a smooth transition model between kinetic and diffusion equations this paper presents a model which provides a smooth transition between a kinetic and a diffusion domain the idea is to use a buffer zone in which both diffusion and kinetic equations will be solved the solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations we use an artificial connecting function which makes the equation on each domain degenerate at the end of the buffer zone thus no boundary condition is needed at the transition point this model avoids the delicate issue of finding the interface condition or iteration in a typical domain decomposition method that couples a kinetic equation with hydrodynamic equations a new asymptotic preserving method for this model is introduced and numerical examples are used to validate this new model and the new numerical method

ofdm based on low complexity transform to increase multipath resilience and reduce papr this paper introduces a new multicarrier system using a low computational complexity transform that combines the walsh hadamard transform wht and the discrete fourier transform dft into a single fast orthonormal unitary transform the proposed transform is used in a new orthogonal frequency division multiplexing t ofdm system leading to a significant improvement in bit error rate ber and reasonable reduction in the peak to average power ratio papr use of the proposed transform with ofdm has been found to attain high frequency diversity gain by combining all data samples resulting in the transmission over many subcarriers consequently the detrimental effect arising from channel fading on the subcarrier power is minimized theoretical analysis of the uncoded t ofdm performance over additive white gaussian noise awgn flat fading quasi static fixed within the entire period of ofdm symbol transmission frequency selective fading channel models with zero forcing zf and minimum mean square error mmse equalizers is presented in this work moreover the low superposition of the subcarriers passing through the t transforms leads to a reduction in the high peak of the transmitted signal whilst preserving the average transmitted power and data rate analytical results confirmed by simulations demonstrated that the proposed t ofdm system achieves lower papr and the same ber over awgn and flat fading channels compared to ofdm t ofdm is found to have better ber when mmse equalizer is used but slightly worse when zf equalizer is used

analysis of the effect of impulse noise on multicarrier and single carrier qam systems the paper first shows the equivalence of the bernoulli gaussian impulse noise model in the discrete time domain to the continuous time model of poisson arriving delta functions with random area distributed according to the power rayleigh probability density function this equivalence is then used to develop a closed form expression for the probability of error for single carrier qam that is easily evaluated furthermore the performance of multicarrier modulation mcm is also analyzed using the same impulse noise model and it is shown that in most cases mcm performs better than single carrier systems specifically when the probability of an impulse is not too high and the impulse power is moderate

an extremal problem in fourier analysis with applications to operator theory a certain minimal extrapolation problem for fourier transforms is known to have consequences for the determination of best possible bounds in some problems in linear operator equations and in perturbation of operators in this paper we estimate the value of the constant in the fourier transform problem by an analytic reformulation

asymptotic induced domain decomposition methods for kinetic and drift diffusion semiconductor equations this paper deals with domain decomposition methods for kinetic and drift diffusion semiconductor equations in particular accurate coupling conditions at the interface between the kinetic and drift diffusion domain are given the cases of slight and strong nonequilibrium situations at the interface are considered and numerical examples are shown

closing the gap in a subspace perturbation bound abstract this paper sharpens an operator inequality from perturbation theory suppose x and y are self adjoint operators on a hilbert space kx x and ky y are two closed sets bounded apart by 0 e is the spectral projector for x belonging to kx and f is the spectral projector for y belonging to ky it is known that 2 x y ef for all operators as described and for any unitary invariant norm in this paper we show 2 is best possible in this inequality we then discuss an analogous bound which applies when x and y are normal

proper complex random processes with applications to information theory the covariance of complex random variables and processes when defined consistently with the corresponding notion for real random variables is shown to be determined by the usual complex covariance together with a quantity called the pseudo covariance a characterization of uncorrelatedness and wide sense stationarity in terms of covariance and pseudo covariance is given complex random variables and processes with a vanishing pseudo covariance are called proper it is shown that properness is preserved under affine transformations and that the complex multivariate gaussian density assumes a natural form only for proper random variables the maximum entropy theorem is generalized to the complex multivariate case the differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum if and only if the random vector is proper gaussian and zero mean the notion of circular stationarity is introduced for the class of proper complex random processes a discrete fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain an application of the theory is presented

