Energy-efficient power allocation for device-to-device communications underlaid cellular networks using stochastic geometry

In this paper, we study an energy efficiency maximization problem in uplink for device-to-device (D2D) communications underlaid with cellular networks on multiple bands. Utilizing stochastic geometry, we derive closed-form expressions for the average sum rate, successful transmission probability, and energy efficiency of cellular and D2D users. Then, we formulate an optimization problem to jointly maximize the energy efficiency of D2D and cellular users and obtain optimum transmission power of both D2D and cellular users. In the optimization problem, we guarantee the quality-of-service of users by taking into account the success transmission probability on each link. To solve the problem, first we convert the problem into canonical convex form. Afterwards, we solve the problem in two phases: energy efficiency maximization of devices and energy efficiency maximization of cellular users. In the first phase, we maximize the energy efficiency of D2D users and feed the solution to the second phase where we maximize the energy efficiency of cellular users. Simulation results reveal that significant energy efficiency can be attained, eg, 10% energy efficiency improvement compared to fix transmission power in a high-density scenario.