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We consider the downlink of a cellular network with multiple cells and multi-antenna base stations. Our model includes distance-dependent pathloss, arbitrary clusters of cooperating cells, and general “fairness” requirements. Beyond Monte Carlo simulation, no efficient computation method to evaluate the ergodic throughput of such systems has been presented, yet. Furthermore, for systems of practical size with tens of cells and hundreds of users per cell, even simulation becomes challenging. We develop an analytic framework based on the combination of results from large random matrix theory and convex optimization. This allows computationally efficient calculation of the system performance in the so-called “large system limit”, i.e., in the limit of a large number of antennas per base station and a large number of users per cell, while the ratio of antennas per user is kept constant. In particular, the system ergodic throughput, subject to per-base station power constraints and to general fairness criteria, is obtained via the iterative solution of a system of fixed-point equations. Comparisons with finite-dimensional simulation results show that the large-system analysis provides remarkably accurate approximations for the actual finite-dimensional systems, even for a small number of users and base station antennas.