Optimized linear physical-layer network coding of full-rate full-diversity in MIMO two-way relay networks

In multiple-input multiple-output (MIMO) two-way relay networks (TWRN), linear physical-layer network coding (LPNC) was proposed to boost the throughput by using spatial multiplexing at source nodes. How to design optimal LPNC for full-rate full-diversity MIMO TWRN is still an open problem. In this paper, we propose a full-rate full-diversity (FRFD) LPNC scheme. In this scheme, two source nodes, each with two antennas, transmit full-rate universal space-time codes to a two-antenna relay simultaneously. Then, the relay applies LPNC to compute multiple network-coded (NC) messages. In particular, we explicitly solve the optimal LPNC mapping to minimize decoding errors of NC messages in the FRFD LPNC scheme. Our analytical results verify that the optimal FRFD LPNC scheme guarantees the full-diversity and full-rate transmission at the same time. Simulation results are consistent with the analytical results and further demonstrate that our optimal FRFD LPNC scheme outperforms the conventional MIMO LPNC scheme.