On the Distribution of the Sum of M\'{a}laga-$\mathcal{M}$ Random Variables and Applications

TL;DR

This paper introduces an accurate approximation method for the sum of Málaga-𝓜 random variables with pointing error, using Fox's H-function, and evaluates its impact on symbol error rate in MRC receivers.

Contribution

It proposes a novel moment-based approximation of the sum's distribution using Fox's H-function, enabling precise performance analysis.

Findings

Approximate PDF matches well with simulations.

Diversity order increases with the number of MRC branches.

Method provides accurate error rate evaluations.

Abstract

In this paper, a very accurate approximation method for the statistics of the sum of M\'{a}laga-$\mathcal{M}$ random variates with pointing error (MRVs) is proposed. In particular, the probability density function of MRV is approximated by a Fox's $H$-function through the moment-based approach. Then, the respective moment-generating function of the sum of $N$ MRVs is provided, based on which the average symbol error rate is evaluated for an $N $-branch maximal-ratio combining (MRC) receiver. The retrieved results show that the proposed approximate results match accurately with the exact simulated ones. Additionally, the results show that the achievable diversity order increases as a function of the number of MRC diversity branches.