α stable interference modeling and cauchy receiver for an ir uwb ad hoc network in this paper we investigate ad hoc networks based on impulse radio ultra wideband due to multiple access the interference distribution is not gaussian one important reason for errors is the presence of close interferers generating pulse collision however such events are rare and we propose an stable model compatible with this fact due to its heavy tailed distribution we derive the analytical expression of the two significant parameters they depend on the attenuation coefficient the users density the pulse collision probability and the pulse shape we finally propose receiver strategies cauchy receiver and p norm that outperforms the classical gaussian receiver

relation of signal set choice to the performance of optimal non gaussian detectors the optimal procedure for detecting the presence of discrete time signals in additive noise can be derived from the likelihood ratio test when the noise has statistically independent identically distributed components the dependence of the detector s performance on signal characteristics can be related to the kullback leibler kl distance between the distributions governing the hypotheses performance predictions based on the central limit theorem are shown to be poor approximations to the true performance performance of the optimal detector has long been known to increase exponentially with increasing kl distance symmetric noise amplitude distributions yield a symmetric dependence on the difference between the signals amplitudes at each time index small signal locally optimal detection performance is shown to depend on signal energy whereas large signal performance depends on the signal waveform when a distance measure can be defined performance depends on a different measure than that used in the detector with one exception the gaussian

uwb receiver designs based on a gaussian laplacian noise plus mai model a more appropriate statistical model for the multiple access interference than the generally used gaussian approximation is proposed to reflect the heavy tailed nature of the multiple access interference in ultra wide bandwidth systems novel receiver structures which surpass the performance of the conventional matched filter receiver are studied for ultrawide bandwidth multiple access communications in both awgn and fading multipath channels a proposed rake receiver is advantageous over the conventional rake receiver when multiuser interference dominates ambient gaussian noise and originates from a small to moderate number of interferers explanation is provided for the inaccuracy of a gaussian approximation with regard to the multiple access interference and the heavy tailed nature of the probability density function of the multiple access interference is also discussed

recursive algorithms for identification of impulse noise channels the class a middleton model is a widely accepted statistical physical parameteric model for impulsive interference superimposed on a gaussian background in the present work a recursive decision directed estimator for online identification of the parameters of the class a model is proposed this estimator is based on an adaptive bayesian classification of each of a sequence of class a envelope samples as an impulsive sample or as a background sample as each sample is so classified recursive updates of the estimates of the second moment of the background component of the interference envelope density the second moment of the impulsive component of the interference envelope density and the probability with which the impulsive component occurs are readily obtained from these estimates estimates of the parameters of the class a model follow straightforwardly since closed form expressions for the parameters exist in terms of these quantities the performance characteristics of this algorithm are investigated and an appropriately modified version is found to yield a recursive algorithm with excellent global performance

efficient estimation of class a noise parameters via the em algorithm the class a middleton noise model is a commonly used statistical physical parametric model for non gaussian interference superimposed on a gaussian background in this study the problem of efficient estimation of the class a parameters for small sample sizes is considered the proposed estimator is based on the em algorithm a two step iterative estimation technique that is ideally suited for the class a estimation problem since the observations can be readily treated as incomplete data for the single parameter estimation problem a closed form expression for the estimator is obtained furthermore for the single parameter estimation problem it is shown that the sequence of estimates obtained via the em algorithm converges and a characterization of the point to which the sequence converges is given in particular it is shown that if the limit point of this convergent sequence is an interior point of the parameter set of interest then it must be a stationary point of the traditional likelihood function in addition for both the single parameter and two parameter estimation problems the small sample size performance of the proposed em algorithm is examined via an extensive simulation study

a general weighted median filter structure admitting negative weights weighted median smoothers which were introduced by edgemore in the context of least absolute regression over 100 years ago have received considerable attention in signal processing during the past two decades although weighted median smoothers offer advantages over traditional linear finite impulse response fir filters it is shown in this paper that they lack the flexibility to adequately address a number of signal processing problems in fact weighted median smoothers are analogous to normalized fir linear filters constrained to have only positive weights it is also shown that much like the mean is generalized to the rich class of linear fir filters the median can be generalized to a richer class of filters admitting positive and negative weights the generalization follows naturally and is surprisingly simple in order to analyze and design this class of filters a new threshold decomposition theory admitting real valued input signals is developed the new threshold decomposition framework is then used to develop fast adaptive algorithms to optimally design the real valued filter coefficients the new weighted median filter formulation leads to significantly more powerful estimators capable of effectively addressing a number of fundamental problems in signal processing that could not adequately be addressed by prior weighted median smoother structures

on the relationship between measures of discrimination and the performance of suboptimal detectors the problem of designing and analyzing suboptimal detectors via statistical distance measures is considered as a preliminary result we show that only the minimum and maximum probability of error are valid measures of discrimination between the input statistics this result would seem then to imply that the use of distance measures in this context can be inappropriate however to overcome this apparent obstacle we demonstrate explicit relationships between various f divergences and the loss in performance of an arbitrary detector relative to the optimal detector in particular we establish both upper and lower bounds on the performance loss of a suboptimal detector in terms of the distance between the pertinent statistics of both the optimal and suboptimal detectors while designing detectors by minimizing these upper bounds can be an elusive task in many practical cases the lower bound presented herein holds with equality in this case minimizing the separation of the output statistics of the detector with respect to a particular f divergence equivalently minimizes the resulting probability of error of the detector to facilitate design other researchers have established conditions under which one may design arbitrary detection strategies with respect to a specific f divergence kullback leibler distance being a principal example we extend this approach by deriving necessary and sufficient conditions under which one may design detection strategies with respect to an arbitrarily chosen f divergence thus when these conditions are met one may optimize a detector with respect to the most analytically tractable distance measure to obtain the minimum probability of error detector over a selected class of detection strategies examples demonstrating the utility of this theory for the problem of designing optimal linear detectors and optimal signal sets are presented

