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

localization for the anderson model on a strip with singular potentials abstract we prove exponential localization in the anderson model on a one dimensional strip for any potential whose probability distribution is not concentrated on a single point and possesses some finite moment in particular we obtain localization for bernoulli potentials on a strip

divisor class groups of singular surfaces we compute divisors class groups of singular surfaces most notably we produce an exact sequence that relates the cartier divisors and almost cartier divisors of a surface to the those of its normalization this generalizes hartshorne s theor em for the cubic ruled surface in p 3 we apply these results to limit the possible curves that can be s et theoretic complete intersection in p 3 in characteristic zero on a nonsingular variety the study of divisors and linear systems is classical in fact the entire theory of curves and surfaces is dependent on this study of codimension one subvarieties and the linear and algebraic families in which they move this theory has been generalized in two directions the weil divisors on a normal variety taking codimension one subvarieties as prime divisors and the cartier divisors on an arbitrary scheme based on locally principal codimension one subschemes most of the literature both in algebraic geometry and commutative algebra up to now has been limited to these kinds of divisors more recently there have been good reasons to consider divisors on non normal varieties jaffe 9 introduced the notion of an almost cartier divisor which is locally principal off a subset of codimension two a theory of generalized divisors was proposed on curves in 14 and extended to any dimension in 15 the latter paper gave a complete description of the generalized divisors on the ruled cubic surface in p 3 in this paper we extend that analysis to an arbitrary integra l surface x explaining the group apicx of linear equivalence classes of almost cartier divisors on x in terms of the picard group of the normalization s of x and certain local data at the singular points of x we apply these results to give limitations on the possible curves that can b e set theoretic compete intersections in p 3 in characteristic zero in section 2 we explain our basic set up comparing divisors on a variety x to its normalization s in section 3 we prove a local isomorphism that computes the group of almost cartier divisors at a singular point of x in terms of the cartier divisors along the curve of singulari ties and its inverse image in the normalization in section 4 we derive some global exact sequences for the groups picx apicx and pics which generalize the results of 15 6 to arbitrary surfaces these results are particularly transparent for surfaces wi th ordinary singularities meaning a double curve with a finite number of pinch points and triple points

new characterizations of the region of complete localization for random schrodinger operators we study the region of complete localization in a class of random operators which includes random schrodinger operators with anderson type potentials and classical wave operators in random media as well as the anderson tight binding model we establish new characterizations or criteria for this region of complete localization given either by the decay of eigenfunction correlations or by the decay of fermi projections these are necessary and sufficient conditions for the random operator to exhibit complete localization in this energy region using the first type of characterization we prove that in the region of complete localization the random operator has eigenvalues with finite multiplicity

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

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

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

a unified framework and sparse bayesian perspective for direction of arrival estimation in the presence of array imperfections self calibration methods play an important role in reducing the negative effects of array imperfections during direction of arrival doa estimation however the dependence of most such methods on the eigenstructure techniques greatly degrades their adaptation to demanding scenarios such as low signal to noise ratio snr and limited snapshots this paper aims at formulating a unified framework and sparse bayesian perspective for array calibration and doa estimation a comprehensive model of the array output is presented first when a single type of array imperfection is considered with mutual coupling gain phase uncertainty and sensor location error treated as typical examples the spatial sparsity of the incident signals is then exploited and a bayesian method is proposed to realize array calibration and source doa estimation the array perturbation magnitudes are assumed to be small according to most application scenarios and the geometries of mutually coupled arrays are assumed to be uniform linear and those of arrays with sensor location errors are assumed to be linear cramer rao lower bounds crlbs for the array calibration and doa estimation precisions are also obtained the sparse bayesian method is finally extended to deal with the doa estimation problem when more than one type of array perturbation coexists

a characterization of the anderson metal insulator transport transition we investigate the anderson metal insulator transition for random schrodinger operators we define the strong insulator region to be the part of the spectrum where the random operator exhibits strong dynamical localization in the hilbert schmidt norm we introduce a local transport exponent e and set the weak metallic transport region to be the part of the spectrum with nontrivial transport i e e 0 we prove that these insulator and metallic regions are complementary sets in the spectrum of the random operator and that the local transport exponent e provides a characterization of the metal insulator transport transition moreover we show that if there is such a transition then e has to be discontinuous at a transport mobility edge more precisely we show that if the transport is nontrivial then e 1 2d where d is the space dimension these results follow from a proof that slow transport of quantum waves in random media implies the starting hypothesis for the authors bootstrap multiscale analysis we also conclude that the strong insulator region coincides with the part of the spectrum where we can perform a bootstrap multiscale analysis proving that the multiscale analysis is valid all the way up to a transport mobility edge

