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A pilot-tone-based maximum likelihood estimator (PBMLE) for carrier frequency offset (CFO) in orthogonal frequency-division multiplexing (OFDM) systems is proposed. To obtain a consistent estimate of the CFO over a frequency-selective fading channel, the proposed method employs a preamble comprising distinctively spaced pilot tones. As a result of this preamble configuration, a large estimation range equal to the bandwidth of the OFDM signal can be achieved. Different from previous ad hoc pilot-tone-based CFO estimators, the PBMLE exploits the relationship between the CFO and the periodogram of the preamble. Analysis shows that the proposed PBMLE is asymptotically unbiased and efficient. To realize this PBMLE in practice, a suboptimal estimator is also introduced, in which a zero-padded fast Fourier transform is invoked and the CFO estimation is split into two phases: coarse and fine estimation. Coarse estimation is obtained through the correlation between the received preamble and its original pattern, whereas fine estimation is obtained by exploiting the magnitude attenuation in the vicinities of those CFO-shifted pilot tones. Both analytical investigations and computer simulations indicate that the accuracy of this simplified suboptimal estimator is proportional to the oversize ratio of zero padding. When the oversize ratio is sufficiently high, the performance of the suboptimal estimator approaches that of the proposed PBMLE.

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