a new approach to multipath correction of constant modulus signals an adaptive digital filtering algorithm that can compensate for both frequency selective multipath and interference on constant envelope modulated signals is presented the method exploits the fact that multipath reception and various interference sources generate incidental amplitude modulation on the received signal a class of so called constant modulus performance functions is developed which sense this am term but are insensitive to the angle modulation simple adaptive algorithms for finite impulse response fir digital filters are developed which employ a gradient search of the performance function one of the resulting algorithms is simulated for the example of an fm signal degraded by specular multipath propagation substantial improvements in noise power ratio npr are observed e g 25 db with moderately rapid convergence time these results are then extended to include tonal interference on a fm signal and intersymbol interference on a qpsk data signal

the goldie theorem for h semiprime algebras abstract the main result states that under certain assumptions about a hopf algebra h every h semiprime right noetherian h module algebra has a quasi frobenius classical right quotient ring another question treated in the paper is concerned with the extension of h module structures to quotient rings these results have an application to the semiprimeness problem for smash product algebras a h

a mackey imprimitivity theory for algebraic groups let g be an affine algebraic group over an algebraically closed field k and let h be a closed subgroup of g if v is a rational h module a comodule for the coordinate ring of h there is a now well known notion of an induced module vi g for g defined as the space morph g v of all h equivariant morphisms from g to a finite dimensional subspace of v with obvious g action the question arises given a rational g module m how can one recognize m as an induced module vig for a finite group g the answer is the mackey imprimitivity theorem the module m is induced if and only if it is a direct sum of subspaces permuted transitively by g with h the stabilizer of one of these subspaces called v one uses this result for example in proving the famous mackey decomposition theorem which describes the restriction of any induced module to a second subgroup l as a direct sum of suitable induced modules given the imprimitivity theorem the proof is just a matter of grouping the summands permuted by g into their orbits under l in the case of algebraic groups the situation is quite different for some subgroups h all g modules are induced this occurs for example if g is connected and k g h k e g if h is parabolic also if g is a connected unipotent group then a rational g module m is induced from some proper subgroup if and only if its endomorphism ring contains a two dimensional submodule e for the conjugation action of g with e k 1 and such that k l is precisely the subspace annihilated by the action of the lie algebra of g on e 27 cf also 5 5 below the latter is an application of a general criterion in case g h is affine a rational g module m is induced if and only if there is an action of the coordinate ring a of g h compatible with the action of g on both a and m note that this generalizes the imprimitivity theorem in the case of finite groups since then a has a k basis of g h orthogonal idempotents permuted transitively by g

coring stabilizers for a hopf algebra coaction abstract the coring stabilizer stab p is introduced for any prime ideal p of a right h comodule algebra a such that the factor ring a p is either right or left goldie this notion is used to obtain hopf algebraic analogs of two category equivalences associated with a homogeneous space the category of linearized quasicoherent sheaves on a noncommutative homogeneous space is interpreted as a suitable quotient category of the category of hopf modules birational invariance of such quotient categories is proved it is shown that for a birational h coequivariant extension b of a properly defined subsets of prime ideals of a and b correspond to each other bijectively

an algorithm for dual channel noiseless signal reconstruction and its performance analysis we present an algorithm for estimating a two input two output system and recovering its inputs from noise free observations of its outputs the algorithm involves minimization of a set of cross correlations between the reconstructed signals and a nonlinear function of these signals a performance analysis of the algorithm is presented it is shown that for the optimal choice of the nonlinear function the performance of the algorithm is close to the cramer rao lower bound crlb other choices of the function provide insights into the performance of moment cumulant based deconvolution techniques

fast and low complexity blind equalization via subgradient projections we propose a novel blind equalization method based on subgradient search over a convex cost surface this is an alternative to the existing iterative blind equalization approaches such as the constant modulus algorithm cma which often suffer from the convergence problems caused by their nonconvex cost functions the proposed method is an iterative algorithm called subgradient based blind algorithm sgba for both real and complex constellations with a very simple update rule it is based on the minimization of the l sub spl infin norm of the equalizer output under a linear constraint on the equalizer coefficients using subgradient iterations the algorithm has a nice convergence behavior attributed to the convex l sub spl infin cost surface as well as the step size selection rules associated with the subgradient search we illustrate the performance of the algorithm using examples with both complex and real constellations where we show that the proposed algorithm s convergence is less sensitive to initial point selection and a fast convergence behavior can be achieved with a judicious selection of step sizes furthermore the amount of data required for the training of the equalizer is significantly lower than most of the existing schemes

blind source separation by nonstationarity of variance a cumulant based approach blind separation of source signals usually relies either on the nongaussianity of the signals or on their linear autocorrelations a third approach was introduced by matsuoka et al 1995 who showed that source separation can be performed by using the nonstationarity of the signals in particular the nonstationarity of their variances in this paper we show how to interpret the nonstationarity due to a smoothly changing variance in terms of higher order cross cumulants this is based on the time correlation of the squares energies of the signals and leads to a simple optimization criterion using this criterion we construct a fixed point algorithm that is computationally very efficient