direction of arrival estimation for wide band signals using the esprit algorithm a novel direction of arrival estimation algorithm is proposed that applies to wideband emitter signals a sensor array with a translation invariance structure is assumed and an extension of the esprit algorithm for narrowband emitter signals is obtained the emitter signals are modeled as the stationary output of a finite dimensional linear system driven by white noise the array response to a unit impulse from a given direction is represented as the impulse response of a linear system the measured data from the sensor array can then be seen as the output of a multidimensional linear system driven by white noise sources and corrupted by additive noise the emitter signals and the array output are characterized by the modes of the linear system the esprit algorithm is applied at the poles of the system the power of the signals sharing the pole is captured and the effect of noise is reduced the algorithm requires no knowledge storage or search of the array manifold as opposed to wideband extensions of the music algorithm this results in a computationally efficient algorithm that is insensitive to array perturbations simulations are presented comparing the wideband and esprit algorithm to the modal signal subspace method and the coherent signal subspace method

a new proof of localization in the anderson tight binding model we give a new proof of exponential localization in the anderson tight binding model which uses many ideas of the frohlich martinelli scoppola and spencer proof but is technically simpler particularly the probabilistic estimates

statistical analysis of an eigendecomposition based method for 2 d frequency estimation abstract an eigendecomposition based method for two dimensional frequency estimation is analyzed in this paper this method to be referred to as matrix pencil mp method computes a smoothed data covariance matrix then its eigendecomposition and then the two dimensional frequencies via a mp approach the mp method is now known to be more efficient in computation than many other methods and able to provide a near optimum performance for relatively large signal to noise ratio snr the aim of this paper is to provide a further analysis of the mp method assuming a moderate snr to make the problem tractable a large two dimensional data set is considered in this paper a number of fundamental relations inherent in the mp method are revealed which lead to a general expression of the large sample covariances of the estimated two dimensional frequencies the large sample covariances are reduced to a very simple form for the single two dimensional frequency case the theoretical covariances are verified by the simulation results

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

cramer rao bound for doa estimators under the partial relaxation framework derivation and comparison a class of computationally efficient doa estimators under the partial relaxation pr framework has recently been proposed conceptually different from conventional doa estimation methods in the literature the estimators under the pr framework rely on the non complete relaxation of the array manifold while performing a spectral search in the field of view this particular type of relaxation essentially implies a modified signal model with partial information loss due to the relaxation the information loss and its impact on the doa estimation performance have not yet been analytically quantified in the literature in this paper the information loss induced by the relaxation of the array manifold is investigated through the cramer rao bound crb the closed form expression of the crb for doa estimation under the pr model on the one hand provides insight on the information loss in the asymptotic region where the number of snapshots tends to infinity on the other hand the proposed crb characterizes the lower bound for the doa estimation performance of all pr estimators we prove that under the assumptions of gaussian source signal and noise the crb of the pr signal model is lower bounded by the conventional stochastic crb we also prove that the previously proposed weighted subspace fitting estimator under the pr framework asymptotically achieves the crb of the pr signal model furthermore it is shown that the asymptotic mean squared errors of all weighted subspace fitting estimators under the pr framework for any positive definite weighting matrix are identical

