An improved model for the simulation of multiple uncorrelated Rayleigh fading waveforms

Multiple independent Rayleigh fading waveforms are often required for the simulation of wireless communication channels. Jakes model and its derivatives based on SoS (Sum-of-Sinusoids) provide simple simulators for Rayleigh fading, but they have shortcomings that their correlation functions are not always approach theoretical value. In this paper, the statistical properties of SoS fading model with a finite number of sinusoids are analyzed, and an improved model for multiple uncorrelated Rayleigh fading waveforms based on SoS model is proposed, which can reduce the computational complexity while maintain the statistical properties well. Compared with other models which proposed before (take MEA and Zheng's model for example), this new model satisfies not only the stochastic characteristics of Rayleigh fading channel but also the independence between pair of fading waveforms. Mathematical derivation and corresponding simulation results are also provided. The simulation results show that the statistics of single waveform of the proposed model are the same as other models while the independence between pair of fading waveforms is obviously better.