maximum likelihood based estimation of frequency and phase offset in dct ofdm systems under non circular transmissions algorithms analysis and comparisons recently the advantages of the discrete cosine transform dct based orthogonal frequency division multiplexing ofdm have come to the light we thus consider dct ofdm with non circular transmission our results cover circular transmission as well and present two blind joint maximum likelihood frequency offset and phase offset estimators both our theoretical analysis and numerical comparisons reveal new advantages of dct ofdm over the traditional discrete fourier transform dft based ofdm these advantages as well as those already uncovered in the early works on dct ofdm support the belief that dct ofdm is a promising multi carrier modulation scheme

cramer rao lower bounds for subcarrier snr estimates over multicarrier channels considering orthogonal frequency division multiplexing transmissions analytical expressions for the cramer rao lower bounds for the subcarrier signal to noise ratio snr estimates are derived the transmitted signal is assumed to be corrupted by additive white gaussian noise on the different subcarriers the channel is assumed to be slowly time varying over the observation interval so that it can be assumed constant it will be shown that the achievable performance on subcarrier snr estimation can be significantly improved by exploiting the mutual information the same experienced noise power between the different tones

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

wavenumber based filtering of marine point source data in seismic processing plane wave decomposition has played a fundamental role serving as a basis for developing sophisticated processing techniques valid for depth dependent models by comparing analytical expressions for the decomposed wavefields we review several processing algorithms of interest for the geophysicist the algorithms may be applied to marine point source data acquired over a horizontally layered viscoelastic and anisotropic medium the plane wave decomposition is based on the fourier transform integral for line source data and the hankel transform integral for point source data the involved wavenumber integrals of the cosine or bessel function type are difficult to evaluate accurately and efficiently however a number of the processing techniques can easily be run as a filtering operation in the spatial domain without transforming to the wavenumber domain the mathematical expressions for the spatial filters are derived using plane wave analysis with numerical examples we demonstra

immanants of combinatorial matrices abstract the arbitrary immanants of three matrices whose determinants are known to be generating functions for sets of combinatorial objects are examined combinatorial interpretations are given for the immanants of the matrix tree matrix and a special case of the jacobi trudi matrix these allow us to deduce immediately the nonnegativity of the coefficients in the expansion of the immanants a conjecture is made about the nonnegativity of coefficients of the expansion of the immanant of the jacobi trudi matrix in the general case this nonnegativity result is seen to fail for the hankel matrix and combinatorial reasons for this failure are given all results can be translated into statements about the nonnegativity of schur function expansions for the related symmetric functions

asymptotically minimum variance second order estimation for noncircular signals with application to doa estimation this paper addresses asymptotically minimum variance amv algorithms within the class of algorithms based on second order statistics for estimating direction of arrival doa parameters of possibly spatially correlated even coherent narrowband noncircular sources impinging on arbitrary array structures to reduce the computational complexity due to the nonlinear minimization required by the matching approach the covariance matching estimation technique comet is included in the algorithm numerical examples illustrate the performance of the amv algorithm

wave equation processing using finite difference propagators part 1 wavefield dissection and imaging of marine multicomponent seismic data abstractmethods for wavefield injection are used in for instance reverse time extrapolation of shot gathers in reverse time migration for correct injection of recorded data without any ambiguity of the propagation direction the wavefield injection methodology requires pressure and particle velocity data such as multicomponent towed marine or seabed seismic recordings we discovered that by carefully considering the models medium parameters and boundary conditions for injection wavefield injection of multicomponent data can also be used to solve several long standing challenges in marine seismic data processing by means of conventional time space domain finite difference propagators we outlined and demonstrated several of these important applications including up down separation of wavefields deghosting direct wave removal source signature estimation multiple removal and imaging using primaries and multiples only acoustic models are considered but the concepts are straightforward to general

blind frequency offset estimation for ofdm oqam systems this paper deals with the problem of blind carrier frequency offset cfo estimation in orthogonal frequency division multiplexing ofdm systems based on offset quadrature amplitude modulation ofdm oqam specifically by assuming that the number of subcarriers is sufficiently large the received signal is modeled as a complex gaussian random vector cgrv since the ofdm oqam signal results to be a noncircular nc process i e its relation function is different from zero by exploiting the generalized probability density function for nc cgrvs the unconditional maximum likelihood algorithm for cfo estimation in nondispersive channel is derived moreover due to its computational complexity a more feasible estimator is considered the performance of the proposed estimators assessed via computer simulation is compared with that of recently proposed cfo estimators exploiting second order cyclostationarity and with the gaussian crameacuter rao bound

closed form crlbs for snr estimation from turbo coded bpsk msk and square qam modulated signals in this contribution we derive for the first time the closed form expressions for the cramer rao lower bounds crlbs of the signal to noise ratio snr estimates from bpsk msk and square qam modulated signals over turbo coded transmissions these crlbs relatively easy to derive from bpsk msk and qpsk transmissions become extremely challenging with higher order square qam modulated signals in the latter by exploiting the structure of the gray mapping we are able to factorize the likelihood function thereby linearizing all the derivation steps for the fisher information matrix fim elements we also propose another approach that allows the evaluation of the considered bounds using extensive monte carlo computer simulations the analytical crlbs coincide exactly with their empirical counterparts validating thereby our new analytical expressions numerical results suggest that the clrbs for code aided ca snr estimates range between the crlbs for non data aided nda snr estimates and those for data aided da ones thereby highlighting the expected potential in snr estimation improvement from the coding gain indeed the ca crlbs improve by decreasing the overall coding rate due to enhanced decoding capabilities however they do increase with the modulation order for a given code rate finally the derived bounds are also valid for ldpc coded systems and they can be evaluated when the latter are decoded using the turbo principal

temperley lieb pfaffinants and schur q positivity conjectures we study pfaffian analogues of immanants which we call pfaffinants our main object is the tl pfaffinants which are analogues of rhoades and skandera s tl immanants we show that tl pfaffinants are positive when applied to planar networks and explain how to decompose products of complementary pfaffians in terms of tl pfaffinants we conjecture in addition that tl pfaffinants have positivity properties related to schur q functions

