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Optimized Hierarchical Nested Array for Enhanced Uniform Degrees of Freedom in Sparse Array DOA Estimation.

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Title: Optimized Hierarchical Nested Array for Enhanced Uniform Degrees of Freedom in Sparse Array DOA Estimation.
Authors: Wang, Guibao1 gbwang@sust.edu.cn, Yu, Keyi1, Wang, Xianghui1, Wang, Shuzhen2,3
Source: Progress in Electromagnetics Research C. 2026, Vol. 167, p21-31. 11p.
Subjects: Degrees of freedom, Direction of arrival estimation, Electromagnetic coupling, Sensor placement, Array processing, Sensor arrays
Abstract: Sparse arrays have been extensively investigated for their capability to enhance degrees of freedom (DOFs). However, a conventional nested array configuration is susceptible to strong mutual coupling (MC), while its achievable uniform DOFs (uDOFs) remains limited. To address these challenges, this paper proposes two optimized hierarchical nested arrays, designated as OHNA-I and OHNA-II. OHNA-I reconstructs the spatial arrangement of subarrays through a hierarchical shifting operation, effectively extending the continuous segment of the difference co-array (DCA). Building on this, OHNA-II further optimizes the subarray geometry via sensor displacement, achieving a better balance between uDOF enhancement and MC suppression, thereby maintaining higher uDOFs while reducing inter-sensor coupling interference. Numerical simulation results demonstrate that, under the same number of physical sensors, the proposed structures -- particularly OHNA-II -- achieve a greater number of uDOFs than existing classical sparse arrays. Furthermore, in scenarios with strong MC, the proposed structure exhibits superior robustness and lower root mean square error (RMSE) in DOA estimation. [ABSTRACT FROM AUTHOR]
Copyright of Progress in Electromagnetics Research C is the property of Electromagnetics Academy 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: Optimized Hierarchical Nested Array for Enhanced Uniform Degrees of Freedom in Sparse Array DOA Estimation.
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  Data: <searchLink fieldCode="AR" term="%22Wang%2C+Guibao%22">Wang, Guibao</searchLink><relatesTo>1</relatesTo><i> gbwang@sust.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Yu%2C+Keyi%22">Yu, Keyi</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Wang%2C+Xianghui%22">Wang, Xianghui</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Wang%2C+Shuzhen%22">Wang, Shuzhen</searchLink><relatesTo>2,3</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Progress+in+Electromagnetics+Research+C%22">Progress in Electromagnetics Research C</searchLink>. 2026, Vol. 167, p21-31. 11p.
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  Data: <searchLink fieldCode="DE" term="%22Degrees+of+freedom%22">Degrees of freedom</searchLink><br /><searchLink fieldCode="DE" term="%22Direction+of+arrival+estimation%22">Direction of arrival estimation</searchLink><br /><searchLink fieldCode="DE" term="%22Electromagnetic+coupling%22">Electromagnetic coupling</searchLink><br /><searchLink fieldCode="DE" term="%22Sensor+placement%22">Sensor placement</searchLink><br /><searchLink fieldCode="DE" term="%22Array+processing%22">Array processing</searchLink><br /><searchLink fieldCode="DE" term="%22Sensor+arrays%22">Sensor arrays</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: Sparse arrays have been extensively investigated for their capability to enhance degrees of freedom (DOFs). However, a conventional nested array configuration is susceptible to strong mutual coupling (MC), while its achievable uniform DOFs (uDOFs) remains limited. To address these challenges, this paper proposes two optimized hierarchical nested arrays, designated as OHNA-I and OHNA-II. OHNA-I reconstructs the spatial arrangement of subarrays through a hierarchical shifting operation, effectively extending the continuous segment of the difference co-array (DCA). Building on this, OHNA-II further optimizes the subarray geometry via sensor displacement, achieving a better balance between uDOF enhancement and MC suppression, thereby maintaining higher uDOFs while reducing inter-sensor coupling interference. Numerical simulation results demonstrate that, under the same number of physical sensors, the proposed structures -- particularly OHNA-II -- achieve a greater number of uDOFs than existing classical sparse arrays. Furthermore, in scenarios with strong MC, the proposed structure exhibits superior robustness and lower root mean square error (RMSE) in DOA estimation. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Progress in Electromagnetics Research C is the property of Electromagnetics Academy 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: 10.2528/PIERC25120702
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      – Code: eng
        Text: English
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        PageCount: 11
        StartPage: 21
    Subjects:
      – SubjectFull: Degrees of freedom
        Type: general
      – SubjectFull: Direction of arrival estimation
        Type: general
      – SubjectFull: Electromagnetic coupling
        Type: general
      – SubjectFull: Sensor placement
        Type: general
      – SubjectFull: Array processing
        Type: general
      – SubjectFull: Sensor arrays
        Type: general
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      – TitleFull: Optimized Hierarchical Nested Array for Enhanced Uniform Degrees of Freedom in Sparse Array DOA Estimation.
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            NameFull: Wang, Guibao
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            NameFull: Yu, Keyi
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            NameFull: Wang, Xianghui
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            NameFull: Wang, Shuzhen
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          Dates:
            – D: 01
              M: 05
              Text: 2026
              Type: published
              Y: 2026
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              Value: 167
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            – TitleFull: Progress in Electromagnetics Research C
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