Interference alignment in the partially connected K-user MIMO interference channel

We consider interference alignment in the partially connected K-user MIMO interference channel (IC). Conversely to the fully-connected case, we show that interference alignment can be achievable for an arbitrary number of users K in the network, while the per-user signaling dimension remains fixed, provided that the number of interference links per user is bounded. For this class of channels, which we denote by L-interfering K-user MIMO IC, we provide a criterion applicable to symmetric systems for the system of IA equations to be proper, according to the framework introduced earlier by Yetis et al. Properness is a necessary condition for IA to be feasible. Interestingly, this criterion is independent from the number of users K. Furthermore, we propose an iterative algorithm to solve the alignment problem for this class of channels.