A performance study of two hop transmission in mixed underlay RF and FSO fading channels

In this work, we present the performance analysis of a dual-hop transmission system composed of asymmetric radio frequency (RF) and free-space optical (FSO) links in underlay cognitive networks. For the RF link, we consider an underlay cognitive network where the secondary users share the spectrum with licensed primary users, where indoor femtocells act as a practical example for such networks. More specifically, we assume that the RF link is subject to an interference constraint. The FSO link accounts for pointing errors and both types of detection techniques (i.e. intensity modulation/direct detection (IM/DD) as well as heterodyne detection). On the other hand, RF link is modeled by the Rayleigh fading distribution that applies power control to maintain the interference at the primary network below a specific threshold whereas the FSO link is modeled by a unified Gamma-Gamma fading distribution. With this model, we derive new exact closed-form expressions for the cumulative distribution function, the probability density function, the moment generating function, and the moments of the end-to-end signal-to-interference plus noise ratio of these systems in terms of the Meijer's G functions. We then capitalize on these results to offer new exact closed-form expressions for the outage probability, the higher-order amount of fading, and the average error rate for binary and Mary modulation schemes, all in terms of Meijer's G functions. All our new analytical results are verified via computer-based Monte-Carlo simulations and are illustrated by some selected numerical results.