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This letter considers a compute-and-forward two-way relaying channel with simultaneous wireless information and power transfer based on nested lattice codes. Two single-antenna nodes exchange information via a multi-antenna intermediate relay station. Meanwhile, energies in wireless signals are beamed and flow from the relay to terminals for static circuit consumption Pc and uplink transmission power Pi. The optimization problem is formulated to minimize the transmit power Pr of relay, while guaranteeing the minimal transmission rate at each terminal. We propose an efficient iterative algorithm to jointly design the beam-former, receiver and power splitter, based on semi-definite relaxation and programming. Numerical results of transmission power comparisons validate our analysis.

Joint Transceiver and Power Splitter Design Over Two-Way Relaying Channel With Lattice Codes and Energy Harvesting