source deghosting by depth apparition abstractmarine seismic data are distorted by ghosts as waves propagating upward reflect downward from the sea surface ghosts appear on the source side and the receiver side however whereas the receiver side ghost problem has been studied in detail and many different solutions have been proposed and implemented commercially the source side ghost problem has remained largely unsolved with few satisfactory solutions available we have developed a new and simple method to remove sea surface ghosts that is related to the recently introduced concept of signal apparition as opposed to the temporal spatial source signature modulation functions used in the original signal apparition theory our source deghosting method relies on using sources at different depths but not at the same lateral positions the new method promises to be particularly suitable for 3d applications on sparse or incomplete acquisition geometries

semiparametric crb and slepian bangs formulas for complex elliptically symmetric distributions the main aim of this paper is to extend the semiparametric inference methodology recently investigated for real elliptically symmetric res distributions to complex elliptically symmetric ces distributions the generalization to the complex field is of fundamental importance in all practical applications that exploit the complex representation of the acquired data moreover the ces distributions has been widely recognized as a valuable and general model to statistically describe the non gaussian behaviour of datasets originated from a wide variety of physical measurement processes the paper is divided in two parts in the first part a closed form expression of the constrained semiparametric cramer rao bound cscrb for the joint estimation of complex mean vector and complex scatter matrix of a set of ces distributed random vectors is obtained by exploiting the so called wirtinger or mathbb c mathbb r calculus the second part deals with the derivation of the semiparametric version of the slepian bangs formula in the context of the ces model specifically the proposed semiparametric slepian bangs ssb formula provides us with a useful and ready to use expression of the semiparametric fisher information matrix sfim for the estimation of a parameter vector parametrizing the complex mean and the complex scatter matrix of a ces distributed vector in the presence of unknown nuisance density generator furthermore we show how to exploit the derived ssb formula to obtain the semiparametric counterpart of the stochastic crb for direction of arrival doa estimation under a random signal model assumption simulation results are also provided to clarify the theoretical findings and to demonstrate their usefulness in common array processing applications

monomials and temperley lieb algebras we classify the fully tight simply laced coxeter groups that is the ones whoseiji avoiding kazhdan lusztig basis elements are monomials in the generatorsbsi we then investigate the basis of the temperley lieb algebra arising from the kazhdan lusztig basis of the associated hecke algebra and prove that the basis coincides with the usual monomial basis

doa estimation of temporally and spatially correlated narrowband noncircular sources in spatially correlated white noise the main contribution of our work consists in developing for the first time a method of estimating the direction of arrival doa parameters assuming noncircular and temporally and spatially correlated signals this new approach based on a significant enhancement of the two sided instrumental variable signal subspace fitting iv ssf method outperforms its classical version in terms of lower bias and error variance moreover it will be shown that our new method is statistically more efficient than the mode method especially in the case of partly and fully coherent signals where only the extended and the classical two sided iv ssf methods are applicable we also derive an explicit expression for the stochastic cramer rao bound crb of the doa estimates from temporally and spatially correlated signals generated from noncircular sources the new crb is compared to those of circular temporally correlated and noncircular independent and identically distributed signals to show that the crb obtained assuming both noncircular sources and temporally correlated signals is lower than the crbs derived considering only one of these two assumptions this illustrates the potential gain that both noncircularity and temporal correlation provide when considered together it will also be proven that the difference between the three crbs increases with the number of snapshots however as the signal to noise ratio snr increases the crbs merge together and decrease linearly moreover at low snr values it will be shown that temporal correlation is more informative about the unknown doa parameters than noncircularity finally the crb derived assuming noncircular and temporally correlated signals depends on the noncircularity rate the circularity phase separation and the doa separation

relations between young s natural and the kazhdan lusztig representations of sn abstract our main result here is that under a suitable order of standard tableaux the classical representation of sn introduced by young in the collected papers of alfred young 1873 1940 univ of toronto press toronto qsa iv and usually referred as the natural representattion the the more recently discovered invent math 53 1979 165 184 kazhdan lusztig k l representation are related by an upper triangular integral matrix with unit diagonal elements we have been led to this discovery by a numerical exploration we noted it in each of the irreducible representations of sn up to n 6 the calculations in these cases were carried out by constructing the corresponding kazhdan lusztig graphs from tables m goresky tables of kazhdan lusztig polynomials unpublished of k l polynomials to extend the calculations to n 7 we have used graphs obtained by means of an algorithm given by lascoux and schutzenberger polynomes de kazhdan lusztig pour les grassmanniennes preprint remarkably the same property holds also for these graphs these findings appear to confirm the assertion made by these authors that their algorithm does indeed yield k l graphs for the case of hook shapes we have obtained an explicit construction of the transforming matrices a result which was also suggested by our numerical data for general shapes the transforming matrices are less explicit and our proof is based on certain properties of the kazhdan lusztig representations given in their article invent math 53 1979 165 184 and on a purely combinatorial construction of the natural representation

a fresh look at the bayesian bounds of the weiss weinstein family minimal bounds on the mean square error mse are generally used in order to predict the best achievable performance of an estimator for a given observation model in this paper we are interested in the bayesian bound of the weiss weinstein family among this family we have bayesian cramer rao bound the bobrovsky mayerwolf zakai bound the bayesian bhattacharyya bound the bobrovsky zakai bound the reuven messer bound and the weiss weinstein bound we present a unification of all these minimal bounds based on a rewriting of the minimum mean square error estimator mmsee and on a constrained optimization problem with this approach we obtain a useful theoretical framework to derive new bayesian bounds for that purpose we propose two bounds first we propose a generalization of the bayesian bhattacharyya bound extending the works of bobrovsky mayer wolf and zakai second we propose a bound based on the bayesian bhattacharyya bound and on the reuven messer bound representing a generalization of these bounds the proposed bound is the bayesian extension of the deterministic abel bound and is found to be tighter than the bayesian bhattacharyya bound the reuven messer bound the bobrovsky zakai bound and the bayesian cramer rao bound we propose some closed form expressions of these bounds for a general gaussian observation model with parameterized mean in order to illustrate our results we present simulation results in the context of a spectral analysis problem

