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We consider efficient communications over the multiple-input multiple-output (MIMO) multiway distributed relay channel (MDRC) with full data exchange, where each user, equipped with multiple antennas and broadcasts messages to all the other users via the help of a number of distributive relays. We propose a physical-layer network coding (PNC)-based scheme involving linear precoding for channel alignment, nested lattice coding for PNC, and lattice-based precoding for interference mitigation. Unlike most existing approaches characterizing the degrees of freedom of MIMO multiway relay channels, we focus on analyzing the rate gap of the proposed scheme towards the fundamental channel capacity. In this regard, we establish a sufficient condition on the system configuration for that distributive relaying achieves the same sum rate as cooperative relaying does in the high SNR regime. We further show that the proposed scheme achieves the asymptotic sum capacity of the MIMO MDRC within a constant gap in the high SNR regime. Numerical results demonstrate that the proposed scheme considerably outperforms the existing schemes including decode-and-forward and amplify-and-forward.

MIMO Multiway Distributed Relay Channel With Full Data Exchange: An Achievable Rate Perspective