  In this paper, we design interference free transceivers for multi-user
two-way relay systems, where a multi-antenna base station (BS) simultaneously
exchanges information with multiple single-antenna users via a multi-antenna
amplify-and-forward relay station (RS). To offer a performance benchmark and
provide useful insight into the transceiver structure, we employ alternating
optimization to find optimal transceivers at the BS and RS that maximizes the
bidirectional sum rate. We then propose a low complexity scheme, where the BS
transceiver is the zero-forcing precoder and detector, and the RS transceiver
is designed to balance the uplink and downlink sum rates. Simulation results
demonstrate that the proposed scheme is superior to the existing zero forcing
and signal alignment schemes, and the performance gap between the proposed
scheme and the alternating optimization is minor.
