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Multicarrier modulations such as orthogonal frequency division multiplexing (OFDM) and multicarrier code division multiple access (MC-CDMA) have been widely developed for wideband cellular communications. MC-CDMA modulation scheme benefits from the advantages of both MC and CDMA techniques: high spectral efficiency, robustness in frequency selective channels with a low-complexity at receiver considering simple one-tap equalization and multiple access capability with high flexibility. In this paper, we propose a simple and efficient receiver design for frame based MC-CDMA in multipath Nakagami-m fading channels which have been found to be a very good fitting for the mobile radio channel. We also illustrate the performance of the proposed model for different values of fading parameter m, different modulation schemes (4, 16 and 64 QAM) and different number of users.