• ELECTRONICS TECHNOLOGY •

### Fast and accurate covariance matrix reconstruction for adaptive beamforming using Gauss-Legendre quadrature

Shuai LIU(), Xue ZHANG(), Fenggang YAN*(), Jun WANG(), Ming JIN()

1. 1 School of Information Science and Engineering, Harbin Institute of Technology, Weihai 264209, China
• Received:2020-02-27 Online:2021-02-18 Published:2021-03-16
• Contact: Fenggang YAN E-mail:liu_shuai_boy@163.com;xuezhang1218@163.com;yfglion@163.com;hitwangjun@126.com;jinming0987@183.com
• About author:|LIU Shuai was born in 1980. He received his B.E. and M.S. degrees from Northwestern Polytechnical University, China, in 2002 and 2005, respectively, and Ph.D. degree in information and communication engineering from Harbin Institute of Technology (HIT), Weihai, China, in 2013. Since 2013, he has been an associate professor of the School of Information Science and Engineering, HIT, Weihai, China. His current research interests are robust adaptive beamforming, conformal array, and polarization sensitive array signal processing. E-mail: liu_shuai_boy@163.com||ZHANG Xue was born in 1994. She received her B.S. degree in information engineering from Qingdao University of Science and Technology College, Qingdao, China, in 2018. She is currently pursuing her M.S. degree in School of Information Science and Engineering, Harbin Institute of Technology, Weihai, China. Her main research interests are array signal processing, and robust adaptive beamforming. E-mail: xuezhang1218@163.com||YAN Fenggang was born in 1983. He received his B.E. degree from Xi’an Jiaotong University, Xi’an, China, in 2005, M.S. degree from the Graduate School of Chinese Science of Academic, Bejing, China, in 2008, and Ph.D. degree from Harbin Institute of Technology (HIT), Harbin, China, in 2014, all in information and communication engineering. From July 2008 to March 2011, he was a research associate with the 5th Research Institute of China Aerospace Science and Technology Corporation, where his research mainly focused on the processing of remote sensing images. Since January 2021, he has been a professor of the School of Information Science and Engineering, HIT, Weihai, China. His current research interests include array signal processing and statistical performance analysis. E-mail: yfglion@163.com||WANG Junwas born in 1976. He received his Ph.D. degree in information and communication engineering from Harbin Institute of Technology (HIT), Harbin, China, in 2014. Since 2015, he has been an associate professor of the School of Information Science and Engineering, HIT, Weihai, China. His current research interests mainly focus on radar signal processing. E-mail: hitwangjun@126.com||JIN Ming was born in 1968. He received his B.E., M.S., and Ph.D. degrees in information and communication engineering from Harbin Institute of Technology (HIT), China, in 1990, 1998, and 2004, respectively. From 1998 to 2004, he was with the Department of Electronics Information Engineering, HIT. Since 2006, he has been a professor of the School of Information Science and Engineering, HIT, Weihai, China. His current research interests include array signal processing, parallel signal processing, and radar polarimetry. E-mail: jinming0987@163.com
• Supported by:
This work was supported by the National Natural Science Foundation of China (61871149; 61971159; 62071144)

Abstract:

Most of the reconstruction-based robust adaptive beamforming (RAB) algorithms require the covariance matrix reconstruction (CMR) by high-complexity integral computation. A Gauss-Legendre quadrature (GLQ) method with the highest algebraic precision in the interpolation-type quadrature is proposed to reduce the complexity. The interference angular sector in RAB is regarded as the GLQ integral range, and the zeros of the three-order Legendre orthogonal polynomial is selected as the GLQ nodes. Consequently, the CMR can be efficiently obtained by simple summation with respect to the three GLQ nodes without integral. The new method has significantly reduced the complexity as compared to most state-of-the-art reconstruction-based RAB techniques, and it is able to provide the similar performance close to the optimal. These advantages are verified by numerical simulations.