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Adaptive modulation in OFDM systems is receiving remarkable attention as a scheme for improving spectral efficiency and error performance simultaneously. A major issue of the system is the necessity of channel information feedback that raises a problem of propagation delays. Linear channel prediction with drawback of biasing effect has been previously proposed to overcome propagation delays. In this paper, to avoid biasing effect, we propose channel prediction based on interpolation. Simulation results show that the proposed scheme has noticeable benefits of not only spectral efficiency but also error performance in OFDM systems using adaptive modulation.