Sparse Planar Array Synthesis Using Matrix Enhancement and Matrix Pencil
Sparse Planar Array Synthesis Using Matrix Enhancement and Matrix Pencil
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DOI：
10.1155/2013/147097
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发表时间：
2013-01-01
影响因子：
1.5
通讯作者：
Liu, Xian-pan
中科院分区：
文献类型：
--
作者：
Zheng, Mei-yan;Chen, Ke-song;Liu, Xian-pan
矩阵增强与矩阵束（MEMP）在现代信号处理中起着重要的作用。本文将MEMP算法应用于二维稀疏阵列综合问题。该方法首先对所需阵列方向图进行采样，形成增强矩阵，作为原始方向图进行近似。在进行奇异值分解（SVD）后，根据先验近似误差丢弃不重要的奇异值，可以获得最少的元素数。其次，对稀疏平面阵列增强矩阵的最优低秩近似矩阵进行广义特征分解，得到特征值，然后利用ESPRIT算法对平面阵列各维特征值进行配对。最后，根据正确的特征值配对，计算出稀疏平面阵的阵元位置和激励。仿真结果表明了该方法的有效性。
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.