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In this paper, we propose a joint carrier frequency offset (CFO) and channel estimation method for the uplink channel of orthogonal frequency division multiple access (OFDMA) systems. The proposed method includes two steps. In the first step, the variable projection (VP) method based on the least squares (LS) criterion is used for CFO estimation. In each iteration of the VP method, the CFOs and channel coefficients are updated separately, which distinguishes the VP method from an existing non-separated minimum mean square error (MMSE) method in which the CFOs and channel coefficients are treated together as a whole. In the second step, the channel is estimated by employing the robust MMSE method. The simulation results show that, compared with the non-separated MMSE method, the proposed method has faster convergence rate in terms of CFO estimation and achieves better channel estimation performance in most of the cases. The computational complexity of the proposed scheme is also lower than that of the non-separated MMSE method for large number of users at high signal-to-noise ratios.