Evolution of capacity lower bound of interference alignment with least-square channel estimation

In this paper, we study the performance of interference alignment (IA) when the channel state information (CSI) is acquired using a least-square (LS) estimator. We reveal how the capacity lower bound for each user varies according to the system parameters such as the training signal-to-noise ratio (SNR), ρ_t. We also illustrate that the gap between the performance in the perfect CSI case and the imperfect CSI case is constant when the transmit SNR, ρ, is proportional to ρ_t. In addition, the saturating SNR, ρ_s, which specifies the SNR where the achievable capacity in the imperfect CSI case departs from that in the perfect case, is derived as a function of ρ_t. An interesting result is that one can achieve the full degree-of-freedom (DoF) with imperfect CSI and also get very close the capacity of the perfect CSI case using IA. However, we illustrate that asymptotically perfect CSI does not guarantee that the capacity achievable at infinite SNR is the same as the capacity achievable in the perfect CSI case.