On verifying the first-order Markovian assumption for a Rayleigh fading channel model

The use of received signal-to-noise ratio (SNR) as the side information in communication systems has been widely accepted especially when the channel quality is time-varying. In many occasions, this side information is treated as the received SNR of the current channel symbol or that of previous symbols. In particular, the finite-state Markov channel (FSMC) provides a mathematically tractable model for time-varying channels and uses only the received SNR of the symbol immediately preceding the current one. The FSMC model is constructed by partitioning the range of the received SNR into a finite number of intervals. Each state of the channel corresponds to one of these intervals. For a first-order Markovian model, given the information of the state immediately preceding the current one, any other previous state should be independent of the current state. Although the experimental measurement confirms the usefulness of the first-order Markovian assumption, one may argue that second or higher-order Markov processes should provide a more accurate model. We answer this question by showing that given the information corresponding to the previous symbol, the amount of uncertainty remaining in the current symbol should be negligible