partition combinatorics and multiparticle scattering theory the recently developed combinatoric methods for handling partition labeled operators in n particle scattering theory are studied from an abstract point of view the relation of these methods to approaches of the cluster cumulant type in many areas of mathematical physics is pointed out the concept of connectedness is defined abstractly and the mathematical structure of the partition lattice is considered in detail many of the useful results of combinatoric scattering theory are shown to be natural expressions of properties of the partition lattice the conditions on these results can then be stated with precision a number of new operator theorems are also obtained by means of applying simple extensions and analogs of the known properties of the partition lattice

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

classical to critical crossovers from field theory we extend our previous determinations of nonasymptotic critical behavior of phys rev b 32 7209 1985 and 35 3585 1987 to accurate expressions of the complete classical to critical crossover in three dimensional field theory in terms of the temperaturelike scaling field i e along the critical isochore for 1 the correlation length the susceptibility and the specific heat in the homogeneous phase for the n vector model n 1 to 3 and 2 the spontaneous magnetization coexistence curve the susceptibility and the specific heat in the inhomogeneous phase for the ising model n 1 the present calculations include the seventh loop order of murray and nickel and closely account for the up to date estimates of universal asymptotic critical quantities exponents and amplitude combinations provided by guida and zinn justin j phys a 31 8103 1998

blind equalization of constant modulus signals using an adaptive observer approach the paper addresses the problem of blind equalization of constant modulus signals which are degraded by frequency selective multipath propagation and additive white noise an adaptive observer is used to update the weights of an fir equalizer in order to restore the signal s constant modulus property the observer gain is selected using fake algebraic riccati methods in order to guarantee local stability the performance of this method is compared to the constant modulus algorithm for simulated fm fdm signals and exhibits significantly better convergence properties particularly for heavy tailed noise

adaptive fractionally spaced blind cma equalization excess mse the performance of the constant modulus algorithm cma a reference algorithm for adaptive blind equalization is studied in terms of the excess mean square error emse due to the nonvanishing step size of the gradient descent algorithm an analytical approximation of emse is provided emphasizing the effect of the constellation size and resulting in design guidelines

nonlinear aspects of the renormalization group flows of dyson s hierarchical model we review recent results concerning the renormalization group rg transformation of dyson s hierarchical model hm this model can be seen as an approximation of a scalar field theory on a lattice we introduce the hm and show that its large group of symmetry simplifies drastically the blockspinning procedure several equivalent forms of the recursion formula are presented with unified notations rigourous and numerical results concerning the recursion formula are summarized it is pointed out that the recursion formula of the hm is inequivalent to both wilson s approximate recursion formula and polchinski s equation in the local potential approximation despite the very small difference with the exponents of the latter we draw a comparison between the rg of the hm and functional rg equations in the local potential approximation the construction of the linear and nonlinear scaling variables is discussed in an operational way we describe the calculation of non universal critical amplitudes in terms of the scaling variables of two fixed points this question appears as a problem of interpolation between these fixed points universal amplitude ratios are calculated we discuss the large n limit and the complex singularities of the critical potential calculable in this limit the interpolation between the hm and more conventional lattice models is presented as a symmetry breaking problem we briefly introduce models with an approximate supersymmetry one important goal of this review is to present a configuration space counterpart suitable for lattice formulations of functional rg equations formulated in momentum space often called exact rg equations and abbreviated erge

joint data and channel estimation using blind trellis search techniques a novel method of maximum likelihood sequence estimation is proposed for data that are transmitted over unknown linear channels this procedure does not require a startup sequence for estimating the channel impulse response rather the data and the channel are simultaneously estimated it is implemented without any loss of optimality by a trellis search algorithm which searches for the best data sequence from among a number of hypothesized trellises which are constructed from the observed sequence the number of states in each trellis and the number of trellises grow exponentially with the channel memory a suboptimal trellis search algorithm is proposed whose complexity at best is slightly higher than that of the adaptive viterbi algorithm operating with a known channel response a simplified channel estimation algorithm when the number of data alphabets is greater than 2 is also proposed fast convergence of the algorithm in estimating the channel is demonstrated for binary pulse amplitude modulation over a variety of channels convergence over a wide range of snr occurs within 100 symbols the channel estimation algorithm for multi level signals converges within 500 1000 symbols we finally present an application of this algorithm to the problem of sequence estimation in the presence of rapidly time varying intersymbol interference the algorithm provides reliable zero delay decisions which results in a better channel tracking algorithm when compared to previously proposed schemes

renormalization group in the local potential approximation in the local potential approximation renormalization group equations reduce to a semilinear parabolic partial differential equation we derive this equation and show the relation with the hierarchical model we construct a family of non trivial fixed points u 2n n 2 3 4 which have the form ofn well potentials and exist in the ranges of dimensions 2 d dn 2 2 n 1 asd dn u 2n tends to zero for the wilson fixed pointu 4 we give bounds on critical exponents in the case of dipole gas in this approximation we show that no non trivial fixed points exist

