Achieving global optimality for wirelessly-powered multi-antenna TWRC with lattice codes

In this paper, we consider the joint optimization of relay transmit-receive beamformers, users' transmit powers, and users' power splitting ratios in wirelessly-powered two-way relay channel under data-rate quality-of-service constraints. In order to solve the problem, we first establish that the uplink data-rate constraints would be active at the global optimum. Then we transform it into an equivalent problem by introducing slack variables and applying the linear matrix inequalities. Based on the transformed problem, the global optimal solution is derived. Numerical results on network power consumption versus circuit power and data-rate QoS show that the proposed algorithm outperforms existing algorithms.