A New Physical-Layer Network Coding Scheme with Eigen-Direction Alignment Precoding for MIMO Two-Way Relaying

We investigate efficient communication over multiple-input multiple-output (MIMO) two-way relay channels (TWRCs), where two multi-antenna users exchange information via a multi-antenna relay. We propose a new MIMO physical-layer network coding (PNC) scheme that includes novel eigen-direction alignment (EDA) precoding. The proposed EDA precoding efficiently aligns the two-user´s eigen-modes into the same set of orthogonal directions, and multiple independent PNC streams are implemented over the aligned eigen-modes. We derive an achievable rate-pair of the proposed scheme, for given EDA precoding parameters, over a MIMO TWRC. To maximize the achievable rate-region, we formulate a design criterion for the EDA precoding parameters, and present solutions to the formulation. Closed-form bounds on the sum-rates of the designed EDA-PNC schemes are derived. Numerical results show that there is only a small gap between the achievable rate of the proposed scheme and the capacity upper bound of the MIMO TWRC. It is shown that the proposed scheme can significantly outperforms existing schemes in the literature.