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

blind identification of mimo fir systems driven by quasistationary sources using second order statistics a frequency domain approach this paper discusses a frequency domain method for blind identification of multiple input multiple output mimo convolutive channels driven by white quasistationary sources the sources can assume arbitrary probability distributions and in some cases they can even be all gaussian distributed we also show that under slightly more restrictive assumptions the algorithm can be applied to the case when the sources are colored nonstationary signals we demonstrate that by using the second order statistics of the channel outputs under mild conditions on the nonstationarity of sources and under the condition that channel is column wise coprime the impulse response of the mimo channel can be identified up to an inherent scaling and permutation ambiguity we prove that by using the new algorithm under the stated assumptions a uniform permutation across all frequency bins is guaranteed and the inherent frequency dependent scaling ambiguities can be resolved hence no post processing is required as is the case with previous frequency domain algorithms we further present an efficient two step frequency domain algorithm for identifying the channel numerical simulations are presented to demonstrate the performance of the new algorithm

matrix representations of sturm liouville problems with transmission conditions we identify a class of sturm liouville equations with transmission conditions such that any sturm liouville problem consisting of such an equation with transmission condition and an arbitrary separated or real coupled self adjoint boundary condition has a representation as an equivalent finite dimensional matrix eigenvalue problem conversely given any matrix eigenvalue problem of certain type and an arbitrary separated or real coupled self adjoint boundary condition and transmission condition we construct a class of sturm liouville problems with this specified boundary condition and transmission condition each of which is equivalent to the given matrix eigenvalue problem

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

matricial nehari problems j inner matrix functions and the muckenhoupt condition abstract the classes of regular and strongly regular generating matrices and j inner matrix valued functions arose in the investigation of the matricial nehari problem bitangential interpolation problems and inverse problems for canonical systems as well as the theory of characteristic functions of operators and operator nodes in this paper new characterizations of these classes are developed in particular the property of strong regularity is characterized in terms of a matricial muckenhoupt a2 condition in the treil volberg form these results are based on parametrizations that are intimately connected with darlington representations of matrix valued functions in the schur and caratheodory classes as a byproduct of this analysis examples of strongly regular generating matrices and entire j inner matrix valued functions that are unbounded on the circle and the real line respectively are presented

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

the absolutely continuous spectrum of jacobi matrices i explore some consequences of a groundbreaking result of brei messer and pearson on the absolutely continuous spectrum of one dimensional schrodinger operators these include an oracle theorem that predicts the potential and rather general results on the approach to certain limit potentials in particular we prove a denisov rakhmanov type theorem for the general nite gap case the main theme is the following it is extremely dicult to produce abso lutely continuous spectrum in one space dimension and thus its existence has strong implications

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

deterministic cca based algorithms for blind equalization of fir mimo channels in this paper a new deterministic technique for blind equalization of multiple input multiple output mimo channels is presented the proposed method relies on the channel order diversity of the finite impulse response mimo channel and it does not make any assumption about the spectra or the finite alphabet property of the sources assuming that the lengths of the single input multiple output channels are known or estimated a priori it is able to extract the sources up to a scale and rotation matrix ambiguity which only affects to those sources associated to single input multiple output simo channels with equal lengths unlike previously proposed techniques the method described in this paper obtains the equalizers and the best linear combination of their outputs in a single step and thus optimally the reformulation of the proposed method as a set of nested canonical correlation analysis problems is exploited to obtain efficient batch and adaptive equalization algorithms finally the performance of the proposed algorithms is evaluated by means of some simulation examples

matrix representations of fourth order boundary value problems with periodic boundary conditions we show that a class of regular self adjoint fourth order boundary value problems bvps is equivalent to a certain class of matrix problems conversely for any given matrix problem in this class there exist fourth order self adjoint bvps which are equivalent to the given matrix problem equivalent here means that they have exactly the same eigenvalues such an equivalence is considered with the special coupled boundary conditions i e periodic boundary conditions

