Testing the Markov property of the multipath fading process

This paper investigates the Markov property of the fading process measured on land mobile satellite (LMS) channel and determines the appropriate order of discrete state and discrete time Markov chain, which is capable to reproduce the original fading process. The investigated radio link is an L- band terrestrial-satellite channel, measured on board of a moving vehicle in different environments (urban and highway), therefore the channel is effected by multipath/shadowing propagation impairments. As a first approach of the problem, the analog received power process will be transformed into a digital fading process in order to handle it as a two-state (fade/non-fade according to the given threshold) process. To correctly reproduce the high order statistics of the fading process an appropriate discrete time and discrete state homogenous Markov chain has to be selected. The order of the model influences its capability to reproduce the channel memory. With properly selected threshold, by transforming the analog fading process into a fading/non-fading digital process a Chi-square test can be applied to determine the order of the process. Our investigations are showing that the order of the two-state fade/non-fade process slightly depends on the threshold of separation the fade and interfade events. The results can be applied also to test the order in case of more than two states, when the quantization of the attenuation amplitude performed for multiple levels.