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

asymptotic properties of the algebraic constant modulus algorithm the algebraic constant modulus algorithm acma is a noniterative blind source separation algorithm it computes jointly beamforming vectors for all constant modulus sources as the solution of a joint diagonalization problem we analyze its asymptotic properties and show that unlike cma it converges to the wiener beamformer when the number of samples or the signal to noise ratio snr goes to infinity we also sketch its connection to the related jade algorithm and derive a version of acma that converges to a zero forcing beamformer this gives improved performance in applications that use the estimated mixing matrix such as in direction finding

quantum variance and ergodicity for the baker s map we prove an egorov theorem or quantum classical correspondence for the quantised baker s map valid up to the ehrenfest time this yields a logarithmic upper bound for the decay of the quantum variance and as a corollary a quantum ergodic theorem for this map

equipartition of the eigenfunctions of quantized ergodic maps on the torus we give a simple proof of the equipartition of the eigenfunctions of a class of quantized ergodic area preserving maps on the torus examples are the irrational translations the skew translations the hyperbolic automorphisms and some of their perturbations

chaos revealing multiplicative representation of quantum eigenstates the quantisation of the two dimensional toric and spherical phase spaces is considered in analytic coherent state representations every pure quantum state admits therein a finite multiplicative parametrisation by the zeros of its husimi function for eigenstates of quantised systems this description explicitly reflects the nature of the underlying classical dynamics in the semiclassical regime the distribution of the zeros in the phase space becomes one dimensional for integrable systems and highly spread out conceivably uniform for chaotic systems this multiplicative representation thereby acquires a special relevance for semiclassical analysis in chaotic systems

exact correlation functions for dual unitary lattice models in 1 1 dimensions we consider a class of quantum lattice models in 1 1 dimensions represented as local quantum circuits that enjoy a particular dual unitarity property in essence this property ensures that both the evolution in time and that in space are given in terms of unitary transfer matrices we show that for this class of circuits generically nonintegrable one can compute explicitly all dynamical correlations of local observables our result is exact nonpertubative and holds for any dimension d of the local hilbert space in the minimal case of qubits d 2 we also present a classification of all dual unitary circuits which allows us to single out a number of distinct classes for the behavior of the dynamical correlations we find noninteracting classes where all correlations are preserved the ergodic and mixing one where all correlations decay and interestingly also classes that are both interacting and nonergodic

ergodicite et limite semi classique consider a self adjoint quantic hamiltonian p h p x hdx whereh 0 is the planck s constant andp some smooth classical observable on the phase space r2n when the classical flow on a compact energy shell p is ergodic we prove that in the limith 0 almost all the eigenfunctions ofp h whose energy is near of are distributed according to the liouville measure on p

entropy of semiclassical measures in dimension 2 we study the high energy asymptotic properties of eigenfunctions of the laplacian in the case of a compact riemannian surfacem of anosov type to do this we look at families of distributions associated to them on the cotangent bundle t m and we derive entropic properties on their accumulation points in the high energy limit the so called semiclassical measures we show that the kolmogorov sinai entropy of a semiclassical measure for the geodesic ow gt is bounded from below by half of the ruelle upper bound i e hks g 1 2 s m d where is the upper lyapunov exponent at point

regression analysis of data from a cluster sample abstract for the case of different regression relationships in different subgroups of a finite population only part of which are sampled the extended least squares estimator of any weighted average of the distinct coefficients is derived under assumptions relating only to the first two moments of the distribution of the coefficients under these assumptions the estimator is shown to be the best linear unbiased estimator while under further distributional assumptions it is also the bayesian estimator for a quadratic loss function for the case of unknown variances a method for estimating them from the sample is proposed the empirical estimator thus obtained is shown to perform well by a simulation comparison with the optimal estimator and with other proposed empirical estimators

no quantum ergodicity for star graphs we investigate statistical properties of the eigenfunctions of the schrodinger operator on families of star graphs with incommensurate bond lengths we show that these eigenfunctions are not quantum ergodic in the limit as the number of bonds tends to infinity by finding an observable for which the quantum matrix elements do not converge to the classical average we further show that for a given fixed graph there are subsequences of eigenfunctions which localise on pairs of bonds we describe how to construct such subsequences explicitly these structures are analogous to scars on short unstable periodic orbits

