the beta model maximum likelihood cramer rao bounds and hypothesis testing we study the maximum likelihood estimator in a setting where the dependent variable is a random graph and covariates are available on a graph level the model generalizes the well known beta model for random graphs by replacing the constant model parameters with regression functions cramer rao bounds are derived for special cases of the undirected beta model the directed beta model and the covariate based beta model the corresponding maximum likelihood estimators are compared with the bounds by means of simulations moreover examples are given on how to use the presented maximum likelihood estimators to test for directionality and significance finally the applicability of the model is demonstrated using temporal social network data describing communication among healthcare workers

joint estimation of porosity and saturation using stochastic rock physics modeling sediment porosity and saturation affect bulk modulus shearmodulus anddensity consequently estimatinghydrocarbon saturation and reservoir porosity from seismic data is a joint estimation problem uncertainty in porosity will lead toerrorsinsaturationprediction andviceversa porosityand saturation can be jointly estimated using stochastic rockphysicsmodelingandformalbayesianestimationmethodology knowledge of shear impedance reduces the uncertainty inporosityandthusalsoreducesuncertaintyinsaturationestimation this study investigates joint estimation of porosity and saturation by using rock physics stochastic modeling and bayesian estimation theory to derive saturation and porosity maps of expected pay sands in the field example the uncertainty in porosity quantified by the standard deviation stdassociatedwiththeposteriorprobabilitydensityfunctionpdf derivedfrominversionofseismicdataismuchless than the uncertainty in the derived saturation for a typical case the std associated with saturation is 24 while porositystdisabout1 34porosityunitsgivenseismic derived inversionattributeswithreasonableaccuracy comparisonof these numbers with prior estimates showed that inversion of seismic data decreased the uncertainty in porosity to 15 of the prior uncertainty while saturation uncertainty was only reduced to 92 of the prior uncertainty although these resultsmayvaryfromonelocationtoanother themethodology isgeneralandcanbeappliedtootherlocations

limits of sensing temporal concentration changes by single cells berg and purcell biophys j 20 193 1977 calculated how the accuracy of concentration sensing by single celled organisms is limited by noise from the small number of counted molecules here we generalize their results to the sensing of concentration ramps which is often the biologically relevant situation e g during bacterial chemotaxis we calculate lower bounds on the uncertainty of ramp sensing by three measurement devices a single receptor an absorbing sphere and a monitoring sphere we contrast two strategies simple linear regression of the input signal versus maximum likelihood estimation and show that the latter can be twice as accurate as the former finally we consider biological implementations of these two strategies and identify possible signatures that maximum likelihood estimation is implemented by real biological systems

fft based homogenization for microstructures discretized by linear hexahedral elements summary the fft based homogenization method of moulinec suquet has recently emerged as a powerful tool for computing the macroscopic response of complex microstructures for elastic and inelastic problems in this work we generalize the method to problems discretized by trilinear hexahedral elements on cartesian grids and physically nonlinear elasticity problems we present an implementation of the basic scheme that reduces the memory requirements by a factor of four and of the conjugate gradient scheme that reduces the storage necessary by a factor of nine compared with a naive implementation for benchmark problems in linear elasticity the solver exhibits mesh and contrast independent convergence behavior and enables the computational homogenization of complex structures for instance arising from computed tomography computed tomography ct imaging techniques there exist 3d microstructures involving pores and defects for which the original fft based homogenization scheme does not converge in contrast for the proposed scheme convergence is ensured also the solution fields are devoid of the spurious oscillations and checkerboarding artifacts associated to conventional schemes we demonstrate the power of the approach by computing the elasto plastic response of a long fiber reinforced thermoplastic material with 172 106 displacement degrees of freedom copyright 2016 john wiley sons ltd

a model order reduction method for computational homogenization at finite strains on regular grids using hyperelastic laminates to approximate interfaces abstract fft based homogenization methods operate on regular voxel grids and cannot resolve interfaces exactly in general in this article we study hyperelastic laminates and associate their effective properties to voxels containing interfaces extending previous ideas successfully applied in the framework of linear elasticity more precisely we show that for strictly rank one convex energy densities of the constituents there is precisely one phase wise affine minimizer of the laminate problem a result of independent interest we demonstrate that furnishing interface voxels with appropriately rotated effective hyperelastic properties of a two phase laminate significantly enhances both the local solution quality and the accuracy of the computed effective elastic properties with only a small computational overhead compared to using classical fft based homogenization in particular for equal accuracy problems with a lower number of degrees of freedom suffice

