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Properties of the partial Cholesky factorization and application to reduced-rank adaptive beamforming

Besson, Olivier and Vincent, François Properties of the partial Cholesky factorization and application to reduced-rank adaptive beamforming. (2020) Signal Processing, 167. 107300-107309. ISSN 0165-1684

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Official URL: https://doi.org/10.1016/j.sigpro.2019.107300

Abstract

Reduced-rank adaptive beamforming is a well established and efficient methodology, notably for disturbance covariance matrices which are the sum of a strong low-rank component (interference) and a scaled identity matrix (thermal noise). Eigenvalue or singular decomposition is often used to achieve rank reduction. In this paper, we study and analyze an alternative, namely a partial Cholesky factorization, as a means to retrieve interference subspace and to compute reduced-rank beamformers. First, we study the angles between the true subspace and that obtained from partial Cholesky factorization of the covariance matrix. Then, a statistical analysis is carried out in finite samples. Using properties of partitioned Wishart matrices, we provide a stochastic representation of the beamformer based on partial Cholesky factorization and of the corresponding signal to interference and noise ratio loss. We show that the latter follows approximately a beta distribution, similarly to the beamformer based on eigenvalue decomposition. Finally, numerical simulations are presented which indicate that a reduced-rank adaptive beamformer based on partial Cholesky factorization incurs almost no loss, and can even perform better in some scenarios than its eigenvalue or singular value-based counterpart.

Item Type:Article
HAL Id:hal-02572620
Audience (journal):International peer-reviewed journal
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Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
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Deposited On:13 May 2020 15:36

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