primitive ideals and orbital integrals in complex exceptional groups in 2 two related problems were studied for complex classical groups determination of the primitive spectrum of the enveloping algebra as a set and fourier inversion of unipotent orbital integrals the first of these was solved completely extending work of joseph and others in sl n c and small groups although our techniques presumably solve the second as well up to determination of normalizing constants we carried out the calculations only for special unipotent classes see 181 we had of course tried to apply the same methods to the exceptional groups but they seem to be inadequate since that work was done however brylinski and kashiwara and beilinson and bernstein have established the kazhdan lusztig conjecture giving character formulas for irreducible highest weight modules 3 71 because of a conjecture of joseph proved in 24 this determines in principle the primitive ideals with a fixed regular integral infinitesimal character they are in one to one correspondence with what kazhdan and lusztig call left cells in the weyl group however the algorithm given by kazhdan and lusztig to compute these cells is enormously complicated requiring one to compute roughly 1 i polynomials of degrees on the order of half the number of positive roots this is very unsatisfactory however it

on seismic deghosting using green s theorem abstractwe have examined theoretically how receiver side deghosting of pressure measurements can be derived from the green s theorem method we split the green s function that obeys dirichlet boundary conditions on the sea surface and at the receiver plane into two contributions the first emitting energy downward only from its source location and the other emitting energy only upward using the normal derivative of the source side downgoing green s function in the green s theorem evaluation over the receiver plane the upgoing part of the pressure field is predicted this is the receiver side deghosted field by inserting the source side upgoing normal derivative green s function in green s theorem its evaluation over the receiver plane predicts the downgoing part of the pressure field for a plane horizontal receiver surface the required green s function can be derived using the image series expansion method to display the fundamental frequencies of this green s function we have applied a fourier se

structure of a hecke algebra quotient let w be a coxeter group with coxeter graph f let 7h be the associated hecke algebra we define a certain ideal i in 7h and study the quotient algebra 7h 7 i we show that when f is one of the infinite series of graphs of type e the quotient is semi simple we examine the cell structures of these algebras and construct their irreducible representations we discuss the case where f is of type b f or h department of mathematics harvard university cambridge massachusetts 02138 e mail address ckf anfmath harvard edu current address school of mathematics institute for advanced study princeton new jersey 08540 this content downloaded from 207 46 13 105 on wed 25 may 2016 06 46 50 utc all use subject to http about jstor org terms

kazhdan lusztig immanants and products of matrix minors abstract using the kazhdan lusztig basis c w 1 w s n for the symmetric group algebra we obtain nonnegativity properties of certain polynomials in matrix minors in particular we show that the application of these polynomials to jacobi trudi matrices yields symmetric functions which are equal to nonnegative linear combinations of schur functions

inequalities and identities for generalized matrix functions abstract let be a character on the symmetric group s n and let a a ij be an n by n matrix the function d a s n n t 1 a t t is called a generalized matrix function if is an irreducible character then d is called an immanent for example if is the alternating character then d is the determinant and if 1 then d is called the permanent denoted per suppose that a is positive semidefinite hermitian we prove that the inequality 1 id d a per a holds for a variety of characters including the irreducible ones corresponding to the partitions n 1 1 and n 2 1 1 of n the main technique used to prove these inequalities is to express the immanents as sums of products of principal subpermanents these expressions for the immanents come from analogous expressions for schur polynomials by means of a correspondence of d e littlewood

complex valued signal processing the proper way to deal with impropriety complex valued signals occur in many areas of science and engineering and are thus of fundamental interest in the past it has often been assumed usually implicitly that complex random signals are proper or circular a proper complex random variable is uncorrelated with its complex conjugate and a circular complex random variable has a probability distribution that is invariant under rotation in the complex plane while these assumptions are convenient because they simplify computations there are many cases where proper and circular random signals are very poor models of the underlying physics when taking impropriety and noncircularity into account the right type of processing can provide significant performance gains there are two key ingredients in the statistical signal processing of complex valued data 1 utilizing the complete statistical characterization of complex valued random signals and 2 the optimization of real valued cost functions with respect to complex parameters in this overview article we review the necessary tools among which are widely linear transformations augmented statistical descriptions and wirtinger calculus we also present some selected recent developments in the field of complex valued signal processing addressing the topics of model selection filtering and source separation

direction of arrival estimation for constant modulus signals in many cases where direction finding is of interest the signals impinging on an antenna array are known to be phase modulated and hence to have a constant modulus cm this is a strong property by itself it is already sufficient for source separation and can be used to construct improved direction finding algorithms we first derive the relevant cramer rao bounds crbs for arbitrary array configurations and specialize to uniform linear arrays we then propose a simple suboptimal direction estimation algorithm in which the signals are separated using the cm property followed by direction finding on the decoupled signals compared with the esprit algorithm and the crb for arbitrary signals the algorithm shows good results

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

gaussian cramer rao bound for direction estimation of noncircular signals in unknown noise fields this paper focuses on the stochastic cramer rao bound crb on direction of arrival doa estimation accuracy for noncircular gaussian sources in the general case of an arbitrary unknown gaussian noise field parameterized by a vector of unknowns explicit closed form expressions of the stochastic crb for doa parameters alone are obtained directly from the slepian bangs formula for general noncircular complex gaussian distributions as a special case the crb under the nonuniform white noise assumption is derived our expressions can be viewed as extensions of the well known results by stoica and nehorai ottersten et al weiss and friedlander pesavento and gershman and gershman et al some properties of these crbs are proved and finally these bounds are numerically compared with the conventional crbs under the circular complex gaussian distribution for different unknown noise field models

clifford algebra analogue of the hopf koszul samelson theorem theρ decompositionc g end vρ c p and the g module structure of g

