On Some First-order Statistics of Fading Signals in Noise†

Abstract

A series of results are derived for some first-order statistics of stationary fading signals when the signal envelope has a Pearson distribution. In particular, expressions are found for the distribution of the instantaneous value of the signal, both in the absence and presence of additive gaussian noise, and for the noisy envelope distribution of the received waveform. These results are useful in the evaluation of the performance of receivers operating in on incoherent fashion on fading signals corrupted by gaussian noise.