Intensity statistics of random signals in Gaussian noise.

The intensity statistics of random signals in the presence of Gaussian noise is obtained by considering 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 signal intensity. The transformation of the intensity statistics can generally be applied to mixtures 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.