Multiuser MIMO Systems Using Space–Time–Frequency Multiple-Access PARAFAC Tensor Modeling

Almeida, André L. F. de; Favier, Gérard; Mota, J.C.M.

doi:10.1007/978-1-4419-0155-2_11

Cited by 2 publications

(5 citation statements)

References 79 publications

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“…-La modélisation et la conception de nouveaux systèmes de communication MIMO (de Almeida et al, 2008), (de Almeida et al, 2009a), (de Almeida et al, 2009b).…”

Section: Resultsunclassified

Identification de modèles de Volterra basée sur la décomposition PARAFAC de leurs noyaux et le filtre de Kalman étendu

Favier¹,

Bouilloc²

2010

Traitement du signal

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Les modèles de Volterra sont très utilisés dans de nombreux domaines d'application du fait qu'ils permettent de représenter, avec une précision arbitraire, tout système non linéaire de mémoire finie. Ils possèdent de plus la propriété d'être linéaires vis-à-vis de leurs paramètres, les coefficients des noyaux. Le principal inconvénient de ces modèles est leur complexité paramétrique qui nécessite d'estimer un très grand nombre de paramètres. Cet article présente une nouvelle méthode permettant de réduire cette complexité paramétrique en considérant les noyaux de Volterra d'ordre supérieur à un comme des tenseurs symétriques et en les décomposant à l'aide de la décomposition PARAFAC. Les modèles de Volterra-Parafac ainsi obtenus peuvent être vus comme une série de modèles de Wiener mis en parallèle. En exploitant cette nouvelle formulation des modèles de Volterra, nous proposons un algorithme d'identification récursif basé sur le filtre de Kalman étendu. Des résultats de simulation illustrent le comportement de la méthode d'identification proposée, dans le cas de systèmes de Volterra cubiques. ABSTRACT. Volterra models are widely used in various application areas. Their usefulness is mainly due to their ability to approximate with an arbitrary precision any fading memory nonlinear system, and their property of linearity with respect to parameters, the kernels coefficients. The main drawback of these models is their parametric complexity needing to estimate a huge number of parameters. Considering Volterra kernels as symmetric tensors, we use their PARAFAC decomposition to derive the Volterra-Parafac models inducing a substantial parametric complexity reduction. We show that these models can be viewed as a set of Wiener models in parallel. Then, we apply the extended Kalman filter for recursively identifying such Volterra-Parafac models. Some simulation results illustrate the effectiveness of the proposed identification method, in the case of cubic Volterra systems.

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“…-La modélisation et la conception de nouveaux systèmes de communication MIMO (de Almeida et al, 2008), (de Almeida et al, 2009a), (de Almeida et al, 2009b).…”

Section: Resultsunclassified

Identification de modèles de Volterra basée sur la décomposition PARAFAC de leurs noyaux et le filtre de Kalman étendu

Favier¹,

Bouilloc²

2010

Traitement du signal

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“…We know that, under condition (4.7), both the matrices C A and B have full column rank. Let X (3) = UΣV H denote the compact SVD of X (3) , where U ∈ C KI×R ; then there exists a nonsingular matrix M ∈ C R×R such that…”

Section: B Zmentioning

confidence: 99%

“…In other words, if one of the factor matrices of the PD is known, say C, and the conditions stated in Theorem 4.6 are satisfied, then even if the known factor matrix does not have full column rank (as opposed to Proposition 3.1), we can find the remaining factor matrices from X (3) . An outline of the proposed method for computing a PD with a known factor matrix is given in Algorithm 1.…”

Section: B Zmentioning

confidence: 99%

“…This condition can numerically be verified by checking if the effective rank of Y (3) is equal to card (S c ). S must also be chosen such that…”

Section: This Implies That R((pcmentioning

confidence: 99%

“…|A ( [1,2], [1,2])| |A ( [1,2], [1,3])| |A ( [1,2], [2,3])| |A ( [1,3], [1,2])| |A ( [1,3], [1,3])| |A ( [1,3], [2,3])| |A ( [1,4], [1,2])| |A ( [1,4], [1,3])| |A ( [1,4], [2,3])| |A ( [2,3], [1,2])| |A ( [2,3], [1,3])| |A ( [2,3], [2,3])| |A ( [2,4], [1,2])| |A ( [2,…”

mentioning

confidence: 99%

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New Uniqueness Conditions for the Canonical Polyadic Decomposition of Third-Order Tensors

Sørensen¹,

Lathauwer²

2015

SIAM J. Matrix Anal. & Appl.

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Abstract. The uniqueness properties of the canonical polyadic decomposition (CPD) of higherorder tensors make it an attractive tool for signal separation. However, CPD uniqueness is not yet fully understood. In this paper, we first present a new uniqueness condition for a polyadic decomposition (PD) where one of the factor matrices is assumed to be known. We also show that this result can be used to obtain a new overall uniqueness condition for the CPD. In signal processing the CPD factor matrices are often constrained. Building on the preceding results, we provide a new uniqueness condition for a CPD with a columnwise orthonormal factor matrix, representing uncorrelated signals. We also obtain a new uniqueness condition for a CPD with a partial Hermitian symmetry, useful for tensors in which covariance matrices are stacked, which are common in statistical signal processing. We explain that such constraints can lead to more relaxed uniqueness conditions. Finally, we provide an inexpensive algorithm for computing a PD with a known factor matrix that is also useful for the computation of the full CPD.

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Multiuser MIMO Systems Using Space–Time–Frequency Multiple-Access PARAFAC Tensor Modeling

Cited by 2 publications

References 79 publications

Identification de modèles de Volterra basée sur la décomposition PARAFAC de leurs noyaux et le filtre de Kalman étendu

Identification de modèles de Volterra basée sur la décomposition PARAFAC de leurs noyaux et le filtre de Kalman étendu

New Uniqueness Conditions for the Canonical Polyadic Decomposition of Third-Order Tensors

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