Sum power minimization for cellular systems with underlay D2D communications

In this paper, we consider a single-cell system where the same radio resources are simultaneously used by a cellular user and a pair of device-to-device (D2D) terminals. The optimization objective is to minimize the sum transmission power of the system while satisfying the user specific minimum rate constraints. We propose joint power control and beamforming algorithms to solve the power minimization problem optimally both in uplink and downlink. In the uplink, the optimal transmit powers for the cellular and D2D users are obtained via fixed-point iterations, whereas the linear minimum mean squared error receiver is used for optimal reception at the base station (BS). In the downlink, the problem is equivalently reformulated as a second-order cone program (SOCP). As a result, the optimal transmit beamformer for the cellular user and the optimal transmit power for the D2D user can be efficiently computed via standard SOCP solvers. Simulation results demonstrate that the sum power performance can be significantly improved as compared with the conventional cellular system. Results also illustrate that the power consumption of the network is highly affected by the locations of the cellular and D2D users, and whether the resources are shared in the uplink or downlink.