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In this paper, the variational expectation-maximization (VEM) algorithm is used to provide channel estimates in a space-time decoder. The proposed estimator works for many types of space-time codes (STC), including full-rate full-diversity (FRFD) codes, Bell Laboratories layered space-time architecture (BLAST) and orthogonal STC's. The principle idea is to treat the channel coefficients as the unknown parameters, and the transmitted symbols as the unobserved variables in the EM algorithm. The posterior distribution of the symbols is approximated by a factorized distribution, whose Kullback-Liebler divergence with the true distribution is minimized, thereby explaining the ``variational'' aspect of the technique. The channel estimates may then be used for coherent decoding -- here we use the K-best detector for a 2×2 system. Simulation results show that the new channel estimator can reduce system complexity greatly compared with traditional schemes, while achieving near-ideal performance.