On the DoF of Two-Way $2\times 2\times 2$ MIMO Relay Networks

This paper studies the degrees of freedom (DoF) of two-way 2 x 2 x 2 MIMO interference networks, a class of twoway four-unicast networks. We first provide upper and lower bounds on the sum DoF of general two-way 2 x 2 x 2 MIMO interference networks with any number of antennas in each node. We then investigate the special case where all user nodes have M antennas and relay nodes have N antennas, and provide the simplified bounds on the sum DoF. We show that our proposed achievable rate for this special case is higher than the achievable rates recently proposed in [1]. Moreover, for this special case, we obtain the exact DoF = 4M when N ≥ 2M, and DoF = 4N when M ≤ 2N.