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In this paper, the issue of multiple-access interference (MAI) suppression for the uplink in an interleaved orthogonal frequency-division multiple-access (OFDMA) system is investigated. In such a system, a carrier frequency offset (CFO) disrupts the orthogonality between the subcarriers and gives rise to MAI among users. Based on the signature vector formulated for each user, we propose a novel detector that performs MAI suppression before CFO compensation and fast Fourier transform (FFT) demodulation. Subspace zero-forcing and minimum mean square error (MMSE) techniques are then developed to suppress MAI. The proposed scheme is shown to become almost MAI free, provided that the CFO estimation is accurate enough. From the obtained simulation results, the proposed scheme is also found to be able to enhance the system performance at low complexity.