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

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

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

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

parameter estimation for middleton class a interference processes the problem of estimating the parameters of the middleton class a interference model is considered on the assumption of the availability of a set of independent samples from class a envelope distribution the asymptotic performances of several estimation procedures are explored from this analysis estimates based on the method of moments are seen to be consistent and computationally desirable but highly inefficient whereas more efficient likelihood based estimators are seen to be computationally unwieldy however an estimator that initiates likelihood iteration with the method of moments estimates is seen to overcome these difficulties in its asymptotic performance unfortunately simulation of this third estimator for practical sample sizes reveals poor performance under these conditions to overcome this lack of small sample efficiency a similar estimator that initiates likelihood iteration with physically motivated but nonoptimal estimates is also proposed simulation of this latter estimator for practical sample sizes indicates that near optimal performance is attained by this technique

a statistical and physical mechanisms based interference and noise model for array observations a statistical noise model is developed from mathematical modeling of the physical mechanisms that generate noise in communication receivers employing antenna arrays such models have been lacking for cases where the antenna observations may be statistically dependent from antenna to antenna the model is developed by generalizing an approach for single antenna cases suggested by middleton 1967 1974 1976 1977 the model derived here is applicable to a wide variety of physical situations the focus is primarily on problems defined by middleton to be class a interference the number of noise sources in a small region of space is assumed to be poisson distributed and the emission times are assumed to be uniformly distributed over a long time interval finally an additive gaussian background component is included to represent the thermal noise that is always present in real receivers

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

robust subspace learning and detection in laplacian noise and interference we address the problem of maximum likelihood subspace learning and detection in the presence of laplacian noise and interference whose subspace may be known or unknown for subspace learning the laplacian problem reduces to a maxmin convex mathematical program with polyhedral cost the minimization involves projection of the measurements onto a subspace orthogonal to the signal and interference spaces and has linear constraints while the maximization produces the subspace and has polyhedral constraints the laplacian noise model for subspace detection and estimation motivated by applications in functional magnetic resonance imaging and applicable in other areas yields maximum likelihood detectors and learned subspaces with unique structure due to the presence of corners in the polyhedrally convex optimization for instance the optimal learned subspace can consist of vectors whose elements take values of 1 or 1 only emergence of such a quantization attests to the robustness property of laplacian learning meaning that the solution is insensitive to perturbation in the data set the resulting detectors are similarly robust to false alarms and have computationally attractive properties

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

performance of optimum and suboptimum receivers in the presence of impulsive noise modeled as an alpha stable process impulsive noise bursts in communication systems are traditionally handled by incorporating in the receiver a limiter which clips the received signal before integration an empirical justification for this procedure is that it generally causes the signal to noise ratio to increase recently very accurate models of impulsive noise were presented based on the theory of symmetric spl alpha stable probability density functions we examine the performance of optimum receivers designed to detect signals embedded in impulsive noise which is modeled as an infinite variance symmetric spl alpha stable process and compare it against the performance of several suboptimum receivers as a measure of receiver performance we compute an asymptotic expression for the probability of error for each receiver and compare it to the probability of error calculated by extensive monte carlo simulation

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

analysis of multiscale products for step detection and estimation we analyze discrete wavelet transform dwt multiscale products for detection and estimation of steps here the dwt is an over complete approximation to smoothed gradient estimation with smoothing varied over dyadic scale as developed by mallat and zhong 1992 the multiscale product approach was first proposed by rosenfeld 1970 for edge detection we develop statistics of the multiscale products and characterize the resulting non gaussian heavy tailed densities the results may be applied to edge detection with a false alarm constraint the response to impulses steps and pulses is also characterized to facilitate the analysis we employ a new general closed form expression for the cramer rao bound crb for discrete time step change location estimation the crb can incorporate any underlying continuous and differentiable edge model including an arbitrary number of steps the crb analysis also includes sampling phase offset effects and is valid in both additive correlated gaussian and independent and identically distributed i i d non gaussian noise we consider location estimation using multiscale products and compare results to the appropriate crb

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

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

the application of fuzzy control theory to an oil fueled annealing furnace abstract what makes the control of an oil fueled annealing furnace difficult is that the coil weight and coil size differ from charge and the least characteristics of the furnace vary constantly with temperature that is to say the process parameters of the furnace are always changing furthermore the process in non linear and noisy with pure time delay it is obviously difficult to apply modern control theory to such a process control in this paper the author adopts fuzzy control methods to control the furnace a modified fuzzy controller is used to control the temperature and pressure and a fuzzy self searching optimal controller is designed to regulate the fuel air ratio required for a rational combustion the operation run of this system shows that it has a good robustness and a satisfactory accuracy the energy saved by this system is considerable

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

non standard h control problem a generalized chain scattering representation approach the non standard h x control problem is the case where the direct feedthroughs from the input to the error and from the exogenous signal to the output are not necessarily of full rank in this paper this problem is reformulated based on the generalized chain scattering representation gcsr the gcsr approach leads naturally to a generalization of the homographic transformation the state space realization for this generalized homographic transformation and a number of fundamental cascade structures of the h x control systems are further studied in a unified framework of gcsr certain sufficient conditions for the solvability of the non standard h x control problem are therefore established via a j j lossless factorization of gcsr these results present extensions to kimura s results on the chain scattering representation csr approach to the h x control in the standard case

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