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One-bit quantization has attracted considerable attention in signal processing for communications and sensing. The arcsine law is a useful relation often used to estimate the normalized covariance matrix of zero-mean stationary input signals when they are sampled by one-bit analog-to-digital converters (ADCs)---practically comparing the signals with a given threshold level. This relation, however, only considers a zero threshold which can cause a remarkable information loss. For the first time in the literature, this paper introduces an approach to extending the arcsine law to the case where one-bit ADCs apply time-varying thresholds. In particular, the proposed method is shown to accurately recover the variance and autocorrelation of the stationary signals of interest. 

Co-array-based Direction of Arrival (DoA) estimation using Sparse Linear Arrays (SLAs) has recently gained considerable attention in array processing thanks to its capability of providing enhanced degrees of freedom for DoAs that can be resolved. Additionally, deployment of one-bit Analog-to-Digital Converters (ADCs) has become an important topic in array processing, as it offers both a low-cost and a low-complexity implementation. Although the problem of DoA estimation from one-bit SLA measurements has been studied in some prior works, its analytical performance has not yet been investigated and characterized. In this paper, to provide valuable insights into the performance of DoA estimation from one-bit SLA measurements, we derive an asymptotic closed-form expression for the performance of One-Bit Co-Array-Based MUSIC (OBCAB-MUSIC). Further, numerical simulations are provided to validate the asymptotic closed-form expression for the performance of OBCAB-MUSIC and to show an interesting use case of it in evaluating the resolution of OBCAB-MUSIC. 

Parameter estimation from noisy and one-bit quantized data has become an important topic in signal processing, as it offers low cost and low complexity in the implementation. On the other hand, Direction-of-Arrival (DoA) estimation using Sparse Linear Arrays (SLAs) has recently gained considerable interest in array processing due to their attractive capability of providing enhanced degrees of freedom. In this paper, the problem of DoA estimation from one-bit measurements received by an SLA is considered and a novel framework for solving this problem is proposed. The proposed approach first provides an estimate of the received signal covariance matrix through minimization of a constrained weighted least-squares criterion. Then, MUSIC is applied to the spatially smoothed version of the estimated covariance matrix to find the DoAs of interest. Several numerical results are provided to demonstrate the superiority of the proposed approach over its counterpart already propounded in the literature.