In this paper, the discrete cosine transform (DCT) is utilized for single carrier frequency division multiple access (SC-FDMA) transmission. Firstly, an improved DCTbased SC-FDMA (DCT SC-FDMA) system is introduced. Then, the paper presents a new transceiver architecture design for the uplink SC-FDMA system that implements a cosine basis function or a complex exponential Fourier basis function. The proposed architecture uses the discrete wavelet transform and a hybrid companding and clipping method for peak-to-average power ratio (PAPR) reduction. From the simulation results, it is shown that the DCT SC-FDMA system achieves a superior bit error rate (BER) performance than that of the discrete Fourier transform based SC-FDMA (DFT SC-FDMA) system. The results also show that the proposed wavelet based transceiver architectures for the DFT SC-FDMA system and the DCT SC-FDMA system can provide a better BER performance and a lower PAPR than the conventional DFT SC-FDMA system.