the equivalence of the total least squares and minimum norm methods signal processing it is shown that the minimum norm solution is equivalent to the total least squares solution it is noted that two versions of the total least squares solution exist one based on the signal subspace and another based on the noise subspace

on the index for array optimization and the discrete prolate spheroidal functions a class of array optimization problems is considered in which we seek to optimize the array response in a specified angular sector the optimization of array directivity is shown to be a special limiting case of these problems as the width of the specified angular sector approaches zero the optimum array patterns are also shown to be related to the well known prolate spheroidal functions

fast algorithm for minimum norm direction of arrival estimation the original minimum norm direction of arrival estimator proposed by kumaresan and tufts employs the noise subspace projection matrix calculated by the eigendecomposition of spatial covariance matrix the present authors propose a novel noneigenvector fast algorithm which calculates the required minimum norm function using the special power basis instead of eigenvector basis the proposed algorithm provides a substantial saving as compared with computational loads of the eigendecomposition based minimum norm algorithm in cases when the number of multiple sources is much lower than the number of array sensors some computer simulation results verifying the high performance and accuracy of the proposed algorithm are presented

spatial spectral filtering with linearly constrained minimum variance beamformers in this paper orthogonal low dimension models for broad band sources as observed by an array delay line structure are developed the models are termed broad band source representation spaces and are subspaces of the observation space they are generated from eigenstructures of source sample covariance matrices and represent sources efficiently in the 2nd order statistical sense for a single broad band source propagating in a pure delay environment and observed with an isotropic array an accurate indication of the model dimension is derived which is independent on the array configuration being a function of the observed source time bandwidth product only using these representations procedures are described for controlling the spatial and spectral response of linearly constrained minimum variance broad band array beamformers the procedures employ linear constraints to control complex gain characteristics over selected bands of frequency for multiple points of 3 d regions of source locations and do not require the use of steering delays the constraints are derived from source representation spaces and are termed eigenvector constraints simulations are presented which illustrate the effectiveness of the new linear constraints

statistical analysis of beam space estimation for direction of arrivals the authors analyze the beam space performance of the doa estimation for several subspace processing algorithms in a unified fashion based on a finite amount of measurements the mean squared errors mse of the beam space doa estimation for these algorithms are expressed in a single formula using physical parameters like array manifold beamformer matrix the important properties of beam space performance are revealed for instance increasing beam space dimension does not always reduce mse for all algorithms also the criteria for designing minimum mean squared error beamformers are discussed

wide band nulling performance versus number of pattern constraints for an array antenna the problem of wide band pattern hulling for an array antenna is addressed in particular the relation between the number of constraints imposed and the sidelobe suppression achieved the two constraint methods considered are multiple nulling over a narrow angular sector and hulling of the pattern and its derivatives at a single point to first order the sidelobe cancellation is shown to be independent of the actual pattern type and is determined by only two parameters the number of null constraints m and the number of sidelobes v to be cancelled the latter parameter directly translates into a desired hulling bandwidth delta f a numerical solution to the problem is offered in the form of curves from which the number of nulls required to suppress a jammer over a given bandwidth can be conveniently estimated this number is indicative of how many degrees of freedom a conventional adaptive antenna system must allocate to attain a specific hulling performance

spatial spectrum estimation in a location sector multiple narrowband source localization using arbitrarily configured arrays and spatial spectrum estimation is considered a new eigenspace based approach which uses projections onto a particular vector or vector set in the estimated noise only subspace is described several closest vector estimators are developed by using different measures of closeness first closest is a novel full dimensional element space approach to spatial spectrum estimation which has important performance advantages relative to pertinent established spatial spectrum estimators it incorporates a priori knowledge of the array manifold over a location sector of interest to provide snr spectral resolution thresholds which are lower than those of min norm for some arrays substantially lower second relationships between the closest approach and several established approaches to spatial spectrum estimation are established for a linear equispaced array min norm is shown to be a special case of the closest approach one which is based on projection onto a noise only subspace vector which is close to the array manifold over the entire field of view