precise determination of the energy levels of the anharmonic oscillator from the quantization of the angle variable using an ansatz motivated by the classical form of el phi where phi is the angle variable we construct operators which satisfy the commutation relations of the creation annihilation operators for the anharmonic oscillator the matrix elements of these operators can be expressed in terms of entire functions in the position complex plane these functions provide solutions of the ricatti equation associated with the time independent schrodinger equation we relate the normalizability of the eigenstates to the global properties of the flows of this equation these exact results yield approximations which complement the wkb approximation and allow an arbitrarily precise determination of the energy levels we give numerical results for the first 10 levels with 30 digits we address the question of the quantum integrability of the system

stochastic blind equalization based on pdf fitting using parzen estimator this work presents a new blind equalization approach that aims to force the probability density function pdf at the equalizer output to match the known constellation pdf quadratic distance between pdf s is used as the cost function to be minimized the proposed method relies on the parzen window method to estimate the data pdf and is implemented by a stochastic gradient descent algorithm the kernel size of the parzen estimator allows a dual mode switch or a soft switch between blind and decision directed equalization the proposed method converges faster than the constant modulus algorithm cma working at the symbol rate with a similar computational burden and reduces the residual error of the cma in multilevel modulations at the same time a comparison with the most common blind techniques is presented

renormalization group analysis of a simple hierarchical fermion model a simple hierarchical fermion model is constructed which gives rise to an exact renormalization transformation in a 2 dimensional parameter space the behaviour of this transformation is studied it has two hyperbolic fixed points for which the existence of aglobal critical line is proven the asymptotic behaviour of the transformation is used to prove the existence of the thermodynamic limit in a certain domain in parameter space also the existence of a continuum limit for these theories is investigated using informatioin about the asymptotic renomralization behaviour it turns out that the trivial fixed point gives rise to a twoparameter family of continuum limits corresponding to that part of parameter space where the renormalization trajectories originate at this fixed point although the model is not very realistic it serves as a simple example of the application of the renormalization group to proving the existence of the thermodynamic limit and the continuum limit of lattice models moreover it illustrates possible complications that can arise in global renormalization group behaviour and that might also be present in other models where no global analysis of the renormalization transformation has yet been achieved

a tractable example of perturbation theory with a field cutoff the anharmonic oscillator for 4 models the introduction of a large field cutoff improves significantly the accuracy that can be reached with perturbative series but the calculation of the modified coefficients remains a challenging problem we show that this problem can be solved numerically and analytically in the limits of large and small field cutoffs for the ground state energy of the anharmonic oscillator for the two lowest orders in the approximate formulae obtained in the large field cutoff limit extend unexpectedly far in the low field cutoff region and there is a significant overlap with the small field cutoff approximation for the higher orders this is not the case however the shape of the transition between the small field cutoff regime and the large field cutoff regime is approximately order independent

blind identification of fir systems driven by markov like input signals we propose a new algorithm for the blind identification and equalization of finite impulse response fir systems using the second order statistics of the received signal the new algorithm is set in the same context as the algorithms of tong et al 1994 and moulines et al 1995 however unlike those earlier approaches it is designed to allow correlated input signals specifically the algorithm accommodates finite memory sources and sources whose autocorrelation function decays exponentially numerical simulations compare the equalization performance of the new algorithm to those of tong and moulines it is shown that our algorithm yields consistently lower bit error rates at a wide variety of signal to noise ratios and at various equalizer lengths moreover the algorithm maintains this advantage even if it has no a priori information of source correlation or if source symbols are uncorrelated

steady state analysis of the multistage constant modulus array the multistage constant modulus cm array is a cascade adaptive beamforming system that can recover several narrowband cochannel signals without training we examine its steady state properties at convergence using a stochastic analysis and computer simulations based on a wiener model of convergence for the gradient adaptive algorithms closed form expressions are derived for the cm array and canceller weight vectors as well as the effective source direction vectors at all stages along the cascade system the signal capture and direction finding capabilities of the system are also discussed computer simulations for stationary and fading sources are presented to confirm the theoretical results and to illustrate the rapid convergence behavior of the adaptive algorithms

on line blind multichannel equalization based on mutually referenced filters this paper presents a novel approach to the blind linear equalization of possibly nonminimum phase and time varying communication channels in the context of channel diversity we introduce the concept of mutually referenced equalizers mres in which several filters are considered the outputs of which act as training signals for each other a corresponding constrained multidimensional mean square error mse cost function is derived the minimization of which is shown to be a necessary and sufficient condition for equalization the links with a standard linear prediction problem are demonstrated the proposed technique exhibits properties of important practical concern 1 the proposed algorithm is globally convergent 2 simple closed form solutions exist for the mres but the mres also lend themselves readily to adaptive implementation in particular the recursive least squares rls algorithm can be used to offer optimal convergence rate 3 the mre method provides a solution for all equalization delays which results in robustness properties with respect to snr and ill defined channel lengths

