A New Quadratic Matrix Inequality Approach to Robust Adaptive Beamforming for General-rank Signal Model
The worst-case robust adaptive beamforming problem for generalrank signal model is considered. This is a nonconvex problem, and an approximate version of it (by introducing a matrix decomposition on the presumed covariance matrix of the desired signal) has been studied in the literature. Herein the...
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| Vydáno v: | Proceedings of the ... IEEE International Conference on Acoustics, Speech and Signal Processing (1998) s. 4335 - 4339 |
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01.05.2019
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| Abstract | The worst-case robust adaptive beamforming problem for generalrank signal model is considered. This is a nonconvex problem, and an approximate version of it (by introducing a matrix decomposition on the presumed covariance matrix of the desired signal) has been studied in the literature. Herein the original robust adaptive beamforming problem is tackled. Resorting to the strong duality of a linear conic program, the robust beamforming problem is reformulated into a quadratic matrix inequality (QMI) problem. There is no general method for solving a QMI problem in the literature. Here- in, employing a linear matrix inequality (LMI) relaxation technique, the QMI problem is turned into a convex semidefinite programming problem. Due to the fact that there often is a positive gap between the QMI problem and its LMI relaxation, a deterministic approximate algorithm is proposed to solve the robust adaptive beamforming in the QMI form. Last but not the least, a sufficient optimality condition for the existence of an optimal solution for the QMI problem is derived. To validate our theoretical results, simulation examples are presented, which also demonstrate the improved performance of the new robust beamformer in terms of the output signal-to-interference- plus-noise ratio. |
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| AbstractList | The worst-case robust adaptive beamforming problem for generalrank signal model is considered. This is a nonconvex problem, and an approximate version of it (by introducing a matrix decomposition on the presumed covariance matrix of the desired signal) has been studied in the literature. Herein the original robust adaptive beamforming problem is tackled. Resorting to the strong duality of a linear conic program, the robust beamforming problem is reformulated into a quadratic matrix inequality (QMI) problem. There is no general method for solving a QMI problem in the literature. Here- in, employing a linear matrix inequality (LMI) relaxation technique, the QMI problem is turned into a convex semidefinite programming problem. Due to the fact that there often is a positive gap between the QMI problem and its LMI relaxation, a deterministic approximate algorithm is proposed to solve the robust adaptive beamforming in the QMI form. Last but not the least, a sufficient optimality condition for the existence of an optimal solution for the QMI problem is derived. To validate our theoretical results, simulation examples are presented, which also demonstrate the improved performance of the new robust beamformer in terms of the output signal-to-interference- plus-noise ratio. |
| Author | Huang, Yongwei Luo, Zhi-Quan Vorobyov, Sergiy A. |
| Author_xml | – sequence: 1 givenname: Yongwei surname: Huang fullname: Huang, Yongwei email: ywhuang@gdut.edu.cn organization: Guangdong Uni. of Technol, University Town, Guangzhou, China – sequence: 2 givenname: Sergiy A. surname: Vorobyov fullname: Vorobyov, Sergiy A. email: svor@ieee.org organization: Aalto Uni, Konemiehentie, Finland – sequence: 3 givenname: Zhi-Quan surname: Luo fullname: Luo, Zhi-Quan email: Luozq@cuhk.edu.cn organization: The Chinese Uni. of Hong Kong (SZ) Longgang, Shenzhen, China |
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| Snippet | The worst-case robust adaptive beamforming problem for generalrank signal model is considered. This is a nonconvex problem, and an approximate version of it... |
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| SubjectTerms | Adaptation models Approximation algorithms Array signal processing Covariance matrices deterministic approximate algorithm general-rank signal model Linear matrix inequalities linear matrix inequality relaxation Matrix decomposition quadratic matrix inequality problem Robust adaptive beamforming Semidefinite programming Signal processing algorithms Signal to noise ratio Speech processing |
| Title | A New Quadratic Matrix Inequality Approach to Robust Adaptive Beamforming for General-rank Signal Model |
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