linear prediction methods for blind fractionally spaced equalization we describe adaptive methods for estimating fir zero forcing blind equalizers with arbitrary delay directly from the linear predictions of the observations while most current methods require inversion or singular value decomposition svd of the correlation matrix our methods need only to solve two linear prediction problems they can be implemented as rls or lms algorithms to recursively update the equalizer estimation they are computationally efficient the computational complexity in each recursion can be less than 15 ln sup 2 in the rls case where ln equals the equalizer length and 3l ln in the lms case where l is the number of subchannels the performance of the proposed methods and comparisons with existing approaches are shown by simulation to demonstrate their effectiveness

blind mai and isi suppression for ds cdma systems using hos based inverse filter criteria cumulant based inverse filter criteria ifc using second and higher order statistics hos proposed by tugnait et al 1993 have been widely used for blind deconvolution of discrete time multi input multi output mimo linear time invariant systems with non gaussian measurements through a multistage successive cancellation procedure but the deconvolved signals turn out to be an unknown permutation of the driving inputs a multistage blind equalization algorithm mbea is proposed for multiple access interference mai and intersymbol interference isi suppression of multiuser direct sequence code division multiple access ds cdma systems in the presence of multipath the proposed mbea which processes the chip waveform matched filter output signal without requiring any path delay information includes blind deconvolution processing using ifc followed by identification of the estimated symbol sequence with the associated user through a user identification algorithm uia then some simulation results are presented to support the proposed mbea and uia finally some conclusions are drawn

a cumulant matrix subspace algorithm for blind single fir channel identification blind identification of discrete time single user fir channels with nonminimum phase is studied here exploiting higher order cumulants of output signals of unknown channels a new closed form solution to the fir channel impulse response is derived the algorithm is simple and fast it relies only on nullspace decomposition of some cumulant matrices this method neither involves the difficult task of iterative global minimization of nonunimodal cost functions nor does it require overparametrization which poses consistency difficulties it can be used either as the final channel estimate or as a good initial point in nonlinear cumulant matching techniques the application of this identification method is broad and not limited to the use of any fixed order cumulants its application in identifying data communication systems shows great potential and promise

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

noncircular complex ica by generalized householder reflections we develop an efficient algorithm for noncircular complex independent component analysis ica by optimizing the rows of separation matrix independently using a generalized householder reflector and newton method we apply the new algorithm to the separation of complex generalized gaussian distributed ggd sources and propose a convenient way to learn the noncircularity of the sources simulation results are reported to study the convergence behavior and confirm the superior performance of the new algorithm

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

non gaussian multivariate adaptive ar estimation using the super exponential algorithm we formulate as a deconvolution problem the causal noncausal non gaussian multichannel autoregressive ar parameter estimation problem the super exponential algorithm presented in a paper by shalvi and weinstein 1993 is generalized to the vector case we present an adaptive implementation that is very attractive since it is higher order statistics hos based but does not present the high computational complexity of methods proposed up to now

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

misadjustment and tracking analysis of the constant modulus array the constant modulus cm array is a blind adaptive beamformer that can separate cochannel signals a follow on adaptive signal canceler may be used to perform direction finding of the source captured by the array in this paper we analyze the convergence and tracking properties of the cm array using a least mean square approximation expressions are derived for the misadjustment of the adaptive algorithms and a tracking model is developed that accurately predicts the behavior of the system during fades it is demonstrated that the adaptive canceler contributes more to the overall misadjustment than does the adaptive cm beamformer computer simulations are presented to illustrate the transient properties of the system and to verify the analytical results

the difference between the weil height and the canonical height on elliptic curves estimates for the difference of the weil height and the canonical height of points on elliptic curves are used for many purposes both theoretical and computational in this note we give an explicit estimate for this difference in terms of the j invariant and discriminant of the elliptic curve the method of proof suggested by serge lang is to use the decomposition of the canonical height into a sum of local heights we illustrate one use for our estimate by computing generators for the mordell weil group in three examples let e be an elliptic curve defined over a number field k say given by a weierstrass equation 1 y2 x ax b with a and b in the ring of integers of k the canonical height on e is a quadratic form h e k r for the definition and basic properties of h see 10 chapter viii 9 or 6 chapter vi the canonical height is determined by this property together with the fact that the difference

entropy minimization for supervised digital communications channel equalization this paper investigates the application of error entropy minimization algorithms to digital communications channel equalization the pdf of the error between the training sequence and the output of the equalizer is estimated using the parzen windowing method with a gaussian kernel and then the renyi s quadratic entropy is minimized using a gradient descent algorithm by estimating renyi s entropy over a short sliding window an online training algorithm is also introduced moreover for a linear equalizer an orthogonality condition for the minimum entropy solution that leads to an alternative fixed point iterative minimization method is derived the performance of linear and nonlinear equalizers trained with entropy and mean square error mse is compared as expected the results of training a linear equalizer are very similar for both criteria since even if the input noise is non gaussian the output filtered noise tends to be gaussian on the other hand for nonlinear channels and using a multilayer perceptron mlp as the equalizer differences between both criteria appear specifically it is shown that the additional information used by the entropy criterion yields a faster convergence in comparison with the mse

