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We start by identifying a relatively efficient version of sphere decoding algorithm (SDA) that performs exact maximum-likelihood (ML) decoding. We develop novel algorithms based on an improved increasing radius search (IIRS), which offer error performance and decoding complexity between two extremes: the ML receiver and the ing-canceling (NC) receiver with detection ordering. With appropriate choices of parameters, our IIRS offers the flexibility to trade error performance for complexity. We provide design intuitions and guidelines, analytical parameter specifications, and a semianalytical error-performance analysis. Simulations illustrate that IIRS achieves considerable complexity reduction, while maintaining performance close to ML.