Journal
IEEE SIGNAL PROCESSING LETTERS
Volume 28, Issue -, Pages 2092-2096Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/LSP.2021.3117443
Keywords
Covariance matrices; Random variables; Gaussian distribution; Symmetric matrices; Reactive power; Radar signal processing; Maximum likelihood estimation; Sample covariance matrix; sample variation; mean squared error; complex Gaussian distribution; complex elliptically symmetric distribution
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Funding
- National Science Foundation [DMS-1812198]
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In this study, we investigate the variance-covariance matrix of affine equivariant matrix-valued statistics when sampling from complex elliptical distributions, and derive the variance-covariance matrix of the sample covariance matrix (SCM) along with its theoretical mean squared error (MSE) when finite fourth-order moments exist. Illustrative examples of the formulas are also provided.
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.
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