The Experts below are selected from a list of 18939 Experts worldwide ranked by ideXlab platform
Jiashu Zhang - One of the best experts on this subject based on the ideXlab platform.
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functional link neural network cascaded with chebyshev Orthogonal Polynomial for nonlinear channel equalization
2008Co-Authors: Haiquan Zhao, Jiashu ZhangAbstract:Nonlinear intersymbol interference (ISI) leads to significant error rate in nonlinear communication and digital storage channel. In this paper, therefore, a novel computationally efficient functional link neural network cascaded with Chebyshev Orthogonal Polynomial is proposed to combat nonlinear ISI. The equalizer has a simple structure in which the nonlinearity is introduced by functional expansion of the input pattern by trigonometric Polynomial and Chebyshev Orthogonal Polynomial. Due to the input pattern and nonlinear approximation enhancement, the proposed structure can approximate arbitrarily nonlinear decision boundaries. It has been utilized for nonlinear channel equalization. The performance of the proposed adaptive nonlinear equalizer is compared with functional link neural network (FLNN) equalizer, multilayer perceptron (MLP) network and radial basis function (RBF) along with conventional normalized least-mean-square algorithms (NLMS) for different linear and nonlinear channel models. The comparison of convergence rate, bit error rate (BER) and steady state error performance, and computational complexity involved for neural network equalizers is provided.
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neural legendre Orthogonal Polynomial adaptive equalizer
2006Co-Authors: Haiquan Zhao, Jiashu Zhang, Mingyuan Xie, Xiangping ZengAbstract:A novel structure of neural network legendre Orthogonal Equalizers is proposed when dealing with severe linear and nonlinear distortion. The equalizer is presented based on characteristic of single layer neural network and structure of legendre Orthogonal Polynomial after the analysis of few parameter nonlinear filter, and adaptive algorithm is deduced with NLMS. To support the analysis, simulation results for nonlinear channel are provided.
Haiquan Zhao - One of the best experts on this subject based on the ideXlab platform.
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functional link neural network cascaded with chebyshev Orthogonal Polynomial for nonlinear channel equalization
2008Co-Authors: Haiquan Zhao, Jiashu ZhangAbstract:Nonlinear intersymbol interference (ISI) leads to significant error rate in nonlinear communication and digital storage channel. In this paper, therefore, a novel computationally efficient functional link neural network cascaded with Chebyshev Orthogonal Polynomial is proposed to combat nonlinear ISI. The equalizer has a simple structure in which the nonlinearity is introduced by functional expansion of the input pattern by trigonometric Polynomial and Chebyshev Orthogonal Polynomial. Due to the input pattern and nonlinear approximation enhancement, the proposed structure can approximate arbitrarily nonlinear decision boundaries. It has been utilized for nonlinear channel equalization. The performance of the proposed adaptive nonlinear equalizer is compared with functional link neural network (FLNN) equalizer, multilayer perceptron (MLP) network and radial basis function (RBF) along with conventional normalized least-mean-square algorithms (NLMS) for different linear and nonlinear channel models. The comparison of convergence rate, bit error rate (BER) and steady state error performance, and computational complexity involved for neural network equalizers is provided.
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neural legendre Orthogonal Polynomial adaptive equalizer
2006Co-Authors: Haiquan Zhao, Jiashu Zhang, Mingyuan Xie, Xiangping ZengAbstract:A novel structure of neural network legendre Orthogonal Equalizers is proposed when dealing with severe linear and nonlinear distortion. The equalizer is presented based on characteristic of single layer neural network and structure of legendre Orthogonal Polynomial after the analysis of few parameter nonlinear filter, and adaptive algorithm is deduced with NLMS. To support the analysis, simulation results for nonlinear channel are provided.
Maurice Duits - One of the best experts on this subject based on the ideXlab platform.
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global fluctuations for multiple Orthogonal Polynomial ensembles
2021Co-Authors: Maurice Duits, Benjamin Fahs, Rostyslav KozhanAbstract:Abstract We study the fluctuations of linear statistics with Polynomial test functions for Multiple Orthogonal Polynomial Ensembles. Multiple Orthogonal Polynomial Ensembles form an important class of determinantal point processes that include random matrix models such as the GUE with external source, complex Wishart matrices, multi-matrix models and others. Our analysis is based on the recurrence matrix for the multiple Orthogonal Polynomials, that is constructed out of the nearest neighbor recurrences. If the coefficients for the nearest neighbor recurrences have limits, then we show that the right-limit of this recurrence matrix is a matrix that can be viewed as representation of a Toeplitz operator with respect to a non-standard basis. This will allow us to prove Central Limit Theorems for linear statistics of Multiple Orthogonal Polynomial Ensembles. A particular novelty is the use of the Baker–Campbell–Hausdorff formula to prove that the higher cumulants of the linear statistics converge to zero. We illustrate the main results by discussing Central Limit Theorems for the Gaussian Unitary Ensembles with external source, complex Wishart matrices and specializations of the Schur measure related to multiple Charlier, multiple Krawtchouk and multiple Meixner Polynomials.
