JZUS - Journal of Zhejiang University SCIENCE

Frontiers of Information Technology & Electronic Engineering 2020 Vol.21 No.9 P.1302-1307

http://doi.org/10.1631/FITEE.1900463

An improved subspace weighting method using random matrix theory

Author(s): Yu-meng Gao, Jiang-hui Li, Ye-chao Bai, Qiong Wang, Xing-gan Zhang
Affiliation(s): School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China; more
Corresponding email(s): ychbai@nju.edu.cn
Key Words: Direction of arrival, Signal subspace, Random matrix theory

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Abstract: The weighting subspace fitting (WSF) algorithm performs better than the multi-signal classification (MUSIC) algorithm in the case of low signal-to-noise ratio (SNR) and when signals are correlated. In this study, we use the random matrix theory (RMT) to improve WSF. RMT focuses on the asymptotic behavior of eigenvalues and eigenvectors of random matrices with dimensions of matrices increasing at the same rate. The approximative first-order perturbation is applied in WSF when calculating statistics of the eigenvectors of sample covariance. Using the asymptotic results of the norm of the projection from the sample covariance matrix signal subspace onto the real signal in the random matrix theory, the method of calculating WSF is obtained. Numerical results are shown to prove the superiority of RMT in scenarios with few snapshots and a low SNR.

基于随机矩阵理论的子空间加权改良算法

高雨濛¹，李姜辉²，柏业超¹，王琼¹，张兴敢¹
¹南京大学电子科学与工程学院，中国南京市，210023
²南安普顿大学声振研究所，英国南安普顿市，SO171BJ

摘要：在低信噪比及信号相关情况下，加权子空间拟合（WSF）算法的性能优于多信号分类（MUSIC）算法。本文使用随机矩阵理论（RMT）改善加权子空间拟合。随机矩阵理论研究随机矩阵维数以同速率增加时，矩阵特征值和特征向量的渐近规律。加权子空间拟合中，运用近似一阶扰动计算样本协方差矩阵特征向量的统计特性。利用随机矩阵理论中关于样本协方差矩阵信号子空间向真实信号投影的范数的渐进结果，获得加权子空间拟合计算方法。仿真结果表明，在低快拍数及低信噪比情况下，本文所提方法具有优越性。

关键词：波达方向；信号子空间；随机矩阵理论

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