This paper considers a MIMO interference system where interference alignment (IA) technique is adopted to manage the problem of interference. We consider a time division duplex (TDD) system where each transmitter estimates its channel state information (CSI) by probing the receivers. In addition, the transmitters share their local CSI estimate between each other using a backhaul links of limited capacity. A quantization over the backhaul is therefore required to reduce the amount of information to exchange. We study in this paper the impact of this quantization on the system performance and determine the optimal number of transmitter-receiver pairs that maximizes the system throughput.