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Detection of spatially multiplexed data transmissions subject to frequency flat fading is considered. Optimal decoders require knowledge of the marginal posterior distributions of the transmitted symbols, but their exact computation is not feasible for practical systems. Hence sub-optimal approaches are generally sought. By recasting this problem into the graphical model framework, we investigate here a recently proposed suboptimal approach which relies on a tree-based reparameterization principle. For quasi-static fading channels, the resulting decoder complexity has an order which is at most quadratic in the number of transmit antennas. However, in its standard form, the algorithm often fails to converge, severely restricting its practical usability. We here develop a novel methodology to ensure systematic convergence of the algorithm in this communication scenario at the expense of the introduction of a minimal bias on the computation of the symbol marginal posterior probabilities. This bias is quantified theoretically and its innocuity for the problem at hand is ultimately demonstrated through numerical simulations. For a system using 16-QAM modulation with four transmit and receive antennas, the proposed detector achieves a bit-error rate of 10-4 requiring only 3 dB greater SNR than the optimal method.