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This paper presents an iterative (turbo) channel estimation and turbo equalization when orthogonal frequency division multiplexing (OFDM) has been concatenated to space-time block code (STBC) over time-varying multipath Rayleigh fading channels. Based on the Kalman filter channel estimator, soft-input-soft-output (SISO) minimum mean square error (MMSE) equalizer and a maximum posterior probability (MAP) decoder, the channel estimate can be improved for each iteration by using soft information feedback from the decoder. Computer simulations show good estimation and tracking by the Kalman filter with only a few training (pilot) symbols even when signals experience deep fading. It is observed from simulations that the overall system performance can be improved by 4 dB after 14 iterations compared to non-iterative channel estimation and equalization. The proposed method is shown to obtain fast channel estimation and low complexity turbo equalization which are requirements in time-varying fading channels.