identification of systems containing linear dynamic and static nonlinear elements identification of nonlinear systems which can be represented by combinations of linear dynamic and static nonlinear elements are considered previous results by the authors based on correlation analysis are combined to provide a unified treatment for this class of systems it is shown that systems composed of cascade feedforward feedback and multiplicative connections of linear dynamic and zero memory nonlinear elements can be identified in terms of the individual component subsystems from measurements of the system input and output only

frequency identification of nonparametric wiener systems containing backlash nonlinearities this paper addresses the problem of identifying wiener systems constituted of nonparametric linear dynamics and backlash nonlinearities the linear subsystem is arbitrary but stable the backlash nonlinearity borders are almost arbitrary shape in particular these are allowed to be nonsmooth noninvertible and crossing a frequency identification method is developed to estimate the system frequency response function at a given set of frequencies and the backlash nonlinearity borders within a given working domain the identification method involves sine excitations and consistent estimators designed using analytic geometry tools e g fictive limit cycles informative backlash limit cycles spread and orientation compatibility

nonparametric density estimation and detection in impulsive interference channels i estimators for pt i see ibid vol 42 no 2 4 p 1684 1697 1994 nonlinear processing significantly enhances detector performance in nongaussian noise relative to that of linear detectors several nonparametric detection schemes for impulsive noise channels are formulated using the nonparametric probability density estimators developed in part i the likelihood ratio test and the small signal locally optimum nonlinearity provide the basis for the formulation of these nonparametric detection schemes several modifications to these basic strategies are used to compensate for inaccuracies in the density estimates in particular for the problem of detecting a known signal in impulsive noise two modifications to the standard likelihood ratio test are considered the first is adapted from robust statistics whereas the second the l sub 1 error based detector is specifically formulated for use with density estimates both schemes are found to perform close to the optimum likelihood ratio detector for a wide variety of impulsive noise densities from the merits of these two tests a new detection scheme that approximates the locally optimum nonlinearity is then developed this detector which uses the nonparametric density estimators developed in part i is shown to perform very well for the wide variety of impulsive and heavy tailed densities considered in the study this nonparametric density estimate based detector is also shown to outperform more conventional nonparametric detectors in impulsive noise

maximum likelihood localization of sources in noise modeled as a stable process this paper introduces a new class of robust beamformers which perform optimally over a wide range of non gaussian additive noise environments the maximum likelihood approach is used to estimate the bearing of multiple sources from a set of snapshots when the additive interference is impulsive in nature the analysis is based on the assumption that the additive noise can be modeled as a complex symmetric spl alpha stable s spl alpha s process transform based approximations of the likelihood estimation are used for the general s spl alpha s class of distributions while the exact probability density function is used for the cauchy case it is shown that the cauchy beamformer greatly outperforms the gaussian beamformer in a wide variety of non gaussian noise environments and performs comparably to the gaussian beamformer when the additive noise is gaussian the cramer rao bound for the estimation error variance is derived for the cauchy case and the robustness of the s spl alpha s beamformers in a wide range of impulsive interference environments is demonstrated via simulation experiments

minlip for the identification of monotone wiener systems this paper studies the minlip estimator for the identification of wiener systems consisting of a sequence of a linear fir dynamical model and a monotonically increasing or decreasing static function given t observations this algorithm boils down to solving a convex quadratic program with o t variables and inequality constraints implementing an inference technique which is based entirely on model complexity control a technique which is dubbed as einstein s razor this technique is proven to yield here almost consistent estimates in case the given data is suitably rich local persistently exciting of sufficient order and if the samples obey a true monotone wiener system satisfying some regularity conditions it is then indicated how to extend the method in order to cope with noisy data and empirical evidence is given in order to support the claim of efficiency

