on the equivalence of time and frequency domain maximum likelihood estimation maximum likelihood estimation has a rich history it has been successfully applied to many problems including dynamical system identification different approaches have been proposed in the time and frequency domains in this paper we discuss the relationship between these approaches and we establish conditions under which the different formulations are equivalent for finite length data a key point in this context is how initial and final conditions are considered and how they are introduced in the likelihood function

complex elliptically symmetric random variables generation characterization and circularity tests complex elliptically symmetric ces distributions constitute a flexible and broad class of distributions for many engineering applications and include the widely used complex gaussian complex complex generalized gaussian and symmetric stable distributions for example their careful statistical characterization is needed moreover the mechanisms for generating random variables from these distributions are not well defined in literature in this paper we provide such treatment in order to provide a better insight on their statistical properties and simplifying proofs and derivations for example insightful expressions for complex kurtosis coefficients of ces distributions are derived providing an interpretation on what complex kurtosis really measures also derived are asymptotic distributions of circularity measures the sample circularity quotient and coefficient assuming i i d samples from an unspecified ces distribution also new wald s type detectors of circularity are proposed that are valid within ces distributions with finite fourth order moments these results are accompanied with examples that are of interest in developing signal processing algorithms for complex valued signals

decay estimates of solutions to the compressible euler maxwell system in r 3 abstract we study the large time behavior of solutions near a constant equilibrium to the compressible euler maxwell system in r 3 we first refine a global existence theorem by assuming that the h 3 norm of the initial data is small but the higher order derivatives can be arbitrarily large if the initial data belongs to h s 0 s 3 2 or b 2 s 0 s 3 2 by a regularity interpolation trick we obtain the various decay rates of the solution and its higher order derivatives as an immediate byproduct the usual l p l 2 1 p 2 type of the decay rates follows without requiring that the l p norm of initial data is small

properness and widely linear processing of quaternion random vectors in this paper the second order circularity of quaternion random vectors is analyzed unlike the case of complex vectors there exist three different kinds of quaternion properness which are based on the vanishing of three different complementary covariance matrices the different kinds of properness have direct implications on the cayley dickson representation of the quaternion vector and also on several well known multivariate statistical analysis methods in particular the quaternion extensions of the partial least squares pls multiple linear regression mlr and canonical correlation analysis cca techniques are analyzed showing that in general the optimal linear processing is full widely linear however in the case of jointly q proper or c proper vectors the optimal processing reduces respectively to the conventional or semi widely linear processing finally a measure for the degree of improperness of a quaternion random vector is proposed which is based on the kullback leibler divergence between two zero mean gaussian distributions one of them with the actual augmented covariance matrix and the other with its closest proper version this measure quantifies the entropy loss due to the improperness of the quaternion vector and it admits an intuitive geometrical interpretation based on kullback leibler projections onto sets of proper augmented covariance matrices

asymptotic properties of robust complex covariance matrix estimates in many statistical signal processing applications the estimation of nuisance parameters and parameters of interest is strongly linked to the resulting performance generally these applications deal with complex data this paper focuses on covariance matrix estimation problems in non gaussian environments and particularly the m estimators in the context of elliptical distributions first this paper extends to the complex case the results of tyler in d tyler robustness and efficiency properties of scatter matrices biometrika vol 70 no 2 p 411 1983 more precisely the asymptotic distribution of these estimators as well as the asymptotic distribution of any homogeneous function of degree 0 of the m estimates are derived on the other hand we show the improvement of such results on two applications directions of arrival doa estimation using the multiple signal classification music algorithm and adaptive radar detection based on the adaptive normalized matched filter anmf test

complex elliptically symmetric distributions survey new results and applications complex elliptically symmetric ces distributions have been widely used in various engineering applications for which non gaussian models are needed in this overview circular ces distributions are surveyed some new results are derived and their applications e g in radar and array signal processing are discussed and illustrated with theoretical examples simulations and analysis of real radar data the maximum likelihood ml estimator of the scatter matrix parameter is derived and general conditions for its existence and uniqueness and for convergence of the iterative fixed point algorithm are established specific ml estimators for several ces distributions that are widely used in the signal processing literature are discussed in depth including the complex t distribution k distribution the generalized gaussian distribution and the closely related angular central gaussian distribution a generalization of ml estimators the m estimators of the scatter matrix are also discussed and asymptotic analysis is provided applications of ces distributions and the adaptive signal processors based on ml and m estimators of the scatter matrix are illustrated in radar detection problems and in array signal processing applications for direction of arrival doa estimation and beamforming furthermore experimental validation of the usefulness of ces distributions for modelling real radar data is given

