direction of arrival estimation using parametric signal models we consider the problem of estimating the directions of arrival doas of narrowband sources with known center frequency the paper evaluates the potential improvement in estimation accuracy by using spatial temporal processing for signals obeying a deterministic parametric model one would expect that prior information about the temporal structure of the signals will yield some gain in performance by deriving the cramer rao bound crb on the doa estimates we quantify this gain and identify the cases for which the gain is significant we show that for the single source case spatial temporal processing does not yield any gain in performance relative to conventional spatial processing for multiple noncoherent signals incorporating temporal processing can achieve the single source performance yielding a significant gain for the case of multiple sources with small spatial separation relative to the beamwidth of the array however spatial temporal processing cannot yield any gain in performance for multiple coherent signals

duality of hardy and bmo spaces associated with operators with heat kernel bounds the introduction and development of hardy and bmo spaces on euclidean spaces r in the 1960s and 1970s played an important role in modern harmonic analysis and applications in partial differential equations these spaces were studied extensively in 32 22 18 19 31 and many others an l function f on r is in the hardy spaceh r if the area integral function of the poisson integral e t f satisfies

completeness of the trajectories of particles coupled to a general force field we analyze the extendability of the solutions to a certain second order differential equation on a riemannian manifold m g which is defined by a general class of forces both prescribed on m or depending on the velocity the results include the general time dependent anholonomic case and further refinements for autonomous systems or forces derived from a potential are obtained these extend classical results for lagrangian and hamiltonian systems several examples show the optimality of the assumptions as well as the utility of the results including an application to relativistic pp waves

square function non tangential maximal function estimates and the dirichlet problem for non symmetric elliptic operators a we consider divergence form elliptic operators l div a x defined in the half space rn 1 n 2 where the coefficient matrix a x is bounded measurable uniformly elliptic t independent and not necessarily symmetric we establish square function non tangential maximal function estimates for solutions of the homogeneous equation lu 0 and we then combine these estimates with the method of approximability to show that l harmonic measure is absolutely continuous with respect to surface measure i e n dimensional lebesgue measure on the boundary in a scale invariant sense more precisely that it belongs to the class a with respect to surface measure equivalently that the dirichlet problem is solvable with data in lp for some p previously these results had been known only in the case n 1

vertical versus conical square functions we study the difference between vertical and conical square functions in the abstract and also in the specific case where the square functions come from an elliptic operator trans amer math soc 364 2012 no 10 5469 5489

global l p continuity of fourier integral operators in this paper we establish global l p r n regularity properties of fourier integral operators the orders of decay of the amplitude are determined for operators to be bounded on l p r n 1 p infinity as well as to be bounded from hardy space h 1 r n to l 1 r n this extends local l p regularity properties of fourier integral operators as well as results of global l 2 r n boundedness to the global setting of l p r n global boundedness in weighted sobolev spaces w s sigma p r n is also established and applications to hyperbolic partial differential equations are given

subspace based estimation of time delays and doppler shifts this paper considers the problem of estimating the time delays and doppler shifts of a known waveform received via several distinct paths by an array of antennas the general maximum likelihood estimator is presented and is shown to require a 2d dimensional nonlinear minimization where d is the number of received signal reflections two alternative solutions based on signal and noise subspace fitting are proposed requiring only a d dimensional minimization in particular we show how to decouple the required search into a two step procedure where the delays are estimated and the dopplers solved for explicitly initial conditions for the time delay search can be obtained by applying generalizations of the music and esprit algorithms which are also outlined in the paper simulation examples are included to illustrate the algorithms performance relative to the cramer rao bound

