Asymptotic performance analysis of interference alignment under imperfect CSI

Interference alignment (IA) is potentially able to deliver more than one degree of freedom (DoF) in wireless networks such that the achievable DoF can be linearly scaled up with the number of users. This improvement, however, comes at the cost of availability of perfect channel state information (CSI) which hinders the practical implementation of IA since only partial CSI may be accessible. In this paper, we quantify the performance of IA under CSI imperfections where the variance of the CSI measurement error depends on the signal-to-noise ratio (SNR). We show that when this error variance is proportional to the inverse of SNR, full DoF is attainable. In this case, an upper bound on asymptotic mean loss in sum rate compared to the perfect CSI case is derived. Furthermore, we also derive a tight lower bound on the achievable DoF when the error variance is proportional to the inverse of SNR to a power of a constant. It is shown that when this constant is bounded between zero and one, a fraction of the total DoF is achievable. Using numerical simulations, we substantiate the analytically derived bounds.