The Limiting Poisson Law of Massive MIMO Detection With Box Relaxation
The Limiting Poisson Law of Massive MIMO Detection With Box Relaxation
复制标题
DOI：
10.1109/jsait.2020.3039964
复制
发表时间：
2020-06
期刊：
影响因子：
--
通讯作者：
Hong Hu;Yue M. Lu
中科院分区：
文献类型：
--
作者：
Hong Hu;Yue M. Lu
从噪声线性测量估计二进制向量是MIMO系统的典型问题。一个流行的算法，称为盒松弛解码器，估计目标信号，通过解决一个最小二乘问题的凸约束。这篇文章表明，该算法的性能，衡量错误解码的比特数，有一个限制泊松定律。当采样率和噪声方差（问题的两个关键参数）随着系统维度的增长而遵循一定的比例时，就会发生这种情况。此外，在一个定义明确的阈值，完美恢复的概率示出经历一个相变，其特征在于由Gumbel分布。数值模拟证实了这些理论预测，表明它们匹配的实际性能的算法，即使在适度的系统尺寸。
Estimating a binary vector from noisy linear measurements is a prototypical problem for MIMO systems. A popular algorithm, called the box-relaxation decoder, estimates the target signal by solving a least squares problem with convex constraints. This article shows that the performance of the algorithm, measured by the number of incorrectly-decoded bits, has a limiting Poisson law. This occurs when the sampling ratio and noise variance, two key parameters of the problem, follow certain scalings as the system dimension grows. Moreover, at a well-defined threshold, the probability of perfect recovery is shown to undergo a phase transition that can be characterized by the Gumbel distribution. Numerical simulations corroborate these theoretical predictions, showing that they match the actual performance of the algorithm even in moderate system dimensions.