some downwards transfer properties for n2 construction d un modele de zermelo fraenkel axiome du choix zfc hypothese du continu generalise ou le cardinal aleph 2 possede des proprietes de transfert descendant

array interpolation and doa mse reduction interpolation or mapping of data from a given real array to data from a virtual array of more suitable geometry is well known in array signal processing this operation allows arrays of any geometry to be used with fast direction of arrival doa estimators designed for linear arrays in an earlier companion paper a first order condition for zero doa bias under such mapping was derived and was also used to construct a design algorithm for the mapping matrix that minimized the doa estimate bias this bias minimizing theory is now extended to minimize not only bias but also to consider finite sample effects due to noise and reduce the doa mean square error mse an analytical first order expression for mapped doa mse is derived and a design algorithm for the transformation matrix that minimizes this mse is proposed generally doa mse is not reduced by minimizing the size of the mapping errors but instead by rotating these errors and the associated noise subspace into optimal directions relative to a certain gradient of the doa estimator criterion function the analytical mse expression and the design algorithm are supported by simulations that show not only conspicuous mse improvements in relevant scenarios but also a more robust preprocessing for low signal to noise ratios snrs as compared with the pure bias minimizing design developed in the previous paper

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

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

modified subspace algorithms for doa estimation with large arrays this paper proposes the use of a new generalized asymptotic paradigm in order to analyze the performance of subspace based direction of arrival doa estimation in array signal processing applications instead of assuming that the number of samples is high whereas the number of sensors antennas remains fixed the asymptotic situation analyzed herein assumes that both quantities tend to infinity at the same rate this asymptotic situation provides a more accurate description of a potential situation where these two quantities are finite and hence comparable in magnitude it is first shown that both music and ssmusic are inconsistent when the number of antennas sensors increases without bound at the same rate as the sample size this is done by analyzing and deriving closed form expressions for the two corresponding asymptotic cost functions by examining these asymptotic cost functions one can establish the minimum number of samples per antenna needed to resolve closely spaced sources in this asymptotic regime next two alternative estimators are constructed that are strongly consistent in the new asymptotic situation i e they provide consistent doa estimates not only when the number of snapshots goes to infinity but also when the number of sensors antennas increases without bound at the same rate these estimators are inspired by the theory of g estimation and are therefore referred to as g music and g ssmusic respectively simulations show that the proposed algorithms outperform their traditional counterparts in finite sample size situations although they still present certain limitations

a many body rage theorem we prove a generalized version of the rage theorem for n body quantum systems the result states that only bound states of systems with 0 leqslant n leqslant n particles persist in the long time average the limit is formulated by means of an appropriate weak topology for many body systems which was introduced by the second author in a previous work and is based on reduced density matrices this topology is connected to the weak topology of states on the algebras of canonical commutation or anti commutation relations and we give a formulation of our main result in this setting

the recursive suppression algorithm for adaptive superresolution the recursive suppression algorithm is an adaptive algorithm that is one of the simplest superresolution algorithms to implement but nevertheless converges approximately as rapidly as the computationally intensive music algorithm simulation results verify the effectiveness of this algorithm in resolving closely spaced signals necessary and sufficient conditions for the convergence of the mean weight vector in the recursive suppression algorithm are derived

statistical analysis of music and subspace rotation estimates of sinusoidal frequencies consideration is given to the analysis of the large sample second order properties of multiple signal classification music and subspace rotation sur methods such as esprit for sinusoidal frequency estimation explicit expressions for the covariance elements of the estimation errors associated with either method are derived these expressions of covariances are then used to analyze and compare the statistical performances of the music and sur estimation sure methods both music and sure are based on the eigendecomposition of a sample data covariance matrix the expressions for the estimation error variances derived are used to study the dependence of music and sure performances on the dimension of the data covariance matrix used

operateurs conjugues et proprietes de propagation we use an algebraic criteria based on local positivity of a commutator which asserts the existence of a direction of propagation for the flowe iht associated to a self adjoint operatorh

