a new approach to multipath correction of constant modulus signals an adaptive digital filtering algorithm that can compensate for both frequency selective multipath and interference on constant envelope modulated signals is presented the method exploits the fact that multipath reception and various interference sources generate incidental amplitude modulation on the received signal a class of so called constant modulus performance functions is developed which sense this am term but are insensitive to the angle modulation simple adaptive algorithms for finite impulse response fir digital filters are developed which employ a gradient search of the performance function one of the resulting algorithms is simulated for the example of an fm signal degraded by specular multipath propagation substantial improvements in noise power ratio npr are observed e g 25 db with moderately rapid convergence time these results are then extended to include tonal interference on a fm signal and intersymbol interference on a qpsk data signal

blind constant modulus equalization via convex optimization in this paper we formulate the problem of blind equalization of constant modulus cm signals as a convex optimization problem the convex formulation is obtained by performing an algebraic transformation on the direct formulation of the cm equalization problem using this transformation the original nonconvex cm equalization formulation is turned into a convex semidefinite program sdp that can be efficiently solved using interior point methods our sdp formulation is applicable to baud spaced equalization as well as fractionally spaced equalization performance analysis shows that the expected distance between the equalizer obtained by the sdp approach and the optimal equalizer in the noise free case converges to zero exponentially as the signal to noise ratio snr increases in addition simulations suggest that our method performs better than standard methods while requiring significantly fewer data samples

a staggered discontinuous galerkin method for wave propagation in media with dielectrics and meta materials some electromagnetic materials exhibit in a given frequency range effective dielectric permittivity and or magnetic permeability which are negative in the literature they are called negative index materials left handed materials or meta materials we propose in this paper a numerical method to solve a wave transmission between a classical dielectric material and a meta material the method we investigate can be considered as an alternative method compared to the method presented by the second author and co workers in particular we shall use the abstract framework they developed to prove well posedness of the exact problem we recast this problem to fit later discretization by the staggered discontinuous galerkin method developed by the first author and co worker a method which relies on introducing an auxiliary unknown convergence of the numerical method is proven with the help of explicit inf sup operators and numerical examples are provided to show the efficiency of the method

convergence and superconvergence of staggered discontinuous galerkin methods for the three dimensional maxwell s equations on cartesian grids in this paper a new type of staggered discontinuous galerkin methods for the three dimensional maxwell s equations is developed and analyzed the spatial discretization is based on staggered cartesian grids so that many good properties are obtained first of all our method has the advantages that the numerical solution preserves the electromagnetic energy and automatically fulfills a discrete version of the gauss law moreover the mass matrices are diagonal thus time marching is explicit and is very efficient our method is high order accurate and the optimal order of convergence is rigorously proved it is also very easy to implement due to its cartesian structure and can be regarded as a generalization of the classical yee s scheme as well as the quadrilateral edge finite elements furthermore a superconvergence result that is the convergence rate is one order higher at interpolation nodes is proved numerical results are shown to confirm our theoretical statements and applications to problems in unbounded domains with the use of pml are presented a comparison of our staggered method and non staggered method is carried out and shows that our method has better accuracy and efficiency

on the non existence of undesirable equilibria of godard blind equalizers existing results in the literature have proved that particular blind equalization algorithms including godard algorithms are globally convergent in an ideal and nonimplementable setting where a doubly infinite dimensional equalizer is available for adaptation contrary to popular conjectures it is shown that implementable finite dimensional equalizers which attempt to approximate the ideal setting generally fail to have global convergence to acceptable equalizer parameter settings without the use of special remedial measures a theory based on the channel convolution matrix nullspace is proposed to explain the failure of godard algorithms for such practical blind equalization situations this nullspace theory is supported by a simple example showing ill convergence of the godard algorithm

the parabolic map abstract in this paper we study certain aspects of bruhat order on coxeter groups letwbe a coxeter group and let p denote the set of parabolic subgroups ofw we construct a mapm w p wand examine its first properties we prove the following characterization wis the longest element of a parabolic subgroup ofwif and only if for anyv w there exists a unique maximal element with respect to bruhat order less than or equal to bothvandw

