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The new wireless standard, Long-Term-Evolution (LTE), needs to support high data rate orthogonal frequency division multiplexing (OFDM) transmission for highly mobile users. Due to users' mobility, the wireless channel becomes time-variant and frequency-selective. The symbol transmission is thus impaired by Doppler spread. As a consequence, the known channel estimation methods do not give satisfactory performances. In this paper, we propose an iterative channel estimation and intercarrier interference (ICI) cancellation method that estimates the wireless channel by utilizing pilot symbols, estimates of the data symbols and Doppler spread information at the receiver. The wireless channel is expressed by a weighted time-domain channel interpolation, where the interpolation weights are designed based on the Doppler spread and time-domain channel correlations. The channel estimates are obtained by employing a least square (LS) method. Once the channel is estimated, the ICI is cancelled by performing a zero-forcing technique. Data symbols are then estimated by a detector. The estimates of data symbols are used to refine the estimation of channel coefficients, iteratively. The simulation results show that the performance degradation of the proposed scheme, when users move at the speed of up to 324 Km/h, compared to a system when users are static and perfect channel state information (CSI) is available at the receiver, is minimal.