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

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

performance analysis of music employing conjugate symmetric beamformers if one incorporates a beamformer composed of conjugate centro symmetric weight vectors as a preprocessor to an eigenstructure direction finding algorithm a real valued decomposition can be employed to estimate the noise and signal subspaces from the sample covariance matrix the effect of employing the real processing methodology on the angle estimation performance of beamspace music is explored specifically the distribution of the real valued signal subspace eigenvectors is derived and used in an asymptotic analysis of the bias and variance of the music estimator the theoretical analysis shows that processing the real part of the beamspace sample covariance matrix offers significant performance gains in addition to the obvious computational benefit relative to the conventional complex valued procedure particularly in the case of correlated sources monte carlo simulations are included to verify the theoretical expressions a trade off study of the estimation accuracy versus the desire to provide adequate rejection of unwanted signals in a sector based interrogation scheme for various beamforming architectures is also presented

schrodinger poisson equations without ambrosetti rabinowitz condition abstract we prove the existence of ground state solutions for a stationary schrodinger poisson equation in r 3 the proof is based on the mountain pass theorem and it does not require the ambrosetti rabinowitz condition

a simple algorithm to achieve desired patterns for arbitrary arrays a simple iterative algorithm which can be used to find array weights that produce array patterns with a given look direction and an arbitrary sidelobe specification is presented the method can be applied to nonuniform array geometries in which the individual elements have arbitrary and differing radiation patterns the method is iterative and uses sequential updating to ensure that peak sidelobe levels in the array meet the specification computation of each successive pattern is based on the solution of a linearly constrained least squares problem the constraints ensure that the magnitude of the sidelobes at the locations of the previous peaks takes on the prespecified values phase values for the sidelobes do not change during this process and problems associated with choosing a specific phase value are therefore avoided experimental evidence suggests that the procedure terminates in remarkably few iterations even for arrays with significant numbers of elements

multiple window based minimum variance spectrum estimation for multidimensional random fields spectrum analysis is viewed as the problem of estimating the power of a process contained within narrow bands this view leads naturally to consideration of filter based methods for estimating spectra multiple window based estimators where the power in a band is estimated as the average of the powers estimated at the outputs of multiple filters are considered the filters are designed using a linearly constrained minimum variance criterion commonly employed in adaptive beamforming this results in filters that automatically adjust their sidelobes to minimize leakage of energy from outside the band of interest expressions for the bias and variance of the power estimates are derived assuming the sample covariance matrix estimate is used to estimate the data covariance matrix and that the data are independent and identically gaussian distributed these expressions lead to the definition of a performance factor that indicates the degree of variance reduction obtained via multiple window processing a technique for obtaining increased suppression of energy leaking through the filter sidelobes at the expense of the response fidelity to energy in the band is presented simulations are presented to illustrate the effectiveness of the technique

a new set of linear constraints for broad band time domain element space processors a new set of linear constraints for designing broad band time domain element space antenna array processors is presented the set of linear constraints is used to ensure that a desired look direction response of the processor over a frequency band of interest can be closely approximated the design technique is posed in such a way that three types of presteering can be handled no presteering coarse presteering and exact presteering the elimination of presteering time delays or the possibility to use coarse presteering is an attractive feature in a digital implementation of antenna array processors the relationship that the new processor has to other broad band processors is also established furthermore the approach enables various types of errors and mismatches between signal model and actual scenario to be incorporated in the problem formulation

a covariance fitting approach to parametric localization of multiple incoherently distributed sources in this paper a new algorithm for parametric localization of multiple incoherently distributed sources is presented this algorithm is based on an approximation of the array covariance matrix using central and noncentral moments of the source angular power densities based on this approximation a new computationally simple covariance fitting based technique is proposed to estimate these moments then the source parameters are obtained from the moment estimates compared with earlier algorithms our technique has lower computational cost and obtains the parameter estimates in a closed form in addition it can be applied to scenarios with multiple sources that may have different angular power densities while other known methods are not applicable to such scenarios

design of two music like estimators based on bias minimization two classes of music like estimators are considered one class called weighted norm music possesses an optimizing functional or null spectrum which is the product of the music null spectrum and an angle dependent weight the second class which is denoted the d sub r estimator has an optimizing functional that is dependent on a parameter r and is a generalized distance between two particular vectors in the signal subspace it is shown that the asymptotic mean square errors of these estimators are the same as music by determining an appropriate weight based on a derived large sample expression for the estimator bias a weighted norm music estimator is found that gives zero bias of order n sup 1 where n is the sample size using an approximate relation between the two types of estimators under consideration a data dependent parameter r spl theta is derived for the d sub r estimator which results in small bias over a wide range of signal to noise ratios snrs for two closely spaced sources

