The code division multiple access (CDMA) system implemented by the direct-sequence (DS) spread spectrum (SS) technique is one of the most promising multiplexing technologies for the wireless communications services. The SS communication adopts a technique of using much wider bandwidth necessary to transmit the information over the channel, and has been proposed for third generation broadband wireless access. The capacity and performance of the DS-CDMA system are mainly limited by the multiple access interference (MAI) and the inter-symbol-interference (ISI) caused by the multipath-fading channel. To circumvent the above-mentioned problems many adaptive multiuser detectors, for instance the minimum mean square error (MMSE) and the minimum output energy (MOE) criteria, subject to certain constraints, have been proposed. Since the LCMV criterion is the linearly constrained (LC) version of MOE, it is high sensitivity to the channel mismatch caused by the unreliable estimation. In order to deal with this problem, the LC constant modulus (LCCM) criterion was considered to avoid capturing the interfering user instead of the desired user when the power of interfering user is much higher than the desired user. In this thesis, based on the Min/Max criterion we propose a novel blind LCCM recursive least-square (RLS) algorithm, with the generalized side-lobe canceller (GSC) structure, named as the CM GSC-RLS algorithm, to effectively alleviate the effect of MAI and ISI for DS-CDMA receiver, for time-varying channel. Due to the variation of channel at the receiver, the desired user amplitude or power is not available and has to be estimated. To solve this problem, we propose a simple scheme to estimate the parameter of constant modulus, adaptively, associated with the CM GSC-RLS algorithm. With the new proposed algorithm, the amplitude variation of desired user, due to changing characteristics of channel, can be tracked, effectively. Thus, better performance achievement, in terms of output signal-to-interference-plus-noise ratio (SINR) and bit error rate (BER), over the conventional GSC-RLS algorithms can be expected.