dynamical delocalization in random landau hamiltonians we prove the existence of dynamical delocalization for random landau hamiltonians near each landau level since typically there is dynamical localization at the edges of each disordered broadened landau band this implies the existence of at least one dynamical mobility edge at each landau band namely a boundary point between the localization and delocalization regimes which we prove to converge to the corresponding landau level as either the magnetic field goes to infinity or the disorder goes to zero in this article we prove the existence of dynamical delocalization for random landau hamiltonians near each landau level more precisely we prove that for these two dimensional hamiltonians there exists at least one energy e near each landau level such that e 1 where e the local transport exponent introduced in gk5 is a measure of the rate of transport in wave packets with spectral support near e since typically there is dynamical localization at the edges of each disordered broadened landau band this implies the existence of at least one dynamical mobility edge at each landau band namely a boundary point between the localization and delocalization regimes which we prove to converge to the corresponding landau level as either the magnetic field goes to infinity or the disorder goes to zero random landau hamiltonians are the subject of intensive study due to their links with the integer quantum hall e ect kli for which von klitzing received the 1985 nobel prize in physics they describe an electron moving in a very thin flat conductor with impurities under the influence of a constant magnetic field perpendicular to the plane of the conductor and play an important role in the understanding of the quantum hall e ect l aoa t h nt ku be avss bees laughlin s argument l as pointed out by halperin h uses the assumption that under weak disorder and strong magnetic field the energy spectrum consists of bands of extended states separated

random dirac operators with time reversal symmetry quasi one dimensional stochastic dirac operators with an odd number of channels time reversal symmetry but otherwise efficiently coupled randomness are shown to have one conducting channel and absolutely continuous spectrum of multiplicity two this follows by adapting the criteria of guivarch raugi and goldsheid margulis to the analysis of random products of matrices in the group so 2l and then a version of kotani theory for these operators absence of singular spectrum can be shown by adapting an argument of jaksic last if the potential contains random dirac peaks with absolutely continuous distribution

local fluctuation of the spectrum of a multidimensional anderson tight binding model we consider the anderson tight binding modelh v acting inl 2 z d and its restrictionh to finite hypercubes z d herev v x x z d is a random potential consisting of independent identically distributed random variables let e j j be the eigenvalues ofh and let j e e j e j 1 be its rescaled eigenvalues then assuming that the exponential decay of the fractional moment of the green function holds for complex energies neare and that the density of statesn e exists ate we shall prove that the random sequence j e j considered as a point process onr 1 converges weakly to the stationary poisson point process with intensity measuren e dx as gets large thus extending the result of molchanov proved for a one dimensional continuum random schrodinger operator on the other hand the exponential decay of the fractional moment of the green function was established recently by aizenman molchanov and graf as a technical lemma for proving anderson localization at large disorder or at extreme energy thus our result in this paper can be summarized as follows near the energye where anderson localization is expected there is no correlation between eigenvalues ofh if is large

a lower bound for the lyapounov exponents of the random schrodinger operator on a strip we consider the random schrodinger operator on a strip of width w assuming the site distribution of bounded density it is shown that the positive lyapounov exponents satisfy a lower bound roughly exponential in w for w the argument proceeds directly by establishing green s function decay but does not appeal to furstenberg s random matrix theory on the strip one ingredient involved is the construction of barriers using the random schrodinger operator theory on mathbb z

analysis of the asymptotic relative efficiency of the music algorithm an analytical performance evaluation of the errors of the direction of arrival estimates obtained by the music algorithm for uncorrelated sources is provided explicit asymptotic formulas are derived for the means and the covariance of the estimates the covariances are then compared to the cramer rao lower bound it is shown that for a single course the music algorithm is asymptotically efficient for multiple sources the algorithm is not efficient in general however it approaches asymptotic efficiency when the snrs signal to noise ratios of all sources tend to infinity it is illustrated by several test cases that the relative efficiency of the music algorithm is nearly one under a wide range of parameter variations the analytic performance evaluation thus confirms empirical evidence to the excellent performance of the music algorithm for narrowband signals

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

anderson localization for bernoulli and other singular potentials we prove exponential localization in the anderson model under very weak assumptions on the potential distribution in one dimension we allow any measure which is not concentrated on a single point and possesses some finite moment in particular this solves the longstanding problem of localization for bernoulli potentials i e potentials that take only two values in dimensions greater than one we prove localization at high disorder for potentials with holder continuous distributions and for bounded potentials whose distribution is a convex combination of a holder continuous distribution with high disorder and an arbitrary distribution these include potentials with singular distributions we also show that for certain bernoulli potentials in one dimension the integrated density of states has a nontrivial singular component

absence of diffusion in the anderson tight binding model for large disorder or low energy we prove that the green s function of the anderson tight binding hamiltonian decays exponentially fast at long distances on v with probability 1 we must assume that either the disorder is large or the energy is sufficiently low our proof is based on perturbation theory about an infinite sequence of block hamiltonians and is related to kam methods

singular continuous spectrum under rank one perturbations and localization for random hamiltonians we consider a selfadjoint operator a and a selfadjoint rank one projection p onto a vector which is cyclic for a in terms of the spectral measure d a we give necessary and sufficient conditions for a p to have empty singular continuous spectrum or to have only point spectrum for a e we apply these results to questions of localization in the one and multi dimensional anderson models

zariski closure of subgroups of the symplectic group and lyapunov exponents of the schrodinger operator on the strip we consider the schrodinger equation with a random potential y n 1 q n ei y n y n 1 0 whereqn is a sequence of independent identically distributed random symmetricm m matrices with real valued elements yn m n e is the real parameter andi is the identity matrix we show that if the smallest jordan algebra of matrices containing the support of the distribution of matricesqn coincides with jordan algebra of all real valued symmetric matrices then for all but maybe a finite number of values ofe all the lyapunov exponents of our schrodinger equation are different and thus the spectrum of the corresponding schrodinger operator is pure point

localization for one dimensional continuum bernoulli anderson models we use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional continuum anderson type models with singular distributions in particular the case of a bernoulli dis tribution is covered the operators we consider model alloys composed of at least two distinct types of randomly dispersed atoms our main tools are the reflection and transmission coefficients for compactly supported single site perturbations of a periodic background which we use to verify the necessary hypotheses of multi scale analysis we show that non reflectionless single sites lead to a discrete set of exceptional energies away from which localization occurs

source association doa and fading coefficients estimation for multipath signals this paper addresses the source association sa direction of arrival doa and fading coefficients fcs estimation problem in multipath environment first we establish a rank reduction property for a multipath signal model with the existence of multiple groups of coherent signals subsequently based on this property effective algorithms for sa doa and fcs estimation have been developed the proposed doa and fcs estimation methods exploit the multipath structure information to achieve improved accuracy the new doa estimation methods work well even in the case that the doas of the multipath signals associated with different sources are nearly overlapped meanwhile the new methods are applicable to arbitrary array geometry while without decreasing the effective array aperture then the stochastic cramer rao bound on doa and fcs estimation of multipath model mcrb exploiting the multipath structure information is derived in closed form numerical simulations have been provided to demonstrate the effectiveness of the proposed methods

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

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

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

log holder continuity of the integrated density of states for stochastic jacobi matrices we consider the integrated density of states k e of a general operator on l2 v of the formh h0 v where h 0 u n sum limits left i right 1 u n i and vu n v n u n wherev is a general bounded ergodic stationary process on v we show that k e k e c log e e 1 when e e 1 2 the key is a thouless formula for the strip

constructive proof of localization in the anderson tight binding model we prove that for large disorder or near the band tails the spectrum of the anderson tight binding hamiltonian with diagonal disorder consists exclusively of discrete eigenvalues the corresponding eigenfunctions are exponentially well localized these results hold in arbitrary dimension and with probability one in one dimension we recover the result that all states are localized for arbitrary energies and arbitrarily small disorder our techniques extend to other physical systems which exhibit localization phenomena such as infinite systems of coupled harmonic oscillators or random schrodinger operators in the continuum

the concentrated solutions on the nonhomogeneous scalar curvature problem abstract we consider the following scalar curvature equation u 1 e k x u 2 1 in r n if k x is nonhomogeneous at the critical points we give the precise description on the concentrated solutions which contains the necessary and existence on the two peak solutions here we generalize the results of cao noussair yan in 6 to the nonhomogeneous case

beamspace esprit most high resolution algorithms for sensor array processing require an eigendecomposition which is a computation that is difficult to implement in parallel and requires o m sup 3 multiplications for an m spl times m matrix corresponding to m sensors beamspace transformation is one way of reducing computation and sometimes improving the estimation accuracy as a consequence of the beamspace transformation performed however arrays such as uniform linear arrays commonly used in direction finding lose their displacement invariance structure as a result computational complexity may actually increase since the computationally efficient esprit algorithm cannot be applied directly in this paper a method for restoring the invariance structure resulting in a beamspace esprit algorithm is described asymptotic performance analysis of beamspace esprit and simulation results are presented as well

