NTIA Technical Memorandum TM-05-423

Analysis of the Markov Character of a General Rayleigh Fading Channel

April 2005

Roger Dalke, George Hufford

Abstract: It has been proposed that first–order Markov channel models can be used to adequately predict the behavior of a mobile "Rayleigh" fading channel and hence improve the reliability of bidirectional mobile communications systems. Previous authors have addressed this question by applying information theory to the amplitude statistics of a stationary mobile communications channel. The previous work required numerical analysis to show that for a particular covariance function and range of relevant parameters (i.e., Doppler frequency, symbol period), the channel is approximately first–order Markov. In our analysis, both amplitude and phase information are used to obtain analytic expressions which can easily be used to determine if a non–stationary arbitrary Rayleigh channel is necessarily first–order Markov. The analytic results are given in terms of arbitrary covariance functions that can readily be applied to measurements. In particular, our results show that the previously studied mobile channel is not first–order Markov in character.

Keywords: Gaussian process; information theory; Markov process; mobile communications; Rayleigh fading; reliability

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