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

Feedback Acquisition and Reconstruction of Spectrum-Sparse Signals by Predictive Level Comparisons

In this letter, we propose a sparsity promoting feedback acquisition and reconstruction scheme for sensing, encoding and subsequent reconstruction of spectrally sparse signals. In the proposed scheme, the spectral components are estimated utilizing a sparsity-promoting, sliding-window algorithm in a feedback loop. Utilizing the estimated spectral components, a level signal is predicted and sign measurements of the prediction error are acquired. The sparsity promoting algorithm can then estimate the spectral components iteratively from the sign measurements. Unlike many batch-based Compressive Sensing (CS) algorithms, our proposed algorithm gradually estimates and follows slow changes in the sparse components utilizing a sliding-window technique. We also consider the scenario in which possible flipping errors in the sign bits propagate along iterations (due to the feedback loop) during reconstruction. We propose an iterative error correction algorithm to cope with this error propagation phenomenon considering a binary-sparse occurrence model on the error sequence. Simulation results show effective performance of the proposed scheme in comparison with the literature

Localization Performance of 1-Bit Passive Radars in NB-IoT Applications

Location-based services form an important use-case in emerging narrowband Internet-of-Things (NB-IoT) networks. Critical to this offering is an accurate estimation of the location without overlaying the network with additional active sensors. The massive number of devices, low power requirement, and low bandwidths restrict the sampling rates of NB-IoT receivers. In this paper, we propose a novel low-complexity approach for NB-IoT target delay estimation in cases where one-bit analog-to-digital-converters (ADCs) are employed to sample the received radar signal instead of high-resolution ADCs. This problem has potential applications in the design of inexpensive NB-IoT radar and sensing devices. We formulate the target estimation as a multivariate fractional optimization problem and solve it via Lasserre's semi-definite program relaxation. Numerical experiments suggest feasibility of the proposed approach yielding high localization accuracy with a very low number of 1-bit samples

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