Locally optimal maximum-likelihood estimate of a Toeplitz matrix of given rank

ABSTRACT We derive an algorithm to compute a maximum-likelihood (ML) estimate of a Toeplitz covariance matrix whose rank is known a priori that is “locally optimal”, by maximising the likelihood ratio in the neighborhood of . This problem arises, for example, in the detection and/or direction-of-arrival (DOA) estimation of uncorrelated plane-wave sources using a nonuniform (sparse) sensor linear antenna array, where (the “superior” case), but the problem is important in its own right, and has application to other areas of signal processing and communications. The algorithm relies upon the solution of a convex linear programming (LP) problem, whose feasibility is guaranteed.