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The paper presents an exact analysis of the effect of the carrier frequency offset on orthogonal frequency division multiplexing (OFDM) systems for a general multipath fading channel. As is well known, the carrier frequency offset attenuates the desired signal and causes intercarrier interference, thus reducing the signal-to-noise ratio (SNR). The SNR degradation due to the carrier frequency offset is evaluated by deriving the exact SNR expression in the presence of the carrier frequency offset. The SNR analysis can be used for the design of a practical OFDM system in determining how small the frequency offset should be in order to maintain the SNR degradation to negligible levels.