Locally optimal covariance matrix estimation techniques for array signal processing applications

Recent results on the detection-estimation of more uncorrelated Gaussian sources than sensors in sparse linear antenna arrays reinforces the need for an accurate maximum likelihood (ML) estimation of structured covariance matrices. A lower bound on the maximum likelihood ratio (LR) is introduced and is shown to be effective in assessing nonoptimal solutions. We show that for this application, estimation techniques based on least-squares criteria lead to results that fail to approach this lower bound, even for an asymptotically large sample volume. We introduce a LR optimisation method that generates a class of solutions that statistically exceed this bound.