on the inverse scattering problem for jacobi matrices with the spectrum on an interval a finite system of intervals or a cantor set of positive length when solving the inverse scattering problem for a discrete sturm liouville operator with a rapidly decreasing potential one gets reflection coefficients s and invertible operators where is the hankel operator related to the symbol s the marchenko faddeev theorem 8 in the continuous case for the discrete case see 4 6 guarantees the uniqueness of the solution of the inverse scattering problem in this article we ask the following natural question can one find a precise condition guaranteeing that the inverse scattering problem is uniquely solvable and that operators are invertible can one claim that uniqueness implies invertibility or vise versa moreover we are interested here not only in the case of decreasing potential but also in the case of asymptotically almost periodic potentials so we merge here two mostly developed cases of the inverse problem for sturm liouville operators the inverse problem with almost periodic potential and the inverse problem with the fast decreasing potential

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

killip simon problem and jacobi flow on gmp matrices abstract one of the first and therefore most important theorems in perturbation theory claims that for an arbitrary self adjoint operator a there exists a perturbation b of hilbert schmidt class with arbitrary small operator norm which destroys completely the absolutely continuous a c spectrum of the initial operator a von neumann however if a is the discrete free 1 d schrodinger operator and b is an arbitrary jacobi matrix of hilbert schmidt class the a c spectrum remains perfectly the same that is the interval 2 2 moreover killip and simon described explicitly the spectral properties for such a b jointly with damanik they generalized this result to the case of perturbations of periodic jacobi matrices in the non degenerated case recall that the spectrum of a periodic jacobi matrix is a system of intervals of a very specific nature christiansen simon and zinchenko posed in a review dedicated to f gesztesy 2013 the following question is there an extension of the damanik killip simon theorem to the general finite system of intervals case in this paper we solve this problem completely our method deals with the jacobi flow on gmp matrices gmp matrices are probably a new object in the spectral theory they form a certain generalization of matrices related to the strong moment problem the latter ones are a very close relative of jacobi and cmv matrices the jacobi flow on them is also a probably new member of the rich family of integrable systems finally related to jacobi matrices of killip simon class analytic vector bundles and their curvature play a certain role in our construction and at least on the level of ideology this role is quite essential

fir channel estimation through generalized cumulant slice weighting we study the problem of linear channel estimation with unknown channel input signals our work stems from the weighted slice algorithm in which cumulant slices of different orders are linearly combined to produce an estimate of a single input single output channel aiming to improve the reliability of estimation the new approach incorporates a certain matrix structure constraint into its weight computation criterion it provides more reliable results for channels with weak leading coefficients this generalized algorithm maintains the advantage of fonollosa and vidal s algorithm in handling the situation with channel order overestimation its natural extension to multiple input multiple output channel estimation is presented along with the channel identifiability conditions required

fast maximum likelihood for blind identification of multiple fir channels this paper develops a fast maximum likelihood method for estimating the impulse responses of multiple fir channels driven by an arbitrary unknown input the resulting method consists of two iterative steps where each step minimizes a quadratic function the two step maximum likelihood tsml method is shown to be high snr efficient i e attaining the cramer rao lower bound crb at high snr the tsml method exploits a novel orthogonal complement matrix of the generalized sylvester matrix simulations show that the tsml method significantly outperforms the cross relation cr method and the subspace ss method and attains the crb over a wide range of snr this paper also studies a fisher information fi matrix to reveal the identifiability of the m channel system a strong connection between the fi based identifiability and the cr based identifiability is established

on subspace methods for blind identification of single input multiple output fir systems blind identification of single input multiple output simo fir systems based on second order statistics has attracted a great deal of research effort we focus on subspace estimation procedures which exploit the structure of the range space of certain matrix valued statistics constructed by arranging in a prescribed order the covariance coefficients of the observations general subspace identifiability results are obtained based on properties of minimal polynomial bases of rational subspaces several subspace estimation procedures are then derived these estimators are all based on a weighted least square solution of an overdetermined system of linear equations an asymptotic statistical analysis of these estimators is carried out to evaluate the potential of these methods and the impact of the weighting

