We propose the application of cosine windowing for the orthogonal frequency-division multiplexing (OFDM) systems to self-cancel intercarrier interference (ICI) in fast time-varying channels prior to receptions. With a time-domain cosine window immediately after the inverse discrete Fourier transform (IDFT) unit in OFDM transmitters, the ICI fractions from adjacent subcarriers significantly cancel one another at the expense of the orthogonality violation among subcarriers in the main lobe. As a result, the frequency-domain channel matrix reshaped by the cosine windowing can be closely approximated to a strictly banded matrix. In the complex exponential basis expansion model (CE-BEM), we present the estimation of the channel matrix with the assistance of the pilot clusters. Simulation results show that the receivers implementing the CE-BEM channel estimation and the low-complexity block turbo minimum mean square error (MMSE) equalization perform with considerably lower bit error rates (BER) even in very fast time-varying channels.