Computationally efficient Maximum-Likelihood estimation of structured covariance matrices

A computationally efficient method for structured covariance matrix estimation is presented. The proposed method provides an Asymptotic (for large samples) Maximum Likelihood estimate of a structured covariance matrix and is referred to as AML. A closed-form formula for estimating Hermitian Toeplitz covariance matrices is derived which makes AML computationally much simpler than most existing Hermitian Toeplitz matrix estimation algorithms. The AML covariance matrix estimator can be used in a variety of applications. We focus on array processing herein and show that AML enhances the performance of angle estimation algorithms, such as MUSIC, by making them attain the corresponding Cramer-Rao bound (CRB) for uncorrelated signals.