Interference alignment limits for K-user frequency-flat MIMO interference channels

Starting from the zero-forcing constraints, some conditions to be satisfied in order to admit an interference alignment (IA) solution for any K-user frequency-flat MIMO interference channel are derived. Our conditions allow for analytical evaluation of the existence of IA solutions (or lack thereof) for a given K-user MIMO interference channel and degree of freedom allocation. We discuss interference alignment duality and the optimality of linear minimum mean squared error (LMMSE) interference reduction at the receiver for user rate maximization. Motivated by this, we suggest an algorithm for distributed interference alignment in a time division duplex (TDD) setting.