bit error rate of binary and quaternary dpsk signals with multiple differential feedback detection a differentially coherent detection scheme with improved bit error rate ber performance is presented for differentially encoded binary and quaternary phase shift keying psk modulation the improvement is based on using l symbol detectors with delays of 1 2 l symbol periods and on feeding back detected psk symbols exact formulas for the bit error probability are derived for the case that correct symbols are fed back the effect of symbol errors in the feedback path on the ber is determined by computer simulations

enhanced multiple bit differential detection of doqpsk in this paper we consider multiple bit differential detection mbdd of differential offset quadrature phase shift keying doqpsk with conventional bit wise differential encoding de we propose two novel mbdd schemes that outperform simon s mbdd and approach the performance of coherent detection cd as the observation window size n increases the first scheme uses the full available detection window spanning n 1 bit intervals and is referred to as f mbdd a careful bit error rate ber analysis shows that a significant performance improvement can be realized by reducing the detection window size to n 3 bit intervals the resulting improved mbdd i mbdd of doqpsk with bit wise de achieves a similar performance as phoel s mbdd of doqpsk with more complex symbol wise de for both f mbdd and i mbdd tight upper bounds and accurate ber approximations are derived in addition since the complexity per bit decision of brute force decoding of mbdd of doqpsk grows exponentially with n we develop optimum and suboptimum fast decoding algorithms with complexities per bit decision of orders log n 1 and n respectively

multiple symbol differential detection with diversity reception in this letter we first consider the maximum likelihood sequence estimator for multiple symbol differential detection msdd over the slow fading diversity channel since this optimum decision metric results in a complex receiver implementation whose average bit error probability bep performance is difficult if not impossible to obtain analytically we then focus our attention on evaluating the average bep for msdd with diversity reception in the form of postdetection equal gain combining egc giving emphasis to its ability to bridge the gap between egc of conventional differentially detected m psk and maximal ratio combining of coherently detected m psk with differential encoding

multiple bit differential detection of offset qpsk analogous to multiple symbol differential detection of quadrature phase shift keying qpsk a multiple bit differential detection scheme is described for offset qpsk that also exhibits continuous improvement in performance with increasing observation interval being derived from maximum likelihood considerations together with the representation of differentially encoded offset qpsk as a continuous phase modulation the proposed scheme is purported to be the most power efficient scheme for such a modulation and detection method

maximum likelihood block detection of noncoherent continuous phase modulation the authors examine maximum likelihood block detection of uncoded full response continuous phase modulation cpm over an additive white gaussian noise awgn channel both the maximum likelihood metrics and the bit error probability performances of the associated detection algorithms are considered the special and popular case of minimum shift keying msk corresponding to h 0 5 and constant amplitude frequency pulse is treated separately the many new receiver structures that result from this investigation can be compared to the traditional ones that have been used in the past both from the standpoint of simplicity of implementation and optimality of performance

the phase of a vector perturbed by gaussian noise and differentially coherent receivers some results are presented regarding the asymptotic distribution of the phase of a vector perturbed by gaussian noise it is shown that for large signal to noise ratio the asymptotic distribution of the phase is of the tikhonov type this framework is then used for the synthesis of differentially coherent receiver structures one for m ary phase shift keying mpsk and the other for minimum shift keying msk the first structure bridges the performance gap between coherent and differentially coherent demodulation of mpsk the msk receiver uses matched filtering with differential demodulation

symbol timing recovery for cpm with correlated data symbols we consider symbol timing recovery for continuous phase modulations cpms with correlated data symbols a popular example of such a scheme is shaped offset quadrature phase shift keying soqpsk we propose an extension to an existing non data aided blind timing error detector ted to make it compatible with such modulation schemes the merits of the modified ted are demonstrated by comparing its performance with and without taking the data correlation into account as a further modification we show that a quantization scheme can be used to yield an extremely low complexity version of the system with only negligible performance losses the s curve of the proposed quantized ted is given which rules out the existence of false lock points the proposed scheme shows great promise in a wide range of applications due to its low complexity its lack of false lock points and its blind nature such applications include timing recovery for noncoherent detection schemes and false lock detectors

separation of variables and exact solutions to quasilinear diffusion equations with nonlinear source abstract a solution of a partial differential equation with two real variables t and x is functionally separable in these variables if q u x t for some single variable functions q and in this paper the generalized conditional symmetry approach is used to study the separation of variables of quasilinear diffusion equations with nonlinear source we obtain a complete list of canonical forms for such equations which admit the functionally separable solutions as a result we get broad families of exact solutions to some quasilinear diffusion equations with nonlinear source the behavior and blow up properties of some solutions are described

extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics an extension of the piecewise parabolic method to treat multidimensional ideal magnetohydrodynamical equations is presented in this paper the multidimensional scheme is constructed from a one dimensional functioning code based on the dimensional splitting method originally suggested by strang the functioning code is built upon a nonlinear riemann solver for ideal mhd equations recently developed by the authors the correctness of the scheme is tested in the steepening of waves in both one and two dimensional situations and in various mhd shock tube problems which involve all the discontinuities in ideal mhd the robust character of the scheme is demonstrated in the shock tube problems and in the interaction between mhd shocks and a cloud the results of these problems show that the scheme keeps the principal advantages of a high order godunov scheme robust operation in the presence of very strong waves thin shock fronts with little attendant noise generation and thin contact discontinuity

multiple bit differential detection of shaped offset qpsk we consider multiple bit differential detection mbdd of differentially encoded shaped offset quadrature phase shift keying soqpsk a highly bandwidth efficient and popular constant envelope modulation we propose two mbdd schemes that are based on a recent continuous phase modulation interpretation of soqpsk we show that the performance of these mbdd schemes approaches that of coherent detection cd as the multiple bit observation n window increases the first scheme uses a detection window that spans the full bit observation window f mbdd and is shown to require very large values of n to approach the performance of cd this presents a practical problem since the complexity of mbdd grows exponentially with n the second scheme is an improved version i mbdd with a detection window that is shortened to n 2 bit intervals although the complexity of i mbdd also increases exponentially with n it represents a significant improvement since only modest values of n are needed for high performance these performance characteristics are identified via a detailed performance analysis which provides asymptotic formulas for the bit error probability that are confirmed with computer simulations the analysis is also used to find the symmetric frequency pulse shapes with the best and worst error performance finally we develop a simplified and practical decision feedback differential detection algorithm that achieves near optimal performance with complexity that grows only linearly with n

multiple symbol differential detection of mpsk a differential detection technique for mpsk multiple phase shift keying which uses a multiple symbol observation interval is presented and its performance is analyzed and simulated the technique makes use of maximum likelihood sequence estimation of the transmitted phases rather than symbol by symbol detection as in the conventional differential detection thus the performance of this multiple symbol detection scheme fills the gap between conventional two symbol observation differentially coherent detection of mpsk and ideal coherent of mpsk with differential encoding the amount of improvement gained over conventional differential detection depends on the number of phases m and the number of additional symbol intervals added to the observation what is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation the analysis and simulation results presented are for uncoded mpsk

pulse shaping for differential offset qpsk pulse shaping is examined as a means to improve the performance of a differential offset quadrature phase shift keying system in a bandwidth constrained environment through optimization with respect to a composite nyquist criterion the derived pulse shapes have comparable performance to a pi 4 differential quadrature phase shift keying in an additive white gaussian noise awgn channel and better performance in a hard limited awgn channel

staggered mixed finite volume finite element method for the navier stokes equations to solve flow problems associated with the navier stokes equations we construct a mixed finite volume finite element method for the spatial approximation of the convective and diffusive parts of the flux respectively the finite volume component of the method is adapted from the authors construction for hyperbolic conservation laws and rectangular or unstructured triangular grids of two dimensional finite volume extensions of the lax friedrichs and nessyahu tadmor central difference schemes in which the resolution of riemann problems at cell interfaces is bypassed thanks to the use of the lax friedrichs scheme on two specific staggered grids muscl type piecewise linear cell interpolants slope limiters and a two step predictor corrector time discretization lead to an oscillation free quasi second order resolution for the viscous terms we use a centered finite element approximation inspired by rostand stoufflet to improve the quality of the resolution we use a grid adaptation algorithm proposed by castro diaz and hecht

motion of level sets by mean curvature i we continue our investigation of the level set technique for describing the generalized evolution of hypersurfaces moving according to their mean curvature the principal assertion of this paper is a kind of reconciliation with the geometric measure theoretic approach pioneered by k brakke we prove that almost every level set of the solution to the mean curvature evolution pde is in fact aunit density varifold moving according to its mean curvature in particular a e level set is endowed with a kind of geometric structure the proof utilizes compensated compactness methods to pass to limits in various geometric expressions

central finite volume schemes with constrained transport divergence treatment for three dimensional ideal mhd we present three dimensional central finite volume methods for solving systems of hyperbolic equations based on the lax friedrichs and nessyahu tadmor one dimensional central finite difference schemes the numerical methods we propose involve an original and a staggered grid in order to avoid the resolution of the riemann problems at the cell interfaces the cells of the original grid are cartesian cubes with faces parallel to the axes while those of the staggered grid are either cartesian or diamond shaped we apply these methods and solve some ideal magnetohydrodynamics problems to satisfy the solenoidal property of the magnetic field in the numerical solution we present an adaptation of evans and hawley s constrained transport method for central schemes which we call ctcs the ctcs method is easy to implement it deals directly with the computed solution and does not require any additional staggering for the magnetic field components furthermore it preserves the second order accuracy of the base scheme even without the application of the ctcs procedure our numerical base schemes do not break down and may even in some cases deliver reasonable results the diamond dual cell scheme has a slight advantage for shocks and contact discontinuities our numerical results are in good agreement with corresponding results appearing in the recent literature

