exact ber analysis of ostbcs in spatially correlated mimo channels the bit error rate ber performance of orthogonal space time block codes stbcs in correlated multiple input multiple output mimo channels is studied we first derive closed form exact ber equations for pulse amplitude modulation quadrature amplitude modulation and phase shift keying constellations in a correlated rayleigh mimo channel the ber expressions can be easily evaluated without any numerical methods then we consider correlated mimo channels where the line of sight components exist and they suffer from shadowing namely correlated shadowed rician mimo channels for three practical channel scenarios the ber is analyzed and closed form ber equations are presented

m psk and m qam ber computation using signal space concepts in this paper we introduce a simple geometric approach that is based on signal space concepts to efficiently evaluate the performance of m ary phase shift keying m psk and m ary quadrature amplitude modulation m qam schemes over an additive white gaussian noise channel in particular new bit error rate approximations are derived and shown to be in excellent agreement with monte carlo simulation results

optimal detection of digital data over the nonselective rayleigh fading channel with diversity reception based on the criterion of minimum symbol error probability an analysis is made of symbol by symbol detection of a sequence of digital data transmitted using linear suppressed carrier modulation over l independent diversity channels with awgn additive white gaussian noise and slow nonselective rayleigh fading the optimal receiver is derived but is found to be difficult to implement in practice because of its exponential growth in complexity as a function of sequence length suboptimal decision feedback approximations are then suggested which are linear and readily implementable and can be integrated as generalized differentially coherent receivers the exact bit error probabilities of these suboptimal receivers are obtained tight upper bounds on these error probabilities are also obtained which show simply how they behave as a function of signal to noise ratio and order of diversity a main conclusion of this work is that optimal data detection on a fading channel should be performed using mmse minimum mean squared error estimates of the quadrature amplitudes of the channel fading processes as a coherent reference

discontinuous galerkin approximations of the stokes and navier stokes equations numerical schemes to compute approximate solutions of the evolutionary stokes and navier stokes equations are studied the schemes are discontinuous in time and conforming in space and of arbitrarily high order fully discrete error estimates are derived and dependence of the viscosity constant is carefully tracked it is shown that the errors are bounded by projection errors of the exact solution which exhibit optimal rates when the solutions are smooth

relation between bit and symbol error probabilities for fsk with ldi detection in m ary gray coded digital communication the bit error probability is usually approximated by the symbol error probability divided by the number of bits in a symbol this approximation is known to be excellent for phase shift keying with coherent detection at high signal to noise ratios and gaussian channel here it is illustrated that this approximation may also be good for m ary frequency shift keying with limiter discriminator integrator detection on gaussian rayleigh and rician channels

on the general ber expression of one and two dimensional amplitude modulations quadrature amplitude modulation qam is an attractive technique to achieve high rate transmission without increasing the bandwidth a great deal of attention has been devoted to the study of bit error rate ber performance of qam and approximate expressions for the bit error probability of qam have been developed in many places in the literature however the exact and general ber expression of qam with an arbitrary constellation size has not been derived yet we provide an exact and general closed form expression of the ber for one dimensional and two dimensional amplitude modulations i e pam and qam under an additive white gaussian noise awgn channel when gray code bit mapping is employed the provided ber expressions offer a convenient way to evaluate the performance of pam and qam systems for various cases of practical interest moreover simple approximations can be found from our expressions which are the same as the well known approximations if only the dominant terms are considered

numerical analysis of quasilinear parabolic equations under low regularity assumptions in this paper we carry out the numerical analysis of a class of quasilinear parabolic equations where the diffusion coefficient depends on the solution of the partial differential equation the goal is to prove error estimates for the fully discrete equation using discontinuous galerkin discretization in time dg 0 combined with piecewise linear finite elements in space this analysis is performed under minimal regularity assumptions on the data in particular we omit any assumption regarding existence of a second derivative in time of the solution

computation of the exact bit error rate of coherent m ary psk with gray code bit mapping the problem of calculating the average bit error probability bep of coherent m ary phase shift keying psk over a gaussian channel has been studied previously in the literature a solution to the problem for systems using a binary reflected gray code brgc to map bits to symbols was first presented by p j lee see ibid vol com 34 p 488 91 1986 we show that the results obtained by lee are incorrect for m spl ges 16 we show that the reason for this is an invalid assumption that the bit error rate ber is independent of the transmitted symbols an assumption which has also propagated to textbooks we give a new expression for the ber of m psk systems using the brgc and compare this with lee s results

computation of the bit error rate of coherent m ary psk with gray code bit mapping efficient computation of the bit error rate ber for the coherent m ary psk signals with gray code bit mapping is considered a closed form expression for the exact ber of 8 ary psk is presented tight upper and lower bounds on ber are also obtained for m ary psk with larger m

discontinuous galerkin methods for ordinary differential equations a class of galerkin methods derived from discontinuous piecewise polynomial spaces is analyzed for polynomials of degree k these methods lead to a family of one step schemes generating approximations up to order 2k 2 for the solution of an ordinary differential equation

an alternative expression for the symbol error probability of mpsk in the presence of i q unbalance this letter provides a new expression for the probability of the phase angle between two vectors perturbed by gaussian noise with in phase quadrature phase i q unbalance in order to simplify the analysis of the error probabilities of m ary phase shift keying mpsk the error probabilities symbol error rates or bit error rates for mpsk with i q balance or unbalance can be presented straightforwardly from the derived expression because the newly derived result is provided in terms of the conventional first order gaussian q function and the joint gaussian q function with a correlation coefficient dependent on m it readily allows rapid evaluation for various cases of practical interest

