DOA estimation of high-dimensional signals based on Krylov subspace and weighted l1-norm

doi:10.23919/JSEE.2023.000145

Journal of Systems Engineering and Electronics ›› 2024, Vol. 35 ›› Issue (3): 532-540.doi: 10.23919/JSEE.2023.000145

• HIGH-DIMENSIONAL SIGNAL PROCESSING • Previous Articles

DOA estimation of high-dimensional signals based on Krylov subspace and weighted l₁-norm

Zeqi YANG¹^,²^,³(), Yiheng LIU¹^,²^,³(), Hua ZHANG¹^,²^,³(), Shuai MA¹^,²^,³(), Kai CHANG⁴(), Ning LIU⁴, Xiaode LYU¹^,²^,*()

¹ Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China
² National Key Laboratory of Microwave Imaging Technology, Beijing 100190, China
³ School of Electronic Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
⁴ Northern Institute of Electronic Equipment, Beijing 100191, China

Received:2023-03-27 Accepted:2023-10-20 Online:2024-06-18 Published:2024-06-19
Contact: Xiaode LYU E-mail:yangzeqi22@mails.ucas.ac.cn;liuyiheng17@mails.ucas.ac.cn;zhanghua211@mails.ucas.ac.cn;mashuai22@mails.ucas.ac.cn;kerkaichance@gmail.com;lvxd@aircas.ac.cn
About author:
YANG Zeqi was born in 2000. She received her B.S. degree from Central South University in 2022. She is working toward her Ph.D. degree in signal and information processing in the University of Chinese Academy of Sciences. Her research interest is radar signal processing. E-mail: yangzeqi22@mails.ucas.ac.cn

LIU Yiheng was born in 1999. He received his B.S. degree from the University of Chinese Academy of Sciences in 2021. He is working toward his Ph.D. degree in signal and information processing in the University of Chinese Academy of Sciences. His research interest is signal processing of passive radar. E-mail: liuyiheng17@mails.ucas.ac.cn

ZHANG Hua was born in 1998. He received his B.S. degree from Nanjing University of Science and Technology in 2021. He is working toward his Ph.D. degree in signal and information processing in University of Chinese Academy of Sciences. His research interests are radar systems and signal processing. E-mail: zhanghua211@mails.ucas.ac.cn

MA Shuai was born in 2000. He received his B.S. degree from Zhengzhou University in 2022. He is working toward his M.E. degree in signal and information processing in the University of Chinese Academy of Sciences. His research interest is radar signal processing. E-mail: mashuai22@mails.ucas.ac.cn

CHANG Kai was born in 1987. He received his Ph.D. degree in precision test and measurement from Beijing Institute of Technology in 2016. He works in Northern Institute of Electronic Equipment. His research interests include information control of multi-unmanned aerial vehicle (UAV) systems and adaptive control. E-mail: kerkaichance@gmail.com

LIU Ning was born in 1965. She received her M.S. degree from the University of Electronic Science and Technology of China. She then joined the Northern Institute of Electronic Equipment, Beijing, China. Her research interests include information control, stochastic geometry, and wireless positioning technology

LYU Xiaode was born in 1969. He received his B.S. and Ph.D. degrees in electrical engineering from Hebei University of Technology, Tianjin, and Xi ’an JiaoTong University, Xi ’an, in 1991 and 1997, respectively. In 1998, he engaged in postdoctoral research in the Department of Electronic Engineering of Beijing Institute of Technology. In 2000, he joined the Aerospace Information Research Institute (AIR, formerly the Institute of Electronics), Chinese Academy of Sciences (CAS). Since 2005, he has been a Principal Investigator (PI) in AIRCAS. His research interests include radar signal processing, airborne/spaceborne synthetic aperture radar (SAR), and applied electromagnetism. E-mail: lvxd@aircas.ac.cn
Supported by:
This work was supported by the National Basic Research Program of China.

Abstract

Abstract:

With the extensive application of large-scale array antennas, the increasing number of array elements leads to the increasing dimension of received signals, making it difficult to meet the real-time requirement of direction of arrival (DOA) estimation due to the computational complexity of algorithms. Traditional subspace algorithms require estimation of the covariance matrix, which has high computational complexity and is prone to producing spurious peaks. In order to reduce the computational complexity of DOA estimation algorithms and improve their estimation accuracy under large array elements, this paper proposes a DOA estimation method based on Krylov subspace and weighted $ {l}_{1} $-norm. The method uses the multistage Wiener filter (MSWF) iteration to solve the basis of the Krylov subspace as an estimate of the signal subspace, further uses the measurement matrix to reduce the dimensionality of the signal subspace observation, constructs a weighted matrix, and combines the sparse reconstruction to establish a convex optimization function based on the residual sum of squares and weighted $ {l}_{1} $-norm to solve the target DOA. Simulation results show that the proposed method has high resolution under large array conditions, effectively suppresses spurious peaks, reduces computational complexity, and has good robustness for low signal to noise ratio (SNR) environment.

Key words: direction of arrival (DOA), compressed sensing (CS), Krylov subspace, $ {l}_{1} $-norm, dimensionality reduction

Zeqi YANG, Yiheng LIU, Hua ZHANG, Shuai MA, Kai CHANG, Ning LIU, Xiaode LYU. DOA estimation of high-dimensional signals based on Krylov subspace and weighted l₁-norm[J]. Journal of Systems Engineering and Electronics, 2024, 35(3): 532-540.

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Algorithm	Algorithm complexity
MUSIC	${ { O} }\left(N{M}^{2}+{M}^{3}\right)$
$ {l}_{1} $-SVD	${ { O} }\left({N}^{3}\right)+{ { O} }\left({\left(N\times K\right)}^{3}\right)$
The proposed algorithm	${ { O} }\left(KMN\right)+{ { O} }\left({\left(P\times K\right)}^{3}\right)$

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DOA estimation of high-dimensional signals based on Krylov subspace and weighted l₁-norm

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