On the stationarity and ergodicity of fading channel simulators basing on Rice´s sum-of-sinusoids

Channel simulators based on Rice´s sum-of-sinusoids are playing an important role in fading channel modelling. However, the parameters of the sum-of-sinusoids have to be determined carefully to fully exploit the potential that this powerful procedure has to offer. This paper presents general conditions under which the sum-of-sinusoids procedure results in a stationary and ergodic channel simulator. Moreover, with the help of the introduced conditions, several established parameter computations methods is investigated with respect to their usability to design stationary and ergodic fading channel generators. It turns out 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 process.