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

finite data performance analysis of mvdr beamformer with and without spatial smoothing the finite data performance of a minimum variance distortionless response mvdr beamformer is analyzed with and without spatial smoothing using first order perturbation theory in particular expressions are developed for the mean values of the power gain in any direction of interest the output power and the norm of the weight error vector as a function of the number of snapshots and the number of smoothing steps it is shown that in general the smoothing in addition to decorrelating the sources can alleviate the effects of finite data perturbations the above expressions are reduced to the case in which no spatial smoothing is used these expressions are valid for an arbitrary array and for arbitrarily correlated signals for this case an expression for the variance of the power gain is also developed for a single interference case it is shown explicitly how the snr spacing of the interference from the desired signal and the correlation between them influence the beamformer performance simulations verify the usefulness of the theoretical expressions

analysis of joint angle frequency estimation using esprit high resolution parameter estimation techniques have been applied to jointly estimate multiple signal parameters we consider the problem of determining the directions and center frequencies of a number of narrowband sources in a band of interest we present a joint angle frequency estimation method based on the multidimensional esprit algorithm a perturbation error analysis gives bounds on the parameter estimates and provides optimal values for the temporal and spatial smoothing parameters the analysis is shown to be consistent with simulation results

dispersive charge transfer model with long range quantum interactions abstract we present a method of proving the asymptotic completeness of wave operators associated with the scattering of a quantum particle in a field of classical particles with long range interactions based on some propagation estimates of the type recently developed in the theory of n body systems the approach allows us to treat a class of dispersive systems where the free hamiltonian has the form h 0 p d covering for example the case of the relativistic hamiltonian p c 2 2 1 2

on long range scattering even if special cases are not well understood it pays sometimes to consider a problem at hand in the most general framework thus addressing the existence of wave operators for the most general potentials hormander ho1 has discovered a natural asymptotic evolution for the long range scattering it is determined by a solution s k t of a certain hamilton jacobi equation

pseudo randomly generated estimator banks a new tool for improving the threshold performance of direction finding a new powerful tool for improving the threshold performance of direction finding is considered the main idea of our approach is to reduce the number of outliers in the doa estimates using a previously proposed joint estimation strategy jes for this purpose multiple different doa estimators are calculated in a parallel manner for the same batch of data i e for a single data record employing these estimators simultaneously the jes improves the threshold performance because it removes outliers and exploits only successful estimators that are sorted out using a hypothesis testing procedure we consider an efficient modification of the jes with application to the pseudo randomly generated eigenstructure estimator banks based on secondand higher order statistics weighted music estimators based on the covariance and contracted quadricovariance matrices are chosen as appropriate underlying techniques for the second and fourth order estimator banks respectively computer simulations with uncorrelated sources verify the dramatic improvements of threshold performance as compared with the conventional second and fourth order music algorithms simulations also show that in the second order case the threshold performance of our technique is close to that of the wsf method and stochastic deterministic ml methods which are known today as the most powerful in the sense of estimation performance and at the same time as the most computationally expensive doa estimation techniques the computational cost of our algorithm is much lower than that of the wsf and ml techniques because no multidimensional optimization is required

martin s maximum saturated ideals and non regular ultrafilters part ii we prove assuming the existence of a huge cardinal the consistency of fully non regular ultrafilters on the successor of any regular cardinal we also construct ultrafilters with ultraproducts of small cardinality part ii is logically independent of part i

instrumental variable approach to array processing in spatially correlated noise fields high performance signal parameter estimation from sensor array data is a problem which has received much attention a number of so called eigenvector ev techniques such as music esprit wsf and mode have been proposed in the literature the ev techniques for array processing require knowledge of the spatial noise correlation matrix that constitutes a significant drawback a novel instrumental variable iv approach to the sensor array problem is proposed the iv technique relies on the same basic geometric properties as the ev methods to obtain parameter estimates however by exploiting the temporal correlation of the source signals no knowledge of the spatial noise covariance is required the asymptotic properties of the iv estimator are examined and an optimal iv method is derived computer simulations are presented to study the properties of the iv estimators in samples of practical length the proposed algorithm is also shown to perform better than music on a full scale passive sonar experiment

