We investigate the MIMO broadcast channels with imperfect channel knowledge due to estimation error and much more users than transmit antennas to exploit multiuser diversity. The channel estimation error causes the interference among users, resulting in the sum-rate loss. A tight upper bound of this sum-rate loss based on zeroforcing beamforming is derived theoretically. This bound only depends on the channel estimation quality and transmit antenna number, but not on the user number. Based on this upper bound, we show this system maintains full multiuser diversity, and always benefits from the increasing transmit power.