a new approach to multipath correction of constant modulus signals an adaptive digital filtering algorithm that can compensate for both frequency selective multipath and interference on constant envelope modulated signals is presented the method exploits the fact that multipath reception and various interference sources generate incidental amplitude modulation on the received signal a class of so called constant modulus performance functions is developed which sense this am term but are insensitive to the angle modulation simple adaptive algorithms for finite impulse response fir digital filters are developed which employ a gradient search of the performance function one of the resulting algorithms is simulated for the example of an fm signal degraded by specular multipath propagation substantial improvements in noise power ratio npr are observed e g 25 db with moderately rapid convergence time these results are then extended to include tonal interference on a fm signal and intersymbol interference on a qpsk data signal

subspace based blind channel estimation generalization and performance analysis in this paper we present a systematic study of the subspace based blind channel estimation method we first formulate a general signal model of multiple simultaneous signals transmitted through vector channels which can be applied to a multitude of modern digital communication systems based on this model we then propose a generalized subspace based channel estimator by minimizing a novel cost function which incorporates the set of kernel matrices of the signals sharing the target channel via a weighted sum of projection errors we investigate the asymptotic performance of the proposed estimator i e bias covariance mean square error mse and cramer rao bound for large numbers of independent observations we show that the performance of the estimator can be optimized by increasing the number of kernel matrices and by using a special set of weights in the cost function finally we consider the application of the proposed estimator to a downlink code division multiple access cdma system operating in a frequency selective fading channel with negligible intersymbol interference isi the results of the computer simulations fully support our analytical developments

a subspace method for signature waveform estimation in synchronous cdma systems synchronous code division multiple access cdma techniques possess intrinsic protection against co channel interference due to orthogonal codes employed and thus offers higher capacity than existing frequency division multiple access fdma or time division multiple access tdma systems in the presence of multipath however each signal is subject to frequency selective fading and the orthogonality condition does not necessarily hold leading to increased cross correlation in these scenarios multiuser detection need to be performed to suppress interference and recover the message symbols to implement such a technique explicit knowledge of the nonorthogonal signature waveforms of all users is required we propose a blind estimation scheme that provides closed form estimates of the signature waveforms by exploiting the structure information of the data output in particular we show that the subspace of the data matrix contains sufficient information for unique determination of the signature waveforms based on this observation a multiple signal classification music like algorithm is derived performance analysis of the new approach is also presented

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

subspace based channel estimation for code division multiple access communication systems we consider the estimation of channel parameters for code division multiple access cdma communication systems operating over channels with either single or multiple propagation paths the multiuser channel estimation problem is decomposed into a series of single user problems through a subspace based approach by exploiting the eigenstructure of the received signal s sample correlation matrix the observation space can be partitioned into a signal subspace and a noise subspace without prior knowledge of the unknown parameters the channel estimate is formed by projecting a given user s spreading waveform into the estimated noise subspace and then either minimizing the likelihood or minimizing the euclidean norm of this projection both of these approaches yield algorithms which are near far resistant and do not require a preamble

subspace multiuser detection for multicarrier ds cdma a subspace based linear minimum mean squared error mmse multiuser detection scheme is proposed for a multicarrier direct sequence code division multiple access mc ds cdma system typically a mc ds cdma system employs a band limited chip waveform the band limited nature of the chip waveform causes problem in applying standard subspace techniques because no nonnull noise subspace can be formed it is shown that channel and timing information needed for the construction of the linear mmse detector can be identified by a multiple signal classification like algorithm based on a finite length truncation approximation of the chip waveform in practice since perturbed versions of the subspaces assumed in the finite length truncation approximation are actually observed and because of the band limited property of the chip waveform the accuracy of the channel estimation and hence the performance of the mmse detector are degraded this effect is investigated in this paper

averaging for diffusions with fine grained boundaries this article investigates the limiting behavior of a diffusion in a half space with a complicated boundary condition the boundary condition implements a reflection condition everywhere except a number of small sets or holes that meet dirichlet or mixed boundary conditions probabilistic methods associated with the feynman kac formula are used to find the limiting behavior of the diffusion equations as the number of holes gets large and the size of each hole is reduced with particular scaling homogenization occurs and we see that the complicated boundary condition is replaced by a simple mixed boundary condition depending on the capacitance and distribution of the holes

