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In a paper by M. Skoglund et al. (see IEEE Trans. Inform. Theory, May 2002) an approach to combined training and coding for an unknown single-input single-output (SISO) frequency-selective fading channel was introduced. The main purpose of the present paper is to extend that work to several antennas and a multiple-input multiple-output (MIMO) scenario. Related previous work includes space-time code design for unknown flat fading channels.