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Space-time coding (STC) schemes for communication systems employing multiple transmit and receive antennas have been attracting increased attention. The so-called linear space-time block codes (STBC) have been of particular interest due to their good performance and low decoding complexity. In this paper we take a systematic maximum-likelihood (ML) approach to the decoding of STBC for unknown propagation channels and unknown noise and interference conditions. We derive a low-complexity ML decoding algorithm based on cyclic maximization of the likelihood function. Furthermore, we discuss the design of optimal training sequences and optimal information transfer to an outer decoder. Numerical examples demonstrate the performance of our algorithm.