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

bias analysis of the music location estimator the authors present a rigorous bias analysis of the music location estimator and they derive an accurate and concise bias expression the analysis is based on the second order taylor series expansion of the derivative of the null spectrum properties of the null spectrum and statistics of the estimated signal eigenvectors it is proven that in the derivation the remainder term in the second order taylor series can be dropped but the second order terms cannot be simulations verify that the bias expression is valid over a wide range of signal to noise ratios snrs extending down into the resolution threshold region of music although asymptotic this expression can be accurately applied to a limited number of snapshot cases the utility of the expression is shown by using it in a study of music location estimator characteristics estimate bias and standard deviation are compared for variations in snr numbers of sensors and snapshots and source correlation music resolvability and estimator performance bounds are addressed accounting for bias

efficient direction finding methods employing forward backward averaging in this paper we develop a general approach for reducing the computational complexity of any direction finding method implemented with forward backward fb averaging we develop simplified fb data matrices in a manner paralleling previous work related to centrohermitian correlation matrices based on these simplified data matrices efficient construction and updating of the fb correlation matrix is developed in addition efficient fb fft fb beamspace fb evd updating fb svd and fb svd updating methods are derived in most cases fb based direction finding methods can be simplified so that the computational complexity is reduced below that of an analogous forward only implementation thus effectively twice the amount of data is processed with less total computation

on the zeros of the linear prediction error filter for deterministic signals the zeros of a linear prediction error filter polynomial for a class of deterministic signals that are a sum of samples of m exponentially damped undamped sinusoids is studied it is assumed that n samples are available for processing and that they are uncorrupted by noise it is shown that the exponent parameters of the m signals can be determined from m zeros called signal zeros of an lth degree prediction error filter polynomial l m if l lies in between m and n m n m 2 in a special case the rest of the l m zeros of the filter polynomial switch are called extraneous zeros are shown to be approximately uniformly distributed with in the unit circle regardless of the type of exponentials in the signal if the prediction filter coefficients are chosen to have minimum euclidean length the results obtained provide insight into the estimation problem with noisy data

performance analysis for finite sample mvdr beamformer with forward backward processing the employment of forward backward fb processing to both batch and adaptive beamformers provides a superior performance than the forward only fo algorithm based on the finite sample minimum variance distortionless response mvdr beamformer a set of closed form expressions for the variance of the weight vector the output signal to interference plus noise ratio sinr and the mean square error mse is derived for both fb and fo algorithms as shown in our analysis all errors of the fb algorithm are only approximately half of the fo case

an analysis of weighted eigenspace methods in the presence of sensor errors among all direction finding methods eigenspace based spectral methods are of interest because they are known to yield asymptotically unbiased and efficient estimates these algorithms require knowledge of the array geometry and its elements characteristics in real systems only approximate knowledge of the required array characterization is available there is valid concern that deviation of nominal sensor gain and phase values can result in degradation of doa estimates we analyze the effects of sensor gain and phase perturbation on weighted eigenspace methods wems we quantify the sensitivity of wems by first and second order statistical analyses simulation results are included to validate our analytical results

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

optimal dimension reduction for array processing generalized the correspondence extends previously reported work on the possibility of achieving optimality of beamspace bs array processing parameter estimators where use is made of dimensionally reduced data vectors the optimality is with respect to the best possible element space esp parameter estimation accuracy i e the cramer rao bound and is valid for multiple parameters per emitter

doa estimation in the asynchronous ds cdma system it was previously shown that the number of array elements must exceed the number of sources for subspace based directional of arrival doa estimation this is clearly not practical for a direct sequence code division multiple access ds cdma wireless system since the number of mobile users is very large to overcome the restriction a doa s estimator employing the code matched filters and parallel music algorithms is proposed in the asynchronous ds cdma system we show that the multiple access interference mai throughout the code matched filter tends toward the real gaussian distribution with zero mean in addition based on the singular value decomposition svd of a finite amount of data we achieve a theoretical expression for the mean squared error mse of the doa s estimation with the advantage of code matched filter inherent in the ds cdma system we prove that the proposed technique can obtain an unbiased doa estimation with low mse even in the environment where the number of mobile users far exceeds the number of array elements simulation results verify the theoretical derivation

