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

indirect dominant mode rejection a solution to low sample support beamforming under conditions of low sample support a low rank solution of the minimum variance distortionless response mvdr equations can yield a higher output signal to interference plus noise ratio sinr than the full rank mvdr beamformer in this paper we investigate several low rank beam forming techniques and we also propose a new beamformer that we refer to as the indirect dominant mode rejection idmr we analyze the degradation in the output sinr caused by residual cross correlations embedded in the sampled covariance matrix due to low sample support the idmr beamformer is based on a parametric estimate of the covariance matrix in which any cross correlation is canceled out simulations reveal that the idmr beamformer yields a dramatic improvement in output sinr relative to the conjugate gradient cg principal component inverse pci and dominant mode rejection dmr beamformers in our investigation of the low rank cg beamformer we address the issue of whether the unity gain constraint in the look direction should be enforced a priori via the use of a blocking matrix or effected a posteriori through simple scaling of the beamforming vector remarkably it is proven that the two methods yield exactly the same low rank beamformer at each and every rank

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

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

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

langlands duality for representations of quantum groups we establish a correspondence or duality between the characters and the crystal bases of finite dimensional representations of quantum groups associated to langlands dual semi simple lie algebras this duality may also be stated purely in terms of semi simple lie algebras to explain this duality we introduce an interpolating quantum group depending on two parameters which interpolates between a quantum group and its langlands dual we construct examples of its representations depending on two parameters which interpolate between representations of two langlands dual quantum groups

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

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

orthogonal eigensubspace estimation using neural networks we present a neural network nn approach for simultaneously estimating all or some of the orthogonal eigenvectors of a symmetric nonindefinite matrix corresponding to its repeated minimum in magnitude eigenvalue this problem has its origin in the constrained minimization framework and has extensive applications in signal processing we recast this problem into the nn framework by constructing an appropriate energy function which the nn minimizes the nn is of feedback type with the neurons having sigmoidal activation function the proposed approach is analyzed to characterize the nature of the minimizers of the energy function the main result is that the matrix w is a minimizer of the energy function if and only if the columns of w are the orthogonal eigenvectors with a given norm corresponding to the smallest eigenvalue of the given matrix further all minimizers are global minimizers bounds on the integration time step that is required to numerically solve the system of differential equations which define the dynamics of the nn have also been derived results of computer simulations are presented to support our analysis

hofstadter s butterfly and langlands duality we address the hofstadter problem on a two dimensional square lattice system we propose a novel perspective on its mathematical structure of the corresponding tight binding hamiltonian from a viewpoint of the langlands duality a mathematical conjecture relevant to a wide range of the modern mathematics including number theory solvable systems representations and geometry it is known that the hamiltonian can be algebraically written by means of the quantum group uq sl2 we claim that hofstadter s fractal is deeply related with the langlands duality of the quantum group in addition from this perspective the existence of the corresponding elliptic curve expression interpreted from the tight binging hamiltonian implies a more fascinating connection with the langlands program and quantum geometry we address the hofstadter problem on a two dimensional square lattice system we propose a novel perspective on its mathematical structure of the corresponding tight binding hamiltonian from a viewpoint of the langlands duality a mathematical conjecture relevant to a wide range of the modern mathematics including number theory solvable systems representations and geometry it is known that the hamiltonian can be algebraically written by means of the quantum group uq sl2 we claim that hofstadter s fractal is deeply related with the langlands duality of the quantum group in addition from this perspective the existence of the corresponding elliptic curve expression interpreted from the tight binging hamiltonian implies a more fascinating connection with the langlands program and quantum geometry