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

combinatorial properties of the kazhdan lusztigr polynomials forsn abstract we point out a deep and surprising connection between the kazhdan lusztigr polynomials forsnand the enumeration and combinatorics of increasing subsequences in permutations this leads to a simple combinatorial recurrence and to several new closed formulas for these polynomials

d functions and immanants of unitary matrices and submatrices motivated by recent results in multiphoton interferometry we expand a result of kostant on immanants of an arbitrary m m unitary matrix to the submatrices of t specifically we show that immanants of principal submatrices of a unitary matrix t are a sum of the diagonal d functions of group element with t determined by the choice of submatrix and the irrep determined by the immanant under consideration we also provide evidence that this result extends to some submatrices that are not principal diagonal and we discuss how this result can be extended to cases where t carries an su m representation that is different from the defining representation

deterministic cramer rao bound for strictly non circular sources and analytical analysis of the achievable gains recently several high resolution parameter estimation algorithms have been developed to exploit the structure of strictly second order so non circular nc signals they achieve a higher estimation accuracy and can resolve up to twice as many signal sources compared to the traditional methods for arbitrary signals as a benchmark for these nc methods we derive the closed form deterministic r d nc cramer rao bound nc crb for the multi dimensional parameter estimation of strictly non circular rectilinear signal sources in this paper assuming a separable centro symmetric r d array we show that in some special cases the deterministic r d nc crb reduces to the existing deterministic r d crb for arbitrary signals this suggests that no gain from strictly non circular sources nc gain can be achieved under the deterministic data assumption in these cases for more general scenarios finding an analytical expression of the nc gain for an arbitrary number of sources is very challenging thus in this paper we simplify the derived nc crb and the existing crb for the special case of two closely spaced strictly non circular sources captured by a uniform linear array ula subsequently we use these simplified crb expressions to analytically compute the maximum achievable asymptotic nc gain for the considered two source case the resulting expression only depends on the various physical parameters and we find the conditions that provide the largest nc gain our analysis is supported by extensive simulation results

approximate solutions of acoustic 3d integral equation and their application to seismic modeling and full waveform inversion abstract over the recent decades a number of fast approximate solutions of lippmann schwinger equation which are more accurate than classic born and rytov approximations were proposed in the field of electromagnetic modeling those developments could be naturally extended to acoustic and elastic fields however until recently they were almost unknown in seismology this paper presents several solutions of this kind applied to acoustic modeling for both lossy and lossless media we evaluated the numerical merits of those methods and provide an estimation of their numerical complexity in our numerical realization we use the matrix free implementation of the corresponding integral operator we study the accuracy of those approximate solutions and demonstrate that the quasi analytical approximation is more accurate than the born approximation further we apply the quasi analytical approximation to the solution of the inverse problem it is demonstrated that this approach improves the estimation of the data gradient comparing to the born approximation the developed inversion algorithm is based on the conjugate gradient type optimization numerical model study demonstrates that the quasi analytical solution significantly reduces computation time of the seismic full waveform inversion we also show how the quasi analytical approximation can be extended to the case of elastic wavefield

an update on minc s survey of open problems involving permanents abstract we summarise the progress which has been made since 1986 on the conjectures and open problems listed in h minc s survey articles on the theory of permanents

an analytical solution for benchmark problem 1 the ideal wedge results from an exact analytical solution for the field in a wedge with pressure release boundaries benchmark problem 1 are presented in the form of transmission loss as a function of horizontal range from the source these computed curves contain no significant error and thus may be used as a primary benchmark for establishing the accuracy of range dependent numerical propagation models

an eigenstructure method for estimating doa and sensor gain phase errors in this paper we consider the problem of direction of arrival doa estimation in the presence of sensor gain phase errors under some mild assumptions we propose a new doa estimation method based on the eigendecomposition of a covariance matrix which is constructed by the dot product of the array output vector and its conjugate by combining the new doa estimation with the conventional gain phase error estimation a method is proposed to simultaneously estimate the doa and gain phase errors without joint iteration theoretical analysis shows that the proposed method performs independently of phase errors and thus behaves well regardless of phase errors however the resolution capability of the proposed method is lower than that of the method in a j weiss and b friedlander eigenstructure methods for direction finding with sensor gain and phase uncertainties circuits systems signal process vol 9 no 3 pp 271 300 1990 named as the wf method in order to improve the resolution capability and maintain phase error independence a combined strategy is developed using the proposed and wf methods the advantage of the proposed methods is that they are independent of phase errors leading to the cancellation of phase error calibration during the operation life of an array moreover the proposed methods avoid the problem of suboptimal convergence which occurs in the wf method the drawbacks of the proposed methods are their high computational complexity and their requirement for the condition that at least two signals are spatially far from each other and they are not applicable to a linear array simulation results verify the effectiveness of the proposed methods

immanant inequalities and 0 weight spaces let n e n and let a aij be an n x n complex matrix let sn be the group of permutations of x 1 n and let w n be the set of all partitions of n as one knows to each a e n we may associate an irreducible complex representation vm sn aut ya such that using standard notation x a is the character of va generalizing the determinant and permanent of a one defines the immanants of a by putting for any a e

schur positivity and schur log concavity we prove okounkov s conjecture a conjecture of fomin fulton li poon and a special case of lascoux leclerc thibon s conjecture on schur positivity and give several more general statements using a recent result of rhoades and skandera we also give an intriguing log concavity property of schur functions