orientation of particle attachment and local isotropy in diffusion limited aggregation dla we simulate 50 off lattice diffusion limited aggregation dla clusters of one million particles each the probability distribution of the angle of attachment of arriving particles with respect to the local radial direction is obtained numerically for increasing cluster size n the distribution crosses over extremely accurately to a cosine with an amplitude which decreases towards zero as a power law in n from this specific viewpoint asymptotically large dla clusters are locally isotropic

non gaussian fixed points of the block spin transformation hierarchical model approximation with the use of analyticity techniques recently developed by the authors the e and 1 n expansion type arguments are turned into a rigorous control of the non gaussian fixed point of the hierarchical model renormalization group the present approach should extend beyond the hierarchical approximation and result in mathematical theory of the critical point of statistical mechanics or quantum field theory in three dimensions for small e or largen

an analytical constant modulus algorithm iterative constant modulus algorithms such as godard 1980 and cma have been used to blindly separate a superposition of cochannel constant modulus cm signals impinging on an antenna array these algorithms have certain deficiencies in the context of convergence to local minima and the retrieval of all individual cm signals that are present in the channel we show that the underlying constant modulus factorization problem is in fact a generalized eigenvalue problem and may be solved via a simultaneous diagonalization of a set of matrices with this new analytical approach it is possible to detect the number of cm signals present in the channel and to retrieve all of them exactly rejecting other non cm signals only a modest amount of samples is required the algorithm is robust in the presence of noise and is tested on measured data collected from an experimental set up

a faster aggregation for 3d fast evanescent wave solvers using rotations a novel technique to accelerate the aggregation and disaggregation stages in evanescent plane wave methods is presented the new method calculates the six plane wave radiation patterns from a multipole expansion aggregation and calculates the multipole expansion of an incoming field from the six plane wave incoming field patterns it is faster than the direct approach for multipole orders larger than one and becomes six times faster for large multipole orders the method relies on a connection between the discretizations of the six integral representations and on the fact that the wigner d matrices become diagonal for rotations around the z axis the proposed technique can also be extended to the vectorial case in two different ways one of which is very similar to the scalar case the other method relies on a beltrami decomposition of the fields and is faster than the direct approach for any multipole order this decomposition is also not limited to evanescent wave solvers but can be used in any vectorial multilevel fast multipole algorithm

from nonlinear scaling fields to critical amplitudes we propose to combine the nonlinear scaling fields associated with the high temperature ht fixed point with those associated with the unstable fixed point in order to calculate the susceptibility and other thermodynamic quantities the general strategy relies on simple linear relations between the ht scaling fields and the thermodynamic quantities and the estimation of rg invariants formed out of the two sets of scaling fields this estimation requires convergent expansions in overlapping domains if in addition the initial values of the scaling fields associated with the unstable fixed point can be calculated from the temperature and the parameters appearing in the microscopic hamiltonian one can estimate the critical amplitudes this strategy has been developed using dyson s hierarchical model where all the steps can be approximately implemented with good accuracy we show numerically that for this model and a simplified version of it the required overlap apparently occurs allowing an accurate determination of the critical amplitudes

the effects of pn sequences on the misconvergence of the constant modulus algorithm cma the constant modulus algorithm cma can misconverge when the received two dimensional 2 d signal is derived from encoding a binary pn sequence the distortion of the probabilistic symmetry of the transmitted constellation can be controlled by careful selection of the underlying binary pn sequence thereby influencing the convergence behavior of cma

direction of arrival estimation for constant modulus signals in many cases where direction finding is of interest the signals impinging on an antenna array are known to be phase modulated and hence to have a constant modulus cm this is a strong property by itself it is already sufficient for source separation and can be used to construct improved direction finding algorithms we first derive the relevant cramer rao bounds crbs for arbitrary array configurations and specialize to uniform linear arrays we then propose a simple suboptimal direction estimation algorithm in which the signals are separated using the cm property followed by direction finding on the decoupled signals compared with the esprit algorithm and the crb for arbitrary signals the algorithm shows good results

simple method to make asymptotic series of feynman diagrams converge we show that for two nontrivial lambda phi 4 problems the anharmonic oscillator and the landau ginzburg hierarchical model improved perturbative series can be obtained by cutting off the large field contributions the modified series converge to values exponentially close to the exact ones for lambda larger than some critical value the method outperforms pade s approximants and borel summations the method can also be used for series which are not borel summable such as the double well potential series we show that semiclassical methods can be used to calculate the modified feynman rules estimate the error and optimize the field cutoff

the oscillatory behavior of the high temperature expansion of dyson s hierarchical model a renormalization group analysis we calculate 800 coefficients of the high temperature expansion of the magnetic susceptibility of dyson s hierarchical model with a landau ginzburg measure log periodic corrections to the scaling laws appear as in the case of an ising measure the period of oscillation appears to be a universal quantity given in good approximation by the logarithm of the largest eigenvalue of the linearized rg transformation in agreement with a possibility suggested by wilson and developed by niemeijer and van leeuwen we estimate to be 1 300 with a systematic error of the order of 0 002 in good agreement with the results obtained with other methods such as the e expansion we briefly discuss the relationship between the oscillations and the zeros of the partition function near the critical point in the complex temperature plane

