One-bit Measurements Research Articles

Noisy One-Bit Compressed Sensing With Side-Information

We consider the problem of sparse signal reconstruction from noisy one-bit compressed measurements when the receiver has access to side-information (SI). We assume that compressed measurements are corrupted by additive white Gaussian noise before quantization and sign-flip error after quantization. A generalized approximate message passing-based method for signal reconstruction from noisy one-bit compressed measurements is proposed which is then extended for the case where the receiver has access to a signal that aids signal reconstruction, i.e., side-information. Two different scenarios of SI are considered-a) SI consisting of support information only, and b) SI consisting of support and amplitude information. SI is either a noisy version of the signal or a noisy estimate of the support of the signal. We develop reconstruction algorithms from one-bit measurements using noisy SI available at the receiver. Laplacian distribution and Bernoulli distribution are used to model the two types of noises which when applied to the signal and the support, yield the SI for the above two cases, respectively. The Expectation-Maximization algorithm is used to estimate the noise parameter using noisy one-bit compressed measurements and the SI. We show that one-bit compressed measurement-based signal reconstruction is quite sensitive to noise, and the reconstruction performance can be significantly improved by exploiting available side-information at the receiver.

Frequency-Selective SIMO Channel Estimation Based on One-Bit Measurements

Frequency-Selective SIMO Channel Estimation Based on One-Bit Measurements

One-Bit Measurements in Microwave Resonators

One-Bit Measurements in Microwave Resonators

One-bit compressed sensing via total variation minimization method

The goal of standard one-bit compressed sensing (1-bit CS) is to recover sparse signals with high fidelity from binary measurements that retain only their sign information. Besides sparsity, there are numerous signals consisting of other structures, such as signals consisting of piecewise constants (i.e., its gradient is sparse). This paper aims to address the recovery of such signals from one-bit measurements. Motivated by the superior performance of total variation (TV) minimization in conventional CS methods, this paper proposes the TV minimization in the 1-bit CS case. The proposed approaches can recover the direction of gradient sparse signals from ordinary one-bit measurements and the magnitude of gradient sparse signals from the thresholded one-bit measurements. We theoretically provide the upper bounds on the recovery errors, ensuring the effectiveness of the proposed methods. In practice, three algorithms: hard thresholding taut-string (HTTS), 1-bit total variation ADMM (TV-ADMM) and Second-Order Cone Programming (SOCP) are proposed to solve the proposed models. The promising performance of the new approach is supported by a series of simulated and real data examples.

Adaptive recovery of dictionary-sparse signals using binary measurements

One-bit compressive sensing (CS) is an advanced version of sparse recovery in which the sparse signal of interest can be recovered from extremely quantized measurements. Namely, only the sign of each measure is available to us. The ground-truth signal is not sparse in many applications yet can be represented in a redundant dictionary. A strong line of research has addressed conventional CS in this signal model, including its extension to one-bit measurements. However, one-bit CS suffers from an extremely large number of required measurements to achieve a predefined reconstruction error level. A common alternative to resolve this issue is to exploit adaptive schemes. We utilize an adaptive sampling strategy to recover dictionary-sparse signals from binary measurements in this work. A multi-dimensional threshold is proposed for this task to incorporate the previous signal estimates into the current sampling procedure. This strategy substantially reduces the required number of measurements for exact recovery. We show that the proposed algorithm considerably outperforms the state-of-the-art approaches through rigorous and numerical analysis.

One-Bit Constrained Measurements of Parametric Signals

This paper introduces a novel estimation framework for the parameters in a linear-in-the-parameters estimation problem, when one-bit measurements are processed. We consider a periodic signal, whose components have unknown amplitudes and phases. This signal is assumed to be quantized by a single comparator, under various problem settings. To provide enough information for the estimation of the signal parameters based on one-bit quantized signal measurements, the threshold in the one-bit comparator is assumed known. Several problem settings are considered. They include synchronous/asynchronous sampling, presence or absence of deterministic or stochastic dither, presence or absence of additive noise. The results obtained by applying three alternative methods are compared and analyzed. Experimental results on a two-component 1.2 GHz signal validate the theoretical analysis. It is shown that several estimation approaches are available, which provide different performance levels, in terms of final estimation accuracy and computational complexity.

