Optimal array signal processing in the presence of coherent wavefronts

The problem of estimating the parameters of several wavefronts from the measurements of multiple sensors is often referred to as array signal processing. The maximum likelihood (ML) estimator in array signal processing for the case of non-coherent signals has been studied extensively. The focus here is on the ML estimator for the case of stochastic coherent signals which arises due to, for example, specular multipath propagation. We show the very surprising fact that the ML estimates of the signal parameters obtained by ignoring the information that the sources are coherent, coincide in large samples with the ML estimates obtained by exploiting the coherent source information. Thus, the ML signal parameter estimator derived for the non-coherent case (or its large-sample realizations such as MODE os WSF) asymptotically achieves the lowest possible estimation error variance (corresponding to the coherent Cramer-Rao bound)