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Single-carrier frequency division multiple access (SC-FDMA) has been adopted as a possible air interface for future wireless networks. It combines most of the advantages of orthogonal frequency division multiple access (OFDMA) and the low peak-to-average-power ratio (PAPR) of single-carrier transmission. This study proposes a new transceiver scheme for SC-FDMA systems implementing the wavelet transform to decompose the transmitted signal into approximation and detail components. The approximation component can be clipped or companded whereas the detail component is left unchanged because of its sensitivity to noise. Wavelet filter banks at the transmitter and the receiver demonstrate the ability to reduce the distortion in the reconstructed signal while retaining all the significant features present in the signal. The performance of the proposed scheme is investigated with different PAPR reduction methods. Simulation results show that the proposed scheme with the hybrid clipping and companding method provides a significant performance enhancement when compared with the conventional SC-FDMA system, while the complexity of the system is slightly increased.