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An exact closed-form bit error rate expression is derived for an orthogonal frequency-division multiplexing system, each subcarrier modulated by π/4-shifted differentially encoded quadrature phase shift keying, in the presence of carrier frequency offset over frequency-selective fast Rayleigh fading channels. Both single channel reception and diversity reception with maximal ratio combining are considered. The closed-form expression allows us to investigate the effect of several channel parameters, including mean delay spread and maximum Doppler shift, on the system bit error rate performance. Particularly, the effect of carrier frequency offset on the system performance can be studied for a more realistic wireless channel environment model. Small carrier frequency offsets have slight influences on the system performance. Compared with the same amount of Doppler shift, carrier frequency offset usually leads to a greater degree of performance degradation. Systems with fewer subcarriers are more sensitive to the channel mean delay spread. By using the exact closed-form bit error rate expression, an optimum number of subcarriers can be found, and the allowable carrier frequency offset, Doppler shift, and mean delay spread for given operating conditions can be determined.