Degrees of freedom of half-duplex MIMO multi-way relay channel with full data exchange

In this paper, we investigate the degrees of freedom (DoF) of the half-duplex multiple-input multiple-output (MIMO) multi-way relay channel (MWRC) with full data exchange, where each user wants to learn all the messages from the other users in the channel. We observe that, unlike the case of pairwise data exchange, the uplink and downlink traffic loads are asymmetric when full data exchange is considered. This asymmetry implies that unequal uplink/downlink time allocation, which is allowed in a half-duplex system, can improve the DoF of the MIMO MWRC. Based on that, we derive the DoF capacity of the half-duplex MIMO MWRC with full data exchange. We show that, as compared to the equal uplink/downlink time allocation, the optimized uplink/downlink time allocation achieves a significant DoF gain.