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We propose an estimator that will jointly estimate the channel and the carrier frequency offset (CFO) for orthogonal frequency-division multiplexing (OFDM) systems based on the maximum-likelihood criterion. The proposed estimator uses only one received OFDM symbol to perform estimation and does not require the knowledge of power delay profile, except that the number of delay paths should be known. The search range for the CFO is first partitioned into a number of subranges. The expectation-maximization (EM) and Newton's methods are then used within each subrange in an alternative manner to jointly obtain the channel and the CFO estimates. By assuming that the transmitted time-domain OFDM signals can be modeled as Gaussian random variables, we show that the EM method has closed-form expressions and, thus, can be efficiently implemented. We then study the mean-square-error (MSE) performance of the estimator under various signal-to-noise (SNRs) ratios and various numbers of cyclic prefix samples through simulations. Finally, we compare the performance of our proposed estimator with that of some existing estimators in terms of bit error rate (BER). Our simulation results show that the proposed estimator performs better than the reported estimator, which sequentially estimates the channel and the CFO. By suitably choosing the number of subranges, our estimator also performs better than a reported estimator, which makes use of pilot symbols to obtain the initial CFO and channel estimates and then uses a decision-directed technique for overall eventual estimation.