center manifolds and contractions on a scale of banach spaces we give a new proof for the existence of a ck center manifold at a nonhyperbolic equilibrium point of a finite dimensional vector field of class ck the problem is reduced to a fixed point problem on a scale of banach spaces these banach spaces consist of mappings with a certain maximal exponential growth at infinity we give conditions under which there is a unique fixed point depending differentiably on the parameters the main difficulty is that the mappings under consideration become only differentiable after composition with appropriate embeddings on the scale of banach spaces

extended mlse diversity receiver for the time and frequency selective channel this paper develops a maximum likelihood sequence estimation mlse diversity receiver for the time and frequency selective channel corrupted by additive gaussian noise when linear constellations m ask m psk m qam are employed the paper extends ungerboeck s derivation of the extended mlse receiver for the purely frequency selective channel to the more general channel although the new receiver structure and metric assume ideal channel state information csi the receiver can be used wherever high quality csi is available such as a comb of pilot tones or time isolated symbols the major contributions of this paper are as follows 1 the derivation of a finite complexity diversity receiver that is maximum likelihood ml for all linear channel models and sources of diversity as long as ideal csi is available 2 a benchmark in that the new receiver s performance is a lower bound on the performance of practical systems which either lack ideal csi or are not ml 3 insight into matched filtering and ml diversity receiver processing for the time and frequency selective channels and 4 bounds on the new receiver s bit error rate ber for ideal csi and pilot tone csi in a fast rayleigh fading channel with multiple independently faded paths the new receiver can seamlessly tolerate square root nyquist pulses without a fading induced isi error floor

integral equation formulations for characteristic modes of dielectric and magnetic bodies five types of surface integral equation ie formulations are presented to determine the characteristic modes of dielectric and magnetic bodies it should be noted that these five formulations are derived in a unified manner instead of directly using the ie coefficient matrices of scattering problems this paper presents the formulations in a more natural and rigorous way the ie formulations result in the generalized real symmetric eigenvalue equations for the characteristic modes it is found that the eigenvalues of the first four formulations indicate the negative or positive imaginary part of the complex power of the characteristic modes which are zero at resonance the first two ie formulations result in two new generalized eigenvalue equations while the last three ie formulations lead to the same generalized eigenvalue equations as in the references moreover the first two formulations can be immune from spurious modes from which the third and fourth formulations suffer

ck invariant manifolds for maps of banach spaces abstract in this work we give a unified proof for the existence under appropriate gap conditions of the standard invariant manifolds for a ck map of a banach space near a fixed point where k 1 is an integer

local contractions of banach spaces and spectral gap conditions abstract we study the linearization problem for a c k 1 k 1 contraction of a banach space e near a fixed point which satisfies a spectral gap condition and a narrow band condition both of order k we also assume that the part of the spectrum in each band satisfies a finite non resonant condition of order k relative to itself together with the part that lies in the larger bands we show that there is a c k linearization for sufficiently small 0 we give a precise estimate on in terms of the gap and band conditions

mom volume integral equation solution for an isolated metal dielectric resonator with the edge based basis functions the objective of the present study is to show that the method of volume integral used in conjunction with the zeroth order edge based basis functions de carvalho and de souza mendes 1999 gives an accurate and stable solution for a metal dielectric resonator when the number of the basis functions remains relatively small special attention is paid to the resonator in the form of a thin dielectric layer backed by two metal sheets the metal surface is described in terms of the rao wilton glisson rwg basis functions

on the determination of resonant modes of dielectric objects using surface integral equations although surface integral equations have been extensively used for solving the scattering problem of arbitrarily shaped dielectric objects when applied to the resonance problem there are still some issues not fully addressed by the literature in this paper the method of moments with rao wilton glisson basis functions is applied to the electric field integral equation efie for solving the resonance problem of dielectric objects the resonant frequency is obtained by searching for the minimum of the reciprocal of the condition number of the impedance matrix in the complex frequency plane and the modal field distribution is obtained through singular value decomposition svd the determinant of the impedance matrix is not used since it is difficult to find its roots for the exterior efie the original basis functions are used as testing functions for the interior efie the basis functions rotated by 90 spl deg are used as testing functions to obtain an accurate modal field solution the impedance matrix needs to be reduced by half before svd is applied to it numerical results are given and compared with those obtained by using the volume integral equation