iterative hos sos ihoss algorithm for direction of arrival estimation and sensor localization a new method for joint direction of arrival doa and sensor position estimation is introduced the sensors are assumed to be randomly deployed except two reference sensors the proposed method exploits the advantages of both higher order statistics hos and second order statistics sos with an iterative algorithm namely iterative higher order second order statistics ihoss a new cumulant matrix estimation technique is proposed for the hos approach by converting the multisource problem into a single source one ihoss performs well even in case of correlated source signals due to the effectiveness of the proposed cumulant matrix estimate a cost function is defined for the joint doa and position estimation the iterative procedure is guaranteed to converge the ambiguity problem in sensor position estimation is solved by observing the source signals at least in two different frequencies the conditions on these frequencies are presented closed form expressions are derived for the deterministic cramer rao bound crb for doa and unknown sensor positions for noncircular complex gaussian noise with unknown covariance matrix simulation results show that the performance of ihoss is significantly better than the hos approaches for doa estimation and closely follows the crb for both doa and sensor position estimations

from moment graphs to intersection cohomology we describe a method of computing equivariant and ordinary intersection cohomology of certain varieties with actions of algebraic tori in terms of structure of the zero and one dimensional orbits the class of varieties to which our formula applies includes schubert varieties in flag varieties and affine flag varieties we also prove a monotonicity result on local intersection cohomology stalks

on seismic deghosting by spatial deconvolution abstractreceiver side deghosting can be derived and implemented in the frequency domain as spatial deterministic deconvolution of marine pressure recordings the deghosting deconvolution operator is found analytically as the inverse fourier transform of the wavenumber domain wave equation deghosting function for a sea surface reflection coefficient of 1 the wavenumber domain deghosting function has well known poles at fundamental frequencies equal to an integer multiple of a function of the receiver depth and the plane wave dip angle relative to the depth axis the first singularity is always at 0 hz the spatial deghosting operator has singularities at fundamental frequencies equal to an integer multiple of a function of the receiver depth independent of its lateral coordinates the first singularity is again at 0 hz in addition the deghosting operator that is applied to 3d data has singularity when its lateral coordinate is zero a simple numerical example demonstrates the method

immanantal invariants of graphs abstract something between an expository note and an extended research problem this article is an invitation to expand the existing literature on a family of graph invariants rooted in linear and multilinear algebra there are a variety of ways to assign a real n n matrix k g to each n vertex graph g so that g and h are isomorphic if and only if k g and k h are permutation similar it follows that g and h are isomorphic only if k g and k h are similar i e that similarity invariants of k g are graph theoretic invariants of g an observation that helps to explain the enormous literature on spectral graph theory the focus of this article is the permutation part i e on matrix functions that are preserved under permutation similarity if not under all similarity

on products of sln characters and support containment abstract let and be dominant weights of sl n satisfying let v denote the highest weight module corresponding to lam postnikov pylyavskyy conjectured a sufficient condition for v v to be contained in v v as sl n modules in this note we prove a weaker version of the conjecture namely we prove that under the conjectured conditions every irreducible sl n module which appears in the decomposition of v v does appear in the decomposition of v v

hook immanantal inequalities for laplacians of trees abstract for an irreducible character x of the symmetric group sn indexed by the partition the immanant function d acting on an n n matrix a aij is defined as d a sn x ni 1 ai i the associated normalized immanant d is defined as d d x identity where identity is the identity permutation p heyfron has shown that for the partitions k 1n k the normalized immanant d k satisfies det a d 1 a d 2 a d n a per a 1 for all positive semidefinite hermitian matrices a when a is restricted to the laplacian matrices of graphs improvements on the inequalities above may be expected indeed in a recent survey paper r merris conjectured that d n 1 a n 2 n 1 d n a 2 wherever a is the laplacian matrix of a tree in this note we establish a refinement for the family of inequalities in 1 when a is the laplacian matrix of a tree that includes 2 as a special case these inequalities are sharp and equality holds if and only if a is the laplacian matrix of the star this is proved via the inequalities d k a d k 1 a d k 1 a d k a for k 2 3 n 1 where a is the laplacian matrix of a tree

multiple level nested array an efficient geometry for 2q th order cumulant based array processing recently direction of arrival estimation doa algorithms based on arbitrary even order 2q cumulants of the received data have been proposed giving rise to new doa estimation algorithms namely the 2q music algorithm in particular it has been shown that the 2q music algorithm can identify o nq statistically independent non gaussian sources however in this paper it is demonstrated that the processing power of the 2qth order cumulant based methods can potentially be even larger it will be shown that the 2qth order cumulant matrix of the data is directly related to the concept of a 2qth order difference co array which can potentially have o n2q virtual sensors leading to identification of o n2q statistically independent non gaussian sources using 2q th order cumulants however the number of actually realizable virtual elements in the 2q th order difference co array depends on the geometry of the physical array in order to ensure that the co array indeed has the desired degrees of freedom a new generic class of linear one dimensional nonuniform arrays namely the 2qth order nested array is proposed whose 2q th order difference co array is proved to contain a uniform linear array with o n2q sensors in order to exploit these increased degrees of freedom of the co array a new algorithm for doa estimation is also developed which acts on the same 2q th order cumulant matrix as the earlier methods and can yet identify o n2q sources it is proved that the proposed method can identify the maximum number of sources among all methods that use 2q th order cumulants

proof of a conjecture on immanants of the jacobi trudi matrix abstract we prove a conjecture on characters of sn which implies another conjecture both due to goulden and jackson that all immanants of the jacobi trudi matrix h h i i j j i j 1 n have nonnegative coefficients

eigenvalues singular values and littlewood richardson coefficients we characterize the relationship between the singular values of a hermitian resp real symmetric complex symmetric matrix and the singular values of its off diagonal block we also characterize the eigenvalues of a hermitian or real symmetric matrix c a b in terms of the combined list of eigenvalues of a and b the answers are given by horn type linear inequalities the proofs depend on a new inequality among littlewood richardson coefficients

nonintersecting paths pfaffians and plane partitions gessel and viennot have developed a powerful technique for enumerating various classes of plane partitions the purpose of this article is to show by similar means that one may use pfaffiants to enumerate configurations of nonintersecting paths in which the initial and or terminal vertices of the paths are allowed to vary over specified regions of the digraph this leads to the possibility of enumerating classes of plane partitions in which the shape is allowed to vary whereas the previous applications of gessel and viennot were largely confined to plane partitions of a given shape

