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This paper investigates the problem of joint estimation of carrier frequency offset (CFO) and channel response for OFDM systems. In deriving the solution of the joint maximum likelihood (JML) estimator, the channel model absorbs the effects of the unknown carrier phase offset and symbol timing error. It is shown that a highly efficient JML algorithm can be cleverly obtained in two steps, consisting of a nonlinear JML-CFO estimator and a linear least squares channel estimator. Especially, the complexity of the JML-CFO estimation can be greatly reduced by exploiting the idempotent property of the projection matrix and using a polynomial approach to transform a brute-force searching into a simple coarse FFT peak finding operation. Finer CFO resolution can then be obtained by iterative zoom-FFT. Finally, simulation result shows that the JML-CFO estimate can approach the theoretical CRLB when the SNR exceeds a low threshold of 0 dB.