Orthogonal frequency division multiplexing (OFDM) is sensitive to carrier frequency offset (CFO), which destroys the orthogonality and causes inter-carrier interference (ICI). ICI self-cancellation schemes based on polynomial cancellation coding (PCC-OFDM) can evidently reduce the sensitivity to CFO. In this paper, we analyze the performance of PCC-OFDM systems impaired by CFO over additive white gaussian noise (AWGN) channels. Two criteria are used to evaluate the effect of CFO on performance degradations. Firstly, the closed-form expressions of the average carrier-to-interference power ratio (CIR) and the statistical average ICI power, both of which reflect the desired power loss, are presented. Simulation and analytical results show that the theoretical expressions depend crucially on the normalized frequency offset and are hardly relevant to the number of subcarriers. Secondly, by exploiting the properties of the Beaulieu series, the effect of CFO on symbol error rate (SER) and bit error rate (BER) performance for PCC-OFDM systems are exactly expressed as the sum of an infinite series in terms of the characteristic function (CHF) of ICI. We consider the systems modulated with binary phase shift keying (BPSK), quadrature PSK (QPSK), 8-ary PSK (8-PSK), and 16-ary quadrature amplitude modulation (16-QAM), and all above modulation schemes are mapped with Gray codes for the evaluations of BER. Orthogonal frequency division multiplexing (OFDM) is sensitive to carrier frequency offset (CFO), which destroys the orthogonality and causes inter-carrier interference (ICI). ICI self-cancellation schemes based on polynomial cancellation coding (PCC-OFDM) can evidently reduce the sensitivity to CFO. In this paper, we analyze the performance of PCC-OFDM systems impaired by CFO over additive white gaussian noise (AWGN) channels. Two criteria are used to evaluate the effect of CFO on performance degradations. Firstly, the closed-form expressions of the average carrier-to-interference power ratio (CIR) and the statistical average ICI power, both of which reflect the desired power loss, are presented. Simulation and analytical results show that the theoretical expressions depend crucially on the normalized frequency offset and are hardly relevant to the number of subcarriers. Secondly, by exploiting the properties of the Beaulieu series, the effect of CFO on symbol error rate (SER) and bit error rate (BER) performance for PCC-OFDM systems are precisely expressed as sum of an infinite series in terms of the characteristic function (CHF) of ICI. We considered the systems modulated with binary phase shift keying (BPSK), quadrature PSK QPSK), 8-ary PSK (8-PSK), and 16-ary quadrature amplitude modulation (16-QAM), and all above modulation schemes are mapped with Gray codes for the evaluations of BER.