an updating algorithm for subspace tracking in certain signal processing applications it is required to compute the null space of a matrix whose rows are samples of a signal with p components the usual tool for doing this is the singular value decomposition however the singular value decomposition has the drawback that it requires o p sup 3 operations to recompute when a new sample arrives it is shown that a different decomposition called the urv decomposition is equally effective in exhibiting the null space and can be updated in o p sup 2 time the updating technique can be run on a linear array of p processors in o p time

the fermi golden rule and its form at thresholds in odd dimensions let h be a schrodinger operator on a hilbert space open image in new window such that zero is a nondegenerate threshold eigenvalue of h with eigenfunction 0 let w be a bounded selfadjoint operator satisfying 0 w 0 0 assume that the resolvent h z 1 has an asymptotic expansion around z 0 of the form typical for schrodinger operators on odd dimensional spaces let h h w for 0 and small we show under some additional assumptions that the eigenvalue at zero becomes a resonance for h in the time dependent sense introduced by a orth no analytic continuation is needed we show that the imaginary part of the resonance has a dependence on of the form 2 2 with the integer 1 and odd this shows how the fermi golden rule has to be modified in the case of perturbation of a threshold eigenvalue we give a number of explicit examples where we compute the location of the resonance to leading order in we also give results in the case where the eigenvalue is embedded in the continuum sharpening the existing ones

nonexponential decay laws in perturbation theory of near threshold eigenvalues we consider a two channel model of the form he hop00e0 e 0w12w210 on h hop c the operator hop is assumed to have the properties of a schrodinger operator in odd dimensions with a threshold at zero as the energy parameter e0 is tuned past the threshold we consider the survival probability 0 e ithe 0 2 where 0 is the eigenfunction corresponding to eigenvalue e0 for e 0 we find nonexponential decay laws for e small and e0 close to zero provided that the resolvent of hop is not at least lipschitz continuous at the threshold zero

spin dependent point potentials in one and three dimensions we consider a system realized with one spinless quantum particle and an array of n spins 1 2 in dimensions 1 and 3 we characterize all the hamiltonians obtained as point perturbations of assigned free dynamics in terms of some generalized boundary conditions for every boundary condition we give the explicit formula for the resolvent of the corresponding hamiltonian we discuss the problem of locality and give two examples of spin dependent point potentials that could be of interest as multi component solvable models

hyperelliptic theta functions and spectral methods a code for the numerical evaluation of hyperelliptic theta functions is presented characteristic quantities of the underlying riemann surface such as its periods are determined with the help of spectral methods the code is optimized for solutions of the ernst equation where the branch points of the riemann surface are parameterized by the physical coordinates an exploration of the whole parameter space of the solution is thus only possible with an efficient code the use of spectral approximations allows for an efficient calculation of all quantities in the solution with high precision the case of almost degenerate riemann surfaces is addressed tests of the numerics using identities for periods on the riemann surface and integral identities for the ernst potential and its derivatives are performed it is shown that an accuracy of the order of machine precision can be achieved these accurate solutions are used to provide boundary conditions for a code which solves the axisymmetric stationary einstein equations the resulting solution agrees with the theta functional solution to very high precision

perturbations of eigenvalues embedded at threshold two dimensional solvable models we consider a family of hamiltonians describing a quantum particle interacting via zero range forces with a localized spin in the plane a sub class of hamiltonians shows eigenvalues and or resonances at the threshold of the continuous spectrum and generates particle dynamics not affecting the localized spin we examine the effect of a small particle spin interaction on the spectral structure of such unperturbed hamiltonians

the probability of a subspace swap in the svd we extend the work of tufts kot and vaccaro tkv published in 1980 to improve the analytical characterization of threshold breakdown in svd methods our results sharpen the tkv results by lower bounding the probability of a subspace swap in the svd our key theoretical result is the characteristic function for a random variable whose probability of exceeding zero bounds the probability of a threshold breakdown

