blind identification of mimo fir systems driven by quasistationary sources using second order statistics a frequency domain approach this paper discusses a frequency domain method for blind identification of multiple input multiple output mimo convolutive channels driven by white quasistationary sources the sources can assume arbitrary probability distributions and in some cases they can even be all gaussian distributed we also show that under slightly more restrictive assumptions the algorithm can be applied to the case when the sources are colored nonstationary signals we demonstrate that by using the second order statistics of the channel outputs under mild conditions on the nonstationarity of sources and under the condition that channel is column wise coprime the impulse response of the mimo channel can be identified up to an inherent scaling and permutation ambiguity we prove that by using the new algorithm under the stated assumptions a uniform permutation across all frequency bins is guaranteed and the inherent frequency dependent scaling ambiguities can be resolved hence no post processing is required as is the case with previous frequency domain algorithms we further present an efficient two step frequency domain algorithm for identifying the channel numerical simulations are presented to demonstrate the performance of the new algorithm

on the virtual array concept for higher order array processing for about two decades many fourth order fo array processing methods have been developed for both direction finding and blind identification of non gaussian signals one of the main interests in using fo cumulants only instead of second order so ones in array processing applications relies on the increase of both the effective aperture and the number of sensors of the considered array which eventually introduces the fo virtual array concept presented elsewhere and allows in particular a better resolution and the processing of more sources than sensors to still increase the resolution and the number of sources to be processed from a given array of sensors new families of blind identification source separation and direction finding methods at an order m 2q q spl ges 2 only have been developed recently in this context the purpose of this paper is to provide some important insights into the mechanisms and more particularly to both the resolution and the maximal processing capacity of numerous 2qth order array processing methods whose previous methods are part of by extending the virtual array concept to an arbitrary even order for several arrangements of the data statistics and for arrays with space angular and or polarization diversity

identifiability results for blind beamforming in incoherent multipath with small delay spread several explicit identifiability results are derived for deterministic blind beamforming in incoherent multipath with small delay spread for example it is shown that if the sum of spatial and fractional sampling diversities exceeds two times the total number of paths then identifiability can be guaranteed even for one symbol snapshot the tools come from the theory of low rank three way array decomposition commonly referred to as parallel factor analysis parafac and data smoothing in one and two dimensions new results regarding the kruskal rank of certain structured matrices are also included and they are of interest in their own right

the eikonal equation in flat space null surfaces and their singularities i the level surfaces of solutions to the eikonal equation define null or characteristic surfaces in this paper we study in minkowski space properties of these surfaces in particular we are interested both in the singularities of these surfaces which can in general self intersect and be only piecewise smooth and in the decomposition of the null surfaces into a one parameter family of two dimensional wavefronts which can also have self intersections and singularities we first review a beautiful method for constructing the general solution to the flat space eikonal equation it allows for solutions either from arbitrary cauchy data or for time independent stationary solutions of the form s t s0 x y z we then apply this method to obtain global asymptotically spherical null surfaces that are associated with shearing bad two dimensional cuts of null infinity the surfaces are defined from the normal rays to the cut this is followed by a study of the caustics and singularities of these surfa

single channel blind separation using pseudo stereo mixture and complex 2 d histogram a novel single channel blind source separation scbss algorithm is presented the proposed algorithm yields at least three benefits of the scbss solution 1 resemblance of a stereo signal concept given by one microphone 2 independent of initialization and a priori knowledge of the sources and 3 it does not require iterative optimization the separation process consists of two steps 1 estimation of source characteristics where the source signals are modeled by the autoregressive process and 2 construction of masks using only the single channel mixture a new pseudo stereo mixture is formulated by weighting and time shifting the original single channel mixture this creates an artificial mixing system whose parameters will be estimated through our proposed weighted complex 2 d histogram in this paper we derive the separability of the proposed mixture model conditions required for unique mask construction based on maximum likelihood are also identified finally experimental testing on both synthetic and real audio sources is conducted to verify that the proposed algorithm yields superior performance and is computationally very fast compared with existing methods

on the symplectic formalism for general relativity a covariant formalism for the hamiltonian formulation of general relativity in arbitrary dimensions is presented specifically a presymplectic form on the solution space for the vacuum equations in n dimensions is given the basic variables are taken to be a soldering form and a torsion free connection on an so p q bundle over the space time manifold m it is shown how the present formalism is related to the standard adm formalism

