cross correlations of diffuse noise in an ocean environment using eigenvalue based statistical inference cross correlations of diffuse noise fields can be used to extract environmental information the influence of directional sources usually ships often results in a bias of the travel time estimates obtained from the cross correlations using an array of sensors insights from random matrix theory on the behavior of the eigenvalues of the sample covariance matrix scm in an isotropic noise field are used to isolate the diffuse noise component from the directional sources a sequential hypothesis testing of the eigenvalues of the scm reveals eigenvalues dominated by loud sources that are statistical outliers for the assumed diffuse noise model travel times obtained from cross correlations using only the diffuse noise component i e by discarding or attenuating the outliers converge to the predicted travel times based on the known array sensor spacing and measured sound speed at the site and are stable temporally i e unbiased estimates data from the shallow water 2006 experiment demonstrates the effectiveness of this approach and that the signal to noise ratio builds up as the square root of time as predicted by theory

robust beamforming via worst case sinr maximization minimum variance beamforming which uses a weight vector that maximizes the signal to interference plus noise ratio sinr is often sensitive to estimation error and uncertainty in the parameters steering vector and covariance matrix robust beamforming attempts to systematically alleviate this sensitivity by explicitly incorporating a data uncertainty model in the optimization problem in this paper we consider robust beamforming via worst case sinr maximization that is the problem of finding a weight vector that maximizes the worst case sinr over the uncertainty model we show that with a general convex uncertainty model the worst case sinr maximization problem can be solved by using convex optimization in particular when the uncertainty model can be represented by linear matrix inequalities the worst case sinr maximization problem can be solved via semidefinite programming the convex formulation result allows us to handle more general uncertainty models than prior work using a special form of uncertainty model we illustrate the method with a numerical example

optimal control of dynamic systems application to spline approximations generally classical polynomial splines tend to exhibit unwanted undulations in this work we discuss a technique based on control principles for eliminating these undulations and increasing the smoothness properties of the spline interpolants we give a generalization of the classical polynomial splines and show that this generalization is in fact a family of splines that covers the broad spectrum of polynomial trigonometric and exponential splines a particular element in this family is determined by the appropriate control data it is shown that this technique is easy to implement several numerical and curve fitting examples are given to illustrate the advantages of this technique over the classical approach finally we discuss the convergence properties of the interpolant

indirect dominant mode rejection a solution to low sample support beamforming under conditions of low sample support a low rank solution of the minimum variance distortionless response mvdr equations can yield a higher output signal to interference plus noise ratio sinr than the full rank mvdr beamformer in this paper we investigate several low rank beam forming techniques and we also propose a new beamformer that we refer to as the indirect dominant mode rejection idmr we analyze the degradation in the output sinr caused by residual cross correlations embedded in the sampled covariance matrix due to low sample support the idmr beamformer is based on a parametric estimate of the covariance matrix in which any cross correlation is canceled out simulations reveal that the idmr beamformer yields a dramatic improvement in output sinr relative to the conjugate gradient cg principal component inverse pci and dominant mode rejection dmr beamformers in our investigation of the low rank cg beamformer we address the issue of whether the unity gain constraint in the look direction should be enforced a priori via the use of a blocking matrix or effected a posteriori through simple scaling of the beamforming vector remarkably it is proven that the two methods yield exactly the same low rank beamformer at each and every rank

reproduction of exponential polynomials by multivariate non stationary subdivision schemes with a general dilation matrix we study scalar multivariate non stationary subdivision schemes with a general integer dilation matrix we characterize the capability of such schemes to reproduce exponential polynomials in terms of simple algebraic conditions on their symbols these algebraic conditions provide a useful theoretical tool for checking the reproduction properties of existing schemes and for constructing new schemes with desired reproduction capabilities and other enhanced properties we illustrate our results with several examples

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

shrinkage of covariance matrices for linear signal estimation using cross validation linear estimation of signals is often based on covariance matrices estimated from training which can perform poorly if the training data are limited and the estimated covariance matrices are ill conditioned shrinking the covariance matrix toward a scaled identity matrix can improve the robustness against the model uncertainty provided the shrinkage factor is appropriately chosen this paper introduces several cross validation schemes for choosing the shrinkage factors in applications where the covariance matrices are replaced with sample covariance matrices or constructed from least squares estimates of the linear model parameters for cases where the training and out of training data are identically distributed we derive leave one out cross validation loocv schemes that repeatedly split the training data with respect to time to determine the optimal shrinkage factors for either model fitting or signal estimation for cases where they are distributed differently we develop alternative loocv schemes that repeatedly split the out of training observations with respect to space we derive computationally efficient implementations of those schemes and provide examples to demonstrate their performance

a fast linear programming algorithm for blind equalization a fast implementation of a special non mse cost function for blind equalization is presented here this baud rate equalization algorithm is based on a convex cost function coupled with a simple linear constraint on the equalizer parameters for a generic class of channels with persistently exciting quadrature amplitude modulation input signals this new algorithm allows the convergence of equalizer parameters to a unique global minimum achieving intersymbol interference suppression and carrier phase recovery

on polynomial ideals of finite codimension with applications to box spline theory we investigate the relation between an ideal i of finite codimension in the space of multivariate polynomials and ideals which are generated by lower order perturbations of some generators for i of particular interest are the codimension of these ideals and the local approximation order of their kernels the discussion stimulated by recent results in approximation theory allows us to provide a simple analysis of the polynomial and exponential spaces associated with box splines we describe their structure dimension and local approximation order and an algorithm for their construction the resulting theory is extended to subspaces of the above exponential polynomial spaces

adaptive uncertainty based iterative robust capon beamformer using steering vector mismatch estimation to overcome the signal to interference and noise ratio sinr performance degradation in the presence of large steering vector mismatches we propose an iterative robust capon beamformer ircb with adaptive uncertainty level the approach iteratively estimates the actual steering vector sv based on conventional robust capon beamformer rcb formulation that uses an uncertainty sphere to model the mismatch between the actual and presumed sv at each iteration the adaptive uncertainty algorithm self adjusts the uncertainty sphere according to the estimated mismatch sv this estimation is derived based on the geometrical interpretation of the mismatch and can be expressed as a simple closed form expression as a function of the presumed sv and the signal subspace projection the other variant of the proposed algorithm that uses a flat ellipsoid to model the mismatch is also proposed simulation results show that the proposed approaches offer better interference suppression capability and achieve higher output sinr as compared to other diagonal loading based approaches

an efficient method to determine the diagonal loading factor using the constant modulus feature the diagonal loading method is a simple and efficient method that improves the robustness of beamformers however determining an ideal diagonal loading factor dlf is not a trivial problem one that still has not been adequately addressed although beamformers are widely used in radar sonar and many other applications in this correspondence we consider a beamformer used only for digital communication applications in digital communications user information is coded into a sequence with the constant modulus cm in the baseband obviously if the beamformer can cancel interference sufficiently well the outputs of the beamformer should satisfy the cm condition more precisely therefore minimizing cm errors can act as a natural criterion for determining dlfs in this correspondence we present a cost function based on the criterion we also propose a direct search algorithm for dlf determination by minimizing the cost function numerical experiments show the effectiveness of the proposed method

a bayesian approach to robust adaptive beamforming an adaptive beamformer that is robust to uncertainty in source direction of arrival doa is derived using a bayesian approach the doa is assumed to be a discrete random variable with a known a priori probability density function pdf that reflects the level of uncertainty in the source doa the resulting beamformer is a weighted sum of minimum variance distortionless response mvdr beamformers pointed at a set of candidate doas where the relative contribution of each mvdr beamformer is determined from the a posteriori pdf of the doa conditioned on previously observed data a simple approximation to the a posteriori pdf results in a straightforward implementation performance of the approximate bayesian beamformer is compared with linearly constrained minimum variance lcmv beamformers and data driven approaches that attempt to estimate signal characteristics or the steering vector from the data

analysis of modified smi method for adaptive array weight control the authors characterize the performance of the diagonally loaded sample matrix inverse smi algorithm versus the number k of snapshots used in the covariance matrix estimate by providing o 1 k statistics bias and variance of the array weights output powers and output power ratios such as signal to interference noise ratio sinr and inr the approach accommodates wideband signals monte carlo simulations verify the theoretical analysis

convergence of the smi and the diagonally loaded smi algorithms with weak interference adaptive array approximations for the power levels at the output of an adaptive array that uses the diagonally loaded sample matrix inversion smi algorithm are derived diagonal loading is a technique where the diagonal of the covariance matrix is augmented with a positive or negative constant prior to inversion the authors examine how the signal to interference plus noise ratio sinr and signal to interference ratio sir at the array output vary with the number of samples taken when the input signals are continuous wave it is shown that positive loading produces more rapid convergence with a reduction in output sir negative loading provides an improved sir level but it is shown that positive loading produces more rapid convergence with a reduction in output sir negative loading provides an improved sir level but it is shown that the output power levels are erratic and slow to converge simulation results which verify the theoretical procedure are given

hierarchical zonotopal spaces zonotopal algebra interweaves algebraic geometric and combinatorial properties of a given linear map x of basic significance in this theory is the fact that the algebraic structures are derived from the geometry via a non linear procedure known as the least map and that the statistics of the algebraic structures e g the hilbert series of various polynomial ideals are combinatorial i e computable using a simple discrete algorithm known as the valuation function on the other hand the theory is somewhat rigid since it deals for the given x with exactly two pairs each of which is made of a nested sequence of three ideals an external ideal the smallest a central ideal the middle and an internal ideal the largest in this paper we show that the fundamental principles of zonotopal algebra as described in the previous paragraph extend far beyond the setup of external central and internal ideals by building a whole hierarchy of new combinatorially defined zonotopal spaces ams subject classification 13f20 13a02 16w50 16w60 47f05 47l20 05b20 05b35 05b45 05c50 52b05 52b12 52b20 52c07 52c35 41a15 41a63

robust design of radar doppler filters this paper considers the design of robust filters for radar pulse doppler processing when the interference is a wide sense stationary random process the figure of merit which is optimized is the signal to interference plus noise ratio sinr at the filter output under a multitude of constraints accounting for doppler filter sidelobes as well as uncertainties both in the received useful signal component and interference covariance matrix the design is analytically formulated as a constrained optimization problem whose solvability is thoroughly studied precisely a polynomial time solution technique to get the optimal filter is proposed exploiting the representation of non negative trigonometric polynomials via linear matrix inequalities the spectral factorization theorem and the duality theory last but not least a detailed analysis of the optimum filter performance is provided showing the tradeoffs involved in the design and the gain achievable over some already known counterparts

least squares approach to blind channel equalization we present a least squares ls algorithm for blind channel equalization based on a reformulation of the godard algorithm a transformation for the equalizer parameters is considered to convert the nonlinear ls problem inherent in the godard algorithm to a linear ls problem unlike the godard 1980 algorithm the proposed ls approach does not suffer from ill convergence to closed eye local minima methods for extracting the equalizer parameters from their transformed version are developed offline and recursive implementations of the ls algorithm are presented the algorithm requires only a small number of channel output observations to estimate the equalizer parameters and is therefore fast vis a vis the godard algorithm the channel input correlation does not impose any restriction on the application of the algorithm as long as a weak sufficient excitation condition is satisfied simulation examples are presented to demonstrate the ls approach and to compare it with the godard algorithm

translates of exponential box splines and their related spaces exponential box splines eb splines are multivariate compactly supported functions on a regular mesh which are piecewise in a space z spanned by exponential polynomials this space can be defined as the intersection of the kernels of certain partial differential operators with constant coefficients the main part of this paper is devoted to algebraic analysis of the space h of all entire functions spanned by the integer translates of an eb spline this investigation relies on a detailed description of z and its discrete analog s the approach taken here is based on the observation that the structure of z is relatively simple when z is spanned by pure exponentials while all other cases can be analyzed with the aid of a suitable limiting process also we find it more efficient to apply directly the relevant differential and difference operators rather than the alternative techniques of fourier analysis thus while generalizing the known theory of polynomial box splines the results here offer a simpler approach and a new insight towards this important special case we also identify and study in detail several types of singularities which occur only for complex eb splines the first is when the fourier transform of the eb spline vanishes at some critical points the second is when z cannot be embedded in y and the third is when h is a proper subspace of z we show among others that each of these three cases is strictly included in its former and they all can be avoided by a refinement of the mesh

an analysis of the projection method for robust adaptive beamforming two causes of performance degradation in adaptive beamforming are perturbation error and sample covariance error these causes were discussed by feldman and griffihs see ieee trans signal processing vol 42 p 867 april 1994 which proposed an approach termed the projection method to reduce the sensitivity of the beamformer performance to both types of error this paper contains an analysis of the expected performance of the beamformer when it is implemented either with or without using the projection method based on a second order taylor series expansion of an approximate expression for the signal to interference plus noise ratio sinr at the beamformer output the analysis provides accurate results when either perturbation error or sample covariance error occurs a less accurate analysis based on a zeroth order taylor series expansion includes results presented by jablon 1986 and chang and yeh see ibid vol 40 no 11 p 1336 1992 as special cases

beamforming using subspace estimation from a diagonally averaged sample covariance the potential benefit of a large aperture sonar array for high resolution target localization is often challenged by the lack of sufficient data required for adaptive beamforming this paper introduces a toeplitz constrained estimator of the clairvoyant signal covariance matrix corresponding to multiple far field targets embedded in background isotropic noise the estimator is obtained by averaging along subdiagonals of the sample covariance matrix followed by covariance extrapolation using the method of maximum entropy the sample covariance is computed from limited data snapshots a situation commonly encountered with large aperture arrays in environments characterized by short periods of local stationarity eigenvectors computed from the toeplitz constrained covariance are used to construct signal subspace projector matrices which are shown to reduce background noise and improve detection of closely spaced targets when applied to subspace beamforming monte carlo simulations corresponding to increasi

robust adaptive beamforming based on steering vector estimation with as little as possible prior information a general notion of robustness for robust adaptive beamforming rab problem and a unified principle for minimum variance distortionless response mvdr rab techniques design are formulated this principle is to use standard mvdr beamformer in tandem with an estimate of the desired signal steering vector found based on some imprecise prior information differences between various mvdr rab techniques occur only because of the differences in the assumed prior information and the corresponding signal steering vector estimation techniques a new mvdr rab technique which uses as little as possible and easy to obtain imprecise prior information is developed the objective for estimating the steering vector is the maximization of the beamformer output power while the constraints are the normalization condition and the requirement that the estimate does not converge to any of the interference steering vectors and their linear combinations the prior information used is only the imprecise knowledge of the antenna array geometry and angular sector in which the actual steering vector lies mathematically the proposed mvdr rab is expressed as the well known non convex quadratically constrained quadratic programming problem with two constraints which can be efficiently and exactly solved some new results for the corresponding optimization problem such as a new algebraic way of finding the rank one solution from the general rank solution of the relaxed problem and the condition under which the solution of the relaxed problem is guaranteed to be rank one are derived our simulation results demonstrate the superiority of the proposed method over other previously developed rab techniques

performance analysis of beamformers using generalized loading of the covariance matrix in the presence of random steering vector errors robust adaptive beamforming is a key issue in array applications where there exist uncertainties about the steering vector of interest diagonal loading is one of the most popular techniques to improve robustness in this paper we present a theoretical analysis of the signal to interference plus noise ratio sinr for the class of beamformers based on generalized i e not necessarily diagonal loading of the covariance matrix in the presence of random steering vector errors a closed form expression for the sinr is derived that is shown to accurately predict the sinr obtained in simulations this theoretical formula is valid for any loading matrix it provides insights into the influence of the loading matrix and can serve as a helpful guide to select it finally the analysis enables us to predict the level of uncertainties up to which robust beamformers are effective and then depart from the optimal sinr

a clt on the snr of diagonally loaded mvdr filters this paper studies the fluctuations of the signal to noise ratio snr of minimum variance distorsionless response mvdr filters implementing diagonal loading in the estimation of the covariance matrix previous results in the signal processing literature are generalized and extended by considering both spatially as well as temporarily correlated samples specifically a central limit theorem clt is established for the fluctuations of the snr of the diagonally loaded mvdr filter under both supervised and unsupervised training settings in adaptive filtering applications our second order analysis is based on the nash poincare inequality and the integration by parts formula for gaussian functionals as well as classical tools from statistical asymptotic theory numerical evaluations validating the accuracy of the clt confirm the asymptotic gaussianity of the fluctuations of the snr of the mvdr filter

generalized eigenspace beamformer based on cg lanczos algorithm the generalized eigenspace beamformer geib has been presented as an efficient way to build a beamformer robust to calibration and pointing errors its main drawback is the great computational cost needed to develop the whole structure mainly associated to obtaining the projection matrix in this paper the relation between conjugate gradient and lanczos algorithm is used to modify the conjugate gradient algorithm robust conjugate gradient method rcgm so the eigenstructure of the correlation matrix can be obtained directly the numerical problems associated to the loss of orthogonality in successive gradient vectors have also been overcome via selective orthogonalization so in this way the proposed rcgm is also robust to numerical problems the overall computational cost in the construction of the geib has been reduced from o n sup 3 n sup 2 to o 3n sup 2 by using the rcgm instead of a conventional projection algorithm computer simulations are also presented to demonstrate the merits of the algorithm

nonlinear shrinkage estimation of large dimensional covariance matrices many statistical applications require an estimate of a covariance matrix and or its inverse when the matrix dimension is large compared to the sample size which happens frequently the sample covariance matrix is known to perform poorly and may suffer from ill conditioning there already exists an extensive literature concerning improved estimators in such situations in the absence of further knowledge about the structure of the true covariance matrix the most successful approach so far arguably has been shrinkage estimation shrinking the sample covariance matrix to a multiple of the identity by taking a weighted average of the two turns out to be equivalent to linearly shrinking the sample eigenvalues to their grand mean while retaining the sample eigenvectors our paper extends this approach by considering nonlinear transformations of the sample eigenvalues we show how to construct an estimator that is asymptotically equivalent to an oracle estimator suggested in previous work as demonstrated in extensive monte carlo simulations the resulting bona fide estimator can result in sizeable improvements over the sample covariance matrix and also over linear shrinkage

approximation by smooth multivariate splines abstract one of the important properties of univariate splines is that in most senses smooth splines approximate just as well as do piecewise polynomials on the same mesh this report shows this to be untrue in the multivariate setting in particular it details the cost in approximating power one may have to pay for the luxury of a smooth piecewise polynomial approximant in an extreme case piecewise polynomials of total degree r on a rectangular grid with all derivatives of order or rho continuous will fail to approximate certain smooth functions at all as the grid goes to zero unless rho is kept below r 3 2 during the analysis of approximation on a certain regular triangular grid a novel kind of bivariate b spline is introduced this b spline in contrast to the established multivariate b spline derived from a simplex can be made to have all its breaklines in a given regular grid this makes it a prime candidate for use in the construction of smooth multivariate piecewise polynomial approximation and its properties will be explored further

robust array beamforming with sidelobe control using support vector machines robust beamforming is a challenging task in a number of applications radar sonar wireless communications etc due to strict restrictions on the number of available snapshots signal mismatches or calibration errors we present a new approach to adaptive beamforming that provides increased robustness against the mismatch problem as well as additional control over the sidelobe level we generalize the conventional linearly constrained minimum variance cost function by including a regularization term that penalizes differences between the actual and the target ideal array responses by using the so called epsi insensitive loss function for the penalty term the final cost function adopts the form of a support vector machine svm for regression in particular the resulting cost function is convex with a unique global minimum that has traditionally been found using quadratic programming qp techniques to alleviate the computational cost of conventional qp techniques we use an iterative reweighted least squares irwls procedure which also converges to the svm solution computer simulations demonstrate an improved performance of the proposed svm based beamformer in comparison with other recently proposed robust beamforming techniques

widely linear versus linear blind multiuser detection with subspace based channel estimation finite sample size effects in a recent paper a s cacciapuoti et al ldquofinite sample performance analysis of widely linear multiuser receivers in ds cdma systems ieee transactions on signal processing vol 56 no 4 pp 1572 1588 apr 2008 we presented the finite sample theoretical performance comparison between linear l and widely linear wl minimum output energy moe receivers for direct sequence code division multiple access ds cdma systems worked out under the assumption that the channel impulse response of the desired user is exactly known the main scope of this paper is to extend such an analysis taking into account not only autocorrelation matrix acm estimation effects but also the accuracy of subspace based blind channel estimation ce we aim to answer the two following questions which of the two estimation processes acm or ce is the main source of degradation when implementing the receivers on the basis of a finite sample size compared with the l moe one is the finite sample wl moe receiver with blind ce capable of achieving the performance gains predicted by the theory to this goal simple and easily interpretable formulas are developed for the signal to interference plus noise ratio sinr at the output of the l and wl moe receivers with blind ce when they are implemented using either the sample acm or its eigendecomposition in addition the derived formulas which are validated by simulations allow one to recognize and discuss interesting tradeoffs between the main parameters of the ds cdma system

robust adaptive beamforming with a novel interference plus noise covariance matrix reconstruction method recently a new robust adaptive beamforming rab technique was proposed to remove the signal of interest soi component from the sample covariance matrix based on interference plus noise covariance matrix reconstruction which utilizes the capon spectrum estimator integrated over a region separated from the direction of the soi however the extreme condition of the reconstruction based technique that the precise information about the array structure is known in advance is almost impossible in practice in this paper a novel method to reconstruct the interference plus noise covariance matrix is proposed considering the imprecise prior information about the array structure which means that the array may be uncalibrated we use an annulus uncertainty set to constrain the steering vectors of the interferences then we integrate the capon spectrum over the surface of the annulus by which we can obtain the reconstructed interference matrix without containing the soi since the integral interval is a high dimensional domain which is very difficult to solve we use a discrete sum method to calculate the integral approximately with the reconstructed interference plus noise matrix the nominal steering vector can be corrected via maximizing the beamformer output power by solving a quadratically constrained quadratic programming qcqp problem the previous reconstruction method can be seen as a special case of the proposed one the main advantage is that the proposed algorithm is robust against unknown arbitrary type mismatches theoretical analysis and simulation results demonstrate the effectiveness and robustness of the proposed algorithm

robust adaptive beamforming based on interference covariance matrix reconstruction and steering vector estimation adaptive beamformers are sensitive to model mismatch especially when the desired signal is present in training snapshots or when the training is done using data samples in contrast to previous works this correspondence attempts to reconstruct the interference plus noise covariance matrix instead of searching for the optimal diagonal loading factor for the sample covariance matrix the estimator is based on the capon spectral estimator integrated over a region separated from the desired signal direction this is shown to be more robust than using the sample covariance matrix subsequently the mismatch in the steering vector of the desired signal is estimated by maximizing the beamformer output power under a constraint that prevents the corrected steering vector from getting close to the interference steering vectors the proposed adaptive beamforming algorithm does not impose a norm constraint therefore it can be used even in applications where gain perturbations affect the steering vector simulation results demonstrate that the performance of the proposed adaptive beamformer is almost always close to the optimal value across a wide range of signal to noise and signal to interference ratios

asymptotically optimal linear shrinkage of sample lmmse and mvdr filters conventional implementations of the linear minimum mean square lmmse and minimum variance distortionless response mvdr estimators rely on the sample matrix inversion smi technique i e on the sample covariance matrix scm this approach is optimal in the large sample size regime nonetheless in small sample size situations those sample estimators suffer a large performance degradation thus the aim of this paper is to propose corrections of these sample methods that counteract their performance degradation in the small sample size regime and keep their optimality in large sample size situations to this aim a twofold approach is proposed first shrinkage estimators are considered as they are known to be robust to the small sample size regime namely the proposed methods are based on shrinking the sample lmmse or sample mvdr filters towards a variously called matched filter or conventional bartlett beamformer in array processing second random matrix theory is used to obtain the optimal shrinkage factors for large filters the simulation results highlight that the proposed methods outperform the sample lmmse and mvdr also provided that the sample size is higher than the observation dimension they improve classical diagonal loading dl and ledoit wolf lw techniques which counteract the small sample size degradation by regularizing the scm finally compared to state of the art dl the proposed methods reduce the computational cost and the proposed shrinkage of the lmmse obtains performance gains

translates of multivarlate splines abstract we study spaces generated by translations of a fixed function over lattice points we provide some new algebraic and approximation properties for these spaces which show their applicability for finite element analysis

finite sample linear filter optimization in wireless communications and financial systems we study the problem of linear filter optimization with finite sample size which has wide applications such as beamformer design in wireless communications and portfolio optimization in finance traditional methods in both fields are not robust against the imprecise channel vector and the noise covariance matrix or the mean return and the covariance of assets in finance due to finite sample size we consider estimation errors both in the channel vector and the noise covariance matrix or the mean return and the covariance simultaneously we resort to high dimensional asymptotics to account for the fact that the observation dimension is of the same order of magnitude as the number of samples and use the diagonal loading method or the shrinkage estimator to improve the robustness the channel vector or mean return and the noise covariance matrix are estimated from the training data and then corrected under several widely used criteria in an asymptotic setting where the number of samples is comparable to the observation dimension we obtain linear filters that are as good as the optimal filters with a shrinkage structure and a perfect channel vector or mean return under different criteria monte carlo simulations show the advantage of our linear filters in the finite sample size regime

robust minimum variance beamforming this paper introduces an extension of minimum variance beamforming that explicitly takes into account variation or uncertainty in the array response sources of this uncertainty include imprecise knowledge of the angle of arrival and uncertainty in the array manifold in our method uncertainty in the array manifold is explicitly modeled via an ellipsoid that gives the possible values of the array for a particular look direction we choose weights that minimize the total weighted power output of the array subject to the constraint that the gain should exceed unity for all array responses in this ellipsoid the robust weight selection process can be cast as a second order cone program that can be solved efficiently using lagrange multiplier techniques if the ellipsoid reduces to a single point the method coincides with capon s method we describe in detail several methods that can be used to derive an appropriate uncertainty ellipsoid for the array response we form separate uncertainty ellipsoids for each component in the signal path e g antenna electronics and then determine an aggregate uncertainty ellipsoid from these we give new results for modeling the element wise products of ellipsoids we demonstrate the robust beamforming and the ellipsoidal modeling methods with several numerical examples

universal attractors for the navier stokes equations of compressible and heat conductive fluid in bounded annular domains in ℝn this paper is concerned with the dynamics for the navier stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains n in n n 2 3 one of the important features of this problem is that the metric spaces h 1 and h 2 we work with are two incomplete metric spaces as can be seen from the constraints 0 and u 0 with and u being absolute temperature and specific volume respectively for any constants 1 2 3 4 5 satisfying certain conditions two sequences of closed subspaces h i h i i 1 2 are found and the existence of two maximal universal attractors in h 1 and h 2 is proved

consistent reduced rank lmmse estimation with a limited number of samples per observation dimension an improved construction of the optimal reduced rank linear minimum mean square error mmse estimator of a signal waveform of interest is derived that is consistent under a limited number of samples per filtering degree of freedom the new filter design generalizes traditional filter realizations based on directly replacing the theoretical covariance matrix by its sample estimate and being consistent when all dimensions in the model but the number of samples remain bounded our solution not only generalizes the conventional estimator but also turns out to appropriately characterize model mismatch constraints due to finite sample size limitations of fundamental importance in practical situations the proposed implementation results from a generalized consistent estimation of the set of mmse filter subspace coefficients on the reduced dimensional subspace results are based on the theory of the spectral analysis of large dimensional random matrices in particular we build on the analytical description of the asymptotic spectrum of sample covariance type matrices in the limiting regime defined as both the number of samples and the observation dimension grow without bound at the same rate as a result the proposed mmse signal waveform estimator is shown to present a superior mean square error performance under a finite sample size by avoiding the breakdown experienced as the selected rank increases

further study on robust adaptive beamforming with optimum diagonal loading significant effort has gone into designing robust adaptive beamforming algorithms to improve robustness against uncertainties in array manifold these uncertainties may be caused by uncertainty in direction of arrival doa imperfect array calibration near far effect mutual coupling and other mismatch and modeling errors a diagonal loading technique is obligatory to fulfil the uncertainty constraint where the diagonal loading level is amended to satisfy the constrained value the major drawback of diagonal loading techniques is that it is not clear how to get the optimum value of diagonal loading level based on the recognized level of uncertainty constraint in this paper an alternative realization of the robust adaptive linearly constrained minimum variance beamforming with ellipsoidal uncertainty constraint on the steering vector is developed the diagonal loading technique is integrated into the adaptive update schemes by means of optimum variable loading technique which provides loading on demand mechanism rather than fixed continuous or ad hoc loading we additionally enrich the proposed robust adaptive beamformers by imposing a cooperative quadratic constraint on the weight vector norm to overcome noise enhancement at low snr several numerical simulations with doa mismatch moving jamming and mutual coupling are carried out to explore the performance of the proposed schemes and compare their performance with other traditional and robust beamformers

global attractor for a nonlinear viscoelastic model in this paper we establish the existence of global attractors of a semiflow and a semigroup for a nonlinear 1 d viscoelasticity in two frameworks we exploit the properties of the analytic semigroup to show the compactness for the semiflow and semigroup generated by the weak global solutions

analytical method for blind binary signal separation the blind separation of multiple co channel binary digital signals using an antenna array involves finding a factorization of a data matrix x into x as where all entries of s are 1 or 1 it is shown that this problem can be solved exactly and noniteratively via a certain generalized eigenvalue decomposition as indicated by simulations the algorithm is robust in the presence of noise an interesting implication is that certain cluster segmentation problems can be solved using eigenvalue techniques

closed form blind mimo channel estimation for orthogonal space time block codes in this paper a new computationally simple approach to blind decoding of orthogonal space time block codes ostbcs is proposed using specific properties of ostbcs the authors approach estimates the channel matrix in a closed form and in a fully blind fashion this channel estimate is then used in the maximum likelihood ml receiver to decode the information symbols the proposed estimation technique provides consistent channel estimates and as a result the performance of the authors blind ml receiver approaches that of the coherent ml receiver which exploits the exact channel state information csi simulation results demonstrate the performance improvements achieved by the proposed blind decoding algorithm relative to the popular differential space time modulation scheme

maximal attractor for the system of a landau ginzburg theory for structural phase transitions in shape memory alloys abstract in this paper a system of nonlinear partial differential equations modelling the dynamics of martensitic phase transitions in shape memory alloys is further investigated in a previous paper published in siam j math anal the global existence of a unique solution and the asymptotic behaviour of the solution as time goes to infinity have been established in the present paper the existence of a compact maximal attractor is proved

global attractors for quasilinear parabolic hyperbolic equations governing longitudinal motions of nonlinearly viscoelastic rods abstract we prove the existence of a global attractor and estimate its dimension for a general family of third order quasilinear parabolic hyperbolic equations governing the longitudinal motion of nonlinearly viscoelastic rods carrying an end mass and subject to interesting body forces the simplest version of the equations has the form w t t n w x w x t x where n is defined on 0 r and is a strictly increasing function of each of its arguments with n as its first argument goes to 0 this limit characterizes a total compression a source of technical difficulty which new delicate a priori estimates prevent we determine how the dimension of the attractor varies with the ratio of the mass of the rod to that of the end mass giving conditions ensuring that the dimension is small the estimates of dimension illuminate asymptotic analyses of the governing equation as this mass ratio goes to 0

