The simulation of independent Rayleigh faders

Multiple independent Rayleigh fading waveforms are often required for the simulation of wireless communications channels. Jakes (1974) Rayleigh fading model and its derivatives based on the sum-of-sinusoids provide simple simulators, but they have major shortcomings in their simulated correlation functions. A novel sum-of-sinusoids fading model is proposed and verified, which generates Rayleigh fading processes satisfying the theoretical independence requirements and providing desired power spectral densities with ideal second-order moment. The effects of replacing sinusoids in the proposed model by their approximate waveforms are also analyzed and tested. Performance evaluation and comparison are provided, using the quality measures of the mean-square-error of autocorrelation function and the second-order moment of the power spectral density.