Second-order statistical properties of the WSS Jakes' fading channel simulator

Recently, an improved Jakes' fading channel simulator was proposed by Pop and Beaulieu to eliminate the stationarity problem occurring in Jakes' original design. In this letter, second-order statistical properties of the improved Jakes' simulator are analyzed. Consistent with Pop and Beaulieu's caution about high-order statistics of the simulator, it is proved that some second-order statistics of both the quadrature components and the envelope do not match the desired ones even if the number of sinusoids approaches infinity. Therefore, care must be taken when the simulator is employed to evaluate algorithms and systems. Index Terms--Fading channel simulator, fading channels, Rayleigh fading, statistics.