# Performance Analysis of FSO-UWOC Mixed Dual-Hop Relay System with Decode-and-Forward Protocol
## 1 Introduction
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Refs** & **Year** & \begin{tabular}{c} **Air Link** \\ **Statistics** \\ \end{tabular} & \begin{tabular}{c} **UWOC Link** \\ **Statistics** \\ \end{tabular} & \begin{tabular}{c} **Pointing** \\ **Error** \\ \end{tabular} & **Path Loss** & **Relay Type** & \begin{tabular}{c} **Detec.** \\ **Method** \\ \end{tabular} & \
\begin{tabular}{c} **Derived** \\ **Metrics** \\ \end{tabular} &
\begin{tabular}{c} **Asym.** \\ **Analysis** \\ \end{tabular} \\ \hline
[6] & 2021 & \begin{tabular}{c} RF/ \\ Generalized K \\ \end{tabular} & EGG & No & No & \begin{tabular}{c} AF/ \\ DF \\ \end{tabular} & \
\begin{tabular}{c} HD, \\ IM/DD \\ \end{tabular} &
\begin{tabular}{c} OP, BER, \\ capacity \\ \end{tabular} & Yes \\ \hline
[7] & 2021 & RF/Nakagami & EGG & No &
\begin{tabular}{c} RF/ \\ Exponent \\ \end{tabular} & DF & IM/DD & OP, BER & No \\ \hline
[8] & 2022 & RF/Rayleigh & EGG & No & No & DF & \
\begin{tabular}{c} HD, \\ IM/DD \\ \end{tabular} &
\begin{tabular}{c} OP, \\ capacity \\ \end{tabular} & Yes \\ \hline
[9] & 2024 & \
\begin{tabular}{c} RF/Fisher- \\ Snedecor F \\ \end{tabular} & Weibull-GGD & UWOC &
\begin{tabular}{c} UWOC/ \\ BL \\ \end{tabular} & DF & IM/DD & OP, BER & No \\ \hline
[10] & 2023 & RF/Rayleigh & Lognormal/GG & No &
\begin{tabular}{c} UWOC/ \\ Elamassie \\ \end{tabular} & DF & IM/DD & capacity & No \\ \hline
[11] & 2021 & FSO/GG & EGG & Dual link & No & AF & \
\begin{tabular}{c} HD, \\ IM/DD \\ \end{tabular} &
\begin{tabular}{c} OP, BER, \\ capacity \\ \end{tabular} & Yes \\ \hline
[12] & 2024 & FSO/GG & Lognormal & FSO & No & DF &
\begin{tabular}{c} HD, \\ IM/DD \\ \end{tabular} & OP, BER & Yes \\ \hline
[13] & 2024 &
\begin{tabular}{c} FSO/Fisher- \\ Snedecor F \\ \end{tabular} & EGG & Dual link & No & AF & IM/DD & OP & No \\ \hline
[14] & 2022 & FSO/GG & Lognormal & Dual link & Dual/BL & DF & IM/DD & OP, BER & No \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dual-hop RF-UWOC/FSO-UWOC analysis: state of the art. In addition to the previously mentioned dual-hop cross-medium relay communication, the study of [20] proposed a three-hop relay system based on RF-FSO-UWOC. It analyzed and derived the closed-form expressions for the system's OP, BER, and their asymptotic approximations. The research in [21] explored the viability of expanding transmission coverage in purely underwater environments via a serial multi-hop relay UWOC system. It analyzed the system performance in terms of OP, BER, and ergodic capacity under both the AF and DF protocols. The study in [22] investigated the BER performance of a multiple-input multiple-output underwater wireless optical communication (MIMO-UWOC) system using different diversity schemes. As previously noted, all the work presented in these papers has certain kinds of limitations. Specifically, they are often limited by three critical drawbacks: (1) incomplete or inaccurate channel modeling (e.g., neglecting the effects of pointing error or path loss on the link performance, and selecting an undesirable or overly complicated turbulence fading statistical expression to characterize oceanic turbulence); (2) a narrow focus on performance metric derivation, typically emphasizing only one or two aspects (e.g., OP or BER) and neglecting complete performance metrics evaluation and associated asymptotic analysis; (3) in terms of detection techniques, many studies have focused only on IM/DD without exploring coherent detection. Regarding alternative relay strategies, to address the challenges of multi-user interference and inter-satellite link limitations in mega-constellation networks, [23] proposed a distributed multi-user detection framework leveraging message passing. Different from the multi-hop delay problem in the ring-shaped topology, this study adopted a multi-branch tree-like message flow orchestration, where satellites are grouped and clustered according to user fairness to reduce the use of inter-satellite link ports.