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

a brief biography and appreciation of calyampudi radhakrishna rao with a bibliography of his books and papers we present a brief biography and appreciation of calyampudi radhakrishna rao to whom this fifth special issue on linear algebra and statistics of linear algebra and its applications is dedicated in celebration of his 75th birthday a bibliography of his books and papers is also included

derived pdf of maximum likelihood signal estimator which employs an estimated noise covariance a probability density function pdf for the maximum likelihood ml signal vector estimator is derived when the estimator relies on a noise sample covariance matrix scm for evaluation by using a complex wishart probabilistic model for the distribution of the scm it is shown that the pdf of the adaptive ml aml signal estimator alias the scm based minimum variance distortionless response mvdr beamformer output and more generally the scm based linearly constrained minimum variance lcmv beamformer output is in general the confluent hypergeometric function of a complex matrix argument known as kummer s function the aml signal estimator remains unbiased but only asymptotically efficient moreover the aml signal estimator converges in distribution to the ml signal estimator known noise covariance when the sample size of the estimated noise covariance matrix is fixed it is demonstrated that there exists a dynamic tradeoff between signal to noise ratio snr and noise adaptivity as the dimensionality of the array data number of adaptive degrees of freedom is varied suggesting the existence of an optimal array data dimension that will yield the best performance

the curvelet representation of wave propagators is optimally sparse this paper argues that curvelets provide a powerful tool for representing very general linear symmetric systems of hyperbolic differential equations curvelets are a recently developed multiscale system 7 9 in which the elements are highly anisotropic at fine scales with effective support shaped according to the parabolic scaling principle width length2 at fine scales we prove that for a wide class of linear hyperbolic differential equations the curvelet representation of the solution operator is both optimally sparse and well organized it is sparse in the sense that the matrix entries decay nearly exponentially fast i e faster than any negative polynomial and well organized in the sense that the very few nonnegligible entries occur near a few shifted diagonals indeed we show that the wave group maps each curvelet onto a sum of curveletlike waveforms whose locations and orientations are obtained by following the different hamiltonian flows hence the diagonal shifts in the curvelet representation a physical interpretation of this result is that curvelets may be viewed as coherent waveforms with enough frequency localization so that they behave like waves but at the same time with enough spatial localization so that they simultaneously behave like particles

autour de la conjecture de l markus sur les varietes affines for any subgroupg of n we introduce some integer discg n called thediscompacity ofg this number measures to what extent the closure ofg is not compact the markus conjecture says that a compact affinely flat unimodular manifold is complete our main result called the discompact theorem is that this conjecture is true under the assumption that the linear holonomy i e the parallel transport has discompacity 1 because discso n 1 1 1 this ensures that a compact flat lorentz manifoldm is geodesically complete hence by a previous result of w goldman and y kamishima gk such am is up to finite covering a solvmanifold this achieves the proof of a bieberbach s theorem for compact lorentz flat manifolds

computationally efficient angle estimation for signals with known waveforms this paper presents a large sample decoupled maximum likelihood deml angle estimator for uncorrelated narrowband plane waves with known waveforms and unknown amplitudes arriving at a sensor array in the presence of unknown and arbitrary spatially colored noise the deml estimator decouples the multidimensional problem of the exact ml estimator to a set of 1 d problems and hence is computationally efficient we shall derive the asymptotic statistical performance of the deml estimator and compare the performance with its cramer rao bound crb i e the best possible performance for the class of asymptotically unbiased estimators we will show that the deml estimator is asymptotically statistically efficient for uncorrelated signals with known waveforms we will also show that for moderately correlated signals with known waveforms the deml estimator is no longer a large sample maximum likelihood ml estimator but the deml estimator may still be used for angle estimation and the performance degradation relative to the crb is small we shall show that the deml estimator can also be used to estimate the arrival angles of desired signals with known waveforms in the presence of interfering or jamming signals by modeling the interfering or jamming signals as random processes with an unknown spatial covariance matrix finally several numerical examples showing the performance of the deml estimator are presented in this paper

