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 forthe case of non-coherent signals has been studied extensively. The focus here is on the ML estimator for thecase of stochastic coherent signals which arises due to, for example, specular multipath propagation. We showthe very surprising fact that the ML estimates of the signal parameters obtained by ignoring the information thatthe sources are coherent, coincide in large samples with the ML estimates obtained by exploiting the coherentsource 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)