Optimal Variable Length Markov Chain (VLMC) Modeling of Fading Channels

Channel characterization and modeling is 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 work. 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. 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 Kullback-Liebler (K-L) distance as the optimization criterion. Finally, we show simulation results that demonstrate the accuracy of the proposed fading channel representation in modeling the Rayleigh fading as well as the log-normal fading.