  We study the degrees of freedom (DOF) of a multiple-input multiple-output
(MIMO) two-way X relay channel, where there are two groups of source nodes and
one relay node, each equipped with multiple antennas, and each of the two
source nodes in one group exchanges independent messages with the two source
nodes in the other group via the relay node. It is assumed that every source
node is equipped with M antennas while the relay is equipped with N antennas.
We first show that the upper bound on the total DOF for this network is
2min{2M,N} and then focus on the case of N \leq 2M so that the DOF is upper
bounded by the number of antennas at the relay. By applying signal alignment
for network coding and joint transceiver design for interference cancellation,
we show that this upper bound can be achieved when N \leq8M/5. We also show
that with signal alignment only but no joint transceiver design, the upper
bound is achievable when N\leq4M/3. Simulation results are provided to
corroborate the theoretical results and to demonstrate the performance of the
proposed scheme in the finite signal-to-noise ratio regime.
