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New simulation models are proposed for Rayleigh and Rician fading channels. First, the statistical properties of Clarke's fading model with a finite number of sinusoids are analyzed. An improved Clarke's model is then proposed for the simulation of Rayleigh fading channels. Based on this improved Rayleigh fading model, a novel simulation model is proposed for Rician fading channels. The new Rician fading model employs a zero-mean stochastic sinusoid as the specular (line-of-sight) component, in contrast to all existing Rician fading simulators that utilize a non-zero mean deterministic specular component. The statistical properties of the proposed Rician fading model are analyzed in detail. It is shown that the probability density function of the Rician fading phase is not only independent of time but also uniformly distributed over (-π, π). This property is different from that of existing Rician fading models. The statistical properties of the new simulators are confirmed by extensive simulation results, finding good agreement with theoretical analysis in all cases. An explicit formula for the level crossing rate is derived for general Rician fading when the specular component has non-zero Doppler frequency.