论文标题
一位抽样数据的协方差恢复，并带有随时间变化的采样阈值i：固定信号
Covariance Recovery for One-Bit Sampled Data With Time-Varying Sampling Thresholds-Part I: Stationary Signals
论文作者
论文摘要
一位量化依赖于将感兴趣的信号与给定阈值水平进行比较，它在信号处理中引起了广泛关注的通信和传感。在这种设置中，协方差恢复的有用工具是Arcsine定律，该定律估计了零均值固定输入信号的归一化协方差矩阵。但是，这种关系仅考虑零采样阈值，这可能会导致显着的信息损失。在本文中，Arcsine定律的思想扩展到了单位类似物对数字转换器（ADC）应用时间变化阈值的情况。具体而言，提出，研究并进行了比较，提出了三种不同的方法，以恢复感兴趣的固定信号的自相关序列。此外，我们将研究Bussgang Law的修改，这是一种著名的关系，促进了一位采样数据与零均值的固定输入信号之间互相关的恢复。与Arcsine Law的案例类似，Bussgang Law仅考虑零采样阈值。该关系还可以扩展，以适应固定输入信号的时变阈值的更一般的情况。
One-bit quantization, which relies on comparing the signals of interest with given threshold levels, has attracted considerable attention in signal processing for communications and sensing. A useful tool for covariance recovery in such settings is the arcsine law, that estimates the normalized covariance matrix of zero-mean stationary input signals. This relation, however, only considers a zero sampling threshold, which can cause a remarkable information loss. In this paper, the idea of the arcsine law is extended to the case where one-bit analog-to-digital converters (ADCs) apply time-varying thresholds. Specifically, three distinct approaches are proposed, investigated, and compared, to recover the autocorrelation sequence of the stationary signals of interest. Additionally, we will study a modification of the Bussgang law, a famous relation facilitating the recovery of the cross-correlation between the one-bit sampled data and the zero-mean stationary input signal. Similar to the case of the arcsine law, the Bussgang law only considers a zero sampling threshold. This relation is also extended to accommodate the more general case of time-varying thresholds for the stationary input signals.
