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In this paper, Moose scheme is used for frequency offset estimation in OFDMA uplink systems due to that the signals from different users can be easily distinguished in frequency domain. However, differential multiple access interference (MAI) will deteriorate the frequency offset estimation performances,especially in interleaved OFDMA system. Analysis and simulation results manifest that frequency offset estimation by Moose scheme in block OFDMA system is more robust than that in interleaved OFDMA system. And an iterative interference cancellation method has been proposed to suppress the differential MAI interference for interleaved OFDMA system, in which Moose scheme is the special case of the number of iteration is equal to one. Simulation results demonstrate that the proposed method can improve the performance with the increase of the number of iterations. In consideration of the performance and complexity,the proposed method with two iterations is selected. And the full comparison results of the proposed iterative method with two iterations and that with one iteration (conventional Moose scheme) are given in the paper, which sufficiently demonstrate that the performance gain can be obtained by the interference cancellation operation in interleaved OFDMA system.