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In this paper, an efficient nonlinear companding scheme is proposed to reduce the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals. By transforming the statistics of original signals into a specified distribution form along with remaining an unchanged average output power level, this scheme can achieve significant reduction in PAPR as well as an improved BER performance simultaneously. Moreover, by properly adjusting the transform parameters, more design flexibility in companding form can also be given by this scheme to satisfy various system requirements. The theoretical analysis results regarding the transform gain, companding distortion and the selection criteria of parameters are derived. It is proved that this scheme may lead to less signal distortion compared to existing companding schemes. Simulation results demonstrate that the proposed scheme can substantially offer better overall performance of OFDM system in terms of PAPR reduction, BER performance and bandwidth efficiency.