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The BLAST (Bell-Labs' layered space-time) system is a multi-input multi-output (MIMO) system that can be used to increase the wireless transmission data rate without increasing the total transmission power or bandwidth. In practice, forward error correction (FEC) codes, such as the convolutional code, are often used to lower the bit-error-rate (BER) drastically. We propose a simple soft-detector for QAM constellations based on the unstructured least-squares approach to obtain the soft-information for the Viterbi convolutional decoder. This soft-detector is very simple since it decouples a multi-dimensional QAM symbol detection into multiple one-dimensional QAM symbol detections. Simulation results show that the performance of our soft-decision algorithm can outperform that of the hard-decision sphere decoding algorithm. Yet our algorithm is computationally much more efficient than the latter.