robust frequency selective filtering using weighted myriad filters admitting real valued weights weighted myriad smoothers have been proposed as a class of nonlinear filters for robust non gaussian signal processing in impulsive noise environments however weighted myriad smoothers are severely limited since their weights are restricted to be non negative this constraint makes them unusable in bandpass or highpass filtering applications that require negative filter weights further they are incapable of amplifying selected frequency components of an input signal in this paper we generalize the weighted myriad smoother to a richer structure a weighted myriad filter admitting real valued weights this involves assigning a pair of filter weights one positive and the other negative to each of the input samples equivalently the filter can be described as a weighted myriad smoother applied to a transformed set of samples that includes the original input samples as well as their negatives the weighted myriad filter is analogous to a normalized linear fir filter with real valued weights whose absolute values sum to unity by suitably scaling the output of the weighted myriad filter we extend it to yield the so called scaled weighted myriad filter which includes but is more powerful than the traditional unconstrained linear fir filter finally we derive stochastic gradient based nonlinear adaptive algorithms for the optimization of these novel myriad filters under the mean square error criterion

locally optimal detection of image watermarks in the wavelet domain using bessel k form distribution a uniformly most powerful watermark detector which applies the bessel k form bkf probability density function to model the noise distribution was proposed by bian and liang in this paper we derive a locally optimum lo detector using the same noise model since the literature lacks thorough discussion on the performance of the bkf lo nonlinearities the performance of the proposed detector is discussed in detail first we prove that the test statistic of the proposed detector is asymptotically gaussian and evaluate the actual performance of the proposed detector using the receiver operating characteristic roc then the large sample performance of the proposed detector is evaluated using asymptotic relative efficiency are and maximum are the experimental results show that the proposed detector has a good performance with or without attacks in terms of its roc curves particularly when the watermark is weak therefore the proposed method is suitable for wavelet domain watermark detection particularly when the watermark is weak

on the finiteness of the capacity of continuous channels evaluating the channel capacity is one of many key problems in information theory in this work we derive rather mild sufficient conditions under which the capacity of continuous channels is finite and achievable these conditions are derived for generic memoryless and possibly nonlinear additive noise channels the results are based on a novel sufficient condition that guarantees the convergence of differential entropies under point wise convergence of probability density functions perhaps surprisingly the finiteness of channel capacity holds for the majority of setups including those where inputs and outputs have possibly infinite second moments

probability density of the empirical wavelet coefficients of a noisy chaos we are interested in the random empirical wavelet coefficients of a noisy signal when this signal is a unidimensional or multidimensional chaos more precisely we provide an expression of the conditional probability density of such coefficients given a discrete observation grid the noise is assumed to be described by a symmetric alpha stable random variable if the noise is a dynamic noise then we present the exact expression of the probability density of each wavelet coefficient of the noisy signal if we face a measurement noise then the noise has a non linear influence and we propose two approximations the first one relies on a taylor expansion whereas the second one relying on an edgeworth expansion improves the first general taylor approximation if the cumulants of the noise are defined we give some illustrations of these theoretical results for the logistic map the tent map and a multidimensional chaos the henon map disrupted by a gaussian or a cauchy noise

robust parameter estimation of a deterministic signal in impulsive noise this paper presents a robust class of estimators for the parameters of a deterministic signal in impulsive noise the proposed technique has the structure of the maximum likelihood estimator mle but has an extra degree of freedom the choice of a nonlinear function which is different from the score function suggested by the mle that can be adjusted to improve robustness the effect of this nonlinear function is studied analytically via an asymptotic performance analysis we investigate the covariance of the estimates and the loss of efficiency induced by nonoptimal choices of the nonlinear function giving special attention to the case of spl alpha stable noise finally we apply the theoretical results to the problem of estimating the parameters of a sinusoidal signal in impulsive noise

performance analysis of ldpc coded diversity combining on rayleigh fading channels with impulsive noise spatial diversity is an effective method to mitigate the effects of fading and when used in conjunction with low density parity check ldpc codes it can achieve excellent error correcting performance noise added at each branch of the diversity combiner is generally assumed to be additive white gaussian noise but there are many applications where the received signal is impaired by noise with a non gaussian distribution in this paper we derive the exact bit error probability of different linear combining techniques on rayleigh fading channels with impulsive noise which is modeled using symmetric alpha stable distributions the relationship for the signal to noise ratios of these linear combiners is derived and then different non linear detectors are presented a detector based on the bi parameter cauchy gaussian mixture model is used and shows near optimal performance with a significant reduction in complexity when compared with the optimal detector furthermore the threshold signal to noise ratio of ldpc codes for different combining techniques on these channels is derived using density evolution and an estimation of the waterfall performance of ldpc codes is derived that reduces the gap between simulated and asymptotic performance

adaptive weighted myriad filter algorithms for robust signal processing in spl alpha stable noise environments stochastic gradient based adaptive algorithms are developed for the optimization of weighted myriad filters wmyfs wmyfs form a class of nonlinear filters motivated by the properties of spl alpha stable distributions that have been proposed for robust non gaussian signal processing in impulsive noise environments the weighted myriad for an n long data window is described by a set of nonnegative weights w sub i sub i l sup n and the so called linearity parameter k 0 in the limit as k spl rarr spl infin the filter reduces to the familiar weighted mean filter which is a constrained linear fir filter necessary conditions are obtained for optimality of the filter weights under the mean absolute error criterion an implicit formulation of the filter output is used to find an expression for the gradient of the cost function using instantaneous gradient estimates an adaptive steepest descent algorithm is then derived to optimize the weights this algorithm involves a very simple update term that is computationally comparable to the update in the classical lms algorithm the robust performance of this adaptive algorithm is demonstrated through a computer simulation example involving lowpass filtering of a one dimensional chirp type signal in impulsive noise

a multidimensional class b noise model based on physical and mathematical analysis class b noise is an important interference in the telecommunication applications in this paper a multidimensional model for class b noise observed at antenna arrays is developed in physical and mathematical analysis the model proposed is considered on both the explicit source distribution and propagation laws i e scenario explicit s e cases an additive white gaussian noise component arising in both internal system and external interferences is also considered in our model finally the joint characteristic function of class b noise is derived and the probability density function is obtained through the fourier transform