log concavity of multiplicities with application to characters ofu the log concavity of the reduction multiplicities for the classical groups of typean bn cnis proved moreover the skew schur functionss are shown to be log concave coefficient by coefficient the results are applied to the calculation of the characters of the infinite dimensional classical groups the log concavity of density of the push forward of the liouville measure on coadjoint orbits under moment map is proved

cramer rao lower bounds of doa estimates from square qam modulated signals in this paper we derive for the first time analytical expressions for the inphase quadrature i q non data aided nda cramer rao lower bounds i q nda crlbs of the direction of arrival doa estimates from square quadrature amplitude qam modulated signals corrupted by additive white circular complex gaussian noise awccgn with any antenna configuration yet the main contribution embodied by this paper consists in deriving for the first time analytical expressions for the nda fisher information matrix fim and then for the stochastic crlb of the nda doa estimates in the case of square qam modulated signals it will be shown that in the presence of any unknown phase offset i e non coherent estimation the ultimate achievable performance on the nda doa estimates holds almost the same irrespectively of the modulation order however the nda crlbs obtained in the absence of the phase offset i e coherent estimation vary in the high snr region from one modulation order to another

inequalities for single hook immanants let dk denote the normalized generalized matrix function based upon the irreducible character of sn associated with the partition k 1 1 of n for all positive semidefinite hermitian n by n a we prove certain inequalities in the chain det a d1 a d2 a dn 1 a dn a per a conjectured for each n this work is in pursuit of the permanent on top conjecture and this conjecture is also verified for another class of immanants the methods involve several new inequalities for eigenvalues and the permanent which may be of independent interest

ribbon tableaux hall littlewood functions quantum affine algebras and unipotent varieties we introduce a new family of symmetric functions which are q analogs of products of schur functions defined in terms of ribbon tableaux these functions can be interpreted in terms of the fock space representation fq of uq sln and are related to hall littlewood functions via the geometry of flag varieties we present a series of conjectures and prove them in special cases the essential step in proving that these functions are actually symmetric consists in the calculation of a basis of highest weight vectors of fq using ribbon tableaux

cisoid parameter estimation in the colored noise case asymptotic cramer rao bound maximum likelihood and nonlinear least squares the problem of estimating the parameters of complex valued sinusoidal signals cisoids for short from data corrupted by colored noise occurs in many signal processing applications we present a simple formula for the asymptotic large sample cramer rao bound crb matrix associated with this problem the maximum likelihood method mlm which estimates both the signal and noise parameters attains the performance corresponding to the asymptotic crb as the sample length increases more interestingly we show that a computationally much simpler nonlinear least squares method nlsm which estimates the signal parameters only achieves the same performance in large samples

integrated receiver deghosting and closed loop surface multiple elimination abstractaccurate surface related multiple removal is an important step in conventional seismic processing and more recently primaries and surface multiples are separated such that each of them is available for imaging algorithms current developments in the field of surface multiple removal aim at estimating primaries in a large scale inversion process using such a so called closed loop process in each iteration primaries and surface multiples will be updated until they fit the measured data the advantage of redefining surface multiple removal as a closed loop process is that certain preprocessing steps can be included which can lead to an improved multiple removal in principle the surface related multiple elimination process requires deghosted data as input thus the source and receiver ghost must be removed we have focused on the receiver ghost effect and assume that the source is towed close to the sea surface such that the source ghost effect is well represented by a dipole source the rece

music like estimation of direction of arrival for noncircular sources this paper examines the asymptotic performance of music like algorithms for estimating directions of arrival doa of narrowband complex noncircular sources using closed form expressions of the covariance of the asymptotic distribution of different projection matrices it provides a unifying framework for investigating the asymptotic performance of arbitrary subspace based algorithms valid for gaussian or non gaussian and complex circular or noncircular sources we also derive different robustness properties from the asymptotic covariance of the estimated doa given by such algorithms these results are successively applied to four algorithms to two attractive music like algorithms previously introduced in the literature to an extension of these algorithms and to an optimally weighted music algorithm proposed in this paper numerical examples illustrate the performance of the studied algorithms compared to the asymptotically minimum variance amv algorithms introduced as benchmarks

stochastic crame spl acute r rao bound for noncircular signals with application to doa estimation after providing an extension of the slepian bangs formula for general noncircular complex gaussian distributions this paper focuses on the stochastic crame spl acute r rao bound crb on direction of arrival doa estimation accuracy for noncircular sources we derive an explicit expression of the crb for doa parameters alone in the case of noncircular complex gaussian sources by two different methods one of them consists of computing the asymptotic covariance matrix of the maximum likelihood ml estimator and the other is obtained directly from our extended slepian bangs formula some properties of this crb are proved and finally it is numerically compared with the crbs under circular complex gaussian and complex discrete distributions of sources

hook immanantal inequalities for trees explained abstract let d k denote the normalized hook immanant corresponding to the partition k ln k of n p heyfron proved the family of immanantal inequalities det a d 1 a d 2 a d n a per a 1 for all positive semidefinite hermitian matrices a motivated by a conjecture of r merris it was shown by the authors that 1 may be improved to d k 1 l t k 2 k 1 d k l t 2 for all 2 k n whenever l t is the laplacian matrix of a tree t the proof of 2 relied on rather involved recursive relations for weighted matchings in the tree t as well as identities of hook characters in this work we circumvent this tedium with a new proof using the notion of vertex orientations this approach makes 2 immediately apparent and more importantly provides an insight into why it holds namely the absence of certain vertex orientations for all trees as a by product we obtain an improved bound 0 1 k 1 d k l t d k l s n k 2 k 1 d k l t d k 1 l t where s n is the star with n vertices the ease with which the inequality in 2 and its improvement are derived points to the value of the concept of vertex orientation in the study of immanantal inequalities on graphs

the coefficients of the immanantal polynomial abstract an expression of the coefficient of immanantal polynomial of an n n matrix is present moreover we give expressions of the coefficient of immanantal polynomials of combinatorial matrices adjacency matrix laplacian matrix signless laplacian matrix as applications we show that the immanantal polynomials for laplacian matrix and signless laplacian matrix of bipartite graphs are the same this is a generalization of the characteristic polynomial for laplacian matrix and signless laplacian matrix of bipartite graphs furthermore we consider the relations between the characteristic polynomial and the immanantal polynomial for trees

