Signal space alignment and degrees of freedom for the two-cluster multi-way relay channel

This paper investigates the degrees of freedom (DoF) of the multi-way relay channel. Specifically, the focus is on the case when there are two clusters and each cluster has two users that wish to exchange messages within the cluster with the help of the relay. It is assumed that the relay has N antennas and each of the users has M antennas. A DoF outerbound is derived and it is shown that for several scenarios of interests the DoF outerbound can be achieved. Specifically, when N ≤ M, a network coding based two-way relaying approach with time division multiplex access (TDMA) is sufficient to achieve the DoF outerbound. When M <; N ≤ 4/3M, the signal space alignment with multiple access and broadcast transmission between the clusters can achieve the DoF outerbound. It is also show that when N ≥ 4M, the DoF outerbound can be achieved by just using multiple access and broadcast transmission between the users.