve an equivalent minimax problem. Numerical results show that, through elaborate dual-function beamforming matrix design, the proposed algorithms can simultaneously achieve superior angle estimation performance as well as high-quality multi-user communications.

In this letter we present a framework for estimating sparse covariance matrices, wherein we solve the l(0)-norm penalized maximum likelihood estimation problem using the extended Bayesian information criterion (EBIC), a high dimensional model selection rule. The framework combines choosing the sparsity pattern and estimating the covariance matrix in a single step, eliminating the need for any hyper-parameter tuning. Using the framework we propose a cyclic majorization-minimization based technique and apply it to synthetic data to evaluate its performance in terms of normalized root mean square error (NRMSE) and Kullback Leibler (KL) divergence.

In this correspondence, we develop an algorithm for maximum likelihood (ML) source localization using received signal strength (RSS) measurements. Unlike the conventional methods that resort to first-order Taylor series approximations to linearize the RSS data model, we use the actual nonlinear data model and propose an algorithm for solving the associated ML estimation problem. More specifically, we reformulate the original ML minimization as a min–max problem, which we solve using a majorization–minimization technique. Each iteration of the resultant algorithm involves solving a simple convex problem and monotonically decreases the (negative) ML criterion. Several numerical simulation results illustrate the accuracy of the proposed method when compared against state-of-the-art methods.

Multistatic localization techniques employ noisy range measurements collected via multiple transmitters and receivers to localize a target. However, in many realistic scenarios the data are corrupted by outliers which may be due to the failure of or malicious attack on one or more sensors. The presence of outliers leads to performance degradation in terms of target localization accuracy. In this letter, we address the problem of multistatic target localization when the measurements contain outliers. We employ a multi-hypothesis testing method based on the false discovery rate (FDR) to detect the outliers. More specifically, we consider a penalized maximum likelihood problem for joint estimation of the number and positions of the outliers as well as the target position, and the noise variance. To solve this problem, an iterative algorithm employing the majorization-minimization technique that minimizes the objective in a monotonic manner is developed. Through numerical simulations, we compare the proposed algorithm with other robust state-of-the-art algorithms and show that the proposed algorithm has superior performance.

Graph learning is an important problem in the field of graph signal processing. However, the data available in real-world applications are often contaminated with outliers, which makes the application of traditional methods challenging. In this paper, we address this problem by developing an algorithm that effectively learns the graph Laplacian matrix from node signals corrupted by outliers. Specifically, we maximize the penalized log-likelihood of the uncorrupted data, where the penalty is chosen via the false discovery rate (FDR) principle, with respect to both the number of outliers and their locations, as well as the precision matrix of the data under the graph Laplacian constraints. To illustrate the robustness to outliers, we compare our method with two state-of-the-art graph learning methods, one that considers outliers in the data and one that does not, using different performance metrics. Our findings demonstrate that the proposed method efficiently detects the number and positions of outliers and accurately learns the graph in their presence.

In this article, we propose a robust technique for direction-of-arrival (DOA) estimation in the presence of outliers, which may be caused by either impulsive noise or malfunctioning sensors in the array. Conventional DOA estimation algorithms like multiple signal classification (MUSIC) cannot accurately estimate the DOAs from outlier-corrupted data because the array covariance matrix is poorly estimated. We propose a penalized likelihood approach to robustly estimate the signal (low-rank) part of the array covariance matrix and apply MUSIC to this estimated covariance matrix to find the DOAs. The penalty in the proposed algorithm is derived from the principle of false discovery rate. Simulation results verify the effectiveness of the proposed approach when compared with state-of-the-art robust DOA estimation algorithms.

Designing optimal measurement operators for quantum state discrimination (QSD) is an important problem in quantum communications and cryptography applications. Prior works have demonstrated that optimal quantum measurement operators can be obtained by solving a convex semidefinite program (SDP). However, solving the SDP can represent a high computational burden for many real-time quantum communication systems. To address this issue, a majorisation-minimisation (MM)-based algorithm, called Quantum Majorisation-Minimisation (QMM) is proposed for solving the QSD problem. In QMM, the authors reparametrise the original objective, then tightly upper-bound it at any given iterate, and obtain the next iterate as a closed-form solution to the upper-bound minimisation problem. Our numerical simulations demonstrate that the proposed QMM algorithm significantly outperforms the state-of-the-art SDP algorithm in terms of speed, while maintaining comparable performance for solving QSD problems in quantum communication applications. A computationally efficient majorisation-minimisation (MM)-based algorithm is proposed for solving the optimal quantum state discrimination (QSD) problem in quantum communications applications.

This monograph presents a theoretical background and a broad introduction to the M in-Max Framework for M ajori- zation-Minimization (MM4MM), an algorithmic methodology for solving minimization problems by formulating them as min-max problems and then employing majorizationminimization. The monograph lays out the mathematical basis of the approach used to reformulate a minimization problem as a min-max problem. With the prerequisites covered, including multiple illustrations of the formulations for convex and non-convex functions, this work serves as a guide for developing MM4MM-based algorithms for solving non-convex optimization problems in various areas of signal processing. As special cases, we discuss using the majorization-minimization technique to solve min-max problems encountered in signal processing applications and min- max problems formulated using the Lagrangian. Lastly, we present detailed examples of using MM4MM in ten signal processing applications such as phase retrieval, source localization, independent vector analysis, beamforming and optimal sensor placement in wireless sensor networks. The devised MM4MM algorithms are free of hyper-parameters and enjoy the advantages inherited from the use of the majorization-minimization technique such as monotonicity.

In this paper, we propose a numerical method for the optimal placement of the receivers in a multistatic target localization system (with a single transmitter and multiple receivers) in order to improve the achievable target estimation accuracy of time-sum-of-arrival (TSOA) localization techniques, for 2D and 3D scenarios. The proposed algorithm is based on the principle of block majorization minimization (block MM) which is a combination of block coordinate descent and majorization-minimization (MM) methods. More precisely, we formulate the design objective for the placement of sensors performing TSOA measurements using A− and D− optimality criteria, and propose an iterative algorithm to find the optimal solution by first splitting the design variable into M blocks (where M is the number of receivers) and then applying the principle of MM on each block. The proposed method can additionally handle the cases where the transmitter also acts as a receiver. The framework can also be applied to the case of non-uniform noise variances at the receivers. Several numerical simulation results are included to show the benefits offered by the developed design algorithm.