Grid-Less DOA Estimation Using Sparse Linear Arrays Based on Wasserstein Distance

Sparse linear arrays, such as nested and co-prime arrays, are capable of resolving O(M2) sources using only O(M) sensors by exploiting their so-called difference coarray model. One popular approach to exploit the difference coarray model is to construct an augmented covariance matrix from the sample covariance matrix. By applying common direction-of-arrival (DOA) estimation algorithms to this augmented covariance matrix, more sources than the number of sensors can be identified. In this letter, inspired by the optimal transport theory, we develop a new approach to construct this augmented covariance matrix. We formulate a structured covariance estimation problem that minimizes the Bures-Wasserstein distance between the sample covariance matrix and the subsampled augmented covariance matrix, which can be either casted to a semi-definite programming problem, or directly solved using gradient-based methods. Our approach contributes to a new grid-less DOA estimation algorithm for sparse linear arrays. Numerical examples show that our approach achieves state-of-art estimation performance.

I. Introduction

Direction-of-arrival (DOA) estimation, which recovers the direction information of multiple incoming waves using the measurements of sensor arrays, is one of the major problems in array signal processing [1]–[3]. With uniform linear arrays (ULAs), classical DOA estimation methods, such as MUtiple SIgnal Classification (MUSIC) [4], can resolve up to sources using sensors. With sparse linear arrays, such as minimum redundancy arrays (MRAs) [5], [6], nested arrays [7], [8], and co-prime arrays [9]–[12], up to uncorrelated sources can be resolved using sensors by exploiting the difference coarray model.