robust linear channel estimation methods for per subcarrier transmit antenna selection the linear minimum mean squared error mse channel estimator for systems employing per subcarrier transmit antenna selection is developed frequency domain correlations after the selection process are shown to be approximated well using a simple function which makes near optimal channel estimation practically possible however the resultant estimators are not robust to errors in the assumed model in terms of the antenna to subcarrier assignment used at transmission as we motivate both analytically and via simulations this is an issue when the channels for conveying this information to the receiver are severely constrained we present windowed channel estimations and new robust estimation algorithms either individually or in combination as solutions to counter this sensitivity the robust estimators are developed based on the principles of 1 minimising the worst case mse over the set of possible models and 2 minimising the expected mse over the set of possible models the latter estimator is preferred due to the lower implementation complexity and better mse performance we also prove theoretical asymptotic in signal to noise ratio performances of the two estimators used with the proposed correlation model simulation results illustrate the performance gains and improved robustness offered by the developed estimators

an accelerated fft algorithm for thermoelastic and non linear composites a fast numerical algorithm to compute the local and overall responses of non linear composite materials is developed this alternative formulation allows us to improve the convergence of the existing method of moulinec and suquet e g comput meth appl mech eng 1998 157 1 2 69 94 in the present method a non linear elastic or conducting material is replaced by infinitely many locally linear thermoelastic materials with moduli that depend on the values of the local fields this makes it possible to use the advantages of an algorithm developed by eyre and milton eur phys j appl phys 1999 6 1 41 47 which has faster convergence the method is applied to compute the local fields as well as the effective response of non linear conducting and elastic periodic composites copyright 2008 john wiley sons ltd

the ceo problem multiterminal source coding we consider a new problem in multiterminal source coding motivated by the following decentralized communication estimation task a firm s chief executive officer ceo is interested in the data sequence x t sub t 1 sup spl infin which cannot be observed directly perhaps because it represents tactical decisions by a competing firm the ceo deploys a team of l agents who observe independently corrupted versions of x t sub t 1 sup spl infin because x t is only one among many pressing matters to which the ceo must attend the combined data rate at which the agents may communicate information about their observations to the ceo is limited to say r bits per second if the agents were permitted to confer and pool their data then in the limit as l spl rarr spl infin they usually would be able to smooth out their independent observation noises entirely then they could use their r bits per second to provide the ceo with a representation of x t with fidelity d r where d spl middot is the distortion rate function of x t in particular with such data pooling d can be made arbitrarily small if r exceeds the entropy rate h of x t suppose however that the agents are not permitted to convene agent i having to send data based solely on his own noisy observations y sub i t we show that then there does not exist a finite value of r for which even infinitely many agents can make d arbitrarily small furthermore in this isolated agents case we determine the asymptotic behavior of the minimal error frequency in the limit as l and then r tend to infinity

combining galerkin approximation techniques with the principle of hashin and shtrikman to derive a new fft based numerical method for the homogenization of composites we report on the mathematical analysis of two different fft based numerical schemes for the homogenization of composite media within the framework of linear elasticity the basic scheme of moulinec and suquet 1994 1998 9 and 10 and the energy based scheme of brisard and dormieux 2010 13 casting these two schemes as galerkin approximations of the same variational problem allows us to assert their well posedness and convergence more importantly we extend in this work their domains of application by relieving some stringent conditions on the reference material which were previously thought necessary the origins of the flaws of each scheme are identified and a third scheme is proposed which seems to combine the strengths of the basic and energy based schemes while leaving out their weaknesses finally a rule is proposed for handling heterogeneous pixels voxels a situation frequently met when images of real materials are used as input to these schemes

on the relation between an operator and its self commutator we show that a bounded operator a on a hilbert space belongs to a certain set associated with its self commutator a a provided that a zi can be approximated by invertible operators for all complex numbers z the theorem remains valid in a general c algebra of real rank zero under the assumption that a zi belong to the closure of the connected component of unity in the set of invertible elements this result implies the brown douglas fillmore theorem and huaxin lin s theorem on almost commuting matrices moreover it allows us to refine the former and to extend the latter to operators of infinite rank and other norms including the schatten norms on the space of matrices the proof is based on an abstract theorem which states that a normal element of a c algebra of real rank zero satisfying the above condition has a resolution of the identity associated with any open cover of its spectrum

