subspace averaging and order determination for source enumeration in this paper we address the problem of subspace averaging with special emphasis placed on the question of estimating the dimension of the average the results suggest that the enumeration of sources in a multi sensor array which is a problem of estimating the dimension of the array manifold and as a consequence the number of radiating sources may be cast as a problem of averaging subspaces this point of view stands in contrast to conventional approaches which cast the problem as one of identifiying covariance models in a factor model we present a robust formulation of the proposed order fitting rule based on majorization minimization algorithms a key element of the proposed method is to construct a bootstrap procedure based on a newly proposed discrete distribution on the manifold of projection matrices for stochastically generating subspaces from a function of experimentally determined eigenvalues in this way the proposed subspace averaging sa technique determines the order based on the eigenvalues of an average projection matrix rather than on the likelihood of a covariance model penalized by functions of the model order by means of simulation examples we show that the proposed sa criterion is especially effective in high dimensional scenarios with low sample support

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

robust methods for model order estimation model order estimation is a subject in time series analysis that deals with fitting a parametric model to a vector of observations this paper focuses on several model order estimators known in the literature and examines their performance under small deviations of the probability distribution of the noise with respect to a nominal distribution assumed in the model it is demonstrated that the standard estimators suffer from high sensitivity to deviations from the nominal distribution and a drastic performance degradation is experienced to overcome this problem robust estimators that are insensitive to small deviations from the nominal distribution are developed these estimators are based on a composition between model order estimation methods and robust statistical inference techniques known in the literature in addition a new estimator based on a locally best test for weak signals is presented both in nonrobust and robust versions the proposed robust model order estimators are developed on a heuristic basis and there is no claim of optimality but experimental results indicate that they provide significant improvement over the standard estimators

determination of number of sources with multiple arrays in correlated noise fields a detection scheme for signals in a noise field is considered the information theoretic criterion is derived and it gives a consistent estimation of the number of signals comparison of this multiarray estimation and those of the two array systems is given through simulations

analysis of subspace fitting and ml techniques for parameter estimation from sensor array data it is shown that the multidimensional signal subspace method termed weighted subspace fitting wsf is asymptotically efficient this results in a novel compact matrix expression for the cramer rao bound crb on the estimation error variance the asymptotic analysis of the maximum likelihood ml and wsf methods is extended to deterministic emitter signals the asymptotic properties of the estimates for this case are shown to be identical to the gaussian emitter signal case i e independent of the actual signal waveforms conclusions concerning the modeling aspect of the sensor array problem are drawn

finite alphabet information and multivariate blind deconvolution and identification of linear systems this article addresses the problem of estimating a multivariate linear system from its output when the input is an unobservable sequence of random vectors with finite alphabet distribution by explicitly utilizing the finite alphabet property an estimation method is proposed under the traditional inverse filtering paradigm as a generalization of a univariate method that has been studied previously identifiability of multivariate systems by the proposed method is proved mathematically under very mild conditions that can be satisfied even if the input is nonstationary and has both cross channel and serial statistical dependencies statistical super efficiency in estimating both parametric and nonparametric systems is also established for an alphabet based cost function

observability conditions for multiple signal direction finding and array sensor localization three observability issues which arise in narrowband signal direction finding in the presence of array sensor location errors are described necessary and sufficient conditions for the phase delay ambiguity and the rank 2 ambiguity are presented however the characterization of the rank n ambiguity is still an open problem and only a conjecture is given barring these ambiguities the minimal numbers of known and unknown signals required for uniquely localizing the sources and sensors are determined under the assumption of no measurement noises

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

analysis of the spatial filtering approach to the decorrelation of coherent sources the recently proposed spatial filtering which is developed to effectively decorrelate coherent signals is analyzed it has been shown that any set of distinct preliminary estimates of directions of arrival doas can be used to obtain a full rank source covariance matrix in addition a particular signal enhancement approach is developed to minimize the effects of the sensor noise statistical analysis of the spatial filtering and its enhanced version are also studied using the monte carlo method

the cauchy problem for the generalized imbq equation in ws p rn in this paper the existence and the uniqueness of the global strong solution and the global classical solution for the cauchy problem of the multidimensional generalized imbq equation are proved the nonexistence of the global solution for the cauchy problem of the generalized imbq equation is discussed

joint data and channel estimation using blind trellis search techniques a novel method of maximum likelihood sequence estimation is proposed for data that are transmitted over unknown linear channels this procedure does not require a startup sequence for estimating the channel impulse response rather the data and the channel are simultaneously estimated it is implemented without any loss of optimality by a trellis search algorithm which searches for the best data sequence from among a number of hypothesized trellises which are constructed from the observed sequence the number of states in each trellis and the number of trellises grow exponentially with the channel memory a suboptimal trellis search algorithm is proposed whose complexity at best is slightly higher than that of the adaptive viterbi algorithm operating with a known channel response a simplified channel estimation algorithm when the number of data alphabets is greater than 2 is also proposed fast convergence of the algorithm in estimating the channel is demonstrated for binary pulse amplitude modulation over a variety of channels convergence over a wide range of snr occurs within 100 symbols the channel estimation algorithm for multi level signals converges within 500 1000 symbols we finally present an application of this algorithm to the problem of sequence estimation in the presence of rapidly time varying intersymbol interference the algorithm provides reliable zero delay decisions which results in a better channel tracking algorithm when compared to previously proposed schemes