efficient maximum likelihood doa estimation for signals with known waveforms in the presence of multipath we present a large sample maximum likelihood ml algorithm for estimating the directions of arrival doa s and signal amplitudes of known possibly coherent signals impinging on an array of sensors the algorithm is an extension of the deml method of li et al that handles coherent multipath that may be present in the signals the algorithm is computationally efficient because the nonlinear minimization step decouples into a set of minimizations of smaller dimension

a simple proof of geodesical completeness for compact space times of zero curvature any riemannian metric on a compact manifold is geodesically complete by contrast it is widely known that incomplete compact lorentzian manifolds exist in this article it will be proven that a compact manifold with a smooth lorentz metric must be complete if the metric is flat everywhere this question of completeness which has significant implications for the classification of compact lorentzian space forms has remained unresolved until quite recently when it was finally established by carriere as a special case of an even more general result here a simple alternative proof of this special case of carriere s theorem is given the proof requires minimal mathematical machinery but still involves the use of some intriguing connections between the topology and global geometry of a compact flat space time

on the full holonomy group of lorentzian manifolds the classification of restricted holonomy groups of n dimensional lorentzian manifolds was obtained about ten years ago however up to now not much is known about the structure of the full holonomy group in this paper we study the full holonomy group of lorentzian manifolds with a parallel null line bundle based on the classification of the restricted holonomy groups of such manifolds we prove several structure results about the full holonomy we establish a construction method for manifolds with disconnected holonomy starting from a riemannian manifold and a properly discontinuous group of isometries this leads to a variety of examples most of them being quotients of pp waves with disconnected holonomy including a non flat lorentzian manifold with infinitely generated holonomy group furthermore we classify the full holonomy groups of solvable lorentzian symmetric spaces and of lorentzian manifolds with a parallel null spinor finally we construct examples of globally hyperbolic manifolds with complete spacelike cauchy hypersurfaces disconnected full holonomy and a parallel spinor

completeness of compact lorentzian manifolds with abelian holonomy we address the problem of finding conditions under which a compact lorentzian manifold is geodesically complete a property which always holds for compact riemannian manifolds it is known that a compact lorentzian manifold is geodesically complete if it is homogeneous or has constant curvature or admits a time like conformal vector field we consider certain lorentzian manifolds with abelian holonomy which are locally modelled by the so called pp waves and which in general do not satisfy any of the above conditions we show that compact pp waves are universally covered by a vector space determine the metric on the universal cover and prove that they are geodesically complete using this we show that every ricci flat compact pp wave is a plane wave

complex amplitude estimation in the known steering matrix and generalized waveform case we consider a special growth curve sgc model with a known steering matrix and generalized waveform in the presence of unknown interference and noise several estimators of the complex amplitude based on this model are derived including the methods of approximate maximum likelihood aml minimum variance distortionless response mvdr and amplitude and phase estimation apes we analyze the statistical properties of these estimators and show that in the presence of temporally white but spatially correlated noise and interference aml is asymptotically statistically efficient for a large snapshot number while mvdr and apes are asymptotically equivalent but not statistically efficient via several numerical examples we also show that when the noise and interference are both spatially and temporally correlated the apes estimator can achieve better estimation accuracy and exhibit greater robustness than the other methods

bayesian complex amplitude estimation and adaptive matched filter detection in low rank interference we propose a bayesian method for complex amplitude estimation in low rank interference we assume that the received signal follows the generalized multivariate analysis of variance gmanova patterned mean structure and is corrupted by low rank spatially correlated interference and white noise an iterated conditional modes icm algorithm is developed for estimating the unknown complex signal amplitudes and interference and noise parameters we also discuss initialization of the icm algorithm and propose a non bayesian adaptive matched filter amf signal detector that utilizes the icm estimation results numerical simulations demonstrate the performance of the proposed methods