ell _ p music robust direction of arrival estimator for impulsive noise environments a family of algorithms named lp music for direction of arrival doa estimation in impulsive noise is proposed the lp music estimator adopts the lp norm 1 p 2 of the residual fitting error matrix as the objective function for subspace decomposition rather than the frobenius norm that is used in the conventional music method although the matrix lp norm minimization based subspace decomposition will lead to a nonconvex optimization problem two iterative algorithms are designed for achieving efficient solutions the first algorithm is the iteratively reweighted singular value decomposition ir svd where the svd of a reweighted data matrix is performed in each iteration the second algorithm solves the nonconvex matrix lp norm minimization by alternating convex optimization two complex valued newton s methods with optimal step size in each iteration are devised to solve the resulting convex problem the convergence of the iterative procedure is also proved numerical results verify that the lp music methodology outperforms the standard music scheme and several existing outlier resistant doa estimation approaches in terms of resolution capability and estimation accuracy

myriad type polynomial filtering linear combinations of polynomial terms yield poor performance in environments characterized by heavy tailed distributions weighted myriad wmy filters however are well known for their outlier suppression and detail preservation properties it is shown here that the wmy methodology is naturally extended to the polynomial sample case yielding filter structures that exploit the higher order statistics of the observed samples while simultaneously being robust to outliers for heavy tailed distributions environments moreover the introduced power weighted myriad pwmy filter class is well motivated by analysis of cross and square term statistics of heavy tailed distributions the effectiveness of the proposed filter is evaluated through simulations

a geometrical characterization of banach spaces in which martingale difference sequences are unconditional we study banach space valued martingale transforms and in particular characterize those banach spaces for which the classical theorems of the real valued case carry over for example if b is a banach space and 1 0 and zeta x y leq x y text if x leq 1 leq y

stochastic calculus with anticipating integrands we study the stochastic integral defined by skorohod in 24 of a possibly anticipating integrand as a function of its upper limit and establish an extended ito formula we also introduce an extension of stratonovich s integral and establish the associated chain rule in all the results the adaptedness of the integrand is replaced by a certain smoothness requirement

spectral measure of the harmonic oscillator with α stable noise we study the coordinate velocity couple of the harmonic oscillator with stable noise as previously shown by sokolov et al the distribution of this couple is bivariate stable in this work we determine explicitly its associated spectral measure exhibiting directly both the non independence and non ellipticity of the coordinate velocity couple knowledge of the spectral measure allows to analyze and quantify the deviation from ellipticity

hybrid polynomial filters for gaussian and non gaussian noise environments traditional polynomial filtering theory based on linear combinations of polynomial terms is able to approximate important classes of nonlinear systems the linear combination of polynomial terms however yields poor performance in environments characterized by gaussian and heavy tailed distributions weighted median and weighted myriad filters in contrast are well known for their outlier suppression and detail preservation properties it is shown here that the weighted median and weighted myriad methodologies are naturally extended to the polynomial sample case yielding hybrid filter structures that exploits the higher order statistics of the observed samples while simultaneously being robust to outliers for both gaussian and heavy tailed distributions environments moreover the introduced hybrid polynomial filter classes are well motivated by analysis of cross and square term statistics of gaussian and heavy tailed distributions a presented asymptotic tail mass analysis shows that polynomial terms both under gaussian and heavy tailed noise statistics have heavier tails than the observed samples indicating that robust combination methods should be utilized to avoid undue influence of outliers further analysis shows weighted median processing of polynomial terms for the gaussian noise case and weighted median and weighted myriad processing of cross and square terms respectively for the heavy tailed noise case are justified from a maximum likelihood perspective filters parameter optimization procedures are also presented finally the effectiveness of hybrid filters is demonstrated through simulations that include temporal spectrum and bispectrum analysis

a new consensus ranking approach for correlated ordinal information based on mahalanobis distance the cohesiveness among experts opinions is addressed from a global point of view a new procedure to codify ordinal information is provided and characterized a measurement of the degree of dissensus designed for possibly correlated alternatives is defined a procedure to obtain a social consensus solution based on the mahalanobis distance is investigated we investigate from a global point of view the existence of cohesiveness among experts opinions we address this general issue from three basic essentials the management of experts opinions when they are expressed by ordinal information the measurement of the degree of dissensus among such opinions and the achievement of a group solution that conveys the minimum dissensus to the experts group accordingly we propose and characterize a new procedure to codify ordinal information we also define a new measurement of the degree of dissensus among individual preferences based on the mahalanobis distance it is especially designed for the case of possibly correlated alternatives finally we investigate a procedure to obtain a social consensus solution that also includes the possibility of alternatives that are correlated in addition we examine the main traits of the dissensus measurement as well as the social solution proposed the operational character and intuitive interpretation of our approaches are illustrated by an explanatory example

detection of unknown signals under complex elliptically symmetric distributions detection of unknown signals is considered under complex elliptically symmetric ces distributions a wide family that includes several well known distributions as special cases we study the detection problem for unknown deterministic signals and random ces signals both corrupted by ces noise for detection of unknown deterministic signals we form the generalized likelihood ratio test and reduce it to a sufficient test statistic which is either the norm of the received vector or a function of it performance analysis is provided under both known and estimated noise scatter matrix for detection of random ces signals we form the likelihood ratio test provide performance analysis and establish conditions under which the sufficient test statistic is given by the norm of the received vector interestingly this norm test statistic is proven to be the uniformly most powerful test for the detection of all ces distributed signals

quasi sure analysis and stratonovich anticipative stochastic differential equations consider a stochastic differential equation on d with smooth and bounded coefficients we apply the techniques of the quasi sure analysis to show that this equation can be solved pathwise out of a slim set furthermore we can restrict the equation to the level sets of a nondegenerate and smooth random variable and this provides a method to construct the solution to an anticipating stochastic differential equation with smooth and nondegenerate initial condition

accurate evaluation of multiple access performance in th ppm and th bpsk uwb systems a characteristic function method is proposed for precisely calculating the bit error probability of time hopping th ultra wideband uwb systems with multiple access interference in an additive white gaussian noise environment the analytical expressions are validated by simulation and used to assess the accuracy of the gaussian approximation the gaussian approximation is shown to be inaccurate for predicting bit error rates bers for medium and large signal to noise ratio snr values the performances of th pulse position modulation ppm and binary phase shift keying bpsk modulation schemes are accurately compared in terms of the ber it is shown that the bpsk system outperforms the binary ppm system for all values of snr the sensitivity of the performance of the modulation schemes to the system parameters is also addressed through numerical examples

