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Random Matrices And Applications To Statistical Signal Processing
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Book Synopsis Random Matrices and Applications to Statistical Signal Processing by : Pascal Vallet
Download or read book Random Matrices and Applications to Statistical Signal Processing written by Pascal Vallet and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we consider the problem of source localization in large sensor networks, when the number of antennas of the network and the number of samples of the observed signal are large and of the same order of magnitude. We also consider the case where the source signals are deterministic, and we develop an improved algorithm for source localization, based on the MUSIC method. For this, we fist show new results concerning the position of the eigen values of large information plus noise complex gaussian random matrices.
Book Synopsis Random Matrix Theory and Wireless Communications by : Antonia M. Tulino
Download or read book Random Matrix Theory and Wireless Communications written by Antonia M. Tulino and published by Now Publishers Inc. This book was released on 2004 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random Matrix Theory and Wireless Communications is the first tutorial on random matrices which provides an overview of the theory and brings together in one source the most significant results recently obtained.
Book Synopsis Random Matrix Methods for Machine Learning by : Romain Couillet
Download or read book Random Matrix Methods for Machine Learning written by Romain Couillet and published by Cambridge University Press. This book was released on 2022-07-21 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified theory of random matrices for applications in machine learning, offering a large-dimensional data vision that exploits concentration and universality phenomena. This enables a precise understanding, and possible improvements, of the core mechanisms at play in real-world machine learning algorithms. The book opens with a thorough introduction to the theoretical basics of random matrices, which serves as a support to a wide scope of applications ranging from SVMs, through semi-supervised learning, unsupervised spectral clustering, and graph methods, to neural networks and deep learning. For each application, the authors discuss small- versus large-dimensional intuitions of the problem, followed by a systematic random matrix analysis of the resulting performance and possible improvements. All concepts, applications, and variations are illustrated numerically on synthetic as well as real-world data, with MATLAB and Python code provided on the accompanying website.
Book Synopsis Application of Large Random Matrices to Multivariate Time Series Analysis by : Daria Tieplova
Download or read book Application of Large Random Matrices to Multivariate Time Series Analysis written by Daria Tieplova and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A number of recent works proposed to use large random matrix theory in the context of high-dimensional statistical signal processing, traditionally modeled by a double asymptotic regime in which the dimension of the time series and the sample size both grow towards infinity. These contributions essentially addressed detection or estimation schemes depending on functionals of the sample covariance matrix of the observation. However, fundamental high-dimensional time series problems depend on matrices that are more complicated than the sample covariance matrix. The purpose of the present PhD is to study the behaviour of the singular values of 2 kinds of structured large random matrices, and to use the corresponding results to address an important statistical problem. More specifically, the observation (y_n)_{nin Z} is supposed to be a noisy version of a M-dimensional time series (u_n)_{nin Z} with rational spectrum that has some particular low rank structure, the additive noise (v_n)_{nin Z} being an independent identically distributed sequence of complex Gaussian vectors with unknown covariance matrix. An important statistical problem is the estimation of the minimal dimension P of the state space representations of u from N samples y_1,.., y_N. If L is any integer larger than P, the traditional approaches are based on the observation that P coincides with the rank of the autocovariance matrix R^L_{f|p} between the ML-dimensional random vectors (y_{n+L}^T,..,y_{n+2L-1}^T)^T and (y_{n}^T,.., y_{n+L-1}^T)^T, as well as with the number of non zero singular values of the normalized matrix C^L = (R^L)^{-1/2}R^L_{f|p} (R^L)^{-1/2} where R^L represents the covariance matrix of the above ML-dimensional vectors. In the low-dimensional regime where N->+infty while M and L are fixed, the matrices R^L_{f|p} and C^L can be consistently estimated by their empirical counterparts hat{R}^L_{f|p} and hat{C}^L, and P can be evaluated from the largest singular values of hat{R}^L_{f|p} and hat{C}^L. If however M and N->+infty in such a way that ML/N converges towards 0 c*
Book Synopsis An Introduction to Statistical Signal Processing by : Robert M. Gray
Download or read book An Introduction to Statistical Signal Processing written by Robert M. Gray and published by Cambridge University Press. This book was released on 2004-12-02 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the essential tools and techniques of statistical signal processing. At every stage theoretical ideas are linked to specific applications in communications and signal processing using a range of carefully chosen examples. The book begins with a development of basic probability, random objects, expectation, and second order moment theory followed by a wide variety of examples of the most popular random process models and their basic uses and properties. Specific applications to the analysis of random signals and systems for communicating, estimating, detecting, modulating, and other processing of signals are interspersed throughout the book. Hundreds of homework problems are included and the book is ideal for graduate students of electrical engineering and applied mathematics. It is also a useful reference for researchers in signal processing and communications.