the zero set of a solution of a parabolic equation on etudie l ensemble nul d une solution u t x de l equation u t a x t u xx b x t u x c x t u sous des hypotheses tres generales sur les coefficients a b et c

shock capturing approach and nonevolutionary solutions in magnetohydrodynamics shock capturing methods have become an effective tool for the solution of hyperbolic partial differential equations both upwind and symmetric tvd schemes in the framework of the shock capturing approach are thoroughly investigated and applied with great success to a number of complicated multidimensional gasdynamic problems the extension of these schemes to magnetohydrodynamic mhd equations is not a simple task first the exact solution of the mhd riemann problem is too multivariant to be used in regular calculations on the other hand the extensions of roe s approximate riemann problem solvers for mhd equations in general case are nonunique and need further investigation that is why some simplified approaches should be constructed in this work the second order of accuracy in time and space high resolution lax friedrichs type scheme is suggested that gives a drastic simplification of the numerical algorithm comparing to the precise characteristic splitting of jacobian matrices the necessity is shown to solve the full set of mhd equations for modeling of multishocked flows even when the problem is axisymmetric to obtain evolutionary solutions for the numerical example the mhd riemann problem is used with the initial data consisting of two constant states lying to the right and to the left from the centerline of the computational domain if the problem is solved as purely coplanar a slow compound wave appears in the self similar solution obtained by any shock capturing scheme if the full set of mhd equations is used and a small uniform tangential disturbance is added to the magnetic field vector a rotational jump splits from the compound wave and it degrades into a slow shock the reconstruction process of the nonevolutionary compound wave into evolutionary shocks is investigated presented results should be taken into account in the development of shock capturing methods for mhd flows

the heat equation shrinking convex plane curves soient m et m des varietes de riemann et f m m une application reguliere si m est une courbe convexe plongee dans le plan r 2 l equation de la chaleur contracte m a un point

comparison of some flux corrected transport and total variation diminishing numerical schemes for hydrodynamic and magnetohydrodynamic problems two versions of flux corrected transport and two versions of total variation diminishing schemes are tested for several one and two dimensional hydrodynamic and magnetohydrodynamic problems two of the schemes ydfct and tvdlf are tested extensively for the first time the results give an insight into the limitations of the methods their relative strengths and weaknesses some subtle points of the algorithms and the effects of selecting different options for certain methods are emphasised

on the error probability of decision feedback differential detection we give a tight approximation for the bit error rate ber of decision feedback differential detection df dd the influence of error propagation is modeled by a markov chain a simple state reduction method is proposed to limit computational complexity our results show that error propagation strongly depends on the chosen feedback filter in particular the popular assumption that error propagation increases ber by a factor of two is not always justified

adaptive linear equalization combined with noncoherent detection for mdpsk signals a novel noncoherent receiver for m ary differential phase shift keying signals transmitted over intersymbol interference channels is presented the noncoherent receiver consists of a linear equalizer and a decision feedback differential detector a significant performance gain over a previously proposed noncoherent receiver can be observed for an infinite number of feedback symbols the optimum equalizer coefficients can be calculated analytically and the performance of the proposed receiver approaches that of a coherent linear minimum mean squared error equalizer moreover a modified least mean square and a modified recursive least squares algorithm for adaptation of the equalizer coefficients are discussed

central finite volume methods with constrained transport divergence treatment for ideal mhd two and three dimensional finite volume extensions of the lax friedrichs lf and nessyahu tadmor one dimensional difference schemes were previously presented and successfully applied to several problems for nonlinear hyperbolic systems and in particular to typical test cases for both inviscid and viscous compressible flows these central schemes by pass the resolution at the cell interfaces of the riemann problems thanks to the use of the staggered lf scheme which serves as the base scheme on which high order finite volume methods can be constructed using van leer s muscl type limited reconstruction principle for this purpose two dual grids are used at alternate time steps these methods are extended here to several problems in one and multi dimensional ideal compressible magnetohydrodynamics using a modified version of the first author s central methods with oblique diamond shaped dual cells in two dimensions the system has eight equations and solving the corresponding riemann problem is an elaborate and time consuming process central methods lead to significant computing time reductions and the numerical experiments presented here suggest the accuracy is quite satisfactory in order to satisfy the physical constraint b 0 we have constructed a strategy ctcs inspired from the constrained transport method of evans and hawley the validity of our base scheme and our ctcs approach is clearly confirmed by the results