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Parallel interference cancellation (PIC) detector is designed to subtract the multi-access interference (MAI), and hence, it has the potential to achieve further performance improvement for direct-sequence code-division multiple access (DS-CDMA) systems. However, its performance depends on the accuracy of its data estimation. In the conventional PIC (CPIC) detector, the data estimation is based on the matched filter (MF), which results in poor performance. Moreover, in multi-cell environment, CPIC suffers from the interference from other cells. These disadvantages limit the potential of PIC. In this paper, a new PIC scheme is proposed and examined in detail, which uses blind adaptive minimum mean square error (MMSE) detectors instead of MFs for data estimation in each cancellation stage. Theoretical performance analyses as well as numerical simulations in varied situations reveal that the scheme has much improved performance over the CPIC. More importantly, it is immune to the near-far problem and is able to suppress the interference from other cells.