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.
Binnan Zhuang, Randall A. Berry, Michael L. Honig