Block normal matrices and Gershgorin-type discs

Kierzkowski, Jakub; Smoktunowicz, Agata

doi:10.13001/1081-3810.1491

Cited by 6 publications

(1 citation statement)

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“…We see that approximatingΣ x by C is equivalent to approximating the eigenvalues of R by r. Gershgorin circles [21] can be used to bound the error of such approximations (replacing the eigenvalues of a matrix by its diagonal elements). Unfortunately, the bounds are much larger than the spread of the statistical distribution of the eigenvalues, indicating that the approximation is too crude to directly derive the distribution of Γ.…”

Section: A Circulant Approximation For Toeplitz Matricesmentioning

confidence: 99%

Scaled Largest Eigenvalue Detection for Stationary Time-Series

Renard¹,

Lampe

Horlin

2016

IEEE Trans. Signal Process.

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Abstract-This paper studies the performance of the Scaled Largest Eigenvalue (SLE) detector used for the detection of stationary time-series. We focus on a singleantenna setup and a blind detection scenario (neither the signal covariance, nor the noise variance are known). The SLE detector has received much attention in the context of Cognitive Radios (CR) due to its simplicity, good performance and robustness to noise level uncertainties. Specifically, our goal is to analyze the detector based on the statistic Γ =, where λ1 ≥ λ2 ≥ . . . ≥ λp represent the ordered eigenvalues of the sample covariance matrix. We derive a large-sample-size closed-form approximation for the test statistic which allows us to derive its statistical distribution and set up the detector to achieve the required Probability of False-Alarm (P f a ) and Probability of Detection (P d ). We also study the robustness of the detector in the presence of noise uncertainty and impulsive-noise and investigate the benefits of the spatial sign filter for such scenarios.

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Section: A Circulant Approximation For Toeplitz Matricesmentioning

confidence: 99%