Direction of Arrival Estimation for Non-Coherent Sub-Arrays via Joint Sparse and Low-Rank Signal Recovery

TL;DR

This paper introduces a novel method for estimating directions of arrival using non-coherent sub-arrays by jointly recovering sparse and low-rank signals, improving accuracy over existing non-coherent and sparsity-based techniques.

Contribution

It formulates DOA estimation for non-coherent sub-arrays as a joint sparse and low-rank matrix recovery problem and proposes a convex relaxation approach with phase correction for enhanced accuracy.

Findings

Outperforms existing non-coherent processing strategies.

Improves DOA estimation accuracy with phase correction.

Demonstrates effectiveness through numerical experiments.

Abstract

Estimating the directions of arrival (DOAs) of multiple sources from a single snapshot obtained by a coherent antenna array is a well-known problem, which can be addressed by sparse signal reconstruction methods, where the DOAs are estimated from the peaks of the recovered high-dimensional signal. In this paper, we consider a more challenging DOA estimation task where the array is composed of non-coherent sub-arrays (i.e., sub-arrays that observe different unknown phase shifts due to using low-cost unsynchronized local oscillators). We formulate this problem as the reconstruction of a joint sparse and low-rank matrix and solve its convex relaxation. While the DOAs can be estimated from the solution of the convex problem, we further show how an improvement is obtained if instead one estimates from this solution the phase shifts, creates "phase-corrected" observations and applies another final (plain, coherent) sparsity-based DOA estimation. Numerical experiments show that the proposed approach outperforms strategies that are based on non-coherent processing of the sub-arrays as well as other sparsity-based methods.