Locally optimum detection: a linear model that explains how it works

Locally optimum (LO) detection is a technique that achieves near optimum detectability of weak signals in non-Gaussian environments. A linearized model for LO detection that both illuminates its operation in the weak signal case and imbues it with a familiar-looking signal-to-noise ratio useful in characterizing detection performance is developed and justified. Though the analysis is quite general with respect to background distributions, numerical examples involving detection of sinusoids in Cauchy noise are presented to corroborate the theory, and analysis results for Cauchy-distributed noise are used throughout to illustrate each theoretical point