spatio temporal spectral analysis by eigenstructure methods this paper presents new algorithms for estimating the spatio temporal spectrum of the signals received by a passive array the algorithms are based on the eigenstructure of the covariance and spectral density matrices of the received signals they allow partial correlation between the sources and thus are applicable to certain kinds of multipath problems simulation results that illustrate the performance of the new algorithms are presented

estimating the number of sinusoids in additive white noise the test proposed uses the eigenvector decomposition of the estimated autocorrelation matrix and is based on matrix perturbation analysis the estimator is shown to be able to resolve closely spaced sinusoids at lower signal to noise ratios than heuristic tests simulation results for two closely spaced sinusoids are detailed several unanswered questions are discussed

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

fast identification of state space models via exploitation of displacement structure the computational burden of state space model identification has prevented its real time application although it offers some important advantages over other methods based on input output transfer functions a recently proposed state space identification method uses ideas from sensor array signal processing to somewhat reduce the computational burden the major costs still remain because of the need for the singular value or sometimes qr decomposition which requires o mn sup 2 hops and o n sup 2 storage when the data matrix has size m spl times n n m it turns out that proper exploitation using results from the theory of displacement structure of the toeplitz like nature of several matrices arising in the procedure reduces the computational effort to o mn flops with o m sup 2 n storage further computational gains are made by using the recently developed fast subspace decomposition methods results of the study of an actual system are described

blind equalization of digital communication channels using high order moments the authors describe algorithms for blind equalization of digital communication channels of the quadrature amplitude modulation qam type these algorithms are based on the fourth order statistical moments of the received data sequence the first of the two is a linear least squares type algorithm the second algorithm is of the nonlinear least squares type the algorithms use the fourth order statistical moments of the symbol sequence to explicitly estimate the channel impulse response the estimated impulse response is used in turn to construct a linear mean square error equalizer the performance of this equalizer is not optimal in any sense but it is adequate for channels with mild intersymbol interference or when the number of data points available for estimating the channel response is very large

tracking performance of least squares mimo channel estimation algorithm in this paper the tracking performance analysis of the least squares ls multiple input multiple output mimo channel estimation and tracking algorithm is presented mimo channel estimation is a novel application of the ls algorithm that presents near optimum performance by karami and shiva in 2003 and 2006 in this paper the mean square error mse of tracking of the ls mimo channel estimator algorithm is derived as a closed form function of the doppler shift forgetting factor channel rank and the length of training sequences in the analysis all training symbols are considered as randomly generated equal power vectors on the unit circle or in other words phase shift keying psk signaling by evaluating this function some insights into the tracking behavior of the ls mimo channel estimator are achieved then the calculated tracking error is compared with the tracking error derived from monte carlo simulation for quaternary psk based training signals to verify the validation of the presented analysis finally the optimum forgetting factor is derived to minimize the error function and it is shown that the optimum forgetting factor is highly dependent on the training length doppler shift and eb no also it is concluded that in low eb no values the number of transmitter antennas has negligible effect on the optimal value of the forgetting factor

subspace based channel estimation for code division multiple access communication systems we consider the estimation of channel parameters for code division multiple access cdma communication systems operating over channels with either single or multiple propagation paths the multiuser channel estimation problem is decomposed into a series of single user problems through a subspace based approach by exploiting the eigenstructure of the received signal s sample correlation matrix the observation space can be partitioned into a signal subspace and a noise subspace without prior knowledge of the unknown parameters the channel estimate is formed by projecting a given user s spreading waveform into the estimated noise subspace and then either minimizing the likelihood or minimizing the euclidean norm of this projection both of these approaches yield algorithms which are near far resistant and do not require a preamble

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

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

a new perturbation analysis for signal enumeration in rotational invariance techniques the esprit algorithm is a subspace based high resolution method used in source localization and spectral analysis which provides very accurate estimates of the signal parameters however the underlying theory assumes a known model order which is usually not the case in many applications in particular it is well known that underevaluating the model order biases the estimation in this paper we analyze the perturbation induced by an erroneous model order and we present an error bound for the estimated parameters based on this theoretical framework we propose a new method for selecting an appropriate modeling order which consists in minimizing the error bound this approach is applied to both synthetic and musical signals and its performance is compared to that of existing methods such as the information theoretic criteria

global existence and blow up of solutions for a general class of doubly dispersive nonlocal nonlinear wave equations this study deals with the analysis of the cauchy problem of a general class of nonlocal nonlinear equations modeling the bi directional propagation of dispersive waves in various contexts the nonlocal nature of the problem is reflected by two different elliptic pseudodifferential operators acting on linear and nonlinear functions of the dependent variable respectively the well known doubly dispersive nonlinear wave equation that incorporates two types of dispersive effects originated from two different dispersion operators falls into the category studied here the class of nonlocal nonlinear wave equations also covers a variety of well known wave equations such as various forms of the boussinesq equation local existence of solutions of the cauchy problem with initial data in suitable sobolev spaces is proven and the conditions for global existence and finite time blow up of solutions are established

