Rank Minimization-based Toeplitz Reconstruction for DoA Estimation Using Coprime Array

TL;DR

This paper introduces a novel low-rank Toeplitz matrix reconstruction method for DoA estimation with coprime arrays, improving resolution and accuracy over existing techniques.

Contribution

It proposes a rank minimization approach using atomic norm and cyclic optimization for enhanced DoA estimation with sparse coprime arrays.

Findings

Improved degrees-of-freedom and spatial resolution.

Superior root-mean-square error performance.

Effective integration with MUSIC algorithm.

Abstract

In this paper, we address the problem of direction finding using coprime array, which is one of the most preferred sparse array configurations. Motivated by the fact that non-uniform element spacing hinders full utilization of the underlying information in the receive signals, we propose a direction-of-arrival (DoA) estimation algorithm based on low-rank reconstruction of the Toeplitz covariance matrix. The atomic-norm representation of the measurements from the interpolated virtual array is considered, and the equivalent dual-variable rank minimization problem is formulated and solved using a cyclic optimization approach. The recovered covariance matrix enables the application of conventional subspace-based spectral estimation algorithms, such as MUSIC, to achieve enhanced DoA estimation performance. The estimation performance of the proposed approach, in terms of the degrees-of-freedom and spatial resolution, is examined. We also show the superiority of the proposed method over the competitive approaches in the root-mean-square error sense.