on the macroscopic description of slow viscous flow past a random array of spheres we give rigorous derivation of brinkman s equation as the effective equation for slow viscous flow in porous media with high porosity the medium is composed of spherical obstacles distributed randomly and the microscopic flow is described by the stokes equation along the road we givew21 convergence estimates for the point sources approximation

a law of large numbers and a central limit theorem for the schrodinger operator with zero range potentials we consider the schrodinger operator with zero range potentials onn points of three dimensional space independently chosen according to a common distributionv x under some assumptions we prove that whenn goes to infinity the sequence converges to a schrodinger operator with an effective potential the fluctuations around the limit operator are explicitly characterized

on an elaboration of m kac s theorem concerning eigenvalues of the laplacian in a region with randomly distributed small obstacles we removem balls of centersw 1 w m with the same radius m from a bounded domain inr 3 with smooth boundary let k m w m denote thek th eigenvalue of the laplacian in m balls under the dirichlet condition we consider k m w m as a random variable on a probability space w 1 w m and we examine a precise behaviour of k m w m asm we give an elaboration of m kac s theorem

blind equalization and multiuser detection in dispersive cdma channels the problem of blind demodulation of multiuser information symbols in a high rate code division multiple access cdma network in the presence of both multiple access interference mai and intersymbol interference isi is considered the dispersive cdma channel is first cast into a multiple input multiple output mimo signal model framework by applying the theory of blind mimo channel identification and equalization it is then shown that under certain conditions the multiuser information symbols can be recovered without any prior knowledge of the channel or the users signature waveforms including the desired user s signature waveform although the algorithmic complexity of such an approach is prohibitively high however in practice the signature waveform of the user of interest is always available at the receiver it is shown that by incorporating this knowledge the impulse response of each user s dispersive channel can be identified using a subspace method it is further shown that based on the identified signal subspace parameters and the channel response two linear detectors that are capable of suppressing both mai and isi i e a zero forcing detector and a minimum mean square error mmse detector can be constructed in closed form at almost no extra computational cost data detection can then be furnished by applying these linear detectors obtained blindly to the received signal the major contribution of this paper is the development of these subspace based blind techniques for joint suppression of mai and isi in the dispersive cdma channels

a general trotter kato formula for a class of evolution operators in this article we prove new results concerning the existence and various properties of an evolution system ua b t s 0 s t t generated by the sum a t b t of two linear time dependent and generally unbounded operators de ned on time dependent domains in a complex and separable banach space b in particular writing l b for the algebra of all linear bounded operators on b we can express ua b t s 0 s t t as the strong limit in l b of a product of the holomorphic contraction semigroups generated by a t and b t respectively thereby proving a product formula of the trotter kato type under very general conditions which allow the domain d a t b t to evolve with time provided there exists a fi xed set d incl t in 0 t d a t b t everywhere dense in b we obtain a special case of our formula when b t 0 which in effect allows us to reconstruct ua t s 0 s t t very simply in terms of the semigroup generated by a t we then illustrate our results by considering various examples of non autonomous parabolic initial boundary value problems including one related to the theory of time dependent singular perturba tions of self adjoint operators we nally mention what we think remains an open problem for the corresponding equations of schrodinger type in quantum mechanics

hydrodynamic friction and the capacitance of arbitrarily shaped objects the translational friction coefficient and the capacitance of a variety of objects are calculated with a probabilistic method involving hitting the probed objects with random walks launched from an enclosing spherical surface this method is applied to exactly solvable examples to test the program accuracy and to physically important and analytically intractable examples cube chain of spheres at the vertices of self avoiding and random walks etc large fluctuations in the friction of polymer chains with a random coil structure are found to give large deviations from the mean field kirkwood riseman theory and hydrodynamic fluctuation effects are found to diminish with the chain swelling accompanying excluded volume interaction capacity applications are reviewed and our probabilistic estimates of polymer friction are compared with previous calculations using alternative methods transients to the capacity and related properties are expressed in terms of fluctuations in the wiener sausage volume volume swept out by a brownian particle where a repeated visit to a spatial region does not contribute to the volume increase in time

