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In OFDM system, because of sensitivity to carrier frequency offset, frequency offset must be compensated before DFT in the receiver. In this paper, we present a maximum likelihood estimation for carrier frequency offset, based on OFDM symbol has no virtual sub-carriers. The estimation are compose of two parts, blind estimation makes use of cyclic prefix for every symbol and data-aid estimation makes use of two consequent OFDM symbols which are similar or relative to each other. Data-aid estimation performs well and simulation result converges upon Cramer-Rao lower bound. Blind estimation performs inferior, but it can be used in tracking mode.