# Deep Learning-Based Optimization for Maritime Relay Networks
## 2 System Model
### Data Acquisition
The mathematical expression for the connectivity probability of a single relay node is presented in Equation (11) as follows:  
\[P_{r}(\gamma_{R_{k}}>\gamma_{0}) = P_{r}\big{(}\min\bigl{\{}\gamma_{R_{k},1},\gamma_{R_{k},2}\bigr{\}} >\gamma_{0}\big{)} \tag{11}\] \[L_{2t}=\sqrt{(d_{2t})^{2}+|h_{2t}-h_{3t}|^{2}}, \tag{4}\]0 \[L_{2t}=\sqrt{(d_{2t})^{2}+|h_{2t}-h_{3t}|^{2}}, \tag{4}\]1 \[L_{2t}=\sqrt{(d_{2t})^{2}+|h_{2t}-h_{3t}|^{2}}, \tag{4}\]2 \[L_{2t}=\sqrt{(d_{2t})^{2}+|h_{2t}-h_{3t}|^{2}}, \tag{4}\]3 \[L_{2t}=\sqrt{(d_{2t})^{2}+|h_{2t}-h_{3t}|^{2}}, \tag{4}\]4 \[L_{2t}=\sqrt{(d_{2t})^{2}+|h_{2t}-h_{3t}|^{2}}, \tag{4}\]5  
For a system with multiple relay nodes, the connectivity probability must consider the scenario where the maximum SNR among all relay nodes exceeds the threshold (\(\gamma_{0}\)). Accordingly, the connectivity probability of the entire system is expressed as:  
\[L_{2t}=\sqrt{(d_{2t})^{2}+|h_{2t}-h_{3t}|^{2}}, \tag{4}\]6  
Since \(\gamma^{*}\) represents the maximum SNR among all relay nodes, the connectivity probability can be further expressed as:  
\[L_{2t}=\sqrt{(d_{2t})^{2}+|h_{2t}-h_{3t}|^{2}}, \tag{4}\]7 \[L_{2t}=\sqrt{(d_{2t})^{2}+|h_{2t}-h_{3t}|^{2}}, \tag{4}\]8 \[L_{2t}=\sqrt{(d_{2t})^{2}+|h_{2t}-h_{3t}|^{2}}, \tag{4}\]9  
where \(K\) denotes the total number of relay nodes. In a multi-hop network, data transmission is performed through hop-by-hop forwarding across multiple relay clusters until the destination node is reached. The success rate of each hop is determined by the selection of the relay node in the preceding hop and its corresponding communication performance. The connection probability of the first hop is defined as the probability that the source node (S), through broadcasting, communicates with the K relay nodes in the first cluster \(C_{1}\) and selects the relay node with the highest SNR. The probability that the SNR of a single relay node exceeds \(\gamma_{0}\) is calculated as:\[v_{1t}=V_{1t}+\Delta_{1t}, \tag{5}\]0 \[v_{1t}=V_{1t}+\Delta_{1t}, \tag{5}\]1 \[v_{1t}=V_{1t}+\Delta_{1t}, \tag{5}\]2  
For the K independent relay nodes in cluster C\({}_{1}\), the probability that the maximum SNR among these nodes exceeds the threshold is expressed as:  
\[v_{1t}=V_{1t}+\Delta_{1t}, \tag{5}\]3 \[v_{1t}=V_{1t}+\Delta_{1t}, \tag{5}\]4 \[v_{1t}=V_{1t}+\Delta_{1t}, \tag{5}\]5  
For the connection probability of the intermediate \(M-1\) hops, each hop is influenced by the SNR distribution of the relay node selected in the preceding hop. Let the connection probability of the \(m\)-th cluster be denoted as \(P_{r}(\gamma_{C_{m}}^{*}>\gamma_{0}\mid\gamma_{C_{m-1}}^{*})\). The SNR of the current relay node follows an exponential distribution, which is expressed as:  
\[v_{1t}=V_{1t}+\Delta_{1t}, \tag{5}\]6  
where \(\lambda_{m,k}\) represents the channel parameter of the \(k\)-th relay node in the \(m\)-th cluster, which is related to the SNR of the previous hop. The cumulative distribution function (CDF) of the maximum SNR in the current cluster is given as:  
\[v_{1t}=V_{1t}+\Delta_{1t}, \tag{5}\]7 (17) \[v_{1t}=V_{1t}+\Delta_{1t}, \tag{5}\]8  
To comprehensively understand the changing trends in the sustainable propagation link states, extensive data were collected while considering multiple factors that influence ship-to-ship communication. By integrating historical data from maritime networks, a thorough analysis of link state variations was performed, resulting in the development of representative training samples.