on the use of perfectly matched layers at corners for scattering problems with sign changing coefficients we investigate in a 2d setting the scattering of time harmonic electromagnetic waves by a plasmonic device represented as a non dissipative bounded and penetrable obstacle with a negative permittivity using the t coercivity approach we first prove that the problem is well posed in the classical framework h loc 1 if the negative permittivity does not lie in some critical interval whose definition depends on the shape of the device when the latter has corners for values inside the critical interval unusual strong singularities for the electromagnetic field can appear in that case well posedness is obtained by imposing a radiation condition at the corners to select the outgoing black hole plasmonic wave that is the one which carries energy towards the corners a simple and systematic criterion is given to define what is the outgoing solution finally we propose an original numerical method based on the use of perfectly matched layers at the corners we emphasize that it is necessary to design an ad hoc technique because the field is too singular to be captured with standard finite element methods

blind detection of asynchronous cdma signals in multipath channels using code constrained inverse filter criterion a code constrained inverse filter criterion based approach is presented for blind detection of asynchronous short code direct sequence code division multiple access ds cdma signals in multipath channels only the spreading code of the desired user is assumed to be known its transmission delay may be unknown we focus on maximization of the normalized fourth cumulant of inverse filtered equalized data with respect to w r t the equalizer coefficients subject to the equalizer lying in a subspace associated with the desired user s code sequence constrained maximization leads to extraction of the desired user s signal whereas unconstrained maximization leads to the extraction of any one of the active users illustrative simulation examples are provided

a fast linear programming algorithm for blind equalization a fast implementation of a special non mse cost function for blind equalization is presented here this baud rate equalization algorithm is based on a convex cost function coupled with a simple linear constraint on the equalizer parameters for a generic class of channels with persistently exciting quadrature amplitude modulation input signals this new algorithm allows the convergence of equalizer parameters to a unique global minimum achieving intersymbol interference suppression and carrier phase recovery

t coercivity and continuous galerkin methods application to transmission problems with sign changing coefficients to solve variational indefinite problems one uses classically the banach ne as babuska theory here we study an alternate theory to solve those problems t coercivity moreover we prove that one can use this theory to solve the approximate problems which provides an alternative to the celebrated fortin lemma we apply this theory to solve the indefinite problem text div sigma nabla u f set in h 1 0 with sigma exhibiting a sign change

a feedback approach to the steady state performance of fractionally spaced blind adaptive equalizers this paper proposes a new approach to the analysis of the steady state performance of constant modulus algorithms cma which are among the most popular adaptive schemes for blind equalization a major feature of the proposed feedback approach is that it bypasses the need for working directly with the weight error covariance matrix in so doing approximate expressions for the steady state mean square error of several cm algorithms are derived including cma2 2 cma1 2 normalized cma and a new normalized cma variant with less bias a comparison among the various algorithms is also performed along with several simulation results the conclusions confirm the superior performance of cma2 2

blind carrier phase tracking with guaranteed global convergence conventional blind carrier recovery algorithms have been observed to show unstable behaviors for large constellation modulation schemes such as 64 qam or 256 qam we propose a new carrier tracking approach that has guaranteed global convergence first we show that the carrier tracking problem is equivalent to a blind source separation problem which involves the separation of a linear unitary mixture of two independent components that are the real and imaginary parts of the emitted signal then by using a blind source separation procedure we derive a new and robust carrier tracking algorithm with guaranteed global convergence some numerical simulations are provided to illustrate the effectiveness of the proposed method

pattern avoidance and rational smoothness of schubert varieties abstract letwbe an element of the weyl groupsn and letxwbe the schubert variety associated towin the flag manifoldsln c b lakshmibai and sandhya showed thatxwis smooth if and only ifwavoids the patterns 4231 and 3412 using two tests for rational smoothness from carrell and peterson we show that rational smoothness ofxwis characterized by pattern avoidance for typesbandcas well a key step in the proof of this result is a sequence of rules for factoring the poincare polynomials for the cohomology ring ofxw generalizing the work of gasharov patterns can also be used to characterize actual smoothness of schubert varieties

rationally smooth schubert varieties and inversion hyperplane arrangements abstract we show that an element w of a finite weyl group w is rationally smooth if and only if the hyperplane arrangement i associated to the inversion set of w is inductively free and the product d 1 1 d l 1 of the coexponents d 1 d l is equal to the size of the bruhat interval e w where e is the identity in w as part of the proof we describe exactly when a rationally smooth element in a finite weyl group has a chain billey postnikov decomposition for finite coxeter groups we show that chain billey postnikov decompositions are connected with certain modular coatoms of i

