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We propose a joint scheme for multicarrier code-division multiple access (MC-CDMA) systems; it jointly estimates the frequency offset for the desired user and eliminates multiuser interference (MUI). In the proposed scheme, the well-known constrained minimum output energy (MOE) detector is designed under the condition that the frequency offset estimate of the desired user is known. Then, the frequency offset estimate is obtained by searching for the value which maximizes the output energy of the conditional MOE detector. Finally, the frequency offset estimate is used for the conditional MOE weight vector, and the joint work is completed. The analytical expression for the estimation error of the proposed frequency offset estimator is derived and compared with simulation results. Other simulation results show that the frequency offset estimate is very close to the true value and the bit error rate (BER) of the proposed scheme is comparable to that of the MOE detector with perfect frequency offset compensation.