# Performance Analysis of FSO-UWOC Mixed Dual-Hop Relay System with Decode-and-Forward Protocol
## 1 Introduction  
Wireless optical communication (WOC) technology is a core method for achieving \"air-sky-ground-sea\" global coverage and high-speed, real-time, and reliable wireless data transmission in future 6 G/B6 G mobile communication networks [1]. In this context, cross-media \"air/sky/ground-sea\" collaborative relay communication based on visible light communication (VLC) has attracted significant attention from researchers. This interest stems from the numerous advantages of WOC in the visible-light spectrum, such as high transmission rates, license-free operation, and strong security in terrestrial environments, as well as superior performance in underwater environments compared with traditional acoustic and radio frequency (RF) counterparts, including higher speeds, lower power consumption, and easier implementation [2]. As part of the fundamental prior work, reference [3] explored a multi-hop mixed radio frequency (RF)-free-space optical (FSO) communication system based on unmanned aerial vehicles (UAVs), analyzing its average outage probability (OP) and bit error rate (BER) performance under the decode-and-forward (DF) protocol. The authors of [4] undertook a study of a multi-user mixed RF/Terahertz (THz) communication system. The studyexamined the system's OP, BER, and average capacity (AC) under both the Amplify-and-Forward (AF) and DF relay protocols, with the receiver leveraging multi-user diversity. The authors of [5] proposed a Reconfigurable Intelligent Surface (RIS)-assisted and UAV-based ground-vehicle-satellite communication network, modeling the ground user-UAV path as an RF link and the UAV-satellite link as an FSO one, and they analyzed the system's OP and BER under the fixed-gain AF protocol. Although these studies provided detailed modeling and theoretical analysis, their main emphasis was on air-ground atmospheric, same-medium relay transmission in terrestrial environments, rather than on cross-medium relay communication. In the domain of cross-medium air/ground-underwater relay communication, reference [6] analyzed the OP, BER, and ergodic capacity of a dual-hop mixed terrestrial RF-underwater wireless optical communication (UWOC) relay system. The authors of [7] derived the OP of a UAV-based mixed RF-UWOC dual-hop system in fading environments and determined the optimal UAV hovering height that minimizes the system's OP. The authors of [8] explored the OP and ergodic capacity of a dual-hop mixed RF-UWOC system employing power-domain Non-Orthogonal Multiple Access (NOMA) to access two separate underwater nodes, developing a model and deriving the optimal power allocation strategy for underwater users to minimize the system's OP. The authors of [9] proposed a multi-hop UWOC and RF mixed uplink system assisted by an RIS mounted on an Autonomous Underwater Vehicle (AUV), analyzing the system's OP and average BER in the case of oceanic turbulence and pointing error conditions. The authors of [10] examined a high-energy-efficiency RF-UWOC dual-hop system by utilizing simultaneous optical information and energy transmission to minimize the total optical energy consumption of the AUV. Evidently, the aforementioned studies primarily analyzed the mixed system's performance by modeling the communication link between air/ground and sea surface relay nodes as a traditional RF link. Compared to RF communication, the FSO counterpart has significant advantages in system capacity and link security. Thus, usage of FSO instead of RF to model the communication link in terrestrial or in air scenarios is a more feasible operation. The authors of [11] explored the performance of a mixed dual-hop communication system composed of FSO and UWOC links under the AF protocol. The study evaluated the OP, BER, and channel capacity of the system. The FSO link was modeled using a Gamma-Gamma (GG) atmospheric turbulence model, and the UWOC link was modeled with an Exponential-Generalized Gamma (EGG) distribution for underwater turbulent channels.