mortar formulation for a class of staggered discontinuous galerkin methods abstract a mortar formulation is developed and analyzed for a class of staggered discontinuous galerkin sdg methods applied to second order elliptic problems in two dimensions the computational domain consists of nonoverlapping subdomains and a triangulation is provided for each subdomain which need not conform across subdomain interfaces this feature allows a more flexible design of discrete models for problems with complicated geometries shocks or singular points a mortar matching condition is enforced on the solutions across the subdomain interfaces by introducing a lagrange multiplier space moreover optimal convergence rates in both l 2 and discrete energy norms are proved numerical results are presented to show the performance of the method

closures of k orbits in the flag variety for u p q we give a pattern avoidance criterion for the conjugates of the bottom vertex of the bruhat graph attached to an on orbit mathcal o in the flag variety of gln to have degree equal to the rank of this graph as a poset this condition is known to be necessary for rational smoothness of overline mathcal o we conjecture that it is also sufficient proving that this holds for n even

a posteriori error estimates for a finite element approximation of transmission problems with sign changing coefficients we perform the a posteriori error analysis of residual type of transmission problem with sign changing coefficients according to bonnet bendhia et al 2010 9 if the contrast is large enough the continuous problem can be transformed into a coercive one we further show that a similar property holds for the discrete problem for any regular meshes extending the framework from bonnet bendhia et al 9 the reliability and efficiency of the proposed estimator are confirmed by some numerical tests

optimal discontinuous galerkin methods for wave propagation we have developed and analyzed a new class of discontinuous galerkin methods dg which can be seen as a compromise between standard dg and the finite element fe method in the way that it is explicit like standard dg and energy conserving like fe in the literature there are many methods that achieve some of the goals of explicit time marching unstructured grid energy conservation and optimal higher order accuracy but as far as we know only our new algorithms satisfy all the conditions we propose a new stability requirement for our dg the stability analysis is based on the careful selection of the two fe spaces which verify the new stability condition the convergence rate is optimal with respect to the order of the polynomials in the fe spaces moreover the convergence is described by a series of numerical experiments

energy stable discontinuous galerkin methods for maxwell s equations in nonlinear optical media abstract the propagation of electromagnetic waves in general media is modeled by the time dependent maxwell s partial differential equations pdes coupled with constitutive laws that describe the response of the media in this work we focus on nonlinear optical media whose response is modeled by a system of first order nonlinear ordinary differential equations odes which include a single resonance linear lorentz dispersion and the nonlinearity comes from the instantaneous electronic kerr response and the residual raman molecular vibrational response to design efficient accurate and stable computational methods we apply high order discontinuous galerkin discretizations in space to the hybrid pde ode maxwell system with several choices of numerical fluxes and the resulting semi discrete methods are shown to be energy stable under some restrictions on the strength of the nonlinearity error estimates are also established when we turn to fully discrete methods the challenge to achieve provable stability lies in the temporal discretizations of the nonlinear terms to overcome this novel strategies are proposed to treat the nonlinearity in our model within the framework of the second order leap frog and implicit trapezoidal time integrators the performance of the overall algorithms are demonstrated through numerical simulations of kink and antikink waves and third harmonic generation in soliton propagation

a modified cma equalizer for the removal of length dependent local minima in ar channels finite length cma equalizers contain undesired minima termed length dependent local minima ldlm we note that for autoregressive ar channels the equalizer output is correlated with a delayed input at these minima this property is then used to modify the cma cost function and remove the ldlm in ar channels

length and cost dependent local minima of unconstrained blind channel equalizers baud rate linear blind equalizers may converge to undesirable stable equilibria due to different mechanisms one such mechanism is the use of linear fir filters as equalizers it is shown that this type of local minima exist for all unconstrained blind equalizers whose cost functions satisfy two general conditions the local minima generated by this mechanism are thus called length dependent local minima another mechanism is generated by the cost function adopted by the blind algorithm itself this type of local minima are called cost dependent local minima it is shown that several well designed algorithms do not have cost dependent local minimum whereas other algorithms such as the decision directed equalizer and the stop and go algorithm sga do unlike many existing convergence analysis the convergence of the godard 1980 algorithms gas and standard cumulant algorithms scas under gaussian noise is also presented computer simulations are used to verify the analytical results

