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The stochastic gradient-based least-mean-square (LMS) algorithm has a significant feature of simple implementations. Its applications in multiple-input-multiple-output (MIMO) layered space-time (LST) systems are considered in this paper. We derive the design criteria of the adaptive iterative/decision-feedback (DFB) LMS receivers in MIMO systems. It has been found that the algorithm converges in accordance with the minimum eigenvalue of the correlation matrices where received symbols and interference estimates are the entries of two correlation matrices respectively.