gold music a variation on music to accurately determine peaks of the spectrum this paper presents a new way of accurately determining peaks of the music multiple emitter location and signal parameter estimation r o schmidt ieee trans antennas and propagation vol ap 34 no 3 pp 276 280 mar 1986 spectrum here considered from the point of view of estimating the directions of arrival doas of narrowband signals it can be used with any smart antenna geometry and for any purpose where music is applicable the music algorithm for doa estimation evaluates the music spectrum for various angles and chooses the maxima or peaks as the angles of arrival the values obtained depend on the interval at which the spectrum is evaluated the coarser the interval the less accurate are the results in case of music to improve accuracy and not depend on the interval root music direction finding for diversely polarized signals using polynomial rooting a j weiss and b friedlander ieee trans signal processing vol 41 no 5 pp 1893 1905 may 1993 which involves finding the roots of a polynomial is available however root music is applicable in its original form only to uniform linear arrays ula the gold music algorithm proposed in this paper is a two stage process the first stage evaluates the objective function at coarse intervals and determines peaks followed by an iterative approach based on gold section univariate gsu minimization algorithms for minimization without derivatives r brent englewood cliffs nj usa prentice hall 1983 to find accurate values of the peaks if the number of peaks found so far is equal to the number of estimated peaks the algorithm stops with this first stage the second stage is an iterative step for fine resolution using finer intervals around the peaks found so far for finding peaks that were missing in previous iterations this paper also presents a method based on a partitioning algorithm for estimating the number of emitters the performance of gold music is described including its advantages and comparison of time complexities for music root music and gold music the proposed algorithm gives good results even when the number of snapshots is small this gives it an additional computational advantage it does not compromise on the resolving power of music

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

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

an efficient algorithm for tracking the angles of arrival of moving targets a novel technique for tracking the angles of arrival of moving targets is presented the targets are modeled as signal sources that continuously emit narrowband signals which impinge on an array of sensors estimates of target angles are obtained by minimizing the norm of an error matrix function involving the covariance of the sensor outputs the algorithm yields estimates that are automatically correctly associated with previous estimates consequently the data association problem does not arise and this results in a much more efficient scheme in comparison to existing methods involving search over n factorial possible measurement target associations where n is the number of targets performance of the algorithm is illustrated by a simulation example

langlands duality for representations and quantum groups at a root of unity we give a representation theoretic interpretation of the langlands character duality of fh and show that the langlands branching multiplicities for symmetrizable kac moody lie algebras are equal to certain tensor product multiplicities for finite type quantum groups the connection with tensor products can be explained in terms of tilting modules

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

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

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

applications of cumulants to array processing iii blind beamforming for coherent signals for pt ii see ibid vol 43 no 7 p 1663 7 1995 we provide a cumulant based blind beamforming method for recovery of statistically independent narrowband source signals in the presence of coherent or perfectly correlated multipath propagation our method is based on the fact that for a blind beamformer the presence of coherent multipaths is equivalent to the case of independent sources with a different steering matrix our approach is applicable to any array configuration having unknown response signal sources must have nonzero fourth order cumulants there is no need to estimate the directions of arrival our method maximizes signal to interference plus noise ratio sinr a comparable result does not exist using just second order statistics

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

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

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

covers of algebraic varieties iii the discriminant of a cover of degree 4 and the trigonal construction in c e a general structure theorem for gorenstein covers of degrree d has been proved such a result has been used for characterizing covers of degree 3 4 and 5 see c e and cs respectively of algebraic varieties more precisely in section 4 resp 3 of c e it is proved that the total space x of each gorenstein cover e x y of degree 4 esp 3 is obta ned inside a suit bl p ojective bundle 7r 11 y of rank 2 resp 1 as the b se locus of a pencil relativ conics resp

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

detection of coherent signals using weighted subspace smoothing a new approach to detecting the number of coherent signals incident upon a uniformly spaced linear array is presented the approach combines a modified spatial smoothing scheme and a modified mdl criterion the modified spatial smoothing scheme referred to as weighted subspace smoothing is actually a generalization of the post smoothing approach proposed by krim and proakis in 1994 it is shown that the noise eigenvalues obtained with weighted subspace smoothing are more accurate than those obtained with the original spatial smoothing we thus attempt to improve the detection performance using these more accurate eigenvalues a novel modification of the minimum description length mdl criterion is proposed to accomplish this computer simulations are presented to study the performance improvement of this new approach

