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We consider the Kalman filter for equalization of a multiple-input multiple-output (MIMO), frequency selective, quasi-static fading channel. More specifically, we consider a coded system, where the incoming bit stream is convolutionally encoded, interleaved and then spatially multiplexed across the transmit antennas before being transmitted over a frequency selective channel. At the receiver, we use a Kalman filter as the MIMO equalizer and modify its structure, enabling it to process the a-priori (soft) information provided by the outer decoder, thereby allowing us to perform iterative (turbo) equalization on the received sequence. The proposed equalizer has a comparable performance with the optimal symbol-by-symbol, maximum a-posteriori probability (MAP) equalizer and provides a considerable complexity reduction, especially for systems with a large number of transmit antennas or long ISI spans.