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In this paper, a new robust linearly constrained constant modulus (LCCM) approach with inverse QRD-RLS algorithm is derived and applied to the multi-carrier code division multiple access (MC-CDMA) system. The proposed algorithm can be employed to reduce the MAI efficiently, due to other users and combat the mismatch problem, when channel parameters can not be estimated perfectly. We show that it outperforms the conventional LCCM-gradient algorithm Miguez et al. (1998), in terms of output SINR and improvement percentage index, for MAI cancellation under a mismatch environment. Moreover, the wavelet-based structure can be used to further improve the performance of the proposed algorithm with pure MC-CDMA system.