Resource allocation optimization (RAO) is a crucial design issue for providing green communications in the sixth generation (6G) of underwater acoustic (UWA) sensor networks (SNs). To have a suitable convergence speed in the machine learning (ML)-based algorithms used for finding the solution of the online RAO problems, the optimal or suboptimal solution of the offline form of the online problem should be utilized as the initial setting. Moreover, knowing the closed-form of the best initial setting in terms of the channel parameters leads to more efficiency in the ML-based algorithms from the robustness standpoint. In this paper, we formulate and solve two new offline RAO problems for joint relay selection and power allocation in the orthogonal frequency division multiplexing UWA cooperative communication systems. We first obtain a new formula for the signal to noise ratio (SNR) per-subcarrier in the cooperative UWA communication system with amplify and forward relaying including multiple users and multiple relays. In our analyses, unlike terrestrial channel and by considering the physical facts seen in the practical UWA channel, we assume non-white Gaussian noise along with the frequency-dependent pathloss for obtaining the SNR per-subcarrier function. Then, we use it in the definition of our RAO problems. Our proposed problems are non-convex and we present a promising method for converting them to the convex problems. In our problems, the objective function is the total power transmitted over the network. In addition, the sum-rate and probability of error are constrained to control the quality of service. Also, we derive some new closed-form formulas for reliable cooperation, relay selection, and power loading. Extensive simulation studies are carried out to assess the convergence, effectiveness, and robustness of our proposed algorithms to the channel impairments for different conditions.

资源分配优化 (RAO) 是在第六代 (6G) 水声 (UWA) 传感器网络 (SN) 中提供绿色通信的关键设计问题。为了在用于寻找在线 RAO 问题的解决方案的基于机器学习 (ML) 的算法中具有合适的收敛速度，应使用在线问题的离线形式的最优或次优解作为初始设置。此外，从鲁棒性的角度来看，根据信道参数了解最佳初始设置的封闭形式可以提高基于 ML 的算法的效率。在本文中，我们制定并解决了两个新的离线 RAO 问题，用于正交频分复用中的联合中继选择和功率分配UWA 协作通信系统。我们首先在具有放大和转发中继（包括多用户和多中继）的协作 UWA 通信系统中获得每子载波信噪比 (SNR) 的新公式。在我们的分析中，与地面信道不同，通过考虑在实际 UWA 信道中看到的物理事实，我们假设非白高斯噪声以及频率相关路径损耗以获得每个子载波函数的 SNR。然后，我们在 RAO 问题的定义中使用它。我们提出的问题是非凸的，我们提出了一种有前途的方法将它们转换为凸问题。在我们的问题中，目标函数是通过网络传输的总功率。此外，总和率和错误概率受到约束以控制服务质量。此外，我们还推导出了一些用于可靠合作、继电器选择和功率加载的新封闭式公式。进行了广泛的仿真研究，以评估我们提出的算法对不同条件下的信道损伤的收敛性、有效性和鲁棒性。