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

Esa Ollila Group

Rutgers, The State University of New Jersey

Research output: Contribution to journal › Article › Scientific › peer-review

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

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