the statistical performance of the music and the minimum norm algorithms in resolving plane waves in noise this paper presents an asymptotic statistical analysis of the null spectra of two eigen assisted methods music 1 and minimum norm 2 for resolving independent closely spaced plane waves in noise particular attention is paid to the average deviation of the null spectra from zero at the true angles of arrival for the plane waves these deviations are expressed as functions of signal to noise ratios number of array elements angular separation of emitters and the number of snapshots in the case of music an approximate expression is derived for the resolution threshold of two plane waves with equal power in noise this result is validated by monte carlo simulations

enhanced puma for direction of arrival estimation and its performance analysis direction of arrival doa estimation is a problem of significance in many applications in practice due to the occurrence of coherent signals and or when the number of available snapshots is small it is a challenge to find doas accurately this problem is revisited here through a new enhanced principal singular vector utilization for modal analysis epuma doa estimation approach which improves the threshold performance by first generating p k doa candidates for k sources where p geq k and then judiciously selecting k of them the asymptotic variance of epuma is theoretically derived and numerical results are provided to validate the asymptotic analysis and illustrate the practical merits of epuma

maximum likelihood array processing in spatially correlated noise fields using parameterized signals this paper deals with the problem of estimating signal parameters using an array of sensors this problem is of interest in a variety of applications such as radar and sonar source localization a vast number of estimation techniques have been proposed in the literature during the past two decades most of these can deliver consistent estimates only if the covariance matrix of the background noise is known in many applications the aforementioned assumption is unrealistic recently a number of contributions have addressed the problem of signal parameter estimation in unknown noise environments based on various assumptions on the noise herein a different approach is taken we assume instead that the signals are partially known the received signals are modeled as linear combinations of certain known basis functions the exact maximum likelihood ml estimator for the problem at hand is derived as well as computationally more attractive approximation the cramer rao lower bound crb on the estimation error variance is also derived and found to coincide with the crb assuming an arbitrary deterministic model and known noise covariance

performance analysis of esprit and tam in determining the direction of arrival of plane waves in noise the authors evaluate two subspace based methods esprit and the toplitz approximation method tam for estimating the direction of arrival doa of plane waves in white noise in the case of linear equispaced sensor array it is shown that the least squares versions of esprit and tam result in the same estimate and are statistically equivalent it is also shown that asymptotically the estimates obtained using least squares esprit and total least squares esprit have the same mean squared error expressions for the asymptotic mean squared error in the estimates of the doa are derived for both methods simple closed form expressions are derived for the one and two source cases to get further insight computer simulation results are provided to substantiate the analysis

topological applications of generic huge embeddings in the foreman laver model obtained by huge cardinal collapse for many p ni implies ofi there are a variety of set theoretic and topo logical applications in particular to paracompactness the key tools are generic huge embeddings and preservation via k centred forcing we also formulate potent axioms a la foreman which enable us to transfer from n to all car dinals one such axiom implies that all n collectionwise normal moore spaces are metrizable it also implies as does martin s maximum that a first count able generalized ordered space is hereditarily paracompact iff every subspace of size ki is paracompact assuming the consistency of a huge cardinal foreman and laver fl con struct a model of zfc gch in which as they put it n2 possesses some downwards transfer properties for example in their model every graph of size and chromatic number n2 has a vertex induced subgraph of size and chro matic number ki and groups of size n2 are the union of ni free subgroups if all their subgroups of size ni are free we shall establish in their model a variety of such transfer propositions in a topological context actually we think of taking properties holding at ni and transferring them to n2 the method of proof is to use an elementary embedding with strong closure properties de finable in an ni centred k2 closed forcing extension of the model to perform the transfer and then argue that the forcing could not have accomplished the transfer unless it already held it is natural to generalize this idea to trans fer from n to other cardinals it is not known at present how to accomplish this from the usual large cardinals so we proceed axiomatically in the style of fo3 our results impinge on a number of areas of set theoretic topology but the most interesting ones deal with paracompactness e g the one mentioned in the abstract the techniques however are widely applicable as can be seen not only from our results on trees and ideals but from those of foreman and laver quoted above the paper is organized as follows we state the basic features of the foreman laver model and use them to go from ni to n2 next we present a variety of counterexamples to show our results do not hold in zfc we then introduce axioms that enable us to transfer from ni to arbitrary cardinals we finish with some results proved from supercompact cardinals and then a list of problems

