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We propose a null sub-carrier based carrier frequency offset (CFO) estimation technique for OFDMA uplink systems. We discuss the effect of multi-user interference and channel nulls on the identifiability of CFO estimation. We also derive the CFO acquisition range of the algorithm and the optimum location of the null sub-carriers. We prove that the identifiability due to multi-user interference is guaranteed under the CFO estimation range supported by the algorithm. The performance of the algorithm is also evaluated through simulation results.