quantum anharmonic oscillators a new approach the determination of the eigenenergies of a quantum anharmonic oscillator consists merely in finding the zeros of a function of the energy namely the wronskian of two solutions of the schr dinger equation which are regular respectively at the origin and at infinity we show in this paper how to evaluate that wronskian exactly except for numerical rounding errors the procedure is illustrated by application to the gx2 x2n n a positive integer oscillator

on some polynomial potentials in d dimensions the d dimensional schrodinger s equation is analyzed with regard to the existence of exact solutions for polynomial potentials under certain conditions on the interaction parameters we show that the polynomial potentials v8 r k 18 krk 8 0 and v10 r k 110 krk 10 0 are exactly solvable by examining the polynomial solutions of certain linear differential equations with polynomial coefficients the necessary and sufficient conditions for the existence of these exact solutions are discussed finding accurate solutions for arbitrary values of the potential parameters using the asymptotic iteration method is also presented

cumulant based inverse filter criteria for mimo blind deconvolution properties algorithms and application to ds cdma systems in multipath tugnait 1995 and chi and chen proposed multi input multi output inverse filter criteria mimo ifc using higher order statistics for blind deconvolution of mimo linear time invariant systems this paper proposes three properties on the performance of the mimo linear equalizer associated with mimo ifc for any signal to noise ratio including p1 perfect phase equalization property p2 a relation to mimo minimum mean square error mimo mmse equalizer and p3 a connection with the one obtained by mimo super exponential algorithm mimo sea that usually converges fast but does not guarantee convergence for finite data based on p2 a fast algorithm for computing the theoretically optimum mimo equalizer is proposed moreover based on p3 a fast mimo ifc based algorithm with performance similar to that of the mimo sea and with guaranteed convergence is proposed as well as its application to suppression of multiple access interference and intersymbol interference isi for multiuser asynchronous ds cdma systems in multipath finally some simulation results are presented to support the analytic results and the proposed algorithms

blind equalization of nonminimum phase channels higher order cumulant based algorithm higher order cumulant analysis is applied to the blind equalization of linear time invariant lti nonminimum phase channels the channel model is moving average based to identify the moving average parameters of channels a higher order cumulant fitting approach is adopted in which a novel relay algorithm is proposed to obtain the global solution in addition the technique incorporates model order determination the transmitted data are considered as independently identically distributed random variables over some discrete finite set e g set or 1 or 3 a transformation scheme is suggested so that third order cumulant analysis can be applied to this type of data simulation examples verify the feasibility and potential of the algorithm performance is compared with that of the noncumulant based sato scheme in terms of the steady state mse and convergence rate

spherical wave operators and the translation formulas translational formulas for both scalar and vector spherical wave solutions of the helmholtz equation are developed in a straightforward manner using differential operator representations for the modal functions and well known expressions for the scalar and dyadic free space green s functions the expansion coefficients are given in compact integral or differential operator forms useful for analytic investigation

blind source separation the location of local minima in the case of finitely many samples cost functions used in blind source separation are often defined in terms of expectations i e an infinite number of samples is assumed an open question is whether the local minima of finite sample approximations to such cost functions are close to the minima in the infinite sample case to answer this question we develop a new methodology of analyzing the finite sample behavior of general blind source separation cost functions in particular we derive a new probabilistic analysis of the rate of convergence as a function of the number of samples and the conditioning of the mixing matrix the method gives a connection between the number of available samples and the probability of obtaining a local minimum of the finite sample approximation within a given sphere around the local minimum of the infinite sample cost function this shows the convergence in probability of the nearest local minima of the finite sample approximation to the local minima of the infinite sample cost function we also answer a long standing problem of the mean squared error mse behavior of the finite sample least squares constant modulus algorithm ls cma namely whether there exist ls cma receivers with good mse performance we demonstrate how the proposed techniques can be used to determine the required number of samples for ls cma to exceed a specified performance the paper concludes with simulations that validate the results

improved high temperature expansion and critical equation of state of three dimensional ising like systems high temperature series are computed for a generalized three dimensional ising model with arbitrary potential three specific improved potentials suppressing leading scaling corrections are selected by monte carlo computation critical exponents are extracted from high temperature series specialized to improved potentials achieving high accuracy our best estimates are gamma 1 2371 4 nu 0 630 02 23 alpha 0 1099 7 eta 0 0364 4 beta 0 326 48 18 by the same technique the coefficients of the small field expansion for the effective potential helmholtz free energy are computed these results are applied to the construction of parametric representations of the critical equation of state a systematic approximation scheme based on a global stationarity condition is introduced the lowest order approximation reproduces the linear parametric model this scheme is used for an accurate determination of universal ratios of amplitudes a comparison with other theoretical and experimental determinations of universal quantities is presented

improved methods for the blind system identification using higher order statistics it is demonstrated by a detailed analysis of blind system identification that under specific system configurations a recently published least squares algorithm shows a poor convergence behavior especially if the system order is overdetermined to overcome these problems a supplementary condition is introduced that guarantees proper convergence in most cases an alternative approach for the blind identification of mixed phase systems the so called cumulant zero matching method is presented in this approach the solution of a set of nonlinear equations which is necessary in the least squares method is replaced by the calculation of zeros of polynomials the main advantage over the least squares solution is that overdetermination of the system order is rather harmless since it only results in additional zeros in the origin of the z plane the different methods for system identification presented are illustrated by simulation results

