Statistical properties of Jakes´ fading channel simulator

Jakes´ (1993) method is often used for the design of effective (Rayleigh) fading channel simulators, but less is known about the achievable degree of accuracy. Our paper fills this gap by studying the statistical properties of Jakes´ simulator. Therefore, analytical expressions are presented for the autocorrelation and cross-correlation function of in-phase and quadrature components, as well as for the probability density function of envelope and phase. Moreover, an analytical investigation of the second order statistics (level-crossing rate and average duration of fades) is also a topic of this paper. All these expressions are fundamental for the investigation of inevitable degradation effects due to a limited number of low-frequency oscillators or due to the inherent insufficiencies of Jakes´ method