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International Journal of Antennas and Propagation
Volume 2013 (2013), Article ID 147097, 7 pages
Research Article

Sparse Planar Array Synthesis Using Matrix Enhancement and Matrix Pencil

1School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
2The Second Research Institute of Civil Aviation of China, Chengdu 610041, China
3School of Astronautics and Aeronautics, University of Electronic Science and Technology of China, Chengdu 611731, China

Received 3 July 2012; Accepted 28 January 2013

Academic Editor: Tat Yeo

Copyright © 2013 Mei-yan Zheng et al. 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.


The matrix enhancement and matrix pencil (MEMP) plays important roles in modern signal processing applications. In this paper, MEMP is applied to attack the problem of two-dimensional sparse array synthesis. Firstly, the desired array radiation pattern, as the original pattern for approximating, is sampled to form an enhanced matrix. After performing the singular value decomposition (SVD) and discarding the insignificant singular values according to the prior approximate error, the minimum number of elements can be obtained. Secondly, in order to obtain the eigenvalues, the generalized eigen-decomposition is employed on the approximate matrix, which is the optimal low-rank approximation of the enhanced matrix corresponding to sparse planar array, and then the ESPRIT algorithm is utilized to pair the eigenvalues related to each dimension of the planar array. Finally, element positions and excitations of the sparse planar array are calculated according to the correct pairing of eigenvalues. Simulation results are presented to illustrate the effectiveness of the proposed approach.