Parallel interference cancellation (PIC) receivers are among the most promising receiver techniques for future code-division multiple-access (CDMA) systems. Interference cancellation efficiency relies on the knowledge of the number of users and propagation paths needed in multiple-access interference (MAI) estimation. In practice, the exact number of users and paths is not known exactly, e.g., due to inter-cell interference, unknown propagation paths or new users trying to connect to the base station. As a result, there will be some residual interference even with perfect cancellation of the known signal components. In many cases, the inter-cell interference can be large enough to significantly degrade the performance of the PIC receivers. For that reason, residual interference suppression is crucial to guarantee that the PIC receivers can operate reliably. Residual interference can be reduced by applying adaptive antennas to PIC receivers. In this paper, another possibility is considered. The approach taken is to combine PIC receivers with blind adaptive interference suppression techniques in single sensor receivers.