Degrees of Freedom of the MIMO 3 -way channel

In the present paper, we consider the Degrees-of-Freedom (DoF) of a multiple-input multiple-output (MIMO) 3-way channel with an arbitrary number of antennas at each user. This channel provides a particular extension of the two-way channel to three users. Therein, three users exchange six messages in total, i. e., there is one message from each user to each of the two other users. We derive upper bounds on the DoF of the channel and show that those are achievable by MIMO interference alignment (IA) and zero-forcing beam-forming. We show that the network has a number of 2M
₂
DoF where M
_j
represents the number of antennas at user j, and M
₁
≥ M
₂
≥ M
₃
.