Simulation models with correct statistical properties for rayleigh fading channels

TLDR

The paper proposes new sum‑of‑sinusoids simulation models for Rayleigh fading channels. These models generate fading waveforms by assigning random path gains, initial phases, and conditional Doppler frequencies to each sinusoid, enabling the creation of multiple uncorrelated waveforms for frequency‑selective, MIMO, and diversity scenarios. The models achieve exact matching of autocorrelation, cross‑correlation, envelope and phase PDFs, level‑crossing rate, average fade duration, and fourth‑order statistics even with a single‑digit number of sinusoids, and numerical results confirm good agreement as the number of sinusoids increases.

Abstract

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.