In this thesis, the problem of multiple access interference (MAI) suppression for the multi-carrier (MC) code division multiple access (CDMA) system, based on the multi-carrier modulation with modified Gaussian wavelet, associated with the combining process is investigated for Rayleigh fading channel. The main concern of this thesis is to derive a new scheme, based on the linearly constrained constant modulus (LCCM) criterion with the robust inverse QR decomposition (IQRD) recursive least squares (RLS) algorithm to improve the performance of the wavelet-based MC-CDMA system with combining process. To verify the merits of the new algorithm, the effect due to imperfect channel parameters estimation and near-far effect are investigated. We show that the proposed robust LCCM IQRD-RLS algorithm outperforms the conventional LCCM-gradient algorithm, in terms of output SINR, for MAI suppression under channel mismatch environment. Also, the performance of the modified Gaussian wavelet-based MC-CDMA system is superior to the one with wavelet-based MC-CDMA system. It is more robust to the channel mismatch and near-far effect. Moreover, the modified Gaussian wavelet-based MC-CDMA system with robust LCCM IQRD-RLS algorithm does have better performance over other conventional approaches, such as the LCCM-gradient algorithm, maximum ratio combining (MRC), and blind adaptation algorithm, in terms of the capability of MAI suppression and bit error rate (BER).