In this paper, the performance analysis of a reconfigurable intelligent surface (RIS) assisted underwater optical communication (UWOC) system with a decode-and-forward (DF) relaying protocol is presented. The radio frequency (RF)-RIS link is subjected to Rayleigh fading while the optical UWOC link experiences mixture Exponential-Gamma distributions subject to heterodyne detection and intensity modulation with direct detection (IMDD). In order to obtain a traceable closed-form expression, the statistical distribution of the RF-RIS link is derived in terms of Meijer-G function. Thus, the exact closed-form expressions for system end-to-end outage probability and average bit error rate (ABER) for different modulation schemes are then derived. To gain further insight about the derived analytical expressions, asymptotic expressions for the system are derived at high signal-to-noise ratio (SNR) through which the diversity gain is obtained. The findings show the significant impact of the number of RIS elements, detection technique, and the UWOC optical turbulence on the system performance. Finally, Monte-Carlo simulation is used to justify the accuracy of the derived analytical results.
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