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It is well known that suboptimal detection schemes for multiple-input multiple-output (MIMO) spatial multiplexing systems (equalization-based schemes as well as ing-and-cancelling schemes) are unable to exploit all of the available diversity, and thus, their performance is inferior to ML detection. Motivated by experimental evidence that this inferior performance is primarily caused by the inability of suboptimal schemes to deal with "bad" (i.e., poorly conditioned) channel realizations, we study the decision regions of suboptimal schemes for bad channels. Based on a simplified model for bad channels, we then develop two computationally efficient detection algorithms that are robust to bad channels. In particular, the novel sphere-projection algorithm (SPA) is a simple add-on to standard suboptimal detectors that is able to achieve near-ML performance and significantly increased diversity gains. The SPA's computational complexity is comparable with that of ing-and-cancelling detectors and only a fraction of that of the Fincke-Phost sphere-decoding algorithm for ML detection.