This paper investigates the capacity of multiple-antenna broadcast channels with partial side information. In Gaussian broadcast channels with M transmit antennas and n single-antenna users, the sum rate capacity scales like $ M \log \log n $ for large n if perfect channel state information (CSI) is available at the transmitter, yet only logarithmically with M if it is not. The paper proposes a scheme that constructs M random beams and 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 throughput of this scheme scales as $ M \log \log nN $, where N is the number of receive antennas of each user. This is the same scaling as with perfect CSI using dirty paper coding. The paper also shows that a linear increase in throughput with M can be obtained provided that M does not grow faster than $ \log n $. The scheme is shown to be fair in a heterogeneous network, with the probability of transmitting to any user converging to $ \frac{1}{n} $, irrespective of its path loss. The paper concludes that using $ M = \alpha \log n $ transmit antennas is a desirable operating point, both in terms of providing linear scaling of the throughput with M and in guaranteeing fairness.This paper investigates the capacity of multiple-antenna broadcast channels with partial side information. In Gaussian broadcast channels with M transmit antennas and n single-antenna users, the sum rate capacity scales like $ M \log \log n $ for large n if perfect channel state information (CSI) is available at the transmitter, yet only logarithmically with M if it is not. The paper proposes a scheme that constructs M random beams and 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 throughput of this scheme scales as $ M \log \log nN $, where N is the number of receive antennas of each user. This is the same scaling as with perfect CSI using dirty paper coding. The paper also shows that a linear increase in throughput with M can be obtained provided that M does not grow faster than $ \log n $. The scheme is shown to be fair in a heterogeneous network, with the probability of transmitting to any user converging to $ \frac{1}{n} $, irrespective of its path loss. The paper concludes that using $ M = \alpha \log n $ transmit antennas is a desirable operating point, both in terms of providing linear scaling of the throughput with M and in guaranteeing fairness.