A Subspace Method for Array Covariance Matrix Estimation

TL;DR

This paper proposes a subspace-based covariance matrix estimator for array signals that improves accuracy by leveraging the low-dimensional subspace where true covariance matrices reside, solved via a convex optimization approach.

Contribution

It introduces a novel subspace method for covariance estimation that is computationally efficient and more accurate than traditional methods, using a semi-definite convex optimization framework.

Findings

Significantly improves covariance estimation accuracy.

Leverages low-dimensional subspace of true covariance matrices.

Offers a nearly closed-form solution for practical implementation.

Abstract

This paper introduces a subspace method for the estimation of an array covariance matrix. It is shown that when the received signals are uncorrelated, the true array covariance matrices lie in a specific subspace whose dimension is typically much smaller than the dimension of the full space. Based on this idea, a subspace based covariance matrix estimator is proposed. The estimator is obtained as a solution to a semi-definite convex optimization problem. While the optimization problem has no closed-form solution, a nearly optimal closed-form solution is proposed making it easy to implement. In comparison to the conventional approaches, the proposed method yields higher estimation accuracy because it eliminates the estimation error which does not lie in the subspace of the true covariance matrices. The numerical examples indicate that the proposed covariance matrix estimator can significantly improve the estimation quality of the covariance matrix.