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

sufficient conditions for the local convergence of constant modulus algorithms the constant modulus cm criterion has become popular in the design of blind linear estimators of sub gaussian i i d processes transmitted through unknown linear channels in the presence of unknown additive interference the existence of multiple cm minima however makes it difficult for cm minimizing schemes to generate estimates of the desired source as opposed to an interferer in multiuser environments in this paper we present three separate sufficient conditions under which gradient descent gd minimization of cm cost will locally converge to an estimator of the desired source at a particular delay the sufficient conditions are expressed in terms of statistical properties of the initial estimates specifically cm cost kurtosis and signal to interference plus noise ratio sinr implications on cm gd initialization methods are also discussed

correspondence between some wave patterns and lissajous figures we study the connections between some specially entangled stationary states and the classical periodic trajectories of two non interacting oscillators the latter are well known lissajous figures which are shown to run precisely over the apogees of their corresponding probability distributions in the above states we propose in this work a very simple criterion enabling us to obtain the best agreement between the quantum and the classical images finally our results are successfully applied to the interpretation of some experimentally observed wave patterns

continuum quantum systems as limits of discrete quantum systems i state vectors abstract dynamical systems on continuum hilbert spaces may be realized as limits of dynamical systems on discrete possibly finite dimensional hilbert spaces in this first of four papers on the topic the continuum and discrete spaces are interfaced to one another algebraically convergence of vectors is defined in such a way as to preserve inner products and a necessary and sufficient coordinate wise criterion for convergence is proved

statistical performance analysis of the algebraic constant modulus algorithm this paper presents a large sample analysis of the covariance of the beamformers computed by the analytical constant modulus algorithm acma method for blindly separating constant modulus sources this can be used to predict the signal to interference plus noise ratio sinr performance of these beamformers as well as their deviation from the nonblind wiener receivers to which they asymptotically converge the analysis is based on viewing acma as a subspace fitting optimization where the subspace is spanned by the eigenvectors of a fourth order covariance matrix the theoretical performance is illustrated by numerical simulations and shows a good match

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

the schrodinger equation and canonical perturbation theory lett0 ev be the schrodinger operator corresponding to the classical hamiltonianh0 ev whereh0 is thed dimensional harmonic oscillator with non resonant frequencies 1 d and the potentialv q1 qd is an entire function of order d 1 1 we prove that the algorithm of classical canonical perturbation theory can be applied to the schrodinger equation in the bargmann representation as a consequence each term of the rayleigh schrodinger series near any eigenvalue oft0 admits a convergent expansion in powers of of initial point the corresponding term of the classical birkhoff expansion moreover ifv is an even polynomial the above result and the kam theorem show that all eigenvalues n e oft0 ev such thatn coincides with a kam torus are given up to order e by a quantization formula which reduces to the bohr sommerfeld one up to first order terms in

low complexity variable forgetting factor mechanism for blind adaptive constrained constant modulus algorithms in this paper we propose a novel low complexity variable forgetting factor vff mechanism for blind adaptive constrained constant modulus ccm recursive least squares rls algorithms applied to linear interference suppression in direct sequence code division multiple access ds cdma systems the proposed variable forgetting factor mechanism employs an updated component related to the time average of the constant modulus cm cost function to automatically adjust the forgetting factor in order to ensure good tracking of the interference and the channel convergence and tracking analyses are carried out analytical expressions for predicting the mean squared error of the proposed adaptation technique are obtained simulation results are presented for nonstationary environments and show that the proposed variable forgetting factor mechanism achieves superior performance to previously reported methods at a reduced complexity

systems of seemingly unrelated regression equations with time varying coefficients an interplay of kalman filtering scoring em and minque method abstract this paper gives a detailed description of the implementation of ml estimation using scoring and em for the hyperparameters of a particular econometric state space we also show how the em method can be turned into an on line estimation method and how this procedure relates to an adaptive method of variance component estimation based on minque theory a small simulation study for a single equation model indicates how much can be gained in terms of computer time by using a combination of scoring and em

benchmarking small area estimators this paper considers benchmarking issues in the context of small area estimation we find optimal estimators within the class of benchmarked linear estimators under linear constraints this extends existing results for external and internal benchmarking and also links the two necessary and sufficient conditions for self benchmarking are found for an augmented model most results of this paper are found using ideas of orthogonal projection copyright 2013 oxford university press

