spectrally accurate contour dynamics we present an exponentially accurate boundary integral method for calculating the equilibria and dynamics of piece wise constant distributions of potential vorticity the method represents contours of potential vorticity as a spectral sum and solves the biot savart equation for the velocity by spectrally evaluating a desingularized contour integral we use the technique in both an initial value code and a newton continuation method our methods are tested by comparing the numerical solutions with known analytic results and it is shown that for the same amount of computational work our spectral methods are more accurate than other contour dynamics methods currently in use

regularization of contour dynamical algorithms i tangential regularization abstract contour dynamical methods are being applied to a variety of inviscid incompressible flows in two dimensions these generalizations of the waterbag method provide simplified models for following the evolution of contours x j that separate regions of constant density which are the sources of the flow the inviscid evolution of contour j x t j is usually an area preserving map for physically unstable problems a piecewise constant initial condition may result in an ill posed problem that is contours may rapidly grow in perimeter and or develop singularities and numerically induced small scale structures in a finite time to avoid such problems and model realistic weakly dissipative or weakly dispersive flows contour regularization procedures are required dissipative and dispersive tangential regularization procedures for one contour are introduced a special case of the former namely t x ss corresponds in lowest order to a linear diffusion operator in two dimensions the contour is parameterized with arc length using cubic splines and an adaptive curvature controlled node adjustment algorithm is used a modified crank nicolson method is used to solve the discrete representation of the full system x t x t x ss numerical results are given for the evolution of initially elliptical shapes according to prescribed area preserving maps the numerical results for area evolution agree with analytical results

a fourier based method for approximating the joint detection probability in mimo communications we propose a numerically efficient technique to approximate the joint detection probability of a coherent multiple input multiple output mimo receiver in the presence of inter symbol interference isi and additive white gaussian noise awgn this technique approximates the probability of detection by numerically integrating the product of the characteristic function cf of the received filtered signal with the fourier transform of the multi dimension decision region naturally the accuracy of the approximation is dependent on the number of points in the numerical integration the proposed method selects the number of points to integrate over by deriving bounds on the approximation error as such a reduction of up to 1 100th of the number points can be achieved when comparing with existing single input single output siso techniques simulation results demonstrate that the proposed method is highly accurate with the calculated errors being well within the bounded approximation error in addition the results are closely matched with those obtained using the monte carlo simulations with a typical error less than 10 4 while requiring only a fraction of the computation time

error rate evaluation of linear equalization and decision feedback equalization with error propagation we propose applying an approximate fourier series to evaluate efficiently the bit error rate ber performance of finite length linear equalization le and decision feedback equalization dfe by extending the fourier series we enable ber calculations for quadrature phase shift keying qpsk transmission on complex channels with in phase and crosstalk intersymbol interference isi the ber calculation is based on determining the residual isi samples and background gaussian noise variance at the equalizer output for static channels or for realizations of quasi static fading channels a simple bound on the series error magnitude in terms of the fourier series parameters ensures the required accuracy and precision improved state transition probability estimates are derived and verified by simulation for an approximate markov model of the dfe error propagation for the case in which residual isi exists even when the previous decisions stored in the feedback filter fbf are correct we demonstrate the ease and widespread applicability of our approach by producing results which elucidate a variety of equalization tradeoffs our analysis includes symbol spaced and fractionally spaced minimum mean square error mmse le zero forcing zf le and mmse dfe with and without error propagation on static isi channels and multipath channels with quasi static rayleigh fading a comparison between suboptimum and optimum receiver filtering in conjunction with equalization and an assessment of the accuracy of some widely used equalization ber approximations and bounds

contour surgery a topological reconnection scheme for extended integrations using contour dynamics abstract a numerical algorithm is described which it is believed can accurately model the dynamics of a two dimensional inviscid incompressible fluid with unparalled spatial resolution the fluid is assumed however to be divided into regions of uniform vorticity conservation of vorticity ensuring that this remains true for all time like contour dynamics the algorithm is concerned with following the evolution of the boundaries of vorticity discontinuity contours unlike contour dynamics the algorithm automatically removes vorticity features smaller than a predefined scale for example two contours enclosing the same uniform vorticity merge into one if they are close enough together also the curvature along a contour is not allowed to exceed the inverse of the cutoff scale at present calculations with contour surgery resolve fluid motions extending over four to five orders of magnitude of scales 13 to 20 octaves such high resolution pictures of two dimensional vortex dynamics have been facilitated by and indeed depend critically upon a nonlocal adaptive node adjustment scheme and a variety of tests quantify the accuracy of the technique

a fast adaptive vortex method for patches of constant vorticity in two dimensions abstract we present a fast numerical method for solving the incompressible euler s equation in two dimensions for the special case when the flow field can be represented by patches of constant vorticity the method is an adaptive vortex method in which cells vortex blobs of multiple scales are used to represent the patches so that the number of vortex blobs needed to approximate the patches is proportional to the length of the boundary curve of the patch and inversely proportional to the width of the smallest blob cell used points along the boundaries of the patches are advected according to the velocity obtained from the approximating vortices