relationships between the constant modulus and wiener receivers the godard 1980 or the constant modulus algorithm cma is an effective technique for blind receiver design in communications however due to the complexity of the constant modulus cm cost function the performance of the cm receivers has primarily been evaluated using simulations theoretical analysis is typically based on either the noiseless case or approximations of the cost function the following question while resolvable numerically for a specific example remains unanswered in a generic manner in the presence of channel noise where are the cm local minima and what are their mean squared errors mse in this paper a geometrical approach is presented that relates the cm to wiener or minimum mse receivers given the mse and the intersymbol user interference of a wiener receiver a sufficient condition is given for the existence of a cm local minimum in the neighborhood of the wiener receiver the mse bounds on cm receiver performance are derived and shown to be tight in simulations the analysis shows that while in some cases the cm receiver performs almost as well as the nonblind wiener receiver it is also possible that due to its blind nature the cm receiver may perform considerably worse than a nonblind wiener receiver

analysis and application of an equivalent berenger s pml model abstract the perfectly matched layer pml is a technique initially proposed by berenger for solving unbounded electromagnetic problems with the finite difference time domain method in this work we first formulate an equivalent pml model from the original berenger pml model in the corner region and then establish its stability we further develop a discontinuous galerkin method to solve this pml model and discrete stability similar to the continuous case is proved to demonstrate the absorbing property of this pml model we apply it to simulate wave propagation in metamaterials

direct estimation of blind zero forcing equalizers based on second order statistics most existing zero forcing equalization algorithms rely either on higher than second order statistics or on partial or complete channel identification we describe methods for computing fractionally spaced zero forcing blind equalizers with arbitrary delay directly from second order statistics of the observations without channel identification we first develop a batch type algorithm then adaptive algorithms are obtained by linear prediction and gradient descent optimization our adaptive algorithms do not require channel order estimation nor rank estimation compared with other second order statistics based approaches ours do not require channel identification at all on the other hand compared with the cma type algorithms ours use only second order statistics thus no local convergence problem exists and faster convergence can be achieved simulations show that our algorithms outperform most typical existing algorithms

billey postnikov decompositions and the fibre bundle structure of schubert varieties a theorem of ryan and wolper states that a type a schubert variety is smooth if and only if it is an iterated fibre bundle of grassmannians we extend this theorem to arbitrary finite type showing that a schubert variety in a generalized flag variety is rationally smooth if and only if it is an iterated fibre bundle of rationally smooth grassmannian schubert varieties the proof depends on deep combinatorial results of billey postnikov on weyl groups we determine all smooth and rationally smooth grassmannian schubert varieties and give a new proof of peterson s theorem that all simply laced rationally smooth schubert varieties are smooth taken together our results give a fairly complete geometric description of smooth and rationally smooth schubert varieties using primarily combinatorial methods

convex cost functions in blind equalization existing blind adaptive equalizers that use nonconvex cost functions and stochastic gradient descent suffer from lack of global convergence to an equalizer setup that removes sufficient isi when an fir equalizer is used the authors impose convexity on the cost function and anchoring of the equalizer away from the all zero setup they establish that there exists a globally convergent blind equalization strategy for 1d pulse amplitude modulation pam systems with bounded input data discrete or continuous even when the equalizer is truncated the resulting cost function is a constrained l sub 1 norm of the joint impulse response of the channel and the equalizer the results apply to arbitrary linear channels provided there are no unit circle zeros and apply regardless of the initial isi that is whether the eye is initially open or closed they also show a globally convergent stochastic gradient scheme based on an implementable approximation of the l sub 1 cost function

a posteriori error analysis for a staggered discontinuous galerkin discretization of the time harmonic maxwell s equations in this paper we present the first a posteriori error analysis for the staggered discontinuous galerkin sdg method specifically we consider the approximation of the time harmonic maxwell s equations by a sdg method and prove that our residual based a posteriori error indicator is both reliable and efficient we validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems

