Beamforming for Simultaneous Wireless Information and Power Transfer in   Two-Way Relay Channels
  This paper studies simultaneous wireless information and power transfer (SWIPT) systems in two-way relaying (TWR) channels. Here, two source nodes receive information and energy simultaneously via power splitting (PS) from the signals sent by a multi-antenna relay node. Our objective is to maximize the weighted sum of the harvested energy at two source nodes subject to quality of service (QoS) constraints and the relay power constraints. Three well-known and practical two-way relay strategies are considered, i.e., amplify-and-forward (AF), bit level XOR based decode-and-forward (DF-XOR) and symbol level superposition coding based DF (DF-SUP). For each relaying strategy, we formulate the joint energy transmit beamforming and PS ratios optimization as a nonconvex quadratically constrained problem. To find a closed-form solution of the formulated problem, we decouple the primal problem into two subproblems. In the first problem, we intend to optimize beamforming vector for a given PS ratio. In the second subproblem, we optimize the PS ratio with a given beamforming vector. It is worth noting that although the corresponding subproblem are nonconvex, the optimal solution of each subproblem can still be found by using certain techniques. We provide numerical results that demonstrate the advantage of adapting the different relaying strategies and weighted factors to harvest energy in two-way relaying channel. 
Wei Wang, Rui Wang and Hani Mehrpouyan
cs.IT math.IT