A Constrained Factor Decomposition With Application to MIMO Antenna Systems

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

doi:10.1109/tsp.2008.917026

Cited by 75 publications

(71 citation statements)

References 30 publications

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“…(4) The CONFAC decomposition of a third-order tensor was originally proposed in [49] in the context of wireless communications to design multiple-antenna transmission schemes with blind detection. Therein, it is shown that the three CONFAC constraint matrices are design parameters of the multiple-antenna transmission system.…”

Section: Preliminaries: the Confac Decompositionmentioning

confidence: 99%

“…In this work, we show that the CGF-based blind identification problem can be more efficiently addressed by means of the constrained factor (CONFAC) decomposition [49]. Under the assumption of complex sources, we show that a collection of secondorder derivatives of the CGFs of the observations can be stored in a third-order tensor following a third-order CONFAC decomposition with known constraint matrices.…”

Section: Introductionmentioning

confidence: 99%

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CONFAC Decomposition Approach to Blind Identification of Underdetermined Mixtures Based on Generating Function Derivatives

Almeida

Luciani

Stegeman

et al. 2012

IEEE Trans. Signal Process.

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Abstract-This work proposes a new tensor-based approach to solve the problem of blind identification of underdetermined mixtures of complex sources exploiting the cumulant generating function (CGF) of the observations. We show that a collection of secondorder derivatives of the CGF of the observations can be stored in a third-order tensor following a constrained factor (CONFAC) decomposition with known constrained structure. In order to increase the diversity, we combine three derivative types into an extended third-order CONFAC decomposition. A detailed uniqueness study of this decomposition is provided, from which easy-to-check sufficient conditions ensuring the essential uniqueness of the mixing matrix are obtained.

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Section: Preliminaries: the Confac Decompositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

CONFAC Decomposition Approach to Blind Identification of Underdetermined Mixtures Based on Generating Function Derivatives

Almeida

Luciani

Stegeman

et al. 2012

IEEE Trans. Signal Process.

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show abstract

“…. , N, the constrained PARAFAC model (42) constitutes a generalization to Nthorder of the third-order CONFAC model, introduced in [65] for designing MIMO communication systems with resource allocation. This CONFAC model was used in [69] http://asp.eurasipjournals.com/content/2014/1/142 for solving the problem of blind identification of underdetermined mixtures based on cumulant generating function of the observations.…”

Section: Confac Modelsmentioning

confidence: 99%

Overview of constrained PARAFAC models

Favier

Almeida

2014

EURASIP J. Adv. Signal Process.

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In this paper, we present an overview of constrained parallel factor (PARAFAC) models where the constraints model linear dependencies among columns of the factor matrices of the tensor decomposition or, alternatively, the pattern of interactions between different modes of the tensor which are captured by the equivalent core tensor. Some tensor prerequisites with a particular emphasis on mode combination using Kronecker products of canonical vectors that makes easier matricization operations, are first introduced. This Kronecker product-based approach is also formulated in terms of an index notation, which provides an original and concise formalism for both matricizing tensors and writing tensor models. Then, after a brief reminder of PARAFAC and Tucker models, two families of constrained tensor models, the co-called PARALIND/CONFAC and PARATUCK models, are described in a unified framework, for Nth-order tensors. New tensor models, called nested Tucker models and block PARALIND/CONFAC models, are also introduced. A link between PARATUCK models and constrained PARAFAC models is then established. Finally, new uniqueness properties of PARATUCK models are deduced from sufficient conditions for essential uniqueness of their associated constrained PARAFAC models.Keywords: Constrained PARAFAC; PARALIND/CONFAC; PARATUCK; Tensor models; Tucker models 1 Review IntroductionTensor calculus was introduced in differential geometry, at the end of the nineteenth century, and then tensor analysis was developed in the context of Einstein's theory of general relativity, with the introduction of index notation, the so-called Einstein summation convention, at the beginning of the twentieth century, which allows to simplify and shorten physics equations involving tensors. Index notation is also useful for simplifying multivariate statistical calculations, particularly those involving cumulant tensors [1]. Generally speaking, tensors are used in physics and differential geometry for characterizing the properties of a physical system, representing fundamental laws of physics, and defining geometrical objects whose components are functions. When these functions are defined over a continuum of points of a mathematical space, the tensor forms what is called a tensor field, a generalization of vector field used to solve problems involving curved surfaces or spaces, as it is the case of After the first tensor developments by mathematicians and physicists, the need of analyzing collections of data matrices that can be seen as three-way data arrays gave rise to three-way models for data analysis, with the pioneering works of Tucker in psychometrics [3], and Harshman in phonetics [4], who proposed what is now referred to as the Tucker and parallel factor (PARAFAC) decompositions, respectively. The PARAFAC decomposition was independently proposed by Carroll and Chang [5] under the name canonical decomposition (CANDE-COMP) and then called CANDECOMP/PARAFAC (CP) in [6]. For a history of the development of multi-way models in the context ...

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“…The tree structure allows common basis vectors in the previous dimensions. The relation of the values in (17) to the ones in the 3D-PARATREE formulation (11) .…”

Section: Higher Order Singular Value Decomposition (Hosvd)mentioning

confidence: 99%

“…If any tensor decomposes into sum of rank-1 tensor, this type of decomposition is often called "Canonical Decomposition" (CANDECOMP) or "Parallel Factors" model (PARAFAC) [8]. It has been applied in many signal processing applications, such as image recognition, acoustics, wireless channel estimation [9] and array signal processing [10], [11]. Recently, a Tucker-model based HOSVD [12] tensor decomposition subspace technique has also been formulated to improve multidimensional harmonic retrieval problems [13].…”

Section: Introductionmentioning

confidence: 99%

A Survey on PARATREE and SUSVD Decomposition Techniques and Their Use in Array Signal Processing

Bhatt¹,

Kumar²

2013

IJIGSP

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-The present manuscript is intended to review few applications of tensor decomposition model in array signal processing. Tensor decomposition models like HOSVD, SVD and PARAFAC are useful in signal processing. In this paper we shall use higher order tensor decomposition in signal processing. Also, a novel orthogonal non-iterative tensor decomposition technique (SUSVD), which is scalable to arbitrary high dimensional tensor, has been applied in MIMO channel estimation. The SUSVD provides a tensor model with hierarchical tree structure between the factors in different dimensions. We shall use a new model known as PARATREE, which is related to PARAFAC tensor models. The PARAFAC and PARATREE both describe a tensor as a sum of rank-1 tensors, but PARATREE has several advantages over PARAFAC, when it is applied as a lower rank approximation technique. PARATREE is orthogonal, fast and reliable to compute, and the order of the decomposition can be adaptively adjusted. The low rank PARATREE approximation has been applied to measure noise suppression for tensor valued MIMO channel sounding measurements.

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A Constrained Factor Decomposition With Application to MIMO Antenna Systems

Cited by 75 publications

References 30 publications

CONFAC Decomposition Approach to Blind Identification of Underdetermined Mixtures Based on Generating Function Derivatives

CONFAC Decomposition Approach to Blind Identification of Underdetermined Mixtures Based on Generating Function Derivatives

Overview of constrained PARAFAC models

A Survey on PARATREE and SUSVD Decomposition Techniques and Their Use in Array Signal Processing

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