s n energy selection combining for mpsk and 16 qam signaling in nakagami m and rician fading channels a signal plus noise s n energy selection diversity combining s n esc scheme for m ary phase shift keying mpsk in rayleigh fading channels is mathematically analyzed also the s n esc scheme for mpsk and 16 quadrature amplitude modulation 16 qam signaling in nakagami m and rician fading channels is studied by computer simulations the s n esc selects the branch with the maximum s n energy for detection the advantage of the s n esc scheme is that it requires no explicit channel estimation for diversity branch selection we show that the symbol error probability sep of the s n esc is the same as that of classical selection combining sc for mpsk signaling in independent and identically distributed i i d rayleigh fading channels also we show that the sep of a weighted s n esc scheme is the same as that of classical sc for mpsk signaling in independent and nonidentically distributed i n d rayleigh fading channels it is shown by computer simulations that the s n esc scheme provides a smaller sep than classical sc for mpsk signaling in nondispersive fading channels such as nakagami m fading channels with nakagami parameter m 1 and rician fading channels with rician parameter k 0 on the other hand the s n esc scheme is shown by computer simulations to have a larger sep than classical sc for 16 qam signaling in nakagami m and rician fading channels

a unified performance analysis of digital communication with dual selective combining diversity over correlated rayleigh and nakagami m fading channels using a simple finite integral representation for the bivariate rayleigh 1889 cumulative distribution function previously discovered by the authors we present expressions for the outage probability and average error probability performances of a dual selective diversity system with correlated slow rayleigh fading either in closed form in particular for binary differential phase shift keying or in terms of a single integral with finite limits and an integrand composed of elementary exponential and trigonometric functions because of their simple form these expressions readily allow numerical evaluation for cases of practical interest the results are also extended to the case of slow nakagami m fading using an alternate representation of the generalized marcum 1950 q function

a note on the convergence of the discontinuous galerkin method for a scalar hyperbolic equation a numerical example is presented which shows that the known l 2 error estimate left u u h right leqq ch k 1 2 left u right k 1 for the discontinuous galerkin method cannot be improved within the class of quasi uniform meshes not even for smooth exact solutions u

virtual branch analysis of symbol error probability for hybrid selection maximal ratio combining in rayleigh fading we derive analytical expressions for the symbol error probability sep for a hybrid selection maximal ratio combining h s mrc diversity system in multipath fading wireless environments with h s mrc l out of n diversity branches are selected and combined using maximal ratio combining mrc we consider coherent detection of m ary phase shift keying mpsk and quadrature amplitude modulation mqam using h s mrc for the case of independent rayleigh fading with equal signal to noise ratio averaged over the fading the proposed problem is made analytically tractable by transforming the ordered physical diversity branches which are correlated into independent and identically distributed i i d virtual branches which results in a simple derivation of the sep for arbitrary l and n we further obtain a canonical structure for the sep of h s mrc as a weighted sum of the elementary seps which are the seps using mrc with i i d diversity branches in rayleigh fading or equivalently the seps of the nondiversity single branch system in nakagami fading whose closed form expressions are well known we present numerical examples illustrating that h s mrc even with l spl lt n can achieve a performance close to that of n branch mrc

convergence of the discontinuous galerkin method for discontinuous solutions we consider linear first order scalar equations of the form rho t rm div rho v a rho f with appropriate initial and boundary conditions it is shown that approximate solutions computed using the discontinuous galerkin method will converge in ltwoltwo when the coefficients v and a and data f satisfy the minimal assumptions required to establish existence and uniqueness of solutions in particular v need not be lipschitz so characteristics of the equation may not be defined and the solutions being approximated my not have bounded variation

discontinuous galerkin method for the solution of a transport level set problem the subject of the paper is the numerical analysis of the transport level set problem discretized by the discontinuous galerkin method without the assumption that the first order nonstationary transport equation contains a reaction term which is used in a standard literature we prove error estimates in the l l 2 norm in the case of the space semidiscretization method of lines and in the case of the space time discontinuous galerkin method in the l 2 l 2 norm numerical experiments support the derived error estimates and show that they are not sharp in the case of the space time discontinuous galerkin method

numerical solution of parabolic integro differential equations by the discontinuous galerkin method the numerical solution of a parabolic equation with memory is considered the equation is first discretized in time by means of the discontinuous galerkin method with piecewise constant or piecewise linear approximating functions the analysis presented allows variable time steps which as will be shown call then efficiently be selected to match singularities in the solution induced by singularities in the kernel of the memory term or by nonsmooth initial data the combination with finite element discretizat in space is also studied

a mathematical theory of energy efficient neural computation and communication a neuroscience based mathematical model of how a neuron stochastically processes data and communicates information is introduced and analyzed call the neuron in question neuron j or just j the information j transmits approximately describes the time varying intensity of the excitation j is continuously experiencing from neural spike trains delivered to its synapses by thousands of other neurons neuron j encodes this excitation history into a sequence of time instants at which it generates neural spikes of its own by propagating these spikes along its axon j acts as a multiaccess partially degraded broadcast channel with thousands of input and output terminals that employs a time continuous version of pulse position modulation the mathematical model features three parameters m and b which largely characterize j as an engine of computation and communication each set of values of these parameters corresponds to a long term maximization of the bits j conveys to its targets per joule it expends doing so which is achieved by distributing the random duration between successive spikes j generates according to a gamma pdf with parameters and b and distributing b a according to a beta probability density with parameters and m where a is the random intensity of the effectively poisson process of spikes that arrive to the union of all of j s synapses at a randomly chosen time instant

effect of mmse channel estimation on ber performance of orthogonal space time block codes in rayleigh fading channels we present a simple closed form expression for the ber of orthogonal space time block codes ostbcs with mmse channel estimation assuming pam and qam constellations and flat rayleigh block fading the ber expression is exact for a certain class of ostbcs and provides a very accurate approximation for other ostbcs

log concavity property of the error probability with application to local bounds for wireless communications a clear understanding of the behavior of error probability ep as a function of signal to noise ratio snr and other system parameters is fundamental for assessing the design of digital wireless communication systems we propose an analytical framework based on the log concavity property of the ep which we prove for a wide family of multidimensional modulation formats in the presence of gaussian disturbances and fading based on this property we construct a class of local bounds for the ep that improve known generic bounds in a given region of the snr and are invertible as well as easily tractable for further analysis this concept is motivated by the fact that communication systems often operate with performance in a certain region of interest roi and thus it may be advantageous to have tighter bounds within this region instead of generic bounds valid for all snrs we present a possible application of these local bounds but their relevance is beyond the example made in this paper