localization for random schrodinger operators with correlated potentials we prove localization at high disorder or low energy for lattice schrodinger operators with random potentials whose values at different lattice sites are correlated over large distances the class of admissible random potentials for our multiscale analysis includes potentials with a stationary gaussian distribution whose covariance functionc x y decays as x y where 0 can be arbitrarily small and potentials whose probability distribution is a completely analytical gibbs measure the result for gaussian potentials depends on a multivariable form of nelson s best possible hypercontractive estimate

unitary esprit how to obtain increased estimation accuracy with a reduced computational burden esprit is a high resolution signal parameter estimation technique based on the translational invariance structure of a sensor array previous esprit algorithms do not use the fact that the operator representing the phase delays between the two subarrays is unitary the authors present a simple and efficient method to constrain the estimated phase factors to the unit circle if centro symmetric array configurations are used unitary esprit the resulting closed form algorithm has an esprit like structure except for the fact that it is formulated in terms of real valued computations throughout since the dimension of the matrices is not increased this completely real valued algorithm achieves a substantial reduction of the computational complexity furthermore unitary esprit incorporates forward backward averaging leading to an improved performance compared to the standard esprit algorithm especially for correlated source signals like standard esprit unitary esprit offers an inexpensive possibility to reconstruct the impinging wavefronts signal copy these signal estimates are more accurate since unitary esprit improves the underlying signal subspace estimates simulations confirm that even for uncorrelated signals the standard esprit algorithm needs twice the number of snapshots to achieve a precision comparable to that of unitary esprit thus unitary esprit provides increased estimation accuracy with a reduced computational burden

optimal utilization of signal free samples for array processing in unknown colored noise fields many algorithms for direction of arrival doa estimation require the noise covariance matrix to be known or to possess a known structure in many cases the noise covariance is in fact estimated from separate measurements this paper addresses the combined effects of finite sample sizes both in the estimated noise covariance matrix and in the data with signals present it is assumed that a batch of signal free samples is available in addition to the signal containing samples no assumption is made on the structure of the noise covariance in this paper the asymptotic covariance of the weighted subspace fitting wsf algorithm is derived for the case in which the data are whitened using an estimated noise covariance the expression obtained suggests an optimal weighting that improves performance compared to the standard choice in addition a new method based on covariance matching is proposed both methods are asymptotically statistically efficient the cramer rao lower bound crb on the covariance of the estimate for the data model is also derived monte carlo simulations show promising small sample performance for the two new methods and confirm the asymptotic results

absence of absolutely continuous spectrum for random scattering zippers a scattering zipper is a system obtained by concatenation of scattering events with equal even number of incoming and outgoing channels the associated scattering zipper operator is the unitary analog of jacobi matrices with matrix entries for infinite identical events and independent and identically distributed random phases lyapunov exponents positivity is proved and yields absence of absolutely continuous spectrum by kotani s theory

direction of arrival estimation using a sparse representation of array covariance vectors a new direction of arrival doa estimation method is proposed based on a novel data model using the concept of a sparse representation of array covariance vectors sracv in which doa estimation is achieved by jointly finding the sparsest coefficients of the array covariance vectors in an overcomplete basis the proposed method not only has high resolution and the capability of estimating coherent signals based on an arbitrary array but also gives an explicit error suppression criterion that makes it statistically robust even in low signal to noise ratio snr cases simulation experiments are conducted to validate the effectiveness of the proposed method the performance is compared with several existing doa estimation methods and the cramer rao lower bound crlb

performance analysis of root music the authors analyze the performance of root music a variation of the music algorithm for estimating the direction of arrival doa of plane waves in white noise in the case of a linear equispaced sensor array the performance of the method is analyzed by examining the perturbation in the roots of the polynomial formed in the intermediate step of root music in particular asymptotic results for the mean squared error in the estimates of the direction of arrival are derived simplified expressions are presented for the one and two source case and compared to those obtained for least squares esprit computer simulations are also presented and they are in close agreement with the theory an important outcome of this analysis is the fact that the error in the signal zeros has a largely radial component this provides an explanation as to why the root music is superior to the spectral music algorithm

