An Information-Theoretic Measure for the Selection of Effective Memory Order in Flat-Fading Channels

In this paper, we consider an information-theoretic measure for the selection of effective memory order in time-varying flat-fading (FF) channels in the Jakes-Clarke’s model. The measure is based on how many past realisations of the fading channel actively contribute to an achievable information rate lower bound through the channel. The lower bound signifies the achievable information rate when the receiver is equipped with a sup-optimal mismatched decoding rule, which would have only been optimal for a finite-state Markov channel (FSMC) with a finite memory order. The sensitivity of the mismatched decoding rule to memory order is used to find the optimum channel memory order for decoding at the receiver side, with a negligible information rate loss. Our case study shows that the FF channel has an effective information-theoretic memory order of M = 1 for the normalised fading rates fDT . 0.01, where fD is the Doppler spread and T is symbol period. For faster fading rates, the use of first-order models at the receiver incurs a non-negligible information rate loss. The results are, generally, in accordance with our previous findings.

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