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This paper addresses the issue of advanced equalization methods for space-time communications over multiple-input multiple-output block fading channel with intersymbol interference. Instead of resorting to conventional multiuser detection techniques (based on the straightforward analogy between antennas and users), we adopt a different point of view, and separate time equalization from space equalization, thus introducing a higher degree of freedom in the overall space-time equalizer design. Time-domain equalization relies on minimum mean-square error criterion and operates on multidimensional modulation symbols, whose individual components can be detected in accordance with another criterion. In particular, when the optimum maximum a posteriori criterion is chosen, substantial performance gains over conventional space-time turbo equalization have been observed for different transmission scenarios, at the price of an increased, albeit manageable, computational complexity.