The paper presents a joint maximum likelihood (ML) estimator for symbol-time and carrier-frequency offsets in orthogonal frequency-division multiplexing (OFDM) systems. The key innovation is the use of the cyclic prefix, which contains redundant information, to estimate these offsets without additional pilots. The authors derive the log-likelihood function for the time offset and carrier frequency offset, and propose an algorithm to maximize this function. Simulations show that the frequency estimator can be used in tracking mode, while the time estimator can be used in acquisition mode. The performance of the estimators is evaluated in both additive white Gaussian noise (AWGN) and time-dispersive channels, demonstrating that the method performs well even in the latter case. The frequency offset estimator outperforms the time offset estimator due to its implicit averaging, and the paper discusses the potential for incorporating pilot symbols to further enhance performance in wireless systems.The paper presents a joint maximum likelihood (ML) estimator for symbol-time and carrier-frequency offsets in orthogonal frequency-division multiplexing (OFDM) systems. The key innovation is the use of the cyclic prefix, which contains redundant information, to estimate these offsets without additional pilots. The authors derive the log-likelihood function for the time offset and carrier frequency offset, and propose an algorithm to maximize this function. Simulations show that the frequency estimator can be used in tracking mode, while the time estimator can be used in acquisition mode. The performance of the estimators is evaluated in both additive white Gaussian noise (AWGN) and time-dispersive channels, demonstrating that the method performs well even in the latter case. The frequency offset estimator outperforms the time offset estimator due to its implicit averaging, and the paper discusses the potential for incorporating pilot symbols to further enhance performance in wireless systems.