  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.
