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Eigenvalue estimation of the exponentially windowed sample covariance matrices

Yazdian, E ; Sharif University of Technology | 2016

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  1. Type of Document: Article
  2. DOI: 10.1109/TIT.2016.2562001
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2016
  4. Abstract:
  5. In this paper, we consider an exponentially windowed sample covariance matrix (EWSCM) and propose an improved estimator for its eigenvalues. We use new advances in random matrix theory, which describe the limiting spectral distribution of the large dimensional doubly correlated Wishart matrices to find the support and distribution of the eigenvalues of the EWSCM. We then employ the complex integration and residue theorem to design an estimator for the eigenvalues, which satisfies the cluster separability condition, assuming that the eigenvalue multiplicities are known. We show that the proposed estimator is consistent in the asymptotic regime and has good performance in finite sample size situations. Simulation results show that the proposed estimator outperforms the traditional estimator, significantly. © 2016 IEEE
  6. Keywords:
  7. Array signal processing ; Eigenvalue estimation ; Limiting Spectral Distribution ; Covariance matrix ; Matrix algebra ; Random variables ; Sampling ; Signal processing ; Eigenvalue estimations ; Limiting spectral distributions ; Random matrix theory ; Stieltjes transform ; Eigenvalues and eigenfunctions
  8. Source: IEEE Transactions on Information Theory ; Volume 62, Issue 7 , 2016 , Pages 4300-4311 ; 00189448 (ISSN)
  9. URL: http://ieeexplore.ieee.org/document/7464307/?reload=true