Asymptotic sum-capacity of MIMO two-way relay channels within 1/2 log 5/4 bit per user-antenna

We propose a novel space-division based network-coding scheme for multiple-input multiple-output (MIMO) two-way relay channels (TWRCs), in which two multi-antenna users exchange information via a multi-antenna relay. In the proposed scheme, the overall signal space at the relay is divided into two subspaces. In one subspace, the spatial streams of the two users have nearly orthogonal directions, and are completely decoded at the relay. In the other subspace, the signal directions of the two users are nearly parallel, and linear functions of the spatial streams are computed at the relay, following the principle of physical-layer network coding (PNC). Based on the recovered messages and message-functions, the relay generates and forwards network-coded messages to the two users. We show that, at high signal-to-noise ratio (SNR), the proposed scheme with optimized precoding achieves the asymptotic sum-rate capacity of MIMO TWRCs within 1/2 log(5/4) ≈ 0.161 bit per user-antenna, for any antenna configuration and any channel realization.