multiple cluster beamspace and resolution enhanced esprit this paper addresses approaches to enhancement of the resolution of one or more clusters of closely spaced emitters the tls esprit algorithm is considered as applied in beamspace and in element space in conjunction with resolution enhancement beamspace bs esprit employs a matrix beamformer as a preprocessor to map the sensor space into a lower dimensional beamspace resolution enhanced re esprit employs a matrix beamformer as a left weighting of the signal subspace eigenvector matrix for enhancing the resolution of esprit this paper specifically discusses several types of these beamformer matrices which differ in the way that they treat source clusters other than of interest our objective is to clearly define approaches and identify their relative merits through discussion and illustrative simulation so as to provide an understanding of how to proceed in designing an esprit algorithm

a central limit theorem for products of random matrices and goe statistics for the anderson model on long boxes we consider products of random matrices that are small independent identically distributed perturbations of a fixed matrix mathcal t 0 focusing on the eigenvalues of mathcal t 0 of a particular size we obtain a limit to a sde in a critical scaling previous results required mathcal t 0 to be a conjugated unitary matrix so it could not have eigenvalues of different modulus from the result we can also obtain a limit sde for the markov process given by the action of the random products on the flag manifold applying the result to random schrodinger operators we can improve some results by valko and virag showing goe statistics for the rescaled eigenvalue process of a sequence of anderson models on long boxes in particular we solve a problem posed in their work

temporal and spatial sampling influence on the estimates of superimposed narrowband signals when less can mean more this paper addresses the influence that the sampling locations have on the estimated frequencies of superimposed sinusoids this problem has application in harmonic time series analysis or direction finding phased array systems generalized mathematical bounds are developed in terms that are independent of the array locations and have an intuitively appealing physical interpretation they establish the influence of the sampling locations on the variance of the frequency estimate and the limit at which two sources can be resolved using signal subspace estimators for the resolution criteria an expression dominated by the fourth central moment of the sensor locations expresses the resolving ability of the sensing array irrespective of the array aperture or number of sensors increasing the fourth central moment increases an array s resolution ability the commonly accepted notion that resolution necessarily depends on the array aperture is misleading and indeed that fewer snapshots from a reduced aperture array can outperform a larger array of more elements for the estimator variance criteria it is found that the product of the number of sensors and the second central moment array variance characterizes the estimator variance lower bound the metrics developed demonstrate that the sampling topology is itself an important factor in determining the performance of the sampling system and not the covariance lags sampled or the aperture spanned simulations are used to describe the results

anderson localization for one and quasi one dimensional systems we prove almost sure exponential localization of all the eigenfunctions and nondegeneracy of the spectrum for random discrete schrodinger operators on one and quasi one dimensional lattices this paper provides a much simpler proof of these results than previous approaches and extends to a much wider class of systems we remark in particular that the singular continuous spectrum observed in some quasiperiodic systems disappears under arbitrarily small local perturbations of the potential our results allow us to prove that e g for strong disorder the smallest positive lyapunov exponent of some products of random matrices does not vanish as the size of the matrices increases to infinity

sensor array processing based on subspace fitting algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem the methods considered are the deterministic maximum likelihood method ml esprit and a recently proposed multidimensional signal subspace method these methods are formulated in a subspace fitting based framework which provides insight into their algebraic and asymptotic relations it is shown that by introducing a specific weighting matrix the multidimensional signal subspace method can achieve the same asymptotic properties as the ml method the asymptotic distribution of the estimation error is derived for a general subspace weighting and the weighting that provides minimum variance estimates is identified the resulting optimal technique is termed the weighted subspace fitting wsf method numerical examples indicate that the asymptotic variance of the wsf estimates coincides with the cramer rao bound the performance improvement compared to the other techniques is found to be most prominent for highly correlated signals

a version of gordon s theorem for multi dimensional schrodinger operators we consider discrete schrodinger operators in h v in l 2 z d with d 1 and study the eigenvalue problem for these operators it is shown that the point spectrum is empty if the potential v is sufficiently well approximated by periodic potentials this criterion is applied to quasiperiodic v and to so called fibonacci type superlattices

weak disorder expansions for the anderson model on a one dimensional strip at the center of the band we study the asymptotic behavior of the averaged diagonal matrix elements of the greens kernel for the anderson model on a one dimensional strip and for a set of special energies close to the center of the band

