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In this paper, the downlink opportunistic scheduling approach is studied in a multiuser environment with single-antenna transmitter and users. Exact bit error rate (BER) expressions are derived under the assumptions of full and quantized channel state information (CSI) at the transmitter. These expressions are then used to optimize the channel state feedback parameters. Moreover, asymptotic BERs are investigated in the limiting cases of a high signal-to-noise ratio (SNR) and a large number of users K. It is shown that both under the full and quantized CSI assumptions, the achieved BER is proportional to SNR-K and K-SNR in these two asymptotic cases, respectively. This means that the diversity order is equal to K, whereas the multiuser diversity gain is equal to SNR. In the case when the CSI feedback is quantized, the impact of feedback errors on the achieved BER is studied. It is shown that the opportunistic scheduling can greatly improve the BER performance even if the feedback is quite low-rate and erroneous.