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This paper presents a computer model for Rayleigh fading channels. The simulated Rayleigh fading channel model is based on Smith's method and shows ease of implementation and greater mathematical tractability. We then investigate the level-crossing rate (LCR), the average duration of fades (ADF), the probability density function (PDF), the cumulative distribution function (CDF) and the autocorrelation functions (ACF) of this proposed model. The simulated results are verified against the analytical Clarke's channel model.