blind identification of fir systems excited by discrete alphabet inputs an algorithm for the identification of finite impulse response fir system parameters from output measurements for systems excited by discrete alphabet inputs is described the approach taken is algebraic it does not rely directly on the statistical properties of the measurements but rather it essentially solves the nonlinear equations appearing in the problem by converting them to equivalent linear equations using the discrete alphabet property of the input signal the proposed algorithm was tested by computer simulations and some of these simulations are illustrated

on the existence of rotating stars in general relativity the newtonian equations of motion and newton s law of gravitation can be obtained by a limit lambda frac 1 c 2 to 0 of einstein s equations for a sufficiently small constant the existence of a set of solutions 0 of einstein s equations of a stationary axisymmetric star is proven this existence is proven in weighted sobolev spaces with the implicit function theorem since the value of the causality constant depends only on the units used to measure the velocity the existence of a solution for any small is physically interesting

mmse interference suppression for direct sequence spread spectrum cdma we consider interference suppression for direct sequence spread spectrum code division multiple access cdma systems using the minimum mean squared error mmse performance criterion the conventional matched filter receiver suffers from the near far problem and requires strict power control typically involving feedback from receiver to transmitter for acceptable performance multiuser detection schemes previously proposed mitigate the near far problem but are complex and require explicit knowledge or estimates of the interference parameters in this paper we present and analyze several new mmse interference suppression schemes which have the advantage of being near far resistant to varying degrees depending on their complexity and can be implemented adaptively when interference parameters are unknown and or time varying numerical results are provided that show that these schemes offer significant performance gains relative to the matched filter receiver we conclude that mmse detectors can alleviate the need for stringent power control in cdma systems and may be a practical alternative to the matched filter receiver

linear multiuser detectors for synchronous code division multiple access channels under the assumptions of symbol synchronous transmissions and white gaussian noise the authors analyze the detection mechanism at the receiver comparing different detectors by their bit error rates in the low background noise region and by their worst case behavior in a near far environment where the received energies of the users are not necessarily similar optimum multiuser detection achieves important performance gains over conventional single user detection at the expense of computational complexity that grows exponentially with the number of users it is shown that in the synchronous case the performance achieved by linear multiuser detectors is similar to that of optimum multiuser detection attention is focused on detectors whose linear memoryless transformation is a generalized inverse of the matrix of signature waveform crosscorrelations and on the optimum linear detector it is shown that the generalized inverse detectors exhibit the same degree of near far resistance as the optimum multiuser detectors the optimum linear detector is obtained

perturbation analysis of an svd based linear prediction method for estimating the frequencies of multiple sinusoids a linear prediction approach is studied for estimating the frequencies of sinusoids in white noise it is shown that in the first step the continuity of the generalized inverse and the concept of angle between subspaces play an important role the continuity concept helps explain the need for a low rank approximation and the quality of the approximation is appraised by using the notion of angle between subspaces for the second step the sensitivity of the zeros of the predictor polynomial becomes an important consideration and is examined it is shown that increasing the order of the predictor polynomial and computing the minimum norm solution provides a mechanism to reduce parameter sensitivity

perturbations of eigenvalues embedded at threshold i one and three dimensional solvable models we examine perturbations of eigenvalues and resonances for a class of multi channel quantum mechanical model hamiltonians describing a particle interacting with a localized spin in dimension d 1 3 we consider unperturbed hamiltonians showing eigenvalues and resonances at the threshold of the continuous spectrum and we analyze the effect of various types of perturbations on the spectral singularities we provide algorithms to obtain convergent series expansions for the coordinates of the singularities

coupling constant thresholds of perturbed periodic hamiltonians we consider schrodinger operators of the form h v w on l2 r 1 2 or 3 with v periodic w short range and a real non negative parameter then the continuous spectrum of h has the typical band structure consisting of intervals separated by gaps in the gaps there may be discrete eigenvalues of h that are functions of the parameter let a b be a gap and e a b an eigenvalue of h we study the asymptotic behavior of e as approaches a critical value 0 called a coupling constant threshold at which the eigenvalue either emerges from or is absorbed into the continuous spectrum a typical question is the following assuming e a as 0 is e a c 0 for some 0 and c 0 or is there an expansion in some other quantity as one expects from previous work in the case v 0 the answer strongly depends on