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

the finite spectrum of sturm liouville problems with transmission conditions for any positive integer n and a set of positive integers m i i 1 2 ldots n 1 we construct a class of regular sturm liouville problems with n transmission conditions which have exactly sum n 1 i 1 m i n 1 eigenvalues and further we show that these sum n 1 i 1 m i n 1 eigenvalues can be distributed arbitrarily throughout the complex plane in the non self adjoint case and anywhere along the real line in the self adjoint case

inverse sturm liouville problems with finite spectrum abstract we study inverse sturm liouville problems of atkinson type whose spectrum consists entirely of a finite set of eigenvalues we show that given two finite sets of interlacing real numbers there exists a class of sturm liouville equations of atkinson type such that the two sets of numbers are the eigenvalues of their associated sturm liouville problems with two different separated boundary conditions parallel results are also obtained for real coupled boundary conditions our approach is to use the equivalence between sturm liouville problems of atkinson type and matrix eigenvalue problems and to apply our development of the well known theory for inverse matrix eigenvalue problems

matrix representations of sturm liouville problems with coupled eigenparameter dependent boundary conditions abstract we study the matrix representations of sturm liouville problems with coupled eigenparameter dependent boundary conditions with a finite spectrum we prove for any positive integer n the considered problems have at most n 3 eigenvalues and show that this kind of sturm liouville problems with coupled eigenparameter dependent boundary conditions is equivalent to a class of matrix eigenvalue problems in the sense that they have exactly the same eigenvalues

the study of jacobi and cyclic jacobi matrix eigenvalue problems using sturm liouville theory abstract we study the eigenvalues of matrix problems involving jacobi and cyclic jacobi matrices as functions of certain entries of particular interest are the limits of the eigenvalues as these entries approach infinity our approach is to use the recently discovered equivalence between these problems and a class of sturm liouville problems and then to apply the sturm liouville theory

kotani last problem and hardy spaces on surfaces of widom type this is a small theory of non almost periodic ergodic families of jacobi matrices with purely however absolutely continuous spectrum the reason why this effect may happen is that under our axioms we found an analytic condition on the resolvent set that is responsible for exactly equivalent to this effect

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

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

dependence of the nth sturm liouville eigenvalue on the problem abstract we consider the nth eigenvalue as a function on the space of self adjoint regular sturm liouville problems with positive leading coefficient and weight functions the discontinuity of the nth eigenvalue is completely characterized

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

spectral properties of jacobi matrices and sum rules of special form abstract in this article we relate the properties of elements of a jacobi matrix from certain class to the properties of its spectral measure the main tools we use are the so called sum rules introduced by case in orthogonal polynomials from the viewpoint of scattering theory j math phys 15 1974 2166 2174 orthogonal polynomials ii j math phys 16 1975 1435 1440 later the sum rules were efficiently applied by killip simon sum rules for jacobi matrices and their applications to spectral theory ann math 158 2003 253 321 to the spectral analysis of jacobi matrices we use a modification of the method that permits us to work with sum rules of higher orders as a corollary of the main theorem we obtain a counterpart of a result of molchanov novitskii vainberg first kdv integrals and absolutely continuous spectrum for 1 d schrodinger operator comm math phys 216 2001 195 213 for a continuous schrodinger operator on a half line

