l shape 2 dimensional arrival angle estimation with propagator method it is known that computational loads of the propagator method pm can be significantly smaller e g one or two order than those of music and esprit because the pm does not require any eigenvalue decomposition evd of the cross correlation matrix and singular value decomposition svd of the received data however the pm of the parallel shape array has nonnegligible drawbacks such as 1 requirement of pair matching between the 2 d azimuth and elevation angle estimation which is an exhaustive search and 2 estimation failure problems when elevation angles are between 70 spl deg and 90 spl deg the purpose of this paper is to show a way to remove these problems in the pm without additional computational loads this paper will employ one or two l shape arrays because the parallel shape used in the pm may cause the aforesaid problems simulation results verify that the pm with one or two l shape configurations can remove these problems and improve the performance of the pm significantly e g almost 5 db in signal to noise ratio for the parameters used in this paper

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

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

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

subspace fitting approaches for frequency estimation using real valued data a novel data covariance model has recently been proposed for the subspace based estimation of multiple real valued sine wave frequencies in this paper we develop weighted subspace fitting approaches using this new data model a new parameterization of the noise subspace is proposed this parameterization is used to solve the subspace fitting problem analytically an expression for the residual covariance matrix is derived this covariance matrix is further used to obtain an optimally weighted gauss markov estimator a computationally efficient suboptimal weighting is also proposed and the associated estimator is close to the gauss markov estimator in performance the suboptimal weighting strategy is quite general and can be used in other related applications the performance of the algorithms are illustrated using numerical simulations the proposed subspace fitting approach shows improved resolution performance it is also robust to additive noise

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

direction finding with partly calibrated uniform linear arrays a new method for direction finding with partly calibrated uniform linear arrays ulas is presented it is based on the conventional estimation of signal parameters via rotational invariance techniques esprit by modeling the imperfections of the ulas as gain and phase uncertainties for a fully calibrated array it reduces to the conventional esprit algorithm moreover the direction of arrivals doas unknown gains and phases of the uncalibrated sensors can be estimated in closed form without performing a spectral search hence it is computationally very attractive the cramer rao bounds crbs of the partly calibrated ulas are also given simulation results show that the root mean squared error rmse performance of the proposed algorithm is better than the conventional methods when the number of uncalibrated sensors is large it also achieves satisfactory performance even at low signal to noise ratios snrs

evolutionary periodogram for nonstationary signals presents a novel estimator for the time dependent spectrum of a nonstationary signal by modeling the signal at any given frequency as having a time varying amplitude accurately represented by an orthonormal basis expansion the authors are able to compute a minimum mean squared error estimate of this time varying amplitude repeating the process over all frequencies they obtain a power distribution as a function of time and frequency that is consistent with the wold cramer evolutionary spectrum based on the model assumptions the authors develop the evolutionary periodogram ep for nonstationary signals an estimator analogous to the periodogram used in the stationary case they also derive the time frequency resolution of the new estimator the approach is free of some of the drawbacks of the bilinear distributions and of the short time fourier transform spectral estimates it is guaranteed to produce nonnegative spectra without the cross term behavior of the bilinear distributions and it does not require windowing of data in the time domain examples illustrating the new estimator are given

rational invariant subspace approximations with applications subspace methods such as music minimum norm and esprit have gained considerable attention due to their superior performance in sinusoidal and direction of arrival doa estimation but they are also known to be of high computational cost in this paper new fast algorithms for approximating signal and noise subspaces and that do not require exact eigendecomposition are presented these algorithms approximate the required subspace using rational and power like methods applied to the direct data or the sample covariance matrix several esprit as well as music type methods are developed based on these approximations a substantial computational saving can be gained comparing with those associated with the eigendecomposition based methods these methods are demonstrated to have performance comparable to that of music yet will require fewer computations to obtain the signal subspace matrix