classification of unique mappings for 8psk based on bit wise distance spectra the performance of bit interleaved coded modulation bicm with or without iterative decoding id is significantly influenced by the mapping of bits to the symbol constellation our main objective in this paper is to develop a systematic design approach for bicm id schemes ensuring the best possible performance with iterative decoding although useful mappings for bicm id have been found based on various search strategies no attempt has been made to systematically enumerate and classify all unique mappers for a given constellation as the basis for a systematic enumeration and classification we define the average bit wise distance spectrum for a mapping from bits to symbols different bit wise distance spectra are derived assuming no prior information or full prior information respectively the bit wise distance spectra determine corresponding bit wise error probability and bit wise mutual information the latter allows us to use the classification of mappings with unique bit wise distance spectra to also classify mappings with unique extremal points in the corresponding extrinsic information transfer exit curves as an example of our approach we classify 8psk mappings into 86 classes of unique mappings according to bit wise distance spectra the classification can be used to significantly reduce the complexity of the search for suitable mappers for bicm id for 8psk and a given encoder only 86 different mappings need to be investigated as examples of the systematic design approach the best 8psk mappings for minimizing the convergence threshold are found for concatenation with the rate 1 2 5 7 8 and 133 171 8 convolutional codes and the rate 1 2 umts turbo code with identical constituent convolutional codes 15 13 8

numerical analysis of a second order pure lagrange galerkin method for convection diffusion problems part ii fully discretized scheme and numerical results we analyze a second order pure lagrange galerkin method for variable coefficient convection diffusion possibly degenerate diffusion equations with mixed dirichlet robin boundary conditions in a previous paper the proposed second order pure lagrangian time discretization scheme was introduced and analyzed for the same problem more precisely the l infty h 1 stability and l infty h 1 error estimates of order o delta t 2 had been obtained moreover for the particular case of incompressible flows stability inequalities with constants independent of the final time have been stated in the present paper l infty h 1 error estimates of order o delta t 2 o h k are obtained for the fully discretized pure lagrange galerkin method to prove these results we use some properties obtained in the previous paper finally numerical tests are presented that confirm the theoretical results

performances of ds ssma communications with mpsk signaling and complex signature sequences we study a direct sequence spread spectrum multiple access ds ssma communication system with m ary phase shift keyed mpsk signaling users in the system employ complex signature sequences which are modeled as deterministic sequences we present upper and lower bounds for the probability of bit error p b e of a reference transmission first the conditional p b e given the multiple user interference mui is obtained then the conditioning is removed by averaging over the discretized probability density function p d f of the mui the result is an upper or lower bound when the discretized p d f is a shifted high or shifted low version of a sectioned p d f this process requires the two dimensional p d f of the mui which is derived arbitrarily tight bounds can be obtained at the cost of increased computation numerical results are presented for complex fzc and near optimal 4 phase sequences as well as real binary gold sequences for bpsk 4 psk and 8 psk gray code bit mapping is assumed although the analysis can be applied to other bit mappings results show that complex sequences can yield better performance than binary sequences in mpsk signaling using complex sequences the number of available signature sequences is greatly enlarged

global minimax approximations and bounds for the gaussian q function by sums of exponentials this paper presents a novel systematic methodology to obtain new simple and tight approximations lower bounds and upper bounds for the gaussian q function and functions thereof in the form of a weighted sum of exponential functions they are based on minimizing the maximum absolute or relative error resulting in globally uniform error functions with equalized extrema in particular we construct sets of equations that describe the behaviour of the targeted error functions and solve them numerically in order to find the optimized sets of coefficients for the sum of exponentials this also allows for establishing a trade off between absolute and relative error by controlling weights assigned to the error functions extrema we further extend the proposed procedure to derive approximations and bounds for any polynomial of the q function which in turn allows approximating and bounding many functions of the q function that meet the taylor series conditions and consider the integer powers of the q function as a special case in the numerical results other known approximations of the same and different forms as well as those obtained directly from quadrature rules are compared with the proposed approximations and bounds to demonstrate that they achieve increasingly better accuracy in terms of the global error thus requiring significantly lower number of sum terms to achieve the same level of accuracy than any reference approach of the same form

numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form cu t bu x au x x f optimal order error estimates in l 2 and w 1 2 are derived for the finite element procedure various error estimates are presented for a variety of finite difference methods the estimates show that for convection dominated problems b gg a these schemes have much smaller time truncation errors than those of standard methods extensions to n space variables and time dependent or nonlinear coefficients are indicated along with applications of the concepts to certain problems described by systems of differential equations

error estimates for discontinuous galerkin approximations of implicit parabolic equations we analyze the classical discontinuous galerkin method for implicit parabolic equations symmetric error estimates for schemes of arbitrary order are presented the ideas developed allow certain assumptions frequently required in previous work to be relaxed for example different discrete spaces are allowed at each time step and the spatial operator is not required to be self adjoint or independent of time error estimates are posed in terms of projections of the exact solution onto the discrete spaces and are valid under the minimal regularity guaranteed by the natural energy estimate these projections are local and enjoy optimal approximation properties when the solution is sufficiently regular

equal gain transmission in multiple input multiple output wireless systems multiple input multiple output mimo wireless systems are of interest due to their ability to provide substantial gains in capacity and quality the paper proposes equal gain transmission egt to provide diversity advantage in mimo systems experiencing rayleigh fading the applications of egt with selection diversity combining equal gain combining and maximum ratio combining are addressed it is proven that systems using egt with any of these combining schemes achieve full diversity order when transmitting over a memoryless flat fading rayleigh matrix channel with independent entries since in practice full channel knowledge at the transmitter is difficult to realize a quantized version of egt is proposed an algorithm to construct a beamforming vector codebook that guarantees full diversity order is presented monte carlo simulation comparisons with various beamforming and combining systems illustrate the performance as a function of quantization

bit error probabilities mdpsk over the nonselective rayleigh fading channel with diversity reception data transmission using m ary differential phase shift keying mdpsk over the nonselective rayleigh fading channel with diversity reception is considered while previous studies on error probability mostly assume no fading fluctuation the author considers exclusively the case in which the fading process fluctuates from one symbol interval to the next exact bit error probability results for 2 4 and 8 dpsk as well as tight upper bounds are derived some applications of the results are discussed