null cones from i and legendre submanifolds it is shown that the main variable z of the null surface formulation of gr is the generating family of a constrained lagrange submanifold that lives on the energy surface h 0 and that its level surfaces z const yield legendre submanifolds on that energy surface thus the singularity structure of past null cones with apex at i is obtained by studying the projection map of the legendre submanifolds to the configuration space the behavior of the coordinate system defined by the variable z at the caustic points is analyzed it is shown that a single function z xa cannot generate the conformal structure of an asymptotically flat space time that satisfies the generic and weak energy condition

parallel factor analysis in sensor array processing this paper links multiple invariance sensor array processing mi sap to parallel factor parafac analysis which is a tool rooted in psychometrics and chemometrics parafac is a common name for low rank decomposition of three and higher way arrays this link facilitates the derivation of powerful identifiability results for mi sap shows that the uniqueness of single and multiple invariance esprit stems from uniqueness of low rank decomposition of three way arrays and allows tapping on the available expertise for fitting the parafac model the results are applicable to both data domain and subspace mi sap formulations the paper also includes a constructive uniqueness proof for a special parafac model

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

feature discovery in non metric pairwise data pairwise proximity data given as similarity or dissimilarity matrix can violate metricity this occurs either due to noise fallible estimates or due to intrinsic non metric features such as they arise from human judgments so far the problem of non metric pairwise data has been tackled by essentially omitting the negative eigenvalues or shifting the spectrum of the associated pseudo covariance matrix for a subsequent embedding however little attention has been paid to the negative part of the spectrum itself in particular no answer was given to whether the directions associated to the negative eigenvalues would at all code variance other than noise related we show by a simple exploratory analysis that the negative eigenvalues can code for relevant structure in the data thus leading to the discovery of new features which were lost by conventional data analysis techniques the information hidden in the negative eigenvalue part of the spectrum is illustrated and discussed for three data sets namely usps handwritten digits text mining and data from cognitive psychology

waves weighted average of signal subspaces for robust wideband direction finding existing algorithms for wideband direction finding are mainly based on local approximations of the gaussian log likelihood around the true directions of arrival doas assuming negligible array calibration errors suboptimal and costly algorithms such as classical or sequential beamforming are required to initialize a local search that eventually furnishes doa estimates this multistage process may be nonrobust in the presence of even small errors in prior guesses about angles and number of sources generated by inherent limitations of the preprocessing and may lead to catastrophic errors in practical applications a new approach to wideband direction finding is introduced and described the proposed strategy combines a robust near optimal data adaptive statistic called the weighted average of signal subspaces waves with an enhanced design of focusing matrices to ensure a statistically robust preprocessing of wideband data the overall sensitivity of waves to various error sources such as imperfect array focusing is also reduced with respect to traditional cssm algorithms as demonstrated by extensive monte carlo simulations

blind separation of instantaneous mixtures of nonstationary sources most source separation algorithms are based on a model of stationary sources however it is a simple matter to take advantage of possible nonstationarities of the sources to achieve separation this paper develops novel approaches in this direction based on the principles of maximum likelihood and minimum mutual information these principles are exploited by efficient algorithms in both the off line case via a new joint diagonalization procedure and in the on line case via a newton like procedure some experiments showing the good performance of our algorithms and evidencing an interesting feature of our methods are presented their ability to achieve a kind of super efficiency the paper concludes with a discussion contrasting separating methods for non gaussian and nonstationary models and emphasizing that as a matter of fact what makes the algorithms work is strictly speaking not the nonstationarity itself but rather the property that each realization of the source signals has a time varying envelope

applications of cumulants to array processing i aperture extension and array calibration an interpretation for the use of cumulants in narrowband array processing problems is proposed it is shown how fourth order cumulants of multichannel observations increase the directional information compared with second order statistics based on the interpretation it is shown how cumulants can be used to increase the effective aperture of an arbitrary antenna array the amount of partial information necessary to jointly calibrate an arbitrary array and estimate the directions of far field sources is also investigated it is proven that the presence of a doublet and use of fourth order cumulants is sufficient to accomplish this task the proposed approach is computationally efficient and more general than covariance based algorithms that have addressed the calibration problem under constraints a class of beamforming techniques is proposed to recover the source waveforms proposed estimation procedures are based on cumulants which bring insensitivity to the spatial correlation structure of additive gaussian measurement noise simulations are provided to illustrate the use of the proposed algorithms

on the regular and the asymptotic characteristic initial value problem for einstein s vacuum field equations the regular characteristic initial value problem for einstein s vacuum field equations where data are given on two intersecting null hypersurfaces is reduced to a characteristic initial value problem for a symmetric hyperbolic system of differential equations this is achieved by making use of the spin frame formalism instead of the harmonic gauge condition the method is applied to the asymptotic characteristic initial value problem for einstein s vacuum field equations where data are given on part of past null infinity and on an incoming null hypersurface a uniqueness theorem for this problem is proved by showing that a solution of the problem must satisfy a regular symmetric hyperbolic system of differential equations in a neighbourhood of past null infinity

