## 5 Properties Analysis of the Functions \(\varphi_{m}^{s}\)
### Single-Resource-Block Maritime User Allocation
Figure 8: Weighted achievable rate of the three multi-subchannel joint optimization schemes vs. number of maritime users: (a) WAR of DP-FPTA with different \(\varepsilon\) and (b) WAR of MCKP-DP and GRAD algorithms. Figure 9: Weighted achievable rate of DP-FPTA and MCKP-DP vs. number of items in each resource block \(4S/\varepsilon\). Figure 10 further compares the calculative complexity of DP-FPTA and MCKP-DP. The complexity of the DP-FPTA scheme increases with the increase in \(4S/\varepsilon\). When the number of normalized items reaches 2900 (\(\varepsilon\leq 0.01\)), its complexity is equivalent to that of the MCKP-DP scheme (\(J=1000\)), and MCKP-DP achieves the optimal WAR. In this case, we do not recommend our proposed DP-FPTA scheme. Combined with the simulation results shown in Figure 9, within the approximate error interval of \(0.01\leq\varepsilon\leq 0.08\), NOMA-based DP-FPTA achieves an approximately optimal WAR performance with far less calculative complexity than MCKP-DP. When the error parameter satisfies \(\varepsilon=0.08\), the WAR of the approximate scheme achieves 99.55% of MCKP-DP, but the complexity is 84.3% lower than the MCKP-DP scheme. Furthermore, the performance of the NOMA-based DP-FPTA is better than that of OMA by 4.48%. Results have shown that while controlling the computational complexity, DP-FPTA can ensure the optimization of WAR by adjusting the approximate error function \(\varepsilon\). Therefore, our proposed scheme successfully achieves the trade-off between optimization performance and calculative delay. ## 8 Conclusions

This paper investigates the WAR optimization problem in the NOMA-based offshore downlink communication scenario of the _South China Sea_. We established a Longley-Rice-based maritime channel model, including various environmental factors and antenna deployment parameters. This model, which has adjustable environmental parameters, can be widely applied to various offshore communication applications around the world. Aiming at the single-resource-block resource allocation problem, we performed pre-computation to simplify the power and marine user allocation. Taking the improvement scheme RBPUA as the basic module, we developed three optimization solutions for multi-resource-block joint power and maritime user allocation. The simulation results indicate that we can regard the GRAD as a performance optimization index. MCKP-DP provides a new idea based on the knapsack problem for resource allocation. Its optimization performance achieved the best value, while the complexity had to be reduced. We proposed the use of the DP-FPTA to effectively weigh the relationship between computation complexity and performance optimization. This algorithm is suitable for a practical NOMA-based maritime communication system with a low time delay. In subsequent work, the NOMA-based relay technology should be introduced into marine communications to expand the network coverage [36]. In addition, we will further expand the single-BS NOMA system to the maritime communication network jointly de

Figure 10: Computational complexity of DP-FPTA and MCKP-DP vs. number of items in each resource block \(4S/\varepsilon\). ployed by multiple offshore BSs. Moreover, motivated by the optimization schemes in this paper, we will delve into the problem of resource allocation in the MIMO-NOMA maritime system. The joint optimization project with beamforming and user clustering represents a significant challenge for our future work [37]. We aim to achieve improved signal strength and regional coverage while reducing signal interference in the next generation of this maritime communication system. Conceptualization, [PERSON] ([PERSON]) and H.L. ([PERSON]); methodology, [PERSON] ([PERSON]) and H.L.