## 1 Introduction
Nevertheless, this does not mean that the WAR optimization problem is also solvable. Several papers have addressed this complex WAR maximization problem. The authors of [17] propose a two-stage dynamic programming scheme that can achieve an optimal WAR at the cost of higher computational complexity. Aiming at a series of non-convex combination optimization problems, the authors of [19] develop a joint user and power allocation scheme based on convex programming differences. Moreover, the authors of [20] propose a bilateral matching scheme derived from game theory to solve the problem of joint subchannel and power allocation. This method is extended to optimize the user and sub-channel pairing problems occurring in [21; 22]. The work of [23] exploits dual theory and the sub-gradient method to maximize the data rate under the NOMA-D2D background. In NOMA-based cognitive radio (CR) networks [24; 25], researchers have put forward some effective resource optimization plans to maximize the achievable throughput in the network. The authors of [26] developed a monotonic optimization scheme to maximize the weighted system throughput. Due to the high complexity of this program, it can only be regarded as an optimization reference index. However, the solutions provided in [27] reduce the complexity by discretizing the power value to achieve the approximate optimal performance. According to the summarization of our reference survey, the research reviewed barely considers the polynomial-time approximation (PTA) algorithm. Nevertheless, this kind of approximate optimization scheme can adjust the calculative complexity according to the optimization requirements. Inspired by the above observations, we propose the use of a fully polynomial-time approximation (FPTA) algorithm for WAR optimization in the downlink scenario of a NOMA-based offshore communication system. The contributions of this work are as follows:  
1. This work applies the NOMA-based resource optimization schemes to offshore communication in the _South China Sea_, improving the spectrum efficiency and data rate of the system. We propose an appropriate channel model based on the Longley-Rice model, including environmental factors and antenna deployment. Our offshore channel can be widely used in various regions of the world just by modifying its parameters. 2. We first analyze the resource optimization strategy using a single resource block. Aiming at the problem of single-resource-block joint power and user allocation, we implement an improved scheme (RBPUA) with higher computational efficiency. 3. Taking the single-resource-block optimization as the basic module, we propose an efficient joint multi-resource-block optimization scheme. This scheme combines low-complexity RBPUA with the gradient descent algorithm (GRAD). The simulation results show that GRAD with an accuracy of 0.0001 can achieve an optimal WAR performance. Moreover, the WAR of the NOMA maritime system is significantly improved compared with orthogonal multiple access (OMA). 4. An innovative solution is introduced for multi-resource-block NOMA maritime communication, which is derived from the multiple-choice knapsack algorithm and dynamic programming (MCKP-DP) [28]. The simulation consequence proves that the MCKP-DP scheme is able to obtain an optimal WAR nearly equal to that of the GRAD algorithm. 5. Inspired by the MCKP, we further develop an FPTA optimization algorithm based on dynamic programming (DP-FPTA). The scheme can perfectly balance the WAR performance optimization and computational complexity by adjusting the error parameter \(\varepsilon\). Therefore, DP-FPTA is more suitable for practical NOMA maritime communications with strict latency requirements. The rest of this paper is organized as follows. In Section 2, we first introduce the improved maritime channel model and system parameters, followed by the construction of a NOMA-based downlink offshore communication system. Section 3 formulates the resource optimization problem with WAR as the objective function.