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Based on an orthogonal frequency division multiplexing (OFDM) training symbol with I identical parts, a novel carrier frequency offset (CFO) estimator is proposed for OFDM systems.The CFO is estimated in two steps, fine estimate and coarse estimate.In the first step, the fine estimation is performed based on the principle of minimum variance.However, the fine estimation has ambiguity since its estimate range is limited.In the second step, the coarse estimation is obtained, which results in a larger estimate range but less precision.Using the coarse estimation, the ambiguity of fine estimation is resolved.To fully use the correlation among L identical parts, the fine estimation resolved the ambiguity and the coarse estimation are optimally combined to obtain the final estimation.Furthermore, the estimation variance of the proposed method is derived.Simulation results demonstrate that the novel two-step estimator outperforms the conventional two-step estimator in terms of estimate performance and computational complexity.