Robust detection using extreme-value theory

The use of extreme-value theory (EVT) in the detection of a binary signal in additive, but statistically unknown, noise is considered. It is shown that the optimum threshold and the probability of error of the system can be accurately estimated by using EVT to obtain properties of the initial probability density functions on their "tails." Both constant signals and slowly fading signals are considered. In the case of a fading signal, the detector becomes adaptive. Detection of the constant signal, both with and without an initial learning period, is studied by computer simulation.