## 2 System Model and Parameters Analysis
As shown in Figure 1, a downlink NOMA marine system is composed of a shore-based base station in the offshore area of the _South China Sea_. We use \(\mathbf{T}\triangleq\{1,2,\ldots,T\}\) to describe the index set of maritime users. This maritime system divides the entire bandwidth \(B\) into \(S\) subchannels, where each bandwidth is \(B_{S}\). This paper refers to a subchannel as a resource block. We adopt \(\mathbf{S}\triangleq\{1,2,\ldots,S\}\) to represent the set of these resource blocks; for each \begin{table}
\begin{tabular}{c c} \hline \hline
**Irregular Terrain** & \(\Delta\mathbf{h}\) **(m)** \\ \hline Flat (or smooth water) & 0 \\ Plains & 30 \\ Hills & 90 \\ Mountains & 200 \\ Rugged mountains & 500 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Reference value for the terrain irregularity parameter. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Medium** & **Relative Permittivity (F/m)** & **Conductivity (S/m)** \\ \hline Average ground & 15 & 0.005 \\ Poor ground & 4 & 0.001 \\ Good ground & 25 & 0.020 \\ Fresh water & 81 & 0.010 \\ Sea water & 81 & 5.0 \\ \hline \hline \end{tabular} For most purposes, use the constants for an average ground.  
\end{table} 
Table 2: Suggested values for the electrical ground constants. resource block, \(s\in S\) satisfies \(\sum\limits_{s\in S}B_{S}=B\). In our maritime system, the resource blocks are of the orthogonal frequency division to ensure that they will not interfere with each other. Suppose that \(P_{t}^{s}\) represents the transmitting power from the coastal BS to a maritime user \(t\in T\) on resource block \(s\). If \(P_{t}^{s}>0\), this means that the maritime user \(t\) obtains power from resource block \(s\). Therefore, we determine that user \(t\) is valid on this resource block. In contrast, \(P_{t}^{s}=0\) indicates an offshore user that does not occupy resource block \(s\); we define this as an invalid user. On resource block \(s\), let \(G_{t}^{s}\) denote the channel gain from BS to maritime user \(t\) and \(\sigma_{t}^{s}\) represent the noise power. To facilitate subsequent simplification, we define a normalized channel noise parameter: \(\widetilde{\sigma}_{t}^{s}\triangleq\frac{\sigma_{t}^{s}}{G_{t}^{s}}\). In this manner, we reduce the number of variables affecting the optimization objective function. Let \(P\triangleq(P_{t}^{s})_{s\in S,t\in T}\) indicate the matrix of the transmitting powers provided by BS for each maritime user. Moreover, \(\mathbf{P}_{s}\triangleq(P_{t}^{s})_{t\in T}\) denotes the vector of powers allocated to each maritime user on resource block \(s\). Successive interference cancellation (SIC) technology is applied in NOMA systems to effectively eliminate signal interference among users. With the increase in the number of multiplexed users, the SIC decoding process becomes very complicated [7]. Therefore, the upper limit of users carried on each resource block is defined as \(A\). We use \(A_{s}\triangleq\{t\in T,P_{t}^{s}>0\}\) to denote the set of valid users on resource block \(s\). Then, the above  
Figure 1: NOMA-based downlink maritime communication system. \begin{table}
\begin{tabular}{c c} \hline \hline
**Climate** & **Surface Refractivity (N-Units)** \\ \hline Equatorial & 360 \\ Continental subtropical & 320 \\ Maritime subtropical & 370 \\ Desert & 280 \\ Continental temperate & 301 \\ Maritime temperate (over land) & 320 \\ Maritime temperate (over sea) & 350 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Suggested values of surface refractivity for different climates. restraint condition can be summarized as \(\mid A_{s}\mid\leq A\), where \(\mid\cdot\mid\) represents the cardinality of a limited set. Referring to the SIC decoding principle described in [30; 31], we denote the SIC decoding order of \(T\) maritime users as \(\beta_{s}\): {1, 2,..., \(T\)}. The index of the \(m\)th decoded maritime user is \(\beta_{s}(m)\) on resource block \(s\), and the inverse function \({\beta_{s}}^{-1}(t)\) indicates the decoding sequence of user \(t\).