canonical detection in spherically invariant noise the paper deals with the detection of signals with unknown parameters in impulsive noise modeled as a spherically symmetric random process the proposed model subsumes several interesting families of noise amplitude distributions generalized cauchy generalized laplace generalized gaussian contaminated normal it also allows handling of the case of correlated noise by a whitening approach the generalized maximum likelihood decision strategy is adopted resulting in a canonical detector which is independent of the amplitude distribution of the noise a general method for performance evaluation is outlined and a comprehensive performance analysis is carried out for the case of m ary equal energy orthogonal signals under several distributional assumptions for the noise the performance is contrasted with that of the maximum likelihood receiver for completely known signals so as to assess the loss due to the a priori uncertainty as to the signal parameters

universal approximation using radial basis function networks there have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables some of these studies deal with cases in which the hidden layer nonlinearity is not a sigmoid this was motivated by successful applications of feedforward networks with nonsigmoidal hidden layer units this paper reports on a related study of radial basis function rbf networks and it is proved that rbf networks having one hidden layer are capable of universal approximation here the emphasis is on the case of typical rbf networks and the results show that a certain class of rbf networks with the same smoothing factor in each kernel node is broad enough for universal approximation

parametric and nonparametric identification of linear systems in the presence of nonlinear distortions a frequency domain approach this paper studies the asymptotic behavior of nonparametric and parametric frequency domain identification methods to model linear dynamic systems in the presence of nonlinear distortions under some general conditions for random multisine excitations in the first part a related linear dynamic system rlds approximation to the nonlinear system nls is defined and it is shown that the differences between the nls and the rlds can be modeled as stochastic variables with known properties in the second part a parametric model for the rlds is identified convergence in probability of this model to the rlds is proven a function of dependency is defined to detect and separate the presence of unmodeled dynamics and nonlinear distortions and to bound the bias error on the transfer function estimate

choice of free parameters in expansions of discrete time volterra models using kautz functions this work tackles the problem of modeling nonlinear systems using volterra models based on kautz functions the drawback of requiring a large number of parameters in the representation of these models can be circumvented by describing every kernel using an orthonormal basis of functions such as the kautz basis the resulting model so called wiener volterra model can be truncated into a few terms if the kautz functions are properly designed the underlying problem is how to select the free design complex poles that fully parameterize these functions a solution to this problem has been provided in the literature for linear systems which can be represented by first order volterra models a generalization of such strategy focusing on volterra models of any order is presented in this paper this problem is solved by minimizing an upper bound for the error resulting from the truncation of the kernel expansion into a finite number of functions the aim is to minimize the number of two parameter kautz functions associated with a given series truncation error thus reducing the complexity of the resulting finite dimensional representation the main result is the derivation of an analytical solution for a sub optimal expansion of the volterra kernels using a set of kautz functions

monte carlo analysis of the critical properties of the two dimensional randomly bond diluted ising model via wang landau algorithm abstract the influence of random bond dilution on the critical properties of the two dimensional ising model on a square lattice with periodic boundary conditions is presented using the monte carlo process with wang landau sampling the lattice linear size is l 20 140 and the concentration of the diluted bonds spans a wide range from weak to strong dilution namely q 0 05 0 1 0 2 0 3 0 4 the respective percolation limit for the square lattice is q c p e r c 0 5 its pure version q 0 has a second order phase transition with vanishing specific heat critical exponent an example of inapplicability of the harris criterion the main effort is focused on the temperature dependence of the specific heat and magnetic susceptibility to estimate the respective maximum values and subsequent pseudocritical temperatures for extracting the relative critical exponents we have also looked at the probability distribution of the susceptibility pseudocritical temperature and specific heat for assessing self averaging the study is carried out in the appropriately restricted but dominant energy subspaces by applying the finite size scaling analysis the critical exponents are estimated the specific heat exponent vanishes the correlation length exponent is equal to one and the critical exponents ratio retains its pure ising model value thus supporting the strong universality hypothesis