complex noise analysis of dmt in this paper we consider discrete multitone dmt or baseband orthogonal frequency division multiplexing ofdm modulation and perform a detailed noise analysis which takes into account dependencies and power variance differences of real and imaginary part after the complex valued discrete fourier transform dft the derivation is based on the so called pseudocovariance matrix of a complex random vector which was introduced by neeser and massey 1993 we show that the relevant pseudocovariance matrix is not the zero matrix in general in contrast to pass band ofdm for which it can be proven under certain assumptions that all occurring pseudocovariance matrices are vanishing we show that for colored noise rotated rectangular symbol constellations are more appropriate than the common quadratic quadrature amplitude modulation qam symbol constellations with respect to capacity and symbol error probability and we derive formulas for the rotation angles and constellation sizes densities finally we extend the results to a multitransceiver multiple input multiple output mimo scenario for which we assume a very general noise model at the inputs of the receivers allowing correlations between the noise signals of different receivers this requires the introduction of pseudocross covariance matrices of complex random vectors which are the important objects together with cross covariance matrices in the mimo situation

a complex generalized gaussian distribution characterization generation and estimation the generalized gaussian distribution ggd provides a flexible and suitable tool for data modeling and simulation however the characterization of the complex valued ggd in particular generation of samples from a complex ggd have not been well defined in the literature in this correspondence we provide a thorough presentation of the complex valued ggd by i constructing the probability density function pdf ii defining a procedure for generating random numbers from the complex valued ggd and iii implementing a maximum likelihood estimation mle procedure for the shape and covariance parameters in the complex domain we quantify the performance of the mle with simulations and actual radar data

the zero electron mass limit in the hydrodynamic model for plasmas abstract the limit of the vanishing ratio of the electron mass to the ion mass in the isentropic transient euler poisson equations with periodic boundary conditions is proved the equations consist of the balance laws for the electron density and current density for a given ion density coupled to the poisson equation for the electrostatic potential the limit is related to the low mach number limit of klainerman and majda in particular the limit velocity satisfies the incompressible euler equations with damping the difference to the zero mach number limit comes from the electrostatic potential which needs to be controlled this is done by a reformulation of the equations in terms of the enthalpy higher order energy estimates and a careful use of the poisson equation

widely linear estimation with complex data mean square estimation of complex and normal data is not linear as in the real case but widely linear the purpose of the paper is to calculate the optimum widely linear mean square estimate and to present its main properties the advantage with respect to the linear procedure is especially analyzed

the multivariate complex normal distribution a generalization the multivariate complex normal distribution usually employed in the literature is a special case since certain restrictions have been imposed on the covariances of the real and imaginary parts of its variables a more general distribution is proposed of which the usual distribution is shown to be a special case

initial layers and zero relaxation limits of euler maxwell equations in this paper we consider zero relaxation limits for periodic smooth solutions of euler maxwell systems for well prepared initial data we propose an approximate solution based on a new asymptotic expansion up to any order for ill prepared initial data we construct initial layer corrections in an explicit way in both cases the asymptotic expansions are valid in time intervals independent of the relaxation time and their convergence is justified by establishing uniform energy estimates

semiparametric crb and slepian bangs formulas for complex elliptically symmetric distributions the main aim of this paper is to extend the semiparametric inference methodology recently investigated for real elliptically symmetric res distributions to complex elliptically symmetric ces distributions the generalization to the complex field is of fundamental importance in all practical applications that exploit the complex representation of the acquired data moreover the ces distributions has been widely recognized as a valuable and general model to statistically describe the non gaussian behaviour of datasets originated from a wide variety of physical measurement processes the paper is divided in two parts in the first part a closed form expression of the constrained semiparametric cramer rao bound cscrb for the joint estimation of complex mean vector and complex scatter matrix of a set of ces distributed random vectors is obtained by exploiting the so called wirtinger or mathbb c mathbb r calculus the second part deals with the derivation of the semiparametric version of the slepian bangs formula in the context of the ces model specifically the proposed semiparametric slepian bangs ssb formula provides us with a useful and ready to use expression of the semiparametric fisher information matrix sfim for the estimation of a parameter vector parametrizing the complex mean and the complex scatter matrix of a ces distributed vector in the presence of unknown nuisance density generator furthermore we show how to exploit the derived ssb formula to obtain the semiparametric counterpart of the stochastic crb for direction of arrival doa estimation under a random signal model assumption simulation results are also provided to clarify the theoretical findings and to demonstrate their usefulness in common array processing applications

on tracking control for affine nonlinear systems by sliding mode abstract the stability problem of output tracking of a bounded time varying reference by decouplable affine nonlinear systems using sliding mode control is investigated it is shown that when the error dynamics on the sliding surface is chosen to be linear time invariant closed loop stability of systems under the presented sliding mode control can be guaranteed only if the systems are minimum phase

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

on the high snr conditional maximum likelihood estimator full statistical characterization in the field of asymptotic performance characterization of the conditional maximum likelihood cml estimator asymptotic generally refers to either the number of samples or the signal to noise ratio snr value the first case has been already fully characterized although the second case has been only partially investigated therefore this correspondence aims to provide a sound proof of a result i e asymptotic in snr gaussianity and efficiency of the cml estimator in the multiple parameters case generally regarded as trivial but not so far demonstrated

