Performance analysis of hybrid RF–FSO systems with amplify-and-forward selection relaying

Abstract

Abstract This paper presents performance analysis for two cooperative amplify-and-forward (AF) relaying systems in which hybrid combinations of radio frequency (RF) and free space optics (FSO) links have been considered, where the receiver employs the selection combining method. In the first considered system, denoted RF–RF/FSO, the first hop of the AF system from source to relay includes a RF link and the second hop of the system from relay to destination includes two links of RF and FSO. In the second system, denoted RF–RF/RF–FSO, it is assumed that there exists two links from source–relay–destination including RF–RF and RF–FSO links. The RF link is assumed to be a Rayleigh fading distributed channel and the FSO link is assumed to have a Gamma–Gamma fading distribution, containing the effects of pointing error as well as the atmospheric turbulence. Two detection techniques are used for the FSO link, including the intensity modulation/direct detection (IM/DD) and the heterodyne detection techniques. To analyze the system performance, we first derive expressions for the probability density function (PDF) and the cumulative distribution function (CDF) of the received signal-to-noise-ratio (SNR) for the RF–RF/FSO and RF–RF/RF–FSO systems. We then derive closed-form expressions for the outage probability, the average bit error rate (BER), and the ergodic capacity for each system. To compare the considered hybrid systems, numerical results are presented. In addition, the performances of the presented hybrid systems are also compared with that of the classical hybrid RF–FSO system employing AF relaying. It is shown that the presented hybrid RF–RF/FSO and RF–RF/RF–FSO systems can provide significant improvement compared to the conventional RF–FSO system. In addition, it is shown that the RF–RF/RF–FSO system achieves the best performance among the considered RF–FSO and RF–RF/FSO systems. It is also shown that the numerical results obtained from derived closed-form expressions are matched closely with the results obtained from Monte-Carlo simulations, indicating the accuracy of the obtained mathematical formulas for each performance metric.