Partial relay selection with variable gain relays and outdated CSI in mixed RF/FSO system

This paper presents analysis of a dual-hop multiple relaying system, which consists of radio frequency (RF)/free-space optical (FSO) links. The analysis is performed under consideration that the system employs partial relay selection (PRS). Variable gain amplify-and-forward (AF) relays are assumed. The estimated channel state information (CSI) is outdated, which is used for both relay selection and variable gain determination. New analytical expression for the outage probability is derived in a power series form, with assumption that the RF links experience Rayleigh fading, while the FSO link is affected by atmospheric turbulence modeled by the Gamma-Gamma distribution. Numerical results are presented and confirmed by Monte Carlo simulations. The effects of atmospheric turbulence strength, FSO link length, number of relays and time-correlation between actual and estimated CSIs on the outage probability are observed. The results show that the outdated CSI used for relay gain determination and relay selection has a strong impact on the outage probability, especially when the FSO hop is influenced by weak turbulence conditions.