a deluxe feti dp algorithm for a hybrid staggered discontinuous galerkin method for h curl elliptic problems summary convergence theories and a deluxe dual and primal finite element tearing and interconnecting algorithm are developed for a hybrid staggered dg finite element approximation of h curl elliptic problems in two dimensions in addition to the advantages of staggered dg methods the basis functions of the new hybrid staggered dg method are all locally supported in the triangular elements and a lagrange multiplier approach is applied to enforce the global connections of these basis functions the interface problem on the lagrange multipliers is further reduced to the resulting problem on the subdomain interfaces and a dual and primal finite element tearing and interconnecting algorithm with an enriched weight factor is then applied to the resulting problem our algorithm is shown to give a condition number bound ofc 1c log h h 2 independent of the two parameters whereh his the number of triangles across each subdomain numerical results are included to confirm our theoretical bounds copyright 2013 john wiley sons ltd received 12 september 2013 accepted 11 november 2013 in this paper a dual and primal finite element tearing and interconnecting feti dp algorithm is developed for a fast and stable solution of a new hybrid staggered dg hsdg method applied to h curl problems staggered dg sdg methods were first introduced in 1 3 for wave propagation problems the idea was subsequently applied to other problems such as convection diffusion equations 4 electromagnetic problems 5 9 stokes equations 10 and multiscale wave simulations 11 12 similar to 5 the advantages of using sdg for h curl problems are the preservation of the structures of the differential operators the local conservation property and the optimal convergence in particular the discretizations of the two curl operators by the sdg method are adjoint to each other and the null space of the discrete curl operator is exactly the gradients moreover the divergence condition is automatically satisfied in an appropriate weak sense despite the aforementioned advantages the implementation of sdg methods requires careful numbering of the supports of the basis functions to allow an easier implementation of the sdg method the hsdg method is introduced in this paper one distinctive advantage of the hsdg method is that the basis functions are all locally supported in the triangular elements hence the numbering can be easily performed the fact that the basis functions are totally discontinuous requires some global couplings in particular we will use the lagrange multiplier approach to enforce the global connection of the basis functions this idea is also related to the hybridized dg methods 13 16 in fact it is shown that the sdg method is the limit of a hybridized dg method

a criterion for smoothness of schubert varieties insp 2n b abstract in this paper we give a criterion for a schubert variety x w in sp 2 n b to be smooth the criterion is given in terms of the permutation giving w

optimal step size constant modulus algorithm the step size leading to the absolute minimum of the constant modulus cm criterion along the search direction can be obtained algebraically at each iteration among the roots of a third degree polynomial the resulting optimal step size cma os cma is compared with other cm based iterative techniques in terms of performance versus complexity trade off

pattern avoidance and smoothness of closures for orbits of a symmetric subgroup in the flag variety abstract we give a pattern avoidance criterion to classify the orbits of sp p c sp q c resp gl n c on the flag variety of type c p q resp d n with rationally smooth closure we show that all such orbit closures fiber with smooth fiber over a smaller flag variety and hence are in fact smooth in addition we prove that the classification is insensitive to isogeny

mathematical and numerical study of wave propagation in negative index materials abstract in this paper we develop a crank nicolson mixed finite element method for modeling wave propagation in negative index materials nims the nims model is formed as a time dependent system involving four dependent vector variables the electric and magnetic fields and the induced electric and magnetic currents optimal error estimates for all four variables are proved for nedelec edge elements numerical examples are presented to show the exotic properties for wave propagation in nims

optimal non dissipative discontinuous galerkin methods for maxwells equations in drude metamaterials simulation of electromagnetic wave propagation in metamaterials leads to more complicated time domain maxwells equations than the standard maxwells equations in free space in this paper we develop and analyze a non dissipative discontinuous galerkin dg method for solving the maxwells equations in drude metamaterials previous discontinuous galerkin methods in the literature for electromagnetic wave propagation in metamaterials were either non dissipative but sub optimal or dissipative and optimal our method uses a different and simple choice of numerical fluxes achieving provable non dissipative stability and optimal error estimates simultaneously we prove the stability and optimal error estimates for both semi and fully discrete dg schemes with the leap frog time discretization for the fully discrete case numerical results are given to demonstrate that the dg method can solve metamaterial maxwells equations effectively

time harmonic wave diffraction problems in materials with sign shifting coefficients some electromagnetic materials present in a given frequency range an effective dielectric permittivity and or magnetic permeability which are negative we are interested in the reunion of such a negative material and a classical one more precisely we consider here a scalar model problem for the simulation of a wave transmission between two such materials this model is governed by a helmholtz equation with a weight function in the d principal part which takes positive and negative real values introducing additional unknowns we have already proposed in bonnet ben dhia et al 2006 1 some new variational formulations of this problem which are of fredholm type provided the absolute value of the contrast of permittivities is large enough and therefore suitable for a finite element discretization we prove here that under similar conditions on the contrast the natural variational formulation of the problem although not coercive plus compact is nonetheless suitable for a finite element discretization this leads to a numerical approach which is straightforward less costly than the previous ones and very accurate

