In this paper, we propose a geometric approach for optimal power control and relay selection in NOMA wireless relay networks. First, for each pair of relays, to derive an optimal vector of transmission power that maximizes the network throughput, we formulate a non-convex optimization problem. To obtain a closed-form solution for the non-convex optimization problem, we adopt ellipses and hyperbolas for classification of transmission power vectors. In addition, the proposed geometric approach could be used to select an optimal pair of relays and an optimal vector of transmission power in polynomial time. Furthermore, we observe that allocating all transmission power of the BS to send data to the stronger relay is not necessarily optimal in a NOMA wireless relay network. Simulation results show that the proposed geometric approach could significantly increase the end-to-end sum rate and reduce the power consumption of wireless communications for NOMA wireless relay networks with low computational complexity.

中文翻译：

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在 NOMA 无线中继网络中优化功率控制和中继选择的几何方法

在本文中，我们提出了一种在 NOMA 无线中继网络中优化功率控制和中继选择的几何方法。首先，对于每对中继，为了获得最大化网络吞吐量的传输功率的最佳向量，我们制定了一个非凸优化问题。为了获得非凸优化问题的封闭形式解，我们采用椭圆和双曲线对传输功率向量进行分类。此外，所提出的几何方法可用于在多项式时间内选择最佳中继对和最佳传输功率向量。此外，我们观察到分配 BS 的所有传输功率以将数据发送到更强的中继在 NOMA 无线中继网络中不一定是最佳的。