Noncolocated Time-Reversal MUSIC: High-SNR Distribution of Null Spectrum

We derive the asymptotic distribution of the null spectrum of the well-known Multiple Signal Classification (MUSIC) in its computational Time-Reversal (TR) form. The result pertains to a single-frequency noncolocated multistatic scenario and several TR-MUSIC variants are investigated here. The analysis builds upon the first-order perturbation of the singular value decomposition and allows a simple characterization of null-spectrum moments (up to the second order). This enables a comparison in terms of spectrums stability. Finally, a numerical analysis is provided to confirm the theoretical findings.

[1]  Albert Fannjiang,et al.  The MUSIC algorithm for sparse objects: a compressed sensing analysis , 2010, ArXiv.

[2]  Benjamin Friedlander.  A sensitivity analysis of the MUSIC algorithm , 1990, IEEE Trans. Acoust. Speech Signal Process..

[3]  D. Bernstein.  Matrix Mathematics: Theory, Facts, and Formulas , 2009 .

[4]  Fernando L. Teixeira,et al.  Statistical Stability of Ultrawideband Time-Reversal Imaging in Random Media , 2014, IEEE Transactions on Geoscience and Remote Sensing.

[5]  Anne Ferréol,et al.  On the Resolution Probability of MUSIC in Presence of Modeling Errors , 2008, IEEE Transactions on Signal Processing.

[6]  A. Lee Swindlehurst,et al.  A Performance Analysis ofSubspace-Based Methods in thePresence of Model Errors { Part I : The MUSIC AlgorithmA , 1992 .

[7]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[8]  Gang Shi,et al.  Maximum likelihood estimation of point scatterers for computational time-reversal imaging , 2005, Commun. Inf. Syst..

[9]  Sverre Holm,et al.  Time-reversal multiple signal classification in case of noise: a phase-coherent approach. , 2011, The Journal of the Acoustical Society of America.

[10]  李廉林,et al.  A Novel Autofocusing Approach for Real-Time Through-Wall Imaging Under Unknown Wall Characteristics , 2010 .

[11]  F.L. Teixeira,et al.  On the Sensitivity of Time-Reversal Imaging Techniques to Model Perturbations , 2008, IEEE Transactions on Antennas and Propagation.

[12]  F. Li,et al.  Analysis of Min-Norm and MUSIC with arbitrary array geometry , 1990 .

[13]  Pierluigi Salvo Rossi,et al.  On the asymptotic distribution of Time-Reversal MUSIC null spectrum , 2017, Digit. Signal Process..

[14]  Fred K. Gruber,et al.  Subspace-Based Localization and Inverse Scattering of Multiply Scattering Point Targets , 2007, EURASIP J. Adv. Signal Process..

[15]  Gang Shi,et al.  Cramér–Rao Bound Analysis on Multiple Scattering in Multistatic Point-Scatterer Estimation , 2006, IEEE Transactions on Signal Processing.

[16]  G. Stewart.  Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems , 1973 .

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

[18]  L. Scharf,et al.  Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals , 2010 .

[19]  Xiaoli Ma,et al.  First-Order Perturbation Analysis of Singular Vectors in Singular Value Decomposition , 2007, 2007 IEEE/SP 14th Workshop on Statistical Signal Processing.

[20]  Anne Ferréol,et al.  On the asymptotic performance analysis of subspace DOA estimation in the presence of modeling errors: case of MUSIC , 2006, IEEE Transactions on Signal Processing.

[21]  Fang Li,et al.  A Novel Autofocusing Approach for Real-Time Through-Wall Imaging Under Unknown Wall Characteristics , 2010, IEEE Transactions on Geoscience and Remote Sensing.

[22]  Mostafa Kaveh,et al.  The statistical performance of the MUSIC and the minimum-norm algorithms in resolving plane waves in noise , 1986, IEEE Trans. Acoust. Speech Signal Process..

[23]  Pierre Borderies,et al.  DORT method as applied to ultrawideband signals for detection of buried objects , 2003, IEEE Trans. Geosci. Remote. Sens..

[24]  A. Fannjiang.  On time reversal mirrors , 2008, 0811.0132.

[25]  Petre Stoica,et al.  MUSIC, maximum likelihood, and Cramer-Rao bound , 1989, IEEE Transactions on Acoustics, Speech, and Signal Processing.

[26]  F. Li,et al.  Performance analysis for DOA estimation algorithms: unification, simplification, and observations , 1993 .

[27]  Xudong Chen,et al.  Applicability of MUSIC-Type Imaging in Two-Dimensional Electromagnetic Inverse Problems , 2008, IEEE Transactions on Antennas and Propagation.

[28]  Benjamin Friedlander,et al.  Analysis of the asymptotic relative efficiency of the MUSIC algorithm , 1988, IEEE Trans. Acoust. Speech Signal Process..

[29]  Francesco Simonetti,et al.  Time-Reversal MUSIC Imaging of Extended Targets , 2007, IEEE Transactions on Image Processing.

[30]  M. Fink,et al.  Time-reversal of ultrasonic fields. III. Theory of the closed time-reversal cavity , 1992, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[31]  Mathias Fink,et al.  Decomposition of the time reversal operator: Detection and selective focusing on two scatterers , 1996 .

[32]  Iickho Song,et al.  Asymptotic distribution of the MUSIC null spectrum , 1993, IEEE Trans. Signal Process..

[33]  Anne Ferréol,et al.  Statistical Analysis of the MUSIC Algorithm in the Presence of Modeling Errors, Taking Into Account the Resolution Probability , 2010, IEEE Transactions on Signal Processing.

[34]  Raffaele Solimene,et al.  Performance Analysis of Time-Reversal MUSIC , 2015, IEEE Transactions on Signal Processing.

[35]  A.J. Devaney.  Time reversal imaging of obscured targets from multistatic data , 2005, IEEE Transactions on Antennas and Propagation.

[36]  M. D. Hossain,et al.  Beamspace Time-Reversal Microwave Imaging for Breast Cancer Detection , 2013, IEEE Antennas and Wireless Propagation Letters.

[37]  Raffaele Solimene,et al.  Some Remarks on Time-Reversal MUSIC for Two-Dimensional Thin PEC Scatterers , 2014, IEEE Geoscience and Remote Sensing Letters.

[38]  Raffaele Solimene,et al.  On MSE performance of time-reversal MUSIC , 2014, 2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM).