Exact Outage Probability Analysis of the Mixed RF/FSO System With Variable-Gain Relays

This paper presents a unified analysis of the mixed radio-frequency (RF)/free-space optics (FSO) relaying system, with multiple variable-gain amplify-and-forward relays. The partial relay selection (PRS) is employed to select the active relay for further re-transmission. Due to fast fading statistics of the first RF hop, it is assumed that the channel state information of the RF link is outdated, which is used for both the relay gain adjustment and the PRS procedure. The RF hops are subject to the Rayleigh fading, while the FSO hop is affected by the atmospheric turbulence and the pointing errors. The intensity fluctuations of the optical signal caused by atmospheric turbulence are modeled by the general Málaga ($ \mathcal {M}$) distribution, which takes into account the effect of multiple scattered components. An exact expression for the outage probability is derived. In addition, high-signal-to-noise-ratio approximations are provided, which can be used to efficiently determine the outage probability floor. Numerical results are validated by Monte Carlo simulations, which are used to examine the effects of the system and channel parameters on the RF/FSO system performance.