convergence analysis of finite length blind adaptive equalizers the paper presents some new analytical results on the convergence of two finite length blind adaptive channel equalizers namely the godard equalizer and the shalvi weinstein equalizer first a one to one correspondence in local minima is shown to exist between the godard and shalvi weinstein equalizers hence establishing the equivalent relationship between the two algorithms convergence behaviors of finite length godard and shalvi weinstein equalizers are analyzed and the potential stable equilibrium points are identified the existence of undesirable stable equilibria for the finite length shalvi weinstein equalizer is demonstrated through a simple example it is proven that the points of convergence for both finite length equalizers depend on an initial kurtosis condition it is also proven that when the length of equalizer is long enough and the initial equalizer setting satisfies the kurtosis condition the equalizer will converge to a stable equilibrium near a desired global minimum when the kurtosis condition is not satisfied generally the equalizer will take longer to converge to a desired equilibrium given sufficiently many parameters and adequate initialization the convergence analysis of the equalizers in pam communication systems can be easily extended to the equalizers in qam communication systems

staggered grid spectral element methods for elastic wave simulations in this paper we develop and analyze a new class of spectral element methods for the simulations of elastic wave propagation the major components of the method are the spatial discretization and the choice of interpolation nodes the spatial discretization is based on piecewise polynomial approximation defined on staggered grids the resulting method combines the advantages of both staggered grid based methods and classical non staggered grid based spectral element methods our new method is energy conserving and does not require the use of any numerical flux because of the staggered local continuity of the basis functions our new method also uses radau points as interpolation nodes and the resulting mass matrix is diagonal thus time marching is explicit and is very efficient moreover we give a rigorous proof for the optimal convergence of the method in terms of dispersion we present a numerical study for the numerical dispersion and show that this error is of very high order finally some numerical convergence tests and applications to unbounded domain problems with perfectly matched layer are shown

smooth points of t stable varieties in g b and the peterson map let g be a connected semi simple algebraic group defined over an algebraically closed field k and let t b p be respectively a maximal torus a borel subgroup and a parabolic subgroup of g inspired by a beautiful result of dale peterson describing the singular locus of a schubert variety in g b we characterize the t fixed points in the singular locus of an arbitrary irreducible t stable subvariety of g p a t variety for short peterson s result cf the deformation theorem 1 says that if k then a schubert variety x g b is smooth at a t fixed point x if and only if it is smooth at every t fixed point y x in the bruhat chevalley order on the fixed point set x t and all the limits c x x lim z x t z x z c c t of the zariski tangent spaces t z x of x coincide as c varies over the set of all t stable curves in x with c t x y where y x using this peterson showed that if g is simply laced and defined over then every rationally smooth point of a schubert variety in g b is smooth more generally the deformation c x x is defined for any k variety x with a t action provided c is what we call good i e c is a curve of the form c overline tz where z is a smooth point of x x t and x c t our first main result theorem 1 4 says that if x x is an attractive fixed point then x is smooth at x if and only if there exist at least two good c containing x such that c x x te x x where te x x denotes the span of the tangent lines of the t stable curves in x containing x in addition if x is cohen macaulay at x and c x x te x x for even one good c then x is smooth at x our second main result theorem 1 6 says that if x is a t variety in g p where g is simply laced then c x x te x x for each good c this is not true for general g but when g has no g2 factors then c x x is always contained in the linear span of the reduced tangent cone to x at x these results lead to several descriptions of the smooth fixed points of a t variety in g p and in particular they give simple proofs of peterson s results valid for any algebraically closed field we also show cf example 7 1 that there can exist t stable subvarieties in g b where g is simply laced which have rationally smooth t fixed points in their singular loci

an analysis of constant modulus receivers this paper investigates connections between non blind wiener receivers and blind receivers designed by minimizing the constant modulus cm cost applicable to both t spaced and fractionally spaced fir equalization the main results include 1 a test for the existence of cm local minima near wiener receivers 2 an analytical description of cm receivers in the neighborhood of wiener receivers 3 mean square error mse bounds for cm receivers when the channel matrix is invertible we also show that the cm receiver is approximately colinear with the wiener receiver and provide a quantitative measure of the size of neighborhoods that contain the cm receivers and the accuracy of the mse bounds

