Design of wide-sense stationary sum-of-sinusoids fading channel simulators

It was recently shown (see Pop, M.F. and Beaulieu, N.C., IEEE Trans. Commun., 2001) that Jakes\´ sum-of-sinusoids Rayleigh fading simulator (see Jakes, W.C., "Microwave Mobile Communications", IEEE Press, 1994) is not wide-sense stationary when averaged across the ensemble of physical fading channels. Here, a wide-sense stationary sum-of-sinusoids simulator design is presented and its stochastic behaviour is analyzed. Analytical expressions for the envelope and phase probability density functions and the simulator output signal autocorrelation function are given. These are used to obtain some design rules that relate the quality of the simulator output to the number of low-frequency oscillators, or equivalently sinusoids, used in the simulator. Our results contradict a common belief that the quality of the simulator output is related to the total number of multipath components. Rather, the quality is shown to depend on the number of distinct Doppler frequency shifts and it cannot be improved by using more multipath components that do not represent distinct Doppler frequency shifts.