  This letter considers a compute-and-forward two-way relaying channel with
simultaneous wireless information and power transfer. Specifically, two
single-antenna users exchange information via a multi-antenna relay station
based on nested lattice codes. Meanwhile, wireless energies flow from the relay
to users for circuit consumption and uplink transmission. Based on this model,
an optimization problem is formulated to minimize the transmit power at relay,
while guaranteeing the minimal transmission rate at each user. To solve the
problem, we propose an efficient iterative algorithm to jointly optimize the
transmitter, receiver and power splitter, based on semi-definite relaxation and
semi-definite programming. Numerical results of relay transmission powers
validate our analysis.
