The technique of direct sequence code division multiple access (DS-CDMA) cellular system has been the focus of increased attention. In this thesis, we will consider the environment of DS-CDMA systems, where the asynchronous narrow band interference due to other systems is joined suddenly to the CDMA system. The suddenly joined narrow band interference will make the system crush down. The main concern of this thesis is to deal with suddenly joined narrow band interference cancellation. An adaptive filtering algorithm based on sliding window criterion and variable forgetting factor is known to be very attractive for violent changing environment. In this thesis, a new sliding window linearly constrained recursive least squares (SW LC-RLS) algorithm and variable forgetting factor linearly constrained recursive least squares (VFF LC-RLS) algorithm on the modified minimum mean squared error (MMSE) structure [9] is devised for RAKE receiver in direct sequence code-division multiple access (DS-CDMA) system over multipath fading channels. Where the channel estimation scheme is accomplished at the output of adaptive filter. The proposed SW LC-RLS algorithm and VFF LC-RLS has the advantage of having faster convergence property and tracking ability, and can be applied to the environment, where the narrow band interference is suddenly joined to the system, to achieve desired performance. Via computer simulation, we show that the performance, in terms of mean square errors (MSE) and signal to interference plus noise ratio (SINR), is superior to the conventional LC-RLS and orthogonal decomposition-based LMS algorithms based on the MMSE structure [9].