Analysis of Large-Scale Periodic Array Antennas by CG-FFT Combined with Equivalent Sub-Array Preconditioner

Huiqing ZHAI
Qiang CHEN
Qiaowei YUAN
Kunio SAWAYA
Changhong LIANG

Publication
IEICE TRANSACTIONS on Communications   Vol.E89-B    No.3    pp.922-928
Publication Date: 2006/03/01
Online ISSN: 1745-1345
DOI: 10.1093/ietcom/e89-b.3.922
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Antennas and Propagation
Keyword: 
large-scale periodic phased arrays,  method of moments (MoM),  block Toeplitz matrices,  conjugate-gradient fast Fourier transform (CG-FFT),  preconditioner of iterative method,  

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Summary: 
This paper presents method that offers the fast and accurate analysis of large-scale periodic array antennas by conjugate-gradient fast Fourier transform (CG-FFT) combined with an equivalent sub-array preconditioner. Method of moments (MoM) is used to discretize the electric field integral equation (EFIE) and form the impedance matrix equation. By properly dividing a large array into equivalent sub-blocks level by level, the impedance matrix becomes a structure of Three-level Block Toeplitz Matrices. The Three-level Block Toeplitz Matrices are further transformed to Circulant Matrix, whose multiplication with a vector can be rapidly implemented by one-dimension (1-D) fast Fourier transform (FFT). Thus, the conjugate-gradient fast Fourier transform (CG-FFT) is successfully applied to the analysis of a large-scale periodic dipole array by speeding up the matrix-vector multiplication in the iterative solver. Furthermore, an equivalent sub-array preconditioner is proposed to combine with the CG-FFT analysis to reduce iterative steps and the whole CPU-time of the iteration. Some numerical results are given to illustrate the high efficiency and accuracy of the present method.