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We consider turbo equalization of space-time-coded transmission over frequency-selective fading multiple-input-multiple-output (MIMO) channels. A MIMO finite-impulse-response prefilter is proposed and shown to reduce the turbo equalizer complexity significantly at a small performance loss. Advantages of the proposed scheme are that we do not alter the equalization algorithm or require the channel to be minimum phase. The prefiltered turbo equalizer is an attractive receiver structure for broadband wireless transmission using spectrally-efficient high-order modulation schemes as in EDGE.