Eigen-Direction Alignment Based Physical-Layer Network Coding for MIMO Two-Way Relay Channels

In this paper, we propose a novel communication strategy which incorporates physical-layer network coding (PNC) into multiple-input multiple output (MIMO) two-way relay channels (TWRCs). At the heart of the proposed scheme lies a new key technique referred to as eigen-direction alignment (EDA) precoding. The EDA precoding efficiently aligns the two-user’s eigen-modes into the same directions. Based on that, we carry out multi-stream PNC over the aligned eigen-modes. We derive an achievable rate of the proposed EDA-PNC scheme, based on nested lattice codes, over a MIMO TWRC. Asymptotic analysis shows that the proposed EDA-PNC scheme approaches the capacity upper bound as the number of user antennas increases towards infinity. For a finite number of user antennas, we formulate the design criterion of the optimal EDA precoder and present solutions. Numerical results show that there is only a marginal gap between the achievable rate of the proposed EDA-PNC scheme and the capacity upper bound of the MIMO TWRC, in the median-to-large SNR region. We also show that the proposed EDA-PNC scheme significantly outperforms existing amplify-and-forward and decode-and-forward based schemes for MIMO TWRCs. This is a manuscript submitted to IEEE Transactions on Information Theory. Tao Yang and Iain. B. Collings are with CSIRO ICT Centre, Australia. The work of Xiaojun Yuan and Li Ping was fully supported by a grant from the University Grants Committee of the Hong Kong Special Administrative Region, China (Project No. AoE/E-02/08). The work of Jinhong Yuan was supported by Australian Research Council under the ARC Discovery Grant DP110104995.