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

multiple target tracking using maximum likelihood principle proposes a method tracking algorithm tal based on the maximum likelihood ml principle for multiple target tracking in near field using outputs from a large uniform linear array of passive sensors the targets are assumed to be narrowband signals and modeled as sample functions of a gaussian stochastic process the phase delays of these signals are expressed as functions of both range and bearing angle track parameters of respective targets a new simplified likelihood function for ml estimation of these parameters is derived from a second order approximation on the inverse of the data covariance matrix maximization of this likelihood function does not involve inversion of the m spl times m data covariance matrix where m denotes number of sensors in the array instead inversion of only a d spl times d matrix is required where d denotes number of targets in practice d spl lt m and hence tal is computationally efficient tracking is achieved by estimating track parameters at regular time intervals wherein targets move to new positions in the neighborhood of their previous positions tal preserves ordering of track parameter estimates of the d targets over different time intervals performance results of tal are presented and it is also compared with methods by sword and by swindlehurst and kailath 1988 almost exact asymptotic expressions for the cramer rao bound crb on the variance of angle and range estimates are derived and their utility is discussed

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

robust covariance matrix estimation in heterogeneous low rank context this paper addresses the problem of robust covariance matrix cm estimation in the context of a disturbance composed of a low rank lr heterogeneous clutter plus an additive white gaussian noise the lr clutter is modeled by a spherically invariant random vector with assumed high clutter to noise ratio in such a context adaptive process should require less training samples than classical methods to reach equivalent performance as in a full rank clutter configuration the main issue is that classical robust estimators of the cm cannot be computed in the undersampled configuration to overcome this issue the current approach is based on regularization methods nevertheless most of these solutions are enforcing the estimate to be well conditioned while in our context it should be lr structured this paper therefore addresses this issue and derives an algorithm to compute the maximum likelihood estimator of the cm for the considered disturbance model several relaxations and robust generalizations of the result are discussed performance is finally illustrated on numerical simulations and on a space time adaptive processing for airborne radar application

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

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

crystal graphs for representations of the q analogue of classical lie algebras the explicit form of the crystal graphs for the finite dimensional representations of the q analogue of the universal enveloping algebras of type a b c and d is given in terms of semi standard tableaux and its analogues

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

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

estimation of the parameters of a random amplitude sinusoid by correlation fitting we consider the best asymptotic accuracy that can be achieved when estimating the parameters of a random amplitude sinusoid from its sample covariances an estimator based on matching in a weighted least squares sense the sample correlation sequence to the theoretical sequence is presented the asymptotic properties of the estimator are analyzed a lower bound on the estimation of the parameters from sample covariances is derived this bound is shown to be attainable by appropriately choosing the weighting matrix however the unweighted nonlinear least squares estimate performance is shown to come close to the lower bound the influence of the number of samples the number of correlation samples and the lowpass envelope characteristics are studied finally a comparison with yule walker yw methods is given

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

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

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

on the smallest singular value of multivariate vandermonde matrices with clustered nodes abstract we prove lower bounds for the smallest singular value of rectangular multivariate vandermonde matrices with nodes on the complex unit circle the nodes are off the grid groups of nodes cluster and the studied minimal singular value is bounded below by the product of inverted distances of a node to all other nodes in the specific cluster by using known and new upper bounds for the smallest singular value this completely settles the univariate case and pairs of nodes in the multivariate case both including reasonable sharp constants for larger clusters we show that the smallest singular value depends also on the geometric configuration within a cluster

on the family of ml spectral estimates for mixed spectrum identification a recently developed point spectrum identification procedure based on a family of ar and ml spectral estimates is exploited to arrive at a mixed spectrum identification procedure to this end a variety of properties of the ar and ml estimates as a function of model order are described these properties relate to amplitude convergence resolution and a characterization of the ar spectral artifact which is used to arrive at improved continuous spectral estimates a variety of examples are presented

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

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

tracking the direction of arrival of multiple moving targets by passive arrays algorithm we propose a maximum likelihood ml approach for tracking the direction of arrival doa of multiple moving targets by a passive array a locally linear model is assumed for the target motion and the multiple target states mtss are defined to describe the states of the target motion the locally linear model is shown to be strongly locally observable almost everywhere the approach is to estimate the initial mts by maximizing the likelihood function of the array data the tracking is implemented by prediction through the target motion dynamics using the initial mts estimate by incorporating the target motion dynamics the algorithm is able to eliminate the spread spectrum effects due to target motion a modified newton type algorithm is also presented which ensures fast convergence of the algorithm finally numerical simulations are included to show the effectiveness of the proposed algorithm

