In this paper, the paradigm of sphere decoding (SD) for solving the integer least square problem (ILS) is revisited, where extra degrees of freedom are introduced to exploit the decoding potential. Firstly, the equivalent sphere decoding (ESD) is proposed, which is essentially the same with the classic Fincke-Pohst sphere decoding but characterizes the sphere radius $D>0$ with two new parameters named as initial searching size $K>1$ and deviation factor $σ>0$. By fixing $σ$ properly, we show that given the sphere radius $D\triangleqσ\sqrt{2\ln K}$, the complexity of ESD in terms of the number of visited nodes is upper bounded by $|S|<nK$, thus resulting in an explicit and tractable decoding trade-off solely controlled by $K$. To the best of our knowledge, this is the first time that the complexity of sphere decoding is exactly specified, where considerable decoding potential can be explored from it. After that, two enhancement mechanisms named as normalized weighting and candidate protection are proposed to further upgrade the ESD algorithm. On one hand, given the same setups of $K$ and $σ$, a larger sphere radius is achieved, indicating a better decoding trade-off. On the other hand, the proposed ESD algorithm is generalized, which bridges suboptimal and optimal decoding performance through the flexible choice of $K$. Finally, further performance optimization and complexity reduction with respect to ESD are also derived, and the introduced tractable and flexible decoding trade-off is verified through large-scale MIMO detection.

翻译：本文重新审视了用于求解整数最小二乘问题的球面解码范式，通过引入额外自由度以挖掘其解码潜力。首先，我们提出了等效球面解码算法，该算法本质上与经典的Fincke-Pohst球面解码相同，但使用两个新参数——初始搜索规模K>1和偏差因子σ>0——来表征球面半径D>0。通过适当固定σ，我们证明当球面半径设定为D≜σ√(2ln K)时，ESD算法访问节点数的复杂度上界为|S|<nK，从而形成仅由K控制的显式且可处理的解码权衡。据我们所知，这是首次精确界定球面解码的复杂度，从中可发掘可观的解码潜力。随后，本文提出归一化加权和候选保护两种增强机制以进一步提升ESD算法性能。一方面，在相同K和σ设置下可获得更大的球面半径，意味着更优的解码权衡；另一方面，所提ESD算法通过K的灵活选择实现了次优与最优解码性能的贯通。最后，本文推导了ESD算法的进一步性能优化与复杂度降低方案，并通过大规模MIMO检测验证了所引入的可处理且灵活的解码权衡机制。