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The multivariate Rayleigh distribution is intractable, a fact which has motivated research into modeling Rayleigh fading using Markov chains. Previous work has focused on amplitude-based Markov chains, but has had limited success in accurately modeling the autocorrelation of the fading channel. A different state-space definition, one that involves both the amplitude and rate-of-change of the envelope of the fading signal is analyzed. The expanded state-space definition is used as the basis for first- and second-order Markov chain models. This expanded state-space improves upon previous models with regard to the shape of the autocorrelation.