Space-time covariance matrix estimation: loss of algebraic multiplicities of Eigenvalues

Faizan A. Khattak; Stephan Weiss; Ian K. Proudler; John G. McWhirter

Space-time covariance matrix estimation: loss of algebraic multiplicities of Eigenvalues

Faizan A. Khattak, Stephan Weiss, Ian K. Proudler, John G. McWhirter

Electronic And Electrical Engineering

Research output: Contribution to conference › Paper › peer-review

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Abstract

Parahermitian matrices in almost all cases admit an eigenvalue decomposition (EVD) with analytic eigenvalues. This decomposition is key in order to extend the utility of the EVD from narrowband multichannel signal processing problems to the broadband case, where the EVD factors are frequency dependent. In the frequency domain, the ground truth analytic eigenvalues may intersect, in this paper we discuss why with estimated space-time covariance matrices such algebraic multiplicities are lost, resulting with probability one in analytic, spectrally majorised eigenvalues that no longer intersect. We characterise this phenomenon and some of its profound consequences for broadband multichannel array signal processing.

Original language	English
Pages	975-979
Number of pages	5
Publication status	Published - 3 Nov 2022
Event	56th Asilomar Conference on Signals, Systems, and Computers - Pacific Grove, CA, United States Duration: 30 Nov 2021 → 3 Nov 2022 https://www.asilomarsscconf.org/

Conference

Conference	56th Asilomar Conference on Signals, Systems, and Computers
Abbreviated title	Asilomar'22
Country/Territory	United States
Period	30/11/21 → 3/11/22
Internet address	https://www.asilomarsscconf.org/

Keywords

space-time covariance
polynomial eigenvalue decomposition
analytic eigenvalue decomposition
estimation

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Access to Document

Khattak-etal-ACSSC-2022-Space-time-covariance-matrix-estimation-loss-of-algebraic-multiplicitiesAccepted author manuscript, 863 KBLicence: Strath_1

1 Finished

Signal Processing in the Information Age (UDRC III)
Weiss, S. (Principal Investigator) & Stankovic, V. (Co-investigator)
EPSRC (Engineering and Physical Sciences Research Council)
1/07/18 → 31/03/24
Project: Research

3 Article
1 Paper

Eigenvalue decomposition of a parahermitian matrix: extraction of analytic eigenvalues
Weiss, S., Proudler, I. K. & Coutts, F. K., 28 Feb 2021, In: IEEE Transactions on Signal Processing. 69, p. 722-737 16 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
36 Citations (Scopus)

123 Downloads (Pure)
Sample space-time covariance matrix estimation
Delaosa, C., Pestana, J., Goddard, N. J., Somasundaram, S. & Weiss, S., 16 May 2019, p. 8033-8037. 5 p.
Research output: Contribution to conference › Paper › peer-review

Open Access
File
Correction to "On the existence and uniqueness of the eigenvalue decomposition of a parahermitian matrix"
Weiss, S., Pestana, J., Proudler, I. K. & Coutts, F. K., 1 Dec 2018, In: IEEE Transactions on Signal Processing. 66, 23, p. 6325-6327 3 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
36 Citations (Scopus)

43 Downloads (Pure)

Cite this

@conference{622bbc42c4fa41b3bf90fbebe83730b8,

title = "Space-time covariance matrix estimation: loss of algebraic multiplicities of Eigenvalues",

abstract = "Parahermitian matrices in almost all cases admit an eigenvalue decomposition (EVD) with analytic eigenvalues. This decomposition is key in order to extend the utility of the EVD from narrowband multichannel signal processing problems to the broadband case, where the EVD factors are frequency dependent. In the frequency domain, the ground truth analytic eigenvalues may intersect, in this paper we discuss why with estimated space-time covariance matrices such algebraic multiplicities are lost, resulting with probability one in analytic, spectrally majorised eigenvalues that no longer intersect. We characterise this phenomenon and some of its profound consequences for broadband multichannel array signal processing.",

keywords = "space-time covariance, polynomial eigenvalue decomposition, analytic eigenvalue decomposition, estimation",

author = "Khattak, {Faizan A.} and Stephan Weiss and Proudler, {Ian K.} and McWhirter, {John G.}",

year = "2022",

month = nov,

day = "3",

language = "English",

pages = "975--979",

note = "56th Asilomar Conference on Signals, Systems, and Computers, Asilomar'22 ; Conference date: 30-11-2021 Through 03-11-2022",

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TY - CONF

T1 - Space-time covariance matrix estimation

T2 - 56th Asilomar Conference on Signals, Systems, and Computers

AU - Khattak, Faizan A.

AU - Weiss, Stephan

AU - Proudler, Ian K.

AU - McWhirter, John G.

PY - 2022/11/3

Y1 - 2022/11/3

N2 - Parahermitian matrices in almost all cases admit an eigenvalue decomposition (EVD) with analytic eigenvalues. This decomposition is key in order to extend the utility of the EVD from narrowband multichannel signal processing problems to the broadband case, where the EVD factors are frequency dependent. In the frequency domain, the ground truth analytic eigenvalues may intersect, in this paper we discuss why with estimated space-time covariance matrices such algebraic multiplicities are lost, resulting with probability one in analytic, spectrally majorised eigenvalues that no longer intersect. We characterise this phenomenon and some of its profound consequences for broadband multichannel array signal processing.

AB - Parahermitian matrices in almost all cases admit an eigenvalue decomposition (EVD) with analytic eigenvalues. This decomposition is key in order to extend the utility of the EVD from narrowband multichannel signal processing problems to the broadband case, where the EVD factors are frequency dependent. In the frequency domain, the ground truth analytic eigenvalues may intersect, in this paper we discuss why with estimated space-time covariance matrices such algebraic multiplicities are lost, resulting with probability one in analytic, spectrally majorised eigenvalues that no longer intersect. We characterise this phenomenon and some of its profound consequences for broadband multichannel array signal processing.

KW - space-time covariance

KW - polynomial eigenvalue decomposition

KW - analytic eigenvalue decomposition

KW - estimation

M3 - Paper

SP - 975

EP - 979

Y2 - 30 November 2021 through 3 November 2022

ER -

Space-time covariance matrix estimation: loss of algebraic multiplicities of Eigenvalues

Abstract

Conference

Keywords

UN SDGs

Access to Document

Fingerprint

Projects

Signal Processing in the Information Age (UDRC III)

Research output

Eigenvalue decomposition of a parahermitian matrix: extraction of analytic eigenvalues

Sample space-time covariance matrix estimation

Correction to "On the existence and uniqueness of the eigenvalue decomposition of a parahermitian matrix"

Cite this