performance analysis of orthogonal space time block codes over time selective channels and applications to code design of gi systems many existing works on space time block codes stbc assume the channels are block wise constant but this assumption does not always hold in the more general case of time selective channels the channel matrix is no longer orthogonal so inter symbol interference esi is generated and the performance is greatly reduced several decoders have been proposed to eliminate the esi but it remains unclear how and to what extent the performance is affected by the isi in this paper we introduce an approach to analyze the performance of stbc over time selective channels with arbitrary numbers of antennas for which orthogonal stbc s are defined exact error performances are obtained in closed form furthermore the analysis reveals the relationship between the isi and the structure of stbc matrices considering g i systems we then propose one proposition and two design criteria following which it is easy to design or search for better stbc s that have less isi compared with the original code matrix

a symbol by symbol channel estimation receiver for space time block coded systems and its performance analysis on the nonselective rayleigh fading channel we present a symbol by symbol channel estimation receiver for an orthogonal space time block coded system and derive its analytical performance on a slow nonselective rayleigh fading channel exact closed form expressions for its bit error probability bep performance for m ary phase shift keying modulations are obtained which enable us to theoretically predict the actual performance achievable under practical conditions with channel estimation error our bep expressions show explicitly the dependence of bep on the mean square error of the channel estimates which in turn depend on the channel fading model and the channel estimator used tight upper bounds are presented that show more clearly the dependence of the bep on various system parameters simulation results using various fading models are obtained to demonstrate the validity of the analysis

variational time discretization methods for optimal control problems governed by diffusion convection reaction equations in this paper the distributed optimal control problem governed by unsteady diffusion convection reaction equation without control constraints is studied time discretization is performed by variational discretization using continuous and discontinuous galerkin methods while symmetric interior penalty galerkin with upwinding is used for space discretization we investigate the commutativity properties of the optimize then discretize and discretize then optimize approaches for the continuous and discontinuous galerkin time discretization a priori error estimates are derived for fully discrete state adjoint and control the numerical results given for convection dominated problems via optimize then discretize approach confirm the theoretically observed convergence rates

a unified approach for calculating error rates of linearly modulated signals over generalized fading channels we present a unified analytical framework to determine the exact average symbol error rate ser of linearly modulated signals over generalized fading channels the results are applicable to systems employing coherent demodulation with maximal ratio combining multichannel reception the analyses assume independent fading paths which are not necessarily identically distributed in all cases the proposed approach leads to an expression of the average ser involving a single finite range integral which can be easily computed numerically in addition as special cases ser expressions for single channel reception are obtained these expressions reduce to well known solutions give alternative often simpler expressions for previous results or provide new formulas that are either closed form expressions or simple to compute numerically

bit error probability for coherent m ary psk systems a simple technique for evaluating the bit error probability of coherent m ary phase shift keying psk with any bit mapping is proposed closed form expressions are given in terms of error functions for half and quadrant plane probabilities in the decision space avoiding the numerical evaluation of complicated integrals that occurs in the direct method bit error probability expressions for m ary psk with gray natural binary and folded binary bit mappings are derived

orthogonal space time block code over time varying flat fading channels channel estimation detection and performance analysis this paper studies the channel estimation detection and performance analysis of mobile wireless communication systems employing space time block codes stbc where the channels exhibit flat rayleigh fading with a significant amount of doppler spread pilot symbol assisted modulation psam is developed to estimate the channels the performance of the channel estimation is evaluated maximum likelihood ml detection is first formulated a linear detector called the symmetric linear sl detector is proposed an interference cancellation ic detector is also developed to improve the performance of the sl detector we derive the closed form analytical expressions for the bit error rate ber or symbol error rate ser of pilot sequence assisted stbc with binary phase shift keying psk quaternary psk 16 quadrature amplitude modulation qam and 64 qam when the sl and ic detectors are used some important design issues in the pilot sequence assisted stbc systems including the selection of pilot spacing and interpolator size are discussed simulation results are presented that verify our analytical results the tradeoffs between the performance and complexity for ml sl and ic detection are also discussed

space shift keying ssk mimo with practical channel estimates in this paper we study the performance of space modulation for multiple input multiple output mimo wireless systems with imperfect channel knowledge at the receiver we focus our attention on two transmission technologies which are the building blocks of space modulation i space shift keying ssk modulation and ii time orthogonal signal design tosd ssk modulation which is an improved version of ssk modulation providing transmit diversity we develop a single integral closed form analytical framework to compute the average bit error probability abep of a mismatched detector for both ssk and tosd ssk modulations the framework exploits the theory of quadratic forms in conditional complex gaussian random variables rvs along with the gil pelaez inversion theorem the analytical model is very general and can be used for arbitrary transmit and receive antennas fading distributions fading spatial correlations and training pilots the analytical derivation is substantiated through monte carlo simulations and it is shown over independent and identically distributed i i d rayleigh fading channels that ssk modulation is as robust as single antenna systems to imperfect channel knowledge and that tosd ssk modulation is more robust to channel estimation errors than the alamouti scheme furthermore it is pointed out that only few training pilots are needed to get reliable enough channel estimates for data detection and that transmit and receive diversity of ssk and tosd ssk modulations are preserved even with imperfect channel knowledge

on the error probability of binary and m ary signals in nakagami m fading channels in this letter we present new closed form formulas for the exact average symbol error rate ser of binary and m ary signals over nakagami m fading channels with arbitrary fading index m using the well known moment generating function based analysis approach we express the average ser in terms of the higher transcendental functions such as the gauss hypergeometric function appell hypergeometric function or lauricella function the results are generally applicable to arbitrary real valued m furthermore with the aid of reduction formulas of hypergeometric functions we show previously published results for rayleigh fading m 1 as special cases of our expressions

a recursive algorithm for the exact ber computation of generalized hierarchical qam constellations hierarchical constellations offer a different degree of protection to the transmitted messages according to their relative importance as such they find interesting application in digital video broadcasting systems as well as wireless multimedia services although a great deal of attention has been devoted in the literature to the study of the bit error rate ber performance of uniform quadrature amplitude modulation qam constellations very few results were published on the ber performance of hierarchical qam constellations we obtain exact and generic expressions in m for the ber of the generalized hierarchical m pam pulse amplitude modulation constellations over additive white gaussian noise awgn and fading channels we also show how these expressions can be extended to generalized hierarchical m qam constellations square and rectangular for the awgn case these expressions are in the form of a weighted sum of complementary error functions and are solely dependent on the constellation size m the carrier to noise ratio and a constellation parameter which controls the relative message importance because of their generic nature these new expressions readily allow numerical evaluation for various cases of practical interest