short note accelerating a fft based solver for numerical homogenization of periodic media by conjugate gradients in this short note we present a new technique to accelerate the convergence of a fft based solver for numerical homogenization of complex periodic media proposed by moulinec and suquet 1 the approach proceeds from discretization of the governing integral equation by the trigonometric collocation method due to vainikko 2 to give a linear system which can be efficiently solved by conjugate gradient methods computational experiments confirm robustness of the algorithm with respect to its internal parameters and demonstrate significant increase of the convergence rate for problems with high contrast coefficients at a low overhead per iteration

a computational scheme for linear and non linear composites with arbitrary phase contrast a numerical method making use of fast fourier transforms has been proposed in moulinec and suquet 1994 1998 to investigate the effective properties of linear and non linear composites this method is based on an iterative scheme the rate of convergence of which is proportional to the contrast between the phases composites with high contrast typically above 104 or infinite contrast those containing voids or rigid inclusions or highly non linear materials cannot be handled by the method this paper presents two modified schemes the first one is an accelerated scheme for composites with high contrast which extends to elasticity a scheme initially proposed in eyre and milton 1999 its rate of convergence varies as the square root of the contrast the second scheme adequate for composites with infinite contrast is based on an augmented lagrangian method the resulting saddle point problem involves three steps the first step consists of solving a linear elastic problem using the fast fourier transform method in the second step a non linear problem is solved at each individual point in the volume element the third step consists of updating the lagrange multiplier applications of this scheme to rigidly reinforced and to voided composites are shown copyright 2001 john wiley sons ltd

a comparative study on low memory iterative solvers for fft based homogenization of periodic media in this paper we assess the performance of four iterative algorithms for solving non symmetric rank deficient linear systems arising in the fft based homogenization of heterogeneous materials defined by digital images our framework is based on the fourier galerkin method with exact and approximate integrations that has recently been shown to generalize the lippmann schwinger setting of the original work by moulinec and suquet from 1994 it follows from this variational format that the ensuing system of linear equations can be solved by general purpose iterative algorithms for symmetric positive definite systems such as the richardson the conjugate gradient and the chebyshev algorithms that are compared here to the eyre milton scheme the most efficient specialized method currently available our numerical experiments carried out for two dimensional elliptic problems reveal that the conjugate gradient algorithm is the most efficient option while the eyre milton method performs comparably to the chebyshev semi iteration the richardson algorithm equivalent to the still widely used original moulinec suquet solver exhibits the slowest convergence besides this we hope that our study highlights the potential of the well established techniques of numerical linear algebra to further increase the efficiency of fft based homogenization methods

estimates of operator moduli of continuity abstract in aleksandrov and peller 2010 2 we obtained general estimates of the operator moduli of continuity of functions on the real line in this paper we improve the estimates obtained in aleksandrov and peller 2010 2 for certain special classes of functions in particular we improve estimates of kato 1973 18 and show that s t c s t log 2 log s t s t for all bounded operators s and t on hilbert space here s def s s 1 2 moreover we show that this inequality is sharp we prove in this paper that if f is a nondecreasing continuous function on r that vanishes on 0 and is concave on 0 then its operator modulus of continuity f admits the estimate f const e f t d t t 2 log t 0 we also study the problem of sharpness of estimates obtained in aleksandrov and peller 2010 2 3 we construct a c function f on r such that f l 1 f lip 1 and f const log 2 0 1 in the last section of the paper we obtain sharp estimates of f a f b in the case when the spectrum of a has n points moreover we obtain a more general result in terms of the e entropy of the spectrum that also improves the estimate of the operator moduli of continuity of lipschitz functions on finite intervals which was obtained in aleksandrov and peller 2010 2

