  On a multi-antenna broadcast channel, simultaneous transmission to multiple
users by joint beamforming and scheduling is capable of achieving high
throughput, which grows double logarithmically with the number of users. The
sum rate for channel state information (CSI) feedback, however, increases
linearly with the number of users, reducing the effective uplink capacity. To
address this problem, a novel space division multiple access (SDMA) design is
proposed, where the sum feedback rate is upper-bounded by a constant. This
design consists of algorithms for CSI quantization, threshold based CSI
feedback, and joint beamforming and scheduling. The key feature of the proposed
approach is the use of feedback thresholds to select feedback users with large
channel gains and small CSI quantization errors such that the sum feedback rate
constraint is satisfied. Despite this constraint, the proposed SDMA design is
shown to achieve a sum capacity growth rate close to the optimal one. Moreover,
the feedback overflow probability for this design is found to decrease
exponentially with the difference between the allowable and the average sum
feedback rates. Numerical results show that the proposed SDMA design is capable
of attaining higher sum capacities than existing ones, even though the sum
feedback rate is bounded.
