On first-order Markov modeling for the Rayleigh fading channel

Recent models far the received signal amplitude of the flat-fading channel that use first-order finite-state Markov chains are examined. The stochasti c properties of a proposed first-order model based on these recent models a re examined. The limitations of using an information theoretic metric, whic h is sometimes used to justify a first-order Markov chain as a sufficient m odel for very slowly fading channels, are discussed. A simple method of qua litatively comparing autocorrelation functions is instead proposed. The usefulness of the first-order Markov chain in representing the flat-fad ing channel is examined by looking at two specific problems in wireless sys tem applications that represent two disparate cases. The first case involve s analysis over a short duration of time, relative to the inverse of the no rmalized Doppler frequency, while the second involves analysis over a long duration of time. Contrary to recent reports, the results indicate that fir st-order Markov chains are not generally suitable for very slowly fading ch annels. Rather, first-order Markov chains can be suitable for very slowly f ading applications, which require analysis over only a short duration of ti me.