Fast subspace decomposition

Xu, Guanghan; Kailath, T.

doi:10.1109/78.277846

Cited by 178 publications

(7 citation statements)

References 20 publications

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“…This cost reduction is made possible thanks to the specific structure of the covariance matrix (i.e all noise subspace vectors are associated to the same eigenvalue σ 2 ). Note that this structure has already been exploited in [14] for the derivation of the fast (batch) subspace method of complexity O(n 2 p).…”

Section: Discussionmentioning

confidence: 98%

Minor subspace tracking using MNS technique

Thameri

Abed-Meraim

Belouchrani

2012

2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper introduces new minor (noise) subspace tracking (MST) algorithms based on the minimum noise subspace (MNS) technique. The latter has been introduced as a computationally efficient subspace method for blind system identification. We exploit here the principle of the MNS, to derive the most efficient algorithms for MST. The proposed method joins the advantages of low complexity and fast convergence rate. Moreover, this method is highly parallelizable and hence its computational cost can be easily reduced to a very low level when parallel architectures are available. Different implementations are proposed for different contexts and they are compared via numerical simulations.

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Section: Discussionmentioning

confidence: 98%

Minor subspace tracking using MNS technique

Thameri

Abed-Meraim

Belouchrani

2012

2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…Note that the complexities are given in terms of complex-valued fops [26][27][28][29]. For the 2D-NC-MUSIC and the SRTRD-p-NC-MUSIC, the EVD of the covariance matrix R Y can use the fast subspace decomposition (FSD) technique [34], and O (4M 2 K) fops are required to use the FSD technique of the covariance matrix R Y . Compared with the 2D-NC-MUSIC, we need to additionally construct the new noise subspace V new and calculate the matrix V † N,2 for the SRTRD-p-NC-MUSIC.…”

Section: Optimal Selection Of Pmentioning

confidence: 99%

A Low-Complexity Direction-of-Arrival Estimation Algorithm for Noncircular Signals via Subspace Rotation Technique

Wang

Zhang

Yao

et al. 2023

International Journal of Antennas and Propagation

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In this paper, we investigate the problem of the heavy computational burden of the direction-of-arrival (DoA) estimation for the noncircular (NC) signals. A novel low-complexity direction-of-arrival estimation algorithm for NC signals via subspace rotation technique (SRT) is proposed. The proposed algorithm divides the noise subspace matrix along its row direction into two submatrices, and the SRT is performed to get a new reduced-dimension noise subspace. Then, utilizing the separation of variables and the orthogonality between the reduced-dimension noise subspace and the space spanned by the columns of the extended manifold matrix, a new one-dimensional spectral search function is derived to estimate DoAs. As the size of the block matrices of the noise subspace matrix has a great impact on the computational complexity of the spectral search, the optimal number of rows of the block matrices is determined. The proposed algorithm not only avoids the two-dimensional spectral search but also efficiently removes the redundancy computations in the one-dimensional spectral search. Theoretical analysis and simulation results show that the proposed algorithm can significantly improve the computational efficiency on the premise of ensuring the accuracy of DoA estimation for the NC signals, especially in scenarios where large numbers of sensors are applied.

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“…The orthogonality of certain submatrices of A plays an important role in specifying those conditions. We also relate the sufficient conditions to a class of matrices with the so-called low-rank-plus-shift structure [6,7,10]. In Section 3, we expand the results in Section 2 to the case where the necessary and sufficient conditions are only approximately satisfied by the given matrix A.…”

Section: A]?mentioning

confidence: 99%

“…As an application of the results established in the above corollaries, we consider a special class of matric~ that possess the so-called low-rank-plus-shift structure. This kind of matrices arises naturally in applications such as array signal processing and Latent Semantic Indexing in information retrieval [6,7,10]. Specifically, a matrix has the low-rank-plus-shift structure if its cross-product is a low-rank perturbation of a positive multiple of the identity matrix (cf.…”

Section: First We Partition a As A=mentioning

confidence: 99%

Structure and Perturbation Analysis of Truncated SVDs for Column-Partitioned Matrices

Zhang

Zha

2001

SIAM J. Matrix Anal. & Appl.

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We present a detailed study of truncated SVD for column-partitioned matrices. In particular, we analyze the relation between the truncated SVD. of a matrix and the truncated SVDs of its submatrices. We give necessary and sufficient conditions under which truncated SVD of a matrix can be constructed from those of its submatrices. We also present perturbation analysis to •show that an approximate truncated SVD can still be computed even if the given necessary and sufficient conditions are only approximately satisfied.

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Fast subspace decomposition

Cited by 178 publications

References 20 publications

Minor subspace tracking using MNS technique

Minor subspace tracking using MNS technique

A Low-Complexity Direction-of-Arrival Estimation Algorithm for Noncircular Signals via Subspace Rotation Technique

Structure and Perturbation Analysis of Truncated SVDs for Column-Partitioned Matrices

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