Sequential matrix diagonalization algorithms for polynomial EVD of parahermitian matrices

Soydan Redif, Stephan Weiss, John G. McWhirter

Research output: Contribution to journalArticlepeer-review

88 Citations (Scopus)
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For parahermitian polynomial matrices, which can be used, for example, to characterise space-time covariance in broadband array processing, the conventional eigenvalue decomposition (EVD) can be generalised to a polynomial matrix EVD (PEVD). In this paper, a new iterative PEVD algorithm based on sequential matrix diagonalisation (SMD) is introduced. At every step the SMD algorithm shifts the dominant column or row of the polynomial matrix to the zero lag position and eliminates the resulting instantaneous correlation. A proof of convergence is provided, and it is demonstrated that SMD establishes diagonalisation faster and with lower order operations than existing PEVD algorithms.
Original languageEnglish
Pages (from-to)81-89
Number of pages9
JournalIEEE Transactions on Signal Processing
Issue number1
Early online date4 Nov 2014
Publication statusPublished - 1 Jan 2015


  • parahermitian matrix
  • paraunitary matrix
  • broadband communication
  • covariance matrices
  • jacobian matrices


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