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Space-time coding is proposed to provide significant capacity gains over the traditional communication systems in fading wireless channels. We consider the problem of blind estimation of the channel parameters along with space-time coded signals. Our proposed approach exploits the finite alphabet property of the space-time coded signals and is based on the unconditional signal model by treating the information sequence as stochastic i.i.d. sequences. The iterative Baum-Welch (1970) algorithm is then adapted to solve the resulting unconditional ML optimization cost function. Finally, some simulation results are presented.