sturm liouville problems with discontinuities at two points in this paper we extend some spectral properties of regular sturm liouville problems to those which consist of a sturm liouville equation with piecewise continuous potentials together with eigenparameter dependent boundary conditions and four supplementary transmission conditions by modifying some techniques of c t fulton two point boundary value problems with eigenvalue parameter contained in the boundary conditions proc roy soc edinburgh sect a 77 1977 293 308 e tunc o sh muhtarov fundamental solutions and eigenvalues of one boundary value problem with transmission conditions appl math comput 157 2004 347 355 o sh mukhtarov e tunc eigenvalue problems for sturm liouville equations with transmission conditions israel j math 144 2004 367 380 and o sh mukhtarov m kadakal f s muhtarov eigenvalues and normalized eigenfunctions of discontinuous sturm liouville problem with transmission conditions rep math phys 54 2004 41 56 we give an operator theoretic formulation for the considered problem and obtain asymptotic formulae for the eigenvalues and eigenfunctions

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

on unique localization of multiple sources by passive sensor arrays necessary and sufficient conditions are derived for the unique localization of narrowband sources having the same known center frequency by passive sensor arrays the conditions specify the maximum number of sources that can be uniquely localized by a general array that satisfies some mild geometric constraints the conditions are expressed in terms of the number of sensors and the rank of the correlation matrix of the sources two different conditions are presented the first guarantees uniqueness for every batch of sampled data the second which is weaker guarantees uniqueness for almost every batch of sampled data with the exception of a set of batches of measure zero it is shown that a condition that is slightly weaker than the second one is also necessary

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

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

strict identifiability of multiple fir channels driven by an unknown arbitrary sequence the problem of blind identification of multiple finite impulse response fir channels driven by a common input arises in a wide range of applications it has received increasing attention in the signal processing community a system of multiple fir channels driven by an unknown input is said to be strictly identifiable if in the absence of noise the given channel outputs can only be realized by a unique up to a constant system impulse response and a unique input sequence we show necessary and sufficient conditions for strict identifiability and establish a connection among strict identifiability a cross relation based cr based identifiability and a fisher information based fi based identifiability

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

scattering theory for jacobi operators with quasi periodic background we develop direct and inverse scattering theory for jacobi operators which are short range perturbations of quasi periodic finite gap operators we show existence of transformation operators investigate their properties derive the corresponding gel fand levitan marchenko equation and find minimal scattering data which determine the perturbed operator uniquely

the stability of nonlinear least squares problems and the cramer rao bound a number of problems of interest in signal processing can be reduced to nonlinear parameter estimation problems the traditional approach to studying the stability of these estimation problems is to demonstrate finiteness of the cramer rao bound crb for a given noise distribution we review an alternate deterministic notion of stability for the associated nonlinear least squares nls problem from the realm of nonlinear programming i e that the global minimizer of the least squares problem exists and varies smoothly with the noise furthermore we show that under mild conditions identifiability of the parameters along with a finite crb for the case of gaussian noise is equivalent to the deterministic stability of the nls problem finally we demonstrate the application of our result which is general to the problems of multichannel blind deconvolution and sinusoid retrieval to generate new stability results for these problems with little additional effort

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

identification of 2 d noncausal gauss markov random fields parameter identification of multidimensional noncausal markov random fields is an important paradigm in multidimensional signal processing and modeling and the solutions to this problem are employed in many areas of image processing an original procedure for estimating the model parameters of discrete index 2 d noncausal gauss markov random fields gmrfs from noisy observations is proposed valid for both finite and infinite lattices and for any kind of boundary conditions starting from a suitable local representation of the gmrf and taking into account the symmetry property of so called field potentials a linear equation set relating the model parameters to the 2 d autocorrelation function known or estimated of the observed field is derived its solution gives the parameter estimates of the gmrf together with the estimate of the possibly unknown variance of the observation noise

