Relevance of polynomial matrix decompositions to broadband blind signal separation

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• 作者：Soydan Redif^a ; ^{sredif@eul.edu.tr} ; Stephan Weiss^b ; ¹ ; ^{stephan.weiss@strath.ac.uk} ; John G. McWhirter^c ; ^{mcwhirterjg@cardiff.ac.uk}
• 关键词：Paraunitary matrix ; Parahermitian matrix ; Polynomial matrix eigenvalue decomposition ; Broadband blind signal separation ; Broadband adaptive beamforming ; Radar ; Sonar
• 刊名：Signal Processing
• 出版年：2017
• 出版时间：May 2017
• 年：2017
• 卷：134
• 期：Complete
• 页码：76-86
• 全文大小：1630 K
• 卷排序：134

文摘

The polynomial matrix EVD (PEVD) is an extension of the conventional eigenvalue decomposition (EVD) to polynomial matrices. The purpose of this article is to provide a review of the theoretical foundations of the PEVD and to highlight practical applications in the area of broadband blind source separation (BSS). Based on basic definitions of polynomial matrix terminology such as parahermitian and paraunitary matrices, strong decorrelation and spectral majorisation, the PEVD and its theoretical foundations will be briefly outlined. The paper then focuses on the applicability of the PEVD and broadband subspace techniques — enabled by the diagonalisation and spectral majorisation capabilities of PEVD algorithms — to define broadband BSS solutions that generalise well-known narrowband techniques based on the EVD. This is achieved through the analysis of new results from three exemplar broadband BSS applications — underwater acoustics, radar clutter suppression, and domain-weighted broadband beamforming — and their comparison with classical broadband methods.