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

rbfn restoration of nonlinearly degraded images we investigate a technique for image restoration using nonlinear networks based on radial basis functions the technique is also based on the concept of training or learning by examples when trained properly these networks are used as spatially invariant feedforward nonlinear filters that can perform restoration of images degraded by nonlinear degradation mechanisms we examine a number of network structures including the gaussian radial basis function network rbfn and some extensions of it as well as a number of training algorithms including the stochastic gradient sg algorithm that we have proposed earlier we also propose a modified structure based on the gaussian mixture model and a learning algorithm for the modified network experimental results indicate that the radial basis function network and its extensions can be very useful in restoring images degraded by nonlinear distortion and noise

optimum detection of fading signals in impulsive noise this paper deals with the synthesis and the analysis of optimum receivers to detect one out of m equally likely equi energy fading signals in impulsive noise modelled as a compound gaussian possibly correlated process we show that the conventional coherent and incoherent detectors are still optimum independent of the noise as well as the fading probability density functions the performance analysis has been carried on with reference to the general case of arbitrarily distributed disturbance in order to simplify the analysis asymptotical expressions have been developed for high signal to noise ratios as well as high signal space dimensionality interestingly enough this allows separating the effect of the noise spikyness from that of the fading law results indicate that for deep fading the noise marginal distribution does not dramatically affect the error probability nor is it influential on the limit operating characteristics corresponding to infinite signal space dimensions for non fluctuating signals instead the noise distribution plays a primary role spiky noise usually produces performance impairment moreover the limit performance in impulsive disturbance may exhibit marked deviations from the well known stepwise shape which is typical of gaussian channels

system identification with generalized orthonormal basis functions a least squares identification method is studied that estimates a finite number of expansion coefficients in the series expansion of a transfer function where the expansion is in terms of recently introduced generalized basis functions the basis functions are orthogonal in h2 and generalize the pulse laguerre and kautz bases one of their important properties is that when chosen properly they can substantially increase the speed of convergence of the series expansion this leads to accurate approximate models with only a few coefficients to be estimated explicit bounds are derived for the bias and variance errors that occur in parameter estimates as well as in the resulting transfer function estimates

maximum likelihood estimation for multivariate observations of markov sources parameter estimation for multivariate functions of markov chains a class of versatile statistical models for vector random processes is discussed the model regards an ordered sequence of vectors as noisy multivariate observations of a markov chain mixture distributions are a special case the foundations of the theory presented here were established by baum petrie soules and weiss a powerful representation theorem by fan is employed to generalize the analysis of baum em et al to a larger class of distributions

a generalized orthonormal basis for linear dynamical systems in many areas of signal system and control theory orthogonal functions play an important role in issues of analysis and design in this paper it is shown that there exist orthogonal functions that in a natural way are generated by stable linear dynamical systems and that compose an orthonormal basis for the signal space l sub 2sup n to this end use is made of balanced realizations of inner transfer functions the orthogonal functions can be considered as generalizations of for example the pulse functions laguerre functions and kautz functions and give rise to an alternative series expansion of rational transfer functions it is shown how we can exploit these generalized basis functions to increase the speed of convergence in a series expansion i e to obtain a good approximation by retaining only a finite number of expansion coefficients consequences for identification of expansion coefficients are analyzed and a bound is formulated on the error that is made when approximating a system by a finite number of expansion coefficients

nonparametric identification of wiener systems by orthogonal series a wiener system i e a system comprising a linear dynamic and a nonlinear memoryless subsystems connected in a cascade is identified both the input signal and disturbance are random white and gaussian the unknown nonlinear characteristic is strictly monotonous and differentiable and therefore the problem of its recovering from input output observations of the whole system is nonparametric it is shown that the inverse of the characteristic is a regression function and a class of orthogonal series nonparametric estimates recovering the regression is proposed and analyzed the estimates apply the trigonometric legendre and hermite orthogonal functions pointwise consistency of all the algorithms is shown under some additional smoothness restrictions the rates of their convergence are examined and compared an algorithm to identify the impulse response of the linear subsystem is proposed

