optimum asymptotic multiuser efficiency of randomly spread cdma this correspondence analyzes the high signal to noise ratio snr performance of optimum multiuser detectors for synchronous direct sequence spread spectrum with random spreading in an additive white gaussian noise channel under very general conditions on the received powers we show that the optimum asymptotic efficiency of a k user system with spreading gain n converges to 1 almost surely as k spl rarr spl infin and k n is kept equal to an arbitrary nonzero constant therefore the asymptotic behavior of the minimum bit error rate is equivalent to that of a single user system

nonlinear scattering theory at low energy abstract we study the scattering theory of a conservative nonlinear one parameter group of operators on a hilbert space x relative to a group of linear unitary operators under certain hypotheses the scattering operator carries a neighborhood of 0 in x into x the theory is designed to apply to the semilinear schrodinger and klein gordon equations

a cdma multiuser detection algorithm on the basis of belief propagation an iterative algorithm for the multiuser detection problem that arises in code division multiple access cdma systems is developed on the basis of pearl s belief propagation bp we show that the bp based algorithm exhibits nearly optimal performance in a practical time scale by utilizing the central limit theorem and self averaging property appropriately whereas direct application of bp to the detection problem is computationally difficult and far from practical we further present close relationships of the proposed algorithm to the thouless anderson palmer approach and replica analysis known in spin glass research

a d n alternating algorithm for exterior 3 d poisson problem with prolate spheroid boundary in this paper a d n alternating algorithm based on the natural boundary reduction nbr is discussed to solve exterior three dimensional 3 d poisson problem with prolate spheroid artificial boundary by the principle of the natural boundary reduction we obtain the natural integral equation on prolate spheroid artificial boundary suggest a d n alternating algorithm and analysis its convergence of the algorithm finally some numerical examples are presented to show the effectiveness of this method

a family of likelihood ascent search multiuser detectors approaching optimum performance via random multicodes with linear complexity tse and verdu proved that the global maximum likelihood gml detector achieves unit asymptotic multiuser efficiency ame in the limit of large random spreading cdma in this paper we show that the wide sense sequential likelihood ascent search wslas detectors achieve unit ame with channel load 1 2 1 4 ln 2 bits s hz in simulations for random multicode equal power systems the wslas with a linear per bit complexity approaches the gml ber in all snr with channel load as high as 1 05 bits s hz

asymptotic normality of linear multiuser receiver outputs this paper proves large system asymptotic normality of the output of a family of linear multiuser receivers that can be arbitrarily well approximated by polynomial receivers this family of receivers encompasses the single user matched filter the decorrelator the minimum mean square error mmse receiver the parallel interference cancelers and many other linear receivers of interest both with and without the assumption of perfect power control we show that the output decision statistic for each user converges to a gaussian random variable in distribution as the number of users and the spreading factor both tend to infinity with their ratio fixed analysis reveals that the distribution conditioned on almost all spreading sequences converges to the same distribution which is also the unconditional distribution this normality principle allows the system performance e g the multiuser efficiency to be completely determined by the output signal to interference ratio sir for large linear systems

a schwarz alternating algorithm for elliptic boundary value problems in an infinite domain with a concave angle in this paper we investigate a schwarz alternating algorithm for elliptic boundary value problems in an infinite domain with a concave angle which is an overlapping domain decomposition method based on natural boundary reduction nbr the algorithm is constructed and its convergence is discussed the finite element and natural boundary element method are alternatively applied to solve a bounded subdomain and a typical unbounded subdomain it has overcome the difficulty met in standard domain decomposition method for problems with unbounded domains the convergence rate is analyzed in details for a typical domain finally some numerical examples are presented to show the effectiveness of this method

strong decay for wave equations with nonlinear nonmonotone damping thus the energy is nonincreasing and the term p represents damping here and always the ymbols i ii denote the norm on the sobolev space wk p o 1 the classical example p d u d a positive constant shows that under reasonable coercivity hypotheses concerning f any solution u u decays to zero exponentially with respect to the trong topology on the energy space hd o 1 x l o 1 this property is preserved even if tl d x with d 0 on a certain nonvoid subinterval i e 0 l see l 4 moreover the same is true if p d g u d as above and g is globally lipschitz and satisfies the growth condition g w w 2 const w2 wer 1 2 cf 3 in the case f 0 3 d x g ut g monotone the strong decay to zero follows from a variant of the lasalle invariance principle see 5 91 in some particular cases the speed of convergence is obtained lo

