The paper presents a joint maximum likelihood (ML) estimator for time and frequency offset in orthogonal frequency-division multiplexing (OFDM) systems. The estimator uses the redundant information in the cyclic prefix of the OFDM signal to estimate both the symbol time offset and the carrier frequency offset without requiring additional pilots. Simulations show that the frequency estimator can be used in a tracking mode, while the time estimator can be used in an acquisition mode. OFDM systems are widely used in various communication applications, including digital broadcast radio, digital broadcast television, and mobile communication systems. The paper addresses two key challenges in OFDM receiver design: the unknown arrival time of the OFDM symbol and the mismatch between the oscillators in the transmitter and receiver. These issues can cause high bit error rates and degrade the performance of symbol synchronizers. The paper proposes a joint ML estimator that exploits the cyclic prefix of the OFDM signal to estimate both the time and frequency offsets. The estimator is derived under the assumption that the channel distortion consists only of additive noise, but simulations show that it performs well even in dispersive channels. The frequency estimator performs better than the time estimator due to its implicit averaging, which allows for coherent contributions from the signal components. The paper also discusses the performance of the estimators in both AWGN and dispersive channels. The results show that the performance of the time estimator is asymptotically independent of the length of the cyclic prefix, provided that the cyclic prefix is longer than a certain threshold. The frequency estimator, on the other hand, shows continued improvement as the length of the cyclic prefix increases. The paper concludes that the proposed ML estimator is effective for estimating time and frequency offsets in OFDM systems. It uses the redundant information in the cyclic prefix to achieve this without requiring additional pilots. The estimator is robust to dispersive channels and can be used in both tracking and acquisition modes. The paper also highlights the importance of pilot symbols in channel estimation and suggests that future research should focus on incorporating pilot symbols into time and frequency estimators.The paper presents a joint maximum likelihood (ML) estimator for time and frequency offset in orthogonal frequency-division multiplexing (OFDM) systems. The estimator uses the redundant information in the cyclic prefix of the OFDM signal to estimate both the symbol time offset and the carrier frequency offset without requiring additional pilots. Simulations show that the frequency estimator can be used in a tracking mode, while the time estimator can be used in an acquisition mode. OFDM systems are widely used in various communication applications, including digital broadcast radio, digital broadcast television, and mobile communication systems. The paper addresses two key challenges in OFDM receiver design: the unknown arrival time of the OFDM symbol and the mismatch between the oscillators in the transmitter and receiver. These issues can cause high bit error rates and degrade the performance of symbol synchronizers. The paper proposes a joint ML estimator that exploits the cyclic prefix of the OFDM signal to estimate both the time and frequency offsets. The estimator is derived under the assumption that the channel distortion consists only of additive noise, but simulations show that it performs well even in dispersive channels. The frequency estimator performs better than the time estimator due to its implicit averaging, which allows for coherent contributions from the signal components. The paper also discusses the performance of the estimators in both AWGN and dispersive channels. The results show that the performance of the time estimator is asymptotically independent of the length of the cyclic prefix, provided that the cyclic prefix is longer than a certain threshold. The frequency estimator, on the other hand, shows continued improvement as the length of the cyclic prefix increases. The paper concludes that the proposed ML estimator is effective for estimating time and frequency offsets in OFDM systems. It uses the redundant information in the cyclic prefix to achieve this without requiring additional pilots. The estimator is robust to dispersive channels and can be used in both tracking and acquisition modes. The paper also highlights the importance of pilot symbols in channel estimation and suggests that future research should focus on incorporating pilot symbols into time and frequency estimators.