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

the high temperature expansion of the hierarchical ising model from poincare symmetry to an algebraic algorithm it is shown that the hierarchical model at finite volume has a symmetry group which can be decomposed into rotations and translations as the familiar poincare groups using these symmetries it is shown that the intricate sums appearing in the calculation of the high temperature expansion of the magnetic susceptibility can be performed at least up to the fourth order using elementary algebraic manipulations which can be implemented with a computer these symmetries appear more clearly if we use the two adic fractions to label the sites then the new algebraic methods are applied to the calculation of quantities having a random walk interpretation in particular it is shown that the probability of returning to the starting point after m steps has poles at d 2 4 2m where d is a free parameter playing a role similar to the dimensionality in nearest neighbor models

a non gaussian renormalization group fixed point for hierarchical scalar lattice field theories a rigorous method is developed to handle the large field problems in the wilson kadanoff renormalization group approach to critical lattice systems of unbounded spins we use this method to study in a hierarchical approximation the non gaussian renormalization group fixed point which governs the infrared behaviour of critical lattice field theories in three dimensions the method is an improvement of the analyticity techniques of gawedzki and kupiainen using borel summation techniques we are able to incorporate the large field region into the perturbative region so that the theory is completely described in terms of convergent expansions

super exponential methods for blind deconvolution a class of iterative methods for solving the blind deconvolution problem i e for recovering the input of an unknown possibly nonminimum phase linear system by observation of its output is presented these methods are universal do not require prior knowledge of the input distribution are computationally efficient and statistically stable and converge to the desired solution regardless of initialization at a very fast rate the effects of finite length of the data finite length of the equalizer and additive noise in the system on the attainable performance intersymbol interference are analyzed it is shown that in many cases of practical interest the performance of the proposed methods is far superior to linear prediction methods even for minimum phase systems recursive and sequential algorithms are also developed which allow real time implementation and adaptive equalization of time varying systems

adaptive deconvolution and identification of nonminimum phase fir systems based on cumulants a novel adaptive deconvolution and system identification scheme is introduced for a linear non minimum phase finite impulse response fir system driven by non gaussian white noise the adaptive scheme is based on approximating the fir system by noncausal autoregressive ar models and using higher order cumulants of the system output as such it is a blind equalization deconvolution scheme the set of updated ar parameters is obtained by using a gradient type algorithm and by using higher order cumulants instead of time samples of the output signal it is demonstrated by means of extensive simulations that the adaptive scheme works well for both stationary and nonstationary cases as expected it outperforms the autocorrelation based gradient method for nonminimum phase system identification and deconvolution performance comparisons to existing methods are given using as figures of merit the probability of errors in the restored input sequence computational complexity and convergence rate

ode analysis and redesign in blind adaptation in blind adaptation the dynamics of an unknown channel system is recovered together with the transmitted symbol sequence input signal this paper generalizes the author s previous algorithm 1994 1997 that is not derived by criterion minimization to include adaptive regressor filtering the resulting scheme which adapts a finite dimensional iir channel model is designed to converge only to a well defined set of parameters when binary symbols are transmitted over the channel this provides a partial solution to the recently discussed ill convergence problem in blind adaptation some connections to adaptive control theory are noted

the tone capture properties of cma based interference suppressors an earlier paper introduced the constant modulus algorithm cma an adaptive filtering technique for correcting multipath and interference induced degradations in constant envelope waveforms such as fm and qpsk signals this algorithm exploits the fact that both multipath propagation and additive interference disrupt the constant envelope property of the received signal by sensing the received envelope variations the adaptive algorithm can reset the coefficients of an fir digital filter so as to remove the variations and in the process suppress the various interference components from the desired signal this paper examines a problem that arises when using cma to suppress narrow band interference if both the interferer and the signal have constant envelope and are spectrally nonoverlapping then it is possible to find two different filter solutions one which suppresses the interferer and another which captures the interferer and suppresses the desired signal this paper examines how capture can occur and how it may be prevented this problem is studied by characterizing the algorithm s behavior to an input consisting of only two sinusoids assuming slow adaptation the n dimensional adaptive weight recursion is shown to compress into a two by two recursion in the tone output amplitudes this simplified recursion is then analyzed to determine what combinations of input amplitudes signal to interference ratios and filter initial conditions lead to lock and which lead to the capture of the interferer the results are then broadened to include multiple input tones and signals with nonzero bandwidth