tracking of signal subspace projectors a new subspace tracking approach that directly operates on the projection matrix onto the signal subspace instead of tracking its unitary eigenbasis is proposed therefore the difficulties arising from introducing a calculus on the manifold of projection matrices are overcome by a proper parameterization of the projectors simulation results are presented from the field of angular frequency retrieval in array signal processing

global existence and asymptotic behaviour of solutions for the generalized boussinesq equation abstract in this paper we prove the existence and the uniqueness of global solution for the cauchy problem for the generalized boussinesq equation under some assumptions we also show that the l norm of small solution of the cauchy problem for the generalized boussinesq equation decays to zero as t tends to the infinity

detection and localization of multiple sources via the stochastic signals model a method for the detection of coherent and noncoherent signals based on the application of j rissanen s 1978 minimum description length principle for model selection to the stochastic signals model is presented the detection and localization are done simultaneously with the location estimator coinciding with the maximum likelihood estimator derived by j f bohme 1986 the proposed method outperforms the method of m wax and i ziskind 1989 especially in the threshold region simulation results demonstrating the improved performance are included

spectral matrix completion by cyclic projection and application to sound source reconstruction from non synchronous measurements a fundamental limitation of the inverse acoustic problem is determined by the size of the array and the microphone density a solution to achieve large array and or high microphone density is to scan the object of interest by moving sequentially a small prototype array which is referred to as sequential measurements in comparison to a large array and or high microphone density array that can acquire simultaneously all the information of the spectral matrix in particular all cross spectra sequential measurements can only acquire a block diagonal spectral matrix while the cross spectra between the sequential measurements remain unknown due to the missing phase relationships between consecutive positions nevertheless these unknown cross spectra are necessary for sound source reconstruction the objective of this paper is to propose an algorithm to recover the missing elements of the spectral matrix in the case where the acoustical field is highly coherent this issue is shown to boil down to a matrix completion problem subject to given constraint of hermitian symmetry measurements fitting reduced rank and spatial continuity of the sound field a cyclic projection cp algorithm is proposed in this work to find an optimal solution at the intersection between three predefined sets the proposed method is analyzed through numerical simulations of diverse setups and is also validated experimentally

the determination of optimum structures for the state space representation of multivariate stochastic processes when identifying a model for a multivariate stationary stochastic process an important problem is that of determining the structure of the state variable model several overlapping parameterizations can usually be fitted to a given process and the question arises as to which structure leads to the most accurate parameter estimates the accuracy of parameter estimates is often measured by the determinant of the fisher information matrix we show that all admissible structures will give asymptotically the same value to this criterion for finite data some structures may still be better than others and two heuristic structure estimation methods are analyzed some simulation results are also presented

recursive blind symbol estimation of convolutionally coded cochannel signals a recursive blind equalizer is presented that directly estimates the transmitted symbols of multiple cochannel signals in the presence of isi the algorithm exploits shift structure present in the data model and the finite alphabet property of the signals the proposed method possesses a separation property that allows the symbol sequences for each user to be estimated independently of the others problematic issues surrounding unknown and mismatched channel lengths for the cochannel users can be handled effectively in the recursive equalizer additionally if the cochannel signals are encoded prior to transmission we show how the code structure can be incorporated into the recursive equalizer to improve its performance

on minima of a functional of the gradient upper and lower solutions abstract this paper studies a scalar minimization problem with an integral functional of the gradient under affine boundary conditions a new approach is proposed using a minimal and a maximal solution to the convexified problem we prove a density result any relaxed solution continuously depending on boundary data may be approximated uniformly by solutions of the nonconvex problem keeping continuity relative to data we also consider solutions to the nonconvex problem having lipschitz dependence on boundary data with the best lipschitz constant

doa estimation by exploiting the symmetric configuration of uniform linear array a new direction of arrival doa estimation method is proposed for uniform linear array in this paper when both uncorrelated and coherent sources are present the uncorrelated and coherent sources are estimated at two different stages the uncorrelated sources are first estimated using conventional subspace methods and then they are eliminated by exploiting the symmetric configuration of the array finally the remaining coherent sources are estimated by reconstructing a non toeplitz matrix the number of sources resolved by our method can exceed the number of array elements simulation results demonstrate the effectiveness and efficiency of our proposed method

detection of coherent signals using weighted subspace smoothing a new approach to detecting the number of coherent signals incident upon a uniformly spaced linear array is presented the approach combines a modified spatial smoothing scheme and a modified mdl criterion the modified spatial smoothing scheme referred to as weighted subspace smoothing is actually a generalization of the post smoothing approach proposed by krim and proakis in 1994 it is shown that the noise eigenvalues obtained with weighted subspace smoothing are more accurate than those obtained with the original spatial smoothing we thus attempt to improve the detection performance using these more accurate eigenvalues a novel modification of the minimum description length mdl criterion is proposed to accomplish this computer simulations are presented to study the performance improvement of this new approach

