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In this paper, we investigate the effect of imperfect channel estimation on the bit error rate (BER) performance of orthogonal space-time block codes (OSTBCs). The multiple-input multiple-output (MIMO) propagation channel is assumed to be affected by uncorrelated flat Rayleigh block fading. We consider a mismatched maximum-likelihood (ML) receiver, which estimates the channel matrix from known pilot symbols according to a minimum mean-square error (MMSE) criterion, and uses the channel estimate in the symbol-by-symbol detection algorithm as if it were the true channel matrix. For both PAM and QAM constellations and OSTBCs satisfying a proposed criterion, we present simple exact closed-form expressions for the BER of the mismatched receiver and the corresponding BER degradation as compared to a receiver that knows the true channel matrix. For OSTBCs that do not satisfy this criterion, a simple approximation of the BER and the associated BER degradation is derived, assuming PAM and QAM constellations. By means of computer simulations, this approximation is shown to be very accurate.