second order analysis of improper complex random vectors and processes we present a comprehensive treatment of the second order theory of complex random vectors and wide sense stationary wss signals the main focus is on the improper case in which the complementary covariance does not vanish accounting for the information present in the complementary covariance requires the use of widely linear transformations based on these we present the eigenanalysis of complex vectors and apply it to the problem of rank reduction through principal components we also investigate joint properties of two complex vectors by introducing canonical correlations which paves the way for a discussion of the wiener filter and its rank reduced version we link the concepts of propriety and joint propriety to eigenanalysis and canonical correlation analysis respectively our treatment is extended to wss signals in particular we give a result on the asymptotic distribution of eigenvalues and examine the connection between wss proper and analytic signals

complex valued signal processing the proper way to deal with impropriety complex valued signals occur in many areas of science and engineering and are thus of fundamental interest in the past it has often been assumed usually implicitly that complex random signals are proper or circular a proper complex random variable is uncorrelated with its complex conjugate and a circular complex random variable has a probability distribution that is invariant under rotation in the complex plane while these assumptions are convenient because they simplify computations there are many cases where proper and circular random signals are very poor models of the underlying physics when taking impropriety and noncircularity into account the right type of processing can provide significant performance gains there are two key ingredients in the statistical signal processing of complex valued data 1 utilizing the complete statistical characterization of complex valued random signals and 2 the optimization of real valued cost functions with respect to complex parameters in this overview article we review the necessary tools among which are widely linear transformations augmented statistical descriptions and wirtinger calculus we also present some selected recent developments in the field of complex valued signal processing addressing the topics of model selection filtering and source separation

approximate linearization by state feedback and coordinate change a nonlinear system can always be approximated to first order by linear systems it has been shown by jakubczyk and respondek 4 and hunt and su 3 that certain nonlinear systems are the exact transforms of linear systems under nonlinear state coordinate change and nonlinear state feedback in this paper we give necessary and sufficient conditions for a nonlinear system to be approximated to higher order by the transform of a linear system the use of this technique in the design of nonlinear compensators has been suggested recently by the author 6

proper complex random processes with applications to information theory the covariance of complex random variables and processes when defined consistently with the corresponding notion for real random variables is shown to be determined by the usual complex covariance together with a quantity called the pseudo covariance a characterization of uncorrelatedness and wide sense stationarity in terms of covariance and pseudo covariance is given complex random variables and processes with a vanishing pseudo covariance are called proper it is shown that properness is preserved under affine transformations and that the complex multivariate gaussian density assumes a natural form only for proper random variables the maximum entropy theorem is generalized to the complex multivariate case the differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum if and only if the random vector is proper gaussian and zero mean the notion of circular stationarity is introduced for the class of proper complex random processes a discrete fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain an application of the theory is presented

on testing the extent of noncircularity in this correspondence we provide a multiple hypothesis test to detect the number of latent noncircular signals in a complex gaussian random vector our method sequentially tests the results of individual generalized likelihood ratio test glrt statistics with known asymptotic distributions to form the multiple hypothesis detector specifically we are able to set a threshold yielding a precise probability of error this test can be used to statistically determine if a given complex observation is circular gaussian and if not how many latent signals in the observation are noncircular simulations are used to quantify the performance of the detector as compared to a detector based on the minimum description length mdl criterion the utility of the detector is shown by applying it to a beamforming application using independent component analysis ica

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

on testing for impropriety of complex valued gaussian vectors we consider the problem of testing whether a complex valued random vector is proper i e is uncorrelated with its complex conjugate we formulate the testing problem in terms of real valued gaussian random vectors so we can make use of some useful existing results which enable us to study the null distributions of two test statistics the tests depend only on the sample size n and the dimensionality of the vector p the basic behaviors of the distributions of the test statistics are derived and critical values thresholds are calculated and presented for certain n p values for one of these tests we derive a distributional approximation for a transform of the statistic potentially very useful in practice for rapid and simple testing we also study the power detection probability of the tests our results mean that testing for propriety can be a practical and undaunting procedure

the real complex normal distribution an expression is derived for the distribution of a mixture of real and complex normal variates the asymptotic distribution of the resulting real complex maximum likelihood estimates is the real complex normal distribution derived the covariance matrix of this distribution is particularly important it is the asymptotic covariance matrix for maximum likelihood estimates and the cramer rao lower bound on the variance of the real complex estimates in general from this covariance matrix the variance of the reconstructed complex valued exit wave then follows using the pertinent propagation formulas the resulting expressions show the dependence of the variance on the free microscope parameters used for experimental design

stochastic time frequency analysis using the analytic signal why the complementary distribution matters we challenge the perception that we live in a proper world where complex random signals can always be assumed to be proper also called circularly symmetric rather we stress the fact that the analytic signal constructed from a nonstationary real signal is in general improper which means that its complementary correlation function is nonzero we explore the consequences of this finding in the context of stochastic time frequency analysis in cohen s class there the analytic signal plays a prominent role because it reduces interference terms however the usual time frequency representation tfr based on the analytic signal gives only an incomplete signal description it must be augmented by a complementary tfr whose properties we develop in detail we show why it is still advantageous to use the pair of standard and complementary tfrs of the analytic signal rather than the tfr of the corresponding real signal

complex ica using nonlinear functions we introduce a framework based on wirtinger calculus for nonlinear complex valued signal processing such that all computations can be directly carried out in the complex domain the two main approaches for performing independent component analysis maximum likelihood and maximization of non gaussianity which are intimately related to each other are studied using this framework the main update rules for the two approaches are derived their properties and density matching strategies are discussed along with numerical examples to highlight their relationships

