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Conventional limited feedback precoded MIMO-OFDM systems generally focus on time-invariant channels throughout transmission. As a result, the optimal precoding matrix can be found during the training blocks and employed over the subsequent data blocks. In contrast to the conventional systems, we consider systems in high mobility environments where the channels vary from one OFDM block to another. In such a scenario, the precoding matrix derived by the receiver based on the previous OFDM block is outdated, which may incur significant system performance degradation. To circumvent this obstacle, a Kalman-filter based channel prediction scheme is proposed for the receiver by modeling the precoding matrices and channel vectors as nonlinear and linear channel parameters of the time-domain received signal, respectively. Based on the predicted channel state information, the optimal precoding matrix for the next OFDM block is selected and returned to the transmitter. Simulation results confirm that precoded MIMO-OFDM systems with the proposed channel prediction can achieve robust performance even over fast time-varying channels.