Intensity Statistics of Random Signals in Gaussian Noise

The intensity statistics of signals in the presence of Gaussian noise is obtained by studying the model of a random signal plus a random phasor sum. The additive Gaussian noise is shown to result in a Bessel transform of the probability density of the signal intensity. The transformation of the intensity statistics can generally be applied to a mixture of independent random signals, one of which being a complex-valued Gaussian random process. It is used to retrieve intensity statistics of microwave pulsed transmission from Gaussian noise at long time delays.