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Channel state information at the transmitter (CSIT) enables high rates in multiuser systems with multiple transmit antennas, as it can be used for multiplexing gain and multiuser diversity. However, CSIT is often obtained through information fedback from the users, and it can be severely quantized to limit overhead. In this case, transmitting to multiple users will typically cause interference among them, which degrades the signal-to-interference-plus-noise ratio (SINR). In this letter, we derive bounds on this SINR, assuming that the transmitter uses zero-forcing beamforming, and that active users are almost orthogonal to one another. Simulation results show that our bounds may be used as a metric for user scheduling.