The Relationship Between the Detection of Sure and Stochastic Signals in Noise

Abstract

The relationship between the detection of a sure and of a stochastic signal in noise is considered when the signal and noise are independent and non-Gaussian and the noise is not necessarily additive. Among other results the following are established. If the detection of almost all sample functions of the stochastic signal is regular, then so is the detection of the stochastic signal, and the likelihood ratio of the stochastic signal is expressed in terms of the likelihood ratio of the sure signal case. If the detection of the stochastic signal is singular, then so is the detection of almost all sample functions of the signal. Some special cases of interest are considered including the problems of detecting spherically invariant signals in additive Gaussian noise, and non-Gaussian signals in additive and/or multiplicative Gaussian noise.