eigenstructure variability of the multiple source multiple sensor covariance matrix with contaminated gaussian data several methods of current interest for counting and locating signal sources using data from a passive array depend on the accuracy of estimating the eigenstructure of the covariance matrix of the array s data vectors when errors in the measured data vectors are gaussian conventional covariance estimation is optimal but robust procedure are required for data with nongaussian additive contamination two different robust covariance estimators are compared by simulation with the conventional one for different degrees of contamination even in relatively good signal to noise ratios however closeness of signal sources in the temporal and spatial frequency domains can cause inaccurate signal related eigenvalue and eigenvector estimates the degree of adversity for these problems is also shown by simulation

tunable line spectral estimators based on state covariance subspace analysis subspace methods for spectral analysis can be adapted to the case where state covariance of a linear filter replaces the traditional toeplitz matrix formed out of a partial autocorrelation sequence of a time series this observation forms the basis of a new framework for spectral analysis the goal of this paper is to quantify potential advantages in working with state covariance data instead of the autocorrelation sequence to this end we identify tradeoffs between resolution and robustness in spectral estimates and how these are affected by the filter dynamics the approach leads to a novel tunable high resolution frequency estimator

tops new doa estimator for wideband signals this paper introduces a new direction of arrival doa estimation algorithm for wideband sources called test of orthogonality of projected subspaces tops this new technique estimates doas by measuring the orthogonal relation between the signal and the noise subspaces of multiple frequency components of the sources tops can be used with arbitrary shaped one dimensional 1 d or two dimensional 2 d arrays unlike other coherent wideband methods such as the coherent signal subspace method cssm and waves the new method does not require any preprocessing for initial values the performance of those wideband techniques and incoherent music is compared with that of the new method through computer simulations the simulations show that this new technique performs better than others in mid signal to noise ratio snr ranges while coherent methods work best in low snr and incoherent methods work best in high snr thus tops fills a gap between coherent and incoherent methods

subspace algorithms for error localization with quantized dft codes recently a class of real number bose chaudhuri hocquengem codes known as discrete fourier transform dft codes have been considered as joint source and channel codes for providing robustness to erasures and errors over wireless networks we propose three subspace algorithms for error localization with quantized dft codes the algorithms are similar to the music the minimum norm and the esprit algorithms used in array signal processing for direction of arrival estimation they provide different but related formulations of the error localizations by first partitioning a vector space into the channel error subspace and its orthogonal complement the noise subspace the locations of the errors are determined from either the error subspace eigenvectors or the noise subspace eigenvectors we also present a brief performance analysis of the localization error in terms of the perturbation of the error subspace due to quantization simulation results show that their localization performances are similar and they perform better than the coding theoretic approach over a broad range of channel error to quantization noise ratios

a new proof of the propagation theorem for n body quantum systems a new proof of i sigal s and a soffer s propagation theorem is given this theorem describes a large class of operators which are kato smooth with respect to ann body schrodinger operator

