We obtain the exact pairwise error probability for an MPSK based
space-time code employing receive diversity and noisy channel
estimates and experiencing fast Rayleigh fading. The exact expression for the pairwise error probability lends itself to the application of classical transfer bounding techniques. We also obtain a union bound by applying the transfer function bound in conjunction with the pairwise error probability, and show that the union bound is within a few dBs for fast Rayleigh fading. In the case of MQAM based space-time codes and/or quasi-static Rayleigh fading channels, the same technique provides an upper bound on the pairwise error probability, which, in conjunction with the transfer function bound, is used to obtain a union bound on the bit error rate.