the laplacian in regions with many small obstacles fluctuations around the limit operator we consider the laplacian m in 3 or in a bounded region of 3 with dirichlet boundary conditions on the surfaces of some identical small neighborhoods ofm randomly distributed points in the limit whenm goes to infinity and their linear size decreases as 1 m we give here a stronger form of the result showing the convergence of the above operator to c x wherec x is the limit density of electrostatic capacity of the obstacles in particular results on the rate of convergence and on the fluctuations of m around the limit operator are given

on the dirichlet problem for stationary and axisymmetric einstein equations in suitable coordinates einstein s field equations for a rigidly rotating perfect fluid in equilibrium can be written as a semilinear system of purely elliptic partial differential equations of second order therefore the formulation of a boundary value problem is appropriate in this situation it is shown that the dirichlet problem for the vacuum region outside a ball and for a ball inside the matter region has a unique regular solution if the boundary data are in a characteristic way limited by the diameter of the ball this restriction seems to be closely connected with stability limits for rotating stars furthermore the used mathematical methods are directly related to a numerical solution technique for such physical systems

blind multiuser detection a subspace approach a new multiuser detection scheme based on signal subspace estimation is proposed it is shown that under this scheme both the decorrelating detector and the linear minimum mean square error mmse detector can be obtained blindly i e they can be estimated from the received signal with the prior knowledge of only the signature waveform and timing of the user of interest the consistency and asymptotic variance of the estimates of the two linear detectors are examined a blind adaptive implementation based on a signal subspace tracking algorithm is also developed it is seen that compared with the previous minimum output energy blind adaptive multiuser detector the proposed subspace based blind adaptive detector offers lower computational complexity better performance and robustness against signature waveform mismatch two extensions are made within the framework of signal subspace estimation first a blind adaptive method is developed for estimating the effective user signature waveform in the multipath channel secondly a multiuser detection scheme using spatial diversity in the form of an antenna array is considered a blind adaptive technique for estimating the array response for diversity combining is proposed it is seen that under the proposed subspace approach blind adaptive channel estimation and blind adaptive array response estimation can be integrated with blind adaptive multiuser detection with little attendant increase in complexity

random media and eigenvalues of the laplacian let be a fixed number 1 we remove m balls of centersw1 w m beta with the same radius m from a bounded domain inr3 we consider the asymptotic behaviour of thekth eigenvalue of the laplacian in omega backslash overline m beta balls under the dirichlet condition as a random variable on a probability space w 1 w m beta in omega m beta whenm

a limit evolution problem for time dependent point interactions abstract we study the diffusion in r 3 of a particle interacting with n fixed points through point interactions whose strength varies in time under mild assumptions on the time dependence of the strengths we prove existence for all times and uniqueness of the solution for which we provide a rather explicit expression we also prove that under a suitable rescaling of the interaction strengths the solution converges when n to the solution of a diffusion equation with a regular killing term potential we use properties of the local self adjoint extensions of the laplacian and results from the theory of fractional integrals and derivatives

puiseux series expansion for an eigenvalue of the generalized friedrichs model with perturbation of rank 1 a family h p 0 of the generalized friedrichs model with perturbation of rank 1 associated with a system of two particles moving on the one dimensional lattice is considered the existence of a unique eigenvalue e p of the operator h p lying below the essential spectrum is proved for any p from a neighborhood of the origin the puiseux series expansion for eigenvalue e p at the point p 0 is found moreover the asymptotics for e p is established as