θ qam a parametric quadrature amplitude modulation family and its performance in awgn and fading channels we study a parametric quadrature amplitude modulation qam family called qam which includes other known constellations such as square qam sqam and triangular qam tqam as special cases the versatile structure of the qam signal constellation which occurs from the varying angle between the signal points results in achieving the minimum symbol error rate ser or bit error rate ber under an average power constraint the theoretical study aims at providing insight into the trade off between error performance and complexity of this parametric modulation scheme exact analytical expressions are obtained for the ser in additive white gaussian noise awgn and nakagami m fading channels while highly accurate ber approximations are presented finally we find the optimum angles in a minimal ser or ber sense for a specific signal to noise ratio snr and modulation order m this serves as an indicator for the appropriate constellation with respect to channel conditions and ser or ber requirements the presented theoretical analysis is validated via extensive computer simulations

an mgf based performance analysis of generalized selection combining over rayleigh fading channels using the notion of the spacing between ordered exponential random variables a performance analysis of the generalized selection combining gsc diversity scheme over rayleigh fading channels is presented and compared with that of the conventional maximal ratio combining and selection combining schemes starting with the moment generating function mgf of the gsc output signal to noise ratio snr we derive closed form expressions for the average combined snr outage probability and average error probability of a wide variety of modulation schemes operating over independently identically distributed i i d diversity paths because of their simple form these expressions readily allow numerical evaluation for cases of practical interest the results are also extended to the case of non i i d diversity paths

adaptive finite element methods for parabolic problems i a linear model problem this paper is the first part in a series of papers on adaptive finite element methods for parabolic problems in this paper an adaptive algorithm is presented and analyzed for choosing the space a

uniform error analysis for lagrange galerkin approximations of convection dominated problems in this paper we present a rigorous error analysis for the lagrange galerkin method applied to convection dominated diffusion problems we prove new error estimates in which the constants depend on norms of the data and not of the solution and do not tend to infinity in the hyperbolic limit this is in contrast to other results in this field for the time discretization uniform convergence with respect to the diffusion parameter of order o k tn is shown for initial values in l2 and o k for initial values in h2 for the spatial discretization with linear finite elements we verify uniform convergence of order o h2 min h h2 k for data in h2 by interpolation of banach spaces suboptimal convergence rates are derived under less restrictive assumptions the analysis is heavily based on a priori estimates uniform in the diffusion parameter for the solution of the continuous and the semidiscrete problem they are derived in a lagrangian framework by transforming the eulerian coordinates completely into subcharacteristic coordinates finally we illustrate the error estimates by some numerical results

discrete maximal parabolic regularity for galerkin finite element methods for nonautonomous parabolic problems the main goal of the paper is to establish time semidiscrete and space time fully discrete maximal parabolic regularity for the lowest order time discontinuous galerkin solution of linear parabolic

moving finite elements i we present new and general numerical methods for dealing with problems whose solutions develop sharp transition layers or near shocks these methods allow many nodes automatically to concentrate in the critical regions and move with them for clarity of exposition we concentrate on the space of piecewise linear functions with movable nodes with burgers equation as our test equation but the generalization to much more general spaces and equations including even certain previous moving vorticity blobs of the first author and s doss for the navier stokes equations becomes clear in this paper we present the theoretical and computational details of our scheme along with computational trial runs for burgers equation showing that the nodes do concentrate sharply and move with the shocks as desired the conclusiveness of these preliminary numerical trials is marred somewhat by the fact that we never successfully debugged a newton s method for our implicit stiff ode solver and were thus limited to ver

space time power optimization of variable rate space time block codes based on successive interference cancellation based on a zero forcing with successive interference cancellation zfsic method we construct variable rate space time block codes stbcs for two three and four transmit antennas in rayleigh fading channels considering the error propagation effect in the zfsic scheme we analyze the bit error rate ber and optimize the transmit power so that the average ber is minimized unlike the approach based on zero forcing zf the method adopted in this paper can construct variable rate stbcs even when the receive antennas are fewer than the transmit antennas in addition to improve the bers further we propose space time power optimization numerical results show that the codes presented in this paper provide much lower bers compared with the codes developed by kim and tarokh

the error performance of gray encoded qpsk and 8 psk schemes in a fading channel with cochannel interference closed form ber bit error rate expressions are derived for gray encoded qpsk quadrature phase shift keying and 8 psk schemes using coherent detection in a slow rayleigh fading narrowband channel with fading cochannel interference earlier work has been limited to deriving the approximate ber using the canonical stein 1961 receiver concept the symbol error rate ser for the qpsk scheme is also derived the desired signal and the cochannel interferer are both psk signals modulated by different baseband pulses with identical signaling rate

error rates of the maximum likelihood detector for arbitrary constellations convex concave behavior and applications motivated by a recent surge of interest in convex optimization techniques convexity concavity properties of error rates of the maximum likelihood detector operating in the awgn channel are studied and extended to frequency flat slow fading channels generic conditions are identified under which the symbol error rate ser is convex concave for arbitrary multidimensional constellations in particular the ser is convex in snr for any one and two dimensional constellation and also in higher dimensions at high snr pairwise error probability and bit error rate are shown to be convex at high snr for arbitrary constellations and bit mapping universal bounds for the ser first and second derivatives are obtained which hold for arbitrary constellations and are tight for some of them applications of the results are discussed which include optimum power allocation in spatial multiplexing systems optimum power time sharing to decrease or increase jamming problem error rate an implication for fading channels fading is never good in low dimensions and optimization of a unitary precoded ofdm system for example the error rate bounds of a unitary precoded ofdm system with qpsk modulation which reveal the best and worst precoding are extended to arbitrary constellations which may also include coding the reported results also apply to the interference channel under gaussian approximation to the bit error rate when it can be expressed or approximated as a nonnegative linear combination of individual symbol error rates and to coded systems

