Direction of arrival estimation in vector-sensor arrays using higher-order statistics

MUSIC algorithm is an effective method in solving the direction-finding problems. Due to the good performance of this algorithm, many variations of it including tesnor-MUSIC for verctor-sensor arrays, have been developed. However, these MUSIC-based methods have some limitations with respect to the number of sources, modeling errors and the noise power. It has been shown that using 2 q th-order $$(q>1)$$ ( q > 1 ) statistics in MUSIC algorithm is very effective to overcome these drawbacks. However, the existing 2 q -order MUSIC-like methods are appropriate for scalar-sensor arrays, which only measure one parameter, and have a matrix of measurements. In vector-sensor arrays, each sensor measures multiple parameters, and to keep this multidimensional structure, we should use a tensor of measurements. The contribution of this paper is to develop a new tensor-based 2 q -order MUSIC-like method for vector-sensor arrays. In this regard, we define a tensor of the cumulants which will be used in the proposed algorithm. The new method is called tensor-2 q -MUSIC. Computer simulations have been used to compare the performance of the proposed method with a higher-order extension of the conventional MUSIC method for the vector-sensor arrays which is called matrix-2 q -MUSIC. Moreover, we compare the performance of tensor-2 q -MUSIC method with the existing second-order methods for the vector-sensor arrays. The simulation results show the better performance of the proposed method.

[1]  Zhang Xiaofei,et al.  Two-dimensional DOA estimation for acoustic vector-sensor array using a successive MUSIC , 2013, Multidimensional Systems and Signal Processing.

[2]  Eric Moulines,et al.  Asymptotic performance analysis of direction-finding algorithms based on fourth-order cumulants , 1995, IEEE Trans. Signal Process..

[3]  Jean Pierre Delmas,et al.  MUSIC-like estimation of direction of arrival for noncircular sources , 2006, IEEE Transactions on Signal Processing.

[4]  Joos Vandewalle,et al.  A Multilinear Singular Value Decomposition , 2000, SIAM J. Matrix Anal. Appl..

[5]  Nicolas Le Bihan,et al.  Vector-Sensor MUSIC for Polarized Seismic Sources Localization , 2005, EURASIP J. Adv. Signal Process..

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

[7]  Yide Wang,et al.  An extended cyclic music algorithm , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[8]  Jerry M. Mendel,et al.  Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications , 1991, Proc. IEEE.

[9]  Yougen Xu,et al.  On the Equivalence of Tensor-MUSIC and Matrix-MUSIC , 2006, 2006 7th International Symposium on Antennas, Propagation & EM Theory.

[10]  Philippe Forster,et al.  Derivation of the theoretical performance of a Tensor MUSIC algorithm , 2016, Signal Process..

[11]  Ying Zhang,et al.  MUSIC-Like DOA Estimation Without Estimating the Number of Sources , 2010, IEEE Transactions on Signal Processing.

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

[13]  Petre Stoica,et al.  Maximum-likelihood DOA estimation by data-supported grid search , 1999, IEEE Signal Processing Letters.

[14]  Petre Stoica,et al.  Maximum likelihood methods for direction-of-arrival estimation , 1990, IEEE Trans. Acoust. Speech Signal Process..

[15]  P. McCullagh.  Tensor Methods in Statistics , 1987 .

[16]  Chang Dong Yoo,et al.  Underdetermined High-Resolution DOA Estimation: A $2\rho$ th-Order Source-Signal/Noise Subspace Constrained Optimization , 2015, IEEE Transactions on Signal Processing.

[17]  Florian Roemer,et al.  Higher-Order SVD-Based Subspace Estimation to Improve the Parameter Estimation Accuracy in Multidimensional Harmonic Retrieval Problems , 2008, IEEE Transactions on Signal Processing.

[18]  Martin Haardt,et al.  Higher order direction finding from rectangular cumulant matrices: The rectangular 2q-MUSIC algorithms , 2017, Signal Process..

[19]  Arye Nehorai,et al.  Nested Vector-Sensor Array Processing via Tensor Modeling , 2014, IEEE Transactions on Signal Processing.

[20]  Xiaofei Zhang,et al.  Blind DOA and polarization estimation for polarization-sensitive array using dimension reduction MUSIC , 2014, Multidimens. Syst. Signal Process..

[21]  Bernard C. Picinbono,et al.  On circularity , 1994, IEEE Trans. Signal Process..

[22]  Georgios B. Giannakis,et al.  Cyclostationary Signal Analysis , 2009 .

[23]  Longting Huang,et al.  Unitary root-MUSIC based on tensor mode-R algorithm for multidimensional sinusoidal frequency estimation without pairing parameters , 2020, Multidimens. Syst. Signal Process..

[24]  A. Ferreol,et al.  High-Resolution Direction Finding From Higher Order Statistics: The$2rm q$-MUSIC Algorithm , 2006, IEEE Transactions on Signal Processing.

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

[26]  J. Chang,et al.  Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition , 1970 .

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

[28]  T. Engin Tuncer,et al.  Classical and Modern Direction-of-Arrival Estimation , 2009 .

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

[30]  Philippe Forster,et al.  Numerical performance of a tensor MUSIC algorithm based on HOSVD for a mixture of polarized sources , 2013, 21st European Signal Processing Conference (EUSIPCO 2013).

[31]  Richard A. Harshman,et al.  Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multi-model factor analysis , 1970 .

[32]  L. Lathauwer,et al.  Signal Processing based on Multilinear Algebra , 1997 .