A Robust and Statistically Efficient Maximum-Likelihood Method for DOA Estimation Using Sparse Linear Arrays

TL;DR

This paper introduces MESA, a robust and efficient maximum-likelihood algorithm for DOA estimation using sparse linear arrays, capable of localizing many sources with high accuracy even under source correlation.

Contribution

It proposes a novel MESA algorithm that combines stochastic maximum likelihood with ADMM, achieving robustness to source correlations and applicability to various sparse array configurations.

Findings

MESA outperforms existing algorithms in statistical efficiency.

MESA is robust to source correlations.

MESA works with arbitrary sparse linear arrays.

Abstract

A recent trend of research on direction-of-arrival (DOA) estimation is to localize more uncorrelated sources than sensors by using a proper sparse linear array (SLA) and the Toeplitz covariance structure, at a cost of robustness to source correlations. In this paper, we make an attempt to achieve the two goals simultaneously by using a single algorithm. In order to statistically efficiently localize a maximal number of uncorrelated sources, we propose an effective algorithm for the stochastic maximum likelihood (SML) method based on elegant problem reformulations and the alternating direction method of multipliers (ADMM). We prove that the SML is robust to source correlations though it is derived under the assumption of uncorrelated sources. The proposed algorithm is usable for arbitrary SLAs (e.g., minimum redundancy arrays, nested arrays and coprime arrays) and is named as {\em m}aximum-likelihood {\em e}stimation via {\em s}equential {\em A}DMM (MESA). Extensive numerical results are provided that collaborate our analysis and demonstrate the statistical efficiency and robustness of MESA among state-of-the-art algorithms.