  In this paper, the degrees of freedom (DoF) regions of constant coefficient
multiple antenna interference channels are investigated. First, we consider a
$K$-user Gaussian interference channel with $M_k$ antennas at transmitter $k$,
$1\le k\le K$, and $N_j$ antennas at receiver $j$, $1\le j\le K$, denoted as a
$(K,[M_k],[N_j])$ channel. Relying on a result of simultaneous Diophantine
approximation, a real interference alignment scheme with joint receive antenna
processing is developed. The scheme is used to obtain an achievable DoF region.
The proposed DoF region includes two previously known results as special cases,
namely 1) the total DoF of a $K$-user interference channel with $N$ antennas at
each node, $(K, [N], [N])$ channel, is $NK/2$; and 2) the total DoF of a $(K,
[M], [N])$ channel is at least $KMN/(M+N)$. We next explore
constant-coefficient interference networks with $K$ transmitters and $J$
receivers, all having $N$ antennas. Each transmitter emits an independent
message and each receiver requests an arbitrary subset of the messages.
Employing the novel joint receive antenna processing, the DoF region for this
set-up is obtained. We finally consider wireless X networks where each node is
allowed to have an arbitrary number of antennas. It is shown that the joint
receive antenna processing can be used to establish an achievable DoF region,
which is larger than what is possible with antenna splitting. As a special case
of the derived achievable DoF region for constant coefficient X network, the
total DoF of wireless X networks with the same number of antennas at all nodes
and with joint antenna processing is tight while the best inner bound based on
antenna splitting cannot meet the outer bound. Finally, we obtain a DoF region
outer bound based on the technique of transmitter grouping.
