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The performance of turbo equalization for the combined equalization and decoding of space-time coded signals in frequency selective channels is investigated. The equalizer considers a multiple input multiple output (MIMO) channel and is based on a variation of the BCJR algorithm providing soft outputs. This in itself is superior to linear or decision feedback equalizers in that it seeks to reap the diversity offered by the time dispersion of the channel. The space-time decoder working on the BCJR algorithm also provides soft outputs of its decisions. These two units are used in an iterative manner to implement turbo equalization of the space-time coded signals. The prohibitive complexity of the equalizer under moderate to severe time dispersion is handled by implementing the M-BCJR algorithm, which only considers a subset of the equalizer states at each time instance. Simulation results show the improved behavior of the reduced state turbo equalizer over separate optimum MAP equalization and decoding.