Positive definite Toeplitz completion in DOA estimation for partially-augmentable nonuniform linear antenna arrays

Maximum-entropy positive-definite completion for partially-specified Toeplitz covariance matrices is developed for DOA estimation in partially-augmentable antenna arrays (those that have an incomplete set of covariance lags). Both the spatial covariance matrix estimation problem and the spatial spectrum estimation problem must be formulated as positive definite Toeplitz completion problems. The latter problem is investigated for two cases; firstly in the case where the available covariance lags ate supposed to be precisely known (deterministic completion). Secondly, we investigate the case where we assume we have sufficient statistics for the DOA estimates in the form of the direct data covariance matrix, obtained by sample averaging on a set of N independent vectors ("snapshots") originating from a complex Gaussian distribution.