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

on seismic deghosting using integral representation for the wave equation use of green s functions with neumann or dirichlet boundary conditions abstractthe recent interest in broadband seismic technology has spurred research into new and improved seismic deghosting solutions one starting point for deriving deghosting methods is the representation theorem which is an integral representation for the wave equation recent research results show that by using green s functions with dirichlet boundary conditions in the representation theorem source side deghosting of already receiver side deghosted wavefields can be achieved we found that the choice of green s functions with neumann boundary conditions on the sea surface and the plane that contains the sources leads to an identical but simpler solution with fewer processing steps in addition we found that pressure data can be receiver side deghosted by introducing green s functions with dirichlet boundary conditions on the sea surface and the plane containing the receivers into a modified representation theorem the deghosting methods derived from the representation theorem are wave theoretic alg

enhanced reactance domain esprit algorithm employing multiple beams and translational invariance soft selection for direction of arrival estimation in the full azimuth an enhanced reactance domain estimation of signal parameters via rotational invariance techniques rd esprit algorithm is proposed for direction of arrival doa estimation in the full azimuth plane unlike the classical rd esprit algorithm the proposed method employs a generalized rd correlation matrix combined with soft selection the proposed algorithm is expected to allow estimating more than one signal doa with improved estimation precision the generalized rd correlation matrix is formed by utilizing a number of beam patterns greater than or equal to the number of array elements the soft selection employed in the enhanced rd esprit consists of two steps first the estimates obtained by applying the generalized rd esprit to three translational invariance configurations are gathered to form a set of doa estimate candidates second selection functions based on a modified music function are used to select the doa estimates from among the estimate candidate set the proposed algorithm is investigated through computer simulations with a seven element electronically steerable parasitic array radiator espar antenna the simulation showed that the proposed algorithm can perform effective doa estimation of up to four incoming signals in the full azimuth plane with slightly improved doa estimation precision so far the classical rd esprit is not effective because it can estimate up to one signal doa moreover the proposed method showed robust estimation capability for up to two incoming signals a robust estimation refers to the fact that a number of doa estimates equal to the number of incoming signals can always be selected from trial to trial a one signal estimation experiment was conducted in an anechoic chamber with a fabricated seven element espar antenna in general the proposed algorithm showed as accurate estimation precision as the classical algorithm in particular using soft selection instead of hard selection increases the estimation precision whereas augmenting the number of beam patterns brings an increase in the estimation precision only when used with hard selection

wave equation processing using finite difference propagators part 2 deghosting of marine hydrophone seismic data abstractwe have developed a new and simple method for deghosting of conventional hydrophone streamer data towed at arbitrary variable depths the method uses a time space domain finite difference fd solution to the wave equation with pressure field boundary conditions to predict and remove ghosts because it operates in the time domain our method is unaffected by any number of notches in the frequency spectrum of the data and therefore will deghost through notches apart from the acquired hydrophone data the method relies on the depth profile of the streamer recording the data beneath a sea surface with a known reflection coefficient as well as the propagation velocity in the water above the streamer the method was applied to simple and more complex synthetic data which illustrated its ability to deal with complex data and any acquisition geometry

laplacian immanantal polynomials and the gts poset on trees abstract let t be a tree on n vertices with laplacian l t and let gts n be the generalised tree shift poset on the set of unlabelled trees on n vertices inequalities are known for coefficients of the characteristic polynomial of l t as we go up the poset gts n in this work we generalise these inequalities to the q laplacian l t q of t and to the coefficients of all immanantal polynomials

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

coupled mode solutions in generalized ocean environments a two way coupled mode model has been developed to solve propagation problems in fluid layered range dependent ocean environments the model incorporates piecewise linear depth dependent range varying sound speed profiles svps a fast and efficient normal mode model which is based on a propagator matrix method is used to obtain the eigenvalues and eigenfunctions the coupling coefficients are expressed in terms of depth integrals of products of airy functions and are solved analytically the coupled equations are solved exactly by an approach referred to as the u k method which incorporates the lanczos method previously used in solving similar coupled channel equations in nuclear theory and successfully applied to nuclear response problems in heavy nuclei knobles solutions of coupled mode equations with a large dimension in underwater acoustics j acoust soc am 96 1741 1747 1994 highlights of the formalism will be presented which expand on the overview given previously stotts et al solutions of coupled mode equations with a large dimension in underwater acoustics j acoust soc am 95 2909 a 1994 several benchmark comparisons will be presented including propagation over a hill upslope wedge propagation and an analytic depth and range dependent svp in a flat waveguide

cramer rao lower bounds for qam phase and frequency estimation in this paper we present the true cramer rao lower bounds crlbs for the estimation of phase offset for common quadrature amplitude modulation qam psk and pam signals in awgn channels it is shown that the same analysis also applies to the qam fsk and pam crlbs for frequency offset estimation the ratio of the modulated to the unmodulated crlbs is derived for all qam psk and pam signals and calculated for specific cases of interest this is useful to determine the limiting performance of synchronization circuits for coherent receivers without the need to simulate particular algorithms the hounds are compared to the existing true crlbs for an unmodulated carrier wave cw bpsk and qpsk we investigated new and existing qam phase estimation algorithms in order to verify the new phase crlb this showed that new minimum distance estimator performs close to the qam bound and provides a large improvement over the power law estimator at moderate to high signal to noise ratios