efficient estimation of a narrow band polynomial phase signal impinging on a sensor array the parameters of interest of a polynomial phase signal observed by a sensor array include the direction of arrival and the polynomial coefficients the direct maximum likelihood estimation of these parameters requires a nonlinear multidimensional search in this paper we present a two step estimation approach the estimation requires only a one dimensional search in the direction of arrival space and involves a simple least squares solution for the polynomial coefficients the efficiency of the estimates is corroborated by monte carlo simulations

structure of lorentzian tori with a killing vector field all lorentzian tori with a non discrete group of isometries are characterized and explicitly obtained they can lie into three cases a flat b conformally flat but non flat and c geodesically incomplete a detailed study of many of their properties including results on the logical dependence of the three kinds of causal completeness on geodesic connectedness and on prescribed curvature is carried out the incomplete case is specially analyzed and several known examples and results in the literature are generalized from a unified point of view

array signal processing in the known waveform and steering vector case the amplitude estimation of a signal that is known only up to an unknown scaling factor with interference and noise present is of interest in several applications including using the emerging quadrupole resonance qr technology for explosive detection in such applications a sensor array is often deployed for interference suppression this paper considers the complex amplitude estimation of a known waveform signal whose array response is also known a priori two approaches viz the capon and the maximum likelihood ml methods are considered for the signal amplitude estimation in the presence of temporally white but spatially colored interference and noise we derive closed form expressions for the expected values and mean squared errors mses of the two estimators a comparative study shows that the ml estimate is unbiased whereas the capon estimate is biased downwards for finite data sample lengths we show that both methods are asymptotically statistically efficient when the number of data samples is large but not when the signal to noise ratio snr is high furthermore we consider a more general scenario where the interference and noise are both spatially and temporally correlated we model the interference and noise vector as a multichannel autoregressive ar random process an alternating least squares als method for parameter estimation is presented we show that in most cases the als method is superior to the model mismatched ml m sup 3 l method which ignores the temporal correlation of the interference and noise

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

bounds on bearing and symbol estimation with side information we develop cramer rao bounds crbs for bearing symbol and channel estimation of communications signals in flat fading channels we do this using the constrained crb formulation of german and hero 1990 and stoica and ng see ieee signal processing lett vol 5 p 177 79 1998 with the unknown parameters treated as deterministic constants the equality constraints may be combined arbitrarily e g we may develop crbs for bearing estimation of constant modulus cm signals where a subset of the symbols are known semi blind cm case the results establish the value of side information in a large variety of communications scenarios we focus on the cm and semi blind properties and develop closed form crbs for these cases examples are presented indicating the relative value of the training and cim property these show the significant amount of signal processing information provided under these two conditions in addition we consider the performance of the maximum likelihood beamformer for the semi blind case assuming the bearings are known this semi blind beamformer achieves the appropriate constrained crb with finite data at finite snr analysis also reveals that in a semi blind scenario with two closely spaced sources ten or more training symbols are sufficient to achieve the asymptotic training regime together with previous results on angle estimation for known sources these results indicate that relatively few training samples enable both angle estimation and closely spaced co channel source separation that approaches the crb with finite data and finite snr

shrinkage approach for spatiotemporal eeg covariance matrix estimation the characterization of the background activity in electroencephalography eeg is of interest in many problems such as in the study of the brain rhythms and in the solution of the inverse problem for source localization in most cases the background activity is modeled as a random process and a basic characterization is done via the second order moments of the process i e the spatiotemporal covariance the general spatiotemporal covariance matrix of the background activity in eeg is extremely large to reduce its dimensionality it is generally decomposed as a kronecker product of a spatial and a temporal covariance matrices they are generally estimated from the data using sample estimators which have numerical and statistical problems when the number of trials is small we present a shrinkage estimator for both eeg spatial and temporal covariance matrices of the background activity we show that this estimator outperforms the commonly used ones when the quantity of available data is low we find sufficient conditions for the consistency of the shrinkage estimator and present some results concerning its numerical stability we compare several shrinkage approaches and show how to improve the estimator by incorporating known structure in the covariance matrix based on background activity models results using simulated and real eeg data support our approach

