The generation of correlated Rayleigh random variates by inverse discrete Fourier transform

A number of different algorithms are used for the generation of correlated Rayleigh random variates. This paper presents an analysis of the statistica l properties of methods based on the inverse discrete Fourier transform (ID FT). A modification of the algorithm of Smith is presented, the new method requiring exactly one-half the number of IDFT operations and roughly two-th irds the computer memory of the original method. Evaluations of and compari sons between various variate generation methods using meaningful quantitati ve measures are believed to be lacking, Recently, new quantitative quality measures for random variate generation hare been proposed that are, in part icular, meaningful and useful for digital communication system simulation, This paper presents the application of these measures to the IDFT method an d three other methods of correlated variate generation, comparing the algor ithms in terms of the quality of the generated samples and the required com putational effort.