Novel PAPR Reduction Scheme Based on Continuous Nonlinear Piecewise Companding Transform for OFDM Systems

In this paper,a novel efficient continuous piecewise nonlinear companding scheme is proposed for reducing the peak-to-average power ratio(PAPR)of orthogonal frequency division multiplexing(OFDM)systems.In the proposed companding transform,signal samples with large amplitudes is clipped for peak power reduction,and the signal samples with medium amplitudes is nonlinear transformed with power compensation.While the signal samples with small amplitudes remain unchanged.The whole companding function is continuous and smooth in the range of positive numbers,which is beneficial for guaranteeing the bit error rate(BER)and power spectral density(PSD)performance.This scheme can achieve a significant reduction in PAPR.And at the same time,it cause little increment in BER and PSD performance.Simulation results indicate the superiority of the proposed scheme over existing companding schemes.

Closed-Form and Analytical BER Expression for OFDM System with μ-Law Companding Operation

The μ-law companding function has been applied widely in orthogonal frequency division multiplexing (OFDM) to reduce the peak-to-average power ratio (PAPR). However, nonlinear distortion caused by the μ-law companding function is considered a key impairment in OFDM communication systems. Few studies have addressed theoretical nonlinear distortion caused by μ-law companding function for OFDM systems. In this paper, we derive a closed-form expression of signal distortion as well as the closed-form bit error rate (BER) of OFDM system caused by the μ-law companding function. Based on the theoretical signal distortion and BER expression, the theoretical BER value and signal distortion value can also be calculated, which can guide us to choose appropriate μ value for different BER condition and bit-to-noise (Eb/N0) condition efficiently. Then the PAPR performance can also be predicted. The results show good agreement on the Monte-Carlo simulation results and the obtained theoretical BER results. Furthermore, based on theoretical signal distortion and theoretical BER expression, the figure of the relationship among BER value, Eb/N0 and μ is also given. Based on this figure, we can find the appropriate μ law for different BER and Eb/N0 condition. And then the PAPR performance can also be predicted.

On the Use of Monotonicity-Preserving Interpolatory Techniques in Multilevel Schemes for Balance Laws

Cost-effective multilevel techniques for homogeneous hyperbolic conservation laws are very successful in reducing the computational cost associated to high resolution shock capturing numerical schemes.Because they do not involve any special data structure,and do not induce savings in memory requirements,they are easily implemented on existing codes and are recommended for 1D and 2D simulations when intensive testing is required.The multilevel technique can also be applied to balance laws,but in this case,numerical errors may be induced by the technique.We present a series of numerical tests that point out that the use of monotonicity-preserving interpolatory techniques eliminates the numerical errors observed when using the usual 4-point centered Lagrange interpolation,and leads to a more robust multilevel code for balance laws,while maintaining the efficiency rates observed forhyperbolic conservation laws.

High-order maximum-principle-preserving and positivity-preserving weighted compact nonlinear schemes for hyperbolic conservation laws

In this paper,the maximum-principle-preserving(MPP)and positivitypreserving(PP)flux limiting technique will be generalized to a class of high-order weighted compact nonlinear schemes(WCNSs)for scalar conservation laws and the compressible Euler systems in both one and two dimensions.The main idea of the present method is to rewrite the scheme in a conservative form,and then define the local limiting parameters via case-by-case discussion.Smooth test problems are presented to demonstrate that the proposed MPP/PP WCNSs incorporating a third-order Runge-Kutta method can attain the desired order of accuracy.Other test problems with strong shocks and high pressure and density ratios are also conducted to testify the performance of the schemes.

Application of a fourth-order relaxation scheme to hyperbolic systems of conservation laws

A fourth-order relaxation scheme is derived and applied to hyperbolic systems of conservation laws in one and two space dimensions. The scheme is based on a fourthorder central weighted essentially nonoscillatory （CWENO） reconstruction for one-dimensional cases, which is generalized to two-dimensional cases by the dimension-by-dimension approach. The large stability domain Runge-Kutta-type solver ROCK4 is used for time integration. The resulting method requires neither the use of Riemann solvers nor the computation of Jacobians and therefore it enjoys the main advantage of the relaxation schemes. The high accuracy and high-resolution properties of the present method are demonstrated in one- and two-dimensional numerical experiments.

