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We address the problem of space-time communications in the context where the turbo principle is used in order to improve the robustness of the transmission. Recovering the sequence of emitted symbols in the wide-band context is known to lead to a computationally very challenging problem. We propose an adaptive numerical approximation of the BCJR algorithm, based on particle filtering/smoothing techniques. When combined with classical estimation techniques for the channel and variance of the observation noise, this algorithm is very efficient, and scales very favourably with the dimension of the problem. This is demonstrated through numerical simulations.