Book Synopsis Random Matrix Theory And Its Applications: Multivariate Statistics And Wireless Communications by : Zhidong Bai
Download or read book Random Matrix Theory And Its Applications: Multivariate Statistics And Wireless Communications written by Zhidong Bai and published by World Scientific. This book was released on 2009-07-27 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random matrix theory has a long history, beginning in the first instance in multivariate statistics. It was used by Wigner to supply explanations for the important regularity features of the apparently random dispositions of the energy levels of heavy nuclei. The subject was further deeply developed under the important leadership of Dyson, Gaudin and Mehta, and other mathematical physicists.In the early 1990s, random matrix theory witnessed applications in string theory and deep connections with operator theory, and the integrable systems were established by Tracy and Widom. More recently, the subject has seen applications in such diverse areas as large dimensional data analysis and wireless communications.This volume contains chapters written by the leading participants in the field which will serve as a valuable introduction into this very exciting area of research.
Book Synopsis Random Matrix Methods for Wireless Communications by : Romain Couillet
Download or read book Random Matrix Methods for Wireless Communications written by Romain Couillet and published by Cambridge University Press. This book was released on 2011-09-29 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Blending theoretical results with practical applications, this book provides an introduction to random matrix theory and shows how it can be used to tackle a variety of problems in wireless communications. The Stieltjes transform method, free probability theory, combinatoric approaches, deterministic equivalents and spectral analysis methods for statistical inference are all covered from a unique engineering perspective. Detailed mathematical derivations are presented throughout, with thorough explanation of the key results and all fundamental lemmas required for the reader to derive similar calculus on their own. These core theoretical concepts are then applied to a wide range of real-world problems in signal processing and wireless communications, including performance analysis of CDMA, MIMO and multi-cell networks, as well as signal detection and estimation in cognitive radio networks. The rigorous yet intuitive style helps demonstrate to students and researchers alike how to choose the correct approach for obtaining mathematically accurate results.
Book Synopsis Random Matrix Methods for Wireless Communications by : Romain Couillet
Download or read book Random Matrix Methods for Wireless Communications written by Romain Couillet and published by . This book was released on 2011 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Blending theoretical results with practical applications, this book provides an introduction to random matrix theory and shows how it can be used to tackle a variety of problems in wireless communications. The Stieltjes transform method, free probability theory, combinatoric approaches, deterministic equivalents and spectral analysis methods for statistical inference are all covered from a unique engineering perspective. Detailed mathematical derivations are presented throughout, with thorough explanation of the key results and all fundamental lemmas required for the reader to derive similar calculus on their own. These core theoretical concepts are then applied to a wide range of real-world problems in signal processing and wireless communications, including performance analysis of CDMA, MIMO and multi-cell networks, as well as signal detection and estimation in cognitive radio networks. The rigorous yet intuitive style helps demonstrate to students and researchers alike how to choose the correct approach for obtaining mathematically accurate results"--
Book Synopsis Random Matrices and Their Applications by : Joel E. Cohen
Download or read book Random Matrices and Their Applications written by Joel E. Cohen and published by American Mathematical Soc.. This book was released on 1986 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features twenty-six expository papers on random matrices and products of random matrices. This work reflects both theoretical and applied concerns in fields as diverse as computer science, probability theory, mathematical physics, and population biology.
Book Synopsis Spectral Theory Of Large Dimensional Random Matrices And Its Applications To Wireless Communications And Finance Statistics: Random Matrix Theory And Its Applications by : Zhaoben Fang
Download or read book Spectral Theory Of Large Dimensional Random Matrices And Its Applications To Wireless Communications And Finance Statistics: Random Matrix Theory And Its Applications written by Zhaoben Fang and published by World Scientific. This book was released on 2014-01-24 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains three parts: Spectral theory of large dimensional random matrices; Applications to wireless communications; and Applications to finance. In the first part, we introduce some basic theorems of spectral analysis of large dimensional random matrices that are obtained under finite moment conditions, such as the limiting spectral distributions of Wigner matrix and that of large dimensional sample covariance matrix, limits of extreme eigenvalues, and the central limit theorems for linear spectral statistics. In the second part, we introduce some basic examples of applications of random matrix theory to wireless communications and in the third part, we present some examples of Applications to statistical finance.
Book Synopsis Smart Grid using Big Data Analytics by : Robert C. Qiu
Download or read book Smart Grid using Big Data Analytics written by Robert C. Qiu and published by John Wiley & Sons. This book was released on 2017-02-08 with total page 983 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at students in communications and signal processing who want to extend their skills in the energy area. It describes power systems and why these backgrounds are so useful to smart grid, wireless communications being very different to traditional wireline communications.
