In this paper, new sum-of-sinusoids statistical simulation models are proposed for Rayleigh fading channels. These new models employ random path gain, random initial phase, and conditional random Doppler frequency for all individual sinusoids. It is shown that the autocorrelations and cross correlations of the quadrature components, and the autocorrelation of the complex envelope of the new simulators match the desired ones exactly, even if the number of sinusoids is as small as a single-digit integer. Moreover, the probability density functions of the envelope and phase, the level crossing rate, the average fade duration, and the autocorrelation of the squared fading envelope which contains fourth-order statistics of the new simulators, asymptotically approach the correct ones as the number of sinusoids approaches infinity, while good convergence is achieved even when the number of sinusoids is as small as eight. The new simulators can be directly used to generate multiple uncorrelated fading waveforms for frequency selective fading channels, multiple-input multiple-output channels, and diversity combining scenarios. Statistical properties of one of the new simulators are evaluated by numerical results, finding good agreements.


Electrical and Computer Engineering

Keywords and Phrases

Rayleigh Channels; Rayleigh Fading Channels; Autocorrelations; Average Fade Duration; Conditional Random Doppler Frequency; Convergence; Cross Correlations; Diversity Combining Scenarios; Fading Waveforms; Fourth Order Statistics; Frequency Selective Fading Channels; Higher Order Statistics; Level Crossing Rate; Mobile Radio; Multiple-Input Multiple-Output Channels; Probability Density Functions; Quadrature Components; Random Initial Phase; Random Path Gain; Simulation Models; Squared Fading Envelope; Statistical Properties; Sum-Of-Sinusoids Statistical Simulation Models

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2003 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jan 2003