mesh requirements for the finite element approximation of problems with sign changing coefficients transmission problems with sign changing coefficients occur in electromagnetic theory in the presence of negative materials surrounded by classical materials for general geometries establishing fredholmness of these transmission problems is well understood thanks to the t coercivity approach moreover for a plane interface there exist meshing rules that guarantee an optimal convergence rate for the finite element approximation we propose here a new treatment at the corners of the interface which allows to design meshing rules for an arbitrary polygonal interface and then recover standard error estimates this treatment relies on the use of simple geometrical transforms to define the meshes numerical results illustrate the importance of this new design

new processing techniques based on the constant modulus adaptive algorithm this paper presents three extensions of the constant modulus algorithm cma introduced in an earlier paper as a means of correcting degradations in constant enyelope waveforms as originally formulated the cma employs an fir filter with complex coefficients and accepts complex quadrature input data in this paper first a real input real coefficient version of the algorithm is shown to perform arbitrarily close to the fully complex version secondly the algorithm is extended for the enhancement of signals having a nonconstant but known envelope as might arise in data signals with pulse shaping lastly a multichannel version of cma wherein several observations are linearly combined is presented for joint adaptation of multiple filters this approach can be used for example as a means of spatial or polarization beamsteering to reject additive interferers and compensate for channel induced polarization rotation

the nil hecke ring and singularity of schubert varieties let g be a semi simple simply connected complex algebraic group and t b a maximal torus and a borel subgroup respectively let lie t be the cartan subalgebra of the lie algebra lie g and w n t t the weyl group associated to the pair g t where n t is the normalizer of t in g we can view any element omega overline omega mod t i w as the element denoted by the corresponding german character xo of g b denned as m overline omega b for any w i w there is associated the schubert variety rm x omega overline b omega b b subset g b and the t fixed points of x w under the canonical left action are precisely rm i omega left o upsilon in wand upsilon leqslant omega right

ill convergence of godard blind equalizers in data communication systems the existence of stable undesirable equilibria for the godard algorithm is demonstrated through a simple autoregressive ar channel model these undesirable equilibria correspond to local but nonglobal minima of the underlying mean cost function and thus permit the ill convergence of the godard algorithms which are stochastic gradient descent in nature simulation results confirm predicted misbehavior for channel input of constant modulus it is shown that attaining the global minimum of the mean cost necessarily implies correct equalization a criterion is also presented for allowing a decision at the equalizer as to whether a global or nonglobal minimum has been reached

static and dynamic convergence behavior of adaptive blind equalizers this paper presents a theoretical analysis of the static and dynamic convergence behavior for a general class of adaptive blind equalizers we first study the properties of prediction error functions of blind equalization algorithms and then we use these properties to analyze the static and dynamic convergence behavior based on the independence assumption we prove in this paper that with a small step size the ensemble average of equalizer coefficients will converge to the minimum of the cost function near the channel inverse however the convergence is not consistent the correlation matrix or equalizer coefficients at equilibrium are determined by a lyapunov equation according to our analysis results for a given channel and stepsize there is an optimal length for an equalizer to minimize the intersymbol interference this result implies that a longer length blind equalizer does not necessarily outperform a shorter one which is contrary to what is conventionally conjectured the theoretical analysis results are confirmed by computer simulations

identification and deconvolution of multichannel linear non gaussian processes using higher order statistics and inverse filter criteria this paper is concerned with the problem of estimation and deconvolution of the matrix impulse response function of a multiple input multiple output mimo system given only the measurements of the vector output of the system the system is assumed to be driven by a temporally i i d and spatially independent non gaussian vector sequence which is not observed an iterative inverse filter criteria based approach is developed using the third order or the fourth order normalized cumulants of the inverse filtered data at zero lag stationary points of the proposed cost functions are investigated the approach is input iterative i e the input sequences are extracted and removed one by one the matrix impulse response is then obtained by cross correlating the extracted inputs with the observed outputs identifiability conditions are analyzed the strong consistency of the proposed approach is also briefly discussed computer simulation examples are presented to illustrate the proposed approaches

mathematical analysis of ziolkowski s pml model with application for wave propagation in metamaterials abstract in this paper we investigate one perfectly matched layer pml model proposed by ziolkowski in 1999 various schemes for solving this pml model have been developed and have been shown to be effective in absorbing outgoing waves when the wave propagation in unbounded domain problem is reduced to a bounded domain problem however a rigorous analysis of this model is lacking in this paper we establish the stability of this pml model and propose a fully discrete finite element scheme to solve this model with edge elements discrete stability and optimal error estimate of this scheme are proved numerical results justifying the analysis and demonstrating the effectiveness of this pml model are presented