correcting wavelet codes using interleaving and trapping a rate k n wavelet code a form of real convolutional code that encodes k numbers into n numerical code symbols using the present and past input numbers may be used to transport numerical data with redundancy factor rm n rm k such codes offer detection and correction within roundoff tolerances wavelet codes can be processed using two different algebraic representations vector matrix or polyphase polynomial when an interleaver intersperses the code symbols any burst of errors within the interelaver s frame length appears in only one component of the polyphase format a special extended polyphase parity check matrix exposes the error bursts directly for redundancies greater than 1 or a deconvolver operation achieves the same when the redundancy factor is 1 the trapped errors correct the symbols by subtraction simulations verify the effectiveness of this trapping technique

efficient asymptotic preserving ap schemes for some multiscale kinetic equations many kinetic models of the boltzmann equation have a diffusive scaling that leads to the navier stokes type parabolic equations as the small scaling parameter approaches zero in practical applications it is desirable to develop a class of numerical schemes that can work uniformly with respect to this relaxation parameter from the rarefied kinetic regimes to the hydrodynamic diffusive regimes an earlier approach in s jin l pareschi and g toscani siam j numer anal 35 1998 pp 2405 2439 reformulates such systems into the common hyperbolic relaxation system by jin and xin for hyperbolic conservation laws used to construct the relaxation schemes and then uses a multistep time splitting method to solve the relaxation system here we observe that the combination of the two time split steps may yield hyperbolic parabolic systems that are more advantageous in both stability and efficiency for numerical computations we show that such an approach yields a class of asymptotic preserving ap schemes which are suitable for the computation of multiscale kinetic problems we use the goldstein taylor and carleman models to illustrate this approach

perturbation of spectra and spectral subspaces we consider the problem of variation of spectral subspaces for linear self adjoint operators with emphasis on the case of off diagonal perturbations we prove a number of new optimal results on the shift of the spectrum and obtain sharp estimates on the norm of the difference of two spectral projections associated with isolated parts of the spectrum of the perturbed and unperturbed operators respectively

one shot blind channel estimation for ofdm systems over frequency selective fading channels this paper presents a blind channel estimation bce technique for orthogonal frequency division multiplexing communications systems the proposed system is based on modulating particular pairs of subcarriers using amplitude shift keying and phase shift keying which enables the realization of a decision directed one shot bce osbce with complexity and accuracy that are comparable to pilot based channel estimation techniques the performance of the proposed estimator is evaluated in terms of the mean squared error mse where an accurate analytical expression is derived and verified using monte carlo simulation under various channel conditions the obtained results show that the mse of the proposed osbce is comparable to pilot based estimators which confirms the efficiency of the proposed osbce

frequency estimation by principal component ar spectral estimation method without eigendecomposition an eigenvalue filtering method is proposed that applies a transformation to an autocorrelation matrix which has the effect of truncating the undesired eigenvalues so that the corresponding matrix function closely approximates the pseudoinverse it is shown using a computer simulation that compared to the forward backward method the proposed method enhances the threshold in snr by about 6 8 db further improvement is obtained by a simple subset selection method and a second eigenvalue filtering iteration

ber minimized ofdm systems with channel independent precoders we consider the minimization of uncoded bit error rate ber for the orthogonal frequency division multiplexing ofdm system with an orthogonal precoder we analyze the ber performance of precoded ofdm systems with zero forcing and minimum mean squared error mmse receivers in the case of mmse receivers we show that for quadrature phase shift keying qpsk there exists a class of optimal precoders that are channel independent examples of this class include the discrete fourier transform dft matrix and the hadamard matrix when the precoder is the dft matrix the resulting optimal transceiver becomes the single carrier system with cyclic prefix sc cp system we also show that the worst solution corresponds to the conventional ofdm system the conventional ofdm system has the largest ber in the case of zero forcing receivers the design of optimal transceiver depends on the signal to noise ratio snr for higher snr solutions of optimal precoders are the same as those of mmse receivers

ber reduction of ofdm based broadband communication systems over multipath channels with impulsive noise this paper presents an efficient technique to jointly mitigate the severe bit error rate ber performance degradation caused by impulsive noise in and multipath fading in broadband transmission systems the proposed system is based on a low complexity interleaving process applied after the inverse fast fourier transform ifft in orthogonal frequency division multiplexing ofdm systems hence it is denoted as time domain interleaving tdi the proposed tdi introduces both time and frequency diversity which can be used to effectively combat impairments such as in and frequency selective fading in addition to its substantial ber reduction capability the tdi does not degrade the spectral efficiency and has low computational complexity in frequency selective fading channels the ber of the proposed system is mathematically equal to that of walsh hadamard precoded ofdm systems 1 in presence of in analytical and simulation results show that tdi can remarkably reduce the level of the error floors that are commonly observed specifically tdi can achieve a ber of 10 5 for less than 1 db difference from the in free case

