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Orthogonal frequency-division multiplexing (OFDM) is a promising technology for communication systems. However, the synchronization of OFDM over dispersive fading channels remains an important and challenging issue. In this paper, a synchronization algorithm for determining the symbol timing offset and the carrier frequency offset (CFO) in OFDM systems, based on the maximum-likelihood (ML) criterion, is described. The new ML approach considers time-dispersive fading channels and employs distinctive correlation characteristics of the cyclic prefix at each sampling time. The proposed symbol timing estimation is found to be a 2-D function of the symbol timing offset and channel length. When compared with previous ML approaches, the proposed likelihood function is optimized at each sampling time without requiring additional pilot symbols. To practically realize the proposed method, a suboptimum approach to the ML estimation is adopted, and an approximate but closed-form solution is presented. Nonlinear operations of the approximate solution can be implemented using a conventional lookup table to reduce the computational complexity. The proposed CFO estimation is also found to depend on the channel length. Unlike conventional schemes, the proposed method fully utilizes the delay spread of dispersive fading channels (which usually reduces the accuracy of estimations). Furthermore, the Cramér-Rao lower bound (CRLB) on the CFO estimate is analyzed, and simulations confirm the advantages of the proposed estimator.