Intensity Statistics of Random Signals in Gaussian Noise

TL;DR

This paper derives the intensity statistics of signals in Gaussian noise using a Bessel transform, applicable to complex signals and microwave transmission, enhancing understanding of signal behavior in noisy environments.

Contribution

It introduces a method to obtain intensity statistics of signals in Gaussian noise via a Bessel transform, applicable to complex-valued processes and microwave transmission.

Findings

Gaussian noise results in a Bessel transform of the signal intensity density.

The method applies to mixtures of independent signals, including complex Gaussian processes.

Effective retrieval of microwave pulse transmission statistics from noise at long delays.

Abstract

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.