Degrees of freedom optimal transmission for the two-cluster MIMO multi-way relay channel

This paper investigates the degrees of freedom (DoF) of the two-cluster multi-way relay channel. Two cases are investigated: the case when there are 2 users in each cluster with arbitrary number of antennas and the case when there are 3 users in each cluster in the symmetric setting, i.e., all the users have the same number of antennas. For the 2-user case, a DoF upper bound is derived based on cut set bound by allowing user cooperation between clusters. Conditions when the DoF upper bound can be achieved using signal space alignment are established based on the relative number of antennas between the users and the relay. For the 3-user case, a new DoF upper bound is derived using genie-aided approach and channel enhancement. The DoF upper bound can be achieved using signal space alignment for several scenarios of interests. The results point out the insight that increasing the number of users in each cluster cannot provide a further DoF gain compared to the 2-user case, when the relay has limited number of antennas.