A Truncated Singular Value Decomposition Enhanced Nested Complex Source Beam Method
This work presents a novel matrix compression algorithm to improve the computational efficiency of the nested complex source beam (NCSB) method. The algorithm is based on the application of the truncated singular value decomposition (TSVD) to the multilevel aggregation, translation, and disaggregati...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | International Journal of Antennas and Propagation |
| Online Access: | http://dx.doi.org/10.1155/2017/9072421 |
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| author | Lianning Song Zaiping Nie |
| author_facet | Lianning Song Zaiping Nie |
| author_sort | Lianning Song |
| collection | DOAJ |
| description | This work presents a novel matrix compression algorithm to improve the computational efficiency of the nested complex source beam (NCSB) method. The algorithm is based on the application of the truncated singular value decomposition (TSVD) to the multilevel aggregation, translation, and disaggregation operations in NCSB. In our implementation, the aggregation/disaggregation matrices are solved by the truncated far-field matching, which is based on the directional far-field radiation property of the complex source beams (CSBs). Furthermore, the translation matrices are obtained according to the beam width of CSBs. Due to the high directivity of the radiation patterns of CSBs, all the far-field related interaction matrices are low-ranked. Therefore, TSVD can be employed and a new set of equivalent sources can be constructed by a linear combination of the original CSBs. It is proved that the radiation power of the new sources is proportional to the square of the corresponding singular values. This provides a theoretical guideline to drop the insignificant singular vectors in the calculation. In doing so, the efficiency of the original NCSB method can be much improved while a reasonably good accuracy is maintained. Several numerical tests are conducted to validate the proposed method. |
| format | Article |
| id | doaj-art-e4bf1da3f1f64648a6e255abe062a1da |
| institution | OA Journals |
| issn | 1687-5869 1687-5877 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Antennas and Propagation |
| spelling | doaj-art-e4bf1da3f1f64648a6e255abe062a1da2025-08-20T02:21:18ZengWileyInternational Journal of Antennas and Propagation1687-58691687-58772017-01-01201710.1155/2017/90724219072421A Truncated Singular Value Decomposition Enhanced Nested Complex Source Beam MethodLianning Song0Zaiping Nie1Department of Microwave Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, ChinaDepartment of Microwave Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, ChinaThis work presents a novel matrix compression algorithm to improve the computational efficiency of the nested complex source beam (NCSB) method. The algorithm is based on the application of the truncated singular value decomposition (TSVD) to the multilevel aggregation, translation, and disaggregation operations in NCSB. In our implementation, the aggregation/disaggregation matrices are solved by the truncated far-field matching, which is based on the directional far-field radiation property of the complex source beams (CSBs). Furthermore, the translation matrices are obtained according to the beam width of CSBs. Due to the high directivity of the radiation patterns of CSBs, all the far-field related interaction matrices are low-ranked. Therefore, TSVD can be employed and a new set of equivalent sources can be constructed by a linear combination of the original CSBs. It is proved that the radiation power of the new sources is proportional to the square of the corresponding singular values. This provides a theoretical guideline to drop the insignificant singular vectors in the calculation. In doing so, the efficiency of the original NCSB method can be much improved while a reasonably good accuracy is maintained. Several numerical tests are conducted to validate the proposed method.http://dx.doi.org/10.1155/2017/9072421 |
| spellingShingle | Lianning Song Zaiping Nie A Truncated Singular Value Decomposition Enhanced Nested Complex Source Beam Method International Journal of Antennas and Propagation |
| title | A Truncated Singular Value Decomposition Enhanced Nested Complex Source Beam Method |
| title_full | A Truncated Singular Value Decomposition Enhanced Nested Complex Source Beam Method |
| title_fullStr | A Truncated Singular Value Decomposition Enhanced Nested Complex Source Beam Method |
| title_full_unstemmed | A Truncated Singular Value Decomposition Enhanced Nested Complex Source Beam Method |
| title_short | A Truncated Singular Value Decomposition Enhanced Nested Complex Source Beam Method |
| title_sort | truncated singular value decomposition enhanced nested complex source beam method |
| url | http://dx.doi.org/10.1155/2017/9072421 |
| work_keys_str_mv | AT lianningsong atruncatedsingularvaluedecompositionenhancednestedcomplexsourcebeammethod AT zaipingnie atruncatedsingularvaluedecompositionenhancednestedcomplexsourcebeammethod AT lianningsong truncatedsingularvaluedecompositionenhancednestedcomplexsourcebeammethod AT zaipingnie truncatedsingularvaluedecompositionenhancednestedcomplexsourcebeammethod |