The detection of signals in impulsive noise

This dissertation addresses the problem of detecting known, discrete-time signals in additive non-Gaussian noise. The case of statistically independent samples is emphasized. After a brief introduction to the detection problem, the characteristics and sources of impulsive noise are discussed. Several models for impulsive noise are then presented. The complexity of these models and the need for simple density functions to approximate the first order characteristics of impulsive noise justify consideration of three systems of densities. These three systems are: a generalized Gaussian noise, the Johnson S(u) System, and a mixture model. These are used throughout this dissertation to provide examples. In many detection problems it may only be possible to define a class of probability densities which contains the actual noise density. In such cases minimax detectors may be used to guarantee a lower bound on detector performance for the entire class. The minimax detector is the optimum detector for the worst case density. It is shown that the worst case density, in terms of minimizing the asymptotic probability of detecting a signal, is that density which minimizes Fisher's Information over the entire class. Several classes of densities are considered and conditions are established for the minimax detectors.