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A Low-Complexity SBL-Based Method for 2-D DOA Estimation with Two L-Shaped Arrays.

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Title: A Low-Complexity SBL-Based Method for 2-D DOA Estimation with Two L-Shaped Arrays.
Authors: Yang, Jie1 (AUTHOR) jieyang@nwpu.edu.cn, Ma, Jingtao2 (AUTHOR) majingtao@shnu.edu.cn, Liang, Guang3 (AUTHOR) hnlg219@163.com, Gong, Wenbin3 (AUTHOR) Spg3@163.com
Source: Circuits, Systems & Signal Processing. May2026, Vol. 45 Issue 5, p3919-3944. 26p.
Subjects: Direction of arrival estimation, Message passing (Computer science), Signal processing, Machine learning, Statistical models, Compressed sensing, Interpolation, Antenna arrays
Abstract: Sparse Bayesian learning (SBL) has become one of the principal foundations of machine learning. This paper focuses on the SBL algorithm for two-dimensional (2-D) direction-of-arrival (DOA) estimation with a three-dimensional (3-D) antenna array structured by two L-shaped arrays. The high complexity of the conventional expectation–maximization (EM)-based SBL approach, which requires matrix inversion, is addressed first, where we consider the application of a computationally efficient message passing technique to the E-step in the SBL paradigm in lieu of matrix inversion. In particular, we formulate the sparse parameter estimation problem at hand as local message passing on a factor graph, which is used to visualize the structure of the probabilistic model drawn from this formalism. We describe how posterior beliefs at each node in the factor graph can be updated by sending messages between nodes. The advantages of the proposed inference scheme include the ability to capture complex temporal dependencies among multiple measurement vectors, the significantly reduced derivation complexity of the estimation scheme, and fewer approximations required in computing marginal probabilities in the distributed factor graph than in existing message passing techniques because of the assumed conditional Gaussian prior on the signal's coefficients. We then introduce quadratic interpolation for signal direction refinement on the basis of the reconstruction result. Finally, we perform pair matching for all estimated angles by using the spatial relationships of these angles. Simulated examples are provided to demonstrate the close to optimal performance of the derived algorithm. [ABSTRACT FROM AUTHOR]
Copyright of Circuits, Systems & Signal Processing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A Low-Complexity SBL-Based Method for 2-D DOA Estimation with Two L-Shaped Arrays.
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  Data: <searchLink fieldCode="AR" term="%22Yang%2C+Jie%22">Yang, Jie</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jieyang@nwpu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Ma%2C+Jingtao%22">Ma, Jingtao</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> majingtao@shnu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Liang%2C+Guang%22">Liang, Guang</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> hnlg219@163.com</i><br /><searchLink fieldCode="AR" term="%22Gong%2C+Wenbin%22">Gong, Wenbin</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> Spg3@163.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Circuits%2C+Systems+%26+Signal+Processing%22">Circuits, Systems & Signal Processing</searchLink>. May2026, Vol. 45 Issue 5, p3919-3944. 26p.
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  Data: <searchLink fieldCode="DE" term="%22Direction+of+arrival+estimation%22">Direction of arrival estimation</searchLink><br /><searchLink fieldCode="DE" term="%22Message+passing+%28Computer+science%29%22">Message passing (Computer science)</searchLink><br /><searchLink fieldCode="DE" term="%22Signal+processing%22">Signal processing</searchLink><br /><searchLink fieldCode="DE" term="%22Machine+learning%22">Machine learning</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+models%22">Statistical models</searchLink><br /><searchLink fieldCode="DE" term="%22Compressed+sensing%22">Compressed sensing</searchLink><br /><searchLink fieldCode="DE" term="%22Interpolation%22">Interpolation</searchLink><br /><searchLink fieldCode="DE" term="%22Antenna+arrays%22">Antenna arrays</searchLink>
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  Data: Sparse Bayesian learning (SBL) has become one of the principal foundations of machine learning. This paper focuses on the SBL algorithm for two-dimensional (2-D) direction-of-arrival (DOA) estimation with a three-dimensional (3-D) antenna array structured by two L-shaped arrays. The high complexity of the conventional expectation–maximization (EM)-based SBL approach, which requires matrix inversion, is addressed first, where we consider the application of a computationally efficient message passing technique to the E-step in the SBL paradigm in lieu of matrix inversion. In particular, we formulate the sparse parameter estimation problem at hand as local message passing on a factor graph, which is used to visualize the structure of the probabilistic model drawn from this formalism. We describe how posterior beliefs at each node in the factor graph can be updated by sending messages between nodes. The advantages of the proposed inference scheme include the ability to capture complex temporal dependencies among multiple measurement vectors, the significantly reduced derivation complexity of the estimation scheme, and fewer approximations required in computing marginal probabilities in the distributed factor graph than in existing message passing techniques because of the assumed conditional Gaussian prior on the signal's coefficients. We then introduce quadratic interpolation for signal direction refinement on the basis of the reconstruction result. Finally, we perform pair matching for all estimated angles by using the spatial relationships of these angles. Simulated examples are provided to demonstrate the close to optimal performance of the derived algorithm. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Circuits, Systems & Signal Processing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00034-025-03391-4
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        Text: English
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      – SubjectFull: Message passing (Computer science)
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      – SubjectFull: Signal processing
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      – SubjectFull: Machine learning
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      – SubjectFull: Statistical models
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      – SubjectFull: Compressed sensing
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      – SubjectFull: Interpolation
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      – SubjectFull: Antenna arrays
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      – TitleFull: A Low-Complexity SBL-Based Method for 2-D DOA Estimation with Two L-Shaped Arrays.
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            NameFull: Yang, Jie
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            NameFull: Ma, Jingtao
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            NameFull: Liang, Guang
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              M: 05
              Text: May2026
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              Y: 2026
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