Table of Contents Author Guidelines Submit a Manuscript
International Journal of Antennas and Propagation
Volume 2017, Article ID 9072421, 7 pages
https://doi.org/10.1155/2017/9072421
Research Article

A Truncated Singular Value Decomposition Enhanced Nested Complex Source Beam Method

Department of Microwave Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China

Correspondence should be addressed to Lianning Song; moc.liamxof@gnosgninnail

Received 15 May 2017; Accepted 8 June 2017; Published 1 August 2017

Academic Editor: Yumao Wu

Copyright © 2017 Lianning Song and Zaiping Nie. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.