soliton and antisoliton interactions in the good boussinesq equation the solitary wave interaction mechanism for the good boussinesq equation is investigated and found to be far more complicated than was previously thought three salient features are that solitary waves only exist for a finite range of velocities that large solitons can turn into so called antisolitons and that it is possible for solitons to merge and split small solitons however appear to be stable the existence of a potential well is linked to the different behaviors observed between small and large initial conditions

nonparametric detection of signals by information theoretic criteria performance analysis and an improved estimator determining the number of sources from observed data is a fundamental problem in many scientific fields in this paper we consider the nonparametric setting and focus on the detection performance of two popular estimators based on information theoretic criteria the akaike information criterion aic and minimum description length mdl we present three contributions on this subject first we derive a new expression for the detection performance of the mdl estimator which exhibits a much closer fit to simulations in comparison to previous formulas second we present a random matrix theory viewpoint of the performance of the aic estimator including approximate analytical formulas for its overestimation probability finally we show that a small increase in the penalty term of aic leads to an estimator with a very good detection performance and a negligible overestimation probability

bounds on maximum likelihood ratio part ii application to antenna array detection estimation with imperfect wavefront coherence the multiple hypothesis testing problem of the detection estimation of an unknown number of independent gaussian point sources is adequately addressed by likelihood ratio lr maximization over the set of admissible covariance matrix models we introduce nonasymptotic lower and upper bounds for the maximum lr since lr optimization is generally a nonconvex multiextremal problem any practical solution could now be tested against these bounds enabling a high probability of recognizing nonoptimal solutions we demonstrate that in many applications the lower bound is quite tight with approximate maximum likelihood ml techniques often unable to approach this bound the introduced lower bound analysis is shown to be very efficient in determining whether or not performance breakdown has occurred for subspace based direction of arrival doa estimation techniques we also demonstrate that by proper lr maximization we can extend the range of signal to noise ratio snr values and or number of data samples wherein accurate parameter estimates are produced yet when the snr and or sample size falls below a certain limit for a given scenario we show that ml estimation suffers from a discontinuity in the parameter estimates a phenomenon that cannot be eliminated within the ml paradigm

order selection of autoregressive models the problem of determining the order of autoregressive models by bayesian predictive densities is addressed a criterion employing noninformative prior densities of the model parameters is derived simulation results which demonstrate the good performance of the criterion are presented comparisons with four popular approaches verify its superiority in many cases

blow up and scattering of solution for a generalized boussinesq equation in this paper we consider the cauchy problem for a class of boussinesq equation we obtain the existence and uniqueness of the local solutions for a class of nonlinearity of the perturbation blow up solutions are obtained furthermore the global existence and nonlinear scattering for small amplitude solutions are established

the most likely path of a differential inclusion can be used in alternative to stochastic processes as a model for systems whose evolution is non deterministic compared with the rich mathemati cal theory which is currently available for random processes however dif ferential inclusions have remained a rather thin subject concerned mainly with the existence of solutions and with the topological properties of the set of trajectories the present paper is an attempt to widen the scope of this theory introducing the notion of likelihood for a solution of a differential inclusion and formulating a corresponding class of estimation prediction and filtering problems to do this a simple approach first comes to mind define some probabil ity measure on the set of trajectories of 1 1 and formulate the prediction and filtering problems accordingly unfortunately there seems to be no canonical probability distribution which is supported precisely on the solution set of 1 1 the choice of any particular distribution would thus require considerable additional information about the system to be modeled for this reason we consider a new definition of likelihood which is entirely independent of probability theory relying solely on the metric structure if 9 denotes the family of all solutions of 1 1 and u e 9 a rough estimate of how many trajectories u e b remain close to u is given by fl d u f iv t u t l 0 as e 0 the i mum of the quantities 1 2 is a well defined number 155

cross spectrum based blind channel identification a novel cross correlation based framework is proposed for the problem of blind equalization in communications we assume that we have access to two observations obtained either by sampling at the symbol rate the outputs of two sensors or by oversampling by a factor of two the output of a single sensor in either case the two observations correspond to the outputs of two channels excited by the same input the channels are estimated using the theory of signal reconstruction from phase only the phase used is the phase of the cross spectrum of the observations filtered through their minimum phase equivalent filters we provide an analytical study of the propagation of noise effects in the phase estimate comparisons with existing methods indicate that the proposed approach is robust to noise and at low signal to noise ratio snr leads to significantly smaller channel estimation errors besides robustness to noise the proposed method does not require knowledge of channel lengths which are determined via an iterative procedure

solutions of vectorial hamilton jacobi equations and minimizers of nonquasiconvex functionals abstract we provide a unified approach to prove existence results for the dirichlet problem for hamilton jacobi equations and for the minimum problem for nonquasiconvex functionals of the calculus of variations with affine boundary data the idea relies on the definition of integro extremal solutions introduced in the study of nonconvex scalar variational problem

