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A linear multiuser receiver for a particular user in a CDMA network gains potential benefits from knowledge of the channels of all users in the system. In fast multipath fading environments we cannot assume that the channel estimates are perfect and the inevitable channel estimation errors will limit this potential gain. We study the impact of channel estimation errors on the performance of linear multiuser receivers, as well as the channel estimation problem itself. Our main results involve asymptotic expressions for the signal-to-interference ratio of linear multiuser receivers in the limit of the large processing gain, with the number of users divided by the processing gain held constant.