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This paper addresses the issue of iterative space-time equalization for multiple-input-multiple-output (MIMO) frequency-selective fading channels. A new soft equalization concept based on successive interference cancellation (SIC) is introduced for a space-time bit-interleaved coded modulation (STBICM) transmission. The proposed equalizer allows us to separate intersymbol interference (ISI) and multiantenna interference (MAI) functions. Soft ISI is successively suppressed using a low-complexity suboptimum minimum mean square error (MMSE) criterion. The decoupling of ISI and MAI offers more flexibility in the design of the whole space-time equalizer. Different multiantenna detection criteria can be considered, ranging from simple detectors to the optimal maximum a posteriori (MAP) criterion. In particular, we introduce two soft equalizers, which are called SIC/SIC and SIC/MAP, and we show that they can provide a good performance-to-complexity tradeoff for many system configurations, as compared with other turbo equalization schemes. This paper also introduces an MMSE-based iterative channel state information (CSI) estimation algorithm and shows that attractive performance can be achieved when the proposed soft SIC space-time equalizer iterates with the MMSE-based CSI estimator.