An Integral of Fox’s H-Functions With Application to the Performance of Hybrid FSO/RF Systems Over Generalized Fading Channels

Abstract

In recent years, Fox’s H-function (FHF) has appeared in the statistical channel models of wireless communication systems. In some cases, the derivation of performance metrics becomes so complicated, particularly for communication systems that operate under two different fading channels, and various conditions. This difficulty pushed the researchers to use approximation methods to derive the performance metrics, such as finite series approximation which is not always computationally effective. Motivated by the need to solve this issue, we evaluate an integral of a product of Fox’s H-functions (FHFs). To verify the validity of the proposed solution, it is utilized to derive performance expressions for a hard switching hybrid free-space optical/radio frequency (FSO/RF) system. The performance analysis is conducted over generalized channel models in the presence of pointing errors (PEs), where the FSO link is characterized by FHF, which involves Málaga $(\mathcal {M})$ , Gamma Gamma $(GG)$ , Fisher-Snedecor $\mathcal {F}$ distributions, and the RF link is modeled using $\alpha -\mu $ fading. New expressions for average bit error rate (ABER) and ergodic capacity are obtained in terms of bivariate Fox’s H-function (BFHF) under subcarrier intensity modulation (SIM) and heterodyne detection (HD). Additionally, asymptotic expressions for these metrics are provided for both detection types. Finally, Monte Carlo (MC) simulations are used to confirm the precision of the obtained expressions.