A Direct-Sequence Code-Division Multiple-Access (DS-CDMA) with rake receiver for multiuser system sets up a new dimension in mobile communication system. We propose a pseudo convex framework using an optimum sparse channel estimation technique for DS-CDMA mobile communication systems. Further, the blind channel estimation problem will be examined for rake-based DS-CDMA communication framework with time variant multi-path fading channels This receiver accomplishes an effective assessment of channel according to a maximum convexity criterion, by means of the sparse technique. This estimation method requires a convenient representation of the discrete multipath fading channel based on the sparse theory. In this paper, we have defined a specialized interior-point method for solving large-scale ℓ1 - problem in multiuser detection. Our method can be generalized to handle a variety of extensions such as various channel conditions. A new solution to DS-CDMA based sparse channel estimation is presented in this paper that assures a global optimal solution. Also, it is proven that the said solution can be used as an apparent program that shall enable solutions utilizing interior point techniques involving polynomial time complexity. Through simulation the rationality of the techniques proposed in this paper has been highlighted by results obtained for various modulation schemes and channel parameters. The execution of a pseudo convex framework using sparse channel estimation technique with rake receiver in DS-CDMA framework for multipath fading channels is explored. The overall performance is evaluated in terms of bit error rate (BER) for a range of values of signal to noise ratio (SNR). This framework gives better performance under various modulation schemes using pseudo noise (PN) spreading code. Furthermore, performance of the proposed system is compared with different detectors.