blind equalization using a tricepstrum based algorithm an adaptive blind equalization method is introduced for nonminimum phase communication channels the method estimates the inverse channel impulse response by using the complex cepstrum of the fourth order cumulants tricepstrum of the synchronously sampled received signal as such the proposed adaptive method depends only on the statistics of the received sequence and is capable of reconstructing separately both the minimum and maximum phase response of the channel it is demonstrated by means of extensive simulations that the proposed tricepstrum based equalization scheme performs well and outperforms other existing blind equalizers at the expense of higher computational complexity

transient and steady state analysis of the affine combination of two adaptive filters in this paper we propose an approach to the transient and steady state analysis of the affine combination of one fast and one slow adaptive filters the theoretical models are based on expressions for the excess mean square error emse and cross emse of the component filters which allows their application to different combinations of algorithms such as least mean squares lms normalized lms nlms and constant modulus algorithm cma considering white or colored inputs and stationary or nonstationary environments since the desired universal behavior of the combination depends on the correct estimation of the mixing parameter at every instant its adaptation is also taken into account in the transient analysis furthermore we propose normalized algorithms for the adaptation of the mixing parameter that exhibit good performance good agreement between analysis and simulation results is always observed

elliptic binomial diophantine equations the complete sets of solutions of the equation n k m l are determined for the cases k l 2 3 2 4 2 6 2 8 3 4 3 6 4 6 4 8 in each of these cases the equation is reduced to an elliptic equation which is solved by using linear forms in elliptic logarithms in all but one case this is more or less routine but in the remaining case k l 3 6 we had to devise a new variant of the method

blind equalization of constant modulus signals using support vector machines in this paper the problem of blind equalization of constant modulus cm signals is formulated within the support vector regression svr framework the quadratic inequalities derived from the cm property are transformed into linear ones thus yielding a quadratic programming qp problem then an iterative reweighted procedure is proposed to blindly restore the cm property the technique is suitable for real and complex modulations and it can also be generalized to nonlinear blind equalization using kernel functions we present simulation examples showing that linear and nonlinear blind sv equalizers offer better performance than cumulant based techniques mainly in applications when only a small number of data samples is available such as in packet based transmission over fast fading channels

improving the tracking capability of adaptive filters via convex combination as is well known hessian based adaptive filters such as the recursive least squares algorithm rls for supervised adaptive filtering or the shalvi weinstein algorithm swa for blind equalization converge much faster than gradient based algorithms such as the least mean squares algorithm lms or the constant modulus algorithm cma however when the problem is tracking a time variant filter the issue is not so clear cut there are environments for which each family presents better performance given this we propose the use of a convex combination of algorithms of different families to obtain an algorithm with superior tracking capability we show the potential of this combination and provide a unified theoretical model for the steady state excess mean square error for convex combinations of gradient and hessian based algorithms assuming a random walk model for the parameter variations the proposed model is valid for algorithms of the same or different families and for supervised lms and rls or blind cma and swa algorithms

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

a unifying maximum likelihood view of cumulant and polyspectral measures for non gaussian signal classification and estimation classification and estimation of non gaussian signals observed in additive gaussian noise of unknown covariance are addressed using cumulants or polyspectra by integrating ideas from pattern recognition and model identification asymptotically optimum maximum likelihood classifiers and arma autoregressive moving average parameter estimators are derived without knowledge of the data distribution identifiability of noncausal and nonminimum phase arma models is established using a finite number of cumulant or polyspectral lags of any order greater than two a unifying view of cumulant and polyspectral discriminant measures utilizes these lags and provides a common framework for development and performance analysis of novel and existing estimation and classification algorithms tentative order determination and model validation tests for non gaussian arma processes are described briefly illustrative simulations are also presented

noncommutative projective schemes an analogue of the concept of projective scheme is defined for noncommutative n graded algebras using the quotient category c of graded right a modules modulo its full subcategory of torsion modules we define proj a c a s where a is the object corresponding to the module aa and s is the autoequivalence defined by the shift of degrees the triples equivalent to proj a for a right noetherian graded algebra a are characterized in terms of a condition on extensions

arma system identification based on second order cyclostationarity previous work has presented novel techniques that exploit cyclostationarity for channel identification in data communication systems the present authors investigate the identifiability of linear time invariant lti arma systems based on second order cyclic statistics they present a parametric and a nonparametric method the parametric method directly identifies the zeros and poles of arma channels with a mixed phase the nonparametric method estimates the channel phase based on the cyclic spectra alone they analyze the phase estimation error of the nonparametric method for finite dimensional arma channels for specific finite dimensional arma channels an improved method is given which combines the parametric method with the nonparametric method computer simulation illustrates the effectiveness of the methods in identifying arma system impulse responses