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

non uniqueness of admissible weak solutions to compressible euler systems with source terms abstract we consider admissible weak solutions to the compressible euler system with source terms which include rotating shallow water system and the euler system with damping as special examples in the case of anti symmetric sources such as rotations for general piecewise lipschitz initial densities and some suitably constructed initial momentum we obtain infinitely many global admissible weak solutions furthermore we construct a class of finite states admissible weak solutions to the euler system with anti symmetric sources under the additional smallness assumption on the initial densities we also obtain multiple global in time admissible weak solutions for more general sources including damping the basic framework are based on the convex integration method developed by de lellis and szekelyhidi 13 14 for the euler system one of the main ingredients of this paper is the construction of specified localized plane wave perturbations which are compatible with a given source term

global ill posedness of the isentropic system of gas dynamics we consider the isentropic compressible euler system in 2 space dimensions with pressure law p 2 and we show the existence of classical riemann data i e pure jump discontinuities across a line for which there are infinitely many admissible bounded weak solutions bounded away from the void we also show that some of these riemann data are generated by a 1 dimensional compression wave our theorem leads therefore to lipschitz initial data for which there are infinitely many global bounded admissible weak solutions c 2015 wiley periodicals inc

a fast squares power inversion array for tracking nonstationary environments this correspondence presents and investigates a fast algorithm tracking of nonstationary environments in power inversion the algorithm is based on the use of iterative least squares techniques and the introduction of an additional gradient vector in the objective function so that both the optimal weight vector and its rate of change are estimated recursively although the algorithm is computationally more complex than conventional least squares methods it has better performance in moving sources as the velocities of the latter are also being estimated

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

steady state analysis of the multistage constant modulus array the multistage constant modulus cm array is a cascade adaptive beamforming system that can recover several narrowband cochannel signals without training we examine its steady state properties at convergence using a stochastic analysis and computer simulations based on a wiener model of convergence for the gradient adaptive algorithms closed form expressions are derived for the cm array and canceller weight vectors as well as the effective source direction vectors at all stages along the cascade system the signal capture and direction finding capabilities of the system are also discussed computer simulations for stationary and fading sources are presented to confirm the theoretical results and to illustrate the rapid convergence behavior of the adaptive algorithms

blind separation of independent sources for virtually any source probability density function the blind source separation bss problem consists of the recovery of a set of statistically independent source signals from a set of measurements that are mixtures of the sources when nothing is known about the sources and the mixture structure in the bss scenario of two noiseless real valued instantaneous linear mixtures of two sources an approximate maximum likelihood ml approach has been suggested in the literature which is only valid under certain constraints on the probability density function pdf of the sources in the present paper the expression for this ml estimator is reviewed and generalized to include virtually any source distribution an intuitive geometrical interpretation of the new estimator is also given in terms of the scatter plots of the signals involved an asymptotic performance analysis is then carried out yielding a closed form expression for the estimator asymptotic pdf simulations illustrate the behavior of the suggested estimator and show the accuracy of the asymptotic analysis in addition an extension of the method to the general bss scenario of more than two sources and two sensors is successfully implemented

a subspace based direction finding algorithm using fractional lower order statistics we propose several classes of fractional lower order moment flom based matrices that can be used with music to estimate the doas of independent circular signals embedded in additive s spl alpha s symmetric spl alpha stable noise e g sea clutter we run simulations with different choices of the flom parameter p for our flom based matrices and conclude that when the noise is s spl alpha s with unknown spl alpha spl ne 2 flom multiple signal classification music with p close to unity yields good performance the performance of flom music and robust covariation based roc music are similar three scenarios that contain circular signals phase modulation pm circularly symmetrical gaussian and quaternary phase shift keying qpsk and one scenario that contains noncircular signals binary phase shift keying bpsk all embedded in the same s spl alpha s noise are tested these simulation results reveal that the scenario containing bpsk signals leads to poor performance indicating that flom music is presently limited to circular signals

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

on admissibility criteria for weak solutions of the euler equations we consider solutions to the cauchy problem for the incompressible euler equations satisfying several additional requirements like the global and local energy inequalities using some techniques introduced in an earlier paper we show that for some bounded compactly supported initial data none of these admissibility criteria singles out a unique weak solution as a byproduct in more than one space dimension we show bounded initial data for which admissible solutions to the p system of isentropic gas dynamics in eulerian coordinates are not unique

dissipative continuous euler flows we show the existence of continuous periodic solutions of the 3d incompressible euler equations which dissipate the total kinetic energy

solution semiflow to the isentropic euler system it is nowadays well understood that the multidimensional isentropic euler system is desperately ill posed even certain smooth initial data give rise to infinitely many solutions and all available selection criteria fail to ensure both global existence and uniqueness we propose a different approach to the well posedness of this system based on ideas from the theory of markov semigroups we show the existence of a borel measurable solution semiflow to this end we introduce a notion of dissipative solution which is understood as time dependent trajectories of the basic state variables the mass density the linear momentum and the energy in a suitable phase space the underlying system of pdes is satisfied in a generalized sense the solution semiflow enjoys the standard semigroup property and the solutions coincide with the strong solutions as long as the latter exist moreover they minimize the energy maximize the energy dissipation among all dissipative solutions

