Degrees of freedom of MIMO two-way X relay channel

In this paper, we study the degrees of freedom of a multiple-input multiple-output (MIMO) two-way X relay channel, i.e., a system with two groups of source nodes and one relay node, where each of the two source nodes in one group wants to exchange independent messages with both the two source nodes in the other group via the relay node. We only consider the symmetric case where each source node is equipped with M antennas while the relay is equipped with N antennas. We first show that the upper bound of the degrees of freedom is 2N when N ≤ 2M. Then by applying physical layer network coding and joint interference cancellation, we propose a novel transmission scheme for the considered network. We show that this scheme can always achieve this upper bound when N ≤ ⌊4M/3⌋.