On the Complexity of Sphere Decoding

Recently, sphere detection has emerged as a powerful means of finding the maximum likelihood solution to the detection problem for multiple-antenna (MIMO) systems. In this paper, we analyze the performance and computational complexity of different sphere detectors and compare it with that of already known MIMO receiver techniques, in uncoded as well as coded transmission1. We propose a number of techniques that allow for reducing the complexity of sphere detection – some at the expense of bit error performance. Our results confirm that for uncoded transmission and low target BERs, sphere detectors outperform all other known receiver techniques with only minor additional complexity. For coded transmission, the complexity of sphere detection essentially scales with the number of candidates, motivating for further research to find techniques that provide good soft outputs with very low numbers of candidates.