A non-Gaussian problem that arises in fused detection in clutter

A common model for sonar clutter is that of the transmitted signal convolved with a colored Gaussian process relating to the sea-bottom profile. Rather surprisingly, this noise becomes strongly non-Gaussian if there are multiple realizations and if a realistic random phase is introduced - the univariate statistics remain Gaussian, but the joint probability density function is not. In this letter, we explore this behavior and we develop optimal detection statistics for a "two-look" situation. It turns out that the gains over a naive assumption of Gaussianity can be substantial.