Multiple-Antenna Interference Network with Receive Antenna Joint Processing and Real Interference Alignment

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 $Mk$ antennas at transmitter $k$, $1\le k\le K$, and $Nj$ antennas at receiver $j$, $1\le j\le K$, denoted as a $(K,[Mk],[Nj])$ 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.