Nonlinear precoding for XOR physical layer network coding in bi-directional MIMO relay systems

This paper proposes novel nonlinear precoding for XORphysical layer network coding (XOR-PNC) to improve the performance of bi-directional MIMO relay systems. The proposed precoder comprises a pre-equalizer and a nonlinear filter, which we also propose in the paper. We theoretically analyze the performance of the XOR-PNC with the proposed nonlinear precoding. As a result, it is shown that the proposed pre-equalizer improves the distribution of the received signals at relays, while the nonlinear precoder not only improves the transmission power efficiency but also simplifies the receiver at the relays. The performance is confirmed by computer simulation. The XOR-PNC with the proposed precoding achieves almost the lower bound in BER performance, which is much better than the amplify-and-forward physical layer network coding (AF-PNC).