The DoF of the 3-User $(p,p+1)$ MIMO Interference Channel

The degrees of freedom (DoF) of the 3-user multiple-input multiple-output (MIMO) interference channel (IC) with full channel state information and constant channel coefficients are investigated when (p,p+1) antennas are deployed at the transmitters and receivers, respectively. The point of departure of this paper is the work of Wang et al., which conjectured but did not prove the DoF for the antenna settings with p>1. Here the achievability of the DoF outer bound is formally proved using linear methods, thereby avoiding the use of the rational dimensions framework. The proposed transmission scheme exploits asymmetric complex signaling together with symbol extensions in time and space interference alignment concepts. While the paper deals with the p=2,3,\ldots,6 cases, providing the specific transmit and receive filters, there are also provided the tools needed for proving the achievability of the optimal DoF for p>6, whose DoF characterization is conjectured.