A new eigen-direction alignment algorithm for physical-layer network coding in MIMO two-way relay channels

We propose a new joint channel coding and physical layer network coding (CPNC) scheme for multiple-input multiple-output (MIMO) two-way relay channels (TWRCs). At the heart of the scheme lies a key technique referred to as eigen-direction alignment (EDA) precoding. This technique efficiently creates multiple aligned parallel channels which facilitates the deployment of multi-stream CPNC. Our analysis shows that the achievable rate of the scheme can approach the capacity upper bound in the median to high signal-to-noise (SNR) region when n T > n R, where n T and n R denote the number of antennas of each user and that of relay, respectively. The gap to the capacity upper bound diminishes as nT/nR increases. Numerical results demonstrate that the proposed scheme significantly outperform other well-known schemes in the literature.