local approximation by certain spaces of exponential polynomials approximation order of exponential box splines and related interpolation problems local approximation order to smooth complex valued functions by a finite dimensional space 7b h spanned by certain products of exponentials by polynomials is investigated the results obtained together with a suitable quasi interpolation scheme are used for the derivation of the approximation order attained by the linear span of translates of an exponential box spline the analysis of a typical 7b h is based here on the identification of its dual with a certain space 7b p of multivariate polynomials this point of view allows us to solve a class of multivariate interpolation problems by the polynomials from 7b p

the failure on continuous dependence on initial data for the navier stokes equations of compressible flow it is shown that physical solutions of the navier stokes equations for one dimensional compressible flow need not depend continuously on their initial data at least when vacuum states are allowed specifically two fluid regions initially separated by a third region of very low density 6 are considered it is shown that as delta to 0 the unique solutions corresponding to delta 0 do not in fact converge to a physical solution but rather to a nonphysical weak solution in which the two fluids cannot collide independent of their initial velocities and whose separate momenta need not be conserved a particular consequence is that solutions of the cavity problem delta 0 are not unique

steering vector estimation in uncalibrated arrays this paper presents an iterative algorithm for estimating the signal steering vectors and associated power levels received by an array of uncalibrated isotropic sensors the inputs are assumed to consist of narrowband uncorrelated directional signals in the presence of additive white noise an iterative algorithm is employed to successively search for estimates that simultaneously satisfy a signal subspace and an orthogonality condition these conditions are shown to be both necessary and sufficient for identification of the underlying steering vectors in the case when the data covariance matrix is known exactly i e for the case of infinite data observation the iterative method employs minimum distance criterion projections to successively map the solution between three constraint sets until a stable point is determined two examples are presented which illustrate the application of the algorithm in direction finding and beamforming

eigenvalue beamforming using a multirank mvdr beamformer and subspace selection we derive eigenvalue beamformers to resolve an unknown signal of interest whose spatial signature lies in a known subspace but whose orientation in that subspace is otherwise unknown the unknown orientation may be fixed in which case the signal covariance is rank 1 or it may be random in which case the signal covariance is multirank we present a systematic treatment of such signal models and explain their relevance for modeling signal uncertainties we then present a multirank generalization of the mvdr beamformer the idea is to minimize the power at the output of a matrix beamformer while enforcing a data dependent distortionless constraint in the signal subspace which we design based on the type of signal we wish to resolve we show that the eigenvalues of an error covariance matrix are fundamental for resolving signals of interest signals with rank 1 covariances are resolved by the largest eigenvalues of the error covariance while signals with multirank covariances are resolved by the smallest eigenvalues thus the beamformers we design are eigenvalue beamformers which extract signal information from eigen modes of an error covariance we address the tradeoff between angular resolution of eigenvalue beamformers and the fraction of the signal power they capture

robust adaptive beamforming for general rank signal models the performance of adaptive beamforming methods is known to degrade severely in the presence of even small mismatches between the actual and presumed array responses to the desired signal such mismatches may frequently occur in practical situations because of violation of underlying assumptions on the environment sources or sensor array this is especially true when the desired signal components are present in the beamformer training data snapshots because in this case the adaptive array performance is very sensitive to array and model imperfections the similar phenomenon of performance degradation can occur even when the array response to the desired signal is known exactly but the training sample size is small we propose a new powerful approach to robust adaptive beamforming in the presence of unknown arbitrary type mismatches of the desired signal array response our approach is developed for the most general case of an arbitrary dimension of the desired signal subspace and is applicable to both the rank one point source and higher rank scattered source fluctuating wavefront desired signal models the proposed robust adaptive beamformers are based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix as well as worst case performance optimization simple closed form solutions to the considered robust adaptive beamforming problems are derived our new beamformers have a computational complexity comparable with that of the traditional adaptive beamforming algorithms while at the same time offer a significantly improved robustness and faster convergence rates

performance analysis of direction finding with large arrays and finite data this paper considers analysis of methods for estimating the parameters of narrow band signals arriving at an array of sensors this problem has important applications in for instance radar direction finding and underwater source localization the so called deterministic and stochastic maximum likelihood ml methods are the main focus of this paper a performance analysis is carried out assuming a finite number of samples and that the array is composed of a sufficiently large number of sensors several thousands of antennas are not uncommon in e g radar applications strong consistency of the parameter estimates is proved and the asymptotic covariance matrix of the estimation error is derived unlike the previously studied large sample case the present analysis shows that the accuracy is the same for the two ml methods furthermore the asymptotic covariance matrix of the estimation error coincides with the deterministic cramer rao bound under a certain assumption the ml methods can be implemented by means of conventional beamforming for a large enough number of sensors we also include a simple simulation study which indicates that both ml methods provide efficient estimates for very moderate array sizes whereas the beamforming method requires a somewhat larger array aperture to overcome the inherent bias and resolution problem

universal attractor in h4 for the nonlinear one dimensional compressible navier stokes equations abstract this paper is concerned with the regularity exponential stability of solutions and existence of universal attractor in h 4 for a nonlinear one dimensional compressible navier stokes equations describing a motion of heat conductive viscous real gas in a bounded domain 0 1 some new ideas and more delicated estimates are introduced to prove these results

