This work deals with interference alignment (IA) in a K-users MIMO interference channel with only incomplete Channel State Information at the Transmitters (CSIT). Incompleteness of CSIT is defined by the perfect knowledge of only a sub-matrix of the global channel matrix. Additionally, each Transmitter (TX) may have different incomplete CSIT. Most IA techniques are developed under a full (complete) CSIT assumption -either explicitly or implicitly when the CSI is progressively acquired in the form of RX-to-TX feedback iterations. In contrast, we are interested here in the feasibility of IA based only on incomplete CSIT. We show that even in antenna settings where no extra-antenna is available in terms of feasibility of IA, which we denote as tightly-feasible, IA can be achieved on some cases with some TXs having incomplete CSIT. Especially, for each antenna setting, we provide an incomplete CSIT sharing preserving feasibility and we adapt IA algorithms from the literature to achieve perfect IA under this condition of incomplete CSIT. We confirm by simulations that the proposed IA algorithm based on incomplete CSIT achieves no significant losses compared to the algorithm based on perfect CSIT sharing.
