On the optimality of network coding in two-way Decode-and-Forward MIMO relay channel

Network coding (NC) has been applied into two-way relay networks to achieve higher throughput and improve energy and spectrum efficiency. In this paper, we investigate the achievable rate region of two-way Decode-and-Forward (DF) MIMO relay downlink channels with multi-antenna relay node and users. To figure out the rate region of NC in multiuser MIMO system, a convex optimization solution is presented in this paper. The two schemes, Network Coding and Zero-Forcing BeamForming (ZFBF), are compared in terms of the achievable rate region with different channel states. When both of the two users know the messages destined for the other a priori, it is proved that NC is always the optimal compared with ZFBF. Meanwhile, ZFBF tends to achieve a larger rate region when the channel matrices of the two users approach to be orthogonal to each other. However, NC suffers from the maximum SNR loss in this special case. In particular, the extreme situation is studied to demonstrate the optimality of NC.