c algebras of real rank zero abstract the concept of real rank of a c algebra is introduced as a non commutative analogue of dimension it is shown that real rank zero is equivalent to the previously defined conditions fs and hp and that it is invariant under strong morita equivalence in particular under stable isomorphism real rank zero is also invariant under inductive limits and split extensions and the class may well be regarded as the conceptual completion of the af algebras in some cases notably when the algebra is matroid it is shown that the multiplier algebra also has real rank zero although that is not true in general by a result of g j murphy this implies a weyl von neumann type result for self adjoint multiplier elements in these cases

consistent estimation of continuous time signals from nonlinear transformations of noisy samples a signal cannot in general be reconstructed from its sign i e from its hard limited version however by the deliberate addition of noise to samples of the signal prior to hard limiting it is shown that the signal can be estimated consistently from its hard limited noisy samples as the sampling rate tends to infinity in fact such estimates are shown to converge with probability one to the signal and to be asymptotically normal although the estimates are in general nonlinear they can be made linear by a proper choice of the noise distribution these rather unexpected results hold for all bounded and uniformly continuous signals in addition to the hard limiter such results are also established for certain monotonic and nonmonotonic nonlinearities

one bit distributed sensing and coding for field estimation in sensor networks this paper formulates and studies a general distributed field reconstruction problem using a dense network of noisy one bit randomized scalar quantizers in the presence of additive observation noise of unknown distribution a constructive quantization coding and field reconstruction scheme is developed and an upper bound to the associated mean squared error mse at any point and any snapshot is derived in terms of the local spatio temporal smoothness properties of the underlying field it is shown that when the noise sensor placement pattern and the sensor schedule satisfy certain weak technical requirements it is possible to drive the mse to zero with increasing sensor density at points of field continuity while ensuring that the per sensor bit rate and sensing related network overhead rate simultaneously go to zero a general condition for the optimization of the rate of decay of the mse upper bound with sensor density is derived specific mse versus sensor density decay rates are illustrated for the constant and lipschitz 1 fields with the former attaining order optimal scaling behavior

energy based comparison between the fourier galerkin method and the finite element method abstract the fourier galerkin method in short ffth has gained popularity in numerical homogenisation because it can treat problems with a huge number of degrees of freedom because the method incorporates the fast fourier transform fft in the linear solver it is believed to provide an improvement in computational and memory requirements compared to the conventional finite element method fem here we systematically compare these two methods using the energetic norm of local fields which has the clear physical interpretation as being the error in the homogenised properties this enables the comparison of memory and computational requirements at the same level of approximation accuracy we show that the methods effectiveness relies on the smoothness regularity of the solution and thus on the material coefficients thanks to its approximation properties fem outperforms ffth for problems with jumps in material coefficients while ambivalent results are observed for the case that the material coefficients vary continuously in space ffth profits from a good conditioning of the linear system independent of the number of degrees of freedom but generally needs more degrees of freedom to reach the same approximation accuracy more studies are needed for other fft based schemes non linear problems and dual problems which require special treatment in fem but not in ffth

signal recovery with cost constrained measurements we are concerned with the problem of optimally measuring an accessible signal under a total cost constraint in order to estimate a signal which is not directly accessible an important aspect of our formulation is the inclusion of a measurement device model where each device has a cost depending on the number of amplitude levels that the device can reliably distinguish we also assume that there is a cost budget so that it is not possible to make a high amplitude resolution measurement at every point we investigate the optimal allocation of cost budget to the measurement devices so as to minimize estimation error this problem differs from standard estimation problems in that we are allowed to design the number and noise levels of the measurement devices subject to the cost constraint our main results are presented in the form of tradeoff curves between the estimation error and the cost budget although our primary motivation and numerical examples come from wave propagation problems our formulation is also valid for other measurement problems with similar budget limitations where the observed variables are related to the unknown variables through a linear relation we discuss the effects of signal to noise ratio distance of propagation and the degree of coherence correlation of the waves on these tradeoffs and the optimum cost allocation our conclusions not only yield practical strategies for designing optimal measurement systems under cost constraints but also provide insights into measurement aspects of certain inverse problems

