Large System Analysis of Interference Alignment Achievable Rates for the MIMO Interference Channel

In this paper, analytical rate expressions of interference alignment (IA) algorithms applied to the multiple-input multiple-output interference channel are derived in the large system limit. A large system analysis is performed by fixing the number of users and letting the number of transmit and receive antennas go to infinity at a finite fixed ratio. The asymptotic eigenvalue distribution of the direct channel gains resulting from IA algorithms is first obtained. Based on that, large system rate expressions under both water-filling power allocation and equal power allocation are derived in closed form. The obtained expressions are functions of the transmit power and noise power at the receivers and are independent of any other system parameters. Simulation results show that the achievable rates of different IA algorithms converge to the large system rates as the number of transmit and receive antennas increases, thereby showing that the large system expressions are valid for different IA variants. Simulation results also show that large system expressions provide accurate estimates of the average achievable rates for small and finite system parameters.