Minimax robust detection of a known signal in a general class of noises

In practical communication environments, it is frequently observed that the underlying noise PDF is not Gaussian and may vary in a wide range from short-tailed to heavy-tailed forms. To provide stable and high quality detection of a known signal, we design an asymptotically minimax (in the Huber sense) minimum distance detection rule under rather general conditions of regularity imposed upon noise PDFs and derive the closed expression for its probability of detection error. In several PDF classes, the least favorable PDFs and corresponding minimax detectors are written down. The minimax robust detectors exhibit robustness of detection in heavy-tailed noise and efficiency in short-tailed noise, both in asymptotics and on finite samples.