Performance of a Free Space Optical Relay-Assisted Hybrid RF/FSO System in Generalized M-Distributed Channels

This paper investigates the average symbol error rate (ASER) performance of a dualhop hybrid relaying system relying on both radio frequency (RF) and free space optical (FSO) links. Specifically, the RF link is used for supporting mobile communication, while the FSO link is adopted as the backhaul of the cellular infrastructure. Considering non-line-of-sight (NLoS) RF transmissions and a generalized atmospheric turbulence (AT) channel, the associated statistical features constituted of both the exact and the asymptotic moment generating functions (MGF) are derived in closed form. They are then used for calculating the ASER of M-ary phase shift keying (PSK), differentially encoded non-coherent PSK (DPSK) and non-coherent frequency-shift keying (FSK). A range of additional asymptotic expressions are also derived for all the modulation schemes under high signal-to-noise ratios (SNR). It is observed from the asymptotic analysis that the ASERs of all the modulation schemes are dominated by the average SNR of the RF link in the hybrid relaying system using a fixed relay gain, while in the relaying system using a dynamic channel dependent relay gain, the ASERs of all the modulation schemes depend both on the average SNR and on the AT condition of the FSO path. We also find that the fixed-gain relaying strategy achieves twice the diversity order of the channeldependent relaying strategy albeit at the cost of requiring a high power amplifier (PA) dynamic range at the relay node. Furthermore, by comparing the asymptotic ASERs, we calculate the SNR differences between the different modulation schemes in both the fixed-gain and the channel-dependent relaying system. Finally, simulation results are presented for confirming the accuracy of our expressions and observations.