blind channel equalization and spl epsiv approximation algorithms we show that a blind equalizer can be obtained without estimating any statistics based on the received data if the constellation alphabet is known the idea is to formulate the blind channel equalization problem into a quadratic optimization with binary constraints then efficient spl epsiv approximation algorithms are presented and applied to find the equalizer coefficients the proposed approach blindly equalizes the channel at symbol baud rates does not rely on estimating any statistics applies to nonminimum phase channels and converges to an spl epsiv neighborhood of a global optimum simulation results support the theoretical analysis

the broadwell model for initial values in l 1 _ bf r the cauchy problem for the broadwell model is shown to have a global mild solution for initial data inl 1 with smalll1 norm and a local solution for arbitrary initial data inl 1 for data which are small inl1 the asymptotic behaviour of the solutions ast is determined moreover it is shown that a global solution exists for all initial values inl 1 with finite entropy if theh theorem holds

performance analysis of godard based blind channel identification we analyze a blind channel impulse response identification scheme based on the cross correlation of blind symbol estimates with the received signal the symbol estimates specified are those minimizing the godard 1980 or constant modulus criterion for which mean squared symbol estimation error bounds have been derived we derive upper bounds for the average squared parameter estimation error aspe of the blind identification scheme that depend on the mean squared error of the wiener equalizer the kurtoses of the desired and interfering sources and the channel impulse response the effects of finite data length and stochastic gradient equalizer design on aspe are also investigated all results are derived in a general multiuser vector channel context

generalized adaptive notch smoothers for real valued signals and systems systems with quasi periodically varying coefficients can be tracked using the algorithms known as generalized adaptive notch filters ganfs ganf algorithms can be considered an extension to the system case of classical adaptive notch filters anfs we show that estimation accuracy of the existing algorithms as well as their robustness to the choice of design parameters can be considerably improved by means of compensating estimation delay effects which occur in the amplitude tracking and frequency tracking loops of ganf anf filters apart from the increased computational burden the price for the achieved improvements is paid in terms of a decision delay the proposed generalized adaptive notch smoothing gans algorithms must be run on delayed input output data sequences since such delay is acceptable in many signal processing and system identification applications the proposed solution seems to be an attractive alternative to the currently available trackers

bi solitons for a class of non linear equations with quadratic non linearity ii abstract we consider the class of non integrable non linear equations l q k k 2 l q 1 i j q aij i x i j t j 0 in 1 1 dimensions we seek rational solutions k 1 2 which we call bi solitons with exponential type variables i exp ix it in this paper we restrict to q 2 and 3 and investigate the general q case in the following paper we find that these bi solitons exist when the operator lq with can be factorized as the product of smaller order differential operators besides the trivial factorized bi solitons we show that there exist non trivial ones whenever k may be written as lmaxx l2fl z 1 2 in order to understand the origin of the factorization property to any polynomial k l2fl z we associate a linear transformation such that lqk has only the power l2 of k2 for q 2 and 3 we find that there exist particular polynomials of this type restraining lq to be a product of smallr order operators for the full non linear equations we verify that all the bi solitons can be obtained from these particular polynomials

adaptive solution for blind identification equalization using deterministic maximum likelihood a deterministic maximum likelihood dml approach is presented for the blind channel estimation problem it is first proposed in a block version which consists of iterating two steps each one solving a least squares problem either in the channel or in the symbols in the noiseless case and under certain conditions this algorithm gives the exact channel and the exact symbol vector with a finite number of samples it is shown that even if the dml method has a single global minimum the proposed iterative procedure can converge to spurious local minima this problem can be detected under some channel diversity conditions by using a numerical test that is proposed in the paper based on these considerations we extend the maximum likelihood block algorithm mlba to recursive implementations maximum likelihood recursive algorithm mlra the mlra is able to track variations of the system by the introduction of an exponential forgetting factor in the dml criterion the link between the adaptive algorithm and a soft decision feedback equalizer sdfe is emphasized low complexity versions of the recursive and adaptive algorithm are presented

joint order detection and blind channel estimation by least squares smoothing a joint order detection and blind estimation algorithm for single input multiple output channels is proposed by exploiting the isomorphic relation between the channel input and output subspaces it is shown that the channel order and channel impulse response are uniquely determined by finite least squares smoothing error sequences in the absence of noise the proposed subspace algorithm is shown to have marked improvement over existing algorithms in performance and robustness in simulations

multistep linear predictors based blind equalization of fir iir single input multiple output channels with common zeros the problem of blind equalization of single input multiple output simo communications channels is considered using only the second order statistics of the data such models arise when a single receiver data is fractionally sampled assuming that there is excess bandwidth or when an antenna array is used with or without fractional sampling we extend the multistep linear prediction approach to infinite impulse response iir channels as well as to the case where the subchannel transfer functions have common zeros in the past this approach has been confined to finite impulse response fir channels with no common subchannel zeros we focus on the design of finite length minimum mean square error mmse blind equalizers knowledge of the nature of the underlying model fir or iir or the model order is not required our approach works when the subchannel transfer functions have common zeros as long as the common zeros are minimum phase zeros illustrative simulation examples are provided

generalized quadratic minimization and blind multichannel deconvolution this paper deals with the problem of quadratic minimization subject to linear equality constraints unlike the standard formulation we assume the most general case of a possibly singular quadratic form we explain that the existing formal solution to this problem has several drawbacks our new approach is free from most of these drawbacks in particular it has a simple interpretation and is relatively easy to implement the practical importance of this result lies in its numerous applications filter design spectral analysis direction finding and blind deconvolution of multiple fir channels here we focus on the blind deconvolution application for which we present a novel solution with enhanced performance