on the smoothing property of the galerkin method for parabolic equations we analyze the galerkin approximation of the general second order parabolic initial boundary value problem for the second order continuous time method with initial data only in l 2 we prove an l 2 error estimate of order o h 2 t analogous results are shown to hold for the error in negative sobolev norms and for the time derivative of the error our analysis uses only elementary energy techniques and the same techniques are shown to give a simple analysis of the backward euler time discretization

error probability performance of l branch diversity reception of mqam in rayleigh fading new exact expressions involving hypergeometric functions are derived for the symbol error rate ser of m ary quadrature amplitude modulation mqam for l branch diversity reception in rayleigh fading and additive white gaussian noise awgn the diversity combining techniques considered are maximum ratio combining mrc and selection combining sc mrc with identical channels and dissimilar channels are analyzed

error rates for rayleigh fading multichannel reception of mpsk signals this paper provides a new closed form expression for calculating the probability that an mpsk signal will lie in a particular decision region when received over n independent and identically distributed rayleigh fading channels corrupted by additive white gaussian noise this expression is applied to provide a unified method to derive the exact symbol error rate and bit error rate for mpsk signals considering n channel diversity reception the n channel diversity reception techniques considered are maximal ratio combining mrc and selection combining mrc with identical channels and dissimilar channels is considered the results for mrc can be extended to provide an approximation for the error rates of mpsk under equal gain combining

a spacetime discontinuous galerkin method for hyperbolic heat conduction non fourier conduction models remedy the paradox of infinite signal speed in the traditional parabolic heat equation for applications involving very short length or time scales hyperbolic conduction models better represent the physical thermal transport processes this paper reviews the maxwell cattaneo vernotte modification of the fourier conduction law and describes its implementation within a spacetime discontinuous galerkin sdg finite element method that admits jumps in the primary variables across element boundaries with arbitrary orientation in space and time a causal advancing front meshing procedure enables a patch wise solution procedure with linear complexity in the number of spacetime elements an h adaptive scheme and a special sdg shock capturing operator accurately resolve sharp solution features in both space and time numerical results for one spatial dimension demonstrate the convergence properties of the sdg method as well as the effectiveness of the shock capturing method simulations in two spatial dimensions demonstrate the proposed method s ability to accurately resolve continuous and discontinuous thermal waves in problems where rapid and localized heating of the conducting medium takes place

symbol error probability and bit error probability for optimum combining with mpsk modulation new expressions are derived for the exact symbol error probability and bit error probability for optimum combining with multiple phase shift keying the expressions are for any numbers of equal power cochannel interferers and receive branches it is assumed that the aggregate interference and noise is gaussian and that both the desired signal and interference are subject to flat rayleigh fading the new expressions have low computational complexity as they contain only a single integral form with finite limits and finite integrand

exact expression for the ber of rectangular qam with arbitrary constellation mapping the exact closed form expression for the bit error rate ber of rectangular quadrature amplitude modulation qam is given the presented formula is independent of the bit mapping and it is thus particularly useful in the design and analysis of modulation schemes employing non gray mapping compared with the so called expurgated bound and the union bound our expression is shown to accurately predict the ber in the low signal to noise ratio range where the bounding techniques fail

tight error bounds for nonuniform signaling over awgn channels we consider a bonferroni type lower bound due to kounias 1968 on the probability of a finite union the bound is expressed in terms of only the individual and pairwise event probabilities however it suffers from requiring an exponentially complex search for its direct implementation we address this problem by presenting a practical algorithm for its evaluation this bound is applied together with two other bounds a recent lower bound the kat bound and a greedy algorithm implementation of an upper bound due to hunter 1976 to examine the symbol error p sub a and bit error p sub b probabilities of an uncoded communication system used in conjunction with m ary phase shift keying psk quadrature amplitude qam psk qam modulations and maximum a posteriori map decoding over additive white gaussian noise awgn channels it is shown that the bounds which can be efficiently computed provide an excellent estimate of the error probabilities over the entire range of the signal to noise ratio snr e sub b n sub 0 the new algorithmic bound and the greedy bound are particularly impressive as they agree with the simulation results even during very severe channel conditions

compactness properties of the dg and cg time stepping schemes for parabolic equations for a broad class of parabolic equations it is shown that numerical solutions computed using the discontinuous galerkin or the continuous galerkin time stepping schemes of arbitrary order will inherit the compactness properties of the underlying equation convergence of numerical schemes for a phase field approximation of the flow of two fluids with surface tension is presented to illustrate these results

numerical analysis of a second order pure lagrange galerkin method for convection diffusion problems part i time discretization we propose and analyze a second order pure lagrangian method for variable coefficient convection possibly degenerate diffusion equations with mixed dirichlet robin boundary conditions first the method is rigorously introduced for exact and approximate characteristics next l infty h 1 stability is proved and l infty h 1 error estimates of order o delta t 2 are obtained moreover l infty l 2 stability and l infty l 2 error estimates of order o delta t 2 with constants bounded in the hyperbolic limit are shown for the particular case of dirichlet boundary conditions diffusion tensor a epsilon i and right hand side f 0 the l infty h 1 stability estimate is independent of epsilon moreover for incompressible flows the constants in the stability inequalities are independent of the final time in a second part of this work the pure lagrangian scheme will be combined with galerkin discretization using finite elements spaces and numerical examples will be presented

accurate evaluation for mdpsk with noncoherent diversity the error probability analysis of m ary differential phase shift keying signals with noncoherent diversity combining over general fading channels is not available in the literature except for some simple cases the difficulty lies in the philosophy which attempts to explicitly determine the phase distribution expressions of the received signal and this often leads to a mathematically intractable issue in this paper we take a novel approach by formulating the phase distribution in terms of joint moment generating functions of the real and imaginary parts of the decision variable at the receiver output we further derive fast convergent techniques for two dimensional 2 d inverse laplace transform enabling us to accurately evaluate the phase distribution the error probability formulas thus obtained involve a twofold integral which can be efficiently evaluated by using our algorithms developed on the basis of the 2 d trapezoidal summation and gauss chebyshev quadrature the new technique is very general taking into account the effects of arbitrary diversity order symbol alphabet size m and arbitrary diversity branches correlation numerical results are also presented for illustration

