In recent years, OFDMA(orthogonal frequency division multiple access) and SC-FDMA(Single Carrier Frequency Division Multiple Access) have been widely studied for the uplink of a mobile communication system. In this paper, PAPR(Peak-to-Average Power Ratio) and BER(Bit Error Rate) performance of the OFDMA and SC-FDMA systems are studied in relation to the uplink of a mobile communication system. Three kinds of sub-carrier allocation methods in the OFDMA system and 2 kinds of sub-carrier allocation methods in SC-FDMA system are suggested to compare and improve system performance. Simulation results show that in the OFDMA system, the first sub-band allocation method has better PAPR reduction performance than the other methods. In the SC-FDMA system, the distributed allocation method offers similar P APR, compared with the sub-band allocation method. P APR can be further reduced by adding a spectrum shaping filter with an appropriate roll of factor. Furthermore, it is found that on average, SC-FDMA can reduce the PAPR by more than 5 dB compared to OFDMA, when the total sub-carrier number is 1,024 and the sub-carrier number allocated to each user changes trom 8 to 512. Because of the frequency diversity and low PAPR characteristics, SC-FDMA system of the distributed sub-carrier allocation method can achieve better BER performance than the OFDMA system.