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

cumulant based approach to harmonic retrieval and related problems a frequently encountered problem in signal processing is that of estimating the frequencies and amplitudes of harmonics observed in additive colored gaussian noise in practice the observed signals are contaminated with spatially and temporally colored noise of unknown power spectral density a cumulant based approach to these problems is proposed the cumulants of complex processes are defined and it is shown that specific 1 d slices of the fourth order cumulant of the noisy signal for the direction of arrival doa and retrieval of harmonics in noise rhn problems are identical to the autocorrelation of a related noiseless signal hence correlation based high resolution methods may be used with fourth order cumulants as well the effectiveness of the proposed methods is demonstrated through standard simulation examples

mismatch of near field bearing range spatial geometry in source localization by a uniform linear array many near field source localization algorithms intentionally simplifies the exact spatial geometry among the emitter and the sensors in order to speed up the signal processing involved for example the fresnel approximation is a second order taylor series approximation such intentional approximation introduces a systemic error in the algorithm s modeling of the actual objective reality from which the measured data arise a mismatch thus exists between the algorithm s presumptions versus the data it processes this modeling mismatch will introduce a systematic bias in the bearing range estimates of the near field source localization algorithm this bias is non random and adds towards the random estimation errors due to the additive and or multiplicative noises the open literature currently offers no rigorous mathematical analysis on this issue this proposed project aims to fill this literature gap by deriving explicit formulas of the degrading effects in three dimensional source localization due to approximating the source sensor geometry by any order of the taylor s series expansion

improving noise robustness in subspace based joint sparse recovery in a multiple measurement vector problem mmv where multiple signals share a common sparse support and are sampled by a common sensing matrix we can expect joint sparsity to enable a further reduction in the number of required measurements while a diversity gain from joint sparsity had been demonstrated earlier in the case of a convex relaxation method using an l1 l2 mixed norm penalty only recently was it shown that similar diversity gain can be achieved by greedy algorithms if we combine greedy steps with a music like subspace criterion however the main limitation of these hybrid algorithms is that they often require a large number of snapshots or a high signal to noise ratio snr for an accurate subspace as well as partial support estimation one of the main contributions of this work is to show that the noise robustness of these algorithms can be significantly improved by allowing sequential subspace estimation and support filtering even when the number of snapshots is insufficient numerical simulations show that a novel sequential compressive music sequential cs music that combines the sequential subspace estimation and support filtering steps significantly outperforms the existing greedy algorithms and is quite comparable with computationally expensive state of art algorithms

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

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

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

direction finding for wide band signals using an interpolated array the authors derive a new direction finding algorithm for multiple wideband signals received by an arbitrary array and analyze its performance using an interpolation technique they generate a set of virtual arrays each for a different frequency band having the same array manifold the convergence matrices of these arrays are added to produce a composite covariance matrix direction of arrival doa estimates are obtained by eigendecomposition of this composite covariance matrix using the narrowband music algorithm or its variants closed form expressions for the asymptotic covariance matrix of the doa estimation errors are derived using a perturbation analysis evaluated for specific cases and compared with the cramer rao lower bound special attention is given to correlated and coherent signals the formulas for the error covariance are quite general and can be modified to provide results for other wideband doa estimation algorithms

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

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

wakimoto modules opers and the center at the critical level abstract wakimoto modules are representations of affine kac moody algebras in fock modules over infinite dimensional heisenberg algebras in this paper we present the construction of the wakimoto modules from the point of view of the vertex algebra theory we then use wakimoto modules to identify the center of the completed universal enveloping algebra of an affine kac moody algebra at the critical level with the algebra of functions on the space of opers for the langlands dual group on the punctured disc giving another proof of the theorem of b feigin and the author

performance analysis of direction finding with large arrays and finite data this paper considers analysis of methods for estimating the parameters of narrow band signals arriving at an array of sensors this problem has important applications in for instance radar direction finding and underwater source localization the so called deterministic and stochastic maximum likelihood ml methods are the main focus of this paper a performance analysis is carried out assuming a finite number of samples and that the array is composed of a sufficiently large number of sensors several thousands of antennas are not uncommon in e g radar applications strong consistency of the parameter estimates is proved and the asymptotic covariance matrix of the estimation error is derived unlike the previously studied large sample case the present analysis shows that the accuracy is the same for the two ml methods furthermore the asymptotic covariance matrix of the estimation error coincides with the deterministic cramer rao bound under a certain assumption the ml methods can be implemented by means of conventional beamforming for a large enough number of sensors we also include a simple simulation study which indicates that both ml methods provide efficient estimates for very moderate array sizes whereas the beamforming method requires a somewhat larger array aperture to overcome the inherent bias and resolution problem