making almost commuting matrices commute suppose two hermitian matrices a b almost commute vert a b vert leq delta are they close to a commuting pair of hermitian matrices a b with vert a a vert vert b b vert leq epsilon a theorem of h lin 3 shows that this is uniformly true in that for every epsilon 0 there exists a 0 independent of the size n of the matrices for which almost commuting implies being close to a commuting pair however this theorem does not specify how depends on epsilon we give uniform bounds relating and epsilon the proof is constructive giving an explicit algorithm to construct a and b we provide tighter bounds in the case of block tridiagonal and tridiagonal matrices within the context of quantum measurement this implies an algorithm to construct a basis in which we can make a projective measurement that approximately measures two approximately commuting operators simultaneously finally we comment briefly on the case of approximately measuring three or more approximately commuting operators using povms positive operator valued measures instead of projective measurements

auditory motivated level crossing approach to instantaneous frequency estimation we address the problem of estimating the instantaneous frequency if of a phase signal using its level crossing lc information based on front end auditory processing motivation we show that the problem of if estimation using lc information can be cast in the framework of estimation from irregularly sampled data the formulation has the generality of estimating different types of if without the need for a quasistationary assumption we consider two types of if polynomial and bandlimited we use polynomial interpolating functions for the former and for the latter we propose a novel line plus sum of sines model the model parameters are estimated by linear regression considering the noisy case lc data for different levels is analyzed and methods for combining different estimators from lcs are discussed theoretical and extensive simulation results show that the performance of the zero crossing zc based if estimator and the level crossing based if estimator with smaller level values is better than those obtained with higher level values or their combinations the new technique reaches the crame spl acute r rao bound crb roughly above 4 db signal to noise ratio snr and its performance does not deteriorate rapidly with mismatch in the if order compared with the other techniques in the literature

use of composite voxels in fft based homogenization abstract fft based homogenization methods operate on regular voxel grids in general such grids cannot resolve interfaces exactly in this article we assign voxels containing an interface a stiffness different from the constituent materials in a systematic fashion more precisely we characterize the class of these so called composite voxels leading to convergence of the discretizations considering the interface in the composite voxel as linear we furnish the voxel with the corresponding laminate stiffness these laminate voxels are shown to increase both the accuracy of the calculated effective properties and the local quality of the strain and stress fields dramatically

universal decentralized estimation in a bandwidth constrained sensor network consider a situation where a set of distributed sensors and a fusion center wish to cooperate to estimate an unknown parameter over a bounded interval u u each sensor collects one noise corrupted sample performs a local estimation and transmits a message to the fusion center while the latter combines the received messages to produce a final estimate this correspondence investigates optimal local estimation and final fusion schemes under the constraint that the communication from each sensor to the fusion center must be a one bit message such a binary message constraint is well motivated by the bandwidth limitation of the communication links fusion center and by the limited power budget of local sensors in the absence of bandwidth constraint and assuming the noises are bounded to the interval u u additive independent but otherwise unknown the classical estimation theory suggests that a total of o u2 epsi2 sensors are necessary and sufficient in order for the sensors and the fusion center to jointly estimate the unknown parameter within epsi root mean squared error mse it is shown in this correspondence that the same remains true even with the binary message constraint furthermore the optimal decentralized estimation scheme suggests allocating 1 2 of the sensors to estimate the first bit of the unknown parameter 1 4 of the sensors to estimate the second bit and so on

distributed estimation of a parametric field algorithms and performance analysis this paper presents a distributed estimator for a deterministic parametric physical field sensed by a homogeneous sensor network and develops a new transformed expression for the cramer rao lower bound crlb on the variance of distributed estimates stochastic models used in this paper assume additive noise in both the observation and transmission channels two cases of data transmission are considered the first case assumes a linear analog modulation of raw observations prior to their transmission to a fusion center in the second case each sensor quantizes its observation to m levels and the quantized data are communicated to a fusion center in both cases parallel additive white gaussian channels are assumed the paper develops an iterative expectation maximization em algorithm to estimate unknown parameters of a parametric field and its linearized version is adopted for numerical analysis the performance of the developed numerical solution is compared to the performance of a simple iterative approach based on newton s approximation numerical examples are provided for the case of a field modeled as a gaussian bell however the distributed estimator and the derived crlb are general and can be applied to any parametric field the dependence of the mean square error mse on the number of quantization levels the number of sensors in the network and the snr of the observation and transmission channels are analyzed the variance of the estimates is compared to the derived crlb

