Finite Dimensional Statistical Inference

Ryan, Øyvind; Masucci, Antonia Maria; Yang, Sheng; Debbah, Mérouane

doi:10.1109/tit.2011.2112010

Cited by 8 publications

(23 citation statements)

References 28 publications

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“…Focusing on the study of random matrices in the finite case, the authors of [40] were able to derive the explicit series expansion of the eigenvalue distribution of various models, namely the case of non-central Wishart distributions as well as one sided correlated zero mean Wishart distributions. In particular, they proposed a general finite dimensional statistical inference framework based on the moments method in the finite case, which takes a set of moments as input and produces sets of moments as output with the dimensions of the matrices considered finite.…”

Section: Masucci and Debbahmentioning

confidence: 99%

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Non-commutative large entries for cognitive radio applications

Masucci

Debbah

2012

J Wireless Com Network

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Cognitive radio has been proposed as a solution for the problem of underutilization of the radio spectrum. Indeed, measurements have shown that large portions of frequency bands are not efficiently assigned since large pieces of bandwidth are unused or only partially used. In the last decade, studies in different areas, such as signal processing, random matrix theory, information theory, game theory, etc., have brought us to the current state of cognitive radio research. These theoretical advancements represents a solid base for practical applications and even further developments. However, still open questions need to be answered. In this study, free probability theory, through the free deconvolution technique, is used to attack the huge problem of retrieving useful information from the network with a finite number of observations. Free deconvolution, based on the moments method, has shown to be a helpful approach to this problem. After giving the general idea of free deconvolution for known models, we show how the moments method works in the case where scalar random variables are considered. Since, in general, we have a situation where more complex systems are involved, the parameters of interest are no longer scalar random variables but random vectors and random matrices. Random matrices are non-commutative operators with respect to the matrix product and they can be considered elements of what is called noncommutative probability space.Therefore, we focus on the case where random matrices are considered. Concepts from combinatorics, such as crossing and non-crossing partitions are useful tools to express the moments of Gaussian and Vandermonde matrices, respectively. Our analysis and simulation results show that free deconvolution framework can be used for studying relevant information in cognitive radio such as power detection, users detection, etc.

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Section: Masucci and Debbahmentioning

confidence: 99%

“…for any positive integer p, Theorem 1 in [40] allows us to express the moments M p in terms of the moments D p . In particular, the first three moments can be written as…”

Section: Masucci and Debbahmentioning

confidence: 99%

Non-commutative large entries for cognitive radio applications

Masucci

Debbah

2012

J Wireless Com Network

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“…the method from [21] applied to the compound observation matrix help us infer the spectrum of 1 N DD H also. We will state the corresponding estimator in Section III.…”

Section: ()mentioning

confidence: 99%

“…To state our estimators, we need the following concepts, taken from [21]. These concepts are better motivated geometrically in terms of pairings of Gaussian elements.…”

Section: Formul At Io N O F T He Est Im At O Rmentioning

confidence: 99%

“…In fact, the literature contains no non-trivial cases of finite matrices which display freeness. In [21], a momentbased framework which applies for Gaussian matrices of any dimensions is presented, and which has many similarities with the moment-based free probability framework. This contribution willl address the following questions on how this framework can be best adapted for spectrum estimation purposes: 1) Observations of the form D+X allow for stacking into a compound observation matrix.…”

Section: Introductionmentioning

confidence: 99%

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