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Since having full channel state information in the transmitter is not reasonable in many applications and lack of channel knowledge does not lead to linear growth of the sum rate capacity as the number transmit antennas increases, it is therefore of interest to investigate transmission schemes that employ only partial CSI. In this paper, we propose a scheme that constructs M random beams and that transmits information to the users with the highest signal-to-noise-plus-interference ratios (SINRs), which can be made available to the transmitter with very little feedback. For fixed M and n increasing, the sum-rate capacity of our scheme scales as M log log n, which is precisely the same scaling obtained with perfect channel information. We furthermore show that linear increase in capacity can be obtained provided that M does not grow faster than O(log n). We also study the fairness of our scheduling scheme and show that, when M is large enough, the system becomes interference-dominated and the probability of transmitting to any user converges to 1/n, irrespective of its path-loss. In fact, using M = α log n transmit antennas emerges as a desirable operating point, both in terms of providing linear increase in capacity as well as in guaranteeing fairness.