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This paper proposes a blind carrier frequency offset (CFO) estimation scheme for OFDM systems. In the proposed scheme, the covariance matrix of the received signal is obtained through the circular shifts of OFDM blocks in the time-domain. From the fact that the covariance matrix has a banded structure in the absence of CFO, we estimate CFO through minimizing the powers of the elements that are outside the band. We show that the proposed scheme is better than the conventional schemes through simulations.