second order statistics of complex signals the second order statistical properties of complex signals are usually characterized by the covariance function however this is not sufficient for a complete second order description and it is necessary to introduce another moment called the relation function its properties and especially the conditions that it must satisfy are analyzed both for stationary and nonstationary signals this leads to a new perspective concerning the concept of complex white noise as well as the modeling of any signal as the output of a linear system driven by a white noise finally this is applied to complex autoregressive signals and it is shown that the classical prediction problem must be reformulated when the relation function is taken into consideration

quaternion ica from second order statistics this paper addresses the independent component analysis ica of quaternion random vectors in particular we focus on the gaussian case and therefore only consider the quaternion second order statistics sos which are given by the covariance matrix and three complementary covariance matrices first we derive the necessary and sufficient conditions for the identifiability of the quaternion ica model which are based on the definition of the properness profile of a quaternion random variable and more specifically on the concept of rotationally equivalent properness profiles second we show that the maximum likelihood ml approach to the quaternion ica problem reduces to the approximated joint diagonalization ajd of the sample mean estimates of the covariance and complementary covariance matrices unlike the complex case these four matrices cannot be simultaneously diagonalized in general and we have to resort to a particular ajd algorithm the proposed technique which can be seen as a quasi newton method is based on the local approximation of the nonconvex ml ica cost function a measure of the entropy loss due to the residual correlation among the estimated quaternion sources and it provides a satisfactory solution of the quaternion ica model the performance of the proposed quaternion ml ica algorithm as well as its relationship to the identifiability conditions are illustrated by means of several numerical examples

class of widely linear complex kalman filters recently a class of widely linear augmented complex valued kalman filters kfs that make use of augmented complex statistics have been proposed for sequential state space estimation of the generality of complex signals this was achieved in the context of neural network training and has allowed for a unified treatment of both second order circular and noncircular signals that is both those with rotation invariant and rotation dependent distributions in this paper we revisit the augmented complex kf augmented complex extended kf and augmented complex unscented kf in a more general context and analyze their performances for different degrees of noncircularity of input and the state and measurement noises for rigor a theoretical bound for the performance advantage of widely linear kfs over their strictly linear counterparts is provided the analysis also addresses the duality with bivariate real valued kfs together with several issues of implementation simulations using both synthetic and real world proper and improper signals support the analysis

blind symbol timing and frequency offset estimation in ofdm systems with real data symbols in this letter the problem of blind symbol timing and frequency offset estimation in orthogonal frequency division multiplexing ofdm systems with real data symbols is considered maximum likelihood ml estimators for the parameters of interest have been derived by modeling the ofdm signal as a proper complex gaussian random process however when data symbols belong to a real constellation the received signal becomes an improper complex random process and hence previously mentioned estimators termed cyclic prefix cp estimators are not ml estimators in this letter minimum mean squared error estimators exploiting the conjugate symmetry property exhibited by the ofdm signal with real data symbols termed msr estimators that greatly outperform cp estimators in additive noise channels are derived moreover a modified msr symbol timing estimator that can assure satisfactory performance in multipath fading channels is proposed

the augmented complex kernel lms recently a unified framework for adaptive kernel based signal processing of complex data was presented by the authors which besides offering techniques to map the input data to complex reproducing kernel hilbert spaces developed a suitable wirtinger like calculus for general hilbert spaces in this short paper the extended wirtinger s calculus is adopted to derive complex kernel based widely linear estimation filters suitable for applications involving noncircular data furthermore we illuminate several important characteristics of the widely linear filters we show that although in many cases the gains from adopting widely linear estimation filters as alternatives to ordinary linear ones are rudimentary for the case of kernel based widely linear filters significant performance improvements can be obtained

the augmented complex particle filter complex gaussian signals in engineering applications are typically noncircular that is they have rotation dependent distributions however current complex valued particle filters pfs have assumed implicitly or explicitly circular signal distributions which for noncircular signals leads to suboptimal performance in this correspondence we employ a recent development in the so called augmented complex statistics and propose the augmented complex pf acpf and the augmented complex gaussian pf acgpf for the sequential estimation of complex states in both circular and noncircular noise the analysis and simulations illuminate theoretical and practical advantages for the proposed solutions

detection and estimation of improper complex random signals nonstationary complex random signals are in general improper not circularly symmetric which means that their complementary covariance is nonzero since the karhunen loeve k l expansion in its known form is only valid for proper processes we derive the improper version of this expansion it produces two sets of eigenvalues and improper observable coordinates we then use the k l expansion to solve the problems of detection and estimation of improper complex random signals in additive white gaussian noise we derive a general result comparing the performance of conventional processing which ignores complementary covariances with processing that takes these into account in particular for the detection and estimation problems considered we find that the performance gain as measured by deflection and mean squared error mse respectively can be as large as a factor of 2 in a communications example we show how this finding generalizes the result that coherent processing enjoys a 3 db gain over noncoherent processing