contour dynamics for the euler equations curvature controlled initial node placement and accuracy abstract we have performed a systematic study of several contour dynamical algorithms for the euler equations for short times we have used the kirchhoff elliptical vortex alone and subject to weak perturbations we have found that if the initial placement of nodes is such that the internodal distance is proportional to curvature p where p 1 3 then errors in short time calculations are minimized this follows because the node density is invariant in time

high accuracy finite element methods for positive symmetric systems abstract a nonstandard type least squares finite element method is proposed for the solution of first order positive symmetric systems this method gives optimal accuracy in a norm similar to the h1 norm when a regularity condition holds it is optimal in l2 as well otherwise it gives errors suboptimal by only h 1 2 where h is the mesh diameter thus it has greater accuracy than usual finite element finite difference or least squares methods for such problems in addition the spectral condition number of the associated linear system is only o h 1 vs o h 2 for the usual least squares methods thus the method promises to be an efficient high accuracy method for hyperbolic systems such as maxwell s equations it is also equally promising for mixed type equations that have a formulation as a positive symmetric system

least squares methods for mixed type equations a least squares method for the numerical solution of a class of second order mixed type partial differential equations is analyzed the method offers a unified computational treatment of both elliptic and hyperbolic parts of a given domain moreover it has the advantage over other methods that its implementation is independent of specific properties of a given problem convergence of the approximation is proved in a natural norm assuming smooth solutions a particular least squares method is implemented using bicubic spline polynomials and numerical results for test problems are presented

a unified analysis of a weighted least squares method for first order systems a unified analysis of a weighted least squares finite element method wlsfem for approximating solutions of a large class of first order differential systems is proposed the method exhibits several advantageous features for example the trial and test functions are not required to satisfy the boundary conditions its discretization results in symmetric and positive definite algebraic systems with condition number o h 2 w 2 and a single piecewise polynomial finite element space may be used for all test and trial functions asymptotic convergence of the least squares approximations with suitable weights is established in a natural norm without requiring extra smoothness of the solutions if instead the solutions are sufficiently regular a priori error estimates can be derived under two suitable assumptions which are related respectively to the symmetric positive systems of friedrichs and first order agmon douglis nirenberg adn elliptic systems numerous model problems fit into these two important systems some selective examples are examined and verified in the unified framework

modified chernoff bounds for pam systems with noise and interference corresp by using principles of analytic continuation upper and lower bounds on the error probability of a canonical binary system corrupted by additive interference and independent zero mean gaussian noise are derived the bounds which are simple functions require only the evaluation or bounding of the moment generating function of the interference for large signal to noise ratios snr and even for moderately large interference the bounds are shown to be tight and useful

efficient computation of erfc x for large arguments a new infinite series representation for the error function is developed it is especially suitable for computing erfc x for large x for instance for any x spl ges 4 the error function can be evaluated with a relative error less than 10 sup 10 by using only eight terms similarly the error function can be evaluated with a relative error less than 8 spl times 10 sup 7 for any x spl ges 2 using just six terms an analytical bound is derived to show that the total error due to series truncation and undersampling rapidly decreases as x increases comparisons with two other series are provided

a gram charlier series method for calculating general signal constellation error probabilities we develop a method for calculating the probability of symbol error via a multivariate gram charlier series for arbitrary coherent modulation schemes with statistically independent source symbols and subject to intersymbol interference isi and additive white gaussian noise awgn the resulting error probability approximations have closed form solutions and yield very accurate results with very little computational expense

steady state solutions of the euler equations in two dimensions rotating and translating v states with limiting cases i numerical algorithms and results new second and third order algorithms are presented for calculating translating and rotating steady state solutions of the 2d incompressible euler equations which we call v states these are piecewise constant regions of vorticity and the contours bounding them are obtained by solving iteratively a nonlinear integro differential equation new limiting contours with corners are obtained and compared with local analytical solutions the precise results correct mistakes for limiting contours that were previously given

a galerkin method for elliptic hyperbolic type equations a certain galerkin type method is proposed for the numerical solution of a class of second order linear mixed type partial differential equations convergence of such an approximation is proved in the whole region of definition error estimates are derived in a natural norm assuming smooth solutions numerical experiments are conducted using bicubic splines the obtained results show that solutions are approximated equally well in both elliptic and hyperbolic regions

comparison of cp based single carrier and ofdm with power allocation existing performance comparisons of single carrier sc and multicarrier transmission are mainly based on simulations in this letter we present a framework to compare the performance of cyclic prefix cp based sc block transmission and orthogonal frequency division multiplexing ofdm in frequency selective fading channels minimum mean squared error equal gain and approximate minimum bit error rate power allocation schemes for cp ofdm are considered performance of these methods is compared analytically and verified by simulations

