Analytical Method for Joint Optimization of Ffe and Dfe Equalizations for Multi-Level Signals

Channel equalization is the efficient method for recovering distorted signal and correspondingly reducing bit error rate (BER). Different type of equalizations, like feed forward equalization (FFE) and decision feedback equalization (DFE) are canceling channel effect and recovering channel response. Separate optimization of tap coefficients for FFE and DFE does not give optimal result. In this case FFE and DFE tap coefficients are found separately and they are not collaborating. Therefore, the final equalization result is not global optimal. In the present paper new analytical method for finding best tap coefficients for FFE and DFE joint equalization is introduced. The proposed method can be used for both NRZ and PAM4 signals. The idea of the methodology is to combine FFE and DFE tap coefficients into one optimization problem and allow them to collaborate and lead to the global optimal solution. The proposed joint optimization method is fast, easy to implement and efficient. The method has been tested for several measured channels and the analysis of the results are discussed

Fast Impedance Prediction for Power Distribution Network using Deep Learning

Modeling and simulating a power distribution network (PDN) for printed circuit boards with irregular board shapes and multi-layer stackup is computationally inefficient using full-wave simulations. This paper presents a new concept of using deep learning for PDN impedance prediction. A boundary element method (BEM) is applied to efficiently calculate the impedance for arbitrary board shape and stackup. Then over one million boards with different shapes, stackup, integrated circuits (IC) location, and decap placement are randomly generated to train a deep neural network (DNN). The trained DNN can predict the impedance accurately for new board configurations that have not been used for training. The consumed time using the trained DNN is only 0.1 s, which is over 100 times faster than the BEM method and 10 000 times faster than full-wave simulations

Large time asymptotic and numerical solution of a nonlinear diffusion model with memory

Computers and Mathematics with Applications, 59, (2010), 254–273The article of record as published may be located at http://dx.doi.org/10.1016/j.camwa.2009.07.052Large time behavior of solutions and finite difference approximation of a nonlinear system of integro-differential equations associated with the penetration of a magnetic field into a substance is studied. Two initial-boundary value problems are investigated: the first with homogeneous conditions on whole boundary and the second with nonhomogeneous boundary data on one side of lateral boundary. The rates of convergence are also given. Mathematical results presented show that there is a difference between stabilization rates of solutions with homogeneous and nonhomogeneous boundary conditions. The convergence of the corresponding finite difference scheme is also proved. The decay of the numerical solution is compared with the analytical results

Galerkin Finite Element Method for One Nonlinear Integro-Differential Model

Applied Mathematics and Computation, 217, (2011), 6883-6892, doi:10.1016/j.amc.2011.01.053.The article of record as published may be located at http://dx.doi.org/10.1016/j.amc.2011.01.053Galerkin finite element method for the approximation of a nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. First type initial-boundary value problem is investigated. The convergence of the finite ele- ment scheme is proved. The rate of convergence is given too. The decay of the numerical solution is compared with the analytical results

Finite difference approximation of a nonlinear integro-differential system

The article of record as published may be located at http://dx.doi.org/10.1016/j.amc.2009.05.061Finite difference approximation of the nonlinear integro-differential system associated with the penetration of a magnetic field into a substance is studied. The convergence of the finite difference scheme is proved. The rate of convergence of the discrete scheme is given. The decay of the numerical solution is compared with the analytical results proven earlier

Large time behavior of solutions and finite difference scheme to a nonlinear integro-differential equation

The large-time behavior of solutions and finite difference approximations of the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance are studied. Asymptotic properties of solutions for the initial boundary value problem with homogeneous Dirichlet boundary conditions is considered. The rates of convergence are given too. The convergence of the semidiscrete and the finite difference schemes are also provided

Large time behavior of solutions to a nonlinear integro-differential system

The article of record as published may be found at http://dx.doi.org/10.1016/j.jmaa.2008.10.016Asymptotic behavior of solutions as t à ¢ à ¢ to the nonlinear integro-differential system associated with the penetration of a magnetic field into a substance is studied. Initialà ¢ boundary value problems with two kinds of boundary data are considered. The first with homogeneous conditions on whole boundary and the second with non-homogeneous boundary data on one side of lateral boundary. The rates of convergence are given too.Authors thank referees for valuable suggestions. The research described in this publication was made possible in part by Award No. NSS #17-07 of the U.S. Civilian Research & Development Foundation (CRDF), the Georgia National Science Foundation (GNSF) and the Georgian Research and Development Foundation (GRDF). The designated project has been fulfilled by financial support of the Georgia National Science Foundation (Grant #GNSF/ST07/3-176). Any idea in this publication is possessed by the authors and may not represent the opinion of the Georgia National Science Foundation itself. The second author thanks the Naval Postgraduate School for hosting him

Large time behavior of solutions and finite difference scheme to a nonlinear integro-differential equation

Computers and Mathematics with Applications, 57, (2009), 799–811.The large-time behavior of solutions and finite difference approximations of the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance are studied. Asymptotic properties of solutions for the initial-boundary value problem with homogeneous Dirichlet boundary conditions is considered. The rates of convergence are given too. The convergence of the semidiscrete and the finite difference schemes are also proved.The article of record as published may be located at http://dx.doi.org/10.1016/j.camwa.2008.09.05

Finite element approximations of a nonlinear diffusion model with memory

The article of record as published may be located at http://dx.doi.org/10.1007/s11075-012-9658-7The convergence of a finite element scheme approximating a nonlinear system of integro-differential equations is proven. This system arises in mathematical modeling of the process of a magnetic field penetrating into a substance. Properties of existence, uniqueness and asymptotic behavior of the solutions are briefly described. The decay of the numerical solution is compared with both the theoretical and finite difference results