estimating the parameters of exponentially damped sinusoids and pole zero modeling in noise we have presented techniques 1 6 based on linear prediction lp and singular value decomposition svd for accurate estimation of closely spaced frequencies of sinusoidal signals in noise in this note we extend these techniques to estimate the parameters of exponentially damped sinusoidal signals in noise the estimation procedure presented here makes use of backward prediction in addition to svd first the method is applied to data consisting of one and two exponentially damped sinusoids the choice of one and two signal components facilitates the comparison of estimation error in pole damping factors and pole frequencies to the appropriate cramer rao cr bounds and to traditional methods of linear prediction second our method is applied to an example due to steiglitz 8 in which the data consists of noisy values of the impulse response samples composed of many exponentially damped sinusoids of a linear system having both poles and zeros the poles of the system are accurately determined by our method and the zeros are obtained subsequently using shanks method

non parametric detection of the number of signals hypothesis testing and random matrix theory detection of the number of signals embedded in noise is a fundamental problem in signal and array processing this paper focuses on the non parametric setting where no knowledge of the array manifold is assumed first we present a detailed statistical analysis of this problem including an analysis of the signal strength required for detection with high probability and the form of the optimal detection test under certain conditions where such a test exists second combining this analysis with recent results from random matrix theory we present a new algorithm for detection of the number of sources via a sequence of hypothesis tests we theoretically analyze the consistency and detection performance of the proposed algorithm showing its superiority compared to the standard minimum description length mdl based estimator a series of simulations confirm our theoretical analysis

on the behavior of information theoretic criteria for model order selection the akaike 1974 information criterion aic and the minimum description length mdl are two well known criteria for model order selection in the additive white noise case our aim is to study the influence on their behavior of a large gap between the signal and the noise eigenvalues and of the noise eigenvalue dispersion our results are mostly qualitative and serve to explain the behavior of the aic and the mdl in some cases of great practical importance we show that when the noise eigenvalues are not clustered sufficiently closely then the aic and the mdl may lead to overmodeling by ignoring an arbitrarily large gap between the signal and the noise eigenvalues for fixed number of data samples overmodeling becomes more likely for increasing the dispersion of the noise eigenvalues for fixed dispersion overmodeling becomes more likely for increasing the number of data samples undermodeling may happen in the cases where the signal and the noise eigenvalues are not well separated and the noise eigenvalues are clustered sufficiently closely we illustrate our results by using simulations from the effective channel order determination area

global existence and asymptotic behavior of solution for the sixth order boussinesq equation with damped term abstract we investigate the small data cauchy problem for the sixth order boussinesq equation with damped term the decay estimates of solutions to the corresponding linear equation are given by using the dyadic decomposition and some properties of bessel functions then we prove the global existence and asymptotic of the small amplitude solution in the time weighted sobolev space by the contraction mapping principle

direct estimation of blind zero forcing equalizers based on second order statistics most existing zero forcing equalization algorithms rely either on higher than second order statistics or on partial or complete channel identification we describe methods for computing fractionally spaced zero forcing blind equalizers with arbitrary delay directly from second order statistics of the observations without channel identification we first develop a batch type algorithm then adaptive algorithms are obtained by linear prediction and gradient descent optimization our adaptive algorithms do not require channel order estimation nor rank estimation compared with other second order statistics based approaches ours do not require channel identification at all on the other hand compared with the cma type algorithms ours use only second order statistics thus no local convergence problem exists and faster convergence can be achieved simulations show that our algorithms outperform most typical existing algorithms

on the observability of fuzzy dynamical control systems ii in this paper we continue to study the fuzzy logic system from the aspect of fuzzy differential equations and discuss the concept of observability given the rule base for the input and the output we can determine rule base for initial value by a formula the significance of this result is that given a deterministic system and fuzzy input and output rule base we can determine the rule base for initial value without solving the equation

on existence of weak solutions for one dimensional forward backward diffusion equations we establish the existence of infinitely many weak solutions for the general one dimensional forward backward diffusion equation ut ux x under the homogeneous neumann boundary condition by rephrasing it as a first order differential inclusion problem

a baire category approach to the bang bang property abstract the aim of this paper is to develop a new technique based on the baire category theorem in order to establish the closedness of reachable sets and the existence of optimal trajectories for control systems without the usual convexity assumptions the bang bang property is proved for a new class of concave multifunctions characterized by the existence of suitable linear selections the proofs rely on lyapunov s theorem in connection with a baire category argument

detection of the number of coherent signals by the mdl principle an approach is presented to the problem of detecting the number of sources impinging on a passive sensor array that is based on j rissanen s 1983 minimum description length mdl principle the approach is applicable to any type of sources including the case of sources which are fully correlated referred to as the coherent signals case two slightly different detection criteria are derived both requiring the estimation of the locations of the sources the first is tailored to the detection problem per se whereas the second is tailored to the combined detection estimation problem consistency of the two criteria is proved and their performance is demonstrated by computer simulations

