An improved subspace weighting method using random matrix theory
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2020 21(9):1302-1307
Frontiers of Information Technology & Electronic Engineering www.jzus.zju.edu.cn; engineering.cae.cn; www.springerlink.com ISSN 2095-9184 (print); ISSN 2095-9230 (online) E-mail: [email protected]
An improved subspace weighting method using random matrix theory∗ Yu-meng GAO1 , Jiang-hui LI2 , Ye-chao BAI†‡1 , Qiong WANG1 , Xing-gan ZHANG1 1School 2Institute
of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, UK † E-mail:
[email protected]
Received Sept. 2, 2019; Revision accepted Dec. 30, 2019; Crosschecked Aug. 10, 2020
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. Key words: Direction of arrival; Signal subspace; Random matrix theory https://doi.org/10.1631/FITEE.1900463 CLC number: TP319
1 Introduction Estimation of the direction of arrival (DOA) of narrow-band signals in array signals has been widely studied (Krim and Viberg, 1996; Zhao et al., 2015). Schmidt (1986) first proposed the multi-signal classification (MUSIC) algorithm, which starts the research of subspace algorithms in array signal processing. Algorithms of MUSIC (Basha et al., 2013) and root MUSIC (Li et al., 2014; Liu et al., 2018) directly give solutions of the parameter estimate and avoid spectral peak search in MUSIC. The process of calculating the weighting matrix is given in the weighting subspace fitting (WSF) method (Viberg et al., 1991; Bai XJ et al., 2014), and the estimation ‡ *
Corresponding author
Project supported by the National Natural Science Foundation of China (No. 61976113) ORCID: Yu-meng GAO, https://orcid.org/0000-0002-30532775; Ye-chao BAI, https://orcid.org/0000-0001-5244-674X c Zhejiang University and Springer-Verlag GmbH Germany, part of Springer Nature 2020
error (Wu and Guo, 2011) of WSF is significantly lower than the error produced by MUSIC with a small number of snapshots and a low signal-to-noise ratio (SNR). Random matrix theory (RMT) (Bai YC et al., 2018; Chen et al., 2018) concentrates on studying the asymptotic behavior of eigenvalues and eigenvectors of random matrices when the dimensions of matrices increase at the same rate, making RMT-based algorithms suitable for
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