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We consider a multicarrier code-division multiple access (MC-CDMA) system over multipath fading channels. We first develop a model for such a system. Then, we propose the channel estimation based on least square (LS) algorithm and linear interpolation in frequency domain. For signal detection, different detection algorithms are introduced including maximum ratio combining (MRC), minimum mean square error (MMSE), parallel interference cancellation (PIC), and interference cancellation based on expectation-maximization (EM) algorithm. Performances of these different algorithms are illustrated by numerical results in a system with 512 subcarriers and 5 MHz bandwidth at 2.5 GHz over some of ITU channel models. Our simulation results demonstrate that with MMSE algorithm significant performance gain is achieved compared to that with MRC algorithm. The system performance can be further improved by PIC and EM algorithms.