Beamforming for Simultaneous Wireless Information and Power Transfer in Two-Way Relay Channels

This paper studies the beamforming designs for simultaneous wireless information and power transfer systems in two-way relaying (TWR) channels. The system consists of two energy-constrained source nodes which employ the power splitting (PS) to receive the information and the energy simultaneously from the power-supply relay. To maximize the weighted sum energy subject to the constraints of the quality of service and the transmit powers, three well-known relaying protocols, i.e., amplify-and-forward, bit level XOR-based decode-and-forward (DF), and symbol level superposition coding-based DF, are considered. For each relaying protocol, we formulate the joint relay beamforming, the source transmit power, and the PS ratios optimization as a nonconvex quadratically constrained problem. To solve the complex nonconvex problem, we decouple the objective problem into two subproblems in which one is to optimize the beamforming vectors while another is to optimize the remaining parameters. We show that the optimal solution of each subproblem can be obtained in the closed-form expressions. The solution is finally obtained with the proposed convergent iterative algorithm. Extensive numerical results demonstrate the advantage of adapting the different relaying strategies and weighted factors to harvest energy in TWR channels.