Efficient Nyström-Based Unitary Single-Tone 2D DOA Estimation for URA Signals
We propose an efficient Nyström-based unitary subspace method for low-complexity two-dimensional (2D) direction-of-arrival (DOA) estimation in uniform rectangular array (URA) signal processing systems. The conventional high-resolution DOA estimation methods often suffer from excessive computational...
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2025-07-01
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| author | Liping Yuan Ke Wang Fengkai Luan |
| author_facet | Liping Yuan Ke Wang Fengkai Luan |
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| description | We propose an efficient Nyström-based unitary subspace method for low-complexity two-dimensional (2D) direction-of-arrival (DOA) estimation in uniform rectangular array (URA) signal processing systems. The conventional high-resolution DOA estimation methods often suffer from excessive computational complexity, particularly when dealing with large-scale antenna arrays. The proposed method addresses this challenge by combining the Nyström approximation with a unitary transformation to reduce the computational burden while maintaining estimation accuracy. The signal subspace is approximated using a partitioned covariance matrix, and a real-valued transformation is applied to further simplify the eigenvalue decomposition (EVD) process. Furthermore, the linear prediction coefficients are estimated via a weighted least squares (WLS) approach, enabling robust extraction of the angular parameters. The 2D DOA estimates are then derived from these coefficients through a closed-form solution, eliminating the need for exhaustive spectral searches. Numerical simulations demonstrate that the proposed method achieves comparable estimation performance to state-of-the-art techniques while significantly reducing computational complexity. For a fixed array size of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mo>=</mo><mi>N</mi><mo>=</mo><mn>20</mn></mrow></semantics></math></inline-formula>, the proposed method demonstrates significant computational efficiency, requiring less than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>50</mn><mo>%</mo></mrow></semantics></math></inline-formula> of the running time compared to conventional ESPRIT, and only <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>6</mn><mo>%</mo></mrow></semantics></math></inline-formula> of the time required by ML methods, while maintaining similar performance. This makes it particularly suitable for real-time applications where computational efficiency is critical. The novelty lies in the integration of Nyström approximation and unitary subspace techniques, which jointly enable efficient and accurate 2D DOA estimation without sacrificing robustness against noise. The method is applicable to a wide range of array processing scenarios, including radar, sonar, and wireless communications. |
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| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-07-01 |
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| spelling | doaj-art-4c16e074fb0f441fb7c77405a8d623e42025-08-20T03:36:41ZengMDPI AGMathematics2227-73902025-07-011315233510.3390/math13152335Efficient Nyström-Based Unitary Single-Tone 2D DOA Estimation for URA SignalsLiping Yuan0Ke Wang1Fengkai Luan2School of Information Engineering, Wuhan University of Technology, Wuhan 430070, ChinaSchool of Information Engineering, Wuhan University of Technology, Wuhan 430070, ChinaSchool of Information Engineering, Wuhan University of Technology, Wuhan 430070, ChinaWe propose an efficient Nyström-based unitary subspace method for low-complexity two-dimensional (2D) direction-of-arrival (DOA) estimation in uniform rectangular array (URA) signal processing systems. The conventional high-resolution DOA estimation methods often suffer from excessive computational complexity, particularly when dealing with large-scale antenna arrays. The proposed method addresses this challenge by combining the Nyström approximation with a unitary transformation to reduce the computational burden while maintaining estimation accuracy. The signal subspace is approximated using a partitioned covariance matrix, and a real-valued transformation is applied to further simplify the eigenvalue decomposition (EVD) process. Furthermore, the linear prediction coefficients are estimated via a weighted least squares (WLS) approach, enabling robust extraction of the angular parameters. The 2D DOA estimates are then derived from these coefficients through a closed-form solution, eliminating the need for exhaustive spectral searches. Numerical simulations demonstrate that the proposed method achieves comparable estimation performance to state-of-the-art techniques while significantly reducing computational complexity. For a fixed array size of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mo>=</mo><mi>N</mi><mo>=</mo><mn>20</mn></mrow></semantics></math></inline-formula>, the proposed method demonstrates significant computational efficiency, requiring less than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>50</mn><mo>%</mo></mrow></semantics></math></inline-formula> of the running time compared to conventional ESPRIT, and only <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>6</mn><mo>%</mo></mrow></semantics></math></inline-formula> of the time required by ML methods, while maintaining similar performance. This makes it particularly suitable for real-time applications where computational efficiency is critical. The novelty lies in the integration of Nyström approximation and unitary subspace techniques, which jointly enable efficient and accurate 2D DOA estimation without sacrificing robustness against noise. The method is applicable to a wide range of array processing scenarios, including radar, sonar, and wireless communications.https://www.mdpi.com/2227-7390/13/15/2335DOA estimationSVDuniform rectangular arrayNyström methodunitary method |
| spellingShingle | Liping Yuan Ke Wang Fengkai Luan Efficient Nyström-Based Unitary Single-Tone 2D DOA Estimation for URA Signals Mathematics DOA estimation SVD uniform rectangular array Nyström method unitary method |
| title | Efficient Nyström-Based Unitary Single-Tone 2D DOA Estimation for URA Signals |
| title_full | Efficient Nyström-Based Unitary Single-Tone 2D DOA Estimation for URA Signals |
| title_fullStr | Efficient Nyström-Based Unitary Single-Tone 2D DOA Estimation for URA Signals |
| title_full_unstemmed | Efficient Nyström-Based Unitary Single-Tone 2D DOA Estimation for URA Signals |
| title_short | Efficient Nyström-Based Unitary Single-Tone 2D DOA Estimation for URA Signals |
| title_sort | efficient nystrom based unitary single tone 2d doa estimation for ura signals |
| topic | DOA estimation SVD uniform rectangular array Nyström method unitary method |
| url | https://www.mdpi.com/2227-7390/13/15/2335 |
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