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

dissipative euler flows with onsager critical spatial regularity for any 0 we show the existence of continuous periodic weak solutions v of the euler equations that do not conserve the kinetic energy and belong to the space lt1 cx1 3 e namely x v x t is e holder continuous in space at a e time t and the integral t 1 3 edt is finite a well known open conjecture of l onsager claims that such solutions exist even in the class lt cx1 3 e 2016 wiley periodicals inc

high dimensionality and h principle in pde in this note we present an analyst s point of view on the nash kuiper theorem and in particular highlight the very close connection to turbulence a paradigm example of a high dimensional phenomenon our aim is to explain recent applications of nash s ideas in connection with the incompressible euler equations and onsager s famous conjecture on the energy dissipation in 3d turbulence

global optimum shape design abstract an optimum shape design problem can be formulated as a minimization problem of a functional subject to certain constraints usually it is nonlinear and nonconvex conventional optimization techniques are gradient based they highly depend on the initial design and are difficult to be applied to find a global solution integral global optimization algorithm is proposed to solve optimum shape design problems three design examples are given to illustrate the effectiveness of the algorithm

coprime sensing via chinese remaindering over quadratic fields part i array designs a coprime antenna array consists of two or more sparse subarrays featuring enhanced degrees of freedom dof and reduced mutual coupling this paper introduces a new class of planar coprime arrays based on the theory of ideal lattices in quadratic number fields a splitting prime p can be decomposed into the product of two distinct prime ideals which give rise to the two sparse subarrays their virtual difference coarray enjoys a quadratic gain in dof thanks to the generalized chinese remainder theorem crt to enlarge the contiguous aperture of the coarray we present hole free symmetric crt arrays with simple closed form expressions the ring of gaussian integers and the ring of eisenstein integers are considered as examples to demonstrate the procedure of designing coprime arrays with eisenstein integers our design yields a difference coarray that is a subset of the hexagonal lattice offering a significant gain in dof over the rectangular lattice given the same physical areas maximization of crt arrays in the aspect of essentialness and the superior performance in the context of angle estimation will be presented in the companion paper part ii

blind source separation based on time frequency signal representations blind source separation consists of recovering a set of signals of which only instantaneous linear mixtures are observed thus far this problem has been solved using statistical information available on the source signals this paper introduces a new blind source separation approach exploiting the difference in the time frequency t f signatures of the sources to be separated the approach is based on the diagonalization of a combined set of spatial t f distributions in contrast to existing techniques the proposed approach allows the separation of gaussian sources with identical spectral shape but with different t f localization properties the effects of spreading the noise power while localizing the source energy in the t f domain amounts to increasing the robustness of the proposed approach with respect to noise and hence improved performance asymptotic performance analysis and numerical simulations are provided

esprit a subspace rotation approach to estimation of parameters of cisoids in noise the application of a subspace invariance approach esprit to the estimation of parameters frequencies and powers of cisoids in noise is described esprit exploits an underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets the new approach has several advantages including improved resolution over pisarenko s technique for harmonic retrieval

direction finding for diversely polarized signals using polynomial rooting a direction finding algorithm for diversely polarized arrays that is based on polynomial rooting is presented using polynomial rooting instead of search reduces significantly the computational requirements of the algorithm and enhances resolution the basic method is limited to linear uniformly spaced arrays however using an interpolation technique the algorithm is extended to a larger class of arrays the performance of the proposed algorithm is analyzed computer simulations are used to demonstrate the performance of the new technique and to verify the performance analysis

consistency and mse performance of music based doa of a single source in white noise with randomly missing data music is a popular algorithm for estimating the direction of arrival doa in array signal processing applications in this paper we analyze the performance of the music algorithm for a single source system in the presence of noisy and missing data when only a random subset of the entries in the data matrix are observed we prove consistency of the doa estimate when signal from a single source is impinging on low coherence arrays and derive an analytic expression for the mean squared error mse performance of music for the case of uniform linear arrays in the large array and relatively large sample setting our analysis is mathematically justified in both the sample rich and deficient regimes the expression for the mse is a simple function of array geometry signal to noise ratio snr the fraction of entries observed and the ratio of the number of sensors to number of snapshots we derive a phase transition threshold which separates a regime where music is consistent from a regime where music is inconsistent this threshold depends upon the snr the probability of observing entries in the data matrix and number of sensors and snapshots in a simple manner which we make explicit