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

causal geometry of einstein vacuum spacetimes with finite curvature flux one of the central difficulties of settling the l2 bounded curvature conjecture for the einstein vacuum equations is to be able to control the causal structure of spacetimes with such limited regularity in this paper we show how to circumvent this difficulty by showing that the geometry of null hypersurfaces of enstein vacuum spacetimes can be controlled in terms of initial data and the total curvature flux through the hypersurface

numerical relativity i the characteristic initial value problem in this the first of a series of papers on numerical relativity the characteristic initial value problem is posed in a form suitable for numerical integration it can be reduced to the solution of two initial value problems for sets of ordinary differential equations on the initial surfaces and the solution of two initial value problems for hyperbolic systems of equations one linear one quasilinear the initial data may be specified freely subsequent papers will develop numerical solutions of einstein s equations with use of this formalism

cauchy problems for the conformal vacuum field equations in general relativity cauchy problems for einstein s conformal vacuum field equations are reduced to cauchy problems for first order quasilinear symmetric hyperbolic systems the hyperboloidal initial value problem where cauchy data are given on a spacelike hypersurface which intersects past null infinity at a spacelike two surface is discussed and translated into the conformally related picture it is shown that for conformal hyperboloidal initial data of classhs s 4 there is a unique up to questions of extensibility development which is a solution of the conformal vacuum field equations of classhs it provides a solution of einstein s vacuum field equations which has a smooth structure at past null infinity

cauchy characteristic evolution and waveforms we investigate a new methodology for the computation of waves generated by isolated sources this approach consists of a global spacetime evolution algorithm based on a cauchy initial value formulation in a bounded interior region and based on characteristic hypersurfaces in the exterior we match the two schemes at their common interface the characteristic formulation allows accurate description of radiative infinity in a compactified finite coordinate interval so that our numerical solution extends to infinity and accurately models the free space problem the matching interface need not be situated far from the sources the wavefronts may have arbitrary nonspherical geometry and strong nonlinearity may be present in both the interior and the exterior regions stability and second order convergence of the algorithms to the exact solution of the infinite domain problem are established numerically in three space dimensions the matching algorithm is compared with examples of both local and nonlocal radiation boundary conditions proposed in the literature for linear problems matching outperformed the local radiation conditions chosen for testing and was about as accurate for the same grid resolution as the exact nonlocal conditions however since the computational cost of the nonlocal conditions is many times that of matching this algorithm may be used with higher grid resolutions yielding a significantly higher final accuracy for strongly nonlinear problems matching was significantly more accurate than all other methods tested this seems to be due to the fact that currently available local and nonlocal conditions are based on linearizing the governing equations in the far field while matching consistently takes nonlinearity into account in both interior and exterior regions

an asymptotic universal focal decomposition for non isochronous potentials galileo in the xvii century observed that the small os cillations of a pendulum seem to have constant period in fact the taylor expansion of the period map of the pendulum is constant up to second order in the initial angular velocity around the stable equi librium it is well known that for small oscillations of the pendulum and small intervals of time the dynamics of the pendulum can be ap proximated by the dynamics of the harmonic oscillator we study the dynamics of a family of mechanical systems that includes the pendulum at small neighbourhoods of the equilibrium but after long intervals of time so that the second order term of the period map can no longer be neglected we analyze such dynamical behaviour through a renor malization scheme acting on the dynamics of this family of mechanical systems the main theorem states that the asymptotic limit of this renormalization scheme is universal it is the same for all the elements in the considered class of mechanical systems as a consequence we obtain an universal asymptotic focal decomposition for this family of mechanical systems this paper is intended to be the first of a series of articles aiming at a semiclassical quantization of systems of the pendu lum type as a natural application of the focal decomposition associated to the two point boundary value problem

