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A new nonlinear companding transform scheme is proposed to reduce the peak-to-average ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) signals. By exploiting statistical distribution of transmitted OFDM signals, the proposed scheme effectively reduces the PAPR by compressing the peak signals and expanding the small signals, while maintaining the average power unchanged by properly choosing transform parameters. The fact that the proposed companding scheme is described by a single-valued function allows to be transformed before amplification and to be restored the signals at the receiver. The proposed scheme can be applicable with any modulation format and subcarriers. Our simulations results confirm that the suggested scheme exhibits a good ability to reduce PAPR and a good BER performance with a solid state power amplifier (SSPA) in an additive white Gaussian noise (AWGN) channel.