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Orthogonal space-time block codes utilize transmit diversity and allow the receiver to have a simple maximum-likelihood decoder. Normally, channel state information is not readily available at the receiver. Hence, channel estimation is necessary for coherent detection. We present analytical bit error rate (BER) expressions as well as the tight Chernoff bound for orthogonal space-time block coded systems employing M-PSK modulation. The results show directly the BER dependence on the transmit diversity and the mean square error of the channel estimator. Simulation results show the accuracy of our BER predictions.