Detection in weibull and log-normal noises

Abstract

The discrete-time detection of narrowband coherent and incoherent pulse train signals in narrowband non-Gaussian noise is investigated. The locally optimum (LO) detector structures are developed and found to be in the form of incorporating a locally optimum zero-memory nonlinearity (LOZNL) into the Neyman-Pearson optimum detector for narrowband Gaussian noise. Many practical detectors belong in the same class of structures with the LO detector. The expressions for the efficacies of the detectors are derived. In particular, Weibull and log-normal noise models are considered. The LOZNL’s, and the efficacies of the detectors are given, and numerical results are graphically presented. It is shown that, in the sense of the Pitman asymptotic relative efficiency (ARE), the asymptotic performance of many detectors whose nonlinearity can more effectively suppress the tail of the noise envelope distribution is apparently better than that of the Neyman-Pearson optimum detector for narrowband Gaussian noise.