beamforming via nonconvex linear regression impulsive processes frequently occur in many fields such as radar sonar communications audio and speech processing and biomedical engineering in this paper we propose a nonconvex linear regression nlr based minimum dispersion beamforming technique for impulsive signals to achieve significant performance improvement over the conventional minimum variance beamformer the proposed beamformer minimizes the ell p norm of the output with p subject to a linear distortionless response constraint resulting in a difficult nonconvex and nonsmooth optimization problem the constrained optimization problem is first reduced to a multivariate linear regression via constraint elimination as a major contribution of this paper a coordinate descent algorithm cda is devised for solving the resultant nlr problem of ell p minimization with p at a computational complexity of cal o mn 2 where m is the number of sensors and n is the sample size at each inner iteration of the cda an efficient algorithm is designed to find the global minimum of each subproblem of univariate linear regression the convergence of the cda is analyzed the nlr beamformer with a single constraint is further generalized to the case of multiple linear constraints which is robust against model mismatch simulation results demonstrate the superior performance of nonconvex optimization based beamformer

robust gaussian and non gaussian matched subspace detection we address the problem of matched filter and subspace detection in the presence of arbitrary noise and interference or interfering signals that may lie in an arbitrary unknown subspace of the measurement space a minmax methodology developed to deal with this uncertainty can also be adapted to situations where partial information on the interference or other uncertainties is available this methodology leads to a hypothesis test with adequate levels of false alarm robustness and signal detection sensitivity the robust test is applicable to a large class of noise density functions in addition generalized likelihood ratio glr detectors are derived for the class of generalized gaussian noise the detectors are generalizations of the spl chi sup 2 t and f statistics used with gaussian noise which are themselves motivated in a new way by the robust test for matched filter detection these expressions are simpler and computationally efficient the robust test reduces to the conventional test when unlearned subspace interference is known to be absent the results demonstrate that when compared with the conventional detector the robust one trades off some detection performance in the absence of interference for the sake of robustness in its presence

a nonparametric approach to signal detection in impulsive interference impulsive interference poses a challenge to conventional detection techniques the spl alpha stable distribution while sometimes providing a good model for impulsive interference has proven to be no exception some of these difficulties have motivated the investigation and development of computationally tractable locally suboptimum correlation and rank correlation detectors for signals embedded in impulsive interference modeled as a symmetric spl alpha stable process the performance of some of these detectors is evaluated and compared with that of the locally optimum lo locally optimum rank lor matched filter and cauchy detectors simulation results show that a rank based detector is able to approach the performance of the computationally intensive lo and lor detectors across a range of values for for spl alpha

expansions of the likelihood ratio and applications the likelihood ratio receiver although optimal is oftentimes difficult to realize to overcome this difficulty suboptimal approximations have been studied in the past one of the simplest approaches is to expand the likelihood ratio and truncate this expansion under the weak signal assumption in this paper we first study the relations between the taylor expansion and the volterra expansion under a weak signal assumption we emphasize the links between the taylor expansion with respect to the snr and the detection criteria on one hand and with robustness on the other in particular using two criteria derived from deflection we show that the minimax robust filter is the matched filter finally an application to underwater signal detection is studied showing that the degradation resulting from the use of the locally optimal receiver is small

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

representation and generation of non gaussian wide sense stationary random processes with arbitrary psds and a class of pdfs a new method for representing and generating realizations of a wide sense stationary non gaussian random process is described the representation allows one to independently specify the power spectral density and the first order probability density function of the random process the only proviso is that the probability density function must be symmetric and infinitely divisible the method proposed models the sinusoidal component frequencies as random variables a key departure from the usual representation a of wide sense stationary random process by the spectral theorem ergodicity in the mean and autocorrelation is also proven under certain conditions an example is given to illustrate its application to the k distribution which is important in many physical modeling problems in radar and sonar

a parametric approach to suboptimal signal detection in alpha stable noise this paper deals with the detection of a known deterministic signal embedded in alpha stable noise the implementation of the optimal receiver requires the explicit expression of the probability density function pdf of the noise unfortunately since there exists no closed form for the pdf of alpha stable distributed random variables numerical integrations are required to avoid such numerical approximations we suggest a low complexity parametric suboptimal detector well matched to essential properties of alpha stable noises this receiver does not require the explicit expression of the noise pdf in addition parameter optimization is fast for several optimization criteria and the selected receiver allows retrieval of the optimal gaussian detector matched filter as well as the locally optimal detector in the cauchy context the performance of the detector is studied and a comparison with the optimal solution along with a variety of classical detectors is given the robustness of the detector against the signal amplitude and the stability index alpha of the noise is discussed

quasi sure analysis of stochastic flows and banach space valued smooth functionals on the wiener space abstract we prove meyer s inequalities for functionals on the wiener space that take values on a banach space belonging to the burkbolder u m d class as an application we analyse the quasi sure regularity in time of the stochastic flow of diffeomorphisms generated by a stochastic differential equation with smooth coefficients

linear detection of a weak signal in additive cauchy noise the detection of a weak signal in additive cauchy noise is of great importance in many applications a locally optimum detector lod exists for such a scenario however it is non linear in nature in general implementation of non linear detectors is difficult in practice and linear detectors with good properties such as high asymptotic relative efficiency are with respect to the lod are often desirable in this paper we propose a linear detector for a weak signal in additive cauchy noise the proposed test statistic is a linear combination of order statistics for the special case of a constant signal in additive cauchy noise we prove the asymptotic normality of the trimmed linear detector and show that the are of the trimmed linear detector with respect to the lod is unity extensive simulation results are provided to demonstrate that the loss in the performance of the linear detector is very small compared with the non linear lod we also discuss the hardware complexities of the lod and the linear detector and demonstrate the advantages of the linear detector over the lod in terms of hardware implementation

the ber optimal linear rake receiver for signal detection in symmetric alpha stable noise the optimal linear rake receiver for the detection of signals contaminated by symmetric alpha stable noise is derived for 1 2 although this structure is suboptimal it is optimal among the class of linear rake receivers in the sense of minimizing the bit error rate the proposed receiver is a very simple form of diversity combiner for signal detection in symmetric alpha stable noise the bit error rate improvements of the optimal linear rake receiver over the maximal ratio combiner and the equal gain combiner are also derived in the form of signal to noise ratio advantage