Entropy convergence of new two-value scheme with slope relaxation for conservation laws

This paper establishes the resolution finite volume scheme with slope entropy convergence of a new two-value high relaxation for conservation laws. This scheme, motivated by the general method of high resolution schemes that have high-order accuracy in smooth regions of solutions and are free of oscillations near discontinuities, unifies and evolves slopes directly with a slope relaxation equation that governs the evolution of slopes in both smooth and discontinuous regions. Proper choices of slopes are realized adaptively via a relaxation parameter. The scheme is shown to be total-variation-bounded （TVB） stable and satisfies cell-entropy inequalities.

A TWO-DIMENSIONAL GLIMM TYPE SCHEME ON CAUCHY PROBLEM OF TWO-DIMENSIONAL SCALAR CONSERVATION LAW

In this paper,we construct a new two-dimensional convergent scheme to solve Cauchy problem of following two-dimensional scalar conservation law{ tu ＋ xf（u） ＋ yg（u） = 0,u（x,y,0） = u0（x,y）.In which initial data can be unbounded.Although the existence and uniqueness of the weak entropy solution are obtained,little is known about how to investigate two-dimensional or higher dimensional conservation law by the schemes based on wave interaction of 2D Riemann solutions and their estimation.So we construct such scheme in our paper and get some new results.

Caching Scheme Based on Power-Law Characteristic in Unstructured P2P Networks

In order to reduce the traffic load and improve the availability of the shared resources in unstructured P2P networks, a caching scheme combining alternative index and adaptive replication （AIAR） is presented. AIAR uses random walk mechanism to disperse the caching information of resources in the network based on its power-law characteristic, and dynamically adjusts replicas according to the visit frequency on resources and the degree information of peers. Subsequent experimental results show that the proposed AIAR scheme is beneficial to improve the search performance of success rate and respond speed. In addition, compared to some existing caching scheme, AIAR can perform much better in success rate, especially in a dynamic environment.

MmB DIFFERENCE SCHEMES FOR TWODIMENSIONAL HYPERBOLIC CONSERVATION LAWS

A new class of second order accuracy semidiscrete difference schemes is presented for the two-dimensional nonlinear scalar hyperbolic conservation laws. It is based on flux splitting, piecewise linear cell-averaged reconstruction and upwind property in the spatial discretization. By using TVD Runge-Kutta time discretization method, the full discrete scheme is obtained and its MmB property is proved. The extension to the two-dimensionalnonlinear hyperbolic conservation law systems is straightforward by using component-wise manner. The main advantage is simple: no Riemann problem is solved, and so field-by-field decomposition is avoided and the complicated computation is reduced. Numerical results of two-dimensional Euler equations of compressible gas dynamics verify the accuracy and robustness of the method.

LARGE TIME STEP GENERALIZATION OF RANDOM CHOICE FINITE DIFFERENCE SCHEME FOR HYPERBOLIC CONSERVATION LAWS

A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of their conserved quantities. We show consistency of the scheme for arbitrarily large Courant numbers. For scalar problems the scheme is total variation diminishing.A brief discussion is given for entropy condition.

Cavitating/non-cavitating flows simulation by third-order finite volume scheme and power-law preconditioning method

Equations of steady inviscid and laminar flows are solved by means of a third-order finite volume （FV） scheme. For this purpose, a cell-centered discretization technique is employed. In this technique, the flow parameters at the cell faces are computed using a third-order weighted averages procedure. A fourth-order artificial dissipation is used for stability of the solution. In order to achieve the steady-state situation, four-step Runge-Kutta explicit time integration method is applied. An advanced progressive preconditioning method, named the power-law preconditioning method, is used for faster convergence. In this method, the preconditioning matrix is adjusted automatically from the velocity and/or pressure flow-field by a power-law relation. Attention is directed towards accuracy and convergence of the schemes. The results presented in the paper focus on steady inviscid and laminar flows around sheet-cavitating and fully-wetted bodies including hydrofoils and circular/elliptical cylinder. Excellent agreements are obtained when numerical predictions are compared with other available experimental and numerical results. In addition, it is found that using the power-law preconditioner significantly increases the numerical convergence speed.