a family of likelihood ascent search multiuser detectors an upper bound of bit error rate and a lower bound of asymptotic multiuser efficiency in this paper the bit error performance of a family of likelihood ascent search las multiuser detectors is analyzed an upper bound on the ber of any las detector is obtained by bounding the fixed point region with the worst initial detector the concept of indecomposable errors developed by verdu is applied to tighten the upper bound in a special instance the upper bound is reduced to that for all the local maximum likelihood detectors the upper bound is comparable with that of the optimum detector obtained by verdu a lower bound on the asymptotic multiuser efficiency ame is then obtained it is shown that there are nontrivial cdma channels such that a las detector can achieve unit ame regardless of user number the ame lower bound provides a means for further seeking a good set of spreading sequences and power distribution for spectral and power efficient cdma

local soltutions for a nonlinear degenerate hyperbolic equation on etudie l existence et l unicite des solutions locales pour le probleme mixte associe a l equation hyperbolique degenere du type 2 u 2 m u x t 2 dx u 0 ou est un ouvert borne de r n a frontiere lisse et x est un vecteur de r n

on solutions of semilinear wave equations under the first initial boundary condition and prove the existence of functions which exist for every t 3 0 and solve the equations in a sense defined in this paper and for some classes of equations with the first order dissipation we find an unbounded set in a subspace of l2 q 12 with a property that if initial value belongs to it then the equation has a global classical solution let x t be a space time variable in ir x 0 03 let us consider the following semilinear wave equations

a finite element method for solving helmholtz type equations in waveguides and other unbounded domains a finite element method is described for solving helmholtz type boundary value problems in unbounded regions including those with infinite boundaries typical examples include the propagation of acoustic or electromagnetic waves in waveguides the radiation condition at infinity is based on separation of variables and differs from the classical sommerfeld radiation condition it is shown that the problem may be replaced by a boundary value problem on a fixed bounded domain the behavior of the solution near infinity is incorporated in a nonlocal boundary condition this problem is given a weak or variational formulation and the finite element method is then applied it is proved that optimal error estimates hold

a domain decomposition method for biharmonic equation abstract the domain decomposition method proposed by schwarz 1 is gaining significance in view of the possibilities for parallel implementation in this paper we apply the domain decomposition method to the biharmonic equation in two overlapping discs in each subdomain a boundary integral formula is used to obtain the solution unlike the finite element or finite difference methods where the iterations have to be performed on the entire domain the iterations of the boundary integral formulation need to be done only at the discretized points of the boundaries another aspect of the paper is that in order to handle the operations with dense matrices arising from the boundary integral formulation the discrete wavelet transform is used to compress the matrices which results in reduced computations without loss of accuracy examples involving a laplace equation in an l shaped region and a domain bounded by a cardioid and a circle are also illustrated

a schwarz alternating algorithm for a three dimensional exterior harmonic problem with prolate spheroid boundary in this paper we investigate a schwarz alternating algorithm for a three dimensional exterior harmonic problem with prolate spheroid boundary based on natural boundary reduction the algorithm is constructed and its convergence is discussed the finite element method and the natural boundary element method are alternatively applied to solve the problem in a bounded subdomain and a typical unbounded subdomain the convergence rate is analyzed in detail for a typical domain two numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method

asymptotics for the nonlinear dissipative wave equation we are interested in the asymptotic behaviour of global classical solutions to the initial boundary value problem for the nonlinear dissipative wave equation in the whole space or the exterior domain outside a star shaped obstacle we shall treat the nonlinear dissipative term like 1 1 x u t u t 1 0 and prove that the energy does not in general decay further we can deduce that the classical solution is asymptotically free and the local energy decays at a certain rate as the time goes to infinity

nonlinear wave equations on a class of bounded fractal sets the nonlinear wave equation u tt u f u with given initial data and zero boundary conditions on a class of bounded self similar fractal sets is investigated the sobolev type inequality is the starting point of this work which holds for a class of fractals including the well known sierpinski gasket we obtain the global existence of strong solutions for suitable f if the spectral dimension ds of the fractal satisfies ds 2 the key is to construct the wave propagator and hilbert spaces of functions on the fractal the main difficulty in obtaining the global existence of a weak solution is establishing a priori estimates depending on a regularity property for f t he regularity property of a weak solution is obtained through a fine analysis in which the sobolev type inequality plays a crucial role 2002 elsevier science usa all rights reserved

