Towards incorporating toeplitz covariance into asymptotic maximum likelihood for estimating nominal direction of spatially distributed source

This paper addresses the covariance matrix estimation for improving the problem of estimating the nominal direction of a spatially distributed source in Rayleigh channel by employing a sensor array at the receiver. Three associated contributions are affordable herein. We first propose a large-sample approximation of maximum likelihood (ML) estimator for estimating a covariance matrix with linearly affine structure. Later, a connection of the proposed estimator to an existed criterion is secondly provided. This is to emphasize that it yields the same solution as the weighted covariance-matching criterion. The application area of such a notification stems from the fact that when invoking the uniform linear array with phase reference at the first element, the array covariance matrix is not only Hermitian but also Toeplitz. Based on such a priori knowledge, it is advantageous to make use of structured covariance matrix in parameter estimation. Towards this end, the last contribution for decreasing the directional estimate error is to incorporate the imposed Toeplitz-Hermitian matrix into another large-sample approximation of the ML estimator. Numerical simulation of the proposition is verified and then indicated that, particularly in non-asymptotic region, the asymptotically efficient estimator with Toeplitz constraint always outperforms the conventional approach without the additional information.