detection of the number of signals using the benjamini hochberg procedure this paper presents a novel approach to detect multiple signals embedded in noisy observations from a sensor array we formulate the detection problem as a multiple hypothesis test to control the global level of the multiple test we apply the false discovery rate fdr criterion proposed by benjamini and hochberg compared to the classical familywise error rate fwe criterion the fdr controling procedure leads to a significant gain in power for large size problems in addition we apply the bootstrap technique to estimate the observed significance level required by the fdr controling procedure simulations show that the fdr controling procedure always provides higher probability of correct detection than the fwe controling procedure furthermore the reliability of the proposed test procedure is not affected by the gain in power of the test

statistical analysis of effective singular values in matrix rank determination a major problem in using svd singular value decomposition as a tool in determining the effective rank of a perturbed matrix is that of distinguishing between significantly small and significantly large singular values to the end conference regions are derived for the perturbed singular values of matrices with noisy observation data the analysis is based on the theories of perturbations of singular values and statistical significance test threshold bounds for perturbation due to finite precision and i i d random models are evaluated in random models the threshold bounds depend on the dimension of the matrix the noisy variance and predefined statistical level of significance results applied to the problem of determining the effective order of a linear autoregressive system from the approximate rank of a sample autocorrelation matrix are considered various numerical examples illustrating the usefulness of these bounds and comparisons to other previously known approaches are given

system identification using a linear combination of cumulant slices a linear approach to identifying the parameters of a moving average ma model from the statistics of the output is presented first it is shown that under some constraints the impulse response of the system can be expressed as a linear combination of cumulant slices then this result is used to obtain a well conditioned linear method for estimating the ma parameters of a nongaussian process the linear combination of slices used to compute the ma parameters can be constructed from different sets of cumulants of different orders provided a general framework in which all the statistics can be combined it is not necessary to use second order statistics autocorrelation slice and therefore the proposed algorithm still provides consistent estimates in the presence of colored gaussian noise another advantage of the method is that while most linear methods give totally erroneous estimates if the order is overestimated the proposed approach does not require a previous estimation of the filter order the simulation results confirm the good numerical conditioning of the algorithm and its improvement in performance in comparison to existing methods

kawahara dynamics in dispersive media abstract in a previous paper it was shown that in the long wave limit the water wave problem without surface tension can be described approximately by two decoupled kdv equations here we study a model problem and prove that in a degenerate case which occurs for the water wave problem with surface tension and near other codimension two points at which the coefficient in front of the leading order dispersive term in the equation of motion vanishes the long wave limit can be rigorously approximated by two decoupled kawahara equations

blind fractionally spaced equalization of noisy fir channels direct and adaptive solutions blind fractionally spaced equalizers reduce intersymbol interference using second order statistics without the need for training sequences methods for finding fir zero forcing blind equalizers directly from the observations are described and adaptive versions are developed in contrast most current methods require channel estimation as a first step to estimating the equalizer the direct methods can be zero forcing minimum mean square error or even minimum mean square error mmse within the class of zero forcing equalizers performance of the proposed methods and comparisons with existing approaches are shown for a variety of channels including an empirically measured digital microwave channel

blind sequence estimation estimating the data sequence from the received signal without knowing the transmission channel is referred to as blind sequence estimation a new blind sequence estimation scheme is proposed by exploiting the second order statistical properties of the source and the algebraic structure of the data sequence an optimal source deterministic correlation estimator and the viterbi algorithm are used to achieve blind sequence estimation the proposed approach also has a special structure particularly attractive for time varying channels

sensor array signal processing via a procrustes rotations based eigenanalysis of the esprit data pencil the authors propose the procrustes rotation based esprit algorithm pro esprit for estimating characteristic parameters associated with a scene of radiating sources given data derived from two identical sensor arrays the x and y arrays which are displaced relative to one another pro esprit uses the inherent redundancy built into the esprit array system to compensate for deviations from the ideal array model this redundancy is manifested by two fundamental properties of the noiseless x and y data matrices comprising the esprit data pencil a they have the same row space the signal subspace and 2 they have the same column space the source subspace these properties are utilized by invoking two primary tools 1 the solution to the procrustes problem for optimally approximating an invariant subspace rotation and 2 the total least squares method for perturbing each of two estimates of a common subspace in a minimal fashion until the two perturbed spaces are the same

music maximum likelihood and cramer rao bound further results and comparisons the problem of determining the direction of arrival of narrowband plane waves using sensor arrays and the related problem of estimating the parameters of superimposed signals from noisy measurements are studied a number of results have been recently presented by the authors on the statistical performance of the multiple signal characterization music and the maximum likelihood ml estimators for the above problems this work extends those results in several directions first it establishes that in the class of weighted music estimators the unweighted music achieves the best performance i e the minimum variance of estimation errors in large samples next it derives the covariance matrix of the ml estimator and presents detailed analytic studies of the statistical efficiency of music and ml estimators these studies include performance comparisons of music and mle with each other as well as with the ultimate performance corresponding to the cramer rao bound finally some numerical examples are given which provide a more quantitative study of performance for the problem of finding two directions with uniform linear sensor arrays