asymptotic performance of second order algorithms this paper re examines the asymptotic performance analysis of second order methods for parameter estimation in a general context it provides a unifying framework to investigate the asymptotic performance of second order methods under the stochastic model assumption in which both the waveforms and noise signals are possibly temporally correlated possibly non gaussian real or complex possibly noncircular random processes thanks to a functional approach and a matrix valued reformulated central limit theorem about the sample covariance matrix the conditions under which the asymptotic covariance of a parameter estimator are dependent or independent of the distribution of the signal involved are specified finally we demonstrate the application of our general results to direction of arrival doa estimation identification of finite impulse response models sinusoidal frequency estimation for mixed spectra time series and frequency estimation of sinusoidal signal with very lowpass envelope

a cumulant interference subspace cancellation method for blind siso channel estimation we present a new linear method for blind estimation of single input single output siso finite impulse response fir channel the channel can be minimum phase or nonminimum phase channel the proposed method is based on a series of fourth order cumulant matrices where it is shown that by employing vectors chosen from the left null space of a concatenated cumulant matrix the interference subspace of the channel convolution matrix can be cancelled and thus channel information can be extracted the proposed method is robust to channel order overestimation and it has a similar computational complexity as other existing methods simulation results are included to validate the performance of the proposed algorithm

adaptive blind channel estimation by least squares smoothing a least squares smoothing lss approach is presented for the blind estimation of single input multiple output simo finite impulse response systems by exploiting the isomorphic relation between the input and output subspaces this geometrical approach identifies the channel from a specially formed least squares smoothing error of the channel output lss has the finite sample convergence property i e in the absence of noise the channel is estimated perfectly with only a finite number of data samples referred to as the adaptive least squares smoothing a lss algorithm the adaptive implementation has a high convergence rate and low computation cost with no matrix operations a lss is order recursive and is implemented in part using a lattice filter it has the advantage that when the channel order varies channel estimates can be obtained without structural change of the implementation for uncorrelated input sequence the proposed algorithm performs direct deconvolution as a by product

subspace methods for blind estimation of time varying fir channels novel linear algorithms are proposed in this paper for estimating time varying fir systems without resorting to higher order statistics the proposed methods are applicable to systems where each time varying tap coefficient can be described with respect to time as a linear combination of a finite number of basis functions examples of such channels include almost periodically varying ones fourier series description or channels locally modeled by a truncated taylor series or by a wavelet expansion it is shown that the estimation of the expansion parameters is equivalent to estimating the second order parameters of an unobservable fir single input many output simo process which are directly computed under some assumptions from the observation data by exploiting this equivalence a number of different blind subspace methods are applicable which have been originally developed in the context of time invariant simo systems identifiability issues are investigated and some illustrative simulations are presented

qr factorization based blind channel identification with second order statistics most eigenstructure based blind channel identification and equalization algorithms with second order statistics need svd or evd of the correlation matrix of the received signal in this paper we address new algorithms based on qr factorization of the received signal directly without calculating the correlation matrix this renders the qr factorization based algorithms more robust against ill conditioned channels i e those channels with almost common zeros among the subchannels first we present a block algorithm that performs the qr factorization of the received data matrix as a whole then a recursive algorithm is developed based on the qr factorization by updating a rank revealing ulv decomposition compared with existing algorithms in the same category our algorithms are computationally more efficient the computation in each recursion of the recursive algorithm is on the order of o m sup 2 if only equalization is required where m is the dimension of the received signal vector our recursive algorithm preserves the fast convergence property of the subspace algorithms thus converging faster than other adaptive algorithms such as the super exponential algorithm with comparable computational complexities moreover our proposed algorithms do not require noise variance estimation numerical simulations demonstrate the good performance of the proposed algorithms

degenerations of sklyanin algebra and askey wilson polynomials a new trigonometric degeneration of the sklyanin algebra is found and the functional realization of its representations in space of polynomials in one variable is studied a further contraction gives the standard quantum algebra uq sl 2 it is shown that the degenerate sklyanin algebra contains a subalgebra isomorphic to algebra of functions on the quantum sphere su 2 so 2 q12 the diagonalization of general quadratic form in its generators leads in the functional realization to the difference equation for askey wilson polynomials

linear prediction error method for blind identification of periodically time varying channels blind channel estimation for single input multiple output simo periodically time varying channels is considered using only the second order statistics of the data the time varying channel is assumed to be described by a complex exponential basis expansion model ce bem the linear prediction error method for blind identification of time invariant channels is extended to time varying channels represented by a ce bem sufficient conditions for identifiability are investigated the cyclostationary nature of the received signal is exploited to consistently estimate the time varying correlation function of the data from a single observation record the proposed method requires the knowledge of the active basis functions but not the channel length an upper bound suffices several existing methods require precise knowledge of the channel length equalization of the time varying channel given the estimated channel is investigated computer simulation examples are presented to illustrate the approach and to compare it with two existing approaches

blind identification of time varying channels using multistep linear predictors blind estimation of a class of single input multiple output simo time varying channels is considered using only the second order statistics of the data the time varying channel is assumed to be described by a complex exponential basis expansion model ce bem the multistep linear predictors based method for blind identification of time invariant channels is extended to time varying channels represented by a ce bem sufficient conditions for channel identifiability are investigated the proposed method requires the knowledge of the active basis functions in the ce bem it is not as sensitive to overestimation of the channel length as some of the existing methods computer simulation examples are presented to illustrate the approach and to compare it with three existing approaches

