First Probability Densities for Receivers with Square Law Detectors

Abstract

The method of Kac and Siegert for finding the output probabi ity density characteristic function for receivers with square law envelope detections is discussed, and a parallel development is given for the square law rectifier. Procedures are then outlined for determining the probability density functions directly, i.e., without solving the eigenvalue problem or inverting the characteristic function. The method depends on expanding the density function in an orthonormal series, the coefficients of which are expressed in terms of cumulants, which in turn are obtained from the system kernel by straightforward quadratures. As an example to illustrate the procedure, a receiver with Gaussian IF and Gaussian audio-frequency pass characteristics is treated in detail, and the output probability density functions are found for various sinusoidal input signal strengths and IF vs audio band-width ratios.