A technique for detecting unknown weak signals in noise that is not additive white Gaussian

A general spectrum-analysis-based approach to the problem of detecting the presence of unknown weak signals in noisy observations is developed. The weak signal assumption enables exploitation of familiar results from the theory of local optimality, from which correlation-based detectors for the presence of known weak signals in additive independent and identically distributed (IID) noise have been derived. The development here follows from the perception that a spectrum analyzer is nothing more than a number of correlators in parallel. The approach has application to any observations that are not IID Gaussian processes. Some practical situations treated here, in which signal presence detection might be better accomplished using the proposed approach, are unknown weak signals: (1) in additive non-Gaussian interference, (2) in additive colored Gaussian noise, and (3) at the output of a nonlinear system, such as a square-law device. Items (2) and (3) required the extension of correlations-based locally optimum detection theory to cover observation processes that are not necessarily signals in additive noise