Book Synopsis Spectral Analysis of Large Dimensional Random Matrices by : Zhidong Bai
Download or read book Spectral Analysis of Large Dimensional Random Matrices written by Zhidong Bai and published by Springer Science & Business Media. This book was released on 2009-12-10 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to introduce basic concepts, main results, and widely applied mathematical tools in the spectral analysis of large dimensional random matrices. The core of the book focuses on results established under moment conditions on random variables using probabilistic methods, and is thus easily applicable to statistics and other areas of science. The book introduces fundamental results, most of them investigated by the authors, such as the semicircular law of Wigner matrices, the Marcenko-Pastur law, the limiting spectral distribution of the multivariate F matrix, limits of extreme eigenvalues, spectrum separation theorems, convergence rates of empirical distributions, central limit theorems of linear spectral statistics, and the partial solution of the famous circular law. While deriving the main results, the book simultaneously emphasizes the ideas and methodologies of the fundamental mathematical tools, among them being: truncation techniques, matrix identities, moment convergence theorems, and the Stieltjes transform. Its treatment is especially fitting to the needs of mathematics and statistics graduate students and beginning researchers, having a basic knowledge of matrix theory and an understanding of probability theory at the graduate level, who desire to learn the concepts and tools in solving problems in this area. It can also serve as a detailed handbook on results of large dimensional random matrices for practical users. This second edition includes two additional chapters, one on the authors' results on the limiting behavior of eigenvectors of sample covariance matrices, another on applications to wireless communications and finance. While attempting to bring this edition up-to-date on recent work, it also provides summaries of other areas which are typically considered part of the general field of random matrix theory.
Book Synopsis Random Matrix Methods for Wireless Communications by : Romain Couillet
Download or read book Random Matrix Methods for Wireless Communications written by Romain Couillet and published by . This book was released on 2014-05-14 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to random matrix theory and its applications to real-world problems in signal processing and wireless communications.
Book Synopsis Free Probability and Random Matrices by : James A. Mingo
Download or read book Free Probability and Random Matrices written by James A. Mingo and published by Springer. This book was released on 2017-06-24 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.
Download or read book Random Matrices written by Alexei Borodin and published by American Mathematical Soc.. This book was released on 2019-10-30 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random matrix theory has many roots and many branches in mathematics, statistics, physics, computer science, data science, numerical analysis, biology, ecology, engineering, and operations research. This book provides a snippet of this vast domain of study, with a particular focus on the notations of universality and integrability. Universality shows that many systems behave the same way in their large scale limit, while integrability provides a route to describe the nature of those universal limits. Many of the ten contributed chapters address these themes, while others touch on applications of tools and results from random matrix theory. This book is appropriate for graduate students and researchers interested in learning techniques and results in random matrix theory from different perspectives and viewpoints. It also captures a moment in the evolution of the theory, when the previous decade brought major break-throughs, prompting exciting new directions of research.
Book Synopsis The Development and Application of Random Matrix Theory in Adaptive Signal Processing in the Sample Deficient Regime by : Milutin Pajovic
Download or read book The Development and Application of Random Matrix Theory in Adaptive Signal Processing in the Sample Deficient Regime written by Milutin Pajovic and published by . This book was released on 2014 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis studies the problems associated with adaptive signal processing in the sample deficient regime using random matrix theory. The scenarios in which the sample deficient regime arises include, among others, the cases where the number of observations available in a period over which the channel can be approximated as time-invariant is limited (wireless communications), the number of available observations is limited by the measurement process (medical applications), or the number of unknown coefficients is large compared to the number of observations (modern sonar and radar systems). Random matrix theory, which studies how different encodings of eigenvalues and eigenvectors of a random matrix behave, provides suitable tools for analyzing how the statistics estimated from a limited data set behave with respect to their ensemble counterparts. The applications of adaptive signal processing considered in the thesis are (1) adaptive beamforming for spatial spectrum estimation, (2) tracking of time-varying channels and (3) equalization of time-varying communication channels. The thesis analyzes the performance of the considered adaptive processors when operating in the deficient sample support regime. In addition, it gains insights into behavior of different estimators based on the estimated second order statistics of the data originating from time-varying environment. Finally, it studies how to optimize the adaptive processors and algorithms so as to account for deficient sample support and improve the performance. In particular, random matrix quantities needed for the analysis are characterized in the first part. In the second part, the thesis studies the problem of regularization in the form of diagonal loading for two conventionally used spatial power spectrum estimators based on adaptive beamforming, and shows the asymptotic properties of the estimators, studies how the optimal diagonal loading behaves and compares the estimators on the grounds of performance and sensitivity to optimal diagonal loading. In the third part, the performance of the least squares based channel tracking algorithm is analyzed, and several practical insights are obtained. Finally, the performance of multi-channel decision feedback equalizers in time-varying channels is characterized, and insights concerning the optimal selection of the number of sensors, their separation and constituent filter lengths are presented.
Book Synopsis An Introduction to Statistical Analysis of Random Arrays by : V. L. Girko
Download or read book An Introduction to Statistical Analysis of Random Arrays written by V. L. Girko and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "An Introduction to Statistical Analysis of Random Arrays".