effects of estimated noise covariance matrix in optimal signal detection there is loss of efficiency when an estimated noise covariance matrix is used in the place of the unknown true noise covariance matrix in the construction of the optimum filter for signal detection in the case of detecting a single signal specified by a real or a complex vector we investigate the extent of this loss by obtaining an exact confidence bound for the realized signal to noise ratio we also give an estimate of this ratio which is useful in optimum selection of features some of these results are extended to the case of discrimination between a number of given signals

strichartz estimates for operators with nonsmooth coefficients and the nonlinear wave equation the aim of this article is threefold first we use the fbi transform to set up a calculus for partial differential operators with nonsmooth coefficients next this calculus allows us to prove strichartz type estimates for the wave equation with nonsmooth coefficients finally we use these strichartz estimates to improve the local theory for second order nonlinear hyperbolic equations 1 introduction the fbi transform is in a way similar to the complex fourier transform in that for each function in rn it provides a representation as a holomorphic function in r2n however in the case of the fbi transform we can identify naturally r2n with the phase space t rn for a pseudodifferential operator with smooth symbol acting on functions in rn one can produce by conjugation a corresponding formal series acting on func tions in r2n9 for which the first term is exactly the multiplication by the symbol this series converges and has a nice representation in the weyl calculus provided that the symbol of the operator is analytic this is how the fbi transform has been used in the study of partial differential operators with analytic coefficients see 12 13 where this machinery is developed here in a way we do the opposite we look at operators with nonsmooth coefficients approximate the conjugated operator by a partial sum of the formal series and prove error estimates in the simplest case the approximate conjugate operator is exactly the multiplication by the symbol this is also related to the cordoba fefferman wave packet transform in 3 in the third section we use the error estimates to reduce the strichartz estimates for second order hyperbolic operators with nonsmooth coefficients to weighted lp lq l2 estimates for the fbi transform these in turn can be proved in the usual fashion using appropriate oscillatory integral esti mates in the last part of the article we explain how one can use the new strichartz type estimates to improve the local theory for nonlinear hyperbolic equations beyond the classical setup these results are not sharp and will be improved in subsequent articles

a diagonal growth curve model and some signal processing applications we consider a variation of the growth curve gc model referred to as the diagonal growth curve dgc model where the steering vectors and waveforms are both known and the complex amplitude matrix is constrained to be diagonal a closed form approximate maximum likelihood aml estimator for this model is derived based on the maximum likelihood principle we analyze the statistical properties of this method theoretically and show that the aml estimate is unbiased and asymptotically statistically efficient for a large snapshot number via several numerical examples in array signal processing and spectral analysis we also show that the proposed aml estimator can achieve better estimation accuracy and exhibit greater robustness than the best existing methods

estimation of directions of arrival of multipath signals in cdma systems an algorithm is proposed for estimating the directions of arrival doas of multipath signals received from multiple users on the uplink of a code division multiple access system the correlation matrices of the received signal before and after code matched filtering are used to provide unique estimates even when the number of required doas exceeds the number of antenna array elements this scenario is well known to cause conventional direction finding algorithms such as music to fail both intersymbol interference isi and multiple access interference mai are modeled exactly and so the algorithm performs much better than those which model isi and mai as gaussian noise

applications of cumulants to array processing i aperture extension and array calibration an interpretation for the use of cumulants in narrowband array processing problems is proposed it is shown how fourth order cumulants of multichannel observations increase the directional information compared with second order statistics based on the interpretation it is shown how cumulants can be used to increase the effective aperture of an arbitrary antenna array the amount of partial information necessary to jointly calibrate an arbitrary array and estimate the directions of far field sources is also investigated it is proven that the presence of a doublet and use of fourth order cumulants is sufficient to accomplish this task the proposed approach is computationally efficient and more general than covariance based algorithms that have addressed the calibration problem under constraints a class of beamforming techniques is proposed to recover the source waveforms proposed estimation procedures are based on cumulants which bring insensitivity to the spatial correlation structure of additive gaussian measurement noise simulations are provided to illustrate the use of the proposed algorithms

