Symmetric Degrees of Freedom of the MIMO 3-way channel with MT × MR antennas

We investigate the symmetric Degrees-of-Freedom (DoF) of a homogeneous multiple-input multiple-output (MIMO) 3-way channel with M_T transmit antennas and M_R receive antennas at each user. The 3-way channel extends the two-way channel to three users, who exchange six messages in total, i. e., there is one message from each user to each of the two other users. We assume that each user operates in a perfect full-duplex mode. Genie-aided upper bounds on the DoF of the channel are derived and it is shown that those are achievable by combining MIMO interference alignment, null-space beam-forming and zero-forcing. A particular gain from this homogeneous setup is that the symmetric DoF allocation providing complete fairness among all users is sum-DoF optimal.