Journal of Systems Engineering and Electronics ›› 2023, Vol. 34 ›› Issue (6): 1483-1489.doi: 10.23919/JSEE.2022.000123

• ELECTRONICS TECHNOLOGY • Previous Articles     Next Articles

An effective array beamforming scheme based on branch-and-bound algorithm

Xiaodong YE(), Li LI(), Hao WANG(), Shifei TAO()   

  1. 1 School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
  • Received:2021-10-22 Accepted:2022-06-13 Online:2023-12-18 Published:2023-12-29
  • Contact: Shifei TAO;;;
  • About author:
    YE Xiaodong was born in 1967. He received his B.S., M.S., and Ph.D. degrees from Nanjing University of Posts and Telecommunications in 1990, Nanjing Institute of Electric Technology in 1993, and Nanjing University of Aeronautics and Astronautics in 1997, respectively. He was a postdoctor in Nanjing University of Science and Technology (NJUST) from 1997 to 1999. He has been an associate professor in NJUST since 1999. His current research interests involve radar data analysis, modern signal processing, and artificial intelligence technique.E-mail:

    LI Li was born in 1996. She received her B.S. degree in electronic information engineering from Henan Polytechnic University, Henan, China, in 2019. She is currently pursuing her M.S. degree in electronics and communication engineering with Nanjing University of Science and Technology, Nanjing, China. Her current research interests include signal processing and convex optimization. E-mail:

    WANG Hao was born in 1980. He received his B.S. and Ph.D. degrees in electrical engineering from Nanjing University of Science and Technology, Nanjing, China, in 2002 and 2009, respectively. He is currently an associate professor with the School of Electronic and Optical Engineering, Nanjing University of Science and Technology. His current research interests include microstrip antennas for wireless communications and terminal antenna subsystem for compass navigation satellite system. E-mail:

    TAO Shifei was born in 1987. He received his B.S. and Ph.D. degrees from the Department of Communication Engineering, Nanjing University of Science and Technology (NJUST), Nanjing, China, in 2008 and 2014, respectively. Since 2017, he has been with NJUST, and now he is an associate professor in the Department of Communication Engineering, NJUST. From 2015 to 2016, he was a postdoctoral research associate in the Department of Electronic and Computer Engineering, Northeastern University, Boston, USA. His current research interests are electromagnetic theory and antenna technology, and SAR images processing. E-mail:
  • Supported by:
    This work was supported by the National Key Research and Development Program (2021YFB3502500).


In this paper, we propose an effective full array and sparse array adaptive beamforming scheme that can be applied for multiple desired signals based on the branch-and-bound algorithm. Adaptive beamforming for the multiple desired signals is realized by the improved Capon method. At the same time, the sidelobe constraint is added to reduce the sidelobe level. To reduce the pointing errors of multiple desired signals, the array response phase of the desired signal is firstly optimized by using auxilary variables while keeping the response amplitude unchanged. The whole design is formulated as a convex optimization problem solved by the branch-and-bound algorithm. In addition, the beamformer weight vector is penalized with the modified reweighted ${l_1}$-norm to achieve sparsity. Theoretical analysis and simulation results show that the proposed algorithm has lower sidelobe level, higher SINR, and less pointing error than the state-of-the-art methods in the case of a single expected signal and multiple desired signals.

Key words: multiple desired signal, auxiliary variable, branch-and-bound algorithm, reweighted ${l_1}$-norm