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A general companding transform method is proposed to effectively reduce peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals. By compressing large signals while enhancing small signals along with taking into account their statistical characteristics, this method can achieve significant reduction in PAPR with low implementation complexity. Specifically, we present the design criteria of the transform, which enable effective tradeoff between reduction in PAPR and bit-error rate performance of the OFDM system. It is shown by simulations that the proposed method may significantly improve the performance of OFDM systems in radio channels by carefully choosing the companding form and parameters.