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

data efficient blind ofdm channel estimation using receiver diversity we investigate non data aided channel estimation for cyclically prefixed orthogonal frequency division multiplexing ofdm systems by exploiting channel diversity using only two receive antennas a blind deterministic algorithm is proposed identifiability conditions are derived that guarantee the perfect channel retrieval in the absence of noise in the presence of noise the proposed method has the desired property of being data efficient only a single ofdm block is needed to achieve good estimation performance for a wide range of snr values the algorithm is also robust to input symbols as it does not have any restriction on the input symbols with regard to their constellation or their statistical properties in addition this diversity based algorithm is computationally efficient and its performance compares favorably to most existing blind algorithms

a subspace algorithm for certain blind identification problems the problem of blind identification of p inputs q outputs fir transfer functions is addressed existing subspace identification methods derived for p 1 are first reformulated in particular the links between the noise subspace of a certain covariance matrix of the output signals on which subspace methods build on and certain rational subspaces associated with the transfer function to be identified are elucidated based on these relations we study the behavior of the subspace method in the case where the order of the transfer function is overestimated next an asymptotic performance analysis of this estimation method is carried out consistency and asymptotical normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are presented to demonstrate the potential of the subspace method finally we take advantage of our new reformulation to discuss the extension of the subspace method to the case p 1 we show where the difficulties lie and we briefly indicate how to solve the corresponding problems the possible connections with classical approaches for ma model estimations are also outlined

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

matrix representations of sturm liouville problems with eigenparameter dependent boundary conditions abstract we show that a class of regular self adjoint sturm liouville problems with eigenparameter dependent boundary conditions are equivalent to a certain class of matrix problems equivalent here means that they have exactly the same eigenvalues

blind identification equalization using deterministic maximum likelihood and a partial prior on the input a semi deterministic maximum likelihood dml approach is presented to solve the joint blind channel identification and blind symbol estimation problem for single input multiple output systems a partial prior on the symbols is incorporated into the criterion which improves the estimation accuracy and brings robustness toward poor channel diversity conditions at the same time this method introduces fewer local minima than the use of a full prior statistical ml in the absence of noise the proposed batch algorithm estimates perfectly the channel and symbols with a finite number of samples based on these considerations an adaptive implementation of this algorithm is proposed it presents some desirable properties including low complexity robustness to channel overestimation and high convergence rate

blind fractionally spaced equalization of noisy fir channels direct and adaptive solutions blind fractionally spaced equalizers reduce intersymbol interference using second order statistics without the need for training sequences methods for finding fir zero forcing blind equalizers directly from the observations are described and adaptive versions are developed in contrast most current methods require channel estimation as a first step to estimating the equalizer the direct methods can be zero forcing minimum mean square error or even minimum mean square error mmse within the class of zero forcing equalizers performance of the proposed methods and comparisons with existing approaches are shown for a variety of channels including an empirically measured digital microwave channel

sufficient conditions for regularity and strict identifiability in mimo systems we consider regularity and identifiability of convolutive multi input multi output mimo systems with additive white gaussian noise modeling the source and finite impulse response fir channel sequences as deterministic unknowns in the blind context the mimo system is not locally identifiable hence its fisher information matrix fim is not regular in fact the dimension of the complex valued blind fim null space is at least the number of sources squared because the fim is singular additional information about the system is required to resolve the degrees of uncertainty and thereby obtain a valid cramer rao bound crb therefore it is of interest to know under what conditions the blind fim nullity reaches its lower bound we develop sufficient conditions for the complex fim to attain its minimum nullity refining previous necessary conditions and extending single input multi output simo results we show that the sufficient conditions for the complex fim to have minimum nullity are also equivalent to sufficient conditions for mimo strict identifiability these provide sufficient conditions on the richness of the sources the required diversity and the source lengths under these conditions additional constraints such as training may be employed to yield an identifiable system with no ambiguities remaining

inverse spectral problems for discontinuous sturm liouville problems of atkinson type abstract we investigate inverse spectral problems for discontinuous sturm liouville problems of atkinson type whose spectrum consists of a finite set of eigenvalues for given two finite sets of interlacing real numbers there exists a class of sturm liouville equations such that the two sets of numbers are exactly the eigenvalues of their associated sturm liouville problems with two different separated boundary conditions the main approach is to give an equivalent relation between sturm liouville problems of atkinson type and matrix eigenvalue problems and the theory of inverse matrix eigenvalue problems