asymptotic eigenvalue distribution of block toeplitz matrices and application to blind simo channel identification szego s 1984 theorem states that the asymptotic behavior of the eigenvalues of a hermitian toeplitz matrix is linked to the fourier transform of its entries this result was later extended to block toeplitz matrices i e covariance matrices of multivariate stationary processes the present work gives a new proof of szego s theorem applied to block toeplitz matrices we focus on a particular class of toeplitz matrices those corresponding to covariance matrices of single input multiple output simo channels they satisfy some factorization properties that lead to a simpler form of szego s theorem and allow one to deduce results on the asymptotic behavior of the lowest nonzero eigenvalue for which an upper bound is developed and expressed in terms of the subchannels frequency responses this bound is interpreted in the context of blind channel identification using second order algorithms and more particularly in the case of band limited channels

a random discrete velocity model and approximation of the boltzmann equation an approximation procedure for the boltzmann equation based on random choices of collision pairs from a fixed velocity set and on discrete velocity models is designed in a suitable limit the procedure is shown to converge to the time discretized and spatially homogeneous boltzmann equation

blind equalization of simo fir channels driven by colored signals with unknown statistics we consider the blind equalization of single input multiple output finite impulse response channel driven by colored signals the statistics of the input colored signals are unknown a priori by exploiting the inherent structural relationship between the source autocorrelation matrices of different delay lags the closed form zero forcing and minimum mean square error equalizers of desired delays are estimated from the second order statistics of the received data the blind equalizability conditions of the proposed method are investigated numerical simulation results are presented to illustrate the performance of the proposed algorithm

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

on a whitening approach to partial channel estimation and blind equalization of fir iir multiple input multiple output channels channel estimation and blind equalization of multiple input multiple output mimo communications channels is considered using primarily the second order statistics of the data such models arise when a single receiver data from multiple sources is fractionally sampled assuming that there is excess bandwidth or when an antenna array is used with or without fractional sampling we consider estimation of partial channel impulse response and design of finite length minimum mean square error mmse blind equalizers the basis of the approach is the design of a zero forcing equalizer that whitens the noise free data we allow infinite impulse response iir channels moreover the multichannel transfer function need not be column reduced our approaches also work when the subchannel transfer functions have common zeros as long as the common zeros are minimum phase zeros the channel length or model orders need not be known the sources are recovered up to a unitary mixing matrix and are further unmixed using higher order statistics of the data a linear prediction approach is also considered under the above conditions of possibly iir channels common subchannel zeros factors and not necessarily column reduced channels four illustrative simulation examples are provided

temperature overshoots for a 4 velocity unidimensional discrete boltzmann model we propose a 4 velocity unidimensional discrete boltzmann model with two different speeds 2 1 and two different masses 1 2 with the three conservation laws of mass momentum and energy satisfied we can introduce a nontrivial temperature first we determine the similarity shock waves satisfying physical properties positivity shock stability inequalities of the subsonic and supersonic flows increase or decrease of both mass and temperature across the shock it results that either the speed of the shock front is higher than the speed 1 of the slow particles and the shocks are compressive or less than 1 and the shocks are rarefactive we observe overshoots of the temperature across the shock with bumps higher and higher as the shock front speed increases second we study the 1 1 dimensional shock waves they represent the superposition and collision of two compressive shocks traveling in opposite directions and we observe temperature overshoots for not too large times

blind and semi blind fir multichannel estimation global identifiability conditions two channel estimation methods are often opposed training sequence methods that use the information induced by known symbols and blind methods that use the information contained in the received signal and possibly hypotheses on the input symbol statistics but without integrating the information from known symbols if present semi blind methods combine both training sequence and blind information and are more powerful than the two methods separately we investigate the identifiability conditions for blind and semi blind finite impulse response fir multichannel estimation in terms of channel characteristics received data length and input symbol excitation modes as well as number of known symbols for semi blind estimation two models corresponding to two different cases of a priori knowledge on the input symbols are studied the deterministic model in which the unknown symbols are considered as unknown deterministic quantities and the gaussian model in which they are considered as gaussian random variables this last model includes the methods using the second order statistics of the received data semi blind methods appear superior to blind and training sequence methods and allow the estimation of any channel with only few known symbols furthermore the gaussian model appears more robust than the deterministic one as it leads to less demanding identifiability conditions

second order statistics based blind equalization of iir single input multiple output channels with common zeros the problem of blind equalization of single input multiple output simo communications channels is considered using only the second order statistics of the data such models arise when a single receiver data is fractionally sampled assuming that there is excess bandwidth or when an antenna array is used with or without fractional sampling we focus on direct design of finite length minimum mean square error mmse blind equalizers unlike the past work on this problem we allow infinite impulse response iir channels our approaches also work when the subchannel transfer functions have common zeros as long as the common zeros are minimum phase zeros illustrative simulation examples are provided

robustness of least squares and subspace methods for blind channel identification equalization with respect to effective channel undermodeling overmodeling the least squares and the subspace methods are two well known approaches for blind channel identification equalization when the order of the channel is known the algorithms are able to identify the channel under the so called length and zero conditions furthermore in the noiseless case the channel can be perfectly equalized less is known about the performance of these algorithms in the practically inevitable cases in which the channel possesses long tails of small impulse response terms we study the performance of the mth order least squares and subspace methods using a perturbation analysis approach we partition the true impulse response into the mth order significant part and the tails we show that the mth order least squares or subspace methods estimate an impulse response that is close to the mth order significant part the closeness depends on the diversity of the mth order significant part and the size of the tails furthermore we show that if we try to model not only the large terms but also some small ones then the quality of our estimate may degrade dramatically thus we should avoid modeling small terms finally we present simulations using measured microwave radio channels highlighting potential advantages and shortcomings of the least squares and subspace methods

