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In fast time-varying environments, an OFDM system needs to insert denser pilot symbols among transmitted symbols for tracking the variation of the channel. To reduce the number of pilots, several algorithms including blind, semi-blind, and decision-directed (DD) approaches are proposed. Most of these algorithms assume the channel varies block-wisely, but remain invariant within one OFDM block duration. However, such channel model neglects the inter-(sub)channel interference (ICI) and may be not practical for fast time-varying channels. In this paper, we propose an ICI self-cancellation algorithm under an architecture that could be readily incorporated into an OFDM system that does not take the ICI into consideration. Our algorithm involves only periodic extension and linear combination, and incurs almost no additional complexity. The ICI can be completely removed if the variation of each path in the channel is linear with time during one extended OFDM block. Our algorithm also provides a trade-off between performance and throughput. To validates the proposed algorithm, we incorporate it into an OFDM system with pseudo-pilot (PP) detection. The simulation validates the efficiency of the proposed algorithm, and that neglecting the ICI in fast time-varying channels is impractical.