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In orthogonal frequency-division multiplexing (OFDM) systems, the carrier frequency offset (CFO) destroys the orthogonality among subcarriers which degrades system performance. Various CFO estimation methods have been developed to compensate for the CFO at the receiver. This paper describes a novel minimum output variance method for OFDM systems with CFO in additive white Gaussian noise channels. This method utilizes the phase and the amplitude of the received signal and reduces the mean square error of the CFO by about 3 dB compared with the original minimum output variance method.