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Performance of both orthogonal frequency division multiplexing (OFDM) and single carrier (SC) systems suffers from a carrier frequency offset (CFO) due to Doppler effect and the carrier instability between the transmitter and the receiver. We investigate the bit error rate (BER) performance degradation of OFDM and SC systems due to the frequency offset in an additive white Gaussian noise (AWGN) channel as well as multipath Rayleigh fading channels. We consider three effects to the BER degradation, i.e., phase shift, useful power decrease and intercarrier interference (ICI). We also derive the approximate expressions of BER under binary phase shift keying (BPSK) and quaternary phase shift keying (QPSK) for both OFDM and SC systems in the presence of CFO. In general, SC is more robust to CFO in the AVVGN channel than OFDM in terms of BER, while both of them suffer similarly from CFO in the multipath Rayleigh fading channels assuming the the same CFO.