An efficient fourth order system identification (FOSI) algorithm utilizing the joint diagonalization procedure

Belouchrani, Adel; Derras, B.

doi:10.1109/ssap.2000.870200

Cited by 7 publications

(31 citation statements)

References 11 publications

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“…up to a permutation of its rows and columns, i.e., there exist permutation matrices 1 ∈ C P n=1 × P n=1 and 2 ∈ C R×R such that 1 A (1) · · · A (P) 2 satisfies the inequalities (5) and (6). Let A (1) · · · A (P) be another matrix with same structure as A (1) · · · A (P) , then Col A (1) · · · A (P) ⊆ Col A (1) · · · A (P) = Col T [P] if and only if A (1) · · · A (P) = A (1) · · · A (P) D, where D is a nonsingular diagonal matrix.…”

Section: Uniqueness Of Cpds With Banded Matrix Factorsmentioning

confidence: 99%

“…By assumption we also assume that there exist permutation matrices 1 and 2 such that 1 A (1) · · · A (P) 2 satisfies the inequalities (5) and (6). Hence, from (7) we get…”

Section: Uniqueness Of Cpds With Banded Matrix Factorsmentioning

confidence: 99%

“…· · · A (P) 2 and 1 A (1) · · · A (P) 2 are banded matrices satisfying (5) and (6) and M = T 2 M 2 is a nonsingular matrix. Due to property (5) the matrix M must be lower triangular and due to property (6) the matrix M must also be upper triangular.…”

Section: Uniqueness Of Cpds With Banded Matrix Factorsmentioning

confidence: 99%

“…Once A (N) and N have been obtained, then from (8) we have the relation F = U N −1 = A (1) A (2) · · · A (N−1) . Thus, we can find the remaining unknown matrix factors from the R decoupled best rank-1 tensor approximation problems…”

Section: Exploiting One Banded Matrix Factormentioning

confidence: 99%

“…Tensor decompositions with banded matrix factors and possibly also (block-) Toeplitz/Hankel structures have found application in signal processing, in particular in cumulant based blind identification of convolutive mixtures [5,22,2,3,12,13] and in tensor based blind equalization of wireless communication systems [10,20,1]. In this case the banded structure of the matrix factors are directly related to the filter orders of the given system we attempt to identify.…”

Section: Introductionmentioning

confidence: 99%

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Tensor decompositions with banded matrix factors

Sørensen¹,

Comon²

2013

Linear Algebra and its Applications

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The computation of the model parameters of a canonical polyadic decomposition (CPD), also known as the parallel factor (PARAFAC) or canonical decomposition (CANDECOMP) or CP decomposition, is typically done by resorting to iterative algorithms, e.g. either iterative alternating least squares type or descent methods. In many practical problems involving tensor decompositions such as signal processing, some of the matrix factors are banded. First, we develop methods for the computation of CPDs with one banded matrix factor. It results in best rank-1 tensor approximation problems. Second, we propose methods to compute CPDs with more than one banded matrix factor. Third, we extend the developed methods to also handle banded and structured matrix factors such as Hankel or Toeplitz. Computer results are also reported.

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Section: Uniqueness Of Cpds With Banded Matrix Factorsmentioning

confidence: 99%

“…By assumption we also assume that there exist permutation matrices 1 and 2 such that 1 A (1) · · · A (P) 2 satisfies the inequalities (5) and (6). Hence, from (7) we get…”

Section: Uniqueness Of Cpds With Banded Matrix Factorsmentioning

confidence: 99%

Section: Uniqueness Of Cpds With Banded Matrix Factorsmentioning

confidence: 99%

Section: Exploiting One Banded Matrix Factormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Tensor decompositions with banded matrix factors

Sørensen¹,

Comon²

2013

Linear Algebra and its Applications

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Using Coevolutionary Genetic Algorithms for Estimation of Blind FIR Channel

Rezaee

2015

Wireless Pers Commun

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Tensor-Based Blind Channel Identification

Fernandes

Favier

Mota

2007

2007 IEEE International Conference on Communications

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International audienceWe propose a blind FIR channel identification method based on the parallel factor (Parafac) analysis of a 3rd-order tensor composed of the 4-th order output cumulants. Our algorithm is based on a single-step least squares (LS) minimization procedure instead of using classical three-step alternating least squares (ALS) methods. Using a Parafac-based decomposition, we avoid any kind of pre-processing such as the prewhitening operation, which is mandatory in most methods using higher-order statistics. Our method retrieves the channel vector without any permutation or scaling ambiguities. In addition, we establish a link between the cumulant tensor decomposition and the joint-diagonalization approach. Computer simulations illustrate the performance gains that our method provides with respect to other classical solutions. Initialization and convergence issues are also addressed

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An efficient fourth order system identification (FOSI) algorithm utilizing the joint diagonalization procedure

Cited by 7 publications

References 11 publications

Tensor decompositions with banded matrix factors

Tensor decompositions with banded matrix factors

Using Coevolutionary Genetic Algorithms for Estimation of Blind FIR Channel

Tensor-Based Blind Channel Identification

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