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