Energy-efficient power control for device-to-device communications with max-min fairness

In this paper, we investigate the energy-efficient power control for device-to-device (D2D) communications underlaying cellular networks with max-min fairness, where uplink resource blocks allocated to one cellular user equipment are reused by multiple D2D pairs to improve the frequency reuse factor, and the minimum individual energy efficiency (EE) is maximized. This is a generalized fractional programming (GFP) problem, and is hard to tackle due to its non-concave nature, which means the complexity of global optimal solution is unaffordable. In order to give sub-optimal solution with reasonable complexity, we first transform the GFP problem into equivalent optimization problem in a parametric subtractive form, and then add constraints on the co-channel interferences to convert the non-concave GFP problem into concave one. The sub-optimal solution, which can be obtained through solving the deduced concave problem based on sophisticated convex optimization methods, gives a tight lower bound on the optimal EE. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.