a fast fixed point algorithm for independent component analysis we introduce a novel fast algorithm for independent component analysis which can be used for blind source separation and feature extraction we show how a neural network learning rule can be transformed into a fixedpoint iteration which provides an algorithm that is very simple does not depend on any user defined parameters and is fast to converge to the most accurate solution allowed by the data the algorithm finds one at a time all nongaussian independent components regardless of their probability distributions the computations can be performed in either batch mode or a semiadaptive manner the convergence of the algorithm is rigorously proved and the convergence speed is shown to be cubic some comparisons to gradient based algorithms are made showing that the new algorithm is usually 10 to 100 times faster sometimes giving the solution in just a few iterations

asymptotically optimal estimation of ma and arma parameters of non gaussian processes from high order moments a description is given of an asymptotically minimum variance algorithm for estimating the ma moving average and arma autoregressive moving average parameters of non gaussian processes from sample high order moments the algorithm uses the statistical properties covariances and cross covariances of the sample moments explicitly a simpler alternative algorithm that requires only linear operations is also presented the latter algorithm is asymptotically minimum variance in the class of weighted least squares algorithms

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

parallel lll reduction for bounding the integral solutions of elliptic diophantine equations stroeker and tzanakis gave convincing numerical and heuristic evidence for the fact that in their ellog method a certain parameter a plays a decisive role in the size of the final bound for the integral points on elliptic curves furthermore they provided an algorithm to determine the mordell weil basis of the curve which corresponds to the optimal choice of a in this paper we show that working with more mordell weil bases simultaneously the final bound for the integral points can be further decreased

on the convergence of ica algorithms with symmetric orthogonalization independent component analysis ica problem is often posed as the maximization minimization of an objective cost function under a unitary constraint which presumes the prewhitening of the observed mixtures the parallel adaptive algorithms corresponding to this optimization setting where all the separators are jointly trained are typically implemented by a gradient based update of the separation matrix followed by the so called symmetrical orthogonalization procedure to impose the unitary constraint this article addresses the convergence analysis of such algorithms which has been considered as a difficult task due to the complication caused by the minimum frobenius or induced 2 norm distance mapping step we first provide a general characterization of the stationary points corresponding to these algorithms furthermore we show that fixed point algorithms employing symmetrical orthogonalization are monotonically convergent for convex objective functions we later generalize this convergence result for nonconvex objective functions at the last part of the article we concentrate on the kurtosis objective function as a special case we provide a new set of critical points based on householder reflection and we also provide the analysis for the minima maxima saddle point classification of these critical points

sequential blind extraction of instantaneously mixed sources this paper presents a general approach to sequential blind extraction of instantaneously mixed sources for several major ill conditioned cases as well as the regular case of full column rank mixing matrices four ill conditioned cases are considered the mixing matrix is square but singular the number of sensors is less than that of sources the number of sensors is larger than that of sources but the column rank of the mixing matrix is deficient and the number of sources is unknown and the column rank of the mixing matrix is deficient first a solvability analysis is presented for a general case a necessary and sufficient condition for extractability is derived a sequential blind extraction approach is then proposed to extract all theoretically separable sources next a principle and a cost function based on fourth order cumulants are presented for blind source extraction by minimizing the cost function under a nonsingularity constraint of the extraction matrix all theoretically separable sources can be extracted sequentially finally simulation results are presented to demonstrate the validity and performance of the blind source extraction approach

blind adaptation of stable discrete time iir filters in state space form blind deconvolution consists of extracting a source sequence and impulse response of a linear system from their convolution in the presence of system zeros close to the unit circle which give rise to very long impulse responses infinite impulse response iir adaptive structures are of use whose adaptation should be carefully designed in order to guarantee stability in this paper we propose a blind type discrete time iir adaptive filter structure realized in state space form that with a suitable parameterization of its coefficients remains stable the theory is first developed for a two pole filter whose numerical behavior is investigated via numerical experiments the proposed structure adaptation theory is then extended to a multipole structure realized as a cascade of two pole filters computer based experiments are proposed and discussed which aim at illustrating the behavior of the filter cascade on several cases of study the numerical results obtained show the proposed filters remain stable during adaptation and provide satisfactory deconvolution results

independent component analysis by entropy bound minimization a novel differential entropy estimator is introduced where the maximum entropy bound is used to approximate the entropy given the observations and is computed using a numerical procedure thus resulting in accurate estimates for the entropy we show that such an estimator exists for a wide class of measuring functions and provide a number of design examples to demonstrate its flexible nature we then derive a novel independent component analysis ica algorithm that uses the entropy estimate thus obtained ica by entropy bound minimization ica ebm the algorithm adopts a line search procedure and initially uses updates that constrain the demixing matrix to be orthogonal for robust performance we demonstrate the superior performance of ica ebm and its ability to match sources that come from a wide range of distributions using simulated and real world data

