Signal Recovery From 1-Bit Quantized Noisy Samples via Adaptive Thresholding

In this paper, we consider the problem of signal recovery from 1-bit noisy measurements. We present an efficient method to obtain an estimation of the signal of interest when the measurements are corrupted by white or colored noise. To the best of our knowledge, the proposed framework is the pioneer effort in the area of 1-bit sampling and signal recovery in providing a unified framework to deal with the presence of noise with an arbitrary covariance matrix including that of the colored noise. The proposed method is based on a constrained quadratic program (CQP) formulation utilizing an adaptive quantization thresholding approach, that further enables us to accurately recover the signal of interest from its 1-bit noisy measurements. In addition, due to the adaptive nature of the proposed method, it can recover both fixed and time-varying parameters from their quantized 1-bit samples.Comment: This is a pre-print version of the original conference paper that has been accepted at the 2018 IEEE Asilomar Conference on Signals, Systems, and Computer

Covariance matrix recovery from one-bit data with non-zero quantization thresholds: Algorithm and performance analysis

Covariance matrix recovery is a topic of great significance in the field of one-bit signal processing and has numerous practical applications. Despite its importance, the conventional arcsine law with zero threshold is incapable of recovering the diagonal elements of the covariance matrix. To address this limitation, recent studies have proposed the use of non-zero clipping thresholds. However, the relationship between the estimation error and the sampling threshold is not yet known. In this article, we undertake an analysis of the mean squared error by computing the Fisher information matrix for a given threshold. Our results reveal that the optimal threshold can vary considerably, depending on the variances and correlation coefficients. As a result, it is inappropriate to adopt a constant threshold to encompass parameters that vary widely. To mitigate this issue, we present a recovery scheme that incorporates time-varying thresholds. Our approach differs from existing methods in that it utilizes the exact values of the threshold, rather than its statistical properties, to increase the estimation accuracy. Simulation results, including those of the direction-of-arrival estimation problem, demonstrate the efficacy of the developed scheme, especially in complex scenarios where the covariance elements are widely separated.The work of Yu-Hang Xiao was supported in part by the National Natural Science Foundation of China under Grant 62201359. The work of Lei Huang was supported in part by the National Science Fund for Distinguished Young Scholars under Grant 61925108, and in part by the National Natural Science Foundation of China under Grant U1913221. The work of David Ramírez was supported in part by MCIN/AEI/10.13039/501100011033/FEDER, UE, under Grant PID2021-123182OB-I00 (EPiCENTER), and in part by the Office of Naval Research (ONR) Global under Contract N62909-23-1-2002.Publicad

One-Bit Algorithm Considerations for Sparse PMCW Radar

Phase Modulated Continuous Wave (PMCW) radar an emerging technology for autonomous cars. It is more flexible than the current frequency modulated systems, offering better detection resolution, interference mitigation, and future development opportunities. The issue preventing PMCW adoption is the need for high sample-rate analog to digital converters (ADCs). Due to device limits, a large increase in cost and power consumption occurs for every added resolution bit for a given sampling rate. This thesis explores radar detection techniques for few-bit and 1-bit ADC measurements. 1-bit quantization typically results in poor amplitude estimation, which can limit detections if the target signals are weak. Time Varying quantization Thresholds (TVTs) are a way to preserve that amplitude information. An existing few-bit Fast Iterative Shrinkage Thresholding Algorithm (FISTA) was adapted to use 1-bit TVT quantization. Three test scenarios compared the original FISTA using 1 and 2-bit quantization to the TVT approach. Tests included widely spaced targets, adjacent targets, and high dynamic range targets. Performance metrics included normalized mean squared error (NMSE) of target amplitude estimation and Receiver operating characteristic (ROC) curves for detection accuracy. Results showed the TVT implementation operated over the widest range of SNR values, had the lowest amplitude estimate NMSE at high SNR, and comparable NMSE with 2-bit FISTA at low SNR. There was an $84-93\%$ reduction in NMSE compared to 1-bit FISTA without TVTs. Few-bit FISTA had the best detection rates at specific SNR values, but was more sensitive to noise. AUC values averaged across the full SNR range for TVT FISTA were the most robust, measuring $13-46\%$ higher than 1-bit FISTA and $48-74\%$ higher than 2-bit FISTA. Advisor: Andrew Harm

One-Bit Covariance Reconstruction with Non-zero Thresholds: Algorithm and Performance Analysis

Covariance matrix reconstruction is a topic of great significance in the field of one-bit signal processing and has numerous practical applications. Despite its importance, the conventional arcsine law with zero threshold is incapable of recovering the diagonal elements of the covariance matrix. To address this limitation, recent studies have proposed the use of non-zero clipping thresholds. However, the relationship between the estimation error and the sampling threshold is not yet known. In this paper, we undertake an analysis of the mean squared error by computing the Fisher information matrix for a given threshold. Our results reveal that the optimal threshold can vary considerably, depending on the variances and correlation coefficients. As a result, it is inappropriate to use a constant threshold to encompass parameters that vary widely. To mitigate this issue, we present a recovery scheme that incorporates time-varying thresholds. Our approach differs from existing methods in that it utilizes the exact values of the threshold, rather than its statistical properties, to enhance the estimation performance. Our simulations, including the direction-of-arrival estimation problem, demonstrate the efficacy of the developed scheme, especially in complex scenarios where the covariance elements are widely separated