on the formulation of hybrid finite element and boundary integral methods for 3 d scattering this paper studies in detail a variety of formulations for the hybrid finite element and boundary integral fe bi method for three dimensional 3 d electromagnetic scattering by inhomogeneous objects it is shown that the efficiency and accuracy of the fe bi method depends highly on the formulation and discretization of the boundary integral equation bie used a simple analysis of the matrix condition number identifies the efficiency of the different fe bi formulations and an analysis of weighting functions shows that the traditional fe bi formulations cannot produce accurate solutions a new formulation is then proposed and numerical results show that the resulting solution has a good efficiency and accuracy and is completely immune to the problem of interior resonance finally the multilevel fast multipole algorithm mlfma is employed to significantly reduce the memory requirement and computational complexity of the proposed fe bi method

joint signal detection and parameter estimation in multiuser communications the problem of simultaneously detecting the information bits and estimating signal amplitudes and phases in a k user asynchronous direct sequence spread spectrum multiple access communication system is addressed the joint maximum likelihood ml estimator has a computational complexity that is exponential in the total number of bits transmitted and thus does not represent a practical solution to the problem an estimator that combines a suboptimum tree search algorithm with a recursive least squares estimator of complex signal amplitude is considered the complexity of this estimator is o k sup 2 computations per decoded bit and its performance is very close to that of the joint ml receiver this receiver has the advantage that the transmitted signal powers and phases are extracted from the received signal in an adaptive fashion without using a test sequence

efficient simulation of rectangular dielectric resonators using volume mpie mom formulation with combined entire domain and subdomain basis functions an efficient method of moments mom formulation using combined entire domain and subdomain basis functions is proposed for simulating the resonant modes of a rectangular dielectric resonator in free space an approximate analytical solution for the resonant mode of the dr is used as the entire domain basis function while a set of tetrahedral basis functions are used as subdomain basis functions since the main profile of the resonant mode can be well represented by the entire domain basis function only small number of subdomain basis functions are needed for further refinement of the representation compared with the mom formulations using only subdomain or entire domain basis functions this method is much faster for the same accuracy numerical results are given and compared with other methods

method of moments solution for a printed patch slot antenna on a thin finite dielectric substrate using the volume integral equation in this paper a volume integral equation vie based modeling method suitable for a patch or slot antenna on a thin finite dielectric substrate is developed and tested two new key features of the method are the use of proper dielectric basis functions and proper vie conditioning close to the metal surface where the surface boundary condition of the zero tangential e component must be extended into adjacent tetrahedra the extended boundary condition is the exact result for the piecewise constant dielectric basis functions the latter operation allows one to achieve a good accuracy with one layer of tetrahedra for a thin dielectric substrate and thereby greatly reduces computational cost the use of low order basis functions also implies the use of low order integration schemes and faster filling of the impedance matrix for some common patch slot antennas the vie based modeling approach is found to give an error of about 1 or less in the resonant frequency for one layer tetrahedral meshes with a relatively small number of unknowns this error is obtained by comparison with fine finite element method fem simulations or with measurements or with the analytical mode matching approach hence it is competitive with both the method of moments surface integral equation approach and with the fem approach for the printed antennas on thin dielectric substrates

tracking properties and steady state performance of rls adaptive filter algorithms adaptive signal processing algorithms derived from ls least squares cost functions are known to converge extremely fast and have excellent capabilities to track an unknown parameter vector this paper treats analytically and experimentally the steady state operation of rls recursive least squares adaptive filters with exponential windows for stationary and nonstationary inputs a new formula for the estimation noise has been derived involving second and fourth order statistics of the filter input as well as the exponential windowing factor and filter length furthermore it is shown that the adaptation process associated with lag effects depends solely on the exponential weighting parameter in addition the calculation of the excess mean square error due to the lag for an assumed markov channel provides the necessary information about tradeoffs between speed of adaptation and steady state error it is also the basis for comparison to the simple lms algorithm in a simple case of channel identification it is shown that the lms and rls adaptive filters have the same tracking behavior finally in the last part we present new rls restart procedures applied to transversal structures for mitigating the disastrous results of the third source of noise namely finite precision arithmetic

