Order estimation of binary hidden Markov wireless channel models in Rayleigh fading

The accurate modeling of error sequences that occur in wireless channels is necessary for a better understanding of network performance and for improving the design of communication system under study. Hidden Markov models are widely used for simulating such error traces produced by wireless channels. The primary advantage of using these models is rapid experimentation and prototyping. Although the parameter estimation of HMM has been studied extensively, its order estimation problem has been addressed only recently. Due to the lack of mathematical theory for HMM order estimation, we apply a simulation-based approach to study the order estimation of binary hidden Markov channel models. The order of a Markov process is defined as the minimum number of states required to model the data accurately. In HMMs, where the observation is probabilistic function of states, the order corresponds to the number of quantized state levels. To avoid local maxima, we run the Baum-Welch Algorithm (BWA) several times with different initial conditions (while keeping the number of states fixed), and use split-data log-likelihood to select the best model.