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There are different approaches in the literature for modeling the Rayleigh fading channel. We focus on a model with low complexity to capture the channel effects which are relevant to simulate a wireless network. We use an algorithm which exploits the Toeplitz form of the channel covariance matrices to identify the coefficients of a coefficient matrix to generate random variates which have the correlation properties defined by the correlation functions in time and frequency. The correlation in time is given by the Doppler spectrum and the correlation in frequency is given by the power delay profile of the wireless channel. We demonstrate the properties of the simulator and show quantitative quality measures of the random variates. Up to now such an approach has not been presented for modeling of fading channels. The advantage of such a model is that the computational complexity may be reduced, depending on the application, by incorporating less taps.