maximum likelihood sequence estimation of cpm signals transmitted over rayleigh flat fading channels a method for the sequential updating of log likelihood functions for maximum likelihood sequence estimation is presented it is shown that in a general case this method can be implemented using kalman filtering techniques for the special case of rayleigh flat fading and continuous phase modulation cpm signaling this approach is shown to lead to an attractive receiver structure this type of receiver called the linear predictive receiver can be implemented in the form of the viterbi algorithm with the trellis updates being computed using a bank of finite pulse response fir filter and square operations simulation results are presented that demonstrate the superiority of the linear predictive receiver over receivers employing differential detection in the presence of fast fading it is shown that the optimal linear predictive receiver does not possess an irreducible error rate for a class of rayleigh fading channels used to model terrestrial mobile channels

determination of resonant modes of dielectric resonators using mom sie with combined entire domain and subdomain basis functions method of moments mom combined with surface integral equation sie is a favorable approach for determining resonant modes of dielectric resonators to decrease the number of unknowns the subdomain basis functions are combined with an entire domain basis function which is an approximate solution of the resonant mode since the main profile of the current distribution can be represented by the entire domain basis function only small refinements are needed for better depiction of the current distribution as an example the te sub 11 spl delta mode of a rectangular dielectric resonator is simulated and compared with other methods

ck centre unstable manifolds we consider the existence and smoothness of global centre unstable manifolds for finite and infinite dimensional flows or maps we show that every global centre unstable manifold can be expressed as a graph of a c k map provided that the nonlinearities are c k smooth the proofs are based on a lemma by d henry on a necessary and sufficient condition for a lipschitz map to be continuously differentiable

mlse for an unknown channel i optimality considerations the problem of performing joint maximum likelihood ml estimation of a digital sequence and unknown dispersive channel impulse response is considered starting from a continuous time ct model previous investigations of this problem have not considered the front end fe processing in detail rather a discrete time signal model has been assumed we show that a fractionally spaced whitened matched filter matched to the known data pulse provides a set of sufficient statistics when a tapped delay line channel model is assumed and that the problem is ill posed when the channel impulse response is generalized to a ct finite length model practical approximations are considered that circumvent this ill posed condition recursive computation of the joint ml metric is developed together the fe processing and metric recursion provide a receiver structure which may be interpreted as the theoretical foundation for the previously introduced technique of per survivor processing and they lead directly to generalizations several fe processors representative of those suggested in the literature are developed and related to the practically optimal fe

sub stable and weak stable manifolds associated with finitely non resonant spectral subspaces in this work we study c k delta 2 leq k leq infty 0 leq delta leq 1 maps of a banach space near a fixed point we show the existence and uniqueness of a class of c k delta local invariant sub manifolds of the stable manifold which correspond to a spectral subspace satisfying a finite non resonance condition of order l leq k and an overriding condition of order l leq k condition 3 of theorem 1 we study the dependence of these invariant manifolds on a parameter that lies in a banach space we also show that a c k delta local weak stable manifold that satisfies these two conditions is unique in the class of c k delta maps the uniqueness is due to the fact that our method does not require a cut off function an infinite dimensional banach space does not always admit smooth cut off functions

on the dual basis for solving electromagnetic surface integral equations a powerful technique for solving electromagnetic em surface integral equations sies for inhomogenous objects by the method of moments mom involves the well known rao wilton glisson rwg basis function to represent the electric current and for field orthogonality and numerical stability reasons a variation of the rwg basis known as the ntilde x rwg basis where ntilde is a unit normal vector at the object surface to represent the magnetic current though this combination provides a numerically efficient and effective solution that has been demonstrated on a variety of structures one cannot feel entirely comfortable because of the presence of fictitious magnetic current associated with the modified basis chen and wilton proposed a different smoother basis in 1990 that avoids the fictitious line charges but because of computational cost issues it has not been used beyond chen s dissertation recently this basis was rediscovered and has received considerable attention our work reexamines the dual basis exploring issues not addressed by chen and wilton and showing accurate solutions for a variety of em scattering structures