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global fluctuations for multiple Orthogonal Polynomial ensembles
2019Co-Authors: Maurice Duits, Benjamin Fahs, Rostyslav KozhanAbstract:We study the fluctuations of linear statistics with Polynomial test functions for Multiple Orthogonal Polynomial Ensembles. Multiple Orthogonal Polynomial Ensembles form an important class of determinantal point processes that include random matrix models such as the GUE with external source, complex Wishart matrices, multi-matrix models and others. Our analysis is based on the recurrence matrix for the multiple Orthogonal Polynomials, that is constructed out of the nearest neighbor recurrences. If the coefficients for the nearest neighbor recurrences have limits, then we show that the right-limit of this recurrence matrix is a matrix that can be viewed as representation of a Toeplitz operator with respect to a non-standard basis. This will allow us to prove Central Limit Theorems for linear statistics of Multiple Orthogonal Polynomial Ensembles. A particular novelty is the use of the Baker--Campbell--Hausdorff formula to prove that the higher cumulants of the linear statistics converge to zero. We illustrate the main results by discussing Central Limit Theorems for the Gaussian Unitary Ensembles with external source, complex Wishart matrices and Markov processes related to multiple Charlier and multiple Krawtchouk Polynomials.
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universality of mesoscopic fluctuations for Orthogonal Polynomial ensembles
2016Co-Authors: Jonathan Breuer, Maurice DuitsAbstract:We prove that the fluctuations of mesoscopic linear statistics for Orthogonal Polynomial ensembles are universal in the sense that two measures with asymptotic recurrence coefficients have the same ...
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Universality of Mesoscopic Fluctuations for Orthogonal Polynomial Ensembles
2016Co-Authors: Jonathan Breuer, Maurice DuitsAbstract:We prove that the fluctuations of mesoscopic linear statistics for Orthogonal Polynomial ensembles are universal in the sense that two measures with asymptotic recurrence coefficients have the same asymptotic mesoscopic fluctuations (under an additional assumption on the local regularity of one of the measures). The convergence rate of the recurrence coefficients determines the range of scales on which the limiting fluctuations are identical. Our main tool is an analysis of the Green’s function for the associated Jacobi matrices.As a particular consequencewe obtain a central limit theorem for the modified Jacobi Unitary Ensembles on all mesoscopic scales.
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the nevai condition and a local law of large numbers for Orthogonal Polynomial ensembles
2013Co-Authors: Jonathan Breuer, Maurice DuitsAbstract:We consider asymptotics of Orthogonal Polynomial ensembles, in the macroscopic and mesoscopic scales. We prove both global and local laws of large numbers (analogous to the recently proven local semicircle law for Wigner matrices) under fairly weak conditions on the underlying measure $\mu$. Our main tools are a general concentration inequality for determinantal point processes with a kernel that is a self-adjoint projection, and a strengthening of the Nevai condition from the theory of Orthogonal Polynomials.
Kai Sundmacher - One of the best experts on this subject based on the ideXlab platform.
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method of moments over Orthogonal Polynomial bases
2014Co-Authors: Naim Bajcinca, Steffen Hofmann, Kai SundmacherAbstract:Abstract A method for the design of approximate models in the form of a system of ordinary differential equations (ODE) for a class of first-order linear partial differential equations of the hyperbolic type with applications to monovariate and multivariate population balance systems is proposed in this work. We develop a closed moment model by utilizing a least square approximation of spatial-dependent factors over an Orthogonal Polynomial basis. A bounded hollow shaped interval of convergence with respect to the order of the approximate ODE model arises as a consequence of the structural and finite precision computation numerical errors. The proposed modeling scheme is of interest in model-based control and optimization of processes with distributed parameters.
Xiangping Zeng - One of the best experts on this subject based on the ideXlab platform.
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neural legendre Orthogonal Polynomial adaptive equalizer
2006Co-Authors: Haiquan Zhao, Jiashu Zhang, Mingyuan Xie, Xiangping ZengAbstract:A novel structure of neural network legendre Orthogonal Equalizers is proposed when dealing with severe linear and nonlinear distortion. The equalizer is presented based on characteristic of single layer neural network and structure of legendre Orthogonal Polynomial after the analysis of few parameter nonlinear filter, and adaptive algorithm is deduced with NLMS. To support the analysis, simulation results for nonlinear channel are provided.