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

a semiblind channel estimation approach for mimo ofdm systems in this paper a very efficient semiblind approach that uses a training based least square criterion along with a blind constraint is proposed for multiple input multiple output orthogonal frequency division multiplexing mimo ofdm channel estimation the blind constraint is derived from the linear prediction of the received mimo ofdm signal and is used in conjunction with a weighting factor in the semiblind cost function an appealing scheme for the determination of the weighting factor is presented as a part of the proposed approach a perturbation analysis of the proposed method is conducted to justify the superiority of the semiblind solution and to obtain a closed form expression for the mean square error mse of the blind constraint further facilitating the calculation of the weighting factor the proposed method is validated through computer simulation based experimentations showing a very high estimation accuracy of the semiblind solution in terms of the mse of the channel estimate

blind mimo channel identification from second order statistics using rank deficient channel convolution matrix for multiuser systems several direct blind identification algorithms require that the linear multiple input multiple output mimo system have a full rank convolution matrix this condition requires that the system transfer function be irreducible and column reduced we show that this restrictive identification condition can be relaxed for some direct blind identification methods to accommodate more practical scenarios algorithms such as the outer product decomposition algorithm only require minor length adjustment to its processing window without the column reduced condition this result allows direct blind identification methods to be applicable to mimo without requiring a full rank channel convolution matrix

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

sturm liouville problems with impulse effects abstract this paper deals with the computation of the eigenvalues of sturm liouville problems with several discontinuity conditions inside a finite interval and parameter dependent boundary conditions using the regularized sampling method a few examples are worked out by computing several eigenvalues and their corresponding eigenfunctions

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

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

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

regularity and strict identifiability in mimo systems we study finite impulse response fir multi input multi output mimo systems with additive noise treating the finite length sources and channel coefficients as deterministic unknowns considering both regularity and identifiability in blind estimation the ambiguity set is large admitting linear combinations of the sources we show that the fisher information matrix fim is always rank deficient by at least the number of sources squared and develop necessary and sufficient conditions for the fim to achieve its minimum nullity tight bounds are given on the required source data lengths to achieve minimum nullity of the fim we consider combinations of constraints that lead to regularity i e to a full rank fim and thus a meaningful cramer rao bound exploiting the null space of the fim we show how parameters must be specified to obtain a full rank fim with implications for training sequence design in multisource systems together with constrained cramer rao bounds crbs this approach provides practical techniques for obtaining appropriate mimo crbs for many cases necessary and sufficient conditions are also developed for strict identifiability id the conditions for strict id are shown to be nearly equivalent to those for the fim nullity to be minimized

cmv matrices with asymptotically constant coefficients szego blaschke class scattering theory abstract we develop a modern extended scattering theory for cmv matrices with asymptotically constant verblunsky coefficients we show that the traditional faddeev marchenko condition is too restrictive to define the class of cmv matrices for which there exists a unique scattering representation the main results are 1 the class of twosided cmv matrices acting in l 2 whose spectral density satisfies the szego condition and whose point spectrum the blaschke condition corresponds precisely to the class where the scattering problem can be posed and solved that is to a given cmv matrix of this class one can associate the scattering data and the fm space the cmv matrix corresponds to the multiplication operator in this space and the orthonormal basis in it corresponding to the standard basis in l 2 behaves asymptotically as the basis associated with the free system 2 from the point of view of the scattering problem the most natural class of cmv matrices is that one in which a the scattering data determine the matrix uniquely and b the associated gelfand levitan marchenko transformation operators are bounded necessary and sufficient conditions for this class can be given in terms of an a 2 kind condition for the density of the absolutely continuous spectrum and a carleson kind condition for the discrete spectrum similar conditions close to the optimal ones are given directly in terms of the scattering data

