Transmitter-side channel information can significantly increase the throughput of wireless systems by allowing for adaptive transmission techniques such as rate/power control and transmitter beamforming. In a multi-user setting (e.g., a downlink channel), channel information also enables multi-user diversity, i.e., only users with good instantaneous channel conditions are selected for transmission. Due to the tremendous benefits of channel information, channel feedback (from receivers to the transmitter) has been the subject of a great deal of research over the past few years and such feedback mechanisms are now an essential component of many contemporary wireless standards (e.g., 3G, WiMax, 802.11n). The channel feedback rate is typically quite limited due to the fast time-scale of channel variation, and thus most work has concentrated on optimizing systems subject to a constraint on the feedback rate per user. However, the total feedback rate summed across all users is clearly a more meaningful measure of system resources than the per-user rate. We therefore consider the following basic system design question in the context of a multiple antenna downlink channel: given a constraint on the total system-wide channel feedback, is it preferable to get low-rate feedback from a large number of receivers or to receive high-rate/high-quality feedback from a smaller number of (randomly selected) receivers? Acquiring feedback from many users allows multi-user diversity to be exploited, while high rate feedback allows for very precise selection of transmit beamforming directions. It is shown that for systems employing multi-user downlink beamforming, it is strongly preferred to have a limited number of users feedback high-rate channel information rather than obtaining low-rate feedback from many users. While capacity increases only double logarithmically with the number of users, the marginal benefit of channel feedback is very significant up to the point where the CSI is essentially perfect.

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