Target parameter estimation in active sensing, and particularly radar signal processing, is a long-standing problem that has been studied extensively. In this paper, we propose a novel approach for target parameter estimation in cases where one-bit analog-to-digital-converters (ADCs), also known as signal comparators with time-varying thresholds, are employed to sample the received radar signal instead of high-resolution ADCs. The considered problem has potential applications in the design of inexpensive radar and sensing devices in civilian applications, and can likely pave the way for future radar systems employing low-resolution ADCs for faster sampling and high-resolution target determination. We formulate the target estimation as a multivariate weighted-least-squares optimization problem that can be solved in a cyclic manner. Numerical results are provided to exhibit the effectiveness of the proposed algorithms.

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 Cramér-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.

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.

The recovery of the input signal covariance values from its one-bit sampled counterpart has been deemed a challenging task in the literature. To deal with its difficulties, some assumptions are typically made to find a relation between the input covariance matrix and the autocorrelation values of the one-bit sampled data. This includes the arcsine law and the recently proposed modified arcsine law which unleashes a promising performance in covariance recovery by taking advantage of time-varying sampling thresholds. However, the modified arcsine law also assumes input signals are stationary, which is typically a simplifying assumption for real-world applications. In fact, in many signal processing applications, the input signals are readily known to be non-stationary with a non-Toeplitz covariance matrix. In this paper, we propose an approach to extending the arcsine law to the case where one-bit ADCs apply time-varying thresholds while dealing with input signals that originate from a non-stationary process. In particular, the recovery methods are shown to accurately recover the time-varying variance and autocorrelation values. Furthermore, we extend the formulation of the Bussgang law to the case where non-stationary input signals are considered.

Sequences with low autocorrelation sidelobes are needed in a diverse set of active sensing applications, including radar, sonar, communications, and biomedicine. The recently proposed and widely adopted methods of the Cyclic Algorithm-New (CAN) and Periodic CAN (PeCAN) are known to be computationally efficient, particularly as they employ fast Fourier transform (FFT) operations to design unimodular (i.e., unit-modulus) sequences with good autocorrelation properties. However, these cyclic algorithms cannot be directly used to design binary sequences with good autocorrelation properties due to the extremely multimodal nature of the associated optimization objectives. In this paper, we combine the notion of converging functions with the CAN and PeCAN frameworks, to considerably enhance their performances for binary sequence synthesis. Moreover, the convergence of these algorithms are established and their convergence properties are thoroughly analyzed. Numerical examples are provided to show that the proposed algorithms can outperform existing approaches for aperiodic and periodic binary sequence synthesis, especially for long sequence designs.

In this work, we consider the problem of one-bit deep compressive sensing from both a system design and a signal recovery perspective. In particular, we develop hybrid model-based deep learning architectures based on the deep unfolding methodology. We further interpret the overall data-acquisition and signal recovery modules as an auto-encoder structure allowing for learning task-specific sensing matrix, quantization thresholds, as well as the latent-parameters of iterative first-order optimization algorithms specifically designed for the problem of one-bit sparse signal recovery. The proposed model-based deep architectures have the ability to adaptively learn the proper quantization thresholds, paving the way for amplitude recovery in one-bit compressive sensing. We further show that the proposed methodology implicitly learns task-specific sensing matrices with very low coherence, which is highly desirable in a compressive sensing setting. Due to the model-based nature of the proposed deep architecture, it enjoys from the interpretability and versatility of model-based techniques as well as benefiting from the expressive power of data-driven methods. Specifically, owing to its model-based nature, it has far fewer parameters and requires far less samples for training as compared to black-box machine learning models. Our results demonstrate a significant improvement compared to state-of-the-art algorithms.