Hidden Markov modeling of fading channels

Hidden Markov models (HMMs) are a popular and powerful tool for modeling stochastic random processes. They are general enough to model with high accuracy a large variety of processes and are relatively simple, allowing us to compute analytically many important parameters of the process which are very difficult to calculate for other models (such as complex Gaussian processes). We fit a HMM to the envelope of a Rayleigh fading process generated by Jakes´ (1974) model. The HMM is constructed from a semi-Markov chain, the state durations of which are approximated by matrix geometric distributions. We demonstrate the accuracy of the model by comparing analytically derived parameters of the HMM, such as the level crossing number distribution, and level crossing rate with those of Jakes´ model