qr based algorithms for multichannel adaptive least squares lattice filters a pair of multichannel least squares lattice filter algorithms is presented each m channel filter stage is numerically stable and computationally efficient with a computational complexity of o m sup 2 both algorithms are based on the recursive qr decomposition of the forward and backward error matrices in each filter stage the first algorithm uses orthogonal givens rotations to compute the qr decomposition the second algorithm uses fast givens rotations for greater efficiency simulation results are presented as well as an example of the algorithms application in the enhancement of magnetoencephalographic signals

adaptive multistage beamforming using cyclic higher order statistics chos a new blind beamforming algorithm for signals that exhibit higher order cyclostationarity is presented exploiting some previous theoretical developments we show how cyclic cumulants of the received signals can be used to obtain the weights of the beamformer that perform blind extraction the method is based on a spatial interpretation of a deconvolution procedure known as the super exponential algorithm the basic block processing algorithm is made fully adaptive using an adaptive urv scheme and applied to a typical mobile communications scenario where several cochannel interferers corrupt the signals of interest

properties of some blind equalization criteria in noisy multiuser environments blind equalization in noisy multiuser channels has met with increasing attention with the advent of multiaccess digital communication systems we examine blind equalizer performance in cases where perfect equalization proves unattainable due to noise and interference from concurrent users in particular we obtain a characterization of stationary points and extrema for a family of blind criteria in undermodeled cases which assimilates the influence of differing source statistics and background noise correlation properties relations to mean square equalization measures are then obtained as a byproduct by re examining a gradient search procedure we obtain domains of attraction of each extremum in a special sufficient order setting we also derive a global step size bound for undermodeled cases which ensures convergence of a gradient search procedure to an extremum of a blind cost function we likewise confirm that the super exponential algorithm results from an optimal choice of this step size parameter

on convergence analysis of fractionally spaced adaptive blind equalizers in this paper we study the convergence analysis of fractionally spaced adaptive blind equalizers we show that based on the trivial and nontrivial nullspaces of a channel convolution matrix all equilibria can be classified as channel dependent equilibria cde or algorithm dependent equilibria ade because oversampling provides channel diversity the nullspace of the channel convolution matrix is affected we show that fractionally spaced equalizers fses do not possess any cde if a length zero condition is satisfied the convergence behavior of these fse are clearly determined by the specific choice of cost function alone we characterize the global convergence ability of several popular algorithms simply based on their ade we also present an fse implementation of the super exponential algorithm we show that the fse implementation does not introduce any nonideal approximation simulation results are also presented to illustrate the robustness and the improved performance of fse under the super exponential algorithm

models of quasiprojective homogeneous spaces for hopf algebras given an affine group scheme g of finite type over a field k a homogeneous space for g is a scheme x over k containing a rational point x such that g operates transitively on x assuming that g operates on the right we may identify x with the quotient k g of g by the left action of the stabilizer k of x in g the representation theoretic significance ofk g is that the induction functor indk from k modules to g modules factors as a category equivalence

two dimensional frequency domain blind system identification using higher order statistics with application to texture synthesis in this paper shalvi and weinstein s 1993 super exponential se algorithm using higher order statistics for blind deconvolution of one dimensional 1 d linear time invariant systems is extended to a two dimensional 2 d se algorithm then a 2 d frequency domain blind system identification bsi algorithm for 2 d linear shift invariant lsi systems using the computationally efficient 2 d se algorithm and the 2 d linear prediction error filter is proposed in addition to the lsi system estimate the proposed bsi algorithm also provides a minimum mean square error mmse equalizer estimate and an mmse signal enhancement filter estimate then a texture synthesis method tsm using the proposed bsi algorithm is presented some simulation results to support the efficacy of the proposed bsi algorithm and some experimental results to support the efficacy of the proposed tsm are presented finally some conclusions are drawn

fast fixed point neural blind deconvolution algorithm the aim of this letter is to introduce a new blind deconvolution algorithm based on fixed point optimization of a bussgang type cost function the cost function relies on approximate bayesian estimation achieved by an adaptive neuron the main feature of the presented algorithm is fast convergence that guarantees good deconvolution performances with limited computational demand as compared with algorithms of the same class

monotonically convergent algorithms for symmetric tensor approximation abstract reduced rank approximations to symmetric tensors find use in data compaction and in multi user blind source separation we derive iterative algorithms which feature monotonic convergence to a minimum of a frobenius norm approximation criterion for a certain rank r tucker product version of the approximation problem the approach exploits the gradient inequality for convex functions to establish monotonic convergence while sparing the cumbersome step size analysis required from a manifold gradient approach it likewise overcomes some limitations of symmetric versions of alternating least squares the computational load per iteration amounts to computing an unfolded matrix and a qr decomposition