convex integration for a class of active scalar equations we show that a general class of active scalar equa tions including porous media and certain magnetostrophic tur bulence models admit non unique weak solutions in the class of bounded functions the proof is based upon the method of convex integration recently implemented for equations of fluid dynamics in 2 3

inviscid limit for the compressible euler system with non local interactions abstract the collective behavior of animals can be modeled by a system of equations of continuum mechanics endowed with extra terms describing repulsive and attractive forces between the individuals this system can be viewed as a generalization of the compressible euler equations with all of its unpleasant consequences e g the non uniqueness of solutions in this paper we analyze the equations describing a viscous approximation of a generalized compressible euler system and we show that its dissipative measure valued solutions tend to a strong solution of the euler system as viscosity tends to zero provided the strong solution exists

generalized and extended subspace algorithms for error correction with quantized dft codes discrete fourier transform dft codes have been used to provide robustness against errors and erasures in various applications this paper focuses on improving error localization of the bose chaudhuri hocquenghem bch dft codes first we analyze how the subspace based error localization outperforms the coding theoretic one then we propose an extension of the subspace based error localization based on additional syndrome that improves the existing one and is naturally suitable for rate adaptive distributed source coding dsc further we propose a new generic subspace based algorithm to decode bch dft codes the proposed approach generalizes the encoding and decoding of this important class of dft codes it introduces many different decoding matrices for a dft code this diversity is then used to diminish the effect of the quantization noise and thus to improve the decoding finally the extended and generalized approaches are combined to maximize the decoding gain simulation results demonstrate the capability of the proposed algorithms to perform significantly better than the existing subspace based error localization in the presence of quantization noise

necessary and sufficient global optimality conditions for convex maximization revisited convex maximization problem throughout this article it is assumed that the global maximum in 1 exists for the state of the art in convex maximization including various algorithms and abundant applications we w x w x refer to the textbooks 10 11 and to the excellent survey 1 in recent years several interesting necessary and sufficient global opti mality conditions characterizing a point x g d satisfying 1 have been proposed other conditions can be derived from optimality criteria formulated for more general global optimization problems in this article four of w x these criteria are revisited the condition hu of hiriart urruty cf 5 9 w x w x with a short elegant proof in 7 the condition s of strekalovski 18 20 which we will reprove generalize and modify the specialization of the w x singer toland duality st to problem 1 e g 13 17 21 22 and a reformulation of an optimality condition cdc for so called canonical w x d c problems originally given in 23 modified as used here and with a

a two stage method for inverse medium scattering we present a novel numerical method to the time harmonic inverse medium scattering problem of recovering the refractive index from noisy near field scattered data the approach consists of two stages one pruning step of detecting the scatterer support and one resolution enhancing step with nonsmooth mixed regularization the first step is strictly direct and of sampling type and it faithfully detects the scatterer support the second step is an innovative application of nonsmooth mixed regularization and it accurately resolves the scatterer size as well as intensities the nonsmooth model can be efficiently solved by a semi smooth newton type method numerical results for two and three dimensional examples indicate that the new approach is accurate computationally efficient and robust with respect to data noise

multiple source location the signal subspace approach the multiple source location problem is solved for a general array geometry using the principal of least squares modeling the incident wavefields may be a mixture of coherent and noncoherent sources that are broadband and or narrowband furthermore the wavefields may be plane waves and or spherical waves an effective algorithmic approach is developed for solving the multiple source location problem in the signal and covariance domains in each domain it is necessary to represent a set of vectors as a linear combination of array steering vectors using this property a generic descent algorithmic approach is developed for estimating the wavefield directions of arrival the success of such iterative approaches is critically dependent on the generation of good estimates to initialize the algorithm an effective initialization procedure is developed for this purpose direction of arrival estimates which arise from the proposed procedure are empirically found to be unbiased and low variance

waveform preserving blind estimation of multiple independent sources the problem of blind estimation of source signals is to estimate the source signals without knowing the characteristics of the transmission channel it is shown that the minimum variance unbiased estimates can be obtained if and only if the transmission channel can be identified blindly it is shown that the channel can be blindly identified if and only if there is not more than one gaussian source this condition suggests that waveform preserving blind estimation can be achieved over a wide range of signal processing applications including those cases in which the source signals have identical nongaussian distributions the constructive proof of the necessary and sufficient condition serves as a foundation for the development of waveform preserving blind signal estimation algorithms examples are presented to demonstrate the applications of the theoretical results