multiple solutions for a nonlinear schrodinger poisson system with sign changing potential this paper deals with the existence and multiplicity of nontrivial solutions for a nonlinear schrodinger poisson system under some suitable conditions some criteria on the existence of nontrivial solutions including a ground state solution two solutions and a sequence of nontrivial solutions u k with u k 0 as k is established by applying the morse theory and variational methods some known results in the literatures are extended and improved

efficient numerically stabilized rank one eigenstructure updating signal processing rank one eigenvalue decomposition evd updating is well suited to the problem of tracking time varying subspaces previously published rank one evd updating algorithms suffer from a linear buildup of roundoff error which makes them impractical for a large number of recursive updates in the present work the authors develop a numerical stabilization technique which eliminates the error buildup problem in a computationally efficient manner and makes the rank one evd update a practical numerical tool for online computation a simplified eigenvalue iteration is also given it reduces the complexity of the algorithm somewhat as well as the computation time simulations are presented to illustrate numerical performance

bias and variance of direction of arrival estimates from music min norm and fine we derive variance and bias expressions of direction of arrival doa estimates for min norm and fine these expressions for arbitrarily configured arrays are valid and accurate over wide ranges of snr and number of snapshots using these expressions we illustrate that both min norm and fine have smaller estimate bias and further fine has comparable estimate variance compared to music

on the eigenstructure of the signal only tempo spatial covariance matrix of broad band sources using a circular array the eigenstructure of the signal only part of the data covariance matrix for broadband sources is considered it is well known that unlike the narrowband case all eigenstructure parameters the matrix rank eigenvalues and eigenvectors depend on source spectral and spatial parameters as well as on the relationship between sources it is proved that when a two dimensional equally spaced circular array with flat spectrum broadband sources is used the eigenstructure of the signal only tempo spatial covariance matrix tscm has properties similar to those for the narrowband case most importantly the effective rank of the tscm depends only on the number of sources consequently the authors suggest an alternative approach for resolving frequency location ambiguity in the broadband case that may lead to an effective eigenstructure based parameter estimation algorithm of the music type

a minimization method and applications to the study of solitons abstract roughly speaking a solitary wave is a solution of a field equation whose energy travels as a localized packet and which preserves this localization in time a soliton is a solitary wave which exhibits some strong form of stability so that it has a particle like behavior in this paper we prove a general abstract theorem theorem 26 which allows to prove the existence of a class of solitons such solitons are suitable minimizers of a constrained functional and they are called hylomorphic solitons then we apply the abstract theory to problems related to the nonlinear schrodinger equation nse and to the nonlinear klein gordon equation nkg

signal processing applications of oblique projection operators oblique projection operators are used to project measurements onto a low rank subspace along a direction that is oblique to the subspace they may be used to enhance signals while nulling interferences in the paper the authors give several basic results for oblique projections including formulas for constructing oblique projections with desired range and null space they analyze the algebra and geometry of oblique projections in order to understand their properties they then show how oblique projections can be used to separate signals from structured noise such as impulse noise damped or undamped interfering sinusoids such as power line interference and narrow band noise in some of the problems addressed the oblique projection provides an alternative way to implement an already known solution expressing these solutions as oblique projections brings geometrical insight to the study of the solution the geometry of oblique projections enables one to compute performance in terms of angles between signal and noise subspaces as a special case of removing impulse noise the authors can use oblique projections to interpolate missing data samples in array processing oblique projections can be used to simultaneously steer beams and nulls in communications oblique projections can be used to remove intersymbol interference

resolution enhanced esprit the authors present a variant of esprit known as the resolution enhanced re esprit that lowers resolution thresholds by incorporating left weighting of the signal eigenvectors to provide sector focusing they discuss the advantages of this new left weighted esprit a compact expression for the asymptotic covariance matrix of the estimates is presented analytical and simulation results are included to show the resolution improvement of esprit

three dimensional vortices in abelian gauge theories abstract in this paper we consider an abelian gauge theory in r 4 equipped with the minkowski metric this theory leads to a system of equations the klein gordon maxwell equations which provide models for the interaction between the electromagnetic field and matter a three dimensional vortex is a finite energy solution of these equations in which the magnetic field looks like the field created by a finite solenoid under suitable assumptions we prove the existence of vortex solutions

