On the performance of hybrid line of sight RF and RF-FSO fixed gain dual-hop transmission systems

In this work, we carry out a unified performance analysis of a dual-branch transmission system composed of a direct radio-frequency (RF) link and a dual-hop fixed gain relay over the asymmetric links composed of both RF and unified free-space optics (FSO) under the effect of pointing errors. RF links are modeled by the Nakagami-m fading channel and the FSO link by the Gamma-Gamma fading channel subject to both types of detection techniques (i.e. heterodyne detection and intensity modulation with direct detection (IM/DD)). Selection combining (SC) and maximum ratio combining (MRC) diversity schemes are investigated. More specifically, for the SC method, we derive new unified closed-form expressions for the cumulative distribution function (CDF), the probability density function (PDF), the moment generating function (MGF), the moments, the outage probability (OP), the average bit-error rate (BER) of a variety of binary modulations, and the ergodic capacity for end-to-end signal-to-noise ratio (SNR). Additionally, using the MGF-based approach, the evaluation of the OP, the average BER, and the ergodic capacity for the MRC diversity technique can be performed based entirely on the knowledge of the MGF of the output SNR without ever having to compute its statistics (i.e. PDF and CDF). By implementing SC or MRC diversity techniques, we demonstrate a better performance of our system relative to the traditional RF path only. Also, our analysis illustrates MRC as the optimum combing method. All the analytical results are verified via computer-based Monte-Carlo simulations.