Maximum likelihood estimation of a linearly structured covariance with application to antenna array processing

The author considers the maximum-likelihood (ML) estimation of the covariance of a zero-mean Gaussian random vector from its samples, when the covariance has a certain known structure that typically arises in antenna array processing. Owing to this structure, the conventional sample covariance is no longer the ML estimator. While previous approaches to ML estimation of similar structured covariances have relied on brute-force nonlinear programming methods to extremize the likelihood function, this approach derives analytical results for the special structure considered. The resulting algorithm is based on the eigendecomposition of a matrix derived from the sample covariance. The algorithm has application in the estimation of spectral parameters of correlated source signals in a wavefield.