ideal membership in polynomial rings over the integers we will reproduce a proof using hermann s classical method in section 3 below note that the computable character of this bound reduces the question of whether fo g fi fn for given fj g f x to solving an enormous system of linear equations over f hence in this way one obtains a naive algorithm for solving the ideal membership problem for f x provided f is given in some explicitly computable manner later buchberger in his ph d thesis 1965 introduced the important concept of a gr bner basis and gave an algorithm for deciding ideal membership for f x which is widely used today see e g 6 the doubly exponential nature of above is essentially unavoidable as a family of examples due to mayr and meyer 27 shows in fact they prove that ideal membership for q x is exponential space hard the amount of space needed by any algorithm to decide ideal membership for q x or z x grows exponentially in the size of the input if we restrict to o n ofa special form often dramatic

a toeplitz induced mapping technique in sensor array processing the paper has a two fold purpose it deals with the signal processing of nonuniform linear array and it indicates a novel approach to achieving significant improvements in signal processing performance in sublattice array scenarios all the efforts are based on a new concept called toeplitz induced mapping tim a real valued matrix associated with the toeplitz induced mapping is constructed in a specific manner from a single vector that is able to be viewed as the coefficient vector of a polynomial if the polynomial has any of roots on the unit circle the real valued matrix is singular and the right singular vectors corresponding to the zero singular values are then associated with the roots on the unit circle and consequently the roots on the unit circle can be computed from these singular vectors by virtue of the observations we are able to implement array aperture interpolation signal recovery and signal enhancement in particular in the presence of highly correlated sources application of a tim based signal enhancement algorithm to doa estimation results in a considerable performance improvement computer simulation results are presented to show the effectiveness of the tim technique

an adaptive generalized sidelobe canceller with derivative constraints an adaptive broad band beamforming structure is presented which employs a gradient based weight adjustment algorithm to minimize output variance subject to a set of j linear constraints on broadband directional derivatives in the desired look direction a generalized sidelobe cancelling structure is employed in which a nonadaptive conventional beamformer operates in parallel with an adaptive beamformer the conventional portion has a broad band beampattern which adheres to the specified constraints while the adaptive path is a cascade of a fixed signal blocking matrix and a set of tapped delay line filters blocking is employed to ensure that all incident waveforms which meet the specified constraints do not reach the tapped delay lines as a result an unconstrained least mean square lms power minimization algorithm is employed to adapt the delay line weights it is shown that with the addition of the directional derivative constraints the beamformer quiescent bcampattern becomes a function of the location of the phase center used to specify the constraints a design criterion for choosing this location is suggested and simulation experiments which illustrate the performance of this new adaptive beamformer are presented

closed form 2 d angle estimation with rectangular arrays in element space or beamspace via unitary esprit the uca esprit is a closed form algorithm developed for use in conjunction with a uniform circular array uca that provides automatically paired source azimuth and elevation angle estimates the 2 d unitary esprit is presented as an algorithm providing the same capabilities for a uniform rectangular array ura in the final stage of the algorithm the real and imaginary parts of the ith eigenvalue of a matrix are one to one related to the respective direction cosines of the ith source relative to the two major array axes the 2 d unitary esprit offers a number of advantages over other proposed esprit based closed form 2 d angle estimation techniques first except for the final eigenvalue decomposition of a dimension equal to the number of sources it is efficiently formulated in terms of real valued computation throughout second it is amenable to efficient beamspace implementations that are presented third it is applicable to array configurations that do not exhibit identical subarrays e g two orthogonal linear arrays finally the 2 d unitary esprit easily handles sources having one member of the spatial frequency coordinate pair in common simulation results are presented verifying the efficacy of the method

source localization using recursively applied and projected rap music a new method for source localization is described that is based on a modification of the well known music algorithm in classical music the array manifold vector is projected onto an estimate of the signal subspace errors in the estimate of the signal subspace can make localization of multiple sources difficult recursively applied and projected rap music uses each successively located source to form an intermediate array gain matrix and projects both the array manifold and the signal subspace estimate into its orthogonal complement the music projection to find the next source is then performed in this reduced subspace special assumptions about the array manifold structure such as vandermonde or shift invariance are not required using the metric of principal angles we describe a general form of the rap music algorithm for the case of diversely polarized sources through a uniform linear array simulation with two highly correlated sources we demonstrate the improved monte carlo error performance of rap music relative to music and two other sequential subspace methods s and ies music we then demonstrate the more general utility of this algorithm for multidimensional array manifolds in a magnetoencephalography meg source localization simulation

