论文标题
限制大规模MIMO检测的泊松法与盒子放松
The Limiting Poisson Law of Massive MIMO Detection with Box Relaxation
论文作者
论文摘要
从嘈杂的线性测量中估算二元载体是MIMO系统的典型问题。一种流行的算法，称为Box-Relaxation解码器，通过用凸约束解决最小二乘问题来估计目标信号。本文表明，该算法的性能通过不正确的钻头数量来衡量，具有有限的泊松法。当采样比和噪声方差（问题的两个关键参数）随着系统维度的增长而遵循某些量表时，就会发生这种情况。此外，在定义明确的阈值下，完美恢复的可能性显示出可以通过牙龈分布来表征的相变。数值模拟证实了这些理论预测，表明它们即使在中等系统维度中也与算法的实际性能相匹配。
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 paper 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.
