2022/03/16 by Arian Eamaz, Eamaz, Arian, Farhang Yeganegi +3
Computer Science · Engineering · #Advanced Electrical Measurement Techniques #FOS: Electrical engineering #Image and Signal Denoising Methods #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #eess.SP #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2203.09460
arxiv created 2022/03/16 · openalex publication_date 2022/03/16 · arxiv updated 2022/03/18 · openalex created_date 2022/04/03 · openalex updated_date 2026/08/04
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.