Effect of unitary transformation on Bayesian information criterion for source numbering in array processing

Johnny, M ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1049/iet-spr.2019.0051
  3. Publisher: Institution of Engineering and Technology , 2019
  4. Abstract:
  5. An approach based on unitary transformation for the problem of estimating the number of signals is proposed in this study. Among the information theoretic criteria, the authors focus on the conventional Bayesian information criterion (BIC) in the presence of a uniform linear array. The sample covariance matrix of this array is transformed into the real symmetric one by using a unitary transformation. This real symmetric matrix has real eigenvalues and eigenvectors. Therefore its eigenvalue decomposition needs only real computations. Since the eigenvalues of this real symmetric matrix are equal to the eigenvalues of the sample covariance matrix, by replacing them in BIC formula, the term log-likelihood of BIC does not change but it is obtained by fewer computations. Also by considering the resulting real eigenvectors instead of the complex eigenvectors as a part of free parameters in the parameter vector of the model, they have a reduction in the number of degrees of freedom in the penalty term of BIC. This reduction makes their proposed method outperform BIC. They refer to this approach as unitary BIC. A series of simulations are included to demonstrate the usefulness of this approach. © The Institution of Engineering and Technology 2019
  6. Keywords:
  7. Array processing ; Covariance matrix ; Degrees of freedom (mechanics) ; Information theory ; Linear transformations ; Bayesian information criterion ; Eigenvalue decomposition ; Eigenvalues and eigenvectors ; Information theoretic criterion ; Number of degrees of freedom ; Sample covariance matrix ; Uniform linear arrays ; Unitary transformations ; Eigenvalues and eigenfunctions
  8. Source: IET Signal Processing ; Volume 13, Issue 7 , 2019 , Pages 670-678 ; 17519675 (ISSN)
  9. URL: https://ieeexplore.ieee.org/abstract/document/8833612