On the Sum of Inverse Gamma RVs and its Application to Wireless Communications Networks

Abstract: Investigating the statistics of the sum of random variables (RVs) is fundamental in wireless communication systems, as it can be used to accurately estimate their performance. In this paper, exact closed-form expressions are derived for the probability density function (PDF) and cumulative distribution function (CDF) of the sum of inverse-gamma (IG) RVs. The IG distribution is especially suitable for performance analysis purposes because it provides a tractable yet accurate model of shadowing/local mean power variations. Unlike prior studies on sums of shadowing RVs, the resulting formulas are simple to evaluate and numerically stable. Their utility is demonstrated in two practical settings: unmanned aerial vehicle (UAV)-assisted networks and high-speed railway communications. Across all considered scenarios, the analytical results are in excellent agreement with the Monte Carlo simulation results, while the asymptotic approximations closely track the exact results