Effective Rate Evaluation with Assistance of Mixture Gamma (MG), Mixture of Gaussian (MoG), and Fox's H-Function Distributions

Abstract

This paper investigates the effective rate when the instantaneous received signal-to-noise ratio (SNR) could be modeled as the mixture Gamma (MG), mixture of Gaussian (MoG), and Fox’s H-function distributed random variable (RV), respectively. Three closed-form expressions are correspondingly derived in terms of the Fox’s H-function. The obtained analytical results are further examined by the Monte-Carlo simulation. One can observe that (i) the analytical solutions provide an excellent match with the Monte-Carlo simulation results; (ii) the MG and MoG approaches provide highly approximated solutions, and the MG is better due to a simpler form; and (iii) the Fox’s H-function solution is exact and offers a unified, general and flexible framework for the effective rate analysis.