On the Variability of the Sample Covariance Matrix Under Complex Elliptical Distributions

Elias Raninen; Esa Ollila; David E. Tyler

doi:10.1109/LSP.2021.3117443

On the Variability of the Sample Covariance Matrix Under Complex Elliptical Distributions

Elias Raninen, Esa Ollila, David E. Tyler

Rutgers, The State University of New Jersey

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Abstract

We derive the form of the variance-covariance matrix for any affine equivariant matrix-valued statistics when sampling from complex elliptical distributions. We then use this result to derive the variance-covariance matrix of the sample covariance matrix (SCM) as well as its theoretical mean squared error (MSE) when finite fourth-order moments exist. Finally, illustrative examples of the formulas are presented.

Original language	English
Article number	9557837
Pages (from-to)	2092-2096
Number of pages	5
Journal	IEEE Signal Processing Letters
Volume	28
DOIs	https://doi.org/10.1109/LSP.2021.3117443
Publication status	Published - 1 Jan 2021
MoE publication type	A1 Journal article-refereed

Keywords

Covariance matrices
Random variables
Gaussian distribution
Symmetric matrices
Reactive power
Radar signal processing
Maximum likelihood estimation

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AB - We derive the form of the variance-covariance matrix for any affine equivariant matrix-valued statistics when sampling from complex elliptical distributions. We then use this result to derive the variance-covariance matrix of the sample covariance matrix (SCM) as well as its theoretical mean squared error (MSE) when finite fourth-order moments exist. Finally, illustrative examples of the formulas are presented.

KW - Covariance matrices

KW - Random variables

KW - Gaussian distribution

KW - Symmetric matrices

KW - Reactive power

KW - Radar signal processing

KW - Maximum likelihood estimation

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DO - 10.1109/LSP.2021.3117443

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JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

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On the Variability of the Sample Covariance Matrix Under Complex Elliptical Distributions

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Keywords

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