In this article a non-heuristic sphere radius determining method for sphere decoding is developed so that the sphere radius could be properly chosen to restrict the complexity as much as possible without incurring evident performance loss. A special bound of symbol error ratio performance of maximum likelihood detection is formulated which can serve as a lower bound in low signal to noise ratio (SNR) region. Thus the sphere radius determining method can be presented with a SNR dependent probability employing the bound. Then a modification of radius determining method is introduced using a compress factor suppressing the sphere radius in low SNR region to make the expected complexity tolerable. The expected complexity analysis is performed based on the expected number of all visited nodes for all search levels. Finally, simulation results show the effectiveness of the proposed sphere radius determining method within the whole SNR region.
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