on the existence of analytic null asymptotically flat solutions of einstein s vacuum field equations this paper proves the existence of analytic solutions of the asymptotic characteristic initial value problem for einstein s field equations for analytic data on past null infinity and on an incoming null hypersurface

stable singularities of wave fronts in general relativity a wave front in a space time m is a family of null geodesics orthogonal to a smooth spacelike two surface in m it is of some interest to know how a wave front can fail to be a smoothly immersed surface in m in this paper we see that the space of null geodesics n of m considered as a contact manifold provides a natural setting for an efficient study of the stable singularities arising in the time evolution of wave fronts

underdetermined high resolution doa estimation a 2 rho th order source signal noise subspace constrained optimization for estimating the direction of arrival doa s of non stationary source signals such as speech and audio a constrained optimization problem cop that exploits the spatial diversity provided by an array of sensors is formulated in terms of a noise eliminated local 2 rho th order cumulant matrix the cop solution provides a weight vector to the look direction such that it is constrained to the 2 rho th order source signal subspace when the look direction is in alignment with the true doa otherwise it is constrained to the 2 rho th order noise subspace this weight vector is incorporated into the spatial spectrum to determine the degree of orthogonality between itself and either the 2 rho th order source signal subspace when the number of sources is unknown or the 2 rho th order noise subspace when the number of sources is known for a uniform linear array ula of m sensors the spatial spectrum for known number of sources can theoretically be shown to identify up to 2 rho m 1 sources realizing the difficulty in identifying stationarity in the received sensor signals the estimate of the noise eliminated local 2 rho th order cumulant matrix is marginalized over various possible stationary segmentations for a more robust doa estimation in this paper we focus on the use of local second and fourth order cumulants rho 1 2 and the proposed algorithms when rho 1 outperformed the kr subspace based algorithms and also the 4 music for globally non stationary non gaussian synthetic data and also for speech audio in various adverse environments we verified that the identifiability for rho 2 is improved by two folds compared to that for rho 1 with an ula

the theory of caustics and wave front singularities with physical applications this is intended as an introduction to and review of the theory of lagrangian and legendrian submanifolds and their associated maps developed by arnold and his collaborators the theory is illustrated by applications to hamilton jacobi theory and the eikonal equation with an emphasis on null surfaces and wave fronts and their associated caustics and singularities

doa estimation of quasi stationary signals with less sensors than sources and unknown spatial noise covariance a khatri rao subspace approach in real world applications such as those for speech and audio there are signals that are nonstationary but can be modeled as being stationary within local time frames such signals are generally called quasi stationary or locally stationary signals this paper considers the problem of direction of arrival doa estimation of quasi stationary signals specifically in our problem formulation we assume i sensor array of uniform linear structure ii mutually uncorrelated wide sense quasi stationary source signals and iii wide sense stationary noise process with unknown possibly nonwhite spatial covariance under the assumptions above and by judiciously examining the structures of local second order statistics soss we develop a khatri rao kr subspace approach that has two notable advantages first through an identifiability analysis it is proven that this kr subspace approach can operate even when the number of sensors is about half of the number of sources the idea behind is to make use of a virtual array structure provided inherently in the local sos model of which the degree of freedom is about twice of that of the physical array second the kr formulation naturally provides a simple yet effective way of eliminating the unknown spatial noise covariance from the signal soss extensive simulation results are provided to demonstrate the effectiveness of the kr subspace approach under various situations

direction finding algorithms based on high order statistics two direction finding algorithms are presented for nongaussian signals which are based on the fourth order cumulants of the data received by the array the first algorithm is similar to music while the second is asymptotically minimum variance in a certain sense the first algorithm requires singular value decomposition of the cumulant matrix while the second is based on nonlinear minimization of a certain cost function the performance of the minimum variance algorithm can be assessed by analytical means at least for the case of discrete probability distributions of the source signals and spatially uncorrelated gaussian noise the numerical experiments performed seem to confirm the insensitivity of these algorithms to the gaussian noise parameters

characteristic initial data and wavefront singularities in general relativity the structure of singularities caustics self intersections of wavefronts null hypersurfaces and wavefront families null coordinates in arbitrary space times is discussed in detail and illustrated by explicit examples of stable wavefront singularities in minkowski space it is shown how characteristic initial data determine the caustics and the self intersections of the characteristics of einstein s field equations