estimation of second order cross moments of generalized almost cyclostationary processes in this paper the problem of estimating second order cross moments of generalized almost cyclostationary gacs processes is addressed gacs processes have statistical functions that are almost periodic functions of time whose generalized fourier series expansions have both frequencies and coefficients that depend on the lag shifts of the processes the class of such nonstationary processes includes the almost cyclostationary acs processes which are obtained as a special case when the frequencies do not depend on the lag shifts acs processes filtered by doppler channels and communications signals with time varying parameters are further examples it is shown that the second order cross moment of two jointly gacs processes is completely characterized by the cyclic cross correlation function moreover it is proved that the cyclic cross correlogram is an asymptotically normal mean square consistent estimator of the cyclic cross correlation function furthermore it is shown that well known consistency results for acs processes can be obtained by specializing the results of this paper

on entropy rate for the complex domain and its application to i i d sampling we derive the entropy rate formula for a complex gaussian random process by using a widely linear model the resulting expression is general and applicable to both circular and noncircular gaussian processes since any second order stationary process can be modeled as the output of a widely linear system driven by a circular white noise furthermore we demonstrate application of the derived formula to an order selection problem we extend a scheme for independent and identically distributed i i d sampling to the complex domain to improve the estimation performance of information theoretic criteria when samples are correlated we show the effectiveness of the approach for order selection for simulated and actual functional magnetic resonance imaging fmri data that are inherently complex valued

a cramer rao lower bound for complex parameters an expression is derived for a cramer rao lower bound on the variance of unbiased estimators of complex parameters

weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift diffusion equation we investigate the relaxation problem for the hydrodynamic isentropic euler poisson system when the momentum relaxation time tends to zero very sharp estimates on the solutions independent of the relaxation time are obtained and used to establish compactness

initial layer and relaxation limit of non isentropic compressible euler equations with damping abstract in this paper we study the relaxation limit of the relaxing cauchy problem for non isentropic compressible euler equations with damping in multi dimensions we prove that the velocity of the relaxing equations converges weakly to the velocity of the relaxed equations while other variables of the relaxing equations converge strongly to the corresponding variables of the relaxed equations we prove that as relaxation time approaches 0 there exists an initial layer for the ill prepared data the convergence of the velocity is strong outside the layer while there is no initial layer for the well prepared data the convergence of the velocity is strong near t 0 the strong convergence rates of all variables are also estimated

a new barankin bound approximation for the prediction of the threshold region performance of maximum likelihood estimators it is well known that the ml estimator exhibits a threshold effect i e a rapid deterioration of estimation accuracy below a certain signal to noise ratio snr or number of snapshots this effect is caused by outliers and is not captured by standard tools such as the cramer rao bound crb the search of the snr threshold value where the crb becomes unreliable for prediction of maximum likelihood estimator variance can be achieved with the help of the barankin bound bb as proposed by many authors the major drawback of the bb in comparison with the crb is the absence of a general analytical formula which compels one to resort to a discrete form usually the mcaulay seidman bound msb requesting the search of an optimum over a set of test points in this paper we propose a new practical bb discrete form that provides for a given set of test points an improved snr threshold prediction in comparison with existing approximations msb abel bound mcaulay hofstetter bound at the expense of the computational complexity increased by a factor les p 1 3 where p is the number of unknown parameters we have derived its expression for the general gaussian observation model to be used in place of existing approximations

essential statistics and tools for complex random variables complex random signals play an increasingly important role in array communications and biomedical signal processing and related fields however the fundamental properties of complex valued signals and mathematical tools needed to process them are scattered in literature we provide a concise unified and rigorous treatment of essential properties and tools of complex random variables and apply these fundamentals to derive complex extensions of leibniz rule faa di bruno s formula and taylor s series the extensions allow establishing relationships among complex moments and cumulants and characterizing the circularity property we propose measures for testing and quantifying circularity and observe that non circularity may be more common in practical applications than previously thought all results are rigorously proved and supplemented with clarifying examples

influence function and asymptotic efficiency of scatter matrix based array processors case mvdr beamformer in this paper we consider array processors that are scale invariant functions of the array covariance matrix the emphasis is on capon s mvdr beamformer we call such an array processor as scatter matrix based smb array processor since the covariance matrix is required only up to a constant scalar and thus a scatter matrix proportional to covariance under finite covariance assumption provides sufficient information in order to establish interesting statistical robustness and large sample properties we derive a general expression for the influence function and the asymptotic covariance structure of smb mvdr beamformer weights our results apply under the class of complex elliptically symmetric distributions which includes the commonly used complex normal distribution as a special case we illustrate the theory by deriving the if and asymptotic relative efficiencies of the conventional smb mvdr beamformer that employs the sample covariance matrix and beamformers that employ robust m estimators of scatter theoretical findings are confirmed by simulations our findings favor beamformers based upon m estimators of scatter since they combine a high efficiency with appealing robustness properties

