Covariance Recovery for One-Bit Sampled Non-Stationary Signals With Time-Varying Sampling Thresholds
Covariance Recovery for One-Bit Sampled Non-Stationary Signals With Time-Varying Sampling Thresholds
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DOI：
10.1109/tsp.2022.3217379
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发表时间：
2022
影响因子：
5.4
通讯作者：
Arian Eamaz;Farhang Yeganegi;M. Soltanalian
中科院分区：
文献类型：
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作者：
Arian Eamaz;Farhang Yeganegi;M. Soltanalian
在文献中，从其一位采样对应物中恢复输入信号协方差值被认为是一项具有挑战性的任务。为了解决这一问题，通常需要对输入协方差矩阵和一位采样数据的自相关值之间的关系进行一些假设。这包括反正弦法和最近提出的修正反正弦法，它利用时变采样阈值在协方差恢复中发挥了很好的作用。然而，修改的反正弦定律还假设输入信号是平稳的，这通常是现实世界应用的简化假设。事实上，在许多信号处理应用中，输入信号很容易被认为是具有非Toeplitz协方差矩阵的非平稳信号。在本文中，我们提出了一种方法，将反正弦定律扩展到一位ADC在处理源自非平稳过程的输入信号时应用时变阈值的情况。特别是，恢复方法示出，以准确地恢复随时间变化的方差和自相关值。此外，我们扩展的Bussgang法律的制定的情况下，被认为是非平稳输入信号。
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 recently proposed modified arcsine law which unleashes a promising performance in covariance recovery by taking advantage of time-varying sampling thresholds. 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.