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

blind spatio temporal equalization and impulse response estimation for mimo channels using a godard cost function equalization and estimation of the matrix impulse response function of multiple input multiple output mimo digital communications channels in the absence of any training sequences is considered an iterative godard 1980 cost based approach is considered for spatio temporal equalization and mimo impulse response estimation stationary points of the cost function are investigated with particular attention to the case when finite length equalizers exist sufficient conditions are derived under which all stable local minima correspond to desirable minima the inputs are extracted and cancelled one by one the matrix impulse response is then obtained by cross correlating the extracted inputs with the observed outputs identifiability conditions are analyzed

an efficient subspace method for the blind identification of multichannel fir systems we present a novel method for the blind identification of linear single input multiple output simo finite impulse response fir systems based on second order statistics our approach called the truncated transfer matrix method ttm proceeds in two major steps first the svd analysis of the lagged covariance matrix gives the subspace of the clipped system transfer matrix and second the block toeplitz structure of the transfer matrix gives extra constraints that allow us to reconstruct the matrix through the solution of a linear system of equations the proposed ttm method is analytical no optimization procedure involved and it is robust to noise we find that the method comes with an increased computational cost but it significantly outperforms state of the art second order methods in low signal to noise ratio snr situations

dynamic channel order estimation algorithm this correspondence develops a robust method to estimate channel order in a single input multiple output simo or an oversampled single input single output siso system current methods based on the use of information theoretic criteria for blind channel order estimation suffer from estimation errors at high signal to noise ratio snr and when a large number of samples is used or when subchannels are correlated the new algorithm exploits spatial oversampling and the fact that the linear prediction approach to channel estimation is robust to the overdetermination of channel order a distinct advantage is that channel estimates are also available after the channel order estimate is made the method is robust over a wide snr range and is independent of correlation in the received channels simulation results are presented showing performance and behavior for various snrs and channel conditions

blind mimo system estimation based on parafac decomposition of higher order output tensors we present a novel framework for the identification of a multiple input multiple output mimo system driven by white mutually independent unobservable inputs samples of the system frequency response are obtained based on parallel factorization parafac of three or four way tensors constructed based on respectively third or fourth order cross spectra of the system outputs the main difficulties in frequency domain methods are frequency dependent permutation and filtering ambiguities we show that the information available in the higher order spectra allows for the ambiguities to be resolved up to a constant scaling and permutation ambiguities and a linear phase ambiguity important features of the proposed approach are that it does not require channel length information needs no phase unwrapping and unlike the majority of existing methods needs no prewhitening of the system outputs

on the computation of the cramer rao bound for arma parameter estimation the cramer rao lower bound crlb provides a useful tool for evaluating the performance of parameter estimation techniques several techniques for the computation of the asymptotic form of the crlb for arma models are presented it is shown that the asymptotic crlb can be expressed as an explicit function of the model parameters

blind mimo system identification based on cumulant subspace decomposition blind identification of multiple input multiple output mimo linear systems can be achieved by utilizing higher order statistics of the output signals we study the blind identification of mimo systems whose inputs are mutually independent temporally white non gaussian source signals based on sub space analysis we develop a new linear batch algorithm to identify mimo systems from the common nullspace of a set of fourth order cumulant matrices of the channel outputs given knowledge of the channel orders the identifiability conditions required by the proposed algorithm are properly established like most subspace based approaches this new algorithm remains sensitive to channel order overestimation simulation results illustrate its performance for various channel models

prediction error method for second order blind identification blind channel identification methods based on the oversampled channel output are a problem of current theoretical and practical interest in this paper we introduce a second order blind identification technique based on a linear prediction approach in contrast to eigenstructure based methods it will be shown that the linear prediction error method is robust to order overdetermination an asymptotic performance analysis of the proposed estimation method is carried out consistency and asymptotic normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are finally presented to demonstrate the potential and the robustness of the proposed method

a semi blind channel estimation method for multiuser multiantenna ofdm systems a subspace based blind method is proposed for estimating the channel responses of a multiuser and multiantenna orthogonal frequency division multiplexing ofdm uplink system it gives estimations to all channel responses subject to a scalar matrix ambiguity and does not need precise channel order information only an upper bound for the orders is required furthermore the scalar ambiguity matrix can be easily resolved by using only one pilot ofdm block given that the number of users is smaller than the number of symbols in the pilot symbol block equalization methods are discussed based on the estimated channels by using partial knowledge of the channels a multipath subspace method is proposed that reduces the computational complexity simulations show that the methods are effective and robust

complete integrability of relativistic calogero moser systems and elliptic function identities poincare invariant generalizations of the galilei invariant calogero moser a particle systems are studied a quantization of the classical integrals s1 sn is presented such that the operators si9 sn mutually commute as a corollary it follows that si9 9sn poisson commute these results hinge on functional equations satisfied by the weierstrass and 0 functions a generalized cauchy identity involving the function leads to an n x n matrix l whose symmetric functions are proportional to sl5 9sn

topics in quantum integrable systems recent developments in the theory of quantum integrable particle systems in one dimension with inverse square interactions are reviewed first the yangian symmetry is introduced and the energy spectra of the related spin models are discussed the character of the su n 1 wznw theory is shown to be closely related with the rogers szego polynomial second the infinite dimensional representation for solutions of the yang baxter equation and the reflection equation is given based on the representation the dunkl operators associated with the classical root systems are constructed the macdonald polynomial and its generalization are discussed in connection with the eigenstates for the trigonometric case finally some results on short range interacting systems are mentioned

