Interference alignment with incomplete CSIT sharing

In this work we study the impact of having only incomplete channel state information at the transmitters (CSIT) over the feasibility of interference alignment (IA) in a K-user MIMO interference channel (IC). Incompleteness of CSIT refers to the perfect knowledge at each transmitter (TX) of only a sub-matrix of the global channel matrix, where the sub-matrix is specific to each TX. This paper investigates the notion of IA feasibility for CSIT configurations being as incomplete as possible, as this leads to feedback overhead reductions in practice. We distinguish between antenna configurations where (i) removing a single antenna makes IA unfeasible, referred to as tightly-feasible settings, and (ii) cases where extra antennas are available, referred to as super-feasible settings. We show conditions for which IA is feasible in strictly incomplete CSIT scenarios, even in tightly-feasible settings. For such cases, we provide a CSIT allocation policy preserving IA feasibility while reducing significantly the amount of CSIT required. For super-feasible settings, we develop a heuristic CSIT allocation algorithm which exploits the additional antennas to further reduce the size of the CSIT allocation. As a byproduct of our approach, a simple and intuitive algorithm for testing feasibility of single stream IA is provided.