As a key technology of the 5G communication system, device-to-device (D2D) communications have drawn significant research interests. However, the advantage of D2D communications may be limited when D2D users are far away from each other or the communication environments are harsh. In order to extend the range of D2D communications, a promising way is to use relaying technique to assist the communications. In this paper, we use a two-way amplify-and-forward (AF) relay to assist the underlay D2D communications and investigate the power control problem. Specifically, we formulate the power control problem as the optimization of the performance of the D2D link while fulfilling the quality-of-service (QoS) requirement of the cellular link. Two optimization objectives are considered for the D2D link, i.e., maximization of the minimum SINR at D2D users and maximization of the sum-rate of D2D users. For the first optimization objective, we can compare the possible optimal solutions for the three boundary conditions and obtain the optimal solutions. For the second optimization objective, we can convert the objective function into a concave function based on difference of convex (D. C.) structure, and use an iterative algorithm to solve the optimization problem. The simulation results show that the proposed power control scheme can improve the performance of the D2D link.
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