The outage probability performance of a hybrid free space optical (FSO)/radio frequency (RF) system with a reconfigurable intelligent surface (RIS) assisted full-duplex relay is presented in this paper. The FSO link follows the Gamma-Gamma distribution over pointing error and atmospheric turbulence with random foggy impairments. The RF link between the relay and the destination is subject to Nakagami-m distributions, while the RIS links and the relay self-interference (SI) link follow Rayleigh fading. As a result, the RIS-to-relay link's cumulative distribution function (CDF) of the signal to interference plus noise ratio (SINR) is obtained. On the basis of this, the system's outage probability is determined according to the decode and forward relay protocol. Thus, Monte-Carlo simulations are utilized to verify the obtained expression's accuracy. Our findings show how atmospheric turbulence, pointing errors, fog conditions, and the number of RIS reflecting elements affect the system performance. Furthermore, it is concluded that, under the identical channel conditions, heterodyne detection performs better than intensity modulation/direct detection (IM/DD).
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