weighted iterative truncated mean filter the iterative truncated arithmetic mean itm filter was proposed recently it offers a way to estimate the sample median by simple arithmetic computing instead of the time consuming data sorting in this paper a rich class of filters named weighted itm witm filters are proposed by iteratively truncating the extreme samples the output of the witm filter converges to the weighted median proper stopping criterion makes the witm filters own merits of both the weighted mean and median filters and hence outperforms the both in some applications three structures are designed to enable the witm filters being low band and high pass filters properties of these filters are presented and analyzed experimental evaluations are carried out on both synthesis and real data to verify some properties of the witm filters

a new adaptive center weighted median filter for suppressing impulsive noise in images in this work a new adaptive center weighted median acwm filter is proposed for improving the performance of median based filters preserving image details while effectively suppressing impulsive noise the proposed filter is an adaptive cwm filter with an adjustable central weight obtained by partitioning the observation vector space to obtain the optimal weight for each block the efficient scalar quantization sq method is used to partition the observation vector space the center weight within each block is obtained by using a learning approach based on the least mean square lms algorithm the noise filtering procedure is progressively applied through several iterations so that the mean square error of the output can be minimized experimental results have demonstrated that the proposed filter outperforms many well accepted median based filters in terms of both noise suppression and detail preservation the proposed new filter also provides excellent robustness at various percentages of impulsive noise

sub optimum receiver architecture for awgn channel with symmetric alpha stable interference in many scenarios the undesirable disturbance at a communication receiver has to be modeled as the sum of gaussian noise and impulsive interference for which closed form probability density function pdf generally does not exist this makes optimum receiver implementation difficult in this paper motivated by the heavy tail nature of the resultant pdf an alternate parametric solution is proposed after estimation of the appropriate parameters the alternate solution may then be written in closed form leading to a relatively simple architecture simulation results show that the proposed receiver performance in terms of bit error rate ber is almost indistinguishable from the optimum receiver while outperforming other sub optimum receivers noise parameter estimation using empirical characteristic functions is also discussed

optimality of the myriad filter in practical impulsive noise environments linear filtering theory has been largely motivated by the characteristics of gaussian signals in the same manner the proposed myriad filtering methods are motivated by the need for a flexible filter class with high statistical efficiency in non gaussian impulsive environments that can appear in practice we introduce several important properties of the myriad filter and prove its optimality in the family of spl alpha stable distributions

euler maruyama approximations for sdes with non lipschitz coefficients and applications abstract in this paper euler maruyama approximation for sde with non lipschitz coefficients is proved to converge uniformly to the solution in l p space with respect to the time and starting points as an application we also study the existence of solution and large deviation principle for anticipative sde with random initial condition

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

locally optimum bayes detection in ergodic markov noise the locally optimum bayes theory of signal detection in non gaussian noise interference environments is extended to include ergodic markov noise models under mild regularity assumptions on the conditional probability density functions the proposed method expresses the log likelihood ratio under the null hypothesis via martingale limit theory as a locally asymptotically normal likelihood ratio which yields under the implied condition of contiguity the statistics of the detection algorithm under the alternative hypothesis thus optimum detection algorithms in both coherent and incoherent cases are obtained which are canonical in signal waveform and noise statistics and which have the desired property of asymptotic optimality acceptably small error probabilities as sample size becomes necessarily large while the terms in the taylor expansion of the log likelihood ratio about the null signal remain fixed furthermore locally optimum detection structures in gauss markov noise are given together with a specific example in the coherent mode of reception in order to demonstrate the significant improvement in performance obtained over independent sampling

fast adaptation and performance characteristics of fir wos hybrid filters fast adaptive algorithms are developed for training weighted order statistic wos filters and fir wos hybrid fwh filters under the mean absolute error mae criterion these algorithms are based on the threshold decomposition of real valued signals introduced in this paper with this method an n length wos filter can be implemented by thresholding the input signals at most n times independent of the accuracy used beside saving in computations the proposed algorithms can be applied to process arbitrary real valued signals directly performance characteristics of fwh filters in 1 d and 2 d signal restoration are investigated through computer simulations we show that both in restoration of signals containing edges and in the case of heavy tailed nongaussian noise considerable improvement in performance can be achieved with fwh filters over wos filters ll filters and adaptive linear filters two new fwh filter design strategies are found for removal of impulsive noise and for restoration of a square wave respectively

a general class of nonlinear normalized adaptive filtering algorithms the normalized least mean square nlms algorithm is an important variant of the classical lms algorithm for adaptive linear filtering it possesses many advantages over the lms algorithm including having a faster convergence and providing for an automatic time varying choice of the lms stepsize parameter that affects the stability steady state mean square error mse and convergence speed of the algorithm an auxiliary fixed step size that is often introduced in the nlms algorithm has the advantage that its stability region step size range for algorithm stability is independent of the signal statistics in this paper we generalize the nlms algorithm by deriving a class of nonlinear normalized lms type nlms type algorithms that are applicable to a wide variety of nonlinear filter structures we obtain a general nonlinear nlms type algorithm by choosing an optimal time varying step size that minimizes the next step mse at each iteration of the general nonlinear lms type algorithm as in the linear case we introduce a dimensionless auxiliary step size whose stability range is independent of the signal statistics the stability region could therefore be determined empirically for any given nonlinear filter type we present computer simulations of these algorithms for two specific nonlinear filter structures volterra filters and the previously proposed class of myriad filters these simulations indicate that the nlms type algorithms in general converge faster than their lms type counterparts

optimality of operator like wavelets for representing sparse ar 1 processes the discrete cosine transform dct is known to be asymptotically equivalent to the karhunen loeve transform klt of gaussian first order auto regressive ar 1 processes since being uncorrelated under the gaussian hypothesis is synonymous with independence it also yields an independent component analysis ica of such signals in this paper we present a constructive non gaussian generalization of this result the characterization of the optimal orthogonal transform ica for the family of symmetric alpha stable ar 1 processes the degree of sparsity of these processes is controlled by the stability parameter 0 with the only non sparse member of the family being the classical gaussian ar 1 process with alpha 2 specifically we prove that for alpha a fixed family of operator like wavelet bases systematically outperforms the dct in terms of compression and denoising ability the effect is quantified with the help of two performance criteria one based on the kullback leibler divergence and the other on stein s formula for the minimum estimation error that can also be viewed as statistical measures of independence finally we observe that for the sparser kind of processes with 0 the operator like wavelet basis as dictated by linear system theory is undistinguishable from the ica solution obtained through numerical optimization our framework offers a unified view that encompasses sinusoidal transforms such as the dct and a family of orthogonal haar like wavelets that is linked analytically to the underlying signal model