potential integrals for uniform and linear source distributions on polygonal and polyhedral domains formulas for the potentials due to uniform and linearly varying source distributions defined on simply shaped domains are systematically developed and presented domains considered are infinite planar strips infinite cylinders of polygonal cross sections planar surfaces with polygonal boundaries and volumetric regions with polyhedral boundaries the expressions obtained are compact in form and their application in the numerical solution of electromagnetics problems by the method of moments is illustrated

autocovariance preserving estimator ape interpretation of the mlsd metric for rayleigh fading channels this paper describes a new interpretation of the maximum likelihood sequence detector metric for a linearly modulated signal and an unknown time varying dispersive rayleigh fading channel the metric which involves the channel and noise autocovariances is transformed into the intuitive mahalanobis distance squared euclidean distance in white noise between the observations and a reference estimated from them a novel estimator called the autocovariance preserving estimator is obtained that trades off increased estimation bias for reduced sequence error probability

approximate ml decoding of coded psk with no explicit carrier phase reference an approximate method is discussed for maximum likelihood estimation of coded psk sequences in the presence of an unknown carrier phase this method makes use of the viterbi algorithm to find an optimum path in the encoder trellis diagram phase estimation is embedded into the structure of the detection algorithm and the branch metrics in the trellis are modified with respect to those employed with known carrier phase comparisons with traditional decoding schemes show that the proposed solution has better performance in terms of acquisition time and cycle slips

invariant manifolds associated to nonresonant spectral subspaces we show that if the linearization of a map at a fixed point leaves invariant a spectral subspace which satisfies certain nonresonance conditions the map leaves invariant a smooth manifold tangent to this subspace this manifold is as smooth as the map when the smoothness is measured in appropriate scales but is unique amongcl invariant manifolds wherel depends only on the spectrum of the linearization or on some more general smoothness classes that we detail we show that if the nonresonance conditions are not satisfied a smooth invariant manifold need not exist and we also establish smooth dependence on parameters we also discuss some applications of these invariant manifolds and briefly survey related work

frequency selective fading channel estimation with a polynomial time varying channel model a rectangular windowed least squares estimator using a polynomial model of the time varying channel taps is proposed for estimating the impulse response of a frequency selective fading channel this method provides a significant improvement in mean square identification error msie over the conventional least mean squares lms and the exponentially weighted recursive least squares ew rls algorithms without a polynomial model a detailed study of the effects of channel parameters such as the fading rate and the signal to noise ratio on the proposed method is carried out the performance of the method depends on the window size of the least squares estimator and the polynomial order being used algorithms to obtain the approximately optimal window size and polynomial order are proposed and are shown to perform well

on the numerical integration of the linear shape functions times the 3 d green s function or its gradient on a plane triangle formulas for the static and dynamic potentials due to linearly varying source distributions defined on a planar triangle are presented the general linear variation of the source is represented in terms of three linear basis functions each one associated with a different vertex of the triangular domain the singular kernels considered are given by the 3 d green s function and its gradient both for the static and dynamic case in the static case the evaluation of potentials is performed analytically and compact form results are given in the dynamic case the results are given in a form suited for numerical integration

alternative surface integral equation formulations for characteristic modes of dielectric and magnetic bodies in this paper the physical meanings and various computing methods of characteristic modes cms of dielectric and magnetic bodies are investigated two types of surface integral equation sie formulations based on the dependent relationships between the equivalent surface electric and magnetic currents are proposed following the two types of sie formulations two generalized eigenvalue equations are established to determine the cms of dielectric or magnetic bodies this is in contrast to the approach using induced volume currents it is found that the eigenvalues possess clear physical meanings similar to those of perfectly electric conducting bodies the cms can be used to describe the resonant features including resonant frequencies and resonant field distributions numerical results are presented to validate the proposed formulations

invariant manifolds for flows in banach spaces on presente une theorie des varietes invariantes lisses basee sur la methode classique de lyapunov penon pour des semi flots continus dans des espaces de banach