a framework for fft based homogenization on anisotropic lattices abstract in order to take structural anisotropies of a given composite and different shapes of its unit cell into account we generalize the basic scheme in homogenization by moulinec and suquet to arbitrary sampling lattices and tilings of the d dimensional euclidean space we employ a fourier transform for these lattices by introducing the corresponding set of sample points the so called pattern and its frequency set the generating set the pattern and the generating set represent the anisotropy of both the shape of the unit cell and the chosen preferences in certain sampling directions in several cases this fourier transform is of lower dimension than the space itself for the so called rank 1 lattices it reduces to a one dimensional fourier transform having the same leading coefficient as the fastest fourier transform implementation available we illustrate the results using the generalized basic scheme on an anisotropic laminate and on a generalized ellipsoidal hashin structure for both we give an analytical solution to the elasticity problem in two and three dimensions respectively we then illustrate the possibilities of choosing a pattern compared to classical grids this introduces both a reduction of computation time and a reduced error of the numerical method it also allows for anisotropic subsampling i e choosing a sub lattice of a pixel or voxel grid based on anisotropy information of the material at hand

exponential rank of c algebras with real rank zero and the brown pedersen conjectures abstract we show that every c algebra with real rank zero has exponential rank 1 consequently c algebras with real rank zero have the property weak fu we also show that if a is a unital c algebra with real rank zero stable rank one and trivial k1 group then its multiplier algebra has real rank zero if a is a unital stable c algebra with stable rank one we show that its multiplier algebra has real rank zero if and only if a has real rank zero and k1 a 0

the reconstruction of analog signals from the sign of their noisy samples the reconstruction of a continuous time signal s t from the sign of its deliberately contaminated samples is considered sequential generally nonlinear estimates of s t are established and their performance is studied error bounds and convergence rates are derived the signal s t need not be band limited the convergence rates obtained here are faster than those obtained previously for nonsequential estimates the degradation in the reconstruction of the signal due to transmission over a noisy channel is also investigated and bounds on the additional error are obtained

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

the implementation of b splines to hashin and shtrikman variational principle based fft method for the homogenization of composite abstract fast fourier transform fft has been successfully used to estimate the effective properties of composites with meso periodic structure for more than two decades numerous improvements have been done to make it adequate for infinite contrast bound elastic energy and composite voxels the hashin and shtrikman variational principle based fft method handles these three problems simultaneously and is very attractive in this paper b splines were adopted to discretize the polarized field the approximate polarized field was substituted into the hashin and shtrikman variational principle to obtain the discretized system the constitutive matrix of a composite voxel was calculated by both the energetically consistent way and the laminate mixing rule numerical example of a square matrix with a circular inclusion shows that the results are more accurate than the remaining cases when the first and second order b splines as well as the laminate mixing constitutive matrix are used for higher order b spline the summation to compute the discrete green operator for periodic boundary conditions converges faster while the discretized polarized field needs more iterations to converge only when the polarized field is sufficiently smooth high order b spline improves the numerical accuracy and efficiency

resilience properties of redundant expansions under additive noise and quantization representing signals using coarsely quantized coefficients of redundant expansions is an interesting source coding paradigm the most important practical case of which is oversampled analog to digital a d conversion signal reconstruction from quantized redundant expansions and the accuracy of such representations are problems which are not well understood and we study them in this paper for uniform scalar quantization in finite dimensional spaces to give a more global perspective we first present an analysis of the resilience of redundant expansions to degradation by additive noise in general and then focus on the effects of uniform scalar quantization the accuracy of signal representations obtained by applying uniform scalar quantization to coefficients of redundant expansions measured as the mean squared euclidean norm of the reconstruction error has been previously shown to be lower bounded by an 1 r sup 2 expression we establish some general conditions under which the 1 r sup 2 accuracy can actually be attained and under those conditions prove a 1 r sup 2 upper error bound for a particular kind of structured expansions which includes many popular frame classes we propose reconstruction algorithms which attain the 1 r sup 2 accuracy at low numerical complexity these structured expansions moreover facilitate efficient encoding of quantized coefficients in a manner which requires only a logarithmic bit rate increase in redundancy resulting in an exponential error decay in the bit rate results presented in this paper are immediately applicable to oversampled a d conversion of periodic bandlimited signals

