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Residual carrier frequency offset (CFO) is one of the most important problems in an orthogonal frequency division multiplexing (OFDM) system, which seriously degrades the performance of the systems due to its time-variant behavior. In this paper, the performance of a pilot-assisted fine CFO estimator in OFDM-based mobile WiMAX systems is analyzed. Analytical closed-form expression of the mean square error (MSE) of the post-FFT based CFO synchronization scheme is reported for time-variant fading channels. Taking into account the frame structure of the IEEE802.16e standard, we verify our analysis in this paper.