# Covariance Recovery for One-Bit Sampled Data With Time-Varying Sampling Thresholds-Part I: Stationary Signals

arXiv: https://arxiv.org/abs/2203.09460 · HTML: https://mlsanity.com/paper/2203.09460/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 48 references that are in the map.
- First posted on arXiv 16 Mar 2022.

## Builds on (most cited first, 4 of 4)

- [Signal Recovery From 1-Bit Quantized Noisy Samples via Adaptive Thresholding](https://mlsanity.com/paper/1812.03977/) (2018)
- [Gridless Parameter Estimation for One-Bit MIMO Radar with Time-Varying Thresholds](https://mlsanity.com/paper/1908.10487/) (2019)
- [Blind Direction-of-Arrival Estimation in Acoustic Vector-Sensor Arrays via Tensor Decomposition and Kullback-Leibler Divergence Covariance Fitting](https://mlsanity.com/paper/2005.08318/) (2020)
- [Efficient Waveform Covariance Matrix Design and Antenna Selection for MIMO Radar](https://mlsanity.com/paper/2002.06025/) (2020)

## Abstract (arXiv)

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.