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Frequency offset is an important problem in orthogonal frequency-division multiplexing (OFDM) systems. This leads to a loss in the orthogonality between subcarriers and results in intercarrier interference (ICI). A simple and effective ICI self-cancellation scheme based on the signal mapper (a,-a) has been proposed to reduce the effect of the frequency offset (see Zhao, Y. and Haggman, S.-G., IEEE Trans. Commun., vol.49, no.7, p.1185-91, 2001). We generalize the signal mapper to (a, μaejθ), and investigate the resulting relationships between the carrier-to-interference ratio (CIR), the normalized frequency offset, and the parameters μ and θ. The optimal values for μ and θ are derived. It is found that when the normalized frequency offset is large, up to 10dB improvement in CIR can be obtained by using the optimal μ. Simulation results are presented to verify the theoretical analysis and to illustrate the better performance of the new generalized scheme.