Structured Autocorrelation Matrix Estimation for Coprime Arrays

TL;DR

This paper introduces a new optimization-based method for estimating the autocorrelation matrix in coprime arrays, ensuring it meets all necessary mathematical properties for improved signal processing accuracy.

Contribution

The work presents a novel estimation framework that guarantees the autocorrelation matrix is positive-definite, Hermitian, Toeplitz, and has equal noise eigenvalues, outperforming existing methods.

Findings

Outperforms standard autocorrelation estimates in error metrics

Improves direction-of-arrival estimation accuracy

Ensures all mathematical properties of the autocorrelation matrix

Abstract

A coprime array receiver processes a collection of received-signal snapshots to estimate the autocorrelation matrix of a larger (virtual) uniform linear array, known as coarray. By the received-signal model, this matrix has to be (i) Positive-Definite, (ii) Hermitian, (iii) Toeplitz, and (iv) its noise-subspace eigenvalues have to be equal. Existing coarray autocorrelation matrix estimates satisfy a subset of the above conditions. In this work, we propose an optimization framework which offers a novel estimate satisfying all four conditions. Numerical studies illustrate that the proposed estimate outperforms standard counterparts, both in autocorrelation matrix estimation error and Direction-of-Arrival estimation.