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

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

schrodinger poisson system with singular potential abstract consider the following schrodinger poisson system sp u v x u x u u p 1 u x y z r 2 r u 2 lim x x 0 where v 1 y with 0 y x 1 x 2 r 2 and y x 1 2 x 2 2 when 0 8 and max 2 2 2 p 5 the existence and a priori estimate of positive solutions of problem sp are established in suitable weighted sobolev space moreover the asymptotic behavior of the solutions as 0 is also discussed

adaptive beamforming with real valued coefficients based on uniform linear arrays a class of adaptive beamforming algorithms with real valued coefficients is proposed based on the uniform linear array structure by introducing a preprocessing transformation matrix it is derived from the beamformer with a minimum mean square error mse or a maximum output signal to interference plus noise ratio sinr depending on the specific design criteria the key parameter of the transformation matrix takes different values for different beamforming scenarios and three representative examples are studied the linearly constrained minimum variance beamformer and the generalized sidelobe canceller the reference signal based beamformer and the class of blind beamformers based on the constant modulus algorithm its advantage is twofold 1 with real valued coefficients the computational complexity of the overall system is reduced significantly 2 a faster convergence speed is achieved and given the same stepsize the system arrives at a lower mse or a higher output sinr

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

eigenstructure based partially adaptive array design a procedure is presented for designing partially adaptive arrays having nearly fully adaptive performance under steady state conditions theory predicts that the required adaptive dimension is less than or equal to the rank of the spatially temporally correlated portion of the interference correlation matrix for arbitrary linearly constrained minimum variance beamformers knowledge of the eigenstructure of the interference correlation matrix is required to implement a beamformer with this adaptive dimension to avoid adaptive estimation of the eigenstructure the eigenstructure of an averaged correlation matrix which spans the interference scenarios of interest is utilized and the adaptive dimension is given by the rank of the averaged correlation matrix construction of a transformation for reducing adaptive dimension is addressed simulations illustrating the utility of the eigenstructure approach are provided

low complexity doa estimation based on compressed music and its performance analysis this paper presents a new computationally efficient method for direction of arrival doa estimation with arbitrary arrays the total angular field of view is first divided into several small sectors and the original noise subspace exploited by the multiple signal classification music algorithm is mapped from one sector to the other sectors by a hadarmard product transformation this transformation gives a new noise like subspace cluster nlsc whose intersection is found to be simultaneously orthogonal to the steering vectors associated with the true doas and several virtual doas based on such a multiple orthogonality a novel compressed music c music spatial spectrum at hand is derived unlike music with tremendous spectral search c music involves a limited search over only one sector and hence it is computationally very attractive to obtain the intersection of nlsc for more than two sectors a low complexity method is also proposed in the present work which shows advantages over the existing alternative projection method apm and singular value decomposition svd techniques furthermore the mean square errors mses of the proposed estimator is derived simulation results illustrate that c music trades off mses by complexity and resolution as compared to the standard music efficiently

adaptive convergence of linearly constrained beamformers based on the sample covariance matrix a statistical analysis of the adaptive convergence behavior of linearly constrained beamformers is given assuming the sample covariance estimator is used to estimate the covariance matrix the sensor data are assumed to be gaussian distributed and independent from data vector to data vector the output power and mean squared error in the absence of the desired signal are shown to be multiples of chi squared random variables the presence of the desired signal results in an excess mean squared error that is beta distributed and depends only on the signal power number of data vectors and number of adaptive degrees of freedom the expected value of the excess mean squared error resulting from the signal presence is directly proportional to the signal power and number of adaptive degrees of freedom but is inversely proportional to the number of data vectors

a generalized null spectrum for direction of arrival estimation a generalization of null spectrum for the estimation of directions of arrival of signal sources is considered the upper and lower bounds of a class of the generalized null spectrum the maximum and minimum null spectra are derived the authors observe that the maximum null spectrum has higher resolution capability than other null spectra including the multiple signal classification and min norm null spectra in addition it is seen that the estimates of the direction of arrival obtained by using the maximum and multiple signal classification null spectra have the same asymptotic distribution through computer simulation the probabilities of resolution of various null spectra are obtained from which they confirmed the resolution capability of the maximum null spectrum