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

asymptotic completeness for n body short range quantum systems a new proof we give an alternative geometrical proof of asymptotic completeness for an arbitrary number of quantum particles interacting through shortrange pair potentials it relies on an estimate showing that the intercluster motion concentrates asymptotically on classical trajectories

the n particle scattering problem asymptotic completeness for short range systems on demontre la completude asymptotique pour des systemes de mecanique quantique a courte portee constitues d un nombre arbitraire de particules

propagation of singularities in many body scattering in the presence of bound states abstract in this paper we describe the propagation of singularities of tempered distributional solutions u s of h u 0 where h is a many body hamiltonian h v 0 v a v a and is not a threshold of h under the assumption that the inter particle e g two body interactions v a are real valued polyhomogeneous symbols of order 1 e g coulomb type with the singularity at the origin removed here the term singularity refers to a microlocal description of the lack of decay at infinity thus we prove that the set of singularities of u is a union of maximally extended broken bicharacteristics of h these are curves in the characteristic variety of h which can be quite complicated due to the existence of bound states we use this result to describe the wave front relation of the s matrices we also analyze lagrangian properties of this relation which shows that the relation is not too large in terms of its dimension

eigenvalues and eigenvectors of covariance matrices for signals closely spaced in frequency the eigenstructures of common covariance matrices are identified for the general case of m closely spaced signals it is shown that the largest signal space eigenvalue is relatively insensitive to signal separation by contrast the ith largest eigenvalue is proportional to delta omega sup 2 i 1 or delta omega sup 4 i 1 where delta omega is a measure of signal separation therefore matrix conditioning degrades rapidly as signal separation is reduced it is also shown that the limiting eigenvectors have remarkably simple structures the results are very general and apply to planar far field direction finding problems involving almost arbitrary scenarios and also to time series analysis of sinusoids exponentials and other signals

a statistical resolution theory of the ar method of spectral analysis the autoregressive ar method of spectral analysis is widely used in diverse areas for its solid theoretical foundation interesting physical interpretation computational efficiency and more importantly high resolution capability various aspects of its statistical performance have been investigated however the resolution probability that provides the most rigorous description of the spectrum resolution capability is still not available in the literature in this paper by formulating the resolution event in the framework of statistical decision theory and directly determining its probability from its characteristic function we obtain an exact asymptotic formula for the probability of resolution on this basis we determine the limiting resolving behavior of the sample ar spectrum and develop the corresponding geometrical insight in the parametric space simulation and numerical results are also presented to confirm and illustrate the theory

on the second order statistics of the evd of sample covariance matrices application to the detection of noncircular or and nongaussian components this correspondence presents an asymptotic analysis of the eigenvalue decomposition evd of the sample covariance matrix associated with independent identically distributed i i d non necessarily circular and gaussian data that extends the well known analysis presented in the literature for circular and gaussian data closed form expressions of the asymptotic bias and variance of the sample eigenvalues and eigenvectors are given as an application of these extended expressions the statistical performance analysis of the widely used minimum description length mdl criterion applied to the detection of the number of noncircular or and non gaussian sources impinging on an array of sensors is considered with a particular attention paid to uncorrelated rectilinear sources

doa estimation via manifold separation for arbitrary array structures in this paper we consider the manifold separation technique mst which stems from the wavefield modeling formalism developed for array processing mst is a method for modeling the steering vector of antenna arrays of practical interest with arbitrary 2 d or 3 d geometry it is the product of a sampling matrix dependent on the antenna array only and a vandermonde structured coefficients vector depending on the wavefield only this allows fast direction of arrival doa algorithms designed for linear arrays to be used on arrays with arbitrary configuration in real world applications the calibration measurements used to determine the sampling matrix are corrupted by noise this impairs the performance of mst based algorithms in particular we study the effect of noisy calibration measurements on subspace based doa algorithms using mst expressions describing the error in the doa estimates due to calibration noise and truncation are derived this allows predicting the performance of mst based algorithms in real world applications the analysis is verified by simulations we established a link between the optimal number of selected modes and the statistics of calibration noise we analyze the modeling error when mst is used for 1 d azimuth doa estimation

