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1. One-Bit Normalized Scatter Matrix Estimation For Complex Elliptically Symmetric Distributions

   https://doi.org/10.1109/ICASSP40776.2020.9053956  

   Liu, Chun-Lin; Vaidyanathan, P. P. (May 2020, Proc. IEEE Int. Conf. Acoust. Speech, and Signal Proc)

   null (Ed.)

   One-bit quantization has attracted attention in massive MIMO, radar, and array processing, due to its simplicity, low cost, and capability of parameter estimation. Specifically, the shape of the covariance of the unquantized data can be estimated from the arcsine law and onebit data, if the unquantized data is Gaussian. However, in practice, the Gaussian assumption is not satisfied due to outliers. It is known from the literature that outliers can be modeled by complex elliptically symmetric (CES) distributions with heavy tails. This paper shows that the arcsine law remains applicable to CES distributions. Therefore, the normalized scatter matrix of the unquantized data can be readily estimated from one-bit samples derived from CES distributions. The proposed estimator is not only computationally fast but also robust to CES distributions with heavy tails. These attributes will be demonstrated through numerical examples, in terms of computational time and the estimation error. An application in DOA estimation with MUSIC spectrum is also presented. 

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2. On the Asymptotic Performance of One-Bit Co-Array-Based MUSIC

   Sedighi, S.; Shankar, B.; Soltanalian, M.; Ottersten, B. (January 2021, Proceedings of the IEEE International Conference on Acoustics Speech and Signal Processing)

   null (Ed.)

   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. 

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3. Modified Arcsine Law for One-Bit Sampled Stationary Signals with Time-Varying Thresholds

   Eamaz, A; Yeganegi, F.; Soltanalian, M. (January 2021, Proceedings of the IEEE International Conference on Acoustics Speech and Signal Processing)

   null (Ed.)

   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. 

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4. A Comparative Study of Invariance-Aware Loss Functions for Deep Learning-based Gridless Direction-of-Arrival Estimation

   https://doi.org/10.1109/ICASSP49660.2025.10889620  

   Chen, Kuan-Lin; Rao, Bhaskar D (April 2025, IEEE)

   Covariance matrix reconstruction has been the most widely used guiding objective in gridless direction-of-arrival (DoA) estimation for sparse linear arrays. Many semidefinite programming (SDP)-based methods fall under this category. Although deep learning-based approaches enable the construction of more sophisticated objective functions, most methods still rely on covariance matrix reconstruction. In this paper, we propose new loss functions that are invariant to the scaling of the matrices and provide a comparative study of losses with varying degrees of invariance. The proposed loss functions are formulated based on the scale-invariant signal-to-distortion ratio between the target matrix and the Gram matrix of the prediction. Numerical results show that a scale-invariant loss outperforms its non-invariant counterpart but is inferior to the recently proposed subspace loss that is invariant to the change of basis. These results provide evidence that designing loss functions with greater degrees of invariance is advantageous in deep learning-based gridless DoA estimation. 

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5. A Non-Convex Approach To Joint Sensor Calibration And Spectrum Estimation

   https://doi.org/10.1109/SSP.2018.8450691  

   Cho, Myung; Liao, Wenjing; Chi, Yuejie (June 2018, 2018 IEEE Statistical Signal Processing Workshop (SSP))

   Blind sensor calibration for spectrum estimation is the problem of estimating the unknown sensor calibration parameters as well as the parameters-of-interest of the impinging signals simultaneously from snapshots of measurements obtained from an array of sensors. In this paper, we consider blind phase and gain calibration (BPGC) problem for direction-of-arrival estimation with multiple snapshots of measurements obtained from an uniform array of sensors, where each sensor is perturbed by an unknown gain and phase parameter. Due to the unknown sensor and signal parameters, BPGC problem is a highly nonlinear problem. Assuming that the sources are uncorrelated, the covariance matrix of the measurements in a perfectly calibrated array is a Toeplitz matrix. Leveraging this fact, we first change the nonlinear problem to a linear problem considering certain rank-one positive semidefinite matrix, and then suggest a non-convex optimization approach to find the factor of the rank-one matrix under a unit norm constraint to avoid trivial solutions. Numerical experiments demonstrate that our proposed non-convex optimization approach provides better or competitive recovery performance than existing methods in the literature, without requiring any tuning parameters. 

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