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A nonlinear spectral-line method utilizing the fourth absolute moment of the receiver discrete Fourier transform output is proposed as a non-data-aided fine carrier frequency synchronization algorithm for OFDM receivers. A simple modification of the algorithm resulting in low implementation complexity is also developed. Analytic expressions are derived for the steady-state frequency error variances of the algorithms and verified to be very accurate via computer simulations over AWGN and frequency selective multipath channels. Numerical results show that the proposed algorithms provide reliable and excellent steady-state performance, especially with PSK modulation. Also, the proposed algorithms are insensitive to symbol timing offsets, only requiring a coarse symbol timing recovery.