使用μ-law压扩算法降低OFDM系统PAPR的分析

提出使用μ-law压扩算法降低OFDM系统PAPR(峰值平均功率比),对PAPR概率分布进行了理论分析。理论分析和仿真结果表明采用压扩技术可有效地降低OFDM系统的PAPR,同时还对采用预失真放大器AWGN信道中的OFDM系统的性能进行了仿真。

An Explicit High Resolution Scheme for Nonlinear Shallow Water Equations

The present study develops a numerical model of the two-dimensional fully nonlinear shallow water equations （NSWE） for the wave run-up on a beach. The finite volume method （FVM） is used to solve the equations, and a second-order explicit scheme is developed to improve the computation efficiency. The numerical fluxes are obtained by the two dimensional Roe＇ s flux function to overcome the errors caused by the use of one dimensional fluxes in dimension splitting methods. The high-resolution Godunov-type TVD upwind scheme is employed and a second-order accuracy is achieved based on monotonic upstream schemes for conservation laws （MUSCL） variable extrapolation; a nonlinear limiter is applied to prevent unwanted spurious oscillation. A simple but efficient technique is adopted to deal with the moving shoreline boundary. The verification of the solution technique is carried out by comparing the model output with documented results and it shows that the solution technique is robust.

Birkhoffian Symplectic Scheme for a Quantum System

In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure- preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f . Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system.

A local energy-preserving scheme for Zakharov system

In this paper, we propose a local conservation law for the Zakharov system. The property is held in any local time- space region which is independent of the boundary condition and more essential than the global energy conservation law. Based on the rule that the numerical methods should preserve the intrinsic properties as much as possible, we propose a local energy-preserving （LEP） scheme for the system. The merit of the proposed scheme is that the local energy conservation law can be conserved exactly in any time-space region. With homogeneous Dirchlet boundary conditions, the proposed LEP scheme also possesses the discrete global mass and energy conservation laws. The theoretical properties are verified by numerical results.

Multi-symplectic scheme for the coupled Schrdinger-Boussinesq equations

In this paper, a multi-symplectic Hamiltonian formulation is presented for the coupled Schrdinger-Boussinesq equations （CSBE）. Then, a multi-symplectic scheme of the CSBE is derived. The discrete conservation laws of the Langmuir plasmon number and total perturbed number density are also proved. Numerical experiments show that the multi-symplectic scheme simulates the solitary waves for a long time, and preserves the conservation laws well.

Conservative and Easily Implemented Finite Volume Semi-Lagrangian WENO Methods for 1D and 2D Hyperbolic Conservation Laws

The paper is devised to propose finite volume semi-Lagrange scheme for approximating linear and nonlinear hyperbolic conservation laws. Based on the idea of semi-Lagrangian scheme, we transform the integration of flux in time into the integration in space. Compared with the traditional semi-Lagrange scheme, the scheme devised here tries to directly evaluate the average fluxes along cell edges. It is this difference that makes the scheme in this paper simple to implement and easily extend to nonlinear cases. The procedure of evaluation of the average fluxes only depends on the high-order spatial interpolation. Hence the scheme can be implemented as long as the spatial interpolation is available, and no additional temporal discretization is needed. In this paper, the high-order spatial discretization is chosen to be the classical 5th-order weighted essentially non-oscillatory spatial interpolation. In the end, 1D and 2D numerical results show that this method is rather robust. In addition, to exhibit the numerical resolution and efficiency of the proposed scheme, the numerical solutions of the classical 5th-order WENO scheme combined with the 3rd-order Runge-Kutta temporal discretization (WENOJS) are chosen as the reference. We find that the scheme proposed in the paper generates comparable solutions with that of WENOJS, but with less CPU time.

Multi-symplectic Geometry and Preissmann Scheme for GSDBM Equation

The multi-symplectic geometry for the GSDBM equation is presented in this paper. The multi-symplectic formulations for the GSDBM equation are presented and the local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. The multi-symplectic discretization of each formulation is exemplified by the multisymplectic Preissmann scheme. The numerical experiments are given, and the results verify the efficiency of the Preissmann scheme.

Regularity of Fluxes in Nonlinear Hyperbolic Balance Laws

This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws.The basic idea is that the“meaningful objects”are the fluxes,evaluated across domain boundaries over time intervals.The fundamental result in this treatment is the regularity of the flux trace in the multi-dimensional setting.It implies that a weak solution indeed satisfies the balance law.In fact,it is shown that the flux is Lipschitz continuous with respect to suitable perturbations of the boundary.It should be emphasized that the weak solutions considered here need not be entropy solutions.Furthermore,the assumption imposed on the flux f(u)is quite minimal-just that it is locally bounded.

On the Conservative Finite Difference Scheme for the Generalized Novikov Equation

In this paper, we investigate a numerical method for the generalized Novikov equation. We propose a conservative finite difference scheme and use Brouwer fixed point theorem to obtain the existence of the solution of the corresponding difference equation. We also prove the convergence and stability of the solution by using the discrete energy method. Moreover, we obtain the truncation error of the difference scheme which is .