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Performance and Complexity Analysis of Infinity-Norm Sphere-Decoding

机译：无穷范数球解码的性能和复杂性分析

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摘要

Promising approaches for efficient detection in multiple-input multiple-output (MIMO) wireless systems are based on sphere-decoding (SD). The conventional (and optimum) norm that is used to conduct the tree traversal step in SD is the l 2 -norm. It was, however, recently observed that using the l ¿-norm instead reduces the hardware complexity of SD considerably at only a marginal performance loss. These savings result from a reduction in the length of the critical path in the circuit and the silicon area required for metric computation, but are also, as observed previously through simulation results, a consequence of a reduction in the computational (i.e., algorithmic) complexity. The aim of this paper is an analytical performance and computational complexity analysis of l ¿-norm SD. For independent and identically distributed (i.i.d.) Rayleigh fading MIMO channels, we show that l ¿-norm SD achieves full diversity order with an asymptotic SNR gap, compared to l 2-norm SD, that increases at most linearly in the number of receive antennas. Moreover, we provide a closed-form expression for the computational complexity of l ¿-norm SD based on which we establish that its complexity scales exponentially in the system size. Finally, we characterize the tree pruning behavior of l ¿-norm SD and show that it behaves fundamentally different from that of l 2-norm SD.
机译：在多输入多输出（MIMO）无线系统中有效检测的有前途的方法是基于球形解码（SD）的。 SD中用于执行树遍历步骤的常规（最佳）范数是l 2范数。但是，最近观察到，使用lÃ-β-norm取而代之的是降低SD的硬件复杂性，而仅造成了很小的性能损失。这些节省是由于电路中关键路径长度的减少和度量计算所需的硅面积的减少，但如先前通过仿真结果所观察到的，也是节省了计算（即算法）复杂性的结果。本文的目的是lâ‚-规范SD的分析性能和计算复杂度分析。对于独立且分布均匀的（iid）Rayleigh衰落MIMO信道，我们显示lÃ-β-范数SD与l 2-范数SD相比最多达到了渐近SNR间隙的完全分集阶数。接收天线的数量呈线性关系。此外，我们为lÂβ-规范SD的计算复杂度提供一个封闭形式的表达式，基于此表达式，我们可以确定其复杂度在系统大小中呈指数级增长。最后，我们表征了lÃ-β规范SD的树修剪行为，并表明它的行为与l 2规范SD的树根本不同。

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