Direction Of Arrival Estimation For Non-Coherent Sub-Arrays Via Joint Sparse And Low-Rank Signal Recovery

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 only 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.

Direction of Arrival Estimation and Phase-Correction for Non-Coherent Sub-Arrays: A Convex Optimization Approach

“…We assume that N snapshots are observed and that there are different unknown phase shifts at every snapshot. 2 A few preliminary single-snapshot results appeared in our conference version [33]. The current extended version generalizes the problem to multiple snapshots, designs an efficient optimization algorithm (which is indispensable for handling cases with multiple snapshots), replaces the naive phase shift estimation in [33] with a well-justified sub-problem that admits a sophisticated tight convex relaxation, and includes a more extensive empirical study.…”