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A blind vector channel estimation (VCE) has been proposed and it outperforms the training-based VCE for the single-user multipath DS-CDMA system in the channel with time-varying normalized Doppler rate. In this paper, we extend it to the multiuser case which has multiple access interference (MAI). Therefore, we propose the use of MMSE multiuser detector to suppress MAI to get good initial channel estimation. Besides, following the joint vector channel estimation and decision-feedback MAP detector, we use the soft-input partial parallel interference cancellation (SIPPIC) to further reduce the remaining interference. The simulation results show that the MMSE-blind VCE-SIPPIC outperforms the MMSE-training-based VCE-SIPPIC.