higher order corrections to instantons the energy levels of the double well potential receive beyond perturbation theory contributions which are non analytic in the coupling strength these are related to instanton effects for example the separation between the energies of odd and even parity states is given at leading order by the one instanton contribution however to determine the energies more accurately multi instanton configurations have also to be taken into account we investigate here the two instanton contributions first we calculate analytically higher order corrections to multi instanton effects we then verify that the difference betweeen numerically determined energy eigenvalues and the generalized borel sum of the perturbation series can be described to very high accuracy by two instanton contributions we also calculate higher order corrections to the leading factorial growth of the perturbative coefficients and show that these are consistent with analytic results for the two instanton effect and with exact data for the first 200 perturbative coefficients

on blind beamforming for multiple non gaussian signals and the constant modulus algorithm a new method for blindly separating multiple cochannel non gaussian signals received by a sensor array is presented the method is based on a cumulant based least squares criterion that for identically distributed negative kurtosis signals is proven to be identical to the 2 2 constant modulus cm cost function commonly used by cm algorithms a computationally simple algorithm is proposed to minimize the criterion the algorithm performs well even when the number of samples is small thus allowing its application in dynamic environments e g moving emitters for the special case of two signals only the minimization is obtained analytically simulation results are included

waveform preserving blind estimation of multiple independent sources the problem of blind estimation of source signals is to estimate the source signals without knowing the characteristics of the transmission channel it is shown that the minimum variance unbiased estimates can be obtained if and only if the transmission channel can be identified blindly it is shown that the channel can be blindly identified if and only if there is not more than one gaussian source this condition suggests that waveform preserving blind estimation can be achieved over a wide range of signal processing applications including those cases in which the source signals have identical nongaussian distributions the constructive proof of the necessary and sufficient condition serves as a foundation for the development of waveform preserving blind signal estimation algorithms examples are presented to demonstrate the applications of the theoretical results

multi stage blind clustering equaliser a multi stage blind clustering algorithm is proposed for equalisation of multi level quadrature amplitude modulation m qam channels a hierarchical decomposition divides the task of equalising a high order qam channel into much simpler sub tasks each sub task can be accomplished fast and reliably using a blind clustering algorithm derived originally for 4 qam signals the constant modulus algorithm cma is used as a benchmark to assess this multi stage blind equaliser it is demonstrated that the new blind algorithm achieves much faster convergence and is very robust when input symbols are not sufficiently white this multi stage clustering equaliser only requires slightly more computations than the cma and like the latter its computational complexity does not increase as the levels of digital symbols increase

efficient fast multipole method for low frequency scattering the solution of the helmholtz and maxwell equations using integral formulations requires to solve large complex linear systems a direct solution of those problems using a gauss elimination is practical only for very small systems with few unknowns the use of an iterative method such as gmres can reduce the computational expense most of the expense is then computing large complex matrix vector products the cost can be further reduced by using the fast multipole method which accelerates the matrix vector product for a linear system of size n the use of an iterative method combined with the fast multipole method reduces the total expense of the computation to n log n there exist two versions of the fast multipole method one which is based on a multipole expansion of the interaction kernel exp ikr r and which was first proposed by v rokhlin and another based on a plane wave expansion of the kernel first proposed by w c chew in this paper we propose a third approach the stable plane wave expansion spw fmm which has a lower computational expense than the multipole expansion and does not have the accuracy and stability problems of the plane wave expansion the computational complexity is n log n as with the other methods

fine structure and complex exponents in power law distributions from random maps discrete scale invariance dsi has recently been documented in time to failure rupture earthquake processes and financial crashes in the fractal geometry of growth processes and in random systems the main signature of dsi is the presence of log periodic oscillations correcting the usual power laws corresponding to complex exponents log periodic structures are important because they reveal the presence of preferred scaling ratios of the underlying physical processes here we present new evidence of log periodicity overlaying the leading power law behavior of probability density distributions of affine random maps with parametric noise the log periodicity is due to intermittent amplifying multiplicative events we quantify precisely the progressive smoothing of the log periodic structures as the randomness increases and find a large robustness our results provide useful markers for the search of log periodicity in numerical and experimental data

a two parameter recursion formula for scalar field theory we present a two parameter family of recursion formulae for scalar field theory the first parameter is the dimension d the second parameter allows one to continuously extrapolate between wilson s approximate recursion formula and the recursion formula of dyson s hierarchical model we show numerically that at fixed d the critical exponent depends continuously on we suggest the use of the independence as a guide to construct improved recursion formulae

performance predictions for parameter estimators that minimize cost functions using wirtinger calculus with application to cm blind equalization we present calculations of the first order bias and first order variance of parameters which are estimated batch wise from the global minimum of a cost function of complex valued signals embedded in zero mean gaussian noise the derivation involves the calculation of the multidimensional taylor series of the non analytic cost function up to third order using the elegant wirtinger calculus whereas closed form expressions for the variance can be obtained straightforwardly from a second order taylor series and have been presented in various other contexts an exact expression for the bias cannot be derived in general in this paper we propose approximate expressions for the first order bias and confirm them in a comparison of results from extensive analytical calculations with results from monte carlo mc simulations for the statistical efficiency of a batch processing blind equalizer using the constant modulus cm criterion we study the equalization of independent and identically distributed i i d random symbols and obtain asymptotic for large batch size expressions for the averages of the bias and variance over zero mean random real valued signals of binary phase shift keying bpsk and complex valued signals of m ary psk modulation m 2 finally we compare the statistical efficiency of the cm estimator with the one of the maximum likelihood ml blind estimation of the path parameters and equalized symbols with cm constraint