critical behavior of the pure and random bond two dimensional triangular ising ferromagnet we investigate the effects of quenched bond randomness on the critical properties of the two dimensional ferromagnetic ising model embedded in a triangular lattice the system is studied in both the pure and disordered versions by the same efficient two stage wang landau method in the first part of our study we present the finite size scaling behavior of the pure model for which we calculate the critical amplitude of the specific heat s logarithmic expansion for the disordered system the numerical data and the relevant detailed finite size scaling analysis along the lines of the two well known scenarios logarithmic corrections versus weak universality strongly support the field theoretically predicted scenario of logarithmic corrections a particular interest is paid to the sample to sample fluctuations of the random model and their scaling behavior that are used as a successful alternative approach to criticality

performance of ds ssma communications in impulsive channels part i linear correlation receivers the performance of digital linear correlation receivers is studied in a multiuser environment there are assumed to be two types of sources interfering with data transmission multiple access interference and additive channel noise which is attributed to impulsive noise sources in the environment the contribution of multiple access interference is examined by considering k asynchronous users transmitting simultaneously over a linear channel using the binary psk direct sequence spreadspectrum multiple access ds ssma technique alternatively the effects of the non gaussian impulsive channel in such a system are studied by modeling the samples of noise after front end filtering errorprobability performance under these conditions is compared to that for additive white gaussian noise awgn channels due to computational complexity exact analysis is limited here to systems utilizing short spreading sequences computationally simple methods are proposed for approximating the average error probability when the length of the signature sequences is large furthermore some asymptotic results are obtained for the case of infinitely long sequences in all cases performance variation is examined as the shape of the noise density varies with snr held constant the results of this analysis indicate that the presence of impulsive noise can cause significant performance degradation over that predicted from an awgn model even when the total noise power does not increase

asymptotically optimum space diversity detection in non gaussian noise the theory of asympoticalllly optimum detection in nongaussian noise is considered to synthesize a space diversity structure for the noncoherent detection of a bandpass signal subject to amplitude fluctuations an asymptotic sufficient statistic is obtained for arbitrary fading laws on the diversity branches and then for rayleigh distributed amplitude fluctuations the asymptotically optimum detector is synthesized the performance of the proposed detection structure is obtained and numerical results and comments are presented moreover a comparison between the asymptotically optimum detector and a simple suboptimum structure is made

signal detection in multivariate class a interference the aim of this article is to identify and evaluate multivariate density functions when the univariate densities are all class a three models are proposed model a for independent random variables model b for dependent random variables model c for uncorrelated random variables for each model the structure of the marginal densities moments and characteristic functions are evaluated truncated forms for the multivariate densities are proposed the error and percentage error due to truncation are evaluated numerically for the two dimensional case finally a signal detection problem is examined the performance of the optimal detector is compared to that achieved by the detector designed using truncated density functions it is shown that the performance difference is negligible when the model parameters are small

frequency domain identification with generalized orthonormal basis functions a method is considered for the identification of linear parametric models based on a least squares identification criterion that is formulated in the frequency domain to this end use is made of the empirical transfer function estimate etfe identified from time domain data as a parametric model structure use is made of a finite expansion sequence in terms of recently introduced generalized basis functions being generalizations of the classical pulse and laguerre and kautz types of bases an asymptotic analysis of the estimated models is provided and conditions for consistency are formulated explicit and transparent bias and variance expressions are established the latter ones also valid in a situation of undermodeling

space alternating generalized expectation maximization algorithm the expectation maximization em method can facilitate maximizing likelihood functions that arise in statistical estimation problems in the classical em paradigm one iteratively maximizes the conditional log likelihood of a single unobservable complete data space rather than maximizing the intractable likelihood function for the measured or incomplete data em algorithms update all parameters simultaneously which has two drawbacks 1 slow convergence and 2 difficult maximization steps due to coupling when smoothness penalties are used the paper describes the space alternating generalized em sage method which updates the parameters sequentially by alternating between several small hidden data spaces defined by the algorithm designer the authors prove that the sequence of estimates monotonically increases the penalized likelihood objective derive asymptotic convergence rates and provide sufficient conditions for monotone convergence in norm two signal processing applications illustrate the method estimation of superimposed signals in gaussian noise and image reconstruction from poisson measurements in both applications the sage algorithms easily accommodate smoothness penalties and converge faster than the em algorithms

