Improved models for the generation of multiple uncorrelated Rayleigh fading waveforms

TLDR

An improved sum‑of‑sinusoids simulation model is proposed for Rayleigh fading channels. The model uses random initial phases and conditionally random Doppler frequencies for each sinusoid in the sum‑of‑sinusoids representation. Its second‑order statistics match the target exactly even with a single‑digit number of sinusoids, higher‑order statistics converge to Clarke’s model as the number grows, and it can generate multiple uncorrelated fading waveforms, with a family of 16 equivalent simulators available.

Abstract

An improved sum-of-sinusoids simulation model is proposed for Rayleigh fading channels. The new model employs random initial phase, and conditional random Doppler frequency for all individual sinusoids. The second-order statistics of the new simulator match the desired ones exactly even if the number of sinusoids is a single-digit integer. Other key statistics of the new simulator approach the desired ones of Clarke's (1968) reference model as the number of sinusoids approaches infinity, while good convergence is achieved when the number of sinusoids is small. Moreover, the new simulator can be directly used to generate multiple uncorrelated fading waveforms; it is also pointed out that a class of 16 different simulators, which have identical statistical properties, can be developed for Rayleigh fading channels.