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The iterative receivers with a list sphere detector (LSD) and a parallel interference canceller (PIC) for multiple-input-multiple-output (MIMO) bit-interleaved coded modulation systems are considered. The convergence behaviors of these iterative detection and decoding schemes are analyzed via variance transfer (VT) functions. For ergodic channels, we show that the waterfall region of an iterative receiver can be predicted using a variance exchange graph. For slow fading channels, we show that the frame error rate of the iterative receiver is essentially limited by the early interception rate of the iterative receiver. Moreover, we show that the VT function of an LSD with a small list size is superior to that of a PIC at a high-variance region, whereas it is worse than that of a PIC at a low-variance region. Then, we propose a detection switching (DSW) approach for the iterative receiver and present a DSW criterion based on cross entropy. By applying the DSW, we show that the near-capacity performance can be achieved with a significantly reduced complexity.