On the variability of the sample covariance matrix under complex elliptical distributions

Elias Raninen, Esa Ollila, David Tyler

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 languageEnglish (US)
Pages (from-to)2092-2096
Number of pages5
JournalIEEE Signal Processing Letters
Volume28
DOIs
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics

Keywords

  • Complex Gaussian distribution
  • Complex elliptically symmetric distribution
  • Mean squared error
  • Sample covariance matrix
  • Sample variation

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