DOA Estimation in Partially Correlated Noise Using Low-Rank/Sparse Matrix Decomposition

TL;DR

This paper introduces a novel low-rank/sparse matrix decomposition method for DOA estimation in environments with partially correlated noise, effectively handling correlated and coherent sources with improved accuracy.

Contribution

The paper presents a new convex optimization approach leveraging low-rank and sparse matrix techniques for DOA estimation in partially correlated noise environments, addressing correlated and coherent sources.

Findings

Method outperforms traditional algorithms in correlated noise scenarios

Achieves near CRB performance in simulations

Handles both uncorrelated and correlated sources effectively

Abstract

We consider the problem of direction-of-arrival (DOA) estimation in unknown partially correlated noise environments where the noise covariance matrix is sparse. A sparse noise covariance matrix is a common model for a sparse array of sensors consisted of several widely separated subarrays. Since interelement spacing among sensors in a subarray is small, the noise in the subarray is in general spatially correlated, while, due to large distances between subarrays, the noise between them is uncorrelated. Consequently, the noise covariance matrix of such an array has a block diagonal structure which is indeed sparse. Moreover, in an ordinary nonsparse array, because of small distance between adjacent sensors, there is noise coupling between neighboring sensors, whereas one can assume that nonadjacent sensors have spatially uncorrelated noise which makes again the array noise covariance matrix sparse. Utilizing some recently available tools in low-rank/sparse matrix decomposition, matrix completion, and sparse representation, we propose a novel method which can resolve possibly correlated or even coherent sources in the aforementioned partly correlated noise. In particular, when the sources are uncorrelated, our approach involves solving a second-order cone programming (SOCP), and if they are correlated or coherent, one needs to solve a computationally harder convex program. We demonstrate the effectiveness of the proposed algorithm by numerical simulations and comparison to the Cramer-Rao bound (CRB).