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In order to attain near-single user performance in uplink multicarrier code division multiple access (MC-CDMA) systems, multiuser detection (MUD) methods may be employed which rely on simultaneous estimation of the channel frequency response of multiple users. In this paper, performance of a MC-CDMA system employing minimum mean-square error (MMSE) MUD at receiver, is evaluated using two pilot symbol assisted (PSA) channel estimation schemes: the maximum likelihood (ML) estimation and the MMSE estimation. In simplified design where multipath fading channels are assumed to have sample-spaced path time delays, the MMSE estimator (MMSEE) slightly outperforms the ML estimator (MLE) at low signal to noise ratios (SNR). At intermediate and high SNRs, both estimators show almost identical performance. We find that the MMSEE provides significant performance gain when path delays are not sample-spaced and channel estimation is carried out considering a general parametric model of the multipath channel.