摘要： As green communication becomes an inevitable trend for future 5G wireless networks, how to maximize the energy efficiency (EE) of device-to-device (D2D) communication has drawn extensive attention recently. However, most of existing works only optimize the EE in the single-cell scenario, while little attention is paid to maximizing the EE of the whole cellular network underlaid with D2D communication with randomly distributed users on multiple bands. In this paper, we first consider the whole cellular network underlaid with D2D communication on multiple bands and derive the exact expressions of the successful transmission probabilities, the average sum rate and the EE based on stochastic geometry theory. Then, we formulate the optimization problem of maximizing the EE subject to four constraints regarding to transmission power and outage probabilities, and the non-convexity of this problem is also verified. After that, by exploiting the objective function property of being the sum of several functions, we propose a derivative-based algorithm to solve this non-convex optimization problem. Our theoretical analysis shows that the computational complexity of the proposed algorithm is significantly lower than that of the conventional branch and bound algorithm. Finally, simulation results demonstrate that the proposed algorithm can achieve the near-optimal EE with much better performance than the conventional algorithm.