subspace projection based blind channel order estimation of mimo systems in this paper a novel algorithm based on subspace projections is developed for blindly estimating the discrete orders of a linear finite impulse response fir multiple input multiple output mimo system the number of subsystems that attain each order as well as the total number of inputs furthermore the proposed algorithm applies to single input multiple output simo system order estimation simulations in the context of blind channel order estimation show good performance in comparison to existing schemes developed for simo systems

a free energy bound for the hopfield model the author gives a simple upper and lower bound on the free energy density of the hopfield model of size n with p stored patterns in the limit where n and p tend to infinity with p n to alpha 1 the two bounds coincide for alpha 0

a blind multichannel identification algorithm robust to order overestimation active research in blind single input multiple output simo channel identification has led to a variety of second order statistics based algorithms particularly the subspace ss and the linear prediction lp approaches the ss algorithm shows good performance when the channel output is corrupted by noise and available for a finite time duration however its performance is subject to exact knowledge of the channel order which is not guaranteed by current order detection techniques on the other hand the linear prediction algorithm is sensitive to observation noise whereas its robustness to channel order overestimation is not always verified when the channel statistics are estimated we propose a new second order statistics based blind channel identification algorithm that is truly robust to channel order overestimation i e it is able to accurately estimate the channel impulse response from a finite number of noisy channel measurements when the assumed order is arbitrarily greater than the exact channel order another interesting feature is that the identification performance can be enhanced by increasing a certain smoothing factor moreover the proposed algorithm proves to clearly outperform the lp algorithm these facts are justified theoretically and verified through simulations

exact solutions of the broadwell model in 1 1 dimensions the author studies the one spatial dimensional 6 velocity broadwell model with four identical densities and three independent ones the author determines solitons one dimensional shock wave solutions and bisolitons two dimensional space plus time solutions which are rational fractions with one or two exponential variables the author obtains three classes of positive exact solutions in 1 1 dimensions space x time t the first one is periodic in the space variable and for large time the solutions correspond to propagating damped linear waves the second is positive only along one semi x axis while the third positive along the whole x axis represents non planar damped shock waves using the same tools in a companion paper for the discrete 2 velocity models the author obtains in a two dimensional space the first two classes of solutions mentioned above this suggests that for the discrete boltzmann models general methods exist for the determination of non trivial exact solutions

affine hecke algebra macdonald polynomials and quantum many body systems the macdonald operators associated with the classical root systems are constructed based on the infinite dimensional representation for solutions of the yang baxter equation and the reflection equation

representation of the yangian invariant motif and the macdonald polynomial the representation of the yangian invariant motif is considered the relationship with the rogers szego polynomial is studied whose one parameter deformation is the macdonald polynomial we propose the deformation of the motifs which provides a new realization of the macdonald polynomials for the one row young diagrams

quantum integrability of the generalized elliptic ruijsenaars models the quantum integrability of the generalized elliptic ruijsenaars models is shown these models are mathematically related to the macdonald operator and the macdonald koornwinder operator which appeared in the q orthogonal polynomial theories we construct these integrable families by using the yang baxter equation and the reflection equation

identification of hammerstein systems without explicit parameterisation of non linearity this article proposes a new approach to identification of hammerstein systems where a non linearity precedes a linear dynamic system driven by piece wise constant inputs the proposed approach does not require an explicit parameterisation of the non linearity moreover the non linearity does not have to be static but could be the one with finite memories like backlash by exploiting input s piecewise constant property the denominator of the linear system described by an arx model is consistently identified from the information of the output only next a subspace direct equalisation method estimates the unmeasurable inner signal based on the resulted denominator estimate and output measurements contrary to the existing blind approaches the numerator of the linear system is not required which leads to a significant improvement of removing an error propagation on the basis of the estimated inner signal the measured input and output the non linearity and linear system are obtained separately the

totally blind channel identification by exploiting guard intervals blind identification techniques estimate the impulse response of a channel by exploiting known finite alphabet or statistical properties of the transmitted symbols alternatively oversampling the output is known to introduce dependencies also exploitable for channel identification this paper proves the feasibility of estimating the channel by relying instead on the short sequences of zeros known as guard intervals or zero padding introduced between transmitted blocks by a number of communication protocols since no property of the transmitted information symbols is assumed the method is called totally blind channel identification it is proved that totally blind channel identification requires only two received blocks to estimate the channel

yang baxter equation in long range interacting systems we consider the su p spin chains with long range interactions and the spin generalization of the calogero sutherland models we show that their properties derive from a transfer matrix obeying the yang baxter equation we obtain the expression of the conserved quantities of the dynamical models and we diagonalise them in the spin chain case we establish the connection between the degeneracies of the spectrum and the representation theory of the yangians we use a correspondence with the dynamical models to diagonalise the hamiltonian finally we extend the previous results to the case of a trigonometric r matrix

deterministic blind identification of iir systems with output switching operations in this paper a deterministic blind identification approach is proposed for linear output switching systems which are modeled by multiple infinite impulse response iir dynamic functions by adopting a new over sampling strategy the concerned single input single output siso output switching system is equivalently transformed into a time invariant multi input multi output mimo system further by exploring the mutual relations among the multiple inputs the time invariant mimo system model and subsequently the output switching system model are identified uniquely up to a scalar constant using the proposed identification approach sufficient identifiability conditions are provided for output switching systems and numerical simulations are carried out to validate the proposed approach

