Wideband Multiple Diversity Tensor Array Processing

This paper establishes a tensor model for wideband coherent array processing including multiple physical diversities. A separable coherent focusing operation is proposed as a preprocessing step in order to ensure the multilinearity of the interpolated data. We propose an alternating least squares algorithm to process tensor data, taking into account the noise correlation structure introduced by the focusing operation. We show through computer simulations that the estimation of direction of arrival and polarization parameters improves compared to existing narrowband tensor processing and wideband MUltiple SIgnal Classification. The performance is also compared to the Cramér-Rao bounds of the wideband tensor model.

[1]  Mostafa Kaveh,et al.  Coherent wide-band ESPRIT method for directions-of-arrival estimation of multiple wide-band sources , 1990, IEEE Trans. Acoust. Speech Signal Process..

[2]  Huawei Chen,et al.  Coherent signal-subspace processing of acoustic vector sensor array for DOA estimation of wideband sources , 2005, Signal Process..

[3]  Arye Nehorai,et al.  Vector-sensor array processing for electromagnetic source localization , 1994, IEEE Trans. Signal Process..

[4]  Mostafa Kaveh,et al.  Focussing matrices for coherent signal-subspace processing , 1988, IEEE Trans. Acoust. Speech Signal Process..

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

[6]  Pierre Comon,et al.  Tensor DoA Estimation With Directional Elements , 2017, IEEE Signal Processing Letters.

[7]  Harry L. Van Trees,et al.  Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory , 2002 .

[8]  Hong Wang,et al.  Coherent signal-subspace processing for the detection and estimation of angles of arrival of multiple wide-band sources , 1985, IEEE Trans. Acoust. Speech Signal Process..

[9]  Arthur Jay Barabell,et al.  Improving the resolution performance of eigenstructure-based direction-finding algorithms , 1983, ICASSP.

[10]  Tamara G. Kolda,et al.  Tensor Decompositions and Applications , 2009, SIAM Rev..

[11]  GIPSA-Lab,et al.  WIDEBAND MULTILINEAR ARRAY PROCESSING THROUGH TENSOR DECOMPOSITION , 2016 .

[12]  Andrzej Cichocki,et al.  Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis , 2014, IEEE Signal Processing Magazine.

[13]  Wei Liu,et al.  Wideband Beamforming: Concepts and Techniques , 2010 .

[14]  Jeffrey L. Krolik,et al.  Focused wide-band array processing by spatial resampling , 1990, IEEE Trans. Acoust. Speech Signal Process..

[15]  Souleymen Sahnoun,et al.  Joint Source Estimation and Localization , 2015, IEEE Transactions on Signal Processing.

[16]  Souleymen Sahnoun,et al.  Tensor decomposition exploiting diversity of propagation velocities: Application to localization of icequake events , 2016, Signal Process..

[17]  H. Clergeot,et al.  New simple implementation of the coherent signal subspace method for wide band direction of arrival estimation , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[18]  David Brie,et al.  The effect of polarization separation on the performance of Candecomp/Parafac-based vector sensor array processing , 2012, Phys. Commun..

[19]  B.D. Van Veen,et al.  Beamforming: a versatile approach to spatial filtering , 1988, IEEE ASSP Magazine.

[20]  Giorgio Ottaviani,et al.  An Algorithm For Generic and Low-Rank Specific Identifiability of Complex Tensors , 2014, SIAM J. Matrix Anal. Appl..

[21]  Thomas Kailath,et al.  ESPRIT-estimation of signal parameters via rotational invariance techniques , 1989, IEEE Trans. Acoust. Speech Signal Process..

[22]  Arye Nehorai,et al.  Acoustic vector-sensor array processing , 1994, IEEE Trans. Signal Process..

[23]  A. Lee Swindlehurst,et al.  Subspace Fitting with Diversely Polarized Antenna Arrays , 1993 .

[24]  Lieven De Lathauwer,et al.  Generic Uniqueness of a Structured Matrix Factorization and Applications in Blind Source Separation , 2016, IEEE Journal of Selected Topics in Signal Processing.

[25]  Benjamin Friedlander,et al.  The root-MUSIC algorithm for direction finding with interpolated arrays , 1993, Signal Process..

[26]  Anthony J. Weiss,et al.  Direction finding for wide-band signals using an interpolated array , 1993, IEEE Trans. Signal Process..

[27]  Björn E. Ottersten,et al.  Direction-of-arrival estimation for wide-band signals using the ESPRIT algorithm , 1990, IEEE Trans. Acoust. Speech Signal Process..

[28]  Arye Nehorai,et al.  Analysis of a polarized seismic wave model , 1996, IEEE Trans. Signal Process..

[29]  Pierre Comon,et al.  Tensors : A brief introduction , 2014, IEEE Signal Processing Magazine.

[30]  Joe Brewer,et al.  Kronecker products and matrix calculus in system theory , 1978 .

[31]  Nikos D. Sidiropoulos,et al.  Cramer-Rao lower bounds for low-rank decomposition of multidimensional arrays , 2001, IEEE Trans. Signal Process..

[32]  André Lima Férrer de Almeida,et al.  Array interpolation based on multivariate adaptive regression splines , 2016, 2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM).

[33]  P. Comon,et al.  Tensor decompositions, alternating least squares and other tales , 2009 .

[34]  Shihua Zhu,et al.  A CANDECOMP/PARAFAC Perspective on Uniqueness of DOA Estimation Using a Vector Sensor Array , 2011, IEEE Transactions on Signal Processing.

[35]  Nikos D. Sidiropoulos,et al.  Parallel factor analysis in sensor array processing , 2000, IEEE Trans. Signal Process..

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

[37]  Pierre Comon 4 - Estimation multivariable complexe , 1986 .

[38]  Florian Roemer,et al.  Multi-dimensional model order selection , 2011, EURASIP J. Adv. Signal Process..

[39]  Anthony J. Weiss,et al.  Coherent wide-band processing for arbitrary array geometry , 1993, IEEE Transactions on Signal Processing.

[40]  Are Hjørungnes,et al.  Complex-Valued Matrix Differentiation: Techniques and Key Results , 2007, IEEE Transactions on Signal Processing.

[41]  Umberto Spagnolini,et al.  Seismic Velocity and Polarization Estimation for Wavefield Separation , 2008, IEEE Transactions on Signal Processing.

[42]  Pierre Comon,et al.  Blind Multilinear Identification , 2012, IEEE Transactions on Information Theory.

[43]  Petre Stoica,et al.  MUSIC, maximum likelihood and Cramer-Rao bound , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.