Channel characterization and modeling are essential to the wireless communication system design. A model that optimally represents a fading channel with a variable-length Markov chain (VLMC) is proposed in this paper. A VLMC offers a general class of Markov chains whose structure has a variable order and a parsimonious number of transition probabilities. The proposed model consists of two main components: 1) the optimal fading partition under the constraint of a transmission policy and 2) the derivation of the best VLMC representation with respect to the Kullback–Leibler (K–L) distance of fading samples. The fading partition is used to discretize a continuous fading channel gain. The optimal discretization criterion is developed based on the cost function of fading channel statistics and the transmission policy used in the system. Once a continuous fading channel gain is discretized, a VLMC is then used to model the channel. To obtain the optimal VLMC representation, we use the K–L distance of the discretized fading samples as the optimization criterion. The K–L distance of the discretized fading samples is used to determine the appropriate transition probabilities characterizing the optimal VLMC. Last, we show simulation results that demonstrate the accuracy and the effectiveness of the proposed fading channel representation in modeling the Rayleigh fading as well as the lognormal fading.
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