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

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

subspace leakage analysis and improved doa estimation with small sample size classical methods of doa estimation such as the music algorithm are based on estimating the signal and noise subspaces from the sample covariance matrix for a small number of samples such methods are exposed to performance breakdown as the sample covariance matrix can largely deviate from the true covariance matrix in this paper the problem of doa estimation performance breakdown is investigated we consider the structure of the sample covariance matrix and the dynamics of the root music algorithm the performance breakdown in the threshold region is associated with the subspace leakage where some portion of the true signal subspace resides in the estimated noise subspace in this paper the subspace leakage is theoretically derived we also propose a two step method that improves the performance by modifying the sample covariance matrix such that the amount of the subspace leakage is reduced furthermore we introduce a phenomenon named as root swap which occurs in the root music algorithm in the low sample size region and degrades the performance of the doa estimation a new method is then proposed to alleviate this problem numerical examples and simulation results are given for uncorrelated and correlated sources to illustrate the improvement achieved by the proposed methods moreover the proposed algorithms are combined with the pseudo noise resampling method to further improve the performance

direction of arrival estimation using rank revealing qr factorization the authors describe a novel technique for direction of arrival estimation based on computing a permutation matrix e and a qr factorization re hb of the permuted covariance matrix r such that a possible rank deficiency of r is revealed in the triangular factor b having a minimum norm lower right block a subset of the columns of the orthogonal matrix h is shown to be orthogonal to the direction vectors of sources and hence can be used to estimate their bearings the cost of this algorithm is only slightly more than that of one qr factorization but is much lower than that of an eigen decomposition simulation results are included to show that the proposed method performs nearly as well as music in terms of signal resolution bias and variance of the estimated bearings

performance analysis of spatial smoothing with interpolated arrays the interpolated spatial smoothing algorithm is a computationally efficient method for estimating the directions of arrival doas of signals some of which may be perfectly correlated it extends the spatial smoothing method to arbitrary array geometries a statistical performance analysis of the algorithm is presented closed form expressions for the covariance matrix of the doa estimation errors are derived using a perturbation analysis evaluating these expressions for specific cases and comparing them to the cramer rao lower bound for the doa estimates provides insight into the statistical efficiency of this algorithm the formulas for the error covariance are quite general and can be specialized to provide results for other doa estimation algorithms as well

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

on the energy dissipation rate of solutions to the compressible isentropic euler system in this paper we extend and complement the results in chiodaroli et al global ill posedness of the isentropic system of gas dynamics 2014 on the well posedness issue for weak solutions of the compressible isentropic euler system in 2 space dimensions with pressure law p 1 first we show that every riemann problem whose one dimensional self similar solution consists of two shocks admits also infinitely many two dimensional admissible bounded weak solutions not containing vacuum generated by the method of de lellis and szekelyhidi ann math 170 1417 1436 2009 arch ration mech anal 195 225 260 2010 moreover we prove that for some of these riemann problems and for 1 3 such solutions have a greater energy dissipation rate than the self similar solution emanating from the same riemann data we therefore show that the maximal dissipation criterion proposed by dafermos in j diff equ 14 202 212 1973 does not favour the classical self similar solutions

dissipative solutions and semiflow selection for the complete euler system to circumvent the ill posedness issues present in various models of continuum fluid mechanics we present a dynamical systems approach aiming at the selection of physically relevant solutions even under the presence of infinitely many solutions to the full euler system describing the motion of a compressible inviscid fluid our approach permits to select a system of solutions one trajectory for every initial condition satisfying the classical semiflow property moreover the selection respects the well accepted admissibility criteria for physical solutions namely maximization of the entropy production rate and the weak strong uniqueness principle consequently strong solutions are always selected whenever they exist and stationary states are stable and included in the selection as well to this end we introduce a notion of dissipative solution which is given by a triple of density momentum and total entropy defined as expectations of a suitable measure valued solution