meridian filtering for robust signal processing a broad range of statistical processes is characterized by the generalized gaussian statistics for instance the gaussian and laplacian probability density functions are special cases of generalized gaussian statistics moreover the linear and median filtering structures are statistically related to the maximum likelihood estimates of location under gaussian and laplacian statistics respectively in this paper we investigate the well established statistical relationship between gaussian and cauchy distributions showing that the random variable formed as the ratio of two independent gaussian distributed random variables is cauchy distributed we also note that the cauchy distribution is a member of the generalized cauchy distribution family recently proposed myriad filtering is based on the maximum likelihood estimate of location under cauchy statistics an analogous relationship is formed here for the laplacian statistics as the ratio of laplacian statistics yields the distribution referred here to as the meridian interestingly the meridian distribution is also a member of the generalized cauchy family the maximum likelihood estimate under the obtained statistics is analyzed motivated by the maximum likelihood estimate under meridian statistics meridian filtering is proposed the analysis presented here indicates that the proposed filtering structure exhibits characteristics more robust than that of median and myriad filtering structures the statistical and deterministic properties essential to signal processing applications of the meridian filter are given the meridian filtering structure is extended to admit real valued weights utilizing the sign coupling approach finally simulations are performed to evaluate and compare the proposed meridian filtering structure performance to those of linear median and myriad filtering

a method for measuring consensus within groups this paper presents a new index of disagreement or measure of consensus for comparison of data collected using likert items this new index which assesses the level of disagreement among group members exploits the conditional distribution of the variance for a given mean the variance is often used as a measure of disagreement with high variance seen as a high disagreement in a group however since the range of the variance is a function of the mean this implies that for a mean close to the end points of the scale the range of the variance is relatively small and for a mean at the center of the scale the range of the variance is larger the index of disagreement introduced in this paper takes into account both the mean and the variance and provides a way to compare two groups that is more meaningful than just considering the variance or other measures of disagreement or consensus that only depend on the variance

stable non gaussian random processes stochastic models with infinite variance stable random variables on the real line multivariate stable distributions stable stochastic integrals dependence structures of multivariate stable distributions non linear regression complex stable stochastic integrals and harmonizable processes self similar processes chentsov random fields introduction to sample path properties boundedness continuity and oscillations measurability integrability and absolute continuity boundedness and continuity via metric entropy integral representation historical notes and extensions

detection of weak signals in non gaussian noise a locally optimum detector structure is derived for the detection of weak signals in non gaussian environments optimum performance is obtained by employing a zero memory nonlinearity prior to the matched filter that would be optimum for detecting the signal were the noise gaussian the asymptotic detection performance of the locally optimum detector under non gaussian conditions is derived and compared with that for the corresponding detector optimized for operations in gaussian noise numerical results for the asymptotic detection performance are shown for signal detection in noise environments of practical interest

optimum quantization for detection vector quantization is a procedure widely used in communications the problem has been solved for the basic detection situation using the locally optimal procedure and with some constraints on the quantization scheme it is stated in its widest sense which consists of finding the partition of the observation space and the values associated with it in such a way that the detection performance is optimal it is solved completely with the deflection criterion and the solution introduces the concept of quantization by a likelihood ratio procedure

a dynamic consensus scheme based on a nonreciprocal fuzzy preference relation modeling in this paper we propose a dynamical consensus scheme which makes use of an index of comparability and of an index of concordance to regulate the information flow in the discussion among the experts in addition to the traditional use of a concordance index to identify the discordant expert who can be invited to review his opinion or to explain his judgment to the other experts here an index of comparability is utilized to identify the experts that have faced difficulties in expressing their preferences with this information at hand a moderator can invite the experts that are confident on their opinions to support the experts that are hesitating in the construction of the fuzzy preference relations

zero order statistics a mathematical framework for the processing and characterization of very impulsive signals impulsive or heavy tailed processes with infinite variance appear naturally in a variety of practical problems that include wireless communications teletraffic hydrology geology and economics most signal processing and statistical methods available in the literature have been designed under the assumption that the processes possess finite variance and they usually break down in the presence of infinite variance although methods based on fractional lower order statistics flos have proven successful in dealing with infinite variance processes they fail in general when the noise distribution has very heavy algebraic tails in this paper we introduce a new approach to statistical moment characterization which is well defined over all processes with algebraic or lighter tails unlike flos these zero order statistics zos as we will call them provide a common ground for the analysis of basically any distribution of practical use known today three new parameters namely the geometric power the zero order location and the zero order dispersion constitute the foundation of zos they play roles similar to those played by the power the expected value and the standard deviation in the theory of second order processes we analyze the properties of the new parameters and derive a zos framework for location estimation that gives rise to a novel mode type estimator with important optimality properties under very impulsive noise several simulations are presented to illustrate the potential of zos methods

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

p order metric uwb receiver structures with superior performance the generalized gaussian probability density function is shown to better approximate the probability density function of the multiple access interference in ultra wide bandwidth systems than the gaussian approximation and the laplacian density approximation two ultra wide bandwidth receiver structures based on this new approximation using a p order metric receiver decision statistic are investigated for the detection of time hopping ultra wide bandwidth wireless signals in multiple access interference channels the first receiver outperforms both the conventional matched filter ultra wide bandwidth receiver and the soft limiting ultra wide bandwidth receiver when only multiple access interference is present in uwb channels the second new receiver with adaptive limiting threshold outperforms the conventional matched filter ultra wide bandwidth receiver the soft limiting ultra wide bandwidth receiver and the adaptive threshold soft limiting ultra wide bandwidth receiver in all multiple access interference plus noise environments in multipath channels a new rake receiver based on the p order metric receiver is proposed for signal detection mathematical analysis and numerical results show that this new rake receiver can achieve larger signal to interference plus noise ratio than the standard matched filter rake receiver when multipath components are resolvable in uwb channels