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

robust harmonic retrieval via block successive upper bound minimization harmonic retrieval hr is a problem of significance with numerous applications many existing algorithms are explicitly or implicitly developed under gaussian noise assumption which however are not robust against non gaussian noise such as impulsive noise or outliers in this paper by employing the ell p fitting criterion and block successive upper bound minimization bsum technique a variant of the classical relax algorithm named as bsum relax is devised for robust hr it is revealed that the bsum relax successively performs alternating optimization along coordinate directions i e it updates one harmonic by fixing the other k 1 components such that the whole problem is split into k single tone hr problems which are then solved by creating a surrogate function that majorizes the objective function of each subproblem to further refine the frequency component the newton s method that takes linear complexity mathcal o n is derived for updating the frequency estimates we prove that under the single tone case bsum relax converges to a karush kuhn tucker point furthermore the bsum relax is extended to the multidimensional hr case numerical results show that the proposed algorithm outperforms the state of the art methods in heavy tailed noise scenarios

on antenna array receiver principles for space time selective rayleigh fading channels optimum in the sense of minimum error probability single symbol diversity detection for fading noisy channels is too complex for practical implementation a simplified near optimum array receiver is proposed which is based on the statistics i e the covariance function matrix of the fading channel this detector is then analyzed by calculating the exact error probability when there is a spread of the direction of arrival of the incident radio waves the proposed detector significantly gains over an adaptive antenna array which forms a weighted sum of the received antenna signals also for this adaptive array a fundamental difference between maximum likelihood weights and least mean square weights is observed

asymptotic behavior of weak solutions for the relativistic vlasov maxwell equations with large light speed abstract we study here the behavior of time periodic weak solutions for the relativistic vlasov maxwell boundary value problem in a three dimensional bounded domain with strictly star shaped boundary when the light speed becomes infinite we prove the convergence toward a time periodic weak solution for the classical vlasov poisson equations

complex valued random vectors and channels entropy divergence and capacity recent research has demonstrated significant achievable performance gains by exploiting circularity noncircularity or properness improperness of complex valued signals in this paper we investigate the influence of these properties on important information theoretic quantities such as entropy divergence and capacity we prove two maximum entropy theorems that strengthen previously known results the proof of the first maximum entropy theorem is based on the so called circular analog of a given complex valued random vector the introduction of the circular analog is additionally supported by a characterization theorem that employs a minimum kullback leibler divergence criterion in the proof of the second maximum entropy theorem results about the second order structure of complex valued random vectors are exploited furthermore we address the capacity of multiple input multiple output mimo channels regardless of the specific distribution of the channel parameters noise vector and channel matrix if modeled as random we show that the capacity achieving input vector is circular for a broad range of mimo channels including coherent and noncoherent scenarios finally we investigate the situation of an improper and gaussian distributed noise vector we compute both capacity and capacity achieving input vector and show that improperness increases capacity provided that the complementary covariance matrix is exploited otherwise a capacity loss occurs for which we derive an explicit expression

robust output tracking for non linear systems the problem of output tracking for a single input single output non linear system in the presence of uncertainties is studied the notions relative degree and minimum phase for non linear systems are reviewed given a bounded desired tracking signal with bounded derivatives a control law is designed for minimum phase non linear systems which results in tracking of this signal by the output this control law is modified in the presence of uncertainties associated with the model vector fields to reduce the effects of these uncertainties on the tracking errors two types of uncertainties are considered those satisfying a generalized matching condition but otherwise unstructured and linear parametric uncertainties it is shown that for systems with the first type of uncertainty high gain control laws can result in small tracking errors of o where e is a small design parameter an alternative scheme based on variable structure control strategy is shown to yield zero tracking errors adaptive control te

a local stabilizing control scheme using an approximate feedback linearization we present a method of stabilizing single input approximately feedback linearizable systems in the generic situation where the linearizing feedback and coordinate transformation map are not directly available in obtaining a stabilizing feedback we utilize a technique of an approximate feedback linearization which is based on an approximate integrating factor calculated from a recursive algorithm we construct a feedback controller for the approximately linearized system so that the system is asymptotically stable in a neighborhood of the origin where the one to one relation holds with the original coordinate system

on the linear equivalents of nonlinear systems this paper studies feedback equivalence of nonlinear systems an equivalence relation is established for the systems x f x u a complete characterization of the class of nonlinear systems which are equivalent to controllable linear systems is obtained

global transformations of nonlinear systems recent results have established necessary and sufficient conditions for a nonlinear system of the form dot x t f x t u t g x t with f 0 0 to be locally equivalent in a neighborhood of the origin in rnto a controllable linear system we combine these results with several versions of the global inverse function theorem to prove sufficient conditions for the transformation of a nonlinear system to a linear system in doing so we introduce a technique for constructing a transformation under the assumptions that g ldot f dotg ad n 1 f ldotg span an n dimensional space and that g ldot f ldot g ad n 2 f ldotg is an involutive set

on circularity circularity is an assumption that was originally introduced for the definition of the probability distribution function of complex normal vectors however this concept can be extended in various ways for nonnormal vectors the first purpose of the paper is to introduce and compare some possible definitions of circularity from these definitions it is also possible to introduce the concept of circular signals and to study whether or not the spectral representation of stationary signals introduces circular components therefore the relationships between circularity and stationarity are analyzed in detail finally the theory of linear mean square estimation for complex signals exhibits some connections with circularity and it is shown that without this assumption the estimation theory must be reformulated

