CTH16-4: Accurate Simulation of Piecewise Continuous Arbitrary Nakagami-m Phasor Processes

Accurate simulation of piecewise continuous complex-valued Nakagami-m (phasor) processes with arbitrary parameters is considered. Two solutions to this problem are discussed. The first is based on the extension of an existing decomposition technique to the general case of piecewise continuous complex-valued processes. The second is an entirely novel contribution in which a Nakagami-m process with arbitrary m is obtained from a mixture of a pair of Nakagami-m processes with positive integer and half-integer m, respectively. In deriving the foundations of the new technique, the characteristic function and entropy of Nakagami-m phase processes, the entropy of Nakagami-m envelope processes and the joint (envelope+phase) moment of Nakagami-m phasor processes are all derived in simple closed-forms, and the moment-determinance of Nakagami- m envelope processes is proved. The mixture probabilities used in the proposed random mixture technique, derived from constraints on the Nakagami-m joint-moment, are computed using a simple rational function of m and its closest integer and half integer neighbors to both sides. The remarkable accuracy achieved by the approximation is quantified analytically using the Kullback-Leibler divergence. It is shown that the proposed random mixture method is far superior to the decomposition method in terms of accuracy of envelope and phase pdfs, as well as higher order statistics, with the addition advantage of being less computationally demanding.