on optimum and nearly optimum data quantization for signal detection the application of companding approximation theory to the quantization of data for detection of coherent signals in a noisy environment is considered this application is twofold allowing for greater simplicity in both analysis and design of quantizers for detection systems most computational methods for designing optimum most efficient quantizers for signal detection systems are iterative and are extremely sensitive to initial conditions companding approximation theory is used here to obtain suitable initial conditions for this problem furthermore the companding approximation idea is applied to design suboptimum quantizers which are nearly as efficient as optimum quantizers when the number of levels is large in this design iteration is not needed to derive the parameters of the quantizer and the design procedure is very simple in this paper we explore this approach numerically and demonstrate its effectiveness for designing and analyzing quantizers in detection systems

comparison of the convergence of two algorithms for adaptive fir digital filters the convergence properties of two different algorithms for the updating of the coefficients of an adaptive fir digital filter are investigated and compared with one another these algorithms are the stochastic iteration algorithm and the sign algorithm in this latter algorithm a one bit gradient estimation is used which makes its implementation very simple the convergence is characterized by the residual echo variance after convergence and a parameter that indicates the speed of the convergence it is shown that the convergence of the sign algorithm can always be assured but is much slower than that of the stochastic iteration algorithm if the same variance of the residual echo is to be obtained

robust l estimation based forms of signal transforms and time frequency representations the l estimation based signal transforms and time frequency tf representations are introduced by considering the corresponding minimization problems in the huber 1981 1998 estimation theory the standard signal transforms follow as the maximum likelihood solutions for the gaussian additive noise environment for signals corrupted by an impulse noise the median based transforms produce robust estimates of the non noisy signal transforms when the input noise is a mixture of gaussian and impulse noise the l estimation based signal transforms can outperform other estimates in quadratic and higher order tf analysis the resulting noise is inherently a mixture of the gaussian input noise and an impulse noise component in this case the l estimation based signal representations can produce the best results these transforms and tf representations give the standard and the median based forms as special cases a procedure for parameter selection in the l estimation is proposed the theory is illustrated and checked numerically

measuring consensus and dissensus a generalized index of disagreement using conditional probability abstract we generalize an index of disagreement recently proposed by akiyama et al 2016 which can be applied only to surveys that measure opinions expressed using the standard 5 scale likert scale to a general case that uses any scale with more than five response levels as stated in the aforementioned study the variance alone computed from a survey that employs the likert scale is not an adequate indicator for measuring the disagreement within a group because the range of the variance is a function of the mean to overcome this limitation they define the disagreement index using a conditional probability density function which allows us to compare responses to questions having different means or between groups across different time periods however developing a measure that considers likert scales larger than five has not yet been developed and our work addresses this lacuna as an example we illustrate an advantage of our generalized measure by calculating the disagreement within consumers price expectations

optimal pivot selection in fast weighted median search weighted median filters are increasingly being used in signal processing applications and thus fast implementations are of importance this paper introduces a fast algorithm to compute the weighted median wm of n samples which has linear time and space complexity as opposed to o n log n which is the time complexity of traditional sorting algorithms a popular selection algorithm often used to find the wm in large data sets is quickselect whose performance is highly dependent on how the pivots are chosen we introduce an optimization based pivot selection strategy which results in significantly improved performance as well as a more consistent runtime compared to traditional approaches the selected pivots are order statistics of subsets in order to find the optimal order statistics as well as the optimal subset sizes a set of cost functions are derived which when minimized lead to optimal design parameters we compare the complexity to floyd and rivest s algorithm select which to date has been the fastest median finding algorithm and we show that the proposed algorithm compared with select requires close to 30 fewer comparisons it is also shown that the proposed selection algorithm is asymptotically optimal for large n

on the asymptotic distribution of the correlation receiver output for time hopped uwb signals in ultra wideband uwb communications based on time hopping th impulse radio one of the most frequently studied receivers is the correlation receiver the multiuser interference mui at the output of this receiver is sometimes modeled as a gaussian random variable in order to justify this assumption the conditions of validity of the central limit theorem clt have to be studied in an asymptotic regime where the number of interferers and the processing gain grow toward infinity at the same rate with the channel degree being kept constant an asymptotic study is made in this paper based on the so called lindeberg s condition for the clt for martingales nonsynchronized users sending their signals over independent multipath channels are considered these users may also have different powers it is shown that when the frame length grows and the repetition factor is kept constant then the mui does not converge in distribution toward a gaussian random variable on the other hand this convergence can be established if the repetition factor grows at the rate of the frame length in this last situation closed form expressions for the signal to interference plus noise ratio sinr are given for th pulse amplitude modulation pam and pulse position modulation ppm uwb transmissions

fast algorithms for weighted myriad computation by fixed point search this paper develops fast algorithms to compute the output of the weighted myriad filter myriad filters form a large and important class of nonlinear filters for robust non gaussian signal processing and communications in impulsive noise environments just as the weighted mean and the weighted median are optimized for the gaussian and laplacian distributions respectively the weighted myriad is based on the class of spl alpha stable distributions which can accurately model impulsive processes the weighted myriad is an m estimator that is defined in an implicit manner no closed form expression exists for it and its direct computation is a nontrivial and prohibitively expensive task in this paper the weighted myriad is formulated as one of the fixed points of a certain mapping an iterative algorithm is proposed to compute these fixed points and its convergence is proved rigorously using these fixed point iterations fast algorithms are developed for the weighted myriad numerical simulations demonstrate that these algorithms compute the weighted myriad with a high degree of accuracy at a relatively low computational cost

optimum diversity detection over fading dispersive channels with non gaussian noise we consider the problem of m ary signal detection over a single input multiple output simo channel affected by frequency dispersive rayleigh distributed fading and corrupted by additive non gaussian noise modeled as a spherically invariant random process we derive both the optimum detection structure and a suboptimal reduced complexity receiver based on the low energy coherence approach interestingly both detection structures are canonical i e they are independent of the actual noise statistics we also carry out a performance analysis of both receivers with reference to the case that the channel is affected by a frequency selective fading and for a binary frequency shift keying signaling format the results obtained through both a chernoff bounding technique and monte carlo simulations reveal that the adoption of diversity also represents a suitable means to restore performance in the presence of dispersive fading and impulsive non gaussian noise interestingly it is also shown that the suboptimal receiver incurs a limited loss with respect to the optimum unrealizable receiving structure

