On the Sum of α-μ/Inverse Gamma Variates with Applications to Diversity Receivers

Abstract

How to model shadow fading by applying the inverse gamma (IGA) distribution has recently gained widespread attention in wireless transmissions. However, the sum of α-μ/IGA variates, and its applications under independent and/or correlated scenarios, have yet to be addressed in open research works. Hence, this paper provides a systematic investigation of the α-μ/IGA model. First, we derive the expressions of the fundamental statistics of the univariate and bivariate α-μ/IGA models including the probability density function, cumulative distribution function, and moment generating function, and propose a mixture α-μ model to approximate the α-μ/IGA model. Then, according to the above statistical expressions, the statistical properties of the sum of α-μ/IGA variates are obtained and employed in the maximal ratio combining receivers. Third, the novel exact and approximated expressions of some performance metrics of interest are also derived, for instance, the average bit/symbol error probability, the outage probability, the average channel capacity, and the effective rate. Moreover, to prove the asymptotic properties of the performance metrics at the high signal-to-noise regions, some examples are performed. Finally, we explore numerical analysis and simulations to demonstrate the accuracy of the theoretical expressions under the different channel and system parameters. These results provide some significant insights into the reliability design and deployment of some conventional and emerging wireless communication applications.