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

a subspace rotation based technique for estimating 2 d arrival angles using nonlinear array configurations this paper presents a subspace rotation based method to estimate 2 d direction of arrival doa angles of narrowband signals radiated by far field sources using planar and volume arrays the new approach automatically pairs 2 d doa angles by computing them directly from the normalized eigenvectors of a newly derived signal space matrix ssm this eliminates the constraint on subarray spacing and the need for a search procedure other advantages include adjustability in the accuracy of the doa angles and maximum detectability of the master array

performance study of conditional and unconditional direction of arrival estimation a numerical and analytical study of conditional and unconditional direction of arrival doa estimation is presented explicit expressions for the unconditional cramer rao bounds on the doa estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given it is shown that many doa estimation methods have the same asymptotic statistical properties under conditional and unconditional models the situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed

the forward backward averaging technique applied to tls esprit processing certain array geometries greatly simplify and enhance high resolution array processing two techniques are used the esprit algorithm which employs two shifted but otherwise identical subarrays and forward backward averaging which can be applied to axis symmetrical arrays the former has been shown to provide an efficient solution to bearing estimation while the latter incorporates the a priori knowledge about the symmetry effectively increasing the number of data vectors available and decorrelating coherent or highly correlated signals a combination of the two techniques implies a special array geometry that includes uniformly spaced linear arrays the resulting algorithm yields parameter estimates that are constrained on the unit circle satisfying the postulated data model provided merely that the arguments of these estimates are distinct however if the arguments of some parameter estimates coincide in a given scenario the esprit algorithm does not yield different results for distinct signals and these estimates can be rejected perhaps the most significant advantage of combining forward backward averaging with esprit parameter estimation is the substantial reduction in computational complexity that can be achieved based on the centro hermitian property of the data and noise covariance matrices the computational complexity of the esprit solution is reduced almost by a factor of four and the algorithm can be formulated entirely over the field of real numbers

asymptotic performance analysis of esprit higher order esprit and virtual esprit algorithms in this paper we present an asymptotic performance analysis of three subspace based methods for direction of arrival doa estimation the esprit algorithm using second order statistics the higher order esprit algorithm using fourth order cumulants and the virtual esprit vespa algorithm using fourth order cumulants we examine the least squares version of these algorithms derive the expressions for the asymptotic variance of the estimated doas and use specific examples to compare the relative performance of the algorithms finally we present monte carlo simulations to validate the theoretical analysis

joint source estimation and localization the estimation of directions of arrival is formulated as the decomposition of a 3 way array into a sum of rank one terms which is possible when the receive array enjoys some geometrical structure the main advantage is that this decomposition is essentially unique under mild assumptions if computed exactly the drawback is that a low rank approximation does not always exist therefore a coherence constraint is introduced that ensures the existence of the latter best approximate which allows to localize and estimate closely located or highly correlated sources then cramer rao bounds are derived for localization parameters and source signals assuming the others are nuisance parameters some inaccuracies found in the literature are pointed out performances are eventually compared with unconstrained reference algorithms such as esprit in the presence of additive complex gaussian noise with possibly noncircular distribution

bootstrap multiscale analysis and localization in random media we introduce an enhanced multiscale analysis that yields subexponentially decaying probabilities for bad events for quantum and classical waves in random media we obtain exponential decay for the resolvent of the corresponding random operators in boxes of side l with probability higher than 1 e l for any 0 1 the starting hypothesis for the enhanced multiscale analysis only requires the verification of polynomial decay of the finite volume resolvent at some sufficiently large scale with probability bigger than 1 d is the dimension note that from the same starting hypothesis we get conclusions that are valid for any 0 1 this is achieved by the repeated use of a bootstrap argument as an application we use a generalized eigenfunction expansion to obtain strong dynamical localization of any order in the hilbert schmidt norm and better estimates on the behavior of the eigenfunctions

esprit like estimation of real valued sinusoidal frequencies subspace based estimation of multiple real valued sine wave frequencies is considered in this paper a novel data covariance model is proposed in the proposed model the dimension of the signal subspace equals the number of frequencies present in the data which is half of the signal subspace dimension for the conventional model consequently an esprit like algorithm using the proposed data model is presented the proposed algorithm is then extended for the case of complex valued sine waves performance analysis of the proposed algorithms are also carried out the algorithms are tested in numerical simulations when compared with esprit the newly proposed algorithm results in a significant reduction in computational burden without any compromise in the accuracy

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