quadratic optimization for simultaneous matrix diagonalization simultaneous diagonalization of a set of matrices is a technique that has numerous applications in statistical signal processing and multivariate statistics although objective functions in a least squares sense can be easily formulated their minimization is not trivial because constraints and fourth order terms are usually involved most known optimization algorithms are therefore subject to certain restrictions on the class of problems orthogonal transformations sets of symmetric hermitian or positive definite matrices to name a few in this paper we present a new algorithm called qdiag that splits the overall optimization problem into a sequence of simpler second order subproblems there are no restrictions imposed on the transformation matrix which may be nonorthogonal indefinite or even rectangular and there are no restrictions regarding the symmetry and definiteness of the matrices to be diagonalized except for one of them we apply the new method to second order blind source separation and show that the algorithm converges fast and reliably it allows for an implementation with a complexity independent of the number of matrices and therefore is particularly suitable for problems dealing with large sets of matrices

a fast algorithm for joint diagonalization with non orthogonal transformations and its application to blind source separation a new efficient algorithm is presented for joint diagonalization of several matrices the algorithm is based on the frobenius norm formulation of the joint diagonalization problem and addresses diagonalization with a general non orthogonal transformation the iterative scheme of the algorithm is based on a multiplicative update which ensures the invertibility of the diagonalizer the algorithm s efficiency stems from the special approximation of the cost function resulting in a sparse block diagonal hessian to be used in the computation of the quasi newton update step extensive numerical simulations illustrate the performance of the algorithm and provide a comparison to other leading diagonalization methods the results of such comparison demonstrate that the proposed algorithm is a viable alternative to existing state of the art joint diagonalization algorithms the practical use of our algorithm is shown for blind source separation problems

estimates for the parametrix of the kohn laplacian on certain domains soit le demi espace superieur degenere generalise dans c 3 d p w 1 w 2 w imw p w 1 w 2 2 ou p c p 0 0 p est reel p 0 p 0 0 k p 0 0 pour k 2 on etudie la taille de la solution fondamentale de b sur des formes 0 1 sur la frontiere de d p

the asymptotic characteristic initial value problem for einstein s vacuum field equations as an initial value problem for a first order quasilinear symmetric hyperbolic system the asymptotic characteristic initial value problem for einstein s vacuum field equations where data are given on an incoming null hypersurface and on part of past null infinity is reduced to a characteristic initial value problem for a first order quasilinear symmetric hyperbolic system of differential equations for which existence and uniqueness of solutions can be shown it is delineated how the same method can be applied to the standard cauchy problems for einstein s vacuum and conformal vacuum equations

non orthogonal joint diagonalization in the least squares sense with application in blind source separation approximate joint diagonalization of a set of matrices is an essential tool in many blind source separation bss algorithms a common measure of the attained diagonalization of the set is the weighted least squares wls criterion however most well known algorithms are restricted to finding an orthogonal diagonalizing matrix relying on a whitening phase for the nonorthogonal factor often such an approach implies unbalanced weighting which can result in degraded performance we propose an iterative alternating directions algorithm for minimizing the wls criterion with respect to a general not necessarily orthogonal diagonalizing matrix under some mild assumptions we prove weak convergence in the sense that the norm of parameters update is guaranteed to fall below any arbitrarily small threshold within a finite number of iterations we distinguish between hermitian and symmetrical problems using bss simulations results we demonstrate the improvement in estimating the mixing matrix resulting from the relaxation of the orthogonality restriction

blind separation of quasi stationary sources exploiting convex geometry in covariance domain this paper revisits blind source separation of instantaneously mixed quasi stationary sources bss qss motivated by the observation that in certain applications e g speech there exist time frames during which only one source is active or locally dominant combined with nonnegativity of source powers this endows the problem with a nice convex geometry that enables elegant and efficient bss solutions local dominance is tantamount to the so called pure pixel separability assumption in hyperspectral unmixing nonnegative matrix factorization respectively building on this link a very simple algorithm called successive projection algorithm spa is considered for estimating the mixing system in closed form to complement spa in the specific bss qss context an algebraic preprocessing procedure is proposed to suppress short term source cross correlation interference the proposed procedure is simple effective and supported by theoretical analysis solutions based on volume minimization volmin are also considered by theoretical analysis it is shown that volmin guarantees perfect mixing system identifiability under an assumption more relaxed than exact local dominance which means wider applicability in practice exploiting the specific structure of bss qss a fast volmin algorithm is proposed for the overdetermined case careful simulations using real speech sources showcase the simplicity efficiency and accuracy of the proposed algorithms