Derivation of the theoretical performance of a Tensor MUSIC algorithm

In this paper, we derive the theoretical performance of a Tensor MUSIC algorithm based on the Higher Order Singular Value Decomposition (HOSVD) that was previously developed to estimate the Direction Of Arrival (DOA) and the polarization parameters of polarized sources. The derivation of this result...

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Bibliographic Details
Published in:Signal processing 2016-12, Vol.129 (12), p.97-105
Main Authors: Forster, P., Ginolhac, G., Boizard, M.
Format: Article
Language:English
Subjects:
Algorithms
Computer simulation
Derivation
DOA
Engineering Sciences
HOSVD
Mathematical analysis
Perturbation analysis
Perturbation methods
Polarization
Polarization sources
Signal and Image processing
Tensor MUSIC
Tensors
Theoretical Mean Square Error
Vectors (mathematics)
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Summary:In this paper, we derive the theoretical performance of a Tensor MUSIC algorithm based on the Higher Order Singular Value Decomposition (HOSVD) that was previously developed to estimate the Direction Of Arrival (DOA) and the polarization parameters of polarized sources. The derivation of this result is done via a perturbation analysis and allows to obtain the theoretical Mean Square Error (MSE) on the DOA and the polarization parameters. The proposed result is also shown to be valid for the Long Vector MUSIC algorithm, i.e. when the multidimensional samples are unfolded into a long vector. The agreement between theoretical and empirical MSEs is illustrated through Monte Carlo simulations. •Considered model: polarized source.•2 MUSIC algorithms: LV-MUSIC (all data are unfolded into a single vector) and T-MUSIC (based on multilinear algebra).•Derivation of theoretical Mean Square Error of DOAs and polarization parameters.•Based on a perturbation analysis.
ISSN:0165-1684
1872-7557
DOI:10.1016/j.sigpro.2016.05.033