error rates for nakagami m fading multichannel reception of binary and m ary signals this paper derives new closed form formulas for the error probabilities of single and multichannel communications in rayleigh and nakagami m 1960 fading closed form solutions to three generic trigonometric integrals are presented as part of the main result providing a unified method for the derivation of exact closed form average symbol error probability expressions for binary and m ary signals with l independent channel diversity reception both selection diversity and maximal ratio combining mrc techniques are considered the results are generally applicable for arbitrary two dimensional signal constellations that have polygonal decision regions operating in a slow nakagami m fading environments with positive integer fading severity index mrc with generically correlated fading is also considered the new expressions are applicable in many cases of practical interest the closed form expressions derived for a single channel reception case can be extended to provide an approximation for the error rates of binary and m ary signals that employ an equal gain combining diversity receiver

probability of bit error for mpsk modulation with diversity reception in rayleigh fading and log normal shadowing channel in an additive white gaussian noise channel subject to rayleigh fading and log normal shadowing consideration is given to diversity reception with k port macroscopic selection and l branch microscopic maximal ratio combining and analytical expressions are derived for upper and lower bounds on the bit error probabilities for bpsk qpsk 8 psk and 16 psk modulations the derived expressions can be evaluated at any location in the serving cell error probability can be calculated by averaging over all possible locations within the serving cell by evaluating these bounds numerical results for the following cases are presented without diversity reception microdiversity combining macrodiversity selection and simultaneous use of macrodiversity selection and microdiversity combining for symmetrical arrangement of macrodiversity ports against the lognormal shadowing error probability at the equidistant point gives upper bounds on the error probabilities for most of the area in the serving cell error probability at the equidistant point is a good estimate of the error probability obtained by averaging over all possible locations in the cell

on the error probability of linearly modulated signals on rayleigh frequency flat fading channels consideration is given to optimal detection of linearly modulated signals subject to multiplicative rayleigh distributed distortion and additive white gaussian noise for coherent detection regenerated amplitude and phase references are employed at the receiver to compensate for amplitude and phase deviations from the correct values a system model is formulated under the assumption of perfect symbol timing and in the absence of intersymbol interference producing a final additive noise term applied just before the detection which contains the effects of the original additive and multiplicative distortions and of the errors in the phase and amplitude references by determining the probability density function of this final noise term for arbitrary types of linear modulation it is possible to perform exact calculations of error probabilities

adaptive finite element methods for parabolic problems ii optimal error estimates in l l 2 and l l optimal error estimates are derived for a complete discretization of linear parabolic problems using space time finite elements the discretization is done first in time using the discontinuous galerkin method and then in space using the standard galerkin method the underlying partitions in time and space need not be quasi uniform and the partition in space may be changed from time step to time step the error bounds show in particular that the error may be controlled globally in time on a given tolerance level by controlling the discretization error on each individual time step on the same given level i e without error accumulation effects the derivation of the estimates is based on the orthogonality of the galerkin procedure and the use of strong stability estimates the particular and precise form of these error estimates makes it possible to design efficient adaptive methods with reliable automatic error control for parabolic problems in the norms under consideration

capacity analysis for integrate and fire neurons with descending action potential thresholds understanding how a biological neuron works has been a major goal in neuroscience under the poisson excitation assumption results from earlier study by suksompong and berger on the timing jitter in the leaky integrate and fire lif model of neurons are used to determine families of neural thresholding functions that are appropriate in certain interesting senses next the neuron is treated as a communication channel for which information theoretic quantities can be calculated in particular the optimal distribution of the poisson excitation intensity is numerically evaluated along with the corresponding capacity using the blahut arimoto algorithm simple formulas which approximate the optimal intensity distribution are given furthermore the jimbo kunisawa algorithm is used to explore energy efficient operations for neuron finally a rate matching argument leads to a unique operating condition which turns out to agree with experimentally observed rate

performance analysis of linear modulation schemes with generalized diversity combining on rayleigh fading channels with noisy channel estimates generalized diversity combining gdc also known as hybrid selection maximal ratio combining or generalized selection combining is a low complexity diversity combining technique by which a fixed subset of a large number of available diversity channels is chosen and then combined using the rules of maximal ratio combining in this paper we analyze the performance of gdc on time correlated rayleigh fading channels with noisy channel estimates we derive expressions for the probability of error for various linear modulation schemes with coherent detection and discuss the conditions under which the analysis can be extended to noncoherent and differentially coherent receiver structures throughout the paper using a fundamental approach to obtain the decision statistic at the combiner output a number of new expressions for the error probabilities are obtained in a rigorous way along with a presentation of their performance with channel estimation errors the final expressions have roughly the same complexity of evaluation as that for the channel with only additive gaussian noise our results correct various inaccuracies in the literature and show that coherent receivers based on imperfectly estimated channel knowledge incur a significant performance loss

symmetric error estimates for moving mesh mixed methods for advection diffusion equations a mixed method allowing a general class of mesh movements is proposed for an advection diffusion equation in either conservative or nonconservative form several symmetric error estimates are derived for the method under certain conditions in one space dimension optimal order l2 convergence and superconvergence are proved as corollaries of the symmetric estimates

on channel capacity per unit cost memoryless communication channels with arbitrary alphabets where each input symbol is assigned a cost are considered the maximum number of bits that can be transmitted reliably through the channel per unit cost is studied it is shown that if the input alphabet contains a zero cost symbol then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions the direct part of this coding theorem admits a constructive proof via stein s lemma on the asymptotic error probability of binary hypothesis tests single user multiple access and interference channels are studied