analysis of asynchronous long code multicarrier cdma systems with correlated fading the effects of inter carrier interference ici and aperiodic random spreading sequences on the performance of asynchronous multicarrier code division multiple access cdma systems with correlated fading between sub carriers are investigated in this research to conduct theoretical analysis for the maximal ratio combining mrc receiver random parameters including asynchronous delays correlated rayleigh fading and spreading sequences are averaged to find the unconditional covariance matrix of the interference plus noise vector we demonstrate that the ici in the system proposed by kondo and milstein 1996 can be mitigated by assigning a common random spreading sequence over all sub carriers for each user rather than using a set of distinct spreading sequences where code sequences are assumed perfectly time synchronized moreover the analytic expression for the bit error probability bep can be obtained with the gaussian approximation simulation results are used to demonstrate the accuracy of our analysis various design tradeoffs including the number of sub carriers fading correlations ici and multipath effect are presented in simulation we conclude that when properly choosing a sufficiently large number of sub carriers the benefit of mitigating multipath interference and exploiting potential hidden frequency diversity shall prevail the impairment brought by increased ici

on first order corrections to the lsw theory ii finite systems we consider first order corrections to the classical theory by lifshitz slyozov and wagner lsw for systems with a finite number of particles numerical simulations in v e fradkov etal phys rev e 53 3925 3932 1996 show a cross over in the scaling of the correction term from 1 3 to 1 2 is the volume fraction of particles when the system size becomes larger than the screening length we rigorously derive this cross over for the rate of change of the energy starting from the monopole approximation the proof exploits the fact that the rate of change of energy has a variational characterization

a unified approach to eigenvalues and resonances of schrodinger operators using fredholm determinants we study in detail the threshold behaviour of eigenvalues and resonances of the schrodinger operator h v in l2 r3 as they are absorbed at the bottom of the continuous spectrum when 0 0 a so called coupling constant threshold using fredholm determinants we give their analytic structure in terms of 0 and compute the first order terms explicitly

on existence and behaviour of asymptotically flat solutions to the stationary einstein equations we show existence and uniqueness of asymptotically flat solutions to the stationary einstein equations ins 3 b r whereb r is a ball of radiousr 0 when a small enough continuous complex function u on s is given regularity and decay estimates imply that these solutions are analytic in the interior ofs and also at infinity when suitably conformally rescaled

fast subspace decomposition many recent signal processing techniques in various areas e g array signal processing system identification and spectrum estimation require a step of extracting the low dimensional subspace from a large space this step is usually called subspace decomposition which is conventionally accomplished by an eigendecomposition ed since an ed requires o m sup 3 flops for an m spl times m matrix it may represent a barrier to the real time implementation of these algorithms the authors present a fast algorithm for signal subspace decomposition which is termed fsd that exploits the special matrix structure low rank plus identity associated with signal subspace algorithms and requires only o m sup 2 d flops where d often spl lt m denotes the signal subspace dimension unlike most of alternatives the dimension of the signal subspace is not assumed known apriori and is estimated as part of the procedure moreover theoretical analysis has been conducted and its results show the strong consistency of the new detection scheme and the asymptotic equivalence between fsd and ed in estimating the signal subspace their new approach can also exploit other matrix structure common in signal processing areas e g toeplitz or hankel and thus achieve another order of computational reduction moreover it can be easily implemented in parallel to reduce further the computation time to as little as o md using o m simple processors

joint timing and channel estimation for bandlimited long code based mc ds cdma a low complexity near optimal algorithm and the crlb joint timing and channel estimation jtce for bandlimited long code aided multi carrier direct sequence code division multiple access mc ds cdma systems is investigated we establish the optimal multiuser timing and channel estimates for the uplink mc ds cdma receiver by minimising a weighted least squares cost function with respect to k independent parameters where k is the number of active users a guided random search procedure known as repeated weighted boosting search rwbs is invoked for numerically solving this challenging multivariate optimisation problem and thereby for producing near optimal timing and channel estimates the cramer rao lower bound crlb for the jtce problem of interest is derived to benchmark the performance of the proposed rwbs based estimator quantitatively for the scenario of k 10 users e b n 0 3 db where e b is the energy per bit and n 0 the single sided noise power spectral density and for a near far ratio of 10 db the rwbs based estimator using an observation window of 20 symbols is shown to approach the crlb at a complexity 10 orders of magnitude lower in comparison to its full maximum likelihood search based counterpart the proposed algorithm does not require the transmission of known pilots yet it is capable of handling time variant channel states