An Application of a Semi Markov Model in Predicting the Fading Occurrences in Wireless Communication Channels

Abstract

The most frustrating and troublesome issue in wireless communication is fading. Estimating the fading occurrence for the design of greatly reliable communication link is crucial. In this paper, we present a novel mathematical method for predicting the future signal fading on the basis of current and past data. The application of a Semi Markov Model as a generalization of the Markov Model is discussed for predicting the deep fading occurrence probabilities of the received envelope in wireless communications channels. This flexible model is given for assessing the system performance with the envelope correlation. 142 deep fading data whose amplitudes are lower than a mean of the amplitudes which occurred in a typical wireless system with the Jakes filtering are considered. The transition probability matrix and the holding time mass functions are calculated for the next 1 to 21 unit times. One unit time is regarded as the inverse of sampling frequency; moreover, the core matrix and the cumulative probability distribution of the waiting time are obtained. Calculating the interval transition probabilities for Amplitude to Amplitude transition for these deep fades demonstrates the forecasting occurrence probabilities in the future and the possibility of forecasting the fading occurrences in dimensions of time and amplitude.