grid free compressive beamforming the direction of arrival doa estimation problem involves the localization of a few sources from a limited number of observations on an array of sensors thus it can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing cs to achieve high resolution imaging on a discrete angular grid the cs reconstruction degrades due to basis mismatch when the doas do not coincide with the angular directions on the grid to overcome this limitation a continuous formulation of the doa problem is employed and an optimization procedure is introduced which promotes sparsity on a continuous optimization variable the doa estimation problem with infinitely many unknowns i e source locations and amplitudes is solved over a few optimization variables with semidefinite programming the grid free cs reconstruction provides high resolution imaging even with non uniform arrays single snapshot data and under noisy conditions as demonstrated on experimental towed array data

a blind source separation technique using second order statistics separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed in many situations no a priori information on the mixing matrix is available the linear mixture should be blindly processed this typically occurs in narrowband array processing applications when the array manifold is unknown or distorted this paper introduces a new source separation technique exploiting the time coherence of the source signals in contrast with other previously reported techniques the proposed approach relies only on stationary second order statistics that are based on a joint diagonalization of a set of covariance matrices asymptotic performance analysis of this method is carried out some numerical simulations are provided to illustrate the effectiveness of the proposed method

spatial evolutionary spectrum for doa estimation and blind signal separation we combine the concepts of evolutionary spectrum and array processing we present a cross power stationary periodogram for both direction of arrival doa estimation and blind separation of nonstationary signals we model the nonstationary signals received by each array sensor as a sum of complex sinusoids with time varying amplitudes these magnitudes carry information about the doa that may also be time varying we first estimate the time varying amplitudes using estimators obtained by minimizing the mean squared error then using the estimated time varying amplitudes we estimate the evolutionary cross power distributions of the sensor next using cross power estimates at time frequency points interest we estimate the doas using one of the existing methods if the directions are time varying we choose time frequency points around the time of interest to estimate spontaneous source locations if the sources are stationary time frequency points of interest can be combined for the estimation of fixed directions whitening and subspace methods used to find the mixing matrix and separate nonstationary signals received by the array we present examples illustrating the performance of the proposed algorithms

doa estimation with enhanced dofs by exploiting cyclostationarity many modulated signals exhibit a cyclostationarity property which has been applied in direction of arrival estimation due to its immunity to interference and noise in this paper we focus on how this cyclostationarity can be effectively integrated with the spatial dimension to enhance both the degrees of freedom and the accuracy of doa estimation first for narrowband signal case by vectorizing the second order cyclic correlation matrix instead of the conventional zero lag covariance matrix one can directly generate an augmented virtual array with sensors at positions defined by the difference coarray of the physical array then for wideband signal case two additional fractional factors are introduced so that the vectorized cyclic correlation matrix can be viewed as a single snapshot received signal from an array with sensors at positions defined by the fractional weighted difference coarray due to the fact that cyclic correlation matrices as special second order statistics allow us to obtain more degrees of freedom the proposed two virtual array models can resolve o n 2 sources by using a sparse linear array consisting of only n physical sensors e g nested coprime array furthermore a scheme of multipseudosampling is proposed in order to reduce the sensitivity to noise and parameter the proposed models can be considered as an extension of difference coarray perspective via the combination of cyclic frequency and temporal lag in the end numerical simulation results validate the effectiveness of the proposed models

matrix based higher order spectral analysis for three wave coupling processes composite linear and quadratic systems produce three wave coupling when stimulated by random phase input sinusoids due to the nonlinearity of the system the output frequencies are arithmetically related to the input using third order cumulant statistics and their associated bispectrum techniques are devised based on phase insensitive matrix structures for detection and frequency estimation of coupling frequencies the separation of the third order cumulant series into symmetric and skew symmetric portions allows one to exploit their characteristic eigendecompositions for frequency estimation after symmetrization biphases can be easily extracted as coefficients of the cumulant sequence using a generalized eigenvector representation one can relate symmetric and skew symmetric bases by a subspace rotation algorithm biphases can be estimated directly from generalized eigenvalues of the matrix pencil formed by symmetric and skew symmetric matrices the dimensionality of the matrices can be reduced through the use of cumulant projections that yield a slice of the bispectrum the radon transform procedure is related to bispectral processing through an isotropic radial slice volterra filter the compact third order kronecker product matrix formulation and algorithms for coupling frequency estimation can also be converted for use in biphase estimation simulations showing the performance of the above procedures are also presented for both synthetic and biomedical time series