classical limit of the quantized hyperbolic toral automorphisms the canonical quantization of any hyperbolic symplectomorphisma of the 2 torus yields a periodic unitary operator on an dimenional hilbert space n 1 h we prove that this quantum system becomes ergodic and mixing at the classical limit n n prime which can be interchanged with the time average limit the recovery of the stochastic behaviour out of a periodic one is based on the same mechanism under which the uniform distribution of the classical periodic orbits reproduces the lebesgue measure the wigner functions of the eigenstates supported on the classical periodic orbits are indeed proved to become uniformly speread in phase space

on the entropy of quantum limits for 2 dimensional cat maps we study semiclassical measures or quantum limits for quantized hyperbolic automorphisms of mathbb t 2 we show that any quantum limit has the following property if a weight is carried on ergodic components of low entropy say entropy less than h0 then a weight must be carried on ergodic components of high entropy hmax h0 where hmax is the maximal entropy this combines some existing partial results towards the classification of quantum limits

moyal quantization with compact symmetry groups and noncommutative harmonic analysis the phase space approach to quantization of systems whose symmetry group is compact and semisimple is developed from two basic principles covariance and traciality this generalizes results and methods already implemented for spin systems j c varilly and j m gracia bondia ann phys 190 107 1989 the twisted product of phase space functions is shown to be the image of group convolution in the context of a novel fourier theory on the coadjoint orbits

classical limit of the harmonic oscillator wigner functions in the bargmann representation writing the wigner functions of any pair of harmonic oscillator eigenstates in the bargmann representation a direct and detailed proof is given of their convergence in the sense of distributions to at the classical limit m n fixed

geometrical characterizations of constant modulus receivers convergence properties of the constant modulus cm and the shalvi weinstein sw algorithms in the presence of noise remain largely unknown a new geometrical approach to the analysis of constant modulus and shalvi weinstein receivers is proposed by considering a special constrained optimization involving norms of the combined channel receiver response this approach provides a unified framework within which various blind and nonblind wiener receivers can all be analyzed by circumscribing an ellipsoid by norm balls of different types a necessary and sufficient condition for the equivalence among constant modulus shalvi weinstein zero forcing and wiener receivers are obtained answers to open questions with regard to cm and sw receivers including their locations and their relationship with wiener receivers are provided for the special orthogonal channel and the general two dimensional 2 d channel receiver impulse response it is also shown that in two dimensions each cm or sw receiver is associated with one and only one wiener receiver

analytic representations in quantum mechanics various euclidean hyperbolic and elliptic analytic representations are introduced and relations among them are discussed the bargmann analytic representation in the complex plane is considered and its relation to other phase space methods for the harmonic oscillator is reviewed the general theory that relates the growth of analytic functions with the density of their zeros is applied to bargmann functions and it leads to theorems on the completeness of sequences of glauber coherent states two hyperbolic analytic representations in the unit disc based on su 1 1 coherent states and also on phase states are introduced a third analytic representation in the complex plane based on barut girardello states is also considered and transformations which relate it to the other ones are studied in the case of systems with finite dimensional hilbert space an elliptic analytic representation in the extended complex plane and also another analytic representation based on theta functions are introduced the berezin formalism in the euclidean hyperbolic and elliptic cases is discussed contour analytic representations in these three cases are also presented

uniform distribution of eigenfunctions on compact hyperbolic surfaces on demontre que les fonctions propres k du laplacien sur une surface hyperbolique compacte x devient uniformement distribuee sur x quand k

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

predicting random effects from finite population clustered samples with response error in many situations there is interest in parameters e g mean associated with the response distribution of individual clusters in a finite clustered population we develop predictors of such parameters using a two stage sampling probability model with response error the probability model stems directly from finite population sampling without additional assumptions and thus is design based the predictors are closely related to best linear unbiased predictors blup that arise from common mixed model methods as well as to model based predictors obtained via super population approaches for survey sampling the context assumes clusters of equal size and equal size sampling of units within clusters target parameters may correspond to clusters realized in the sample as well as nonrealized clusters in either case the predictors are linear and unbiased and minimize the expected mean squared error they correspond to the sum of predictors of responses for realized and nonrealized units in the cluster a

