论文标题
一位抽样数据的协方差恢复，具有随时间变化的采样阈值-II：非平稳信号
Covariance Recovery for One-Bit Sampled Data With Time-Varying Sampling Thresholds-Part II: Non-Stationary Signals
论文作者
论文摘要
从其一位采样的对应物中恢复输入信号协方差值在文献中被认为是一项艰巨的任务。为了应对其困难，通常会做出一些假设来找到输入协方差矩阵与一位采样数据的自相关值之间的关系。这包括Arcsine法律和这项工作第一部分中讨论的修改后的Arcsine法律[2]。我们表明，通过促进时变阈值的部署，修改后的Arcsine法律在协方差恢复方面具有有希望的表现。但是，修改后的Arcsine定律还假设输入信号是固定的，这通常是对现实世界应用程序的简化假设。实际上，在许多信号处理应用中，对于非toeplitz协方差矩阵而言，很容易知道输入信号是非平稳的。在本文中，我们提出了一种将Arcsine定律扩展到一位ADC应用时变阈值的情况，同时处理源自非平稳过程的输入信号。特别是，恢复方法被证明可以准确恢复随时间变化的方差和自相关值。此外，我们将Bussgang Law的配方扩展到考虑非平稳输入信号的情况。
The recovery of the input signal covariance values from its one-bit sampled counterpart has been deemed a challenging task in the literature. To deal with its difficulties, some assumptions are typically made to find a relation between the input covariance matrix and the autocorrelation values of the one-bit sampled data. This includes the arcsine law and the modified arcsine law that were discussed in Part I of this work [2]. We showed that by facilitating the deployment of time-varying thresholds, the modified arcsine law has a promising performance in covariance recovery. However, the modified arcsine law also assumes input signals are stationary, which is typically a simplifying assumption for real-world applications. In fact, in many signal processing applications, the input signals are readily known to be non-stationary with a non-Toeplitz covariance matrix. In this paper, we propose an approach to extending the arcsine law to the case where one-bit ADCs apply time-varying thresholds while dealing with input signals that originate from a non-stationary process. In particular, the recovery methods are shown to accurately recover the time-varying variance and autocorrelation values. Furthermore, we extend the formulation of the Bussgang law to the case where non-stationary input signals are considered.
