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The multicarrier code division multiple access (MC-CDMA) is a flexible and adaptive radio interface to provide dynamical bit rate transmission and a variety of services on radio channels. It can sufficiently utilize the subcarrier diversity and meet the demand of diverse multimedia services; therefore it is broadly considered as an effective approach for future wireless multimedia communications. However, it is very sensitive to carrier drifts, while the orthogonal property between the subcarriers is lost with frequency offset. An accurate channel estimate allows the use of multiuser detection. After reviewing some blind channel estimation algorithms with the signal time domain structure and statistic characteristic, we propose a constant modulus based adaptive blind channel estimation at the base station for MC-CDMA systems in a frequency-selective fading channel environment with the consideration of carrier offset compensation. Compared with the SVD-based method and finite alphabet-based method, it illustrates the effectiveness with numerical simulations.