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

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

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

multichannel blind deconvolution of nonminimum phase systems using filter decomposition in this paper we present a new filter decomposition method for multichannel blind deconvolution of nonminimum phase systems with this approach we decompose a doubly finite impulse response filter into a cascade form of two filters a causal finite impulse response fir filter and an anticausal fir filter after introducing a lie group to the manifold of fir filters we discuss geometric properties of the fir filter manifold using the nonholonomic transform we derive the natural gradient on the fir manifold by simplifying the mutual information rate we present a very simple cost function for blind deconvolution of nonminimum phase systems subsequently the natural gradient algorithms are developed both for the causal fir filter and for the anticausal fir filter simulations are presented to illustrate the validity and favorable learning performance of the proposed algorithms

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

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

cross relation based blind simo identifiability in the presence of near common zeros and noise the blind identification of single input multiple output simo systems is often performed by exploiting a cross relation cr between channel pairs it has been shown that this property allows an estimation of channel impulse responses up to a common gain factor if certain identifiability conditions are met in this case the estimated channels can be evaluated by a gain compensated system distance known as normalized projection misalignment npm current algorithms for blind channel identification however suffer in the presence of insufficient channel diversity and observation noise in this paper we first demonstrate that in the absence of noise the cr identification error for channels with exact common zeros is given by a single channel pole zero transfer function next we extend our analysis to the realistic case of near common zeros and noise for which we show that the effective error can still be approximated by a common transfer function as long as the distance between the channel zeros remains below a signal to noise ratio dependent threshold a finite impulse response fir modeling of the error then enables us to define a common filter error compensated system distance termed normalized filter projection misalignment nfpm which establishes a natural extension to the npm analysis by finally considering realistic channels which we blindly estimate with the adaptive multichannel least mean square mclms algorithm we demonstrate that the nfpm reliably reaches the noise floor confirming that the effective error can be approximated by a common fir filter

a multidimensional phase locked loop for blind multiuser detection this paper concerns the problem of blind multiuser detection a special case of the blind source separation problem in which the source signals have finite alphabets specifically we address the problem of identifying and resolving the n spl times n unitary matrix ambiguity u that results from whitening the receiver observations where n is the number of sources we propose the multidimensional phase locked loop mpll as a generalization of a scalar decision directed pll to vector valued signals the mpll adapts an estimate of u according to the recursion u spl circ sub k 1 u spl circ sub k r sub k where r sub k is an n dimensional householder like rotation depending on only the kth receiver observation the o n sup 2 complexity of an efficient implementation of the algorithm is extremely low nevertheless simulation results demonstrate good convergence properties and superior steady state performance when compared with prior techniques the algorithm is also able to accommodate large alphabets and shaped alphabets

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

a blind approach to closed loop identification of hammerstein systems this paper is a continuing study of the blind approach for the hammerstein identification in sun et al 1999 and bai and fu 2002 in the framework of a closed loop sampled data system the output is sampled faster than the updating period of the input the parameters of the linear dynamics are consistently estimated from the information of the output only after which the unmeasurable inner signal is uniquely reconstructed the noise effect is explicitly considered in both the parameter and inner signal estimation the estimation of the system orders and time delay are studied on the basis of two groups of basic equations obtained by polyphase decomposition the proposed blind approach is validated and illustrated by a simulated numerical example

sturm liouville problems with finite spectrum abstract for every positive integer n we construct a class of regular self adjoint and non self adjoint sturm liouville problems with exactly n eigenvalues these n eigenvalues can be located anywhere in the complex plane in the non self adjoint case and anywhere along the real line in the self adjoint case the latter complements the well known general result for right definite sturm liouville problems with an infinite number of eigenvalues which must go to infinity asymptotically like n2 does with an appropriate and natural interpretation of a zero the eigenfunctions have the usual zero properties

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

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