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

parameter estimation of superimposed signals using the em algorithm a computationally efficient algorithm for parameter estimation of superimposed signals based on the two step iterative em estimate and maximize with an e step and an m step algorithm is developed the idea is to decompose the observed data into their signal components and then to estimate the parameters of each signal component separately the algorithm iterates back and forth using the current parameter estimates to decompose the observed data better and thus increase the likelihood of the next parameter estimates the application of the algorithm to the multipath time delay and multiple source location estimation problems is considered

dichotomy results for the l1 norm of the discrepancy function abstract it is a well known conjecture in the theory of irregularities of distribution that the l 1 norm of the discrepancy function of an n point set satisfies the same asymptotic lower bounds as its l 2 norm in dimension d 2 this fact has been established by halasz while in higher dimensions the problem is wide open in this note we establish a series of dichotomy type results which state that if the l 1 norm of the discrepancy function is too small smaller than the conjectural bound then the discrepancy function has to be large in some other function space

an explicit construction of optimal order quasi monte carlo rules for smooth integrands in a recent paper by the authors it is shown that there exists a quasi monte carlo qmc rule which achieves the best possible rate of convergence for numerical integration in a reproducing kernel hilbert space consisting of smooth functions in this paper we provide an explicit construction of such an optimal order qmc rule our approach is to exploit both the decay and the sparsity of the walsh coefficients of the reproducing kernel simultaneously this can be done by applying digit interlacing composition due to dick to digital nets with large minimum hamming and niederreiter rosenbloom tsfasman metrics due to chen and skriganov to our best knowledge our construction gives the first qmc rule which achieves the best possible convergence in this function space

analysis of subspace fitting and ml techniques for parameter estimation from sensor array data it is shown that the multidimensional signal subspace method termed weighted subspace fitting wsf is asymptotically efficient this results in a novel compact matrix expression for the cramer rao bound crb on the estimation error variance the asymptotic analysis of the maximum likelihood ml and wsf methods is extended to deterministic emitter signals the asymptotic properties of the estimates for this case are shown to be identical to the gaussian emitter signal case i e independent of the actual signal waveforms conclusions concerning the modeling aspect of the sensor array problem are drawn

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

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

detection and estimation in sensor arrays using weighted subspace fitting the problem of signal parameter estimation of narrowband emitter signals impinging on an array of sensors is addressed a multidimensional estimation procedure that applies to arbitrary array structures and signal correlation is proposed the method is based on the recently introduced weighted subspace fitting wsf criterion and includes schemes for both detecting the number of sources and estimating the signal parameters a gauss newton type method is presented for solving the multidimensional wsf and maximum likelihood optimization problems the global and local properties of the search procedure are investigated through computer simulations most methods require knowledge of the number of coherent noncoherent signals present a scheme for consistently estimating this is proposed based on an asymptotic analysis of the wsf cost function the performance of the detection scheme is also investigated through simulations

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

the power of online thinning in reducing discrepancy consider an infinite sequence of independent uniformly chosen points from 0 1 d after looking at each point in the sequence an overseer is allowed to either keep it or reject it and this choice may depend on the locations of all previously kept points however the overseer must keep at least one of every two consecutive points we call a sequence generated in this fashion a two thinning sequence here the purpose of the overseer is to control the discrepancy of the empirical distribution of points that is after selecting n points to reduce the maximal deviation of the number of points inside any axis parallel hyper rectangle of volume a from na our main result is an explicit low complexity two thinning strategy which guarantees discrepancy of o log 2d 1 n for all n with high probability compare with theta sqrt n log log n without thinning the case d 1 of this result answers a question of benjamini we also extend the construction to achieve the same asymptotic bound for 1 beta thinning a set up in which rejecting is only allowed with probability beta independently for each point in addition we suggest an improved and simplified strategy which we conjecture to guarantee discrepancy of o log d 1 n compare with theta log d n the best known construction of a low discrepancy sequence finally we provide theoretical and empirical evidence for our conjecture and provide simulations supporting the viability of our construction for applications

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

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

mds poset codes satisfying the asymptotic gilbert varshamov bound in hamming weights we prove that mds linear poset codes satisfy gilbert varshamov bound for their hamming weights asymptotically we also construct mds linear poset codes on arbitrary poset metric spaces by using the dilworth s chain decomposition theorem and results about the hermite interpolation problem over a finite field we prove that there exist linear poset codes with large weights for both poset metrics and hamming metrics as well

optimum localization of multiple sources by passive arrays the maximum likelihood ml estimator of the location of multiple sources and the corresponding cramer rao lower bound on the error covariance matrix are derived the derivation is carried out for the general case of correlated sources so that multipath propagation is included as a special case it is shown that the ml processor consists of a bank of beam formers each focused to a different source followed by a variable matrix filter that is controlled by the assumed location of the sources in the special case of uncorrelated sources and very low signal to noise ratio this processor reduces to an aggregate of ml processors for a single source with each processor matched to a different source iterative algorithms for the actual computation of the ml estimator are also presented

an iterative method for the computation of nonlinear wide angle pulsed acoustic fields of medical diagnostic transducers the development and optimization of medical ultrasound transducers and imaging modalities require a computational method that accurately predicts the nonlinear acoustic pressure field a prospective method should provide the wide angle pulsed field emitted by an arbitrary planar source distribution and propagating in a three dimensional large scale domain holding a nonlinear acoustic medium in this paper a method is presented that is free of any assumed wavefield directionality the nonlinear acoustic wave equation is solved by treating the nonlinear term as a contrast source this formulation leads to an iterative scheme that involves the repetitive solution of a linear wave problem through green s function method it is shown that accurate field predictions may be obtained within a few iterations moreover by employing a dedicated numerical convolution technique the method allows for a discretization down to two points per wavelength or period of the highest frequency of interest the performance of the method is evaluated through a number of nonlinear field predictions for pulsed transducers with various geometries the results demonstrate the directional independence of the method moreover comparison with results from several existing methods shows that the method accurately predicts the nonlinear field for weak to moderate nonlinearity

on unique localization of multiple sources by passive sensor arrays necessary and sufficient conditions are derived for the unique localization of narrowband sources having the same known center frequency by passive sensor arrays the conditions specify the maximum number of sources that can be uniquely localized by a general array that satisfies some mild geometric constraints the conditions are expressed in terms of the number of sensors and the rank of the correlation matrix of the sources two different conditions are presented the first guarantees uniqueness for every batch of sampled data the second which is weaker guarantees uniqueness for almost every batch of sampled data with the exception of a set of batches of measure zero it is shown that a condition that is slightly weaker than the second one is also necessary

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

detection of the number of coherent signals by the mdl principle an approach is presented to the problem of detecting the number of sources impinging on a passive sensor array that is based on j rissanen s 1983 minimum description length mdl principle the approach is applicable to any type of sources including the case of sources which are fully correlated referred to as the coherent signals case two slightly different detection criteria are derived both requiring the estimation of the locations of the sources the first is tailored to the detection problem per se whereas the second is tailored to the combined detection estimation problem consistency of the two criteria is proved and their performance is demonstrated by computer simulations