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The optimal maximum-likelihood (ML) detector for a single-carrier (SC) multiple-input multiple-output (MIMO) system is often prohibitive due to its enormous computational complexity. In this paper, we propose a low complexity layered space-frequency equalization with time domain noise prediction (LSFE-NP) structure, where at each stage of the detector, a given data stream is detected by a multiple-input single-output (MISO) frequency domain equalization with time domain noise prediction (FDE-NP). It is shown that the proposed structure is optimal in the minimum mean square error (MMSE) sense, and the coefficients of the feedback filter are independent of the feedforward equalizer. Therefore, an alterable feedback taps LSFE-NP scheme is outlined for the coded SC MIMO system, which can feed as many reliable decisions as possible back to the equalizer to achieve better performance. Simulation results show that our proposed scheme can outperform the conventional LSFE and the MIMO FDE-NP significantly.