a nontrivial renormalization group fixed point for the dyson baker hierarchical model we prove the existence of a nontrivial renormalization group rg fixed point for the dyson baker hierarchical model ind 3 dimensions the single spin distribution of the fixed point is shown to be entire analytic and bounded by exp const t6 for large real values of the spint our proof is based on estimates for the zeros of a rg fixed point for gallavotti s hierarchical model we also present some general results for the heat flow on a space of entire functions including an order preserving property for zeros which is used in the rg analysis

bussgang zero crossing equalization an integrated hos sos approach an integrated higher order statistics hos and second order statistics sos based equalization technique is presented as an extension of the bussgang equalization algorithm this extension allows one to simultaneously take account of the statistical knowledge about the data source as done in the conventional hos approaches and in particular by bussgang like equalization algorithms such as super exponential constant modulus etc and the spectral redundancy usually present in pulse amplitude modulation pam and quadrature amplitude modulation qam modulated signals exploited by sos based approaches the technique presented employs a new form of sos equalization that naturally integrates into the bussgang scheme it is based on a zero crossing zc property of the received signal when it is passed through a suitable filter the novel equalization scheme is presented in a bayesian estimation framework after illustration of the general bussgang paradigm and of the principles of the zc approach from simulated experiments results show that the extended bussgang zc equalizer not only outperforms conventional bussgang equalizers but is also robust to situations where hos and sos approaches individually fail

shrinkage linear and widely linear complex valued least mean squares algorithms for adaptive beamforming in this paper shrinkage linear complex valued least mean squares sl clms and shrinkage widely linear complex valued least mean squares swl clms algorithms are devised for adaptive beamforming by exploiting the relationship between the noise free a posteriori and a priori error signals the sl clms method is able to provide a variable step size to update the weight vector for the adaptive beamformer significantly enhancing the convergence speed and decreasing the steady state misadjustment on the other hand besides adopting a variable step size determined by minimizing the square of the augmented noise free a posteriori errors the swl clms approach exploits the noncircular properties of the signal of interest which considerably improves the steady state performance simulation results are presented to illustrate their superiority over the clms complex valued normalized lms variable step size recursive least squares rls algorithms and their corresponding widely linear based schemes additionally our proposed algorithms are more computationally efficient than the rls solutions though they may have a slightly slower convergence rate

conformal mappings versus other power series methods for solving ordinary differential equations illustration on anharmonic oscillators the simplicity and the efficiency of a quasi analytical method for solving nonlinear ordinary differential equations ode is illustrated on the study of anharmonic oscillators ao with a potential v x x2 x2m m 0 the method bervillier 2008 nucl phys b801 296 applies a priori to any ode with two point boundaries one being located at infinity the solution of which has fixed singularities in the complex plane of the independent variable x a conformal mapping of a suitably chosen angular sector of the complex plane of x upon the unit disc centered at the origin makes convergent the transformed taylor series of the generic solution so that the boundary condition at infinity can be easily imposed in principle this constraint when applied on the logarithmic derivative of the wavefunction determines the eigenvalues to an arbitrary level of accuracy in practice for 0 or slightly negative the accuracy of the results obtained is astonishingly large with regard to the modest computing power used various aspects of the method and comparisons with some seemingly similar methods based also on expressing the solution as a taylor series are shortly reviewed presented and discussed

on the nonvanishing stability of undesirable equilibria for fir godard blind equalizers the existence of undesirable equilibria of godard 1980 or constant modulus algorithms cma is demonstrated for all finite dimensional fir equalizers sufficient stability conditions are presented for these equilibria it is shown that for the godard 2 algorithm these undesirable equilibria are locally stable as long as the equalizer length remains finite results indicate that merely increasing the equalizer length does not necessarily nullify the potential for local convergence by godard algorithms

computation of hierarchical renormalization group fixed points and their e expansions we compute hierarchical renormalization group fixed points as solutions to an algebraic equation for the coupling constants this method does not rely on an iteration of renormalization group transformations and therefore avoids the problem of fine tuning we solve truncated versions of the fixed point equation numerically for different values of the dimension parameter in the range 2 d 4 and different orders of truncations the method is well suited even for multicritical fixed points with any number of unstable directions precise numerical data are presented for the first three nontrivial fixed points and their critical indices we also develop an e expansion for the hierarchical models using computer algebra the numerical results are compared with the e expansion

blind equalization for correlated input symbols a bussgang approach this paper addresses the problem of blind equalization in the case of correlated input symbols and it shows how the knowledge of the symbol sequence probability distribution can be directly incorporated in a bussgang blind equalization scheme numerical results pertaining to both linear and nonlinear modulation schemes show that a significant improvement in equalization performance is obtained by exploiting the symbol sequence probability distribution using the approach herein described

