A Geometric Approach for Optimal Power Control and Relay Selection in NOMA Wireless Relay Networks

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.