The Simulation Models for Rayleigh Fading Channels

Rayleigh fading channel is the foundation of mobile radio channel modeling. This paper summarizes four classes of the simulation models for Rayleigh fading channels based on sum-of-sinusoids by a uniform expression, according to the different definition of the assumed parameters in the expression. Among these parameters, the initial phases should be set as random variables and we conclude three cases of phases´ definition. With the help of these discussions, it can be seen that the ergodicity and the stationary can not exist simultaneously when the number of multipath wave is finite. Based on this conclusion, some conditions on an effective channel model are proposed, and these conclusions are useful to model the new effective mobile radio channels.