On verifying a first-order Markovian model for the multi-threshold success/failure process for Rayleigh channel

The effect of the Rayleigh fading channel on data block transmission is investigated. In a packet communication system the correctness or incorrectness of the received blocks is usually strictly related to a comparison of the signal-to-noise ratio (SNR) with a set of thresholds. The possibility of fitting a Markovian model to the quantized fading process is investigated, assuming the states of the model are coincident with the quantization levels (symbols). The two-threshold case is considered and the suitability of a first-order Markov model or even a zero-order Markov model (that means independent and identically distributed symbols) in describing such a process is verified. For this purpose, the parameters of a second-order Markov model are estimated and the table of contingency analysis for Markov chains is applied. It is shown that, in the fast fading case, process symbols can be considered as independent and identically distributed, while in the slow fading case the first-order Markovian model only approximates the real behavior of the fading