Capacity of CDMA system is limited to interference due to other users. System performance is degraded by near-far problem when undesired users are closer to base station. Beside, the channel parameters could not be estimated perfectly at receiver, refer to as mismatch problem, which would also degrade the system performance. We would like to consider the MAI and near-far interference cancellation by adaptive linear constraint algorithms to implement linear constraint minimum variance (LCMV) approach. To exploit the linearly constrained filtering, the structure of the generalized side-lobe canceller (GSC) has been employed, where the constrained problem is converted into an unconstrained form with fewer parameters. GSC structure is an indirect but simpler implementation of LCMV algorithm. Moreover, it is also known that the constant modulus (CM) criteria has advantage to combat the channel mismatch, and the performance of the adaptive constraint algorithm based on CM criteria will be investigate. In this thesis, we will derive a new GSC-IQRD-RLS algorithm to combat MAI and near-far problems by combining LC-IQRD-RLS algorithm [1][5] and GSC structure [17]; and prove that the GSC and LC structures based IQRD-RLS algorithms are equivalent, which means that the good performance of LC-IQRD-RLS algorithm can be achieved by a simpler GSC structure algorithm. We will also derive a new GSC-CM-IQRD-RLS algorithm to improve the system performance under mismatch problem by combining CM criteria [20] and GSC-IQRD-RLS algorithm.