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. On many occasions, this side information is treated as the received SNR of the current channel symbol or that of previous symbols. In particular, the first-order Markov channel provides a mathematically tractable model for time-varying channels and uses only the received SNR of the symbol immediately preceding the current one. With the first-order Markovian assumption, given the information of the symbol immediately preceding the current one, any other previous symbol should be independent of the current one. Although the experimental measurements confirm the usefulness of the first-order Markovian assumption, one may argue that second or higher-order Markov processes should provide a more accurate model. In this paper, 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.