Joint Space Decomposition-and-Synthesis Theory for K-User MIMO Channels: Interference Alignment and DoF Region

The degree-of-freedom (DoF) region for a general interference-aligned multi-user multiple-input multiple-output (MIMO) channel is of theoretic importance. Yet, its exact characterization is not available in the literature, due to the lack of an appropriate theoretical framework. A joint space decompositionand-synthesis theory is developed in the paper. The joint decomposition is done on the receive spaces to uncover the geometric mechanism behind interference formation and alignment which, alongside the parametrization of the augmented interference channel matrices, forms a foundation to synthesize the required precoders at transmitters. The new framework leads to exact DoF regions for the 3-user channel with arbitrary number of antennas at receivers and transmitters, and an inner and an outer bound for the DoF region of K-user (K > 3) MIMO interference channels. It also covers the existing results for the 2-user MIMO channel as a special case.