## 2 System and Channel Model  
Consider a Radio Frequency-Underwater Wireless Optical Communication (RF-UWOC) hybrid two-hop relay transmission system as shown in Figure 1. It is assumed that there is an Unmanned Aerial Vehicle (UAV) hovering base station in the air on land, which serves as the signal source (S). It communicates with the underwater destination node (D) through a buoy relay node (R) with the Decode-and-Forward (DF) capability. The Radio Frequency signal S is first sent to R through the Radio Frequency (RF) link. After photoelectric conversion, the optical signal is then transmitted to D through the Underwater Wireless Optical Communication(UWOC) link. It is assumed that the RF link experiences Generalized K fading and atmospheric path loss, and the UWOC link is modeled as a complex mixed fading that includes the turbulence effect of the Generalized Gamma Distribution (GGD), zero line-of-sight pointing error, and underwater path loss. As can be seen from Figure 1 above, the distance \(d_{UR}\) between the UAV and the relay R can be expressed as \(d_{UR}=\sqrt{h^{2}+r_{1}^{2}}\), where \(h\) is the height of the UAV above the horizontal plane, and \(r_{1}\) is the horizontal distance between the UAV and the relay R. \(\theta\) is pitch (angle of view). Derivation of the Probability Density Function of the Instantaneous Received SNR of the S-R Composite Fading Link  
In the RF link, the baseband Radio Frequency signal received at the relay node R can be expressed as follows [12]:  
\[y_{SR}=\frac{\sqrt{P_{1}}h_{1}x_{t}}{\sqrt{L_{UR}}}+n_{1}, \tag{1}\]  
in the above formula, \(x_{t}\) is the unit-amplitude On-off Keying (OOK) signal transmitted from S; \(P_{1}\) is the signal transmission power; \(h_{1}\) is the channel fading coefficient between \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Ref.**} & \multirow{2}{*}{**Year**} & \multicolumn{2}{c}{**Systematic Distribution**} & \multicolumn{1}{c}{**Pointing**} & \multirow{2}{*}{**Path Loss**} & \multirow{2}{*}{**Link Model**} \\  & & **Model** & & & \\ \hline
[3] & 2022 & GG, Lognormal & No & No & PSO-UWOC \\ \hline
[4] & 2021 & GG, EGG & No & No & PSO-UWOC \\ \hline
[5] & 2024 & GG, Lognormal & No & No & PSO-UWOC \\ \hline
[6] & 2021 & Nakagami-m, Rayleigh, EGG & zero Boresight & FFIR implicit path loss & PSO-UWOC \\ \hline
[7] & 2021 & Nakagami-m, EGG & No & No & RF-UWOC \\ \hline
[8] & 2022 & GGD & No & No & RF-UWOC \\ \hline
[9] & 2024 & EGG & zero Boresight & Beer-Lambert & RF-UWOC \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Key differences between the proposed model and related works. Figure 1: RF-UWOC hybrid two-hop transmission system model. the UAV and R, which follows a Generalized K distribution (including the comprehensive influence of small-scale Nakagami fading and Lognormal shadowing effect); \(L_{\text{{L}}tk}=Ada_{\text{{U}}tk}^{*}\) is the path loss, where \(A\) is a constant related to the signal frequency and the transmission environment, \(d_{\text{{U}}tk}\) is the transmission distance between the UAV and R, and \(\alpha\) is the path loss exponent; \(n_{1}\) is the Additive White Gaussian Noise (AWGN) with a mean of zero and a noise power of \(\sigma_{1}^{2}\). The path loss exponent \(\alpha\) is a function of \(\theta\) and can be expressed as \(\alpha(\theta)=a_{1}P_{\text{{L}}OS}(\theta)+b_{1}\)[13], where \(a_{1}\) and \(b_{1}\) are parameters related to the environment and the signal frequency: \(P_{\text{{L}}OS}(\theta)=1/(1+a_{2}e^{-b_{2}\theta})\) represents the probability that the transmission path between the source S and the relay R can be regarded as a Line of Sight (LOS) transmission. Obviously, the larger \(\theta\) is, the larger the probability value \(P_{\text{{L}}OS}(\theta)\) should be reasonably. There is \(P_{\text{{L}}OS}(\pi/2)=1,P_{\text{{L}}OS}(0)=0\), so the coefficients \(a_{2}\) and \(b_{2}\) are determined by empirical values. Without loss of generality, \(a_{2}=200\), \(b_{2}=10\).