On Channel Inseparability and the DoF Region of MIMO Multi-way Relay Channels

TL;DR

This paper investigates the DoF region of a full-duplex MIMO multi-way relay channel with three users and a common relay, revealing the necessity of joint coding over sub-channels due to channel inseparability.

Contribution

It introduces a channel diagonalization and network coding strategy that achieves the optimal DoF region when relay antennas are fewer or equal to user antennas, and demonstrates the inseparability of the MIMO Y-channel.

Findings

Optimal DoF region achieved for N ≤ M

Joint encoding over sub-channels is necessary

MIMO Y-channel is inseparable

Abstract

Full-duplex multi-way relaying is a potential solution for supporting high data rates in future Internet-of-Things (IoT) and 5G networks. Thus, in this paper the full-duplex MIMO multi-way channel consisting of 3 users (Y-channel) with $M$ antennas each and a common relay node with $N$ antennas is studied. Each user wants to exchange messages with all the other users via the relay. A transmission strategy is proposed based on channel diagonalization that decomposes the channel into parallel sub-channels, and physical-layer network coding over these sub-channels. It is shown that the proposed strategy achieves the optimal DoF region of the channel if $N\leq M$. Furthermore, the proposed strategy that requires joint encoding over multiple sub-channels is compared to another strategy that encodes over each sub-channel separately. It turns out that coding jointly over sub-channels is necessary for an optimal transmission strategy. This shows that the MIMO Y-channel is inseparable.