Analysis of error in the estimation of the temporal ACF of ergodic sum-of-cisoids simulators for mobile fading channels

Mobile fading channel simulators based on ergodic sum-of-cisoids (SOC) processes have been proposed in several papers as a solution to accurately approximate the channel's autocorrelation function (ACF) in a single simulation run. However, despite the encouraging results presented in the literature, it is not clear whether the ergodicity of this type of simulators is meaningful in practice, where in contrast to what theory assumes, the waveforms generated by the simulator have finite lengths. To clarifying this issue, we present in this paper a comprehensive analysis of the random error observed when the temporal ACF (TACF) of ergodic SOC processes is estimated from waveforms of finite duration. We start by computing the instantaneous error produced by three different estimators, namely the biased, the unbiased, and the half-interval estimators. We then derive compact expressions for some insightful statistical quantities of the estimation error, such as the mean, the variance, and the mean-squared value. Based on the obtained results, we discuss the conditions under which an ergodic SOC simulator can be considered to perform similarly in theory and practice. The analysis presented in this paper can be used as a framework for testing, calibration, and performance validation of new ergodic SOC channel simulators.