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Several new "sum-of-sinusoids" models have recently been introduced for the simulation of Rayleigh fading channels. These models are statistical in nature implying that their simulation parameters such as the Doppler frequencies are random. They have been shown to accurately reproduce some of the desired statistical properties of the faded envelope such as the time autocorrelation and the level crossing rate. However, a comparative analysis of these models, hitherto scattered throughout the literature, is not available. This paper compares these models in terms of their complexity and performance. The performance assessment is based upon the variance of the time average statistical properties from their ideal ensemble averages.