widely linear alamouti receiver for the reception of real valued constellations corrupted by interferences the alamouti saic maic concept orthogonal space time block codes stbc and the alamouti scheme in particular are of particular interest in multiple input multiple output mimo systems since they achieve full spatial diversity over fading channels and are decoded from linear processing at the receiver nevertheless due to the expensive spectral resource increasing network capacity requires the development of interference cancellation ic techniques allowing several users to share the same spectral resources without impacting the transmission quality in this context several ic schemes have been developed during this last decade where each user is equipped with multiple antennas and employs stbc at transmission however these ic techniques require multiple antennas at reception which remains a challenge at the handset level due to cost and size limitations for this reason low complexity single antenna interference cancellation saic techniques currently operational in gsm handsets have been developed recently for single antenna users using real valued modulations or complex filtering of real valued modulations by using a widely linear wl filtering at reception extension to multiple antennas at reception is called multiple antenna interference cancellation maic technique the purpose of this paper is to extend the saic maic technology to users using both real valued constellations such as amplitude shift keying ask constellations and the alamouti scheme at transmission a wl minimum mean square error mmse receiver completely new for ic purposes in the context of radio communications systems using the alamouti scheme is proposed and analyzed this receiver which corresponds to the maximum likelihood ml receiver for synchronous intranetwork interferences is able to separate up to 2 n alamouti users from n antennas at reception hence saic capability for n 1

price s theorem for complex variates price s 1958 theorem is derived for complex valued variates the derivation differs from the existing derivation in two respects first the normal variates are not assumed to be circularly complex thus the result is more general second the characteristic function of the complex variates is not used

some numerical aspects of approximate linearization of single input non linear systems we characterize approximate linearization to order m of a single input non linear system in terms of the existence of an integrating factor to order m 2 which is equivalent to the well known condition that a system of vector fields be order m 1 involutive we present a constructive method to obtain the required transformation for approximate linearization which results in substantial computational savings

on probability density functions for complex variables complex random variables arise naturally in many settings and their properties are of general interest past work on complex variables has mainly focused on their second order structure as well as that of their conjugates whereas the main purpose of this correspondence is to clarify the concept of a density function for a complex random variable and to discuss its properties two different functions play the role that the density of a real univariate random variable holds only one of these two functions can be correctly interpreted as a density but both functions clarify the nature of a complex variable the role played by the complex conjugate of the variable in this formulation is clarified and the complex scalar nature of z is discussed as the properties of complex random variables are most naturally specified in terms of the complex quantities directly and given in terms of the distribution of the complex variables rather than formulated in terms of the real and imaginary parts ensuring that an interpretable complex formulation exists is important

the non relativistic limit of euler maxwell equations for two fluid plasma abstract this paper is concerned with two fluid time dependent non isentropic euler maxwell equations in a torus for plasmas or semiconductors by using the method of formal asymptotic expansions we analyze the non relativistic limit for periodic problems with the prepared initial data it is shown that the small parameter problems have unique solutions existing in the finite time interval where the corresponding limit problems compressible euler poisson equations have smooth solutions moreover the formal limit is rigorously justified by an iterative scheme and an analysis of asymptotic expansions up to any order

locally most powerful invariant tests for the properness of quaternion gaussian vectors previous works have addressed the second order statistical characterization of quaternion random vectors introducing different properness definitions and presenting the generalized likelihood ratio tests glrts for determining the kind of quaternion properness this paper considers the more challenging problem of deriving the locally most powerful invariant tests lmpits which can be obtained even without an explicit expression for the maximal invariants thanks to the wijsman s theorem specifically we consider three binary hypothesis testing problems involving the two main kinds of quaternion properness and show that the lmpit statistics are given by the frobenius norm of three previously defined sample coherence matrices the proposed detectors exhibit interesting connections with the problem of testing for the properness of a complex vector and with the problems of testing for the sphericity of a four dimensional real or two dimensional complex proper vector additionally some numerical examples show that in general the proposed lmpits outperform their glrt counterparts and in some cases the performance gap is very noticeable

shallow water acoustic response and platform motion modeling via a hierarchical gaussian mixture model a hierarchical gaussian mixture model is proposed to characterize shallow water acoustic response functions that are time varying and sparse the mixture model is based on the assumption that acoustic paths can be partitioned into two sets the first is a relatively coherent set of arrivals that on average exhibit doppler spreading about a mean doppler and the remaining set is of multiple surface scattered paths that exhibit a spectrally flat doppler the hierarchy establishes constraints on the parameters of each of these gaussian models such that coherent components of the response are both sparse and in the ensemble obey the doppler spread profile this is accomplished with a bernoulli model that indicates the ensonification state of each element in the bi frequency representation of the acoustic response function estimators of the time varying acoustic response for the full duration of a broadband transmission are developed and employed to compensate for the shared time varying dilation process among the coherent arrivals the approach ameliorates response coherence degradation and can be employed to enhance coherent multi path combining and is a useful alternative to time recursive estimation the model is tested with acoustic communication recordings taken in shallow water at low signal to noise ratios

