  In this paper, we consider the arbitrary MIMO two-way relay channels, where
there are $K$ source nodes, each equipped with $M_i$ antennas, for
$i=1,2,\cdots,K$, and one relay node, equipped with $N$ antennas. Each source
node can exchange independent messages with arbitrary other source nodes
assisted by the relay. We extend our newly-proposed transmission scheme,
generalized signal alignment (GSA) in [1], to arbitrary MIMO two-way relay
channels when $N>M_i+M_j$, $\forall i \neq j$. The key idea of GSA is to cancel
the interference for each data pair in its specific subspace by two steps. This
is realized by jointly designing the precoding matrices at all source nodes and
the processing matrix at the relay node. Moreover, the aligned subspaces are
orthogonal to each other. By applying the GSA, we show that a necessary
condition on the antenna configuration to achieve the DoF upper bound $\min
\{\sum_{i=1}^K M_i, 2\sum_{i=2}^K M_i,2N\}$ is $N \geq \max\{\sum_{i=1}^K
M_i-M_s-M_t+d_{s,t}\mid \forall s,t\}$. Here, $d_{s,t}$ denotes the DoF of the
message exchanged between source node $s$ and $t$. In the special case when the
arbitrary MIMO two-way relay channel reduces to the $K$-user MIMO Y channel, we
show that our achievable region of DoF upper bound is larger than the previous
work.