brief paper choice of free parameters in expansions of discrete time volterra models using kautz functions this work tackles the problem of modeling nonlinear systems using volterra models based on kautz functions the drawback of requiring a large number of parameters in the representation of these models can be circumvented by describing every kernel using an orthonormal basis of functions such as the kautz basis the resulting model so called wiener volterra model can be truncated into a few terms if the kautz functions are properly designed the underlying problem is how to select the free design complex poles that fully parameterize these functions a solution to this problem has been provided in the literature for linear systems which can be represented by first order volterra models a generalization of such strategy focusing on volterra models of any order is presented in this paper this problem is solved by minimizing an upper bound for the error resulting from the truncation of the kernel expansion into a finite number of functions the aim is to minimize the number of two parameter kautz functions associated with a given series truncation error thus reducing the complexity of the resulting finite dimensional representation the main result is the derivation of an analytical solution for a sub optimal expansion of the volterra kernels using a set of kautz functions

iterative multiuser receivers for cdma channels an em based approach maximum likelihood detection for the multiuser code division multiple access cdma channel is prohibitively complex this paper considers new iterative multiuser receivers based on the expectation maximization em algorithm and related more powerful space alternating algorithms the latter algorithms include the sage algorithm and a new missing parameter space alternating algorithm that alternately updates individual parameter components or treats them as probabilistic missing data application of these em based algorithms to the problem of discrete parameter estimation i e data detection in the gaussian multiple access channel leads to a variety of convergent receiver structures that incorporate soft decision feedback for interference cancellation and or sequential updating of iterative bit estimates convergence and performance analyses are based on well known properties of the em algorithm and on numerical simulation

an adaptive spatial diversity receiver for non gaussian interference and noise standard linear diversity combining techniques are not effective in combating fading in the presence of non gaussian noise an adaptive spatial diversity receiver is developed for wireless communication channels with slow flat fading and additive non gaussian noise the noise is modeled as a mixture of gaussian distributions and the expectation maximization em algorithm is used to derive estimates for the model parameters the transmitted signals are detected using a likelihood ratio test based on the parameter estimates the new adaptive receiver converges rapidly its bit error rate performance is very close to optimum when relatively short training sequences are used and it appears to be relatively insensitive to mismatch between the noise model and the actual noise distribution simulation results are included that illustrate various aspects of the adaptive receiver performance

parametric identification of transfer functions in the frequency domain a survey this paper gives a survey of frequency domain identification methods for rational transfer functions in the laplace s or z domain the interrelations between the different approaches are highlighted through a study of the equivalent cost functions the properties of the various estimators are discussed and illustrated by several examples

identification of block oriented nonlinear systems starting from linear approximations a survey abstract block oriented nonlinear models are popular in nonlinear system identification because of their advantages of being simple to understand and easy to use many different identification approaches were developed over the years to estimate the parameters of a wide range of block oriented nonlinear models one class of these approaches uses linear approximations to initialize the identification algorithm the best linear approximation framework and the approximation framework or equivalent frameworks allow the user to extract important information about the system guide the user in selecting good candidate model structures and orders and prove to be a good starting point for nonlinear system identification algorithms this paper gives an overview of the different block oriented nonlinear models that can be identified using linear approximations and of the identification algorithms that have been developed in the past a non exhaustive overview of the most important other block oriented nonlinear system identification approaches is also provided throughout this paper

threshold detection in narrow band non gaussian noise the middleton class a narrow band non gaussian noise model 9 12 is examined it is shown that this noise model which is known to fit closely a variety of non gaussian noises can itself be closely approximated by a computationally much simpler noise model it is then shown by numerical examples that for the problem of locally optimum detection the simplest form of this approximation yields nearly optimal asymptotic performance the performance of other simple suboptimal threshold detectors in class a noise is also examined finally a useful relationship between the class a model and the e mixture model is developed

