Detection of multiplicative noise in stationary random processes using second- and higher order statistics

This paper addresses the problem of detecting the presence of colored multi plicative noise, when the information process can he modeled as a parametri c ARMA process. For the case of zero-mean multiplicative noise, a cumulant based suboptimal detector is studied. This detector tests the nullity of a specific cumulant slice, A second detector is developed when the multiplica tive noise is nonzero mean. This detector consists of filtering the data by an estimated AR filter. Cumulants of the residual data are then shown to b e well suited to the detection problem. Theoretical expressions for the asy mptotic probability of detection are given. Simulation-derived finite-sampl e ROC curves are shown for different sets of model parameters.