bayesian techniques for blind deconvolution this paper introduces extended bayesian filters ebfs a new family of blind deconvolution filters for digital communications the blind deconvolution problem is formulated as a nonlinear and non gaussian fixed lag minimum mean square error filtering problem and the ebf is derived as a suboptimal recursive estimator the model based setting makes extensive use of the transmitted symbol and noise distributions a key feature of the ebf is that the filter lag can be chosen to be larger than the channel length while the complexity is exponential in a parameter which is typically chosen to be smaller than both the channel length and the filter lag extensive simulations characterizing the performance of ebfs in severe intersymbol interference channels are presented the fast convergence and robust equalization of the ebfs are demonstrated for uncoded linearly modulated signals e g differentially encoded quaternary phase shift keying qpsk transmitted over unknown channels comparisons are made to other blind symbol by symbol demodulation algorithms the results show that the ebf provides much better performance at increased complexity compared to the constant modulus algorithm and the extended kalman filter and achieves a better performance complexity trade off than other bayesian demodulation algorithms the simulations also show that the ebf is applicable with large constellations and shaped modulations

recursive least squares constant modulus algorithm for blind adaptive array we consider the problem of blind adaptive signal separation with an antenna array based on the constant modulus cm criterion an approximation to the cm cost function is proposed which allows the use of the recursive least squares rls optimization technique a novel rls constant modulus algorithm rls cma is derived where the modulus power of the array output can take on arbitrary positive real values i e fractional values allowed simulations are performed to compare the performance of the proposed rls cma to other well known algorithms for blind adaptive beamforming results indicate that the rls cma has a significantly faster convergence rate and better tracking ability

monotonic convergence of fixed point algorithms for ica we re examine a fixed point algorithm proposed by hyvarinen for independent component analysis wherein local convergence is proved subject to an ideal signal model using a square invertible mixing matrix here we derive step size bounds which ensure monotonic convergence to a local extremum for any initial condition our analysis does not assume an ideal signal model but appeals rather to properties of the contrast function itself and so applies even with noisy data and or more sources than sensors the results help alleviate the guesswork that often surrounds step size selection when the observed signal does not fit an idealized model

a gradient search interpretation of the super exponential algorithm this article reviews the super exponential algorithm proposed by shalvi and weinstein 1993 for blind channel equalization the principle of this algorithm hadamard exponentiation projection over the set of attainable combined channel equalizer impulse responses followed by a normalization is shown to coincide with a gradient search of an extremum of a cost function the cost function belongs to the family of functions given as the ratio of the standard l sub 2p and l sub 2 sequence norms where p 1 this family is very relevant in blind channel equalization tracing back to donoho s 1981 work on minimum entropy deconvolution and also underlying the godard 1980 or constant modulus and the earlier shalvi weinstein algorithms using this gradient search interpretation which is more tractable for analytical study we give a simple proof of convergence for the super exponential algorithm finally we show that the gradient step size choice giving rise to the super exponential algorithm is optimal

undermodeled equalization a characterization of stationary points for a family of blind criteria we attack specific problems related to equalizer performance in undermodeled cases in which assumptions of perfect equalizability are dismissed in favor of a more realistic situation in which no equalizer setting may achieve perfect channel equalization we derive a characterization of candidate convergent points for a family of blind criteria which appeal tacitly or wittingly to maximizing the ratio of different sequence norms of the combined channel equalizer impulse response this may be accomplished in a practical implementation by using equalizer output cumulants of different orders the popular godard and shalvi weinstein schemes are accommodated at one extreme of the family of criteria we also show that each maximum at the other extreme of the family involving progressively higher order output cumulants yields precisely a wiener response this suggests that blind algorithms using progressively higher order statistics may converge more closely to a wiener response than those using more modest order statistics we show moreover that the superexponential family of algorithms is also included and establish a convergence proof for undermodeled cases that appeals to no approximation finally some apparently novel bounds on attainable open eye measures in undermodeled cases are also derived

multichannel arma processes parametric modeling of multichannel time series is accomplished by using higher than second order statistics hos of the observed nongaussian data cumulants of vector processes are defined using a kronecker product formulation and consistency of their sample estimators is addressed identifiability results in connection with the hos based parameter estimation of causal and noncausal multivariate arma processes are established estimates of the parameters of causal arma models are obtained as the solution to a set of linear equations whereas those of noncausal arma models are obtained as the solution to a cumulant matching algorithm conventional approaches based on second order statistics can identify a multichannel system only to within post multiplication by a unimodular matrix hos based methods yield solutions that are unique to within post multiplication by an extended permutation matrix additionally the multiminimum phase assumption can be relaxed and the observations may be contaminated with colored gaussian noise frequency domain methods for nonparametric system identification are discussed briefly simulations results validating the multichannel parameter estimation algorithms are provided

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

multichannel signal separation methods and analysis the problem of multichannel signal separation has attracted considerable interest in recent literature a variety of methods and criteria have been proposed to solve the problem based on statistical independence between the source signals most of these criteria involve the computation of high order statistics of the observed signals we present a unified framework for many of these criteria and analyze their statistical variance

new processing techniques based on the constant modulus adaptive algorithm this paper presents three extensions of the constant modulus algorithm cma introduced in an earlier paper as a means of correcting degradations in constant enyelope waveforms as originally formulated the cma employs an fir filter with complex coefficients and accepts complex quadrature input data in this paper first a real input real coefficient version of the algorithm is shown to perform arbitrarily close to the fully complex version secondly the algorithm is extended for the enhancement of signals having a nonconstant but known envelope as might arise in data signals with pulse shaping lastly a multichannel version of cma wherein several observations are linearly combined is presented for joint adaptation of multiple filters this approach can be used for example as a means of spatial or polarization beamsteering to reject additive interferers and compensate for channel induced polarization rotation

projectivity and freeness over comodule algebras let h be a hopf algebra and a an h simple right h comodule algebra it is shown that under certain hypotheses every h a hopf module is either projective or free as an a module and a is either a quasi frobenius or a semisimple ring as an application it is proved that every weakly finite in particular every finite dimensional hopf algebra is free both as a left and a right module over its finite dimensional right coideal subalgebras and the latter are frobenius algebras similar results are obtained for h simple h module algebras

super exponential blind adaptive beamforming the objective of the beamforming with the exploitation of a sensor array is to enhance the signals of the sources from desired directions suppress the noises and the interfering signals from other directions and or simultaneously provide the localization of the associated sources in this paper we present a higher order cumulant based beamforming algorithm namely the super exponential blind adaptive beamforming algorithm which is extended from the super exponential algorithm sea and the inverse filter criteria ifc while both sea and ifc assume noise free conditions this requirement is no longer needed and all the noise components are taken into account in the proposed algorithm two special conditions are derived under which the proposed blind beamforming algorithm achieves the performance of the corresponding optimal nonblind beamformer in the sense of minimum mean square error mmse simulation results show that the proposed algorithm is effective and robust to diverse initial weight vectors its performance with the use of the fourth order cumulants is close to that of the nonblind optimal mmse beamformer

new results on the bijectivity of antipode of a hopf algebra abstract two results giving sufficient conditions for the bijectivity of the antipode of a hopf algebra are proved

cumulant based identification of multichannel moving average models given cumulants of a stationary perhaps noisy non gaussian r variate moving average ma q process identifiability conditions are studied under which the ma coefficient matrices the input statistics and the order q can be uniquely determined the selection of a unique representative from the equivalence class corresponding to a given cumulant structure involves fewer restrictions than that corresponding to a given covariance structure two algorithms are derived for estimating the possibly nonminimum phase ma coefficient matrices

blind source separation by sparse decomposition in a signal dictionary the blind source separation problem is to extract the underlying source signals from a set of linear mixtures where the mixing matrix is unknown this situation is common in acoustics radio medical signal and image processing hyperspectral imaging and other areas we suggest a two stage separation process a priori selection of a possibly overcomplete signal dictionary for instance a wavelet frame or a learned dictionary in which the sources are assumed to be sparsely representable followed by unmixing the sources by exploiting the their sparse representability we consider the general case of more sources than mixtures but also derive a more efficient algorithm in the case of a nonovercomplete dictionary and an equal numbers of sources and mixtures experiments with artificial signals and musical sounds demonstrate significantly better separation than other known techniques

maximum likelihood and lower bounds in system identification with non gaussian inputs we consider the problem of estimating the parameters of an unknown discrete linear system driven by a sequence of independent identically distributed i i d random variables whose probability density function pdf may be non gaussian we assume a general system structure that may contain causal and noncausal poles and zeros the parameters characterizing the input pdf may also be unknown we derive an asymptotic expression for the cramer rao lower bound and show that it is the highest worst in the gaussian case indicating that the estimation accuracy can only be improved when the input pdf is non gaussian it is further shown that the asymptotic error variance in estimating the system parameters is unaffected by lack of knowledge of the pdf parameters and vice verse computationally efficient gradient based algorithms for finding the maximum likelihood estimate of the unknown system and pdf parameters which incorporate backward filtering for the identification of non causal parameters are presented the dual problem of blind deconvolution equalization is considered and asymptotically attainable lower bounds on the equalization performance are derived these bounds imply that it is preferable to work with compact equalizer structures characterized by a small number of parameters as the attainable performance depend only on the total number of equalizer parameters

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

noetherian pi hopf algebras are gorenstein we prove that every noetherian affine pi hopf algebra has finite injective dimension which answers a question of brown 1998

on estimating noncausal nonminimum phase arma models of non gaussian processes the authors address the problem of estimating the parameters of non gaussian arma autoregressive moving average processes using only the cumulants of the noisy observation the measurement noise is allowed to be colored gaussian or independent and identically non gaussian distributed the arma model is not restricted to be causal or minimum phase and may even contain all pass factors the unique parameter estimates of both the ma and ar parts are obtained by linear equations the structure of the proposed algorithm facilitates asymptotic performance evaluation of the parameter estimators and model order selection using cumulant statistics the method is computationally simple and can be viewed as the least squares solution to a quadratic model fitting of a sampled cumulant sequence identifiability issues are addressed simulations are presented to illustrate the proposed algorithm

computing all integer solutions of a genus 1 equation the elliptic logarithm method has been applied with great success to the problem of computing all integer solutions of equations of degree 3 and 4 defining elliptic curves we extend this method to include any equation f u v 0 where f z u v is irreducible over oq defines a curve of genus 1 but is otherwise of arbitrary shape and degree we give a detailed description of the general features of our approach and conclude with two rather unusual examples corresponding to equations of degree 5 and degree 9

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

an algorithm for rls identification parameters that vary quickly with time an alternative to the standard recursive least squares rls algorithm for fixed order systems with exponential data weighting is presented the approach uses givens orthogonal transformations to update the cholesky factor of the information matrix without ever needing to form it the resulting algorithm gives higher precision control and is less sensitive to ill conditioning when compared to other reported approaches it is demonstrated by an example that ill conditioned problems with parameters that vary quickly can be modified to stabilize erratic parameter fluctuations

the cumulant theory of cyclostationary time series i foundation the problem of characterizing the sine wave components in the output of a polynomial nonlinear system with a cyclostationary random time series input is investigated the concept of a pure nth order sine wave is introduced and it is shown that pure nth order sine wave strengths in the output time series are given by scaled fourier coefficients of the polyperiodic temporal cumulant of the input time series the higher order moments and cumulants of narrowband spectral components of time series are defined and then idealized to the case of infinitesimal bandwidth such spectral moments and cumulants are shown to be characterized by the fourier transforms of the temporal moments and cumulants of the time series it is established that the temporal and spectral cumulants have certain mathematical and practical advantages over their moment counterparts to put the contributions of the paper in perspective a uniquely comprehensive historical survey that traces the development of the ideas of temporal and spectral cumulants from their inception is provided

blind wideband spatio temporal filtering based on higher order cyclostationarity properties in this paper a new method for blind minimum mean square error mmse spatio temporal signal filtering is proposed to obtain a blind version of the mmse filter the proposed method utilizes the signal selectivity property of the higher order cyclostationary statistics hocs exhibited by the signal of interest an accurate estimate of the transfer function of the mmse filter is obtained also in the presence of strong frequency overlapped interfering signals which would render standard stationarity based techniques ineffective the method is useful when the desired signal cannot be accurately extracted by exploiting its second order cyclostationarity properties because they are too weak and or they are shared by the interference and noise signals as well the performance analysis which is carried out by computer simulations in the case of quadrature amplitude modulated qam modulated signals with partially overlapping bands substantiates the effectiveness of the proposed method

robust super exponential methods for deflationary blind source separation of instantaneous mixtures the so called super exponential methods sems are attractive methods for solving blind signal processing problems the conventional sems however have such a drawback that they are very sensitive to gaussian noise to overcome this drawback we propose a new sem while the conventional sems use the second and higher order cumulants of observations the proposed sem uses only the higher order cumulants of observations since higher order cumulants are insensitive to gaussian noise the proposed sem is robust to gaussian noise which is referred to as a robust super exponential method rsem to show the validity of the proposed rsem some simulation results are presented

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

circular lattice filtering using pagano s method recently pagano has found a one to one relationship between multivariate autoregression and scalar periodic autoregressions and derived a set of fundamental yule walker yw type equations for estimating the parameters of the periodic autoregressions in this paper we first obtain a levinson type recursive algorithm for solving the above mentioned yw equations then using this recursion we show a circular lattice structure of the process this enables us to obtain a burg type algorithm which guarantees the filter stability lastly we modify it to an adaptive form for on line computation this circular lattice filter simultaneously performs whitening and orthogonalization of the components of multivariate input samples the most salient feature of the algorithm is that it consists of calculations of scalar quantities thus completely avoiding matrix manipulations accompanying usual multivariate processing methods

a newton like algorithm for complex variables with applications in blind equalization although the newton algorithm has been extended to the complex domain in different forms none of them seems to be directly applicable to blind equalization therefore the objective of this correspondence is to develop an algorithm for blind equalization in the complex domain we propose a newton like algorithm based on a complex taylor series stochastic newton like algorithms snla for two blind equalization cost functions are developed simulations show that the new algorithms perform slightly better than the self orthogonalizing algorithm

gradient algorithms for complex non gaussian independent component vector extraction question of convergence we revise the problem of extracting one independent component from an instantaneous linear mixture of signals the mixing matrix is parameterized by two vectors one column of the mixing matrix and one row of the demixing matrix the separation is based on the non gaussianity of the source of interest while the remaining background signals are assumed to be gaussian three gradient based estimation algorithms are derived using the maximum likelihood principle and are compared with the natural gradient algorithm for independent component analysis and with one unit fastica based on negentropy maximization the ideas and algorithms are also generalized to the extraction of a vector component when the extraction proceeds jointly from a set of instantaneous mixtures throughout this paper we address the problem concerning the size of the region of convergence for which the algorithms guarantee the extraction of the desired source we show that the size is influenced by the signal to interference ratio on the input channels simulations comparing several algorithms confirm this observation they show a different size of the region of convergence under a scenario in which the source of interest is dominant or weak here our proposed modifications of the gradient methods taking into account the dominance weakness of the source show improved global convergence