Optimal power control for energy efficiency of device-to-device communication underlaying cellular networks

Device-to-device (D2D) communication can effectively meet the demands of high data rate by providing a direct link between two mobile users in cellular networks. In this paper, we analyze the optimal power control for energy efficiency of D2D communication underlaying cellular networks. Based on the stochastic geometry, we firstly use the homogeneous Poisson point process (PPP) to characterize the random distribution of both cellular and D2D users. Then, the successful transmission probabilities and energy efficiency (EE) of D2D communication are derived. We further analyze the optimization problem of D2D power with the constraints of outage and power. With the help of convex optimization, the convexity of D2D EE is verified, and the optimal D2D power for maximizing EE is evaluated in closed form. Simulation results demonstrate the impact of system parameters on the optimal D2D power as well as the influence of interference to the maximum EE of D2D communication.