Mixture models for underwater burst noise and their relationship to a simple bivariate density representation

Many non-Gaussian processes have been modeled as having simple mixtures for their univariate densities. In this paper a switched-source model is presented and is shown to be such a process. The bivariate density of samples arising from this model is derived; this density is a particularly simple bivariate density, the Frechet density. It is further shown that any symmetric Frechet density can be thought of as being produced by some switched-source model. This bivariate density is used to derive the locally optimal memoryless nonlinearity, which, in a wide class of models, turns out to be identical to that derived under an independence assumption. Suboptimal detectors taking advantage of dependence are derived, and a simulation is carried out under this model. It is seen that there is some improvement possible through knowledge of dependence.