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This paper introduces new blind time domain equalization (TEQ) techniques for downlink multicarrier code division multiple access (MC-CDMA) systems. This equalization exploits the guard interval (GI) redundancy together with the excess codes (EC) to restore the structural properties of MC-CDMA signal destroyed by multipath fading channels. Indeed, since in CDMA based wireless systems, the number of users per cell is significantly less than the spreading factor, a base station can set apart a subset of the codes, the excess codes that will not be used for spreading. It is shown that the joint use of the EC and GI redundancy improves significantly the equalization performance compared to the GI only or EC only cases. A second contribution consists in exploiting the previous information together with the one given by a pilot sequence in a semi blind scheme to further improve the performance. Finally, we propose a new adaptive algorithm for the estimation and tracking of the equalizer that has a faster convergence rate compared to existing algorithms of similar complexity order. Simulation based performance evaluations are given at the end of this paper to assess the effectiveness of the proposed methods in MC-CDMA.