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New coherent receivers are derived for a pilot-symbol-aided distributed space-time block-coded system with imperfect channel state information which do not perform channel estimation at the destination by using the received pilot signals directly for decoding. The derived receivers are based on new metrics that use distribution of the channels and the noise to achieve improved symbol-error-rate (SER) performance. The SER performance of the derived receivers is further improved by utilizing the decision history in the receivers. The decision history is also incorporated in the existing Euclidean metric to improve its performance. Simulation results show that, for 16-quadrature-amplitude-modulation in a Rayleigh fading channel, a performance gain of up to 2.5 dB can be achieved for the new receivers compared with the conventional mismatched coherent receiver.