degrees of freedom in adaptive modulation a unified view we examine adaptive modulation schemes for flat fading channels where the data rate transmit power and instantaneous ber are varied to maximize spectral efficiency subject to an average power and ber constraint both continuous rate and discrete rate adaptation are considered as well as average and instantaneous ber constraints we find the general form of power ber and data rate adaptation that maximizes spectral efficiency for a large class of modulation techniques and fading distributions the optimal adaptation of these parameters is to increase the power and data rate and decrease the ber as the channel quality improves surprisingly little spectral efficiency is lost when the power or rate is constrained to be constant hence the spectral efficiency of adaptive modulation is relatively insensitive to which degrees of freedom are adapted

optimized nonuniform psk for multiclass traffic and its application to space time block codes we construct nonuniform phase shift keying psk constellations that provide unequal error protection for multiclass traffic such as compressed voice and video data then closed form expressions expression for the exact bit error rate ber of the nonuniform psk constellations is derived in multiple receive antenna systems over rayleigh fading channels based on this ber analysis we optimize the nonuniform psk constellations such that the bers of all the bits of each class are equalized or such that the total transmission power is minimized subject to the average ber constraints in particular we demonstrate that even for transmitting single class traffic the optimized nonuniform psk constellations can be better than the conventional uniform psk finally we extend the nonuniform psk constellations to space time coded communications systems with multiple transmit and multiple receive antennas

relation between bit and symbol error probabilities for dpsk and fsk with differential phase detection in m ary gray coded dpsk and fsk with differential phase detection the bit error probability is usually approximated by the symbol error probability divided by the number of bits in a symbol this approximation is known to be excellent for psk with large signal to noise ratios in a gaussian channel in other cases this approximation may be questionable here we compute the exact values of bit error probability for dpsk and fsk in gaussian rayleigh and rician channels we also compute the relative error involved in this approximation the conclusion is that except for very low values of signal to noise ratio the approximation is good for all channels

error estimates for discontinuous galerkin time stepping schemes for robin boundary control problems constrained to parabolic pdes we consider fully discrete finite element approximations of a robin optimal boundary control problem constrained by linear parabolic pdes with rough initial data conforming finite element methods for spatial discretization combined with discontinuous time stepping galerkin schemes are being used for the space time discretization error estimates are proved under weak regularity hypotheses for the state adjoint and control variables computational examples validating our expected rates of convergence are also provided

anisotropic hp adaptive discontinuous galerkin method for the numerical solution of time dependent pdes we deal with the numerical solution of time dependent problems with the aid of anisotropic hp grids we present an algorithm which generates a sequence of anisotropic triangular grids and the corresponding polynomial approximation degrees in such a way that the interpolation error measured in the discrete l 0 t l q norm q 1 and r 2 is under a given tolerance and the number of degrees of freedom is as small as possible the efficiency of the algorithm is demonstrated by numerical experiments

on the optimality of bit detection of certain digital modulations in this paper we study the optimality of bit detection for coherent m ary phase shift keying psk and m ary quadrature amplitude modulation qam and noncoherent m ary frequency shift keying fsk signal sets for m psk and m qam signal constellations we employ gray mapping consider 8 psk and 16 qam signal sets as representative of the general results and derive the log likelihood ratio llr for each bit forming the symbol using the llrs we derive the average bit error probability bep for the individual bits and show that the decision regions and the corresponding average bep for the case of m psk coincide with those obtained with the optimal symbol based detector whereas in general this is not the case for both m qam and m fsk

bounds and approximations for rapid evaluation of coherent mpsk error probabilities the error probability for mpsk detection is expressed here as a sum of a familiar upper bound approximation and a correction term which is well suited for numerical integration an asymptotic expansion of the correction term is derived from which simple and extremely tight upper and lower bounds are obtained relative errors in using these bounds and approximations of them are graphed for cases of practical interest

error analysis for nonuniform signaling over rayleigh fading channels we investigate the error performance of a communication system where a nonuniform memoryless binary source is transmitted via gray mapped m ary phase shift keying or quadrature amplitude modulation over memoryless rayleigh fading channels and demodulated via optimal maximum a posteriori detection using recently derived upper and lower bounds on the probability of a general union of events which are tight and can be efficiently computed the system symbol error p sub s and bit error p sub b rates are evaluated for a wide range of channel conditions since for nonuniform signaling gray mapping is not necessarily optimal for minimizing p sub s or p sub b as was recently shown by takahara et al we also evaluate the system performance under the map obtained by takahara et al and compare it with a gray mapped system

on the optimality of the binary reflected gray code this paper concerns the problem of selecting a binary labeling for the signal constellation in m psk m pam and m qam communication systems gray labelings are discussed and the original work by frank gray is analyzed as is noted the number of distinct gray labelings that result in different bit error probability grows rapidly with increasing constellation size by introducing a recursive gray labeling construction method called expansion the paper answers the natural question of what labeling among all possible constellation labelings will give the lowest possible average probability of bit errors for the considered constellations under certain assumptions on the channel the answer is that the labeling proposed by gray the binary reflected gray code is the optimal labeling for all three constellations which has surprisingly never been proved before

a forward approach to numerical data assimilation variational data assimilation problems are concerned with computing unknown initial values for the simulation and prediction of natural phenomena most notably in weather prediction and are usually solved via an ill posed optimal control problem for the initial state at the time of the first available measurements an alternative forward approach focuses on computation of the final state after this interval which is just as suitable for prediction purposes and is well posed without additional regularization specifically it is possible to compute projections of the unknown final state on all elements of an orthonormal basis which theoretically allows for the complete reconstruction of the final state in this paper an efficient numerical method for linear evolution equations of diffusive type is presented and convergence of the numerical approximation based on a discontinuous galerkin discretization is proved the key of this method is the computation of an adaptively ordered orthonormal basis using proper orthogonal decomposition numerical examples for a scalar convection diffusion equation in two and three dimensions show the effectiveness of the method

error estimates for the discontinuous galerkin methods for parabolic equations the classical discontinuous galerkin method for a general parabolic equation is analyzed symmetric error estimates for schemes of arbitrary order are presented the ideas developed below relax many assumptions required in previous work for example different discrete spaces may be used at each time step and the spatial operator need not be self adjoint or independent of time our error estimates are posed in terms of projections of the exact solution onto the discrete spaces and are valid under the minimal regularity guaranteed by the natural energy estimate these projections are local and enjoy optimal approximation properties when the solution is sufficiently regular