A generalized simulation model for Rayleigh fading channels with accurate second-order statistics

In this paper, a new, sum-of-sinusoids statistical simulation model is proposed for Rayleigh fading channels. The new model employs random path gain, random initial phase, and conditional random Doppler frequency for all individual sinusoids. It is shown that the autocorrelations and crosscorrelations of the quadrature components, the autocorrelation of the complex envelope of the new simulator match the desired ones exactly even if the number of sinusoids is as small as a single-digit integer. Furthermore, the probability density functions of fading envelope and phase, the level crossing rate and the average fade duration of the new simulator asymptotically approach the desired ones as the number of sinusoids approaches infinity, while good convergence is achieved when the number of sinusoids is small. Statistical properties of the new, simulator are evaluated by numerical results, finding good agreement in all cases.