An Ergodic Sum-of-Cisoids Simulator for Multiple Uncorrelated Rayleigh Fading Channels Under Generalized Scattering Conditions

In this paper, we present a new method for the design of ergodic sum-of-sinusoids (SOS) simulators for multiple uncorrelated narrowband Rayleigh fading channels. The method, which is intended for a special class of SOS models known as sum-of-cisoids (SOC) models, enables the generation of an unlimited number of mutually uncorrelated Rayleigh fading waveforms with specified autocorrelation properties. This is in contrast to all known methods proposed for SOS simulators, which are restricted to the simulation of multiple uncorrelated Rayleigh fading channels characterized by autocorrelation functions (ACFs) derived under the isotropic scattering assumption. The excellent performance of this new method is exemplarily demonstrated by comparing the correlation properties and the envelope distribution of a set of waveforms generated by the simulator with the corresponding quantities of a reference set of multiple uncorrelated Rayleigh fading channels. The method's performance is evaluated in not only theoretical simulation scenarios, where the lengths of the generated waveforms approach infinity, but also practical scenarios, where the waveform lengths are limited. The simulation approach described in this paper is important to the performance analysis of mobile broadband communication systems using diversity, multicarrier, or multiple-input-multiple-output (MIMO) techniques under generalized scattering conditions.