analytical distribution of linearly modulated cochannel interferers the closed form expressions of the probability density function pdf the cumulative distribution function cdf and the characteristic function of the disturbance due to a multilevel cochannel interferer are obtained the analysis assumes l level amplitude shift keying l ask modulated signals nonreturn to zero nrz pulses transmission over a distortion free channel and matched filter reception the distribution for the multiple cochannel interferers case can then be obtained by means of the characteristic function method as an application example the closed form expression of the error floor for an l ask system in the presence of one cochannel interferer is given the comparison with respect to the gaussian approximation is also discussed

probability of error calculation of ofdm systems with frequency offset orthogonal frequency division multiplexing ofdm is sensitive to the carrier frequency offset cfo which destroys orthogonality and causes intercarrier interference ici previously two methods were available for the analysis of the resultant degradation in performance firstly the statistical average of the ici could be used as a performance measure secondly the bit error rate ber caused by cfo could be approximated by assuming the ici to be gaussian however a more precise analysis of the performance i e ber or ser degradation is desirable in this letter we propose a precise numerical technique for calculating the effect of the cfo on the ber or symbol error in an ofdm system the subcarriers can be modulated with binary phase shift keying bpsk quaternary phase shift keying qpsk or 16 ary quadrature amplitude modulation 16 qam used in many ofdm applications the bpsk case is solved using a series due to beaulieu 1990 for the qpsk and 16 qam cases we use an infinite series expression for the error function in order to express the average probability of error in terms of the two dimensional characteristic function of the ici

the evaluation of error probabilities for intersymbol and cochannel interference an efficient series that can be used to calculate the probability of error in a binary symmetric channel with intersymbol interference and additive noise is derived the series is derived by representing the noise complementary probability distribution function by an exact or approximate fourier series bounds on the accuracy of the estimate are derived for gaussian noise examples show that only a small numerical effort may be required to compute error probabilities of interest using the series applications to both finite and infinite intersymbol interference systems are discussed a similar technique is used to derive series representations for the probability of error of additive noise channels with cochannel interference or with combined intersymbol and cochannel interferences the accuracy of the results is bounded for gaussian noise

calculating error probabilities for intersymbol and cochannel interference the probability of error in a binary symmetric channel with intersymbol interference and additive noise is efficiently calculated by numerical quadrature of a laplace inversion integral along a contour in the complex plane passing through a saddlepoint of the integrand for gaussian noise a bound is set on the truncation error incurred by necessarily restricting the integration to a finite interval the probability of error resulting from cochannel interference is calculated by a similar technique

further results on the beaulieu series a frequent problem in digital communications is the computation of the probability density function pdf and cumulative distribution function cdf given the characteristic function chf of a random variable rv this problem arises in signal detection equalizer performance equal gain diversity combining intersymbol interference and elsewhere often it is impossible to analytically invert the chf to get the pdf and cdf in closed form beaulieu 1990 1991 has derived an infinite series for the cdf of a sum of rvs that has been widely used we rederive his series using the gil pelaez 1951 inversion formula and the poisson sum formula this derivation has several advantages including both the bridging of the well known sampling theorem with beaulieu s series and yielding a simple expression for calculating the truncation error term it is also shown that the pdf and cdf can be computed directly using a discrete fourier transform

a simple and accurate method of probability of bit error analysis for asynchronous band limited ds cdma systems this paper considers probability of bit error p sub e analysis in asynchronous band limited direct sequence code division multiple access ds cdma systems it presents a simple and accurate method of p sub e analysis the proposed method can serve as an attractive alternative to the only two techniques currently available for band limited systems the standard gaussian approximation sga and the characteristic function method the former is prone to inaccuracy while the latter large computational complexity the method generalizes the simplified improved gaussian approximation siga derived previously for rectangular pulses this paper also outlines a generalization of another method referred to as the improved gaussian approximation iga numerical examples demonstrate the far greater accuracy of the generalized siga with respect to the sga the examples consider the is 95 and square root raised cosine sqrt rc pulses as well as uniform and nonuniform received power conditions

a simple adaptive technique for nonlinear wave problems abstract a method for the numerical integration of the nonlinear schrodinger equation is derived which uses variable time steps and a moving spatial grid the benefits of adaptation are clearly demonstrated in the numerical experiments reported the simple technique employed to move the nodes can be applied with little coding effort to general one dimensional systems of pdes

exact a posteriori error analysis of the least squares finite element method1this work was supported by nsc under grant nsc87 2115 m 009 005 taiwan 1 a residual type a posteriori error estimator is presented for the least squares finite element method the estimator is proved to equal the exact error in a norm induced by some least squares functional the error indicator of each element is equal to the exact error norm restricted to the element as well in other words the estimator is perfectly effective and reliable for error control and for adaptive mesh refinement the exactness property requires virtually no assumptions on the regularity of the solution and on the finite element order in the approximation or in the estimation the least squares method is in a very general setting that applies to various linear boundary value problems such as the elliptic systems of first order and of even order and the mixed type partial differential equations numerical results are given to demonstrate the exactness