LoRD-Net: Unfolded Deep Detection Network With Low-Resolution Receivers

The need to recover high-dimensional signals from their noisy low-resolution quantized measurements is widely encountered in communications and sensing. In this paper, we focus on the extreme case of one-bit quantizers, and propose a deep detector entitled LoRD-Net for recovering information symbols from one-bit measurements. Our method is a model-aware data-driven architecture based on deep unfolding of first-order optimization iterations. LoRD-Net has a task-based architecture dedicated to recovering the underlying signal of interest from the one-bit noisy measurements without requiring prior knowledge of the channel matrix through which the one-bit measurements are obtained. The proposed deep detector has much fewer parameters compared to black-box deep networks due to the incorporation of domain-knowledge in the design of its architecture, allowing it to operate in a data-driven fashion while benefiting from the flexibility, versatility, and reliability of model-based optimization methods. LoRD-Net operates in a blind fashion, which requires addressing both the non-linear nature of the data-acquisition system as well as identifying a proper optimization objective for signal recovery. Accordingly, we propose a two-stage training method for LoRD-Net, in which the first stage is dedicated to identifying the proper form of the optimization process to unfold, while the latter trains the resulting model in an end-to-end manner. We numerically evaluate the proposed receiver architecture for one-bit signal recovery in wireless communications and demonstrate that the proposed hybrid methodology outperforms both data-driven and model-based state-of-the-art methods, while utilizing small datasets, on the order of merely $\sim 500$ samples, for training.

On the Performance of One-Bit DoA Estimation via Sparse Linear Arrays

Direction of Arrival (DoA) estimation using Sparse Linear Arrays (SLAs) has recently gained considerable attention in array processing thanks to their capability to provide enhanced degrees of freedom in resolving uncorrelated source signals. Additionally, deployment of one-bit Analog-to-Digital Converters (ADCs) has emerged as an important topic in array processing, as it offers both a low-cost and a low-complexity implementation. In this paper, we study the problem of DoA estimation from one-bit measurements received by an SLA. Specifically, we first investigate the identifiability conditions for the DoA estimation problem from one-bit SLA data and establish an equivalency with the case when DoAs are estimated from infinite-bit unquantized measurements. Towards determining the performance limits of DoA estimation from one-bit quantized data, we derive a pessimistic approximation of the corresponding Cram\'{e}r-Rao Bound (CRB). This pessimistic CRB is then used as a benchmark for assessing the performance of one-bit DoA estimators. We also propose a new algorithm for estimating DoAs from one-bit quantized data. We investigate the analytical performance of the proposed method through deriving a closed-form expression for the covariance matrix of the asymptotic distribution of the DoA estimation errors and show that it outperforms the existing algorithms in the literature. Numerical simulations are provided to validate the analytical derivations and corroborate the resulting performance improvement.

One-Bit Radar Imaging Via Adaptive Binary Iterative Hard Thresholding

One-bit radar imaging has received much attention due to the low cost of the analog-to-digital converter (ADC) and the low storage and transmission burden. The one-bit radar imaging results using conventional one-bit compressive sensing (CS) algorithms, such as the binary iterative hard thresholding (BIHT) algorithm, are always contaminated by artifacts, especially under noisy conditions. In this paper, we present an adaptive-BIHT (A-BIHT) algorithm to mitigate artifacts and improve the one-bit radar imaging performance. In the proposed A-BIHT algorithm, we devise a quantization level parameter, and update the quantization level parameter and the imaging result in an iterative fashion by employing a relaxed quantization consistency condition. The relaxed quantization consistency condition is designed to allow some noisy one-bit measurements to be inconsistent. In this way, the proposed algorithm mitigates the effect of noise on consistent reconstruction, and thus, alleviates artifacts and improves the imaging quality. Simulations and experimental results demonstrate that the proposed A-BIHT method can provide superior imaging performance with suppressed artifacts compared with the conventional BIHT method.

Gridless One-Bit Direction-of-Arrival Estimation Via Atomic Norm Denoising

In this letter, a gridless one-bit direction-of-arrival (DOA) estimation approach with one-snapshot is proposed to be robust against the off-grid errors and sign inconsistency because of the one-bit measurements corrupted by additive noise. Different with the existing off-grid DOA estimators, an atomic norm minimization is considered to mitigate the grid mismatch with atoms instead of pre-divided discretized dictionary. Then, the sign inconsistency of one-bit measurements is solved by introducing a linear loss function. The resulting optimization problem is convex and can be equivalent to a semidefinite programming (SDP) problem, which, however, is computational demanding. Therefore, alternating direction multiplier method (ADMM) is employed to speed up the implementation. To avoid the spectrum searching, an effective dual polynomial method is developed with closed-form solution for DOA estimation. Meanwhile, the proposed method does not require $a~prior$ information of the number of targets. Simulation results demonstrate the superiority and effectiveness of the proposed method.