global optimality conditions for quadratic optimization problems with binary constraints we consider nonconvex quadratic optimization problems with binary constraints our main result identifies a class of quadratic problems for which a given feasible point is global optimal we also establish a necessary global optimality condition these conditions are expressed in a simple way in terms of the problem s data we also study the relations between optimal solutions of the nonconvex binary quadratic problem versus the associated relaxed and convex problem defined over the l infty norm our approach uses elementary arguments based on convex duality

performance analysis of the enhanced minimum variance spatial spectrum estimator the performance of the enhanced minimum variance emv spatial spectrum estimator is studied expressions are presented fur the variance and bias of direction of arrival estimators based on general functions of the covariance matrix and these expressions are then used to study the emv estimator finite data effects and random perturbations on the ideal modeling assumptions are studied separately

optimality conditions in global optimization and their applications in this paper we derive necessary and sufficient conditions for some problems of global minimization our approach is based on methods of abstract convexity we use a representation of an upper semicontinuous function as the lower envelope of a family of convex functions we discuss applications of conditions obtained to the examination of some tractable sufficient conditions for the global minimum and to the theory of inequalities

markov based eigenanalysis method for frequency estimation this paper proposes an eigenanalysis based method for estimating the frequencies of complex valued sine waves the basic idea behind this method consists of using a set of linearly independent vectors that are orthogonal to the signal subspace spanned by the principal eigenvectors of the data covariance matrix exploiting that orthogonality condition gives an overdetermined system of linear equations the unknown parameters of which are uniquely related to the frequencies analytical expressions are derived for the covariances of the equation errors in the sample version of the aforementioned linear system of equations based on these expressions a markov like estimate of the unknown parameters is introduced which asymptotically with respect to either the number of data samples or the signal to noise ratio provides the minimum variance frequency estimates in a fairly large class of consistent estimators the paper includes monte carlo simulations that support the theoretical analysis results and show that those results may apply to scenarios with rather low values of the number of data samples and the signal to noise ratio

on oscillatory solutions to the complete euler system abstract the euler system in fluid dynamics is a model of a compressible inviscid fluid incorporating the three basic physical principles conservation of mass momentum and energy we show that the cauchy problem is basically ill posed for the l initial data in the class of weak entropy solutions as a consequence there are infinitely many measure valued solutions for a vast set of initial data finally using the concept of relative energy we discuss a singular limit problem for the measure valued solutions where the mach and froude number are proportional to a small parameter

ramanujan sums in the context of signal processing part ii fir representations and applications the mathematician ramanujan introduced a summation in 1918 now known as the ramanujan sum c q n in a companion paper part i properties of ramanujan sums were reviewed and ramanujan subspaces s q introduced of which the ramanujan sum is a member in this paper the problem of representing finite duration fir signals based on ramanujan sums and spaces is considered first it is shown that the traditional way to solve for the expansion coefficients in the ramanujan sum expansion does not work in the fir case two solutions are then developed the first one is based on a linear combination of the first n ramanujan sums with n being the length of the signal the second solution is based on ramanujan subspaces with q 1 q 2 q k denoting the divisors of n it is shown that x n can be written as a sum of k signals x qi n s qi furthermore the i th signal x qi n has period q i and any pair of these periodic components is orthogonal the components x qi n can be calculated as orthogonal projections of x n onto ramanujan spaces s qi then the ramanujan periodic transform rpt is defined based on this and is useful to identify hidden periodicities it is shown that the projection matrices which compute x qi n from x n are integer matrices except for an overall scale factor the calculation of projections is therefore rendered easy to estimate internal periods n n of x n one only needs to know which projection energies are nonzero

direction of arrival estimation in time modulated linear arrays with unidirectional phase center motion a novel approach for estimating the direction of arrivals doas in time modulated linear arrays tmlas with unidirectional phase center motion upcm scheme is proposed in this paper based on the fact that the main beams of the patterns at different sidebands can be directed at different directions the corresponding received signals can be used to compose a received data space thus the spatial locations of the far field sources can be estimated by using multiple signal classification music algorithm simulation results of the doa estimation in an 8 element tmla with the upcm scheme validate the proposed approach where the performance such as the accuracy and resolution of the doa estimation is obtained through monte carlo simulations as compared to the doa estimation based on conventional uniform linear arrays ulas a much better resolution performance is obtained

