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This paper considers the problem of Gaussian symbols detection in MIMO systems in the presence of channel estimation errors. Under this framework we develop a computationally efficient approximations of the MAP detector. The new detectors are based on a relaxation of the discrete nature of the digital constellation and on the channel estimation error statistics. This leads to a non-convex program that is solved efficiently via a hidden convexity minimization approach. Additionally, we show that using a Bayesian EM approach, comparable BER performance to that of the MAP detector can be achieved. Next we extend the detection scheme to the case where the noise variance is unknown. We present a modified Bayesian EM approach with annealed Gibbs sampling to perform joint noise variance estimation and symbols detection. Simulation results in a random MIMO system show that the proposed algorithm outperforms the linear MMSE receiver in terms of BER.