fundamental performance limits of communications systems impaired by impulse noise in this paper we investigate the ultimate performance limits in terms of achievable information rate ir of communication systems impaired by impulse noise we compare single carrier sc and multi carrier mc transmission systems employing quadrature amplitude modulation qam formats more precisely we consider sc schemes with coded modulations and mc systems based on orthogonal frequency division modulation ofdm for the mc schemes we introduce a theoretically equivalent channel model which makes the computation of the ir feasible this simple channel model will be referred to as interleaved mc we show that in the presence of impulse noise and except for systems operating at very high spectral efficiency the ir of mc schemes is lower than that of sc schemes more precisely use of mc schemes may lead to an unavoidable fundamental loss with respect to sc schemes at typical coding rates whereas mc schemes are to be preferred for very high coding rates or in uncoded systems these results hold for additive white gaussian noise awgn and dispersive channels either considering plain ofdm or mc schemes employing water filling and bit loading algorithms in order to validate our theoretical results we also obtain the bit error rate ber performance of sc and mc schemes through monte carlo simulations a few trellis coded modulation tcm and low density parity check ldpc coded schemes are considered the obtained snr loss in the ber curves between the awgn and impulse noise channels matches well with the corresponding ir gap

performance analysis of zf and mmse equalizers for mimo systems an in depth study of the high snr regime this paper presents an in depth analysis of the zero forcing zf and minimum mean squared error mmse equalizers applied to wireless multiinput multioutput mimo systems with no fewer receive than transmit antennas in spite of much prior work on this subject we reveal several new and surprising analytical results in terms of output signal to noise ratio snr uncoded error and outage probabilities diversity multiplexing d m gain tradeoff and coding gain contrary to the common perception that zf and mmse are asymptotically equivalent at high snr we show that the output snr of the mmse equalizer conditioned on the channel realization is mmse zf ssrsnr where zf is the output snr of the zf equalizer and that the gap ssrsnr is statistically independent of zf and is a nondecreasing function of input snr furthermore as ssr snr ura ssrsnr converges with probability one to a scaled f random variable it is also shown that at the output of the mmse equalizer the interference to noise ratio inr is tightly upper bounded by ssrsnr zf using the decomposition of the output snr of mmse we can approximate its uncoded error as well as outage probabilities through a numerical integral which accurately reflects the respective snr gains of the mmse equalizer relative to its zf counterpart the e outage capacities of the two equalizers however coincide in the asymptotically high snr regime we also provide the solution to a long standing open problem applying optimal detection ordering does not improve the d m tradeoff of the vertical bell labs layered space time v blast architecture it is shown that optimal ordering yields a snr gain of 10log10n db in the zf v blast architecture where n is the number of transmit antennas whereas for the mmse v blast architecture the snr gain due to ordered detection is even better and significantly so

impulsive noise cancellation in multicarrier transmission a parallel between reed solomon codes in the complex field and multicarrier transmission using orthogonal frequency division multiplexing ofdm is first presented this shows that when the signal is sent over some channel composed of gaussian plus impulsive noise the impulsive noise can be removed by a procedure similar to channel decoding using information carried by the syndrome this result is first derived in a simple situation oversampled discrete multitone additive channel which is merely of theoretical interest in any case consecutive zeros in the output of the ofdm modulator do not correspond to real subcarriers pilot tones are transmitted for synchronization or channel estimation purposes these pilot tones are generally scattered among the information ones our approach is to use these pilot tones as syndromes in order to correct impulsive noise we show that the correction capacity is conditioned by the position of these pilot tones in the transmitted sequence a protection subsystem based on hypotheses tests is introduced after the decoding operation in order to detect malfunctions of this decoder the efficiency of this technique is corroborated with simulations in the slightly modified hiperlan2 context other extensions are then provided in order to increase the practical usefulness of the method

a walsh hadamard coded spectral efficient full frequency diversity ofdm system a full frequency diversity cofdm fd cofdm scheme based on sub channel