cauchy problem for dissipative holder solutions to the incompressible euler equations we consider solutions to the cauchy problem for the incompressible euler equations on the 3 dimensional torus which are continuous or holder continuous for any exponent theta frac 1 16 using the techniques introduced in de lellis and szekelyhidi inventiones mathematicae 9 377 407 2013 dissipative euler flows and onsager s conjecture 2012 we prove the existence of infinitely many holder continuous initial vector fields starting from which there exist infinitely many holder continuous solutions with preassigned total kinetic energy

lack of uniqueness for weak solutions of the incompressible porous media equation in this work we consider weak solutions of the incompressible two dimensional porous media ipm equation by using the approach of de lellis szekelyhidi we prove non uniqueness for solutions in l in space and time

maximal dissipation in equations of evolution abstract the subject of this paper is evolutionary equations such as the hunter saxton equation or hyperbolic conservation laws with the property that the initial value problem admits a multitude of solutions along which a certain energy functional decays at different rates the aim is to examine whether solutions that dissipate the energy at maximal rate command special status

kalman based estimator for doa estimations we introduce a new kalman based noise subspace estimator combined with the root music for direction of arrival doa estimation of uncorrelated narrow band plane waves impinging on an array of sensors without both a priori knowledge of the number of sources and the inflation method presented by yang and kaveh 1988 we show that the kalman based estimator can approximately estimate the complete noise subspace with small bias for high input signal to noise ratio snr scenario the proposed algorithm needs slightly more computation operations per adaptive cycle than yang and kaveh s lms based algorithm but with much more rapid convergence simulations demonstrate the effectiveness of the proposed algorithm

first order perturbation analysis of singular vectors in singular value decomposition singular value decomposition svd is an important technique in signal processing in the literature the perturbation analysis of svd has been well documented in the context of subspace decomposition the contribution of the signal subspace to the perturbation of the singular vectors that span the signal subspace is often ignored as it is treated as second and higher order terms and thus the first order perturbation is typically given as the column span of the noise subspace in this correspondence we show that not only the noise subspace but also the signal subspace contribute to the first order perturbation of the singular vectors we further show that the contribution of the signal subspace does not impact on the performance analysis of algorithms that rely on the signal subspace for parameter estimation but it affects the analysis of algorithms that depends on the individual basis vectors for the latter we also give a condition under which the contribution of the signal subspace to the perturbation of singular vectors may be ignored in the statistical sense numerical examples are provided to validate our theoretic claims

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

reduced complexity maximum likelihood direction of arrival estimation based on spatial aliasing spatial aliasing is an undesirable phenomenon that prevents the unique determination of the direction of arrival doa of impinging signals in array signal processing however the characteristics of spatial aliasing that generates ambiguous doas can be also used to reduce the computational complexity in maximum likelihood ml doa estimation this paper proposes a structural method to dramatically reduce the computational complexity of the ml doa estimation using the spatial aliasing generated by a nested array structure with a doubly scaled aper ture an ml full grid search is computationally simplified by the highly compressed searching range and the small number of candidate values to be searched which are derived based on spatial aliasing performance analyses based on the theoretical bounds and computational complexity with computer simulations show that the proposed method requires an extremely reduced computational load compared to the conventional ml doa estimation with a uniform linear array ula while achieving the performance enhancement in the estimation accuracy due to the enlarged array aperture

perturbation analysis of subspace based methods in estimating a damped complex exponential we present a study of mode variance statistics for three svd based estimation methods in the case of a single mode damped exponential the methods considered are namely kumaresan tufts matrix pencil and kung s direct data approximation through first order perturbation analysis we derive closed form expressions of the variance of the complex mode frequency and damping factor estimates these expressions are used to compare the different methods and to determine the optimal prediction order for matrix pencil and direct data approximation methods application to the undamped case shows the coherence of the results with those already stated in the literature it is also found that the variances converge linearly towards the cramer rao bound finally the theoretical results are verified using monte carlo simulations

the euler equations as a differential inclusion we propose a new point of view on weak solutions of the euler equations describing the motion of an ideal incompressible fluid in r n with n 2 we give a reformulation of the euler equations as a differential inclusion and in this way we obtain transparent proofs of several celebrated results of v scheffer and a shnirelman concerning the non uniqueness of weak solutions and the existence of energy decreasing solutions our results are stronger because they work in any dimension and yield bounded velocity and pressure