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A dithered signed-error constant modulus algorithm with linearly constrained criteria is presented for blind adaptive multiuser detection in DS-CDMA systems. Steps of algorithm derivation are presented and convergence is theoretically analysed. Comparisons among different reported algorithms are made based on the results of simulations in a multipath environment with signal mismatch. Compared with other reported algorithms, the studies show that with the reduced computational complexity achieved by using signed-error technique, the proposed algorithm obtains balanced improvements on a few important issues, such as the SIR performance, convergence, tracking and robustness properties in dynamic environments.