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Blind adaptive and iterative interference cancellation (IC) receiver structures for direct sequence code division multiple access systems in multipath channels are proposed. A code-constrained constant modulus design criterion based on constrained optimisation techniques and adaptive algorithms for receiver and channel parameter estimation are described for successive IC (SIC) and parallel IC (PIC) detectors and a new hybrid IC (HIC) scheme in scenarios subject to multipath fading. The proposed HIC structure combines the strengths of linear, SIC and PIC receivers and is shown to outperform the conventional linear, SIC and PIC structures. A novel iterative detection approach that generates different cancellation orders and selects the most likely symbol estimate on the basis of the instantaneous minimum constant modulus criterion is also proposed and combined with the new HIC structure to further enhance performance. Simulation results for an uplink scenario assess the algorithms, the proposed blind adaptive IC detectors against existing receivers and evaluate the effects of error propagation of the new cancellation techniques.