In this thesis, the multi-carrier (MC) code division multiple access (CDMA) system is considered in Rayleigh fading channel. The main concern of this thesis is to devise a new direct linearly constrained constant modulus (LCCM) inverse QRD-RLS algorithm for multiple access interference (MAI) cancellation and the problem due to the mismatch of the channel estimator. In the conventional approach, two significant detectors are applied to the system for multiuser interference suppression, one is the blind adaptation algorithm and the other is adaptive linearly constrained PLIC approach. However, the mirror effect may occur when the blind adaptation algorithm is employed. It might affect the performance in terms of bit error rate (BER), although the desired signal to interference (due to other users) improvement is still acceptable. Moreover, in case that the channel coefficients could not be estimated perfectly, the mismatch problem may occur to degrade the performance of the adaptive linearly constrained PLIC approach with the LMS or RLS algorithm. To overcome the mismatch problem, the conventional approach is to use the LCCM criterion with gradient algorithm. However, the convergence rate of the gradient algorithm is too slow to be implemented in real-time wireless communication system. In this thesis, to have fast convergence rate and to circumvent the mismatch problem, the robust LCCM-IQRD algorithm is devised and applied to the MC-CDMA system in Rayleigh fading channel. The proposed robust LCCM-IQRD algorithm has shown to be more effective in terms of MAI cancellation and the mismatch due to imperfect channel estimator. The performance, in terms of BER, of the proposed algorithm is superior to that of the conventional PLIC based algorithms, the blind adaptation algorithm, and the conventional LCCM gradient algorithm.