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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Bibliographic Details
Published in:Proceedings of the ... IEEE International Conference on Acoustics, Speech and Signal Processing (1998) pp. 4335 - 4339
Main Authors: Huang, Yongwei, Vorobyov, Sergiy A., Luo, Zhi-Quan
Format: Conference Proceeding
Language:English
Published: IEEE 01.05.2019
Subjects:
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
ISSN:2379-190X
Online Access:Get full text
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Summary: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.
ISSN:2379-190X
DOI:10.1109/ICASSP.2019.8683645