finite sample size effect on minimum variance beamformers optimum diagonal loading factor for large arrays minimum variance beamformers are usually complemented with diagonal loading techniques in order to provide robustness against several impairments such as imprecise knowledge of the steering vector or finite sample size effects this paper concentrates on this last application of diagonal loading techniques i e it is assumed that the steering vector is perfectly known and that diagonal loading is used to alleviate the finite sample size impairments the analysis herein is asymptotic in the sense that it is assumed that both the number of antennas and the number of samples are high but have the same order of magnitude borrowing some results of random matrix theory the authors first derive a deterministic expression that describes the asymptotic signal to noise plus interference ratio sinr at the output of the diagonally loaded beamformer then making use of the statistical theory of large observations also known as general statistical analysis or g analysis the authors derive an estimator of the optimum loading factor that is consistent when both the number of antennas and the sample size increase without bound at the same rate because of that the estimator has an excellent performance even in situations where the quotient between the number of observations is low relative to the number of elements of the array

regularity of non stationary subdivision a matrix approach in this paper we study scalar multivariate non stationary subdivision schemes with integer dilation matrix m and present a unifying general approach for checking their convergence and for determining their holder regularity latter in the case m mi m ge 2 m mi m 2 the combination of the concepts of asymptotic similarity and approximate sum rules allows us to link stationary and non stationary settings and to employ recent advances in methods for exact computation of the joint spectral radius as an application we prove a recent conjecture by dyn et al on the holder regularity of the generalized daubechies wavelets we illustrate our results with several examples

multivariate discrete splines and linear diophantine equations in this paper we investigate the algebraic properties of multivariate discrete splines it turns out that multivariate discrete splines are closely related to linear diophantine equations in particular we use a solvability condition for a system of linear diophantine equations to obtain a necessary and sufficient condition for the integer translates of a discrete box spline to be linearly independent in order to understand the local structure of discrete splines we develop a general theory for certain systems of linear partial difference equations using this theory we prove that the integer translates of a discrete box spline are locally linearly independent if and only if they are linearly independent

on the solution of certain systems of partial difference equations and linear dependence of translates of box splines on resout des systemes d equations aux differences partielles qui apparaissent dans l etude de la dependance lineaire des translatees de splines en boite

using spectral estimation techniques in adaptive processing antenna systems improved spectral estimation techniques hold promise for becoming a valuable asset in adaptive processing array antenna systems their value lies in the considerable amount of additional useful information which they can provide about the interference environment utilizing a relatively small number of degrees of freedom dof the superresolution capabilities estimation of coherence and relative power level determination serve to complement and refine the data from faster conventional estimation techniques two conceptual application area examples for using such techniques are discussed partially adaptive low sidelobe arrays and fully adaptive tracking arrays for the partially adaptive area the information is utilized for efficient assignment of a limited number of dof in a beamspace constrained adaptive system in order to obtain a stable main beam retention of low sidelobes considerably faster response and reduction in overall cost these benefits are demonstrated via simulation examples computed for a 16 element linear array for the fully adaptive tracking array area the information is utilized in an all digital processing system concept to permit stable hulling of coherent interference sources in the main beam region efficient assignment control of the available dof and greater flexibility in time domain adaptive filtering strategy

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

robust adaptive beamformers based on worst case optimization and constraints on magnitude response in this paper novel robust adaptive beamformers are proposed with constraints on array magnitude response with the transformation from the array output power and the magnitude response to linear functions of the autocorrelation sequence of the array weight the optimization of an adaptive beamformer which is often described as a quadratic optimization problem in conventional beamforming methods is then reformulated as a linear programming lp problem unlike conventional robust beamformers the proposed method is able to flexibly control the robust response region with specified beamwidth and response ripple in practice an array has many imperfections besides steering direction error in order to make the adaptive beamformer robust against all kinds of imperfections worst case optimization is exploited to reconstruct the robust beamformer by minimizing array output power with the existence of the worst case array imperfections the robust beamforming can be expressed as a second order cone programming socp problem the resultant beamformer possesses superior robustness against arbitrary array imperfections with the proposed methods a large robust response region and a high signal to interference plus noise ratio sinr enhancement can be achieved readily simple implementation flexible performance control as well as significant sinr enhancement support the practicability of the proposed methods

asymptotic behaviour and changes of phase in one dimensional nonlinear viscoelasticity in this paper we study the asymptotic behaviour as t co of solutions u x t to the nonlinear partial differential equation ut m4 a o o 1 1 with initial conditions u 0 q x u x u x o 0 1 3a

sinr analysis of the subtraction based smi beamformer the sample matrix inversion smi beamformer suffers from performance degradation due to the finite sample size effect and the arrival angle mismatch problem a simple technique to provide robustness to the conventional smi beamformer is to block the desired signal from the received data before calculating the beamformer s weight vector which leads to the subtraction based smi s smi beamformer in this correspondence closed form approximations of the expected value of the signal to interference plus noise ratio sinr for the s smi beamformer and the smi beamformer are derived where the effect of both finite sample size and arrival angle mismatch are considered simulations show that the derived approximations are close enough to represent the true values of the sinr when the sample size is small and the arrival direction mismatch exists

equivalence of adaptive array diagonal loading and omnidirectional jamming diagonal loading where a diagonal matrix is added to the estimate of the covariance matrix is often used in adaptive arrays to minimize the array s responsiveness to random fluctuations in the estimate of the interference environment poor estimates of the covariance matrix often result in high random sidelobes in the sample matrix inversion smi adapted pattern it is shown in this communication that an omnidirectional spread of uniform jammers arriving at a linear array of half wavelength spaced elements with cosine element patterns also produces a diagonal matrix this equivalence of form is useful in visualizing the effects of diagonal loading and understanding the resulting patterns