mean squared error and threshold snr prediction of maximum likelihood signal parameter estimation with estimated colored noise covariances an interval error based method mie of predicting mean squared error mse performance of maximum likelihood estimators mles is extended to the case of signal parameter estimation requiring intermediate estimation of an unknown colored noise covariance matrix an intermediate step central to adaptive array detection and parameter estimation the successful application of mie requires good approximations of two quantities 1 interval error probabilities and 2 asymptotic snrrarrinfin local mse performance of the mle exact general expressions for the pairwise error probabilities that include the effects of signal model mismatch are derived herein that in conjunction with the union bound provide accurate prediction of the required interval error probabilities the crameacuter rao bound crb often provides adequate prediction of the asymptotic local mse performance of mle the signal parameters however are decoupled from the colored noise parameters in the fisher information matrix for the deterministic signal model rendering the crb incapable of reflecting loss due to colored noise covariance estimation a new modification of the crb involving a complex central beta random variable different from but analogous to the reed mallett and brennan beta loss factor provides a working solution to this problem facilitating mse prediction well into the threshold region with remarkable accuracy

orthogonal space time block codes maximum likelihood detection for unknown channels and unstructured interferences space time coding stc schemes for communication systems employing multiple transmit and receive antennas have been attracting increased attention the so called orthogonal space time block codes ostbcs have been of particular interest due to their good performance and low decoding complexity in this paper we take a systematic maximum likelihood ml approach to the decoding of ostbc for unknown propagation channels and unknown noise and interference conditions we derive a low complexity ml decoding algorithm based on cyclic minimization and assisted by a minimum amount of training data furthermore we discuss the design of optimal training sequences and optimal information transfer to an outer decoder numerical examples demonstrate the performance of our algorithm

strichartz estimates for second order hyperbolic operators with nonsmooth coefficients ii in an earlier work we have proved some estimates of strichartz type for second order hyperbolic operators with c s coefficients for 0 s 1 here we improve these estimates and extend the range of s to 0 s 2 in particular for s 2 we obtain the full strichartz estimates

the geometry of homogeneous submanifolds of hyperbolic space we prove in a purely geometric way that there are no connected irreducible proper subgroups of so n 1 moreover a weakly irreducible subgroup of so n 1 must either act transitively irreducible subgroup of so n 1 must either act transitively on the hyperbolic space or on a horosphere this has obvious consequences for lorentzian holonomy and in particular explains clasification results of marcel berger s list e g the fact that an irreducible lorentzian locally symmetric space has constant curvatures we also prove that a minimal homogeneous submanifold of hyperbolic space must be totally geodesic

a low complexity blind estimator of narrowband polynomial phase signals consider the problem of estimating the parameters of multiple polynomial phase signals observed by a sensor array in practice it is difficult to maintain a precisely calibrated array the array manifold is then assumed to be unknown and the estimation is referred to as blind estimation to date only an approximated maximum likelihood estimator amle was suggested for blindly estimating the polynomial coefficients of each signal however this estimator requires a multidimensional search over the entire coefficient space instead we propose an estimation approach which is based on two steps first the signals are separated using a blind source separation technique which exploits the constant modulus property of the signals then the coefficients of each polynomial are estimated using a least squares method applied to the unwrapped phase of the estimated signal this estimator does not involve any search in the coefficient spaces the computational complexity of the proposed estimator increases linearly with respect to the polynomial order whereas that of the amle increases exponentially simulation results show that the proposed estimator achieves the cramer rao lower bound at moderate or high signal to noise ratio