fundamental limits of linear equalizers diversity capacity and complexity linear equalizers les have been widely adopted for practical systems due to their low computational complexity however it is also well known that les provide inferior performance relative to a maximum likelihood equalizer mle or other near mles because les usually cannot collect the diversity order enabled by the transmitter and at the same time they lose mutual information more importantly unlike mle or near mles the performance of les has not been well quantified this hinders more general applications of les in wireless systems in this paper we reveal a fundamental link between a channel parameter orthogonality deficiency od of the channel matrix and the diversity and capacity of les we identify that when the od of channel matrix has an upper bound strictly less than 1 the same diversity order as that of mles is collected by les and the outage capacity loss relative to mles is also a constant over signal to noise ratio snr these results can be applied to designing a framework for hybrid equalizers furthermore by studying the statistical properties of the od and comparing the complexity of different equalizers we show that hybrid equalizers can trade off between performance and complexity by tuning the channel matrix od the theoretical analysis is corroborated by computer simulations

on posterior distributions for signals in gaussian noise with unknown covariance matrix a bayesian approach to estimate parameters of signals embedded in complex gaussian noise with unknown color is presented the study specifically focuses on a bayesian treatment of the unknown noise covariance matrix making up a nuisance parameter in such problems by integrating out uncertainties regarding the noise color an enhanced ability to estimate both the signal parameters as well as properties of the error is exploited several noninformative priors for the covariance matrix such as the reference prior the jeffreys prior and modifications to this are considered some of the priors result in analytical solutions whereas others demand numerical approximations in the linear signal model connections are made between the standard adaptive maximum likelihood aml estimate and a bayesian solution using the jeffreys prior with adjustments to the jeffreys prior correspondence to the regularized solution is also established this in turn enables a formal treatment of the regularization parameter simulations indicate that significant improvements compared to the aml estimator can be obtained by considering both the derived regularized solutions as well as the one obtained using the reference prior the simulations also indicate the possibility of enhancing the predictions of properties of the error as uncertainties in the noise color are acknowledged

hybrid fm polynomial phase signal modeling parameter estimation and cramer rao bounds parameter estimation for a class of nonstationary signal models is addressed the class contains combination of a polynomial phase signal pps and a frequency modulated fm component of the sinusoidal or hyperbolic type such signals appear in radar and sonar applications involving moving targets with vibrating or rotating components a novel approach is proposed that allows us to decouple estimation of the fm parameters from those of the pps relying on properties of the multilag high order ambiguity function ml haf the accuracy achievable by any unbiased estimator of the hybrid fm pps parameters is investigated by means of the cramer rao lower bounds crlbs both exact and large sample approximate expressions of the bounds are derived and compared with the performance of the proposed methods based on monte carlo simulations

quasi ml period estimation from incomplete timing data given a noisy sequence of possibly shifted integer multiples of a certain period it is often of interest to accurately estimate the period with known integer regressors the problem is classical linear regression in many applications however the regressors are unknown integers and only loose bounds on the period are available examples include hop period and timing estimation wherein hops may be missed at the output of the frequency discriminator or the emitter may hop out of band pulse repetition interval pri analysis and passive rotating beam radio scanning we study several pertinent period estimators our emphasis is on a quasi maximum likelihood approach developed herein and an earlier method based on the fourier transform of a dirac delta train representation of the data surprisingly both are capable of attaining the clairvoyant crame spl acute r rao bound at moderate signal to noise ratios snrs even for short e g 10 samples we carefully address parameter identifiability issues and corroborate our findings with extensive simulations

functions of normal operators under perturbations abstract in peller 1980 27 peller 1985 28 aleksandrov and peller 2009 2 aleksandrov and peller 2010 3 and aleksandrov and peller 2010 4 sharp estimates for f a f b were obtained for self adjoint operators a and b and for various classes of functions f on the real line r in this paper we extend those results to the case of functions of normal operators we show that if a function f belongs to the holder class r 2 0 1 of functions of two variables and n 1 and n 2 are normal operators then f n 1 f n 2 const f n 1 n 2 we obtain a more general result for functions in the space r 2 f f 1 f 2 const 1 2 for an arbitrary modulus of continuity we prove that if f belongs to the besov class b 1 1 r 2 then it is operator lipschitz i e f n 1 f n 2 const f b 1 1 n 1 n 2 we also study properties of f n 1 f n 2 in the case when f r 2 and n 1 n 2 belongs to the schatten von neumann class s p