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We propose a novel approach to estimating multiple-input-multiple-output (MIMO) channels in space-time coded systems. The channel is assumed to introduce dispersion in both the spatial and temporal dimensions. The channel estimator is obtained by applying the maximum likelihood principle, not only over a known pilot sequence, as in classical least-squares approaches, but also over all the symbols (both known and unknown) in a data frame. Since this results in an optimization problem without closed-form solution, we utilize an iterative method, the expectation-maximization (EM) algorithm, to calculate the solution. The resulting channel estimator is particularly suitable to be used in a turbo equalizing structure because it benefits from the a posteriori probabilities about the transmitted symbols computed at each decoding iteration of the turbo process.