Robust Reconstruction of Block Sparse Signals from Adaptively One‐Bit Measurements

Though various theoretical results and algorithms have been proposed in one-bit Compressed sensing (1-bit CS), there are few studies on more structured signals, such as block sparse signals. We address the problem of recovering block sparse signals from one-bit measurements. We first propose two recovery schemes, one based on second-order cone programming and the other based on hard thresholding, for common non-adaptively thresholded one-bit measurements. Note that the worst-case error in recovering sparse signals from non-adaptively thresholded one-bit measurements is bounded below by a polynomial of oversampling factor. To break the limit, we introduce a recursive strategy that allows the thresholds in quantization to be adaptive to previous measurements at each iteration. Using the scheme, we propose two iterative algorithms and show that corresponding recovery errors are both exponential functions of the oversampling factor. Several simulations are conducted to reveal the superiority of our methods to existing approaches.

Subspace and sparse reconstruction based near-field sources localization in uniform linear array

This work studies the near-field localization problem using a symmetry uniform linear array (ULA). To decouple the range and direction of arrival (DOA), by exploiting the symmetry property of the array, two spatial correlation sequences are constructed, where each sequence only corresponds to one parameter, i.e., DOA or range. After decoupling, an attractive property is that the resulting sequences still share the similar ULA spatial structure. To perform DOA estimation, two approaches have been developed. The first one is based on the power of R (POR) method, which obtains the noise subspace without the eigendecomposition and prior information of the number of sources. The second one is developed using atomic norm minimization, which eliminates the off-grid issue. For range estimation, since the constructed sequence that corresponds to the range parameter shares the same spatial structure with the DOA sequence, the developed approaches are readily applied to obtain the range estimates. The proposed approach is also studied under one-bit measurement to show its robustness. The numerical studies including simulation and real-world data demonstrate the performance of the proposed method.

One-bit compressed sensing via ℓp(0 < p < 1)-minimization method

One-bit compressed sensing aims to recover unknown sparse signals from extremely quantized linear measurements which just capture their signs. In this paper, we propose a nonconvex ℓp(0 < p < 1) minimization model for one-bit compressed sensing problem and define the set of ℓp effectively s-sparse signals which contains genuinely s-sparse signals. Utilizing properties of covering number, we show that our method can recover the direction of ℓp effectively s-sparse signals with error order . We also employ thresholded one-bit measurements to estimate the magnitude of signals and prove that any ℓp effectively s-sparse bounded signal x can be estimated using augmented ℓp minimization model and empirical distribution function method respectively. Especially, to recover ℓp effectively s-sparse signals in practice, we introduce an adaptive binary iterative thresholding algorithm which can be utilized without knowing the sparsity of underlying signals. Numerical experiments on both synthetic and real-world data sets are conducted to demonstrate the superiority of our algorithm.

Direction Finding of Electromagnetic Sources on a Sparse Cross-Dipole Array Using One-Bit Measurements

Sparse array arrangement has been widely used in vector-sensor arrays because of increased degree-of-freedoms for identifying more sources than sensors. For large-size sparse vector-sensor arrays, one-bit measurements can further reduce the receiver system complexity by using low-resolution ADCs. In this paper, we present a sparse cross-dipole array with one-bit measurements to estimate Direction of Arrivals (DOA) of electromagnetic sources. Based on the independence assumption of sources, we establish the relation between the covariance matrix of one-bit measurements and that of unquantized measurements by Bussgang Theorem. Then we develop a Spatial-Smooth MUSIC (SS-MUSIC) based method, One-Bit MUSIC (OB-MUSIC), to estimate the DOAs. By jointly utilizing the covariance matrices of two dipole arrays, we find that OB-MUSIC is robust against polarization states. We also derive the Cramer-Rao bound (CRB) of DOA estimation for the proposed scheme. Furthermore, we theoretically analyze the applicability of the independence assumption of sources, which is the fundamental of the proposed and other typical methods, and verify the assumption in typical communication applications. Numerical results show that, with the same number of sensors, one-bit sparse cross-dipole arrays have comparable performance with unquantized uniform linear arrays and thus provide a compromise between the DOA estimation performance and the system complexity.

Joint Angle and Frequency Estimation Using One-Bit Measurements.

Joint angle and frequency estimation is an important branch in array signal processing with numerous applications in radar, sonar, wireless communications, etc. Extensive attention has been paid and numerous algorithms have been developed. However, existing algorithms rely on accurately quantified measurements. In this paper, we stress the problem of angle and frequency estimation for sensor arrays using one-bit measurements. The relationship between the covariance matrices of one-bit measurement and that of the accurately quantified measurement is extended to the tensor domain. Moreover, a one-bit parallel factor analysis (PARAFAC) estimator is proposed. The simulation results show that the angle and frequency estimation can be quickly achieved and correctly paired.

