2-D DOA Estimation for Acoustic Vector Sensor Array Based on Greedy Block Coordinate Descent Algorithm

Keywords: two-dimensional direction of arrival (DOA) estimation, acoustic vector sensor (AVS), greedy block coordinate descent(GBCD). Abstract. This paper presents an approach for the estimation of two-directional (2D)direction-of-arrival (DOA) using Acoustic Vector Sensor array based on greedy block coordinate descent(GBCD) algorithm, which can achieve faster convergence rate and better estimation accuracy. Moreover, a weighted form of block selection rule is proposed with the MUSIC prior. The identifiability of the presented approach is studied using computer simulations. It is demonstrated that the 2D DOAs of AVS can be realized using the approach, which has a superior resolution

A Compact Formulation for the ℓ2,1\ell_{2,1} Mixed-Norm Minimization Problem

Parameter estimation from multiple measurement vectors (MMVs) is a fundamental problem in many signal processing applications, e.g., spectral analysis and direction-of- arrival estimation. Recently, this problem has been address using prior information in form of a jointly sparse signal structure. A prominent approach for exploiting joint sparsity considers mixed-norm minimization in which, however, the problem size grows with the number of measurements and the desired resolution, respectively. In this work we derive an equivalent, compact reformulation of the $\ell_{2,1}$ mixed-norm minimization problem which provides new insights on the relation between different existing approaches for jointly sparse signal reconstruction. The reformulation builds upon a compact parameterization, which models the row-norms of the sparse signal representation as parameters of interest, resulting in a significant reduction of the MMV problem size. Given the sparse vector of row-norms, the jointly sparse signal can be computed from the MMVs in closed form. For the special case of uniform linear sampling, we present an extension of the compact formulation for gridless parameter estimation by means of semidefinite programming. Furthermore, we derive in this case from our compact problem formulation the exact equivalence between the $\ell_{2,1}$ mixed-norm minimization and the atomic-norm minimization. Additionally, for the case of irregular sampling or a large number of samples, we present a low complexity, grid-based implementation based on the coordinate descent method

Support Recovery of Greedy Block Coordinate Descent Using the Near Orthogonality Property

In this paper, using the near orthogonal property, we analyze the performance of greedy block coordinate descent (GBCD) algorithm when both the measurements and the measurement matrix are perturbed by some errors. An improved sufficient condition is presented to guarantee that the support of the sparse matrix is recovered exactly. A counterexample is provided to show that GBCD fails. It improves the existing result. By experiments, we also point out that GBCD is robust under these perturbations

Hybrid Precoding for Multiuser Millimeter Wave Massive MIMO Systems : A Deep Learning Approach

© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In multi-user millimeter wave (mmWave) multiple-input-multiple-output (MIMO) systems, hybrid precoding is a crucial task to lower the complexity and cost while achieving a sufficient sum-rate. Previous works on hybrid precoding were usually based on optimization or greedy approaches. These methods either provide higher complexity or have sub-optimum performance. Moreover, the performance of these methods mostly relies on the quality of the channel data. In this work, we propose a deep learning (DL) framework to improve the performance and provide less computation time as compared to conventional techniques. In fact, we design a convolutional neural network for MIMO (CNN-MIMO) that accepts as input an imperfect channel matrix and gives the analog precoder and combiners at the output. The procedure includes two main stages. First, we develop an exhaustive search algorithm to select the analog precoder and combiners from a predefined codebook maximizing the achievable sum-rate. Then, the selected precoder and combiners are used as output labels in the training stage of CNN-MIMO where the input-output pairs are obtained. We evaluate the performance of the proposed method through numerous and extensive simulations and show that the proposed DL framework outperforms conventional techniques. Overall, CNN-MIMO provides a robust hybrid precoding scheme in the presence of imperfections regarding the channel matrix. On top of this, the proposed approach exhibits less computation time with comparison to the optimization and codebook based approaches.Peer reviewe

Low-complexity DCD-based sparse recovery algorithms

Sparse recovery techniques find applications in many areas. Real-time implementation of such techniques has been recently an important area for research. In this paper, we propose computationally efficient techniques based on dichotomous coordinate descent (DCD) iterations for recovery of sparse complex-valued signals. We first consider $\ell_2 \ell_1$ optimization that can incorporate \emph{a priori} information on the solution in the form of a weight vector. We propose a DCD-based algorithm for $\ell_2 \ell_1$ optimization with a fixed $\ell_1$-regularization, and then efficiently incorporate it in reweighting iterations using a \emph{warm start} at each iteration. We then exploit homotopy by sampling the regularization parameter and arrive at an algorithm that, in each homotopy iteration, performs the $\ell_2 \ell_1$ optimization on the current support with a fixed regularization parameter and then updates the support by adding/removing elements. We propose efficient rules for adding and removing the elements. The performance of the homotopy algorithm is further improved with the reweighting. We then propose an algorithm for $\ell_2 \ell_0$ optimization that exploits homotopy for the $\ell_0$ regularization; it alternates between the least-squares (LS) optimization on the support and the support update, for which we also propose an efficient rule. The algorithm complexity is reduced when DCD iterations with a \emph{warm start} are used for the LS optimization, and, as most of the DCD operations are additions and bit-shifts, it is especially suited to real time implementation. The proposed algorithms are investigated in channel estimation scenarios and compared with known sparse recovery techniques such as the matching pursuit (MP) and YALL1 algorithms. The numerical examples show that the proposed techniques achieve a mean-squared error smaller than that of the YALL1 algorithm and complexity comparable to that of the MP algorithm