existence of global smooth solutions to the initial boundary value problem for the quasi linear wave equation with a degenerate dissipative term let c be a bounded domain with smooth boundary dq in the n dimen sional euclidean space rn and let us consider the initial boundary value problem for the classical quasi linear wave equation with a dissipation u v a lvul vu u x u o in qx o ce 4x 0 uo

approximate belief propagation density evolution and statistical neurodynamics for cdma multiuser detection we present a theory to analyze the performance of the parallel interference canceller pic for code division multiple access cdma multiuser detection applied to a randomly spread fully synchronous baseband uncoded cdma channel model with additive white gaussian noise under perfect power control in the large system limit we reformulate pic as an approximation to the belief propagation algorithm for the detection problem we then apply the density evolution framework to analyze its detection dynamics it turns out that density evolution for pic is essentially the same as statistical neurodynamics a theory to describe dynamics of a certain type of neural network model adopting this correspondence we develop the density evolution framework for pic using statistical neurodynamics the resulting formulas however are only approximately correct for describing detection dynamics of pic even in the large system limit because we ignore the onsager reaction terms in the derivation we then propose a modified pic algorithm in which we subtract the onsager reaction terms algorithmically for which the density evolution formulas give a correct description of the detection dynamics in the large system limit

a statistical mechanics approach to large system analysis of cdma multiuser detectors we present a theory based on statistical mechanics to evaluate analytically the performance of uncoded fully synchronous randomly spread code division multiple access cdma multiuser detectors with additive white gaussian noise awgn channel under perfect power control and in the large system limit application of the replica method a tool developed in the literature of statistical mechanics allows us to derive analytical expressions for the bit error rate as well as the multiuser efficiency of the individually optimum io and jointly optimum jo multiuser detectors over the whole range of noise levels the information theoretic capacity of the randomly spread cdma channel and the performance of decorrelating and linear minimum mean square error mmse detectors are also derived in the same replica formulation thereby demonstrating validity of the statistical mechanical approach

global existence of classical solutions to the initial boundary value problem of the semilinear wave equations with a degenerate dissipative term we consider the initial boundary value problem for a typical semilinear wave equation u tt u u 2k 1 0 on 0 u x 0 u 0 x u t x 0 u 1 x and u x t 0 where k is a positive integer

the coupling of boundary integral and finite element methods for the exterior steady oseen problem abstract in this article we present a new numerical method for solving the steady oseen equations in an unbounded plane domain the technique consists in coupling the boundary integral and the finite element methods an artificial smooth boundary is introduced separating an interior inhomogeneous region from an exterior homogeneous one the solution in exterior region is represented by an integral equation over the artificial boundary this integral equation is incorporated into a velocity pressure formulation for the interior region and a finite element method is used to approximate the resulting variational problem finally the optimal error estimates of the numerical solution are derived computer results will be discussed in a forthcoming paper

existence of global classical solutions of the initial boundary value problem for some nonlinear wave equations in fact we shall assume a x u is strictly increasing in u and also impose a certain smallness condition on the initial data zq u and the forcing term f but it is weaker compared with earlier works see theorem 1 1 for a moment we assume further g x u u 3 0 for simplicity when n 1 the global existence of the smooth solutions for o l 0 2 is easily proved by a standard energy method cf strauss 121 nakao 7 when iv 2 we can also prove a similar result if b x o satisfies the conditions 8 x u du b 0

global existence of small solutions to nonlinear evolution equations abstract we study the global existence and asymptotic behaviour of small solutions of a large class of nonlinear partial differential equations if the nonlinear terms are of high degree the solutions will be asymptotic to solutions of the linear equation

error estimates of the dtn finite element method for the exterior helmholtz problem a priori error estimates are established for the dtn dirichlet to neumann finite element method applied to the exterior helmholtz problem the error estimates include the effect of truncation of the dtn boundary condition as well as that of the finite element discretization a property of the hankel functions which plays an important role in the proof of the error estimates is introduced

an adaptive coupling method for exterior anisotropic elliptic problems in this paper we propose an adaptive coupling method for solving anisotropic elliptic pdes in unbounded domains firstly the existence and the uniqueness of the solution for the coupling method are proven and the a priori error estimates in h1 norm and l2 norm that depend on the size of the fem mesh the location of the elliptic artificial boundary and the truncation of the infinite series in the artificial boundary integral condition are derived secondly the a posteriori error estimates and the a posteriori error indicator of the coupling method are obtained finally the adaptive coupling method refines the mesh distribution by the arc length equidistribution principle and the a posteriori error indicator successively numerical examples confirm the advantage in accuracy and efficiency for the proposed method