The generation of independent Rayleigh faders

The simulation of wireless communication channels often requires the generation of multiple complex waveforms satisfying the following conditions. (1) The real and imaginary parts are independent zero-mean random Gaussian processes with identical auto-correlation functions. (2) The complex waveforms are independent so that the cross-correlation function between any two waveforms is zero. We first analyze previously proposed methods based on Jakes fading model to demonstrate that the above two conditions have not been satisfied. We then propose a novel method for the generation of multiple Rayleigh faders, which uses improved arrival angle patterns and incident wave phases. The auto-correlation and cross-correlation functions are derived to prove theoretically that the above two conditions are satisfied. Finally the statistical properties are verified by numerical results.