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

optimal discontinuous galerkin methods for the acoustic wave equation in higher dimensions in this paper we develop and analyze a new class of discontinuous galerkin dg methods for the acoustic wave equation in mixed form traditional mixed finite element fe methods produce energy conserving schemes but these schemes are implicit making the time stepping inefficient standard dg methods give explicit schemes but these approaches are typically dissipative or suboptimally convergent depending on the choice of numerical fluxes our new method can be seen as a compromise between these two kinds of techniques in the way that it is both explicit and energy conserving locally and globally moreover it can be seen as a generalized version of the raviart thomas fe method and the finite volume method stability and convergence of the new method are rigorously analyzed and we have shown that the method is optimally convergent furthermore in order to apply the new method for unbounded domains we apply our new method with the first order absorbing boundary condition the stability of the resulting numerical scheme is analyzed

the staggered dg method is the limit of a hybridizable dg method we show in the framework of steady state diffusion boundary value problems that the staggered discontinuous galerkin sdg method siam j numer anal 47 2009 pp 3820 3848 can be obtained from a hybridizable discontinuous galerkin hdg method siam j numer anal 47 2009 pp 1319 1365 by setting its stabilization function to zero at some suitably chosen element faces and by letting it go to infinity at all the remaining others we then show that this point of view allows the sdg method to immediately acquire new properties all inherited from the hdg methods namely their efficient implementation by hybridization their postprocessings and their superconvergence properties

blind and semi blind equalization based on the constant power criterion this paper focuses on the constant power cp criterion for blind linear equalization of digital communication channels this recently proposed criterion is specially designed for the extraction of q ary phase shift keying q psk signals using finite impulse response equalizers when zero forcing equalizers exist the cp cost function accepts exact analytic solutions that are unaffected by undesired local extrema and spare costly iterative optimization a subspace based method exploiting the toeplitz like structure of the solution space is put forward to recover the minimum length equalizer impulse response from the overestimated length solutions the proposed method is more robust to the relative weights of the minimum length equalizer taps than existing techniques in less ideal scenarios where the analytic solutions are only approximate minimizers of the criterion a gradient descent algorithm is proposed to minimize the cost function to reduce the detrimental effects of suboptimal equilibria and accelerate convergence the iterative algorithm is initialized with the approximate closed form solution and an optimal step size is incorporated into its updating rule this optimal step size which globally minimizes the cost function along the search direction can be computed algebraically a semi blind implementation which is useful when training data are available further reduces the impact of undesired local extrema and enhances the convergence characteristics particularly the robustness to the equalizer initialization of the iterative algorithm from just a few pilot symbols all these beneficial features are demonstrated with an experimental study of the proposed cp based methods in a variety of channels and simulation conditions

fractionally spaced equalization using cma robustness to channel noise and lack of disparity in the noise free case the fractionally spaced equalization using constant modulus fse cm criterion has been studied previously its minima were shown to achieve perfect equalization when zero forcing zf conditions are satisfied and to be able to still achieve fair equalization when there is lack of disparity however to our best knowledge the effect of additive channel noise on the fse cm cost function minima has not been studied in this paper we show that the noisy fse cm cost function is subject to a smoothing effect with respect to the noise free cost function the result of which is a tradeoff between achieving zero forcing and noise enhancement furthermore we give an analytical closed form expression for the loss of performance due to the noise in terms of input output mean square error mse under the zf conditions the fse cm mse is shown to be mostly due to output noise enhancement and not to residual intersymbol interference isi when there is lack of disparity an irreducible amount of isi appears independently of the algorithm it is the lower equalizability bound for given channel conditions and equalizer length the so called minimum mse mmse the mmse lower bound is the sum of the mmse and of additional mse mostly due to noise enhancement finally we compare the fse cm mse to this lower bound

blind equalization without gain identification blind equalization up to a constant gain of linear time invariant channels is studied dropping the requirement of gain identification allows equalizer anchoring this results in the elimination of a degree of freedom that causes ill convergence of conventional blind equalizers and affords the possibility of using simple update rules based on the stochastic approximation of output energy unlike conventional blind equalizers truncations of the nonrecursive infinite dimensional realizations of those equalizers inherit the convergence properties of their infinitely parametrized counterparts a globally convergent blind recursive equalizer for channels without all pass sections is obtained based on the exact equalization of the minimum phase part of the channel and the identification of its nonminimum phase zeros