Interference alignment feasibility in constant coefficient MIMO interference channels

We consider the K-link constant coefficient multiple-input-multiple-output interference channel (MIMO IFC) where inter-link interference is treated as Gaussian noise (Noisy MIMO IFC). Starting from Interference Alignment (IA) constraints, analytical conditions that need to be satisfied in order to admit an IA solution for such a MIMO IFC are derived. For a given degrees of freedom allocation, these conditions, along with a recursive algorithm to check its validity in a given K-link MIMO IFC, allow an analytical evaluation of the existence of IA solutions (or lack thereof). While such an attempt has been made recently for several interesting cases in published literature, to the best of our knowledge, this is the first time that such conditions have been derived in full generality (including the multiple stream case). Moreover, for the cases addressed in our approach evaluates the existence of IA solution with much lower complexity.