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We consider wireless OFDM communications over rapidly varying channels as occurring e.g. in high-mobility scenarios. Here, intercarrier interference (ICI) is the major source of impairment that limits the transmission quality. In this paper, we propose novel equalizers to combat ICI and enable reliable communications even at high Doppler frequencies. In contrast to existing frequency-domain approaches, our schemes operate in the time domain. This allows a low-complexity implementation without introducing any systematic channel approximation errors. Numerical simulations illustrate the effectiveness of our approach and show that in conjunction with channel coding our methods achieve significant Doppler diversity.