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This paper proposes an efficient blind deterministic carrier frequency offset (CFO) estimation method for orthogonal frequency division multiplexing (OFDM) systems. In the proposed method, two OFDM symbols with time difference are generated by exploiting both the oversampled OFDM signal and the cyclic prefix, and a cost function is introduced for CFO estimation. It is shown that the cost function can be expressed as a cosine function. Using a property of the cosine function, a formula for estimating the CFO is derived. The estimator of the CFO requires three independent cost function values calculated at three different frequency offsets. Using the formula, the CFO can be estimated without searching all the frequency offset range. The proposed method is very suitable for real wireless environments since it requires only one OFDM symbol for blind reliable estimation of CFO. The computer simulations show that the performance of the proposed method is superior to those of the MUSIC method and the oversampling method . Unlike the conventional methods such as MUSIC method and the oversampling method, the accuracy of the proposed method is independent of the searching step.