a new simultaneous estimation of directions of arrival and channel parameters in a multipath environment we present two new blind techniques for simultaneous estimation of the direction of arrival doa and the channel parameters for a uniform linear array in a multipath environment the first method is based on the sum of weighted complex exponentials and pade spl acute approximation and the second method determines the transfer function of a linear time invariant system given its impulse response for each method we introduce a rational function whose complex poles contain the desired doa the magnitude of its residues are the channel gains and the phase of its residues are in terms of the channel delays we also derive and numerically evaluate the pertinent crame spl acute r rao lower bound crlb for the estimation process our error analysis based on a perturbation series formulation of the parameter estimation reveals that doa and the channel parameters are extracted from a gaussian signal dependent noise for both methods the amount of computations are also determined some simulations are provided to assess the capabilities of the new methods

spectral cluster estimates for c 1 1 metrics in this paper we establish l p norm bounds for spectral clusters on compact manifolds under the assumption that the metric is c 1 1 precisely we show that the l p estimates proven by sogge in the case of smooth metrics hold under this limited regularity assumption it is known by examples of smith sogge that such estimates fail for c 1 metrics if 1

maximum likelihood angle estimation for signals with known waveforms maximum likelihood estimation mle of the arrival angles of narrowband plane waves when one or all signals have known waveforms is considered computationally efficient and rapidly converging algorithms that iteratively maximize the likelihood functions are presented cramer rao bounds for these estimators are obtained the conditions under which incorporating knowledge of one or all of the signal waveforms in the estimators improves the accuracy of the angle estimates are described

performance analysis of multivariate complex amplitude estimators we consider multivariate complex amplitude estimation in the presence of unknown interference and noise two multivariate approaches maximum likelihood ml and capon are provided we derive the closed form expression of the crame spl acute r rao bound crb for the unknown complex amplitudes we also analyze the bias properties and mean squared errors mse of the two estimators a comparative study shows that the multivariate ml estimator is unbiased whereas the multivariate capon estimator is biased downward for finite snapshots both estimators are asymptotically statistically efficient when the number of snapshots is large

on the completeness of geodesics obtained as a limit the process to obtain a geodesic as a limit from a sequence of geodesics in a lorentzian manifold is analyzed in detail it is found that the limit of incomplete geodesics in a compact manifold is not incomplete in general a new class of incomplete compact lorentzian manifolds one of them showing this anomalous behavior is constructed thus a counterexample to the proof given by u yurtsever j math phys 33 1295 1992 to the result originally proven by y carriere invent math 95 615 1989 in a quite different way is given that proof should imply that an incomplete compact lorentzian manifold must be null incomplete it is not known if this assertion is true and hence remains as an open question

compact affine manifolds with precompact holonomy are geodesically complete abstract this note proves the geodesic completeness of any compact manifold endowed with a linear connection such that the closure of its holonomy group is compact

hardy and bmo spaces associated to divergence form elliptic operators consider a second order divergence form elliptic operator l with complex bounded measurable coefficients in general operators based on l such as the riesz transform or square function may lie beyond the scope of the calderon zygmund theory they need not be bounded in the classical hardy bmo and even some l p spaces in this work we develop a theory of hardy and bmo spaces associated to l which includes in particular a molecular decomposition maximal and square function characterizations duality of hardy and bmo spaces and a john nirenberg inequality

time delay and spatial signature estimation using known asynchronous signals this paper considers the problem of estimating the parameters of known signals received asynchronously by an array of antennas the parameters of primary interest are the time delays of the signals and their spatial signatures at the array estimates of the signal directions of arrival are also considered but are of secondary importance in this work maximum likelihood algorithms and more computationally efficient approximations are developed for both the case where all received signals are identical the channel estimation overlapping echo problem and where they are all distinct conditions are also derived under which the standard matched filter approach yields consistent and statistically efficient parameter estimates the issue of solution uniqueness is addressed and in particular an upper bound on the number of signals whose parameters may be uniquely identified is derived for a number of different cases typically the bound is far greater than the number of sensors and is limited only by the number of data samples collected some representative simulation examples are also included to illustrate the algorithms performance relative to the cramer rao bound

