Limitations of sum-of-sinusoids fading channel simulators

Rayleigh signal fading due to multipath propagation in wireless channels is widely modeled using sum-of-sinusoids simulators.. In particular, Jakes' simulator and derivatives of Jakes' simulator have gained widespread acceptance. Despite this, few in-depth studies of the simulators' statistical behaviors have been reported in the literature. Here, the extent to which Jakes' simulator adequately models the multipath Rayleigh fading propagation environment is examined. The results show that Jakes' simulator does not reproduce some important properties of the physical fading channel. Some possible improvements to Jakes' simulator are examined. The significances of the number and the symmetries of the Doppler frequency shifts on the validity of the simulator's reproduction of the physical fading channel are elucidated.