Degrees of Freedom of the Two-Way Relay MIMO Interference Channel

We investigate the symmetric degrees of freedom (DoF) of the K-pair (2K users) two-way relay Multiple-Input Multiple-Output (MIMO) Gaussian interference channel for K = 2, 3 where each user is equipped with M antennas and the relay node is equipped with N antennas. The two users of each pair communicate with each other via the help of the relay only. Expressing the DoF characterization as a function of the ratio γ = M/N , we find that the DoF value per user is piecewise linear depending on M and N alternately. As we will show in this paper, while the DoF achievability only needs linear beamforming transmission and zero-forcing reception, inter-pair signal subspace alignment is essential at the relay node as well as the users. In addition, the DoF converse is first developed based on the linear dimension counting approach, which can be further translated to the information theoretic statement.