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Abstract High-speed railway communication implemented based on Long-Term Evolution-Railway (LTE-R) Platform has strict requirements for quality of services to support high data-rate transmission for numerous mobile users. In such environment, there often exists inter-carrier interference. In this paper, we exploit a robust channel estimation method in the time domain for very fast time-varying LTE-railway channels, and then, we propose an effective and adaptive frequency-domain equalizer that can offer a tradeoff between performance and computational complexity. The simulation results show the robustness of our proposed method compared with previous ones. The computational complexity of the proposed method retain at a decent number by exploiting specified properties of channel matrices. more...