  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.
