A general Variational Bayesian framework for iterative data and parameter estimation for coherent detection is introduced as a generalization of the EM-algorithm. Explicit solutions are given for MIMO channel estimation with Gaussian prior and noise covariance estimation with inverse-Wishart prior. Simulation of a GSM-like system provides empirical proof that the VBEM-algorithm is able to provide better performance than the EM-algorithm. However, if the posterior distribution is highly peaked, the VBEM-algorithm approaches the EM-algorithm and the gain disappears. The potential gain is therefore greatest in systems with a small amount of observations compared to the number of parameters to be estimated.
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