Degrees of Freedom Region of the MIMO X channel with an Arbitrary Number of Antennas

 Abstract— We characterize the total degrees of freedom (DoF) of the full-rank MIMO X channel with arbitrary number of antennas at each node. We elucidate that the existing outer bound is tight for any antenna configuration and provide transmit and receive filter designs that attain this outer bound. The proposed achievable scheme exploits channel extensions in terms of both, symbol and asymmetric complex signaling when the communication is carried out over a constant channel case, and is also applicable to time varying channels. The proposed scheme represents a general framework for the derivation of the total DoF of any two-by-two multiuser channels. Furthermore, the rank-deficient MIMO channels case is naturally addressed, and it is shown that the total DoF of the interference (IC) and MIMO X channels are in general superior to the full rank MIMO case.