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In this paper, the nonlinear least-squares (NLS) estimator for frequency offset in flat-fading channels is systematically derived. A simple interpolation technique is introduced to improve the estimation accuracy of the resulting NLS estimator, especially when the number of zeros padded in FFT is insufficient. Furthermore, we propose an approximated NLS estimator which significantly simplifies the implementation complexity of the full structure NLS estimator. The degree of simplification is defined by the approximated number of complex multiplications required by each estimator. All the estimators derived in this paper do not require any information about the channel correlation as needed for most of the existing techniques. The simulation results show that the performances of two simplified NLS estimators are as good as that obtained from the full structure NLS estimator.