Markov chain modelling of ordered Rayleigh fading channels in non-orthogonal multiple access wireless networks

A first-order finite-state Markov chain (FSMC) typically models the Rayleigh fading channel in the open literature because the first-order FSMC is analytically tractable and can derive closed-form results. Non-orthogonal multiple access (NOMA) has been recognised as a novel wireless technology that addresses challenges in the next generation of mobile communications. According to the power-domain NOMA protocol, channels in the NOMA wireless network are sorted by the channel gain. Then considering NOMA, there is insufficient information on how to further form a suitable model for ordered Rayleigh fading channels based on the first-order FSMC. Given the mathematical statement on how to model the order statistics of multidimensional Markov chains for ordered Rayleigh fading channels, the authors consider these order statistics as a Markov chain, and propose specific processes of representing the state space and constructing the transition probability matrix accordingly. Numerical and simulation results validate the mathematical correctness and accuracy of these novel processes. In addition, for ordered Rayleigh fading channels, the performances of various methods of partitioning the entire signal-to-noise ratio range are compared. The performance comparison results are the same as those obtained for the individual unordered Rayleigh fading channel.