optimum blind multichannel equalization using the linear prediction algorithm the linear prediction lp algorithm estimates a zero forcing zf equalizer from the channel output s second order statistics sos we show that it allows in fact to determine a whole subspace of but not all zf equalizers the one obtained by maximizing the signal to noise ratio snr at the equalizer output not only outperforms the original lp equalizer but also attains the lowest achievable by any no delay zf equalizer mean square error mse the increase in complexity is only marginal but equalization performance can be enhanced significantly especially in the practical case of a small leading channel coefficient

conserved operators of the generalized elliptic ruijsenaars models we construct the integrable families of the generalized elliptic ruijsenaars models by use of the yang baxter equation and the reflection equation the higher order conserved operators of these models are explicitly presented

on the robustness of the linear prediction method for blind channel identification with respect to effective channel undermodeling overmodeling we study the performance of the linear prediction lp method for blind channel identification when the true channel is of order m whereas the channel model is of order m with m m by partitioning the true channel into the mth order significant part and the unmodeled tails we show that the lp method furnishes an approximation to the mth order significant part the closeness depends on the diversity of the mth order significant part and the size of the unmodeled tails furthermore we show that two frequently encountered claims concerning the lp method namely that a the method is robust with respect to channel overmodeling and b the performance of the method depends critically on the size of the first impulse response term are not correct in realistic scenarios

blind system identification using precise and quantized observations this paper studies the blind identification of multi channel fir systems using precise and quantized observations first a new deterministic blind identification dbi algorithm is presented for multi channel fir systems using precise observations in which the system parameters can be consistently estimated and the common source signal can be stably recovered when the observed samples are quantized by a static finite level quantizer an iterative deterministic blind identification idbi method is then provided the asymptotic characters of the proposed idbi method are discussed and the quantization effect on the identification performance is analyzed numerical simulations are given to support the developed dbi method and idbi method

exact 2 1 dimensional solutions for two discrete velocity boltzmann models with four independent densities for the square discrete velocity boltzmann model the authors obtain exact 2 1 dimensional space x y time t solutions these are rational solutions with three exponential variables relaxing towards non uniform maxwellian equilibrium states with two exponential variables these are also solutions of another model with four independent densities and eight velocities oriented towards the eight corners of a cube the positivity problem for the densities is non trivial

a cholesky factorization based approach for blind fir channel identification for blind channel identification various techniques including transmitter induced cyclostationarity based approaches have been proposed in literature to induce cyclostationarity at the transmitter zero padding to every symbol packet can be considered some subspace methods are proposed for the channel estimation by exploiting the induced cyclostationarity due to zero padding the covariance matrix of received signal vectors can have a special structure utilizing this structure we can estimate channel impulse responses through factorization in this correspondence we propose a factorization based approach to estimate channel impulse responses in general the proposed factorization based approach can work with a small number of samples and becomes much more computationally efficient than the subspace method when the length of packets is long

blind decision feedback equalization of time varying channels with dpsk inputs this paper presents a new method to the blind equalization of a class of linear time varying mobile channels for differentially encoded channel input signals through reparameterization the equivalent discrete system can be modeled as a single input multiple output system unlike some existing methods this new algorithm does not require prior knowledge on the cyclic frequency of the channel response the algorithm is simple and relies only on a decision feedback structure and the differential encoding nature of the channel input signals the convergence analysis of the decision feedback system is presented along with simulation examples

mimo blind second order equalization method and conjugate cyclostationarity the blind identification of vector valued fir transfer functions using exclusively second order statistics of the output has become conventional the so called subspace method provides a nice and efficient way of solving the problem however the extension to the multi input multi output mimo case is not that straightforward and for instance some indetermination drawbacks may occur we show in this correspondence that the introduction of some cyclostationarity at the input which still leads to feasible systems may lead to an algorithm that is far more satisfactory because for both it is less prone to indetermination problems and the required assumptions are not too sophisticated

on a class of nonintegrable equations in 1 1 dimensions with factorized associated linear operators we consider a class of nonintegrable nonlinear equations with powerlike nonlinearities kn xkn k being the solutions and n 2 n integer building explicitly their exponential type bisolitons the denominators of the bisolitons have no soliton couplings and the linear differential operators of the linear part of the equations are factorized operators we extend our study to a larger class of nonlinearities polynomial nonlinearities which are linear combinations of powerlike nonlinearities we study the two extreme possibilities either the bisoliton is specific of a mixed nonlinearity not being a solution of any component nonlinearity or the bisoliton is common to all components different properties occur depending whether the components are kn or xkn for kn nonlinearities in order to understand the origin of the factorization of the linear operators we give a criterion which is easily checked at an almost entirely linear level of constraints we conjecture that all possible bisolitons are of th

macdonald polynomials from sklyanin algebras a conceptual basis for the p adics quantum group connection we establish a previously conjectured connection betweenp adics and quantum groups we find in sklyanin s two parameter elliptic quantum algebra and its generalizations the conceptual basis for the macdonald polynomials which interpolate between the zonal spherical functions of related real andp adic symmetric spaces the elliptic quantum algebras underlie thez n baxter models we show that in then limit the jost function for the scattering offirst level excitations in the 1 1 dimensional field theory model associated to thez n baxter model coincides with the harish chandra likec function constructed from the macdonald polynomials associated to the root systema 1 the partition function of thez 2 baxter model itself is also expressed in terms of this macdonald harish chandrac function albeit in a less simple way we relate the two parametersq andt of the macdonald polynomials to the anisotropy and modular parameters of the baxter model in particular thep adic regimes in the macdonald polynomials correspond to a discrete sequence of xxz models we also discuss the possibility of q deforming euler products

