Interference alignment in MIMO cellular networks

We explore the feasibility of linear interference alignment (IA) in MIMO cellular networks. Each base station (BTS) has Nt transmit antennas, each mobile has Nr receive antennas, and a BTS transmits a single beam to each active user. We present a necessary Zero-Forcing (ZF) condition for zero interference in terms of the number of users, the number of cells, Nt and Nr. We then examine the performance of iterative (forward-backward) algorithms for jointly optimizing the transmit precoders with linear receivers. Modifications of the max-SINR and minimum leakage algorithms are presented, which are observed to converge to a ZF solution whenever the necessary conditions are satisfied. In contrast, convergence of the (original) max-SINR algorithm is problematic when the necessary conditions are satisfied with (near) equality. A more restrictive ZF condition is presented, which predicts when these convergence problems are unlikely to occur.