a full mean square analysis of clms for second order noncircular inputs a full mean square transient and steady state analysis of the complex least mean square clms algorithm is provided for strictly linear estimation of general second order noncircular improper gaussian inputs to this end we also consider the performance assessment in terms of the evolution of the complementary mean square error cmse and the complementary covariance pseudocovariance matrix of the weight error vector of clms this makes it possible to measure the degrees of noncircularity of the output error and the weight error vector which arise due to second order noncircularity improperness of the system input and system noise the recently introduced approximate uncorrelating transform which allows for joint direct diagonalization of both the input covariance and complementary covariance matrices with a single singular value decomposition is then employed in order to derive a unified bound on the step size which guarantees the convergence of both the standard mse and the proposed cmse a joint consideration of the standard mean square performance analysis and the proposed complementary performance analysis is shown to provide full second order closed form statistical descriptions of both the transient and steady state performances of clms for second order noncircular improper gaussian input data simulations in the system identification setting support the analysis

generalized likelihood ratios for testing the properness of quaternion gaussian vectors in a recent paper the second order statistical analysis of quaternion random vectors has shown that there exist two different kinds of quaternion widely linear processing which are associated with the two main types of quaternion properness in this paper we consider the problem of determining from a finite number of independent vector observations whether a quaternion gaussian vector is proper or not specifically we derive three generalized likelihood ratio tests glrts for testing the two main kinds of quaternion properness and show that the glrts reduce to the estimation of three previously proposed quaternion improperness measures interestingly the three glrt statistics improperness measures can be interpreted as an estimate of the entropy loss due to the quaternion improperness additionally we analyze the case in which the orthogonal basis for the representation of the quaternion vector is unknown which results in the problem of estimating the principal bbc properness direction i e the pure unit quaternion minimizing the bbc improperness measure although this estimation problem is not convex we propose a technique based on successive convex approximations which can be solved in closed form finally some simulation examples illustrate the performance and practical application of the proposed tests

time and spectral domain relative entropy a new approach to multivariate spectral estimation the concept of spectral relative entropy rate is introduced for jointly stationary gaussian processes using classical information theoretic results we establish a remarkable connection between time and spectral domain relative entropy rates this naturally leads to a new spectral estimation technique where a multivariate version of the itakura saito distance is employed it may be viewed as an extension of the approach called three introduced by byrnes georgiou and lindquist in 2000 which in turn followed in the footsteps of the burg jaynes maximum entropy method spectral estimation is here recast in the form of a constrained spectrum approximation problem where the distance is equal to the processes relative entropy rate the corresponding solution entails a complexity upper bound which improves on the one so far available in the multichannel framework indeed it is equal to the one featured by three in the scalar case the solution is computed via a globally convergent matricial newton type algorithm simulations suggest the effectiveness of the new technique in tackling multivariate spectral estimation tasks especially in the case of short data records

second order complex random vectors and normal distributions complex random vectors are usually described by their covariance matrix this is insufficient for a complete description of second order statistics and another matrix called the relation matrix is necessary some of its properties are analyzed and used to express the probability density function of normal complex vectors various consequences are presented

asymptotic frequency shift properizer for block processing of improper complex second order cyclostationary random processes in this paper the block processing of a discrete time dt improper complex second order cyclostationary socs random process is considered in particular it is of interest to find a preprocessing operation that enables the adoption of conventional signal processing techniques and algorithms developed for the filtering of proper complex signals and that leads to computationally efficient near optimal postprocessing an invertible linear conjugate linear lcl operator named the dt frequency shift fresh properizer is first proposed it is shown that the dt fresh properizer converts a dt improper complex socs random process input to an equivalent dt proper complex socs random process output by utilizing the information only about the cycle period of the input an invertible lcl block processing operator named the asymptotic fresh properizer is then proposed that mimics the operation of the dt fresh properizer but processes a finite number of consecutive samples of a dt improper complex socs random process it is shown that the output of the asymptotic fresh properizer is not proper but asymptotically proper and that its frequency domain covariance matrix converges to a highly structured block matrix with diagonal blocks as the block size tends to infinity two representative estimation and detection problems are presented to demonstrate that asymptotically optimal low complexity postprocessors can be easily designed by exploiting these asymptotic second order properties of the output of the asymptotic fresh properizer

survey approximate linearization via feedback an overview fostered by a growing interest in nonlinear control theory and catalyzed by the discovery in the early 1980s of the exact conditions under which a nonlinear plant can be linearized by static state feedback and coordinate transformation in the last decades there has been a rapid increase of interest in the search for approximate solutions to the problem of linearizing nonlinear systems by state or output feedback main reason for that is the limited applicability of the rigorous methods and the complexity sensitivity and design difficulties of the exact linearizing compensators if any in the present paper the literature on the subject is reviewed and organized in what is believed to be a new and consistent perspective recent works especially in the area of data based techniques are in fact described and related whenever possible to fundamental results previously obtained by model based differential geometric methods this is expected to bring modern system linearization methods closer to the needs of practicing control engineers and to stimulate further research eventually able to fill visible gaps in this direction