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In this paper, the performance of limited feedback precoded spatial multiplexing multiple-input multiple-output orthogonal frequency division multiplexing (MIMO - OFDM) systems is investigated in time varying fading channels. Most studies into limited feedback precoded (MIMO - OFDM) systems are based on the notion of time invariant channels throughout transmission. Therefore, the precoding matrix for each subcarrier can be designed at the receiver in terms of the current channel state, fed back to the transmitter, and used for the subsequent block of data symbols. However, in time varying channels, the feedback information becomes outdated, which results in significant system performance degradation. To mitigate this system performance degradation caused by outdated information due to a delay in the feedback channel, this paper considers a more practical system, where the channel varies from one block of symbols to another. A method is proposed based on modelling the channel as an autoregressive (AR) model and using a Kalman filter linear predictor at the receiver to predict the channels states, required to design the precoding matrices for the next OFDM symbol carriers whose indexes are fed back to the transmitter. The performance of this method is investigated using computer simulation, and the results obtained for the proposed channel prediction demonstrate improved bit error rate performance for time-varying Rayleigh fading channels, even in systems with high mobility.