Markov Chain Approximation of Rayeleigh Fading Channel

Slow Rayleigh fading channels are characterized by slower channel variations compared to variations of the baseband signal. The fading process exhibits memory as the fading amplitude remains at a certain value for a given symbol duration. Thus the fading process is characterized by a correlation in the temporal domain. In other words, the channel remains relatively longer in a given state. Thus, by properly specifying a threshold for the fading amplitude, it is possible to capture different states of the channel assuming Markov chain models. In this paper, we develop a two-state Markov chain approximation for slow Rayleigh fading channels. Properties of the Markov chain are used to characterize parameters of the fading channel such as fade duration and level crossing rate. Based on the approximate model, we derived analytic expressions for the average bit error probability over a Rayleigh fading channel. We observe that a two-state Markov chain may not capture well the fading dynamics at the bit-level.