Two Ways to Simulate a Rayleigh Fading Channel Based on a Stochastic Sinusoidal Model

This letter deals with a new Rayleigh channel simulator. In many cases, the channel is modeled by an autoregressive process, but this choice is not well suited due to the band limitation of the theoretical Rayleigh channel power spectrum density. Therefore, we suggest using a low-pass filtered version of the so-called stochastic sinusoidal process. It consists of sinusoids in quadrature with random magnitudes modeled by autoregressive processes. Unlike the autoregressive channel modeling, this simulator has the advantage of exhibiting the power spectrum density (PSD) peaks at the maximum Doppler frequency. Since estimating the autoregressive parameters of the amplitudes directly using a matrix approach from the theoretical Rayleigh channel autocorrelation leads to numerical errors, we propose two alternative methods using either the asymptotic behavior of the Bessel function or genetic algorithms.