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This paper introduces a simple but efficient reception algorithm for the MIMO systems with spatial multiplexing or Bell Laboratories Layered Space-Time (BLAST) architecture and soft decoding. We also analyze the optimal maximum likelihood algorithm as well as the minimum mean squared error (MMSE) and MMSE with ordered successive interference cancellation (MMSE-OSIC) algorithms. The performance of these algorithms at the decoder input and output when soft and hard decoding are used is studied. A novel simple MMSE with soft decisions enhancement (MMSE-SDE) algorithm is proposed with improved characteristics for soft decoding. This algorithm provides up to 3 dB gain over MMSE and MMSE-OSIC in the ill-conditioned MIMO channel.