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A lot of conventional algorithms have tried to cancel the residual frame synchronization error (RFSE), which causes the performance degradation of channel estimation when using interpolation between pilot sub-carriers in comb-type pilot-aided OFDM systems. Among them, a tracking method has been attractive to provide good performance by eliminating the effects of RFSE. However, it requires high computational complexity because of its compensation process including many complex multiplications. In this paper, we propose a new method which significantly reduces computational costs by adjusting the starting point of FFT window in order to compensate for the RFSE. For the performance verification, we apply the proposed method to the IEEE 802.16e mobile WiMAX system and estimate its computational power compared to the tracking method. Simulation and implementation results show that the proposed algorithm has the performance similar to the tracking method and is very efficient for low power implementation in comb-type pilot-aided OFDM systems because it consumes only 40.5% of the tracking method's power.