oscillator eigenstates concentrated on classical trajectories the highly degenerate eigenspaces of the two dimensional isotropic harmonic oscillator are proven to contain eigenstates that are optimally localized on the closed trajectories of the classical dynamics as h cross to 0 their phase space probability density converges to the unique probability density on the corresponding trajectory which is invariant under the classical flow

domains of attraction of shalvi weinstein receivers domains of attraction doa of shalvi weinstein 1990 receivers are analyzed it is shown that there is a one to one correspondence between doa in the receiver parameter space and those in the global or combined channel receiver parameter space for general noiseless channels doa of sw receivers in the global response space are the minimum distance decision regions on a unit sphere in the presence of noise and for the class of orthogonal channels doa of sw receivers for independent and identically distributed i i d input signals are the minimum distance decision regions on an ellipsoid determined by the channel coefficients and the noise variance the doa in the receiver parameter space are also characterized for the general nonuniformly distributed sources the size of the doa is shown to be affected by the signal power the signal constellation the noise level and the channel condition it is also demonstrated that although the optima of the shalvi weinstein algorithm and those of the constant modulus algorithm are one to one correspondent their doa are different in general

quantization of a class of piecewise affine transformations on the torus we present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of chaoticity the systems to be quantized are piecewise affine maps on the two torus viewed as phase space and include the automorphisms translations and skew translations we then treat some discontinuous transformations such as the baker map and the sawtooth like maps our approach extends some ideas from geometric quantization and it is both conceptually and calculationally simple

spectra of phase point operators in odd prime dimensions and the extended clifford group we analyze the role of the extended clifford group in classifying the spectra of phase point operators within the framework laid out by gibbons et al phys rev a 70 062101 2004 for setting up wigner distributions on discrete phase spaces based on finite fields to do so we regard the set of all the discrete phase spaces as a symplectic vector space over the finite field auxiliary results include a derivation of the conjugacy classes of esl 2 fn

universality in the flooding of regular islands by chaotic states we investigate the structure of eigenstates in systems with a mixed phase space in terms of their projection onto individual regular tori depending on dynamical tunneling rates and the heisenberg time regular states disappear and chaotic states flood the regular tori for a quantitative understanding we introduce a random matrix model the resulting statistical properties of eigenstates as a function of an effective coupling strength are in very good agreement with numerical results for a kicked system we discuss the implications of these results for the applicability of the semiclassical eigenfunction hypothesis

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

commensurate anisotropic oscillator su 2 coherent states and the classical limit we demonstrate a formally exact quantum classical correspondence between the stationary coherent states associated with the commensurate anisotropic two dimensional harmonic oscillator and the classical lissajous orbits our derivation draws upon the earlier work of louck et al 1973 j math phys 14 692 wherein they have provided a non bijective canonical transformation that maps within a degenerate eigenspace the commensurate anisotropic oscillator on to the isotropic oscillator this mapping leads in a natural manner to a schwinger realization of su 2 in terms of the canonically transformed creation and annihilation operators through the corresponding coherent states built over a degenerate eigenspace we directly effect the classical limit via the expectation values of the underlying generators our work completely accounts for the fact that the su 2 coherent state in general corresponds to an ensemble of lissajous orbits

chaotic eigenfunctions in phase space we study individual eigenstates of quantized area preserving maps on the 2 torus which are classically chaotic in order to analyze their semiclassical behavior we use the bargmann husimi representations for quantum states as well as their stellar parametrization which encodes states through a minimal set of points in phase space the constellation of zeros of the husimi density we rigorously prove that a semiclassical uniform distribution of husimi densities on the torus entails a similar equidistribution for the corresponding constellations we deduce from this property a universal behavior for the phase patterns of chaotic bargmann eigenfunctions which is reminiscent of the wkb approximation for eigenstates of integrable systems though in a weaker sense in order to obtain more precise information on chaotic eigenconstellations we then model their properties by ensembles of random states generalizing former results on the 2 sphere to the torus geometry this approach yields statistical predictions for the constellations which fit quite well the chaotic data we finally observe that specific dynamical information e g the presence of high peaks like scars in husimi densities can be recovered from the knowledge of a few long wavelength fourier coefficients which therefore appear as valuable order parameters at the level of individual chaotic eigenfunctions