  This paper studies the achievable degrees of freedom for multi-user MIMO
two-way relay channels, where there are $K$ source nodes, each equipped with
$M$ antennas, one relay node, equipped with $N$ antennas, and each source node
exchanges independent messages with an arbitrary set of other source nodes via
the relay. By allowing an arbitrary information exchange pattern, the
considered channel model is a unified one. It includes several existing channel
models as special cases: $K$-user MIMO Y channel, multi-pair MIMO two-way relay
channel, generalized MIMO two-way X relay channel, and $L$-cluster MIMO
multiway relay channel. Previous studies mainly considered the achievability of
the DoF cut-set bound $2N$ at the antenna configuration $N < 2M$ by applying
signal alignment. This work aims to investigate the achievability of the DoF
cut-set bound $KM$ for the case $N\geq 2M$. To this end, we first derive
tighter DoF upper bounds for three special cases of the considered channel
model. Then, we propose a new transmission framework, generalized signal
alignment, to approach these bounds. The notion of GSA is to form network-coded
symbols by aligning every pair of signals to be exchanged in a compressed
subspace at the relay. A necessary and sufficient condition to construct the
relay compression matrix is given. We show that using GSA, the new DoF upper
bound is achievable when i) $\frac{N}{M} \in \big(0, 2+\frac{4}{K(K-1)}\big]
\cup \big[K-2, +\infty\big)$ for the $K$-user MIMO Y channel; ii) $\frac{N}{M}
\in \big(0, 2+\frac{4}{K}\big] \cup \big[K-2, +\infty\big)$ for the multi-pair
MIMO two-way relay channel; iii) $\frac{N}{M} \in \big(0, 2+\frac{8}{K^2}\big]
\cup \big[K-2, +\infty\big)$ for the generalized MIMO two-way X relay channel.
We also provide the antenna configuration regions for the general multi-user
MIMO two-way relay channel to achieve the total DoF $KM$.
