MUSIC Algorithm for Vector-Sensors Array Using Biquaternions

In this paper, we use a biquaternion formalism to model vector-sensor signals carrying polarization information. This allows a concise and elegant way of handling signals with eight-dimensional (8-D) vector-valued samples. Using this model, we derive a biquaternionic version of the well-known array...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 55; no. 9; pp. 4523 - 4533
Main Authors: Le Bihan, N., Miron, S., Mars, J.I.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.09.2007
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Applied sciences
Array signal processing
Arrays
Biquaternion MUSIC (BQ-MUSIC)
Biquaternions and biquaternion-valued matrices
Computational modeling
Computer Science
Decomposition
Detection, estimation, filtering, equalization, prediction
Direction of arrival estimation
eigenvalue decomposition (EVD) of biquaternionic matrices
Eigenvalues
Eigenvalues and eigenfunctions
Exact sciences and technology
Information Retrieval
Information, signal and communications theory
Materials handling
Matrix decomposition
Miscellaneous
Multiple signal classification
Music
Noise robustness
Polarization
Quaternions
Signal and communications theory
Signal processing
Signal representation. Spectral analysis
Signal, noise
Spectra
Spectral analysis
Studies
Telecommunications and information theory
vector-sensor array processing
Performance evaluation
vector-sensor array processing
Direction-of-arrival estimation
Parameter estimation
Array signal processing
Quaternion
Signal estimation
Hermitian matrix
Subspace method
Eigenvalue
Biquaternion MUSIC (BQ-MUSIC)
Biquaternions and biquaternion-valued matrices
Vector method
Algorithm
Orthogonal polynomial
eigenvalue decomposition (EVD) of biquaternionic matrices
Simulation
Spectrum analysis
Sensor array
Signal analysis
Antenna array
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Description
Summary:In this paper, we use a biquaternion formalism to model vector-sensor signals carrying polarization information. This allows a concise and elegant way of handling signals with eight-dimensional (8-D) vector-valued samples. Using this model, we derive a biquaternionic version of the well-known array processing MUSIC algorithm, and we show its superiority to classically used long-vector approach. New results on biquaternion valued matrix spectral analysis are presented. Of particular interest for the biquaternion MUSIC (BQ-MUSIC) algorithm is the decomposition of the spectral matrix of the data into orthogonal subspaces. We propose an effective algorithm to compute such an orthogonal decomposition of the observation space via the eigenvalue decomposition (EVD) of a Hermitian biquaternionic matrix by means of a newly defined quantity, the quaternion adjoint matrix. The BQ-MUSIC estimator is derived and simulation results illustrate its performances compared with two other approaches in polarized antenna processing (LV-MUSIC and PSA-MUSIC). The proposed algorithm is shown to be superior in several aspects to the existing approaches. Compared with LV-MUSIC, the BQ-MUSIC algorithm is more robust to modelization errors and coherent noise while it can detect less sources. In comparaison with PSA-MUSIC, our approach exhibits more accurate estimation of direction of arrival (DOA) for a small number of sources, while keeping the polarization information accessible.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2007.896067