Multi-cell MIMO downlink with fairness criteria: The large system limit

We consider the downlink of a cellular network with multiple cells and multi-antenna base stations under arbitrary inter-cell cooperation, realistic distance-dependent pathloss, and general "fairness" requirements. Beyond Monte Carlo simulation, no efficient computation method to evaluate the ergodic throughput of such systems has been provided so far. We propose an analytic method based on the combination of the large random matrix theory with Lagrangian optimization. The proposed method is computationally much more efficient than Monte Carlo simulation and provides a very accurate approximation (almost indistinguishable) for the actual finite-dimensional case, even for of a small number of users and base station antennas. Numerical examples include linear 2-cell and planar three-sectored 7-cell layouts, with no inter-cell cooperation, sector cooperation, and full cooperation.