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Mode- Subspace Projection of a Tensor for Multidimensional Harmonic Parameter Estimations

In Multidimensional Harmonic Retrieval (MHR) problems, it is understood that the multidimensional structure of the measurement data, with a tensor representation, can be exploited to improve the parameter estimation accuracy. In this paper, the mode-ℜ subspace of the tensor representation, based on... Full description

Journal Title: IEEE Transactions on Signal Processing 01 June 2013, Vol.61(11), pp.3002-3014
Main Author: Yang Li
Other Authors: Jian Qiu Zhang
Format: Electronic Article Electronic Article
Language: English
Subjects:
ID: ISSN: 1053-587X ; E-ISSN: 1941-0476 ; DOI: 10.1109/TSP.2013.2255044
Link: https://ieeexplore.ieee.org/document/6488880
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recordid: ieee_s6488880
title: Mode- Subspace Projection of a Tensor for Multidimensional Harmonic Parameter Estimations
format: Article
creator:
  • Yang Li
  • Jian Qiu Zhang
subjects:
  • Mode- {\Cal R} Subspace
  • Multidimensional Harmonic Retrieval
  • Tensor
  • Engineering
ispartof: IEEE Transactions on Signal Processing, 01 June 2013, Vol.61(11), pp.3002-3014
description: In Multidimensional Harmonic Retrieval (MHR) problems, it is understood that the multidimensional structure of the measurement data, with a tensor representation, can be exploited to improve the parameter estimation accuracy. In this paper, the mode-ℜ subspace of the tensor representation, based on the general matricization of the tensor, is first defined. It is found that there is a subordinate relation among the different mode- ℜ signal subspaces. As a result, the measurement tensor can be projected to the mode- ℜ signal subspaces in a bottom-up way, and the long-vector signal subspace required by the many signal subspace based parameter estimation algorithms can be refined. As an example, a mode-ℜ projection based Tensor-ESPRIT algorithm is presented. The reason why mode-ℜ subspace projections bring about performance improvement becomes obvious by the first order perturbation analyses. These analyses also generate two criteria on how the mode-ℜ subspace based projection technique should be carried out. Simulations are conducted to verify the effectiveness of the algorithm and the analytical results.
language: eng
source:
identifier: ISSN: 1053-587X ; E-ISSN: 1941-0476 ; DOI: 10.1109/TSP.2013.2255044
fulltext: fulltext
issn:
  • 1053-587X
  • 1053587X
  • 1941-0476
  • 19410476
url: Link


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subjectMode- {\Cal R} Subspace ; Multidimensional Harmonic Retrieval ; Tensor ; Engineering
descriptionIn Multidimensional Harmonic Retrieval (MHR) problems, it is understood that the multidimensional structure of the measurement data, with a tensor representation, can be exploited to improve the parameter estimation accuracy. In this paper, the mode-ℜ subspace of the tensor representation, based on the general matricization of the tensor, is first defined. It is found that there is a subordinate relation among the different mode- ℜ signal subspaces. As a result, the measurement tensor can be projected to the mode- ℜ signal subspaces in a bottom-up way, and the long-vector signal subspace required by the many signal subspace based parameter estimation algorithms can be refined. As an example, a mode-ℜ projection based Tensor-ESPRIT algorithm is presented. The reason why mode-ℜ subspace projections bring about performance improvement becomes obvious by the first order perturbation analyses. These analyses also generate two criteria on how the mode-ℜ subspace based projection technique should be carried out. Simulations are conducted to verify the effectiveness of the algorithm and the analytical results.
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In Multidimensional Harmonic Retrieval (MHR) problems, it is understood that the multidimensional structure of the measurement data, with a tensor representation, can be exploited to improve the parameter estimation accuracy. In this paper, the mode-ℜ subspace of the tensor representation, based on the general matricization of the tensor, is first defined. It is found that there is a subordinate relation among the different mode- ℜ signal subspaces. As a result, the measurement tensor can be projected to the mode- ℜ signal subspaces in a bottom-up way, and the long-vector signal subspace required by the many signal subspace based parameter estimation algorithms can be refined. As an example, a mode-ℜ projection based Tensor-ESPRIT algorithm is presented. The reason why mode-ℜ subspace projections bring about performance improvement becomes obvious by the first order perturbation analyses. These analyses also generate two criteria on how the mode-ℜ subspace based projection technique should be carried out. Simulations are conducted to verify the effectiveness of the algorithm and the analytical results.

pubIEEE
doi10.1109/TSP.2013.2255044
date2013-06-01