One-Bit Spectrum Sensing in Cognitive Radio Sensor Networks

This paper proposes a spectrum sensing algorithm from one-bit measurements in a cognitive radio sensor network. A likelihood ratio test (LRT) for the one-bit spectrum sensing problem is derived. Different from the one-bit spectrum sensing research work in the literature, the signal is assumed to be a discrete random correlated Gaussian process, where the correlation is only available within immediate successive samples of the received signal. The employed model facilitates the design of a powerful detection criteria with measurable analytical performance. One-bit spectrum sensing criterion is derived for one sensor which is then generalized to multiple sensors. Performance of the detector is analyzed by obtaining closed-form formulas for the probability of false alarm and the probability of detection. The proposed one-bit LRT detector exhibits comparable performance to that of non-one-bit detectors (i.e., quadratic and energy detectors) with the lower computational complexity. Simulation results corroborate the theoretical findings and confirm the efficacy of the proposed detector in the context of highly correlated signals.

One-Bit Compressive Sensing via Schur-Concave Function Minimization

Much effort has been devoted to recovering sparse signals from one-bit measurements in recent years. However, it is still quite challenging to recover signals with high fidelity, which is desired in practical one-bit compressive sensing (1-bit CS) applications. We introduce the notion of Schur-concavity in this paper and propose to construct signals by taking advantage of Schur-Concave functions , which are capable of enhancing sparsity. Specifically, the Schur-concave functions can be employed to measure the degree of concentration, and the sparse solutions are obtained at the minima. As a representative of the Schur-concave family, the normalized $\ell _1$ Shannon entropy function ( $\ell _1$ -SEF) is exploited. The resulting optimization problem is nonconvex. Hence, we convert it into a series of weighted ${\ell _1}$ -norm subproblems, which are solved iteratively by a generalized fixed-point continuation algorithm. Numerical results are provided to illustrate the effectiveness and superiority of the proposed 1-bit CS algorithm.

Analysis of hard-thresholding for distributed compressed sensing with one-bit measurements

Abstract A simple hard-thresholding operation is shown to be able to uniformly recover $L$ signals $\textbf{x}_1,...,\textbf{x}_L \in{\mathbb{R}}^n$ that share a common support of size $s$ from $m = \mathscr{O}(s)$ one-bit measurements per signal if $L \geqslant \ln (en/s)$. This result improves the single signal recovery bounds with $m = \mathscr{O}(s\ln (en/s))$ measurements in the sense that asymptotically fewer measurements per non-zero entry are needed. Numerical evidence supports the theoretical considerations.

Distributed Detection of Weak Signals From One-Bit Measurements Under Observation Model Uncertainties

We consider the distributed detection of weak signals from one-bit measurements collected by a sensor network where observation model uncertainties exist at all the sensor nodes. To solve this problem, a one-bit locally most powerful test (LMPT) detector is proposed in this letter. Moreover, asymptotically optimal one-bit quantizers at all the sensor nodes are designed for the proposed one-bit LMPT detector. In this letter, model uncertainties are interpreted as multiplicative noise and its variance represents the strength of model uncertainties. Theoretical analysis indicates that, when the strength of model uncertainties is finite, the proposed detector using one-bit data with $\pi N/2$ sensors approximately achieves the same detection performance as the clairvoyant detector that directly uses analog measurements with $N$ sensors. Simulation results corroborate our theoretical analysis and show that, compared to the one-bit generalized likelihood ratio test detector, the proposed one-bit LMPT detector provides better detection performance in the presence of model uncertainties.

Mono-bit millimeter-wave channel estimation: Bayesian and adaptive quantization frameworks

To achieve a more reasonable cost, employment of a mono-bit quantization structure is essential in wide bandwidth millimeter-wave communications (mmW). However, in mmW channel estimation, one of the critical challenges of mono-bit quantization in each branch of the antenna is the loss of data amplitude. The latest researches offer several approaches to estimate the channel in mono-bit single and multiple antenna structures. Such methods not consider the recovery of channel amplitude and consequently are limited to finding direction. Moreover, they do not provide sparsity into account. Thus, two new schemes are introduced based on a non-adaptive Bayesian algorithm and adaptive sigma–delta modulation (SDM) to tackle these issues. In both methods, we exploit the sparsity of mmWC channel in the angle domain. To extract the sparse-based Laplacian density in case that the sparsity level is unknown, we propose a Bayesian algorithm which employs a hierarchical chain composed of Gaussian and exponential prior. Furthermore, in case that the sparsity level of an application is known or can be estimated, the adaptive mono-bit quantization schemes is proposed which retrieves the amplitude of the sparse channel by the aid of SDM and CS tools. Simulation results show that the adaptive mono-bit estimator outperforms the non-adaptive Bayesian approach comparing the mean square error as an index. Also, the proposed adaptive method, especially when a sufficient number of one-bit measurements are available, can asymptotically converge into optimum full-bit observations with lower computational complexity.