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

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

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

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

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

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

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

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

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

combining sparsity and rotational invariance in eeg meg source reconstruction we introduce focal vector field reconstruction fvr a novel technique for the inverse imaging of vector fields the method was designed to simultaneously achieve two goals a invariance with respect to the orientation of the coordinate system and b a preference for sparsity of the solutions and their spatial derivatives this was achieved by defining the regulating penalty function which renders the solutions unique as a global l 1 norm of local l 2 norms we show that the method can be successfully used for solving the eeg inverse problem in the joint localization of 2 3 simulated dipoles fvr always reliably recovers the true sources the competing methods have limitations in distinguishing close sources because their estimates are either too smooth loreta minimum l 1 norm or too scattered minimum l 2 norm in both noiseless and noisy simulations fvr has the smallest localization error according to the earth mover s distance emd which is introduced here as a meaningful measure to compare arbitrary source distributions we also apply the method to the simultaneous localization of left and right somatosensory n20 generators from real eeg recordings compared to its peers fvr was the only method that delivered correct location of the source in the somatosensory area of each hemisphere in accordance with neurophysiological prior knowledge

a new optimization technique for adaptive antenna arrays an adaptive nulling algorithm for adjusting the array weights under the soft constraint of the weight norm being very much less than 1 or equal to 1 based on the measured correlations between the array and element outputs is described the algorithm can be regarded as an extension of the constrained least mean square algorithm it is derived from the same concept of signal and noise subspaces defined in the multiple signal classification music algorithm one of the unique features of the present algorithm is that the number of the iterations required to adapt the array weights to form nulls is exactly equal to the number of interferers

tracking the direction of arrival of multiple moving targets the authors focus on the problem of tracking the direction of arrival doa of multiple moving targets the targets are assumed to be moving with constant accelerations subject to minor random perturbations and emitting narrow band signals that impinge on an array of passive sensors estimates of the doa vector of the targets are obtained from the sensor data based on the maximum likelihood ml principle in such a way that the association between the estimates made at different time points is maintained at each stage the current ml estimates of doa are treated as measurements and refined via a kalman filter tracking is accomplished without the need to perform unduly heavy computations an efficient strategy for dealing with closely spaced targets is also presented finally the performance of the tracking algorithm is illustrated via computer simulations

source localization in a waveguide using polynomial rooting source localization in acoustic waveguides involves a multidimensional search procedure we propose a new algorithm in which the search in the depth direction is replaced by polynomial rooting using the proposed algorithm range and depth estimation by a vertical array requires a 1 d search procedure for a 3 d localization problem i e range depth and direction of arrival doa estimation the algorithm involves a 2 d search procedure consequently the proposed algorithm requires significantly less computation than other methods that are based on a brute force search procedure over the source location parameters in order to evaluate the performance of the algorithm an error analysis is carried out and monte carlo simulations are performed the results are compared with the cramer rao bound crb and to the maximum likelihood ml simulation performance the algorithm is shown to be efficient while being computationally simpler than the ml or the bartlett processors the disadvantage of the algorithm is that its snr threshold occurs in lower snr than in the ml algorithm

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

subspace based adaptive method for estimating direction of arrival with luenberger observer in this paper we propose a computationally simple and efficient subspace based adaptive method for estimating directions of arrival amend for multiple coherent narrowband signals impinging on a uniform linear array ula where the previously proposed qr based method is modified for the number determination a new recursive least squares rls algorithm is proposed for null space updating and a dynamic model and the luenberger state observer are employed to solve the estimate association of directions automatically the statistical performance of the rls algorithm in stationary environment is analyzed in the mean and mean squares senses and the mean square error mse and mean square derivation msd learning curves are derived explicitly furthermore an analytical study of the rls algorithm is carried out to quantitatively compare the performance between the rls and least mean square lms algorithms in the steady state the theoretical analyses and effectiveness of the proposed rls algorithm are substantiated through numerical examples

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

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

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

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

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