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 wireless communications services. The SS communication adopts a technique of using much wider bandwidth necessary to transmit the information over the channel. In the DS-CDMA system, due to the inherent structure interference, referred to as the multiple access interference (MAI), the system performance might degrade. Next, for DS-CDMA systems over frequency-selective fading channels, the effect of inter symbol interference (ISI) will exist, such that a multiuser RAKE receiver has to be employed to combat the ISI as well as MAI. Since, in practical wireless communication environment, there may have several communication systems operated in the same area at the same time. In this thesis, we consider the environment of DS-CDMA systems, where the asynchronous narrow band interference (NBI) due to other systems is joined suddenly to the CDMA system. In general, when a system works in a stable state with adaptive detectors, a suddenly joined NBI signal will cause the system performance to be crash down. Under such circumstance, the existing conventional adaptive RAKE detectors may not be able to track well for the rapidly sudden changing NBI associated with the problems of ISI and MAI. It is known that the adaptive filtering algorithms, based on the sliding window linear constrained recursive least squares (SW LC-RLS), is very attractive to a violent changing environment. The main concern of this thesis is to propose a novel sliding window constant modulus RLS (SW CM-RLS) algorithm, based on the Min/max criterion, to deal with the NBI for DS-CDMA system over multipath channels. For simplicity and having less system complexity the generalized side-lobe canceller (GSC) structure is employed, and is referred to as the SW CM-GSC-RLS algorithm. The aim of the SW CM-GSC-RLS algorithm is used to alleviate the effect of NBI. It has the advantages of having faster convergence property and tracking ability, and can be applied to the environment in which the NBI is suddenly joined to the system under the effect of channel mismatch to achieve desired performance. At the end of this thesis, we extend the idea of the proposed algorithm to the space-time DS-CDMA RAKE receiver, in which the adaptive beamformer with temporal domain DS-CDMA receiver is employed. Via computer simulation results, we show that our new proposed schemes outperform the conventional CM GSC-RLS algorithm as well as the GSC-RLS algorithm (the so-called LCMV approach), in terms of mean square error of estimating channel impulse response, output signal to interference plus noise ratio and bit-error-rate.