a mixed form fast multipole algorithm the fast multipole algorithm manifests in two very different forms at low frequencies and at mid frequencies each can operate in their respective regimes but are not tenable in the other regimes the paper reports on a way to factorize the green s function for fast algorithm using a mixed form the low frequency fast multipole algorithm lf fma will be used at low frequencies or the long wavelength regime and the multilevel fast multipole algorithm mlfma will be used for the mid frequencies or the shorter wavelength regime for object modeling where both long wavelength and wave physics are important we propose a mixed form fast multipole algorithm mf fma this algorithm has no low frequency break down and it can work seamlessly from static where circuit physics is important to dynamic where wave physics is important

arbitrarily accurate eigenvalues for one dimensional polynomial potentials we show that the riccati form of the one dimensional schrodinger equation can be reformulated in terms of two linear equations depending on an arbitrary function g when g and the potential as for anharmonic oscillators are polynomials the solutions of these two equations are entire functions l and k and the zeros of k are identical to those of the wavefunction requiring such a zero at a large but finite value of the argument yields low energy eigenstates with exponentially small errors approximate formulae for these errors are provided we explain how to choose g in order to dramatically improve the numerical treatment the method yields many significant digits with modest computer means we discuss the extension of this method in the case of several variables

regularity properties and pathologies of position space renormalization group transformations scope and limitations of gibbsian theory we reconsider the conceptual foundations of the renormalization group rg formalism and prove some rigorous theorems on the regularity properties and possible pathologies of the rg map our main results apply to local in position space rg maps acting on systems of bounded spins compact single spin space regarding regularity we show that the rg map defined on a suitable space of interactions formal hamiltonians is always single valued and lipschitz continuous on its domain of definition this rules out a recently proposed scenario for the rg description of first order phase transitions on the pathological side we make rigorous some arguments of griffiths pearce and israel and prove in several cases that the renormalized measure is not a gibbs measure for any reasonable interaction this means that the rg map is ill defined and that the conventional rg description of first order phase transitions is not universally valid for decimation or kadanoff transformations applied to the ising model in dimension d 3 these pathologies occur in a full neighborhood 0 h e of the low temperature part of the first order phase transition surface for block averaging transformations applied to the ising model in dimension d 2 the pathologies occur at low temperatures for arbitrary magnetic field strength pathologies may also occur in the critical region for ising models in dimension d 4 we discuss the heuristic and numerical evidence on rg pathologies in the light of our rigorous theorems in addition we discuss critically the concept of gibbs measure which is at the heart of present day classical statistical mechanics we provide a careful and we hope pedagogical overview of the theory of gibbsian measures as well as the less familiar non gibbsian measures emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations we give a rather complete catalogue of the known examples of such occurrences the main message of this paper is that despite a well established tradition gibbsiannessshould not be taken for granted

broadband multilevel fast multipole algorithm for electric magnetic current volume integral equation a volume integral equation method given in terms of the equivalent electric and magnetic volume currents and discretized using non conforming element wise constant approximations is applied to electromagnetic scattering analysis of inhomogeneous and anisotropic objects a broadband version of the multilevel fast multipole algorithm mlfma combining low frequency stable planewave expansion technique with the high frequency mlfma and utilizing global interpolators based on trigonometric polynomials is used to accelerate the computations

on the renormalization group transformation for scalar hierarchical models we give a new proof for the existence of a non gaussian hierarchical renormalization group fixed point using what could be called a beta function for this problem we also discuss the asymptotic behavior of this fixed point and the connection between the hierarchical models of dyson and gallavotti

a diagonalized multilevel fast multipole method with spherical harmonics expansion of the k space integrals diagonalization of the fast multipole method fmm for the helmholtz equation is usually achieved by expanding the multipole representation in propagating plane waves the resulting k space integral over the ewald sphere is numerically evaluated storing the k space quadrature samples of the method of moments mom basis functions constitutes a large portion of the overall memory requirements of the resulting algorithm for solving the integral equations of scattering and radiation problems in this paper it is proposed to expand the k space representation of the basis functions by spherical harmonics in order to reduce the sampling redundancy introduced by numerical quadrature rules aggregations plane wave translations and disaggregations in the realized multilevel fast multipole method mlfmm are carried out using the k space samples of a numerical quadrature rule however the incoming plane waves on the finest mlfmm level are expanded in spherical harmonics again thus due to the orthonormality of spherical harmonics the testing integrals for the individual testing functions are simplified into series over products of spherical harmonics expansion coefficients overall the resulting mlfmm can save a considerable amount of memory without compromising accuracy and numerical speed

a complete renormalization group trajectory between two fixed points we give a rigorous nonperturbative construction of a massless discrete trajectory for wilson s exact renormalization group the model is a three dimensional euclidean field theory with a modified free propagator the trajectory realizes the mean field to critical crossover from the ultraviolet gaussian fixed point to an analog recently constructed by brydges mitter and scoppola of the wilson fisher nontrivial fixed point