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

statistical resolution limit of the uniform linear cocentered orthogonal loop and dipole array among the family of polarization sensitive arrays we can find the so called cocentered orthogonal loop and dipole uniform linear array cold ula the cold ula exhibits some interesting properties e g the insensibility of the polarization vector with respect to the source localization in the plan of the array in this correspondence we derive the statistical resolution limit srl characterizing the minimal separation in terms of direction of arrivals to resolve two closely spaced known polarized sources impinging on a cold ula toward this end nonmatrix closed form expressions of the deterministic cramer rao bound crb are derived and thus the srl is deduced a comparison between the srl of the cold ula and the classical ula are given particularly it is shown that in the case of orthogonal known signal sources the srl of the cold ula is equal to the srl of the ula meaning that it is not a function of polarization parameters furthermore due to the derived srl it is shown that under some general conditions the srl of the cold ula is smaller than the one of the ula

some new function spaces and their applications to harmonic analysis abstract in this paper a family of spaces is introduced which seems well adapted for the study of a variety of questions related to harmonic analysis and its applications these spaces are the tent spaces they provide the natural setting for the study of such things as maximal functions the relevant space here is t p and also square functions where the space t2p is relevant as such these spaces lead to unifications and simplifications of some basic techniques in harmonic analysis thus they are closely related to lp and hardy spaces important parts of whose theory become corollaries of the description of tent spaces also as proc conf harmonic analysis cortona lect notes in math vol 992 springer verlag berlin new york 1983 already indicated where these spaces first appeared explicitly the tent spaces can be used to simplify some of the results related to the cauchy integral on lipschitz curves and multilinear analysis in retrospect one can recognize that various ideas important for tent spaces had been used if only implicitly for quite some time here one should mention carleson s inequality its simplifications and extensions the theory of hardy spaces and atomic decompositions

maximum likelihood methods for direction of arrival estimation five methods of direction of arrival doa estimation which can be derived from the maximum likelihood ml principle are considered the ml method mlm results from the application of the ml principle to the statistics of the observed raw data the standard multiple signal classification music procedure called music 1 is obtained as a brute force approximation of the mlm an improved music procedure named music 2 is obtained by applying the ml principle to the statistics of certain linear combinations of the sample noise space eigenvectors a procedure which compromises between the good performance of the mlm and the computational simplicity of music is a method of direction estimation mode 1 which is derived as a large sample realization of the mlm a fifth method called mode 2 is obtained by using the ml principle on the statistics of certain linear combinations of the sample eigenvectors mode 2 is computationally less demanding than the mlm it is of the same complexity as mode 1 and statistically more efficient a numerical comparison of these five doa estimation methods is presented it confirms the analytic results on their theoretical performance levels

joint estimation of time delays and directions of arrival of multiple reflections of a known signal we present an efficient algorithm for estimating the time delays and the directions of arrival doas of multiple reflections of a known signal the algorithm is based on an iterative scheme that transforms the multidimensional maximum likelihood criterion into two sets of simple one dimensional 1 d maximization problems simulation results illustrating the performance of the algorithm in comparison with the cramer rao bound are included

iterative generalized likelihood ratio test for mimo radar we consider a multiple input multiple output mimo radar system where both the transmitter and receiver have multiple well separated subarrays with each subarray containing closely spaced antennas because of this general antenna configuration both the coherent processing gain and the spatial diversity gain can be simultaneously achieved we compare several spatial spectral estimators including capon and apes for target detection and parameter estimation we introduce a generalized likelihood ratio test glrt and a conditional generalized likelihood ratio test cglrt for the general antenna configuration based on glrt and cglrt we then propose an iterative glrt iglrt procedure for target detection and parameter estimation via several numerical examples we show that iglrt can provide excellent detection and estimation performance at a low computational cost