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Orthogonal frequency division multiplexing (OFDM) is robust against inter-symbol interference (ISI) due to the increase of the symbol duration. However, for mobile applications, channel variations during one OFDM symbol introduce inter-carrier-interference (ICI), which degrades the performance. This gets more severe as mobile speed, carrier frequency or OFDM symbol duration increases. We introduce two new methods to mitigate ICI in an OFDM system with coherent channel estimation. Both methods use a piece-wise linear model to approximate channel variations. The first method extracts channel variations information from the cyclic prefix. The second method estimates these variations utilizing the next symbol. Since mathematical analysis of the whole system becomes intractable in a long delay spread environment, we provide a mathematical analysis that investigates the effect of linearization for the case of a time-variant one path channel. Then our simulation results show how these methods would improve the performance in a highly time-variant environment with a long delay spread.