A subspace method for array covariance matrix estimation

Abstract

This paper introduces a subspace method for the estimation of an array covariance matrix. When the received signals are uncorrelated, it is shown that the array covariance matrices lie in a special subspace defined through all possible correlation vectors of the received signals and whose dimension is typically much smaller than the ambient dimension. Based on this observation, a subspace-based covariance matrix estimator is proposed 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 that is easily implementable is proposed. The proposed approach is shown to yield higher estimation accuracy than conventional approaches since it eliminates the estimation error that does not lie in the subspace of the true covariance matrices. The numerical examples demonstrate that the proposed estimator can significantly improve the estimation quality of the covariance matrix.