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

TLDR

Correlated Rayleigh random variate generation uses many algorithms, yet evaluations and comparisons using meaningful quantitative measures are lacking. The paper analyzes IDFT-based correlated Rayleigh variate generation, proposes new quantitative quality measures, and applies them to compare IDFT with three other methods in terms of sample quality and computational effort. The authors modify Smith’s 1975 algorithm to halve IDFT operations and reduce memory usage by two‑thirds, and introduce new quantitative quality measures to evaluate and compare the IDFT method with three other correlated variate generation algorithms.

Abstract

A number of different algorithms are used for the generation of correlated Rayleigh random variates. This paper presents an analysis of the statistical properties of methods based on the inverse discrete Fourier transform (IDFT). A modification of the algorithm of Smith (1975) is presented, the new method requiring exactly one-half the number of IDPT operations and roughly two-thirds the computer memory of the original method. Evaluations of and comparisons between various variate generation methods using meaningful quantitative measures are believed to be lacking. New quantitative quality measures for random variate generation have been proposed that are, in particular, meaningful and useful for digital communication system simulation. This paper presents the application of these measures to the IDFT method and three other methods of correlated variate generation, comparing the algorithms in terms of the quality of the generated samples and the required computational effort.