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IET Wireless Sensor Systems

Micro & Nano Letters

The Journal of Engineering

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

Content Provider	IET Digital Library
Author	Johnny, Maryam Aref, Mohammad Reza Razzazi, Farbod
Abstract	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.
Starting Page	670
Ending Page	678
Page Count	9
ISSN	17519675
Volume Number	13
e-ISSN	17519683
Issue Number	Issue 7, Sep (2019)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-spr/13/7
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-spr.2019.0051
Journal	IET Signal Processing
Publisher Date	2019-06-14
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Algebra Approximation Theory Array Processing Authors Focus Bayes Method BIC Formula Conventional Bayesian Information Criterion Covariance Matrices Direction of Arrival Estimation Eigen Values Eigen Values And Eigen Function Eigenvalue Decomposition Graph Theory Information Theoretic Criteria Matrix Algebra Method Outperform BIC Sample Covariance Matrix Set Theory Signal Processing And Detection Source Numbering Statistics Symmetric Matrix Uniform Linear Array Unitary BIC Unitary Transformation
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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