Abstract
In this paper, we present a fundamental study on the stationarity and ergodicity of eight classes of sum-of-cisoids (SOC) processes for the modeling and simulation of frequency-nonselective mobile Rayleigh fading channels. The purpose of this study is to determine which classes of SOC models enable the design of channel simulators that accurately reproduce the channel’s statistical properties without demanding information on the time origin or the time-consuming computation of an ensemble average. We investigate the wide-sense stationarity, first-order stationarity of the envelope, mean ergodicity, and autocorrelation ergodicity of the underlying random processes characterizing the different classes of stochastic SOC simulators. The obtained results demonstrate that only the class of SOC models comprising cisoids with constant gains, constant frequencies, and random phases is defined by a set of stationary and ergodic random processes. The analysis presented here can easily be extended with respect to the modeling and simulation of frequency-selective single-input single-output (SISO) and multiple-input multiple-output channels. For the case of frequency-selective SISO channels, we investigate the stationarity and ergodicity in both time and frequency of 16 different classes of SOC simulation models. The findings presented in this paper can be used in the laboratory as guidelines to design efficient simulation platforms for the performance evaluation of modern mobile communication systems.
Highlights
Computer simulators have become fundamental tools for the design, test, and optimization of modern mobile communication systems [1]
If the gains cn are equal to cn = σ0 2/N and the frequencies f n are given by (23), it is straightforward to show that the autocorrelation function (ACF) rμμ (τ ) of the stochastic simulation model is identical to the ACF rμμ(τ ) of the reference model, i.e., rμμ (τ ) = rμμ(τ )
We conclusively demonstrated that only the class defined by SOC models having cisoids with constant gains, constant Doppler frequencies, and random phases enables the design of channel simulators possessing the desired wide-sense stationary (WSS), ME, AE, and first-order stationary (FOS) properties
Summary
Computer simulators have become fundamental tools for the design, test, and optimization of modern mobile communication systems [1]. Despite the significant attention that SOC channel simulation models have attracted, a comprehensive study on their stationary and ergodic properties is still lacking in the literature To close this gap, we present in this paper a systematic analysis of the wide-sense stationarity, firstorder stationarity of the envelope, mean ergodicity, and autocorrelation ergodicity of eight fundamental classes of SOC simulation models for frequency-nonselective SISO Rayleigh fading channels. They investigated the widesense stationarity and the first-order stationarity of the IQ components of all eight classes of SOS channel simulators It is shown in [28,29,30] that an SOS process is stationary and ergodic if and only if the sinusoids’ gains and Doppler frequencies are constant quantities and the phases are random variables. For the performance evaluation of SOC simulation models with random/constant parameters, it is important to know the conditions for which the resulting stochastic process ζ (t) is stationary.
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