channel matrix recursion for blind effective channel order estimation channel order estimation is a critical task for blind system identification the performance of the blind system identification algorithms depends on the accuracy and robustness of the channel order estimation in this paper a new effective channel order estimation algorithm with high accuracy and robustness is proposed for single input multi output simo systems the proposed algorithm is guaranteed to find the true channel order for the noise free case and it performs significantly better than the alternative algorithms for noisy observations this algorithm shows a consistent performance when the number of observations channels and channel order are changed the proposed algorithm is integrated with the least squares smoothing lss algorithm for blind identification of the channel coefficients comparisons are done with a variety of different algorithms including linear prediction lp based methods it is shown that significant gain can be obtained compared to the alternative approaches in effective channel order estimation

blind channel identification with colored sources by exploiting properties of companion matrices this paper proposes a new second order statistics based method for blind multiple input multiple output mimo finite impulse response fir channel estimation driven by colored sources it is assumed that the second order statistics sos of the input sources are known a priori by exploiting the new derived properties of the companion matrices an original proof for the uniqueness of the system solution is provided which serves as a theoretical basis for the proposed new method that admits a closed form solution the corresponding identifiability conditions and the computational complexity of the proposed method are discussed and compared with other existing method numerical simulation results are presented to illustrate the performance of the proposed algorithm

multistep linear predictors based blind identification and equalization of multiple input multiple output channels channel estimation and blind equalization of multiple input multiple output mimo communications channels is considered using primarily the second order statistics of the data such models arise when single receiver data from multiple sources is fractionally sampled assuming that there is excess bandwidth or when an antenna array is used with or without fractional sampling we consider the estimation of partial channel impulse response and design of finite length minimum mean square error mmse blind equalizers we extend the multistep linear prediction approach to mimo channels where the multichannel transfer function need not be column reduced moreover we allow infinite impulse response iir channels as well as the case where the subchannel transfer functions have common zeros in the past this approach has been confined to simo finite impulse response fir channels with no common subchannel zeros a related existing approach applicable to mimo channels is restricted to fir column reduced systems with equal length subchannels in our approach the knowledge of the nature of the underlying model fir or iir or the model order is not required our approach works when the subchannel transfer functions have common zeros as long as the common zeros are minimum phase zeros the sources are recovered up to a unitary mixing matrix and are further unmixed using higher order statistics of the data illustrative computer simulation examples are provided

deterministic linear prediction methods for blind channel estimation based on dual concept of zero forcing equalization this paper investigates a class of second order blind channel estimation algorithms based on deterministic linear prediction which includes double sided as well as forward and backward single sided for single input multiple output simo finite impulse response fir channels by introducing the dual problem of well known zero forcing equalization concept we first derive a double sided deterministic linear prediction d dlp algorithm that has good channel estimation performance with the knowledge of exact channel order by further exploiting the interference subspace cancellation technique and the triangular block toeplitz structure of a portion of the channel filtering matrix upper left or lower right part we obtain the forward and backward single sided deterministic linear prediction fs dlp and bs dlp algorithms that can work in the absence of knowledge of channel order with a cost of relatively poor channel estimate moreover a channel order estimation method is also studied based on results from both fs dlp and bs dlp simulation examples are finally presented to demonstrate the potential of the proposed methods

on shock wave solutions in extended discrete kinetic theory exact traveling wave solutions joining asymptotic maxwellians in the frame of discrete velocity models of the boltzmann equation are investigated and discussed in an extended formulation which also allows for removal creation and scattering collisions with the particles of a given background it is shown that the classical broadwell shock wave structure does not carry over to any extended problem on the other hand families of exact shock wave solutions do exist for extended two velocity models for which such waves are lacking in the classical i e unextended case

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

blind channel identification subspace tracking method without rank estimation subspace ss methods are an effective approach for blind channel identification however these methods also have two major disadvantages 1 they require accurate channel length estimation and or rank estimation of the correlation matrix which is difficult with noisy channels and 2 they require a large amount of computation for the singular value decomposition svd which makes it inconvenient for adaptive implementation although many adaptive subspace tracking algorithms can be applied the computational complexity is still o m sup 3 where m is the data vector length in this paper we introduce new recursive subspace algorithms using ulv updating and successive cancellation techniques the new algorithms do not need to estimate the rank of the correlation matrix furthermore the channel length can be overestimated initially and be recovered at the end by a successive cancellation procedure which leads to more convenient implementations the adaptive algorithm has computations of o m sup 2 in each recursion the new methods can be applied to either the single user or the multiuser cases simulations demonstrate their good performance

blind equalization using least squares lattice prediction second order statistics of the received signal can be used to equalize a communication channel without knowledge of the transmitted sequence blind zero forcing zf and minimum mean square error mmse equalization can be achieved with linear prediction error filtering the equivalence with the equalizers derived by giannakis and halford see ibid vol 45 p 2277 92 1997 is shown and adaptive predictors that result in a lattice filtering structure are applied the required channel coefficient vector is obtained with adaptive eigen pair tracking either forward or backward prediction errors can be used the performance of the blind equalizer is examined by simulations the mmse of the optimum fse is approached and the algorithm exhibits robustness to channels with common subchannel zeros

eigenanalysis based blind methods for identification equalization and inversion of linear time invariant channels some blind algorithms are presented for estimation of equalizers for linear time invariant lti channels from the eigenvectors of certain rank one matrices constructed from the second order statistics of the oversampled received signal it is shown that the channel can also be identified from the same matrices it can be shown that in multipath dominated environments equalizers with symbol spread of only one referred to as inverters can be used when sufficient diversity is available because of the manner in which structure in the channel distortion is exploited the proposed identification and equalization algorithms are also applicable to this case for the same reason the proposed algorithms do not require estimation of the channel memory only an upper bound is required equalizers of desired delay are estimated directly independent of others

