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The use of finite state Markov chains (FSMC) for the simulation of the Rayleigh channel has been generalized in the last years. Several parameters influence the construction of the chain. The chain can be defined in terms of the complex channel response, the envelope of the received signal or the Signal to Noise Ratio. Moreover the partition method has to be selected among various options. This paper presents an evaluation of the FSMC, including a novel partition method that makes a uniform division of the density function of the desired signal and a comparison with other methods of generation of the fading channel. First and second order statistics and other performance parameters are examined in order to shed more light on the advantages and limitations of the Markov modeling.