cramer rao bounds of doa estimates for bpsk and qpsk modulated signals this paper focuses on the stochastic cramer rao bound crb of direction of arrival doa estimates for binary phase shift keying bpsk and quaternary phase shift keying qpsk modulated signals corrupted by additive circular complex gaussian noise explicit expressions of the crb for the doa parameter alone in the case of a single signal waveform are given these crbs are compared on the one hand with those obtained with different a priori knowledge and on the other hand with crbs under the noncircular and circular complex gaussian distribution and with different deterministic crbs it is shown in particular that the crbs under the noncircular respectively circular complex gaussian distribution are tight upper bounds on the crbs under the bpsk respectively qpsk distribution at very low and very high signal to noise ratios snrs only finally these results and comparisons are extended to the case of two independent bpsk or qpsk distributed sources where an explicit expression of the crb for the doa parameters alone is given for large snr

statistical performance of music like algorithms in resolving noncircular sources this paper addresses the resolution of the conventional and noncircular music algorithms for arbitrary circular and noncircular second order distributions of two uncorrelated closely spaced transmitters observed by an arbitrary array an explicit closed form expression of the mean null spectrum of the conventional and noncircular music algorithms is derived using an analysis based on perturbations of the noise projector instead of those of the eigenvectors based on these results theoretical and approximate interpretable closed form expressions of the threshold array signal to noise ratios asnr at which these two algorithms are able to resolve two closely spaced transmitters along the cox and the sharman and durrani criteria are given it is proved that the threshold asnrs given by the conventional music algorithm do not depend on the distribution of the sources including their noncircularity in contrast to the noncircular music algorithm for which they are very sensitive to the noncircularity phase separation of the sources this threshold asnr given by the noncircular music algorithm is proven to be comfortably lower than that given by the conventional music algorithm except for weak phase separations of the sources for which the resolving powers of these two algorithms are very close finally these results are analyzed through several illustrations and monte carlo simulations

improved cramer rao lower bounds for phase and frequency estimation with m psk signals we derive new cramer rao lower bounds crbs for the estimation of carrier phase and frequency offset from an unmodulated carrier or from a m psk data signal the new crbs are obtained formally from the exact likelihood function for the carrier phase and frequency offset build from a block of received phase samples and are applicable for a general alphabet size m the bounds are compared with other previously obtained bounds which also take into account the effect of random phase modulation and with the performance of some popular feedforward algorithms for carrier phase and frequency offset estimation

ml based symbol timing and frequency offset estimation for ofdm systems with noncircular transmissions this paper deals with the problem of joint symbol timing and carrier frequency offset cfo estimation in orthogonal frequency division multiplexing ofdm systems with noncircular nc transmissions maximum likelihood ml estimators of symbol timing and cfo have been derived under the assumption of nondispersive channel and by modeling the ofdm signal vector as a circular complex gaussian random vector c cgrv the gaussian assumption is reasonable when the number of subcarriers is sufficiently large however if the data symbols belong to an nc constellation the received signal vector becomes an nc cgrv i e a cgrv whose relation matrix defined as the statistical expectation of the product between the vector and its transpose is not identically zero hence in this case previously mentioned estimators termed mlc estimators are not ml estimators in this paper by exploiting the joint probability density function for nc cgrvs ml estimators are derived moreover since their implementation complexity is high feasible computational algorithms are considered finally refined symbol timing estimators apt to counteract the degrading effects of intersymbol interference isi in dispersive channels are suggested the performance of the derived estimators is assessed via computer simulation and compared with that of mlc estimators and that of modified mlc mmlc estimators exploiting only isi free samples of the cyclic prefix

noise attenuation by a hard wedge shaped barrier this paper is concerned with the problem of sound screening by a wedge like barrier the sound source is assumed to be point like and the receiver is located in the shadow of the source sound field so that according to geometrical optics only the field diffracted by the edge of the barrier is considered first for the hard wedge in space three models are used for calculating the amplitude of the edge diffracted field these are the uniform theory of diffraction utd the hadden pierce model both in the frequency domain and the biot tolstoy theory of diffraction which is a time domain formulation it is first shown that even at relatively low frequencies the frequency domain models perform quite satisfactorily as compared to the exact time domain theory hence and due to its relative simplicity the utd is proposed as an accurate calculation scheme for solving problems with edge diffraction by hard wedges it is also proved from theoretical calculations that the amplitude of the edge diffracted field increases for an increasing angle of the wedge and consequently the hard half plane gives the lowest field amplitude in the shadow zone some applications are then considered for evaluating the performance of a barrier on a flat ground either completely hard or with mixed homogeneous boundary conditions an improvement of the scheme for calculating the sound field in the all hard case is achieved through considering the multiple diffraction in this case only to the second order between the top of the wedge barrier and its base the results show that for usually occurring situations increasing the angle of the hard wedge barrier affects negatively its efficiency through diminishing its insertion loss these conclusions are also supported by the results of some experimental measurements conducted at a scale model level

second order complex random vectors and normal distributions complex random vectors are usually described by their covariance matrix this is insufficient for a complete description of second order statistics and another matrix called the relation matrix is necessary some of its properties are analyzed and used to express the probability density function of normal complex vectors various consequences are presented

hook immanantal and hadamard inequalities for q laplacians of trees abstract let t be a tree on n vertices with laplacian matrix l and q laplacian l q let k be the character of the irreducible representation of s n indexed by the hook partition k 1 n k and let d k l be the normalized hook immanant of l corresponding to the character k inequalities for d k l as k increases are known by assigning a statistic to vertex orientations on trees we generalize these inequalities to the q analogue l q of l for all q r and to the bivariate q t laplacian l q t for some values q t our statistic based approach also generalizes several other inequalities including the changing index k l of the hadamard inequality for l to the matrix l q and l q t thus we extend several results about l to l q which includes the case when l q is not positive semidefinite