non gaussian noise models in signal processing for telecommunications new methods an results for class a and class b noise models the subject here is generalized i e non gaussian noise models and specifically their first order probability density functions pdfs attention is focused primarily on the author s canonical statistical physical class a and class b models in particular class a noise describes the type of electromagnetic interference emi often encountered in telecommunication applications where this ambient noise is largely due to other intelligent telecommunication operations on the other hand ambient class b noise usually represents man made or natural nonintelligent i e nonmessage bearing noise and is highly impulsive class a noise is not an spl alpha stable process nor is it reducible to such except in the limiting gaussian cases of high density noise by the central limit theorem class b noise is also asymptotically normal before model approximation under rather broad conditions principally governed by the source propagation and distribution scenarios the pdf of class b noise alone no gaussian component can usually be approximated by 1 a symmetric gaussian spl alpha stable s spl alpha s model in the case of narrowband reception or when the pdf spl omega sub 1 spl alpha of the amplitude is symmetric and 2 a nonsymmetric spl alpha stable ns spl alpha s model no gaussian component can be constructed in broadband regimes new results here include i counting functional methods for constructing the general qth order characteristic functions cfs of class a and class b noise from which all moments and in principle the pdfs follow ii the first order cfs pdfs and cumulative probabilities apds of nonsymmetric broadband class b noise extended to include additive gauss noise agn iii proof of the existence of all moments in the basic class a and class b models iv the key physical role of agn and the fact that agn removes spl alpha stability v the explicit roles of the propagation and distribution scenarios and vi extension to noise fields although telecommunication applications are emphasized class a and class b noise models apply selectively but equally well to other physical regimes e g underwater acoustics and em radar optics etc supportive empirical data are included

geometrical properties of optimal volterra filters for signal detection linear quadratic filters are a special example of volterra filters that are limited to the second order it is shown that all the results recently published which are valid in the linear quadratic case can be extended with the appropriate notations to volterra filters of arbitrary order particularly the optimum volterra filter giving the maximum of the deflection for detecting a signal in noise is wholly calculated in addition several geometrical properties of optimal volterra filters are investigated by introducing appropriate scalar products in particular the concept of space orthogonal to the signal and the noise alone reference nar property are introduced allowing a decomposition of the optimal filter that exhibits a relation between detection and estimation extensions to the infinite case and relations with the likelihood ratio are also investigated

noise benefits in quantizer array correlation detection and watermark decoding quantizer noise can improve statistical signal detection in array based nonlinear correlators in neyman pearson and maximum likelihood ml detection this holds even for infinite variance symmetric alpha stable channel noise and for generalized gaussian channel noise noise enhanced correlation detection leads to noise enhanced watermark extraction based on such nonlinear detection at the pixel or bit level this yields a noise based algorithm for digital watermark decoding using two new noise benefit theorems the first theorem gives a necessary and sufficient condition for quantizer noise to increase the detection probability of a constant signal for a fixed false alarm probability if the channel noise is symmetric and if the sample size is large the second theorem shows that the array must contain more than one quantizer for such a stochastic resonance noise benefit if the symmetric channel noise is unimodal it also shows that the noise benefit rate improves in the small quantizer noise limit as the number of array quantizers increases the second theorem further shows that symmetric uniform quantizer noise gives the optimal rate for an initial noise benefit among all finite variance symmetric scale family noise two corollaries give similar results for stochastic resonance noise benefits in ml detection of a signal sequence with known shape but unknown amplitude

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

on properties of the support of capacity achieving distributions for additive noise channel models with input cost constraints we study the classical problem of characterizing the channel capacity and its achieving distribution in a generic fashion we derive a simple relation between three parameters the input output function the input cost function and the noise probability density function one which dictates the type of the optimal input in layman terms we prove that the support of the optimal input is bounded whenever the cost grows faster than a cutoff growth rate equal to the logarithm of the inverse of the noise probability density function evaluated at the input output function furthermore we prove a converse statement that says whenever the cost grows slower than the cutoff rate the optimal input has necessarily an unbounded support in addition we show how the discreteness of the optimal input is guaranteed whenever the triplet satisfy some analyticity properties we argue that a suitable cost function to be imposed on the channel input is one that grows similarly to the cutoff rate our results are valid for any cost function that is super logarithmic they summarize a large number of previous channel capacity results and give new ones for a wide range of communication channel models such as gaussian mixtures generalized gaussians and heavy tailed noise models that we state along with numerical computations

malliavin calculus and decoupling inequalities in banach spaces abstract we develop a theory of malliavin calculus for banach space valued random variables using radonifying operators instead of symmetric tensor products we extend the wiener ito isometry to banach spaces in the white noise case we obtain two sided l p estimates for multiple stochastic integrals in arbitrary banach spaces it is shown that the malliavin derivative is bounded on vector valued wiener ito chaoses our main tools are decoupling inequalities for vector valued random variables in the opposite direction we use meyer s inequalities to give a new proof of a decoupling result for gaussian chaoses in umd banach spaces

error performance of multi antenna receivers in a poisson field of interferers a stochastic geometry approach in this paper we introduce an analytical framework for performance analysis and design of single input multiple output simo wireless systems in the presence of noise fading and radio frequency interference produced by randomly distributed active interferers surrounding an intended probe receiver the framework leverages recent application of stochastic geometry and poisson point processes ppps theory to network interference modeling to assess the impact of spatial dependence across multiple receive antennas three models of network interference are studied i the isotropic model where all receive antennas see interferers belonging to the same ppp ii the independent model where each receive antenna sees interferers belonging to an independent ppp and iii the mixture model which is a superposition of isotropic and independent interferences depending on the fading distribution of the interferers the nakagami m fading parameter of the probe link and the number of receive antennas either exact or upper bound formulas of the error probability averaged over noise fading and spatial interference are given our analysis shows that depending on the interference model performance can either improve or get worse with multiple antennas at the receiver the proposed analytical methodology is applicable to single and multi ppps interference environments

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

optimal linear detectors for additive noise channels in an attempt to gain insight into the design of linear detectors for additive white noise channels discrete time case we describe several procedures both optimal and suboptimal using the wiener representation for nonlinear systems we derive an ad hoc suboptimal design procedure exact designs are found when the noise amplitude s probability distribution is stable and when the noise is laplacian considering all the linear detectors thus derived no general form for the optimal linear detector s unit sample response becomes apparent performance analyses and simulations indicate substantial performance losses occur when linear detectors are used instead of optimal likelihood ratio ones