Classes of Sum-of-Sinusoids Rayleigh Fading Channel Simulators and Their Stationary and Ergodic Properties

– Channel simulators based on Rice’s sum-of-sinusoids are playing an important role in mobile fading channel modelling. However, the parameters of the sum-of-sinusoids have to be determined sophisticated to fully exploit the great potential that this powerful procedure has to offer. This paper provides a fundamental work on the stationary and ergodic properties of sum-of-sinusoids-based Rayleigh fading channel simulators. Altogether eight classes of Rayleigh fading channel simulators are introduced, where four of them are new. Each individual class is systematically investigated with respect to its stationary and ergodic properties. This allows us to establish general conditions under which the sum-of-sinusoids procedure results in a stationary and ergodic channel simulator. Moreover, with the help of the proposed classification scheme, several popular parameter computation methods are investigated concerning their usability to design efficient fading channel simulators. The treatment of the problem shows that if and only if the gains and frequencies are constant quantities and the phases are random variables, then the sum-of-sinusoids defines a stationary and ergodic stochastic process. For simplicity reasons, we restrict our investigations to Rayleigh fading channels, but the presented results are of general interest, wherever the principle of Rice’s sum-of-sinusoids is employed.