## 5 Properties Analysis of the Functions \(\varphi_{m}^{s}\)
### Single-Resource-Block Maritime User Allocation
(1) If the input scale of the problem is small, the search strategy can be used to solve the problem in exponential time. If the input scale is large, (2) a random algorithm can accurately solve the problem with a high probability in polynomial time or (3) an approximate solution for the problem can be obtained in polynomial time. In [27], other approximate schemes are also mentioned. The central concept is to adopt the random sampling of sub-channels with probability \(\rho\) to avoid the traversal search. The simulation results show that, compared with the traditional optimization algorithm, the greedy-based approximate scheme saves 66% of the running time while maintaining the approximate optimal data rate. The question of whether the FPTA is the most desirable approximation algorithm will be explored in our future work. ## 7 Numerical Results and Discussion

In this paper, the model scenario simulated is located within the region of the _South China Sea_. Therefore, the _tropical ocean climate_ is taken for the setting of the climate parameter. The coastal 5G BS serves an offshore area with a radius of 5 km, and there are \(T\) maritime users (ships or offshore reef islands) randomly distributed across the sea. The total channel bandwidth \(B\) of the offshore communication system is 5 MHz. Moreover, the system channel is allocated to 10 resource blocks with a bandwidth of \(B_{s}=B/S=0.5\) MHz. When there is no typhoon, the sea surface is relatively calm, with the irregular terrain parameter taken as 0 [29]. Table 1 shows the reference values of the terrain irregularity parameter \(\Delta h\). The coastal BS is located in a high-lying area with a broad view. Therefore, its deployment parameter is _very careful_. In contrast, the deployment parameters of maritime users are relatively _random_. The effective heights of the BS transmitting antenna and the maritime user receiving antenna are 15 m and 5 m, respectively. In the multiple-choice knapsack program, we set the minimum discrete power to 0.01 W. Table 4 shows more detailed simulation parameters. First, we test the path loss of the Longley-Rice model with the increase in communication distance under an offshore background. Our objective is to investigate the influence of these two parameters on the maritime channel model, including BS transmitting antennas with different heights \(H_{T}\) and different degrees of irregularity \(\Delta h\). After that, we test the performance optimization and complexity of the proposed algorithm RBPUA based on NOMA and traditional OMA, respectively. Furthermore, we evaluate the three multi-resource-block joint optimization schemes not only in terms of the WAR performance optimization results but also in terms of the calculative complexity. When the height of the BS antenna varies from 5 to 25 m, Figure 2 shows that the Longley-Rice transmission loss results in the increase in the transmission distance. Specifically, within 5 km, the transmission loss of the 5 m transmitting antenna is significantly greater than that of the antenna transmitting over 10 m. At a distance of 5 km, the loss values of the 10 m to 25 m antennas are almost equal to 114.7 dB. With the expansion of the communication range, the transmission loss corresponding to the 10 m BS antenna will increase instantaneously. When the distance reaches 8 km, the 15 m antenna will expose the defect of limited coverage compared with the antenna above 20 m. Considering the limited coverage of the shore-based 5G BS, the communication range in this paper is within a radius