Flexible Detection Criterion for Source Enumeration in Array Processing

Two new procedures are proposed using random matrix theory to evaluate theoretically the performance of the Bayesian information criterion (BIC) for source enumeration in array processing. The proposed procedures can predict precisely the estimation results of the BIC. Also, they shed light on the behavior of the BIC. In order to remedy the limitation of the BIC, that is, the BIC tends to underestimate the number of sources by one in most cases, an extra parameter is introduced into the BIC formulation, which results in a new criterion for source enumeration, referred to as the flexible detection criterion (FDC). By carefully choosing this parameter, the FDC is capable of substantially reducing the probability of underestimation, which is validated by theoretical analysis and simulations. Note that the FDC is consistent and has low computational complexity, as the BIC.

[1]  J. W. Silverstein,et al.  No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices , 1998 .

[2]  Thomas C.M. Lee,et al.  Information and Complexity in Statistical Modeling , 2008 .

[3]  Phillip A. Regalia,et al.  On the behavior of information theoretic criteria for model order selection , 2001, IEEE Trans. Signal Process..

[4]  Z. Bai,et al.  CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data , 2017, Statistical Papers.

[5]  M. Viberg,et al.  Two decades of array signal processing research: the parametric approach , 1996, IEEE Signal Process. Mag..

[6]  Y. Selen,et al.  Model-order selection: a review of information criterion rules , 2004, IEEE Signal Processing Magazine.

[7]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[8]  Z. Bai,et al.  Central limit theorems for eigenvalues in a spiked population model , 2008, 0806.2503.

[9]  T. W. Anderson.  ASYMPTOTIC THEORY FOR PRINCIPAL COMPONENT ANALYSIS , 1963 .

[10]  R. Muirhead.  Aspects of Multivariate Statistical Theory , 1982, Wiley Series in Probability and Statistics.

[11]  Calyampudi R. Rao.  Theory of Statistical Inference , 2008 .

[12]  S. Péché,et al.  Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices , 2004, math/0403022.

[13]  Tiee-Jian Wu,et al.  A comparative study of model selection criteria for the number of signals , 2008 .

[14]  Abdefihak M. Zoubir,et al.  Bootstrap Methods and Applications , 2007, IEEE Signal Processing Magazine.

[15]  J. W. Silverstein,et al.  Spectral Analysis of Large Dimensional Random Matrices , 2009 .

[16]  Florian Roemer,et al.  Source enumeration using the bootstrap for very few samples , 2011, 2011 19th European Signal Processing Conference.

[17]  Zhi-Dong Bai,et al.  On rates of convergence of efficient detection criteria in signal processing with white noise , 1989, IEEE Trans. Inf. Theory.

[18]  Abdelhak M. Zoubir,et al.  Source enumeration using the pdf of sample eigenvalues via information theoretic criteria , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[19]  Alan Edelman,et al.  Sample Eigenvalue Based Detection of High-Dimensional Signals in White Noise Using Relatively Few Samples , 2007, IEEE Transactions on Signal Processing.

[20]  Abdelhak M. Zoubir,et al.  Detection of sources using bootstrap techniques , 2002, IEEE Trans. Signal Process..

[21]  Petre Stoica,et al.  On maximum likelihood estimation in factor analysis - An algebraic derivation , 2009, Signal Process..

[22]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[23]  Thomas Kailath,et al.  Detection of signals by information theoretic criteria , 1985, IEEE Trans. Acoust. Speech Signal Process..

[24]  V. Marčenko,et al.  DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES , 1967 .

[25]  Mohammad Reza Aref,et al.  Statistical Performance Analysis of MDL Source Enumeration in Array Processing , 2010, IEEE Transactions on Signal Processing.

[26]  Hagit Messer,et al.  On the use of order statistics for improved detection of signals by the MDL criterion , 2000, IEEE Trans. Signal Process..

[27]  Hong Wang,et al.  On the theoretical performance of a class of estimators of the number of narrow-band sources , 1987, IEEE Trans. Acoust. Speech Signal Process..

[28]  Wenyuan Xu,et al.  Analysis of the performance and sensitivity of eigendecomposition-based detectors , 1995, IEEE Trans. Signal Process..

[29]  Mérouane Debbah,et al.  Eigen-Inference for Energy Estimation of Multiple Sources , 2010, IEEE Transactions on Information Theory.

[30]  D. Lawley.  TESTS OF SIGNIFICANCE FOR THE LATENT ROOTS OF COVARIANCE AND CORRELATION MATRICES , 1956 .

[31]  J. W. Silverstein.  Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices , 1995 .

[32]  Hagit Messer,et al.  Order statistics approach for determining the number of sources using an array of sensors , 1999, IEEE Signal Processing Letters.

[33]  Hong Wang,et al.  On the performance of signal-subspace processing- Part I: Narrow-band systems , 1986, IEEE Trans. Acoust. Speech Signal Process..

[34]  James P. Reilly,et al.  Statistical analysis of the performance of information theoretic criteria in the detection of the number of signals in array processing , 1989, IEEE Trans. Acoust. Speech Signal Process..

[35]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[36]  Hagit Messer,et al.  Submitted to Ieee Transactions on Signal Processing Detection of Signals by Information Theoretic Criteria: General Asymptotic Performance Analysis , 2022 .

[37]  Enes Makalic,et al.  The Consistency of MDL for Linear Regression Models With Increasing Signal-to-Noise Ratio , 2012, IEEE Transactions on Signal Processing.

[38]  Abdelhak M. Zoubir,et al.  Source number estimation in impulsive noise environments using bootstrap techniques and robust statistics , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[39]  Jean Pierre Delmas,et al.  Performance analysis of MDL criterion for the detection of noncircular or/and nonGaussian components , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[40]  Boaz Nadler,et al.  Nonparametric Detection of Signals by Information Theoretic Criteria: Performance Analysis and an Improved Estimator , 2010, IEEE Transactions on Signal Processing.

[41]  P. R. Nelson.  The algebra of random variables , 1979 .

[42]  Raj Rao Nadakuditi,et al.  Fundamental Limit of Sample Generalized Eigenvalue Based Detection of Signals in Noise Using Relatively Few Signal-Bearing and Noise-Only Samples , 2009, IEEE Journal of Selected Topics in Signal Processing.

[43]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[44]  Z. Bai,et al.  On detection of the number of signals in presence of white noise , 1985 .

[45]  D. Hinkley.  On the ratio of two correlated normal random variables , 1969 .

[46]  Boaz Nadler,et al.  Non-Parametric Detection of the Number of Signals: Hypothesis Testing and Random Matrix Theory , 2009, IEEE Transactions on Signal Processing.

[47]  A. Edelman,et al.  Global spectrum fluctuations for the β-Hermite and β-Laguerre ensembles via matrix models , 2005, math-ph/0510043.