eigenvalue estimation of parameterized covariance matrices of large dimensional data this article deals with the problem of estimating the covariance matrix of a series of independent multivariate observations in the case where the dimension of each observation is of the same order as the number of observations although such a regime is of interest for many current statistical signal processing and wireless communication issues traditional methods fail to produce consistent estimators and only recently results relying on large random matrix theory have been unveiled in this paper we develop the parametric framework proposed by mestre and consider a model where the covariance matrix to be estimated has a known finite number of eigenvalues each of it with an unknown multiplicity the main contributions of this work are essentially threefold with respect to existing results and in particular to mestre s work to relax the restrictive separability assumption to provide joint consistent estimates for the eigenvalues and their multiplicities and to study the variance error by means of a central limit theorem

decay and scattering of solutions for a generalized boussinesq equation abstract in this paper we consider the long time behavior of small solutions of the cauchy problem for a generalized boussinesq equation a scattering operator and the nonlinear scattering for small amplitude solutions of the boussinesq equation are established under certain hypotheses

minimization of functionals of the gradient by baire s theorem we give sufficient conditions for the existence of solutions of the minimum problem cal p u 0 qquad hbox minimize quad int omega g du x dx quad u in u 0 w 0 1 p omega bbb r based on the structure of the epigraph of the lower convex envelope of g which is assumed be lower semicontinuous and to grow at infinity faster than the power p with p larger than the dimension of the space no convexity conditions are required on g and no assumptions are made on the boundary datum u 0 in w 0 1 p omega bbb r

optimal existence theorems for nonhomogeneous differential inclusions abstract in this paper we address the question of solvability of the differential inclusions 1 1 our approach to these problems is based on the idea of constructing a sequence of approximate solutions which converges strongly and makes use of gromov s idea following earlier work of nash and kuiper to control convergence of the gradients by appropriate selection of the elements of the sequence in this paper we identify an optimal setting of this method in particular we show that the existence result holds for general upper semicontinuous functions h without extra requirements like quasiconvexity of h with respect to du which was assumed in previous works where the idea to apply the baire category lemma to the sets of approximate solutions was developed we also apply our result to identify the minimal sets where the function h should vanish to guarantee solvability of the inclusions

small amplitude solutions of the generalized imbq equation in this paper the global existence of small amplitude solution for the cauchy problem of the multidimensional generalized imbq equation is proved moreover we obtain a nonlinear scattering result of the cauchy problem of the imbq equation for small initial data

noisy data and impulse response estimation this paper investigates the impulse response estimation of linear time invariant lti systems when only noisy finite length input output data of the system is available the competing parametric candidates are the least square impulse response estimates of possibly different lengths it is known that the presence of noise prohibits using model sets with large number of parameters as the resulting parameter estimation error can be quite large model selection methods acknowledge this problem hence they provide metrics to compare estimates in different model classes such metrics typically involve a combination of the available least square output error which decreases as the number of parameters increases and a function that penalizes the size of the model in this paper we approach the model class selection problem from a different perspective that is closely related to the involved denoising problem the method primarily focuses on estimating the parameter error in a given model class of finite order using the available least square output error we show that such an estimate which is provided in terms of upper and lower bounds with certain level of confidence contains the appropriate tradeoffs between the bias and variance of the estimation error consequently these measures can be used as the basis for model comparison and model selection furthermore we demonstrate how this approach reduces to the celebrated aic method for a specific confidence level the performance of the method as the noise variance and or the data length varies is explored and consistency of the approach as the data length grows is analyzed

performance analysis of the total least squares esprit algorithm the asymptotic distribution of the estimation error for the total least squares tls version of esprit is derived the application to a uniform linear array is treated in some detail and a generalization of esprit to include row weighting is discussed the cramer rao bound crb for the esprit problem formulation is derived and found to coincide with the asymptotic variance of the tls esprit estimates through numerical examples a comparison of this method to least squares esprit music and root music as well as to the crb for a calibrated array is also presented tls esprit is found to be competitive with the other methods and the performance is close to the calibrated crb for many cases of practical interest for highly correlated signals however the performance deviates significantly from the calibrated crb simulations are included to illustrate the applicability of the theoretical results to a finite number of data

blind sequence detection without channel estimation this paper proposes a new blind sequence estimation method for single input single output siso systems utilizing an optimal trellis search which is performed by a channel independent viterbi algorithm civa in contrast to the traditional viterbi algorithm that requires accurate channel estimation civa does not require channel coefficients instead the metrics are calculated from a bank of test vectors designed off line the proposed algorithm has outstanding performance under most of the channel conditions specifically it does not suffer from ill conditioned channels in addition it does not depend on channel correlation estimation and therefore has fast convergence simulations demonstrate its superior performance over even most training based equalization algorithms

