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An orthogonal frequency-division-multiplexing signal is very sensitive to the nonlinear distortion of the power amplifier (PA) as a result of its high peak-to-average power ratio. Predistortion, which is an effective countermeasure for balancing off the nonlinearity of a PA, is usually necessary for the sake of mitigating the in-band distortion and the spectrum regrowth. In general, a feedback path is required to estimate the PA characteristic, and a memoryless polynomial is used in modeling the PA characteristic or constructing the predistorter. The polynomial coefficients are solved by least-square (LS) estimation or adaptive identification algorithms in the time domain. In this paper, we examine the estimation problem from the frequency domain and propose five predistortion schemes. The advantage of using frequency-domain estimation is that it is much easier to compensate the delay effect caused by the transmission and receiving filters in the feedback path. Two different criteria are used in the proposed algorithms. The first one is based on the minimization of the square error of the PA input, which is termed as the PA-input-LS criterion. The second one is based on the minimization of the square error between the input of the predistorter and the output of the PA, which is termed as PA-output-LS criterion. We also propose an easy method to cope with the delay effect caused by the transmission and receiving filters in the feedback path. The performances of the proposed schemes are compared in the simulation. The simulation results show that by using the proposed schemes, the power efficiency of the PA can be increased by at least 7 dB in the sense of total degradation for a practical IEEE 802.11a wireless local area network system with a 64-quadrature-amplitude-modulation signal constellation.