Performance Analysis of Equal-Gain Combining Receivers Over Composite Multipath/ Shadowing Fading Channels

Abstract

In this paper, we assess the performance of an equal-gain combining (EGC) diversity receiver operating over composite Fisher-Snedecor fading channels. The Fisher-Snedecor fading model results from the amalgamation of two well-known physical phenomena that greatly degrade the wireless signal: multipath and shadowing. More precisely, the Fisher-Snedecor $\mathcal {F}$ distribution is formed by the ratio of two independent Nakagami-m random variables (RVs)—the Nakagami-m RV in the numerator models multipath fading while the Nakagami-m RV in the denominator characterizes shadowing fading. To evaluate the performance of the considered EGC diversity receiver, we first derive exact expressions for the probability density function (PDF) and the cumulative distribution function (CDF) of the sum of the ratio of independent Nakagami-m RVs. To achieve this goal, we utilize a Laplace- and residue-based approach. Additionally, we employ the moment-matching method and the Beta Prime distribution to effectively approximate the sum of the ratio of independent Nakagami-m RVs. Subsequently, we apply the obtained exact and approximate sums statistics to compute the performance metrics of the EGC receiver subject to Fisher-Snedecor $\mathcal {F}$ fading channels, such as the outage probability (OP) and the average bit-error rate (ABER). We aspire that the findings presented in this work not only enhance the theoretical comprehension of wireless communication systems but also offer valuable insights for optimizing the design and performance of these systems in real-world scenarios.

Keywords

• Beta prime distribution
• composite fading channels
• equal-gain combing receivers
• Fisher-Snedecor F distribution
• sum of the ratio of Nakagami-m random variables