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We propose an adaptive multistage detection scheme with low complexity for direct-sequence code-division multiple-access (DS-CDMA) systems in the presence of flat and frequency-selective fading. The first stage consists of a blind adaptive multiuser detector based on the linear constrained minimum variance (LCMV) criterion. The interference cancellation (IC) occurs in the second stage. The performance of the proposed iterative detector over both flat and frequency-selective fading channels is investigated and compared to the single-user bound. In all cases, the proposed iterative receiver is shown to offer a substantial performance improvement and a large gain in user capacity relative to the standard LCMV. In flat fading channels, our results show that the performance of the proposed detector is very close to the single-user bound. On the other hand, the performance of the iterative receiver over frequency-selective channels is noted to be in the order of 1 dB far from the single-user bound.