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

the resolution threshold of a direction finding algorithm for diversely polarized arrays subspace based algorithms for narrowband direction of arrival doa estimation require detailed knowledge of the array response the array manifold and assume that the noise covariance matrix is known up to a scaling factor in practice these quantities are not known precisely resolution and estimation accuracy can degrade significantly when the array response or the noise covariance deviate from their nominal values we examine the resolution threshold of a recently proposed subspace based algorithm for direction finding with diversely polarized arrays we study finite sample effects and the effects of modeling errors errors in the array manifold or the noise covariance on the resolution threshold a comparison is made between the resolution thresholds of the music algorithm for uniformly polarized arrays and the proposed algorithm for diversely polarized arrays

analysis of linear prediction by matrix approximation the authors present a new method of analysis of the effects of data perturbations on the estimates of signal parameters which are obtained by the method of linear prediction the variances of signal parameter obtained from linear prediction methods are computed although the results appear to have wide applicability for simplicity the authors restrict their examples to signals which are linear combinations of complex valued exponential functions

schrodinger operators in the twentieth century this paper reviews the past fifty years of work on spectral theory and related issues in nonrelativistic quantum mechanics

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

optimality of high resolution array processing using the eigensystem approach in the classical approach to underwater passive listening the medium is sampled in a convenient number of look directions from which the signals are estimated in order to build an image of the noise field in contrast a modern trend is to consider the noise field as a global entity depending on few parameters to be estimated simultaneously in a gaussian context it is worthwhile to consider the application of likelihood methods in order to derive a detection test for the number of sources and estimators for their locations and spectral levels this paper aims to compute such estimators when the wavefront shapes are not assumed known a priori this justifies results previously found using the asymptotical properties of the eigenvalue eigenvector decomposition of the estimated spectral density matrix of the sensor signals they have led to a variety of high resolution array processing methods more specifically a covariance matrix test for equality of the smallest eigenvalues is presented for source detection for source localization a best fit method and a test of orthogonality between the smallest eigenvectors and the source vectors are discussed

asymptotic completeness for 3 particle long range systems we prove asymptotic completeness for 3 particle systems with pair potentials satisfying the virial condition and decreasing at infinity as for 1 2

analytical performance assessment of multi dimensional matrix and tensor based esprit type algorithms in this paper we present a generic framework for the asymptotic performance analysis of subspace based parameter estimation schemes it is based on earlier results on an explicit first order expansion of the estimation error in the signal subspace obtained via an svd of the noisy observation matrix we extend these results in a number of aspects firstly we demonstrate that an explicit first order expansion of the higher order svd hosvd based subspace estimate can be derived secondly we show how to obtain explicit first order expansions of the estimation error of arbitrary esprit type algorithms and provide the expressions for r d standard esprit r d unitary esprit r d standard tensor esprit as well as r d unitary tensor esprit thirdly we derive closed form expressions for the mean square error mse and show that they only depend on the second order moments of the noise hence to apply this framework we only need the noise to be zero mean and possess finite second order moments additional assumptions such as gaussianity or circular symmetry are not needed

esprit based coherent source localization with forward and backward vectors novel methods are presented which estimate the direction of arrival doa of coherent signals by efficiently exploiting forward and backward vectors some correlation vectors or the eigenvector corresponding to the largest eigenvalue of the covariance matrix is used as the forward vector and the backward vector is then obtained by reversing the order of the complex conjugated elements of the forward one the use of both forward and backward vectors allows us to find a signal subspace of larger dimension than in the existing method which obtains that from a toeplitz matrix the proposed methods with an increased effective array aperture resolve more signals and provide better doa estimates than the toeplitz based method

compactification of complete kahler surfaces with negative ricci curvature it is a classical result of satake 17 baily borel 3 and ash mumford rapoport tai 2 that quotients of bounded symmetric domain by arithmetic groups of automorphism can be compactified the methods employed are essentially algebraic in nature along another direction andreott i grauert 1 siu yau 19 and nadel tsuji 14 obtained results which cover the above manifolds using the analytic properties of pseudoconcavity on the other hand it is believed that complete k ihler manifolds satisfying purely differential geometric conditions of bounded sectional curvature and negative ricci curvature can be compactified using differential geometric methods in 12 mok started a systematic scheme of attacking the problem and results in the work of mok zhong 13 the present article can be considered as a continuation of this scheme in particular we prove the conjecture in case of dimensional two more precisely we prove