on posterior distributions for signals in gaussian noise with unknown covariance matrix a bayesian approach to estimate parameters of signals embedded in complex gaussian noise with unknown color is presented the study specifically focuses on a bayesian treatment of the unknown noise covariance matrix making up a nuisance parameter in such problems by integrating out uncertainties regarding the noise color an enhanced ability to estimate both the signal parameters as well as properties of the error is exploited several noninformative priors for the covariance matrix such as the reference prior the jeffreys prior and modifications to this are considered some of the priors result in analytical solutions whereas others demand numerical approximations in the linear signal model connections are made between the standard adaptive maximum likelihood aml estimate and a bayesian solution using the jeffreys prior with adjustments to the jeffreys prior correspondence to the regularized solution is also established this in turn enables a formal treatment of the regularization parameter simulations indicate that significant improvements compared to the aml estimator can be obtained by considering both the derived regularized solutions as well as the one obtained using the reference prior the simulations also indicate the possibility of enhancing the predictions of properties of the error as uncertainties in the noise color are acknowledged

decay and scattering of small solutions of a generalized boussinesq equation abstract we study the long time behavior of small solutions of the initial value problem for a generalized boussinesq equation we obtain a lower bound for the degrees of nonlinearity which allows us to establish a nonlinear scattering result for small perturbations that is the small solutions of the nonlinear problem behave asymptotically like the solution of the associated linear problem under certain hypotheses we can construct a scattering operator for the boussinesq equation which carries a neighborhood of 0 in the energy space x into x

source localization in a waveguide using polynomial rooting source localization in acoustic waveguides involves a multidimensional search procedure we propose a new algorithm in which the search in the depth direction is replaced by polynomial rooting using the proposed algorithm range and depth estimation by a vertical array requires a 1 d search procedure for a 3 d localization problem i e range depth and direction of arrival doa estimation the algorithm involves a 2 d search procedure consequently the proposed algorithm requires significantly less computation than other methods that are based on a brute force search procedure over the source location parameters in order to evaluate the performance of the algorithm an error analysis is carried out and monte carlo simulations are performed the results are compared with the cramer rao bound crb and to the maximum likelihood ml simulation performance the algorithm is shown to be efficient while being computationally simpler than the ml or the bartlett processors the disadvantage of the algorithm is that its snr threshold occurs in lower snr than in the ml algorithm

a projection approach for robust adaptive beamforming it is well known that calibration errors can seriously degrade performance in adaptive arrays particularly when the input signal to noise ratio is large the effect is caused by the perturbation of the presumed steering vector from its optimal value although it is not as widely known similar degradation occurs in sampled matrix inversion processing when the covariance matrix is estimated while the desired signal is present in the snapshot data under these conditions performance loss is due to errors in the estimated covariance matrix and occurs even when the steering vector is known exactly in the paper a new method based of modification of the steering vector is proposed to overcome both the problems of perturbation and of sample covariance errors the method involves projection of the presumed steering vector onto the observed signal plus interference subspace an analysis is also presented illustrating that the sample covariance errors can be viewed as a particular type of perturbation error and a simple approximation is derived for the expected beamformer performance as a function of the number of data snapshots both analytical and experimental results are presented that illustrate the advantages of the proposed method

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

global solution for a generalized boussinesq equation this paper considers the existence and uniqueness of the solution to the cauchy problem for a class of boussinesq equation proves the global existence and finite time blowup of the solution to the problem by the potential well method

extremal solutions of differential inclusions via baire category a dual approach abstract let f be a continuous multifunction on r n with compact convex values for any vector w let f w x f x be the subset of points which maximize the inner product with w call w the set of all continuous functions w 0 t r n with the following property all solutions to the cauchy problem x t f w t x t x 0 0 are also solutions to x t ext f x t we prove that w is residual in c 0 t r n

svd based information theoretic criteria for detection of the number of damped undamped sinusoids and their performance analysis following the information theoretic approach to model selection the authors develop criteria for detection of the number of damped undamped sinusoids these criteria are matched to the singular value decomposition svd based methods such as modified forward backward and forward backward linear prediction so well that the extra computations needed over and above those required for computing the svd are marginal next an analytical framework for analyzing the performance of these criteria is developed in the development of the analysis some approximations which become better for large signal to noise ratio are made simulations are used to verify the usefulness of the analysis and to compare the performance of the method with that of j j fuchs 1988

on the use of order statistics for improved detection of signals by the mdl criterion the minimum description length mdl criterion for model selection has been successfully applied to the problem of estimating the number of sources in noise we show that by employing an order statistics approach in the existing solution a new processor with uniformly improved performance is constructed at the cost of greater complexity we prove that the resulting mdl based processor is consistent results of simulations of practical scenarios of interest demonstrate how significant the performance improvement can be

global existence of smooth solutions and stability of solitary waves for a generalized boussinesq equation certain generalizations of one of the classical boussinesq type equations u tt u xx u 2 u xx xx are considered it is shown that the initial value problem for this type of equation is always locally well posed it is also determined that the special solitary wave solutions of these equations are nonlinearly stable for a range of their phase speeds these two facts lead to the conclusion that initial data lying relatively close to a stable solitary wave evolves into a global solution of these equations this contrasts with the results of blow up obtained recently by kalantarov and ladyzhenskaya for the same type of equation and casts additional light upon the results for the original version of this class of equations obtained via inverse scattering theory by deift tomei and trubowitz