construction of positive exact 2 1 dimensional shock wave solutions for two discrete boltzmann models it is proved that 2 1 dimensional spacex y timet positive exact shock wave solutions of two discrete boltzmann models exist for each densityni these solutions are linear combinations of three similarity shock waves n i n0i j n ji 1 d j exp j y y j x j t j 1 2 3 two models with four independent densities are investigated the square discrete velocity boltzmann model and the model with eight velocities oriented toward the eight corners of a cube the positivity problem for the densities is nontrivial two classes of solutions are considered for which the two first similarity shock wave components depend on only one spatial dimension j const j j 1 2 for the positivity if 1 2 0 it is sufficient to prove that the 16 asymptotic shock limitsn0i n0i n3i j 0 2 n ji j 0 3 n ji are positive the density solutions are built up with five arbitrary parameters and we prove that there exist subdomains of the arbitrary parameter space in which the 16 shock limits are positive we study numerically two explicit shock wave solutions we are interested in the movement of the shock front when the time is growing and in the possible appearance of bumps in the space at intermediate times these bumps represent populations of particles which are larger than at initial time or at equilibrium time

asymptotic theory of mixed time averages and kth order cyclic moment and cumulant statistics we generalize parzen s 1961 analysis of asymptotically stationary processes to mixtures of deterministic stationary nonstationary and generally complex time series under certain mixing conditions expressed in terms of joint cumulant summability we show that time averages of such mixtures converge in the mean square sense to their ensemble averages we additionally show that sample averages of arbitrary orders are jointly complex normal and provide their covariance expressions these conclusions provide us with statistical tools that treat random and deterministic signals on a common framework and are helpful in defining generalized moments and cumulants of mixed processes as an important consequence we develop consistent and asymptotically normal estimators for time varying and cyclic moments and cumulants of kth order cyclostationary processes and provide computable variance expressions some examples are considered to illustrate the salient features of the analysis

low complexity equalization of time varying channels with precoding this correspondence deals with time varying tv single input multiple output simo channels which are both frequency selective due to high data rate and time selective due to mobility a complex exponential basis expansion model ce bem is used to model the channel we consider a block transmission system where on the transmit side a precoder is employed to enable the maximum available diversity for a ce bem channel after direct decoding on the receive side the resulting channel resembles a finite impulse response fir filter on both block and symbol level we therefore propose an equalizer that bears a structure analogous to the effective channel in comparison with a standard block minimum mean square error decision feedback equalizer bmmse dfe that involves the inversion of a large size matrix the proposed parametric equalizer renders a similar performance but at a lower computational cost if there are multiple outputs present another contribution of this correspondence is a semiblind algorithm to estimate this equalizer when the channel state information is not available the equalizer taps and the information symbol estimates are refined recursively by means of normalized least mean squares nlms adaptation

on blind multiuser forward link channel estimation by the subspace method identifiability results blind channel estimation for periodic sequence ds cdma systems can be cast into the framework of structured blind estimation of multi input multi output mimo fir systems where the structure is imposed by the user s signatures a possible approach to tackle this problem consists in looking for a structured solution to one of the blind mimo fir systems proposed previously this is the approach undertaken by several authors however most of them did not address identifiability issues in this paper we first recall and reformulate some general mimo fir identification results of meraim loubaton and moulines see ieee trans inform theory vol 43 p 499 511 1997 and point out some difficulties posed by the subspace approach next we use the above material in order to analyze the behavior of the subspace forward link channel estimate of cdma systems we derive new results showing that the subspace method is not robust to an over determination of the channel order greater than the spreading factor if however the over determination error is less than the spreading factor we show that the subspace estimate is consistent if the codes of the users are properly designed

blind identification of simo systems and simultaneous estimation of multiple time delays from hos based inverse filter criteria higher order statistics based inverse filter criteria ifc have been effectively used for blind equalization of single input multiple output simo systems recently chi and chen reported a relationship between the unknown simo system and the optimum equalizer designed by the ifc for finite signal to noise ratio snr in this paper based on this relationship an iterative fast fourier transform fft based nonparametric blind system identification bsi algorithm and an fft based multiple time delay estimation mtde algorithm are proposed with a given set of non gaussian measurements the proposed bsi algorithm allows the unknown simo system to have common subchannel zeros and its performance estimation accuracy is superior to that of the conventional ifc based methods the proposed mtde algorithm can simultaneously estimate all the p 1 time delays with respect to a reference sensor with space diversity of sensors exploited therefore its performance estimation accuracy is robust to the nonuniform distribution of snrs of p spl ges 2 sensors due to channel fading some simulation results are presented to support the efficacy of the proposed bsi algorithm and mtde algorithm

performance bounds for multistep prediction based blind equalization blind equalization attempts to remove the interference caused by a communication channel without using any known training sequences blind equalizers may be implemented with linear prediction error filters pefs for many practical channel types a suitable delay at the output of the equalizer allows for achieving a small estimation error the delay cannot be controlled with one step predictors consequently multistep pef based algorithms have been suggested as a solution to the problem the derivation of the existing algorithms is based on the assumption of a noiseless channel which results in zero forcing equalization we consider the effects of additive noise at the output of the multistep pef analytical error bounds for two pef based blind equalizers in the presence of noise are derived the obtained results are verified with simulations the effect of energy concentration in the channel impulse response on the error bound is also addressed