detection of random signals in gaussian mixture noise a locally optimal detection algorithm for random signals in dependent noise is derived and applied to independent identically distributed complex valued gaussian mixture noise the resulting detector is essentially a weighted sum of power detectors the power detector is the locally optimal detector for random signals in gaussian noise the weighting functions are modified to enhance the detection performance for small sample sizes an implementation of the mixture detector using the expectation maximization algorithm is described moments of these detectors are calculated from piecewise polynomial approximations of the weighting functions the sum of sufficiently many independent identically distributed detector outputs is then approximated by a normal distribution probability distributions are also derived for the power detector in gaussian mixture noise for a particular set of noise parameters the theoretical distributions are compared with those obtained from monte carlo simulation and seen to be quite close the theoretical distributions are then used to compare the performance of the mixture and power detectors in gaussian mixture noise over a range of parameters and to assess the impact of parameter error on detection performance in this study the signal gain of the mixture detectors varies from 15 to 38 db and the degradation of the probability of detection due to parameter estimation error is relatively minor

wiener system identification with generalized orthonormal basis functions many nonlinear systems can be described by a wiener schetzen model in this model the linear dynamics are formulated in terms of orthonormal basis functions obfs the nonlinearity is modeled by a multivariate polynomial in general an infinite number of obfs are needed for an exact representation of the system this paper considers the approximation of a wiener system with finite order infinite impulse response dynamics and a polynomial nonlinearity we propose to use a limited number of generalized obfs gobfs the pole locations needed to construct the gobfs are estimated via the best linear approximation of the system the coefficients of the multivariate polynomial are determined with a linear regression this paper provides a convergence analysis for the proposed identification scheme it is shown that the estimated output converges in probability to the exact output fast convergence rates in the order o p n f n r e p 2 can be achieved with n f the number of excited frequencies and n r e p the number of repetitions of the gobfs

identification of hammerstein wiener models this paper develops and illustrates a new maximum likelihood based method for the identification of hammerstein wiener model structures a central aspect is that a very general situation is considered wherein multivariable data non invertible hammerstein and wiener nonlinearities and colored stochastic disturbances both before and after the wiener nonlinearity are all catered for the method developed here addresses the blind wiener estimation problem as a special case

scaling analysis of the site diluted ising model in two dimensions a combination of recent numerical and theoretical advances are applied to analyze the scaling behavior of the site diluted ising model in two dimensions paying special attention to the implications for multiplicative logarithmic corrections the analysis focuses primarily on the odd sector of the model i e that associated with magnetic exponents and in particular on its lee yang zeros which are determined to high accuracy scaling relations are used to connect to the even thermal sector and a first analysis of the density of zeros yields information on the specific heat and its corrections the analysis is fully supportive of the strong scaling hypothesis and of the scaling relations for logarithmic corrections

incoherent receivers in alpha stable impulsive noise we compute an incoherent receiver for demodulation of signals with random phase in additive impulsive noise modeled as a bivariate isotropic cauchy process monte carlo simulation clearly shows that the proposed cauchy receiver has a significantly improved operating characteristic over the corresponding gaussian receiver moreover the cauchy receiver is very robust in the entire class of bivariate isotropic symmetric alpha stable impulsive noises

sequence estimation in the presence of random parameters via the em algorithm the expectation maximization em algorithm was first introduced in the statistics literature as an iterative procedure that under some conditions produces maximum likelihood hit parameter estimates in this paper we investigate the application of the em algorithm to sequence estimation in the presence of random disturbances and additive white gaussian noise as examples of the use of the em algorithm we look at the random phase and fading channels and show that a formulation of the sequence estimation problem based on the em algorithm can provide a means of obtaining ml sequence estimates a task that has been previously too complex to perform