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In this paper, we investigate the energy-efficient power control for device-to-device (D2D) communications underlaying cellular networks, where uplink resource blocks allocated to one cellular user equipment are reused by multiple D2D pairs and co-channel interference caused by resource sharing becomes a significant challenge. We consider both the total energy efficiency (EE) and individual EE optimization problems, which are fractional programming and generalized fractional programming problems, respectively, and are hard to tackle due to their non-concave nature. We first transform them into equivalent optimization problems in parametric subtractive forms, which fit in a class of non-concave optimization methods known as difference of two concave functions programming, and then solve them using Dinkelbach and branch-and-bound methods to give global optimal solutions. Due to the unaffordable complexity of the global optimal solution, we further propose sub-optimal schemes through adding constraints on the interferences to convert the non-concave problems into concave ones and to give sub-optimal solutions with reasonable complexity. The sub-optimal solution gives a tight lower bound on the optimal EE. Simulation results are presented to demonstrate the effectiveness of the proposed schemes.
Yang et al. (Tue,) studied this question.