Rules of postdetector detection of weak signals in non-Gaussian noise of unknown power

Locally most powerful rank and parametric invariant (to noise level) rules of detection are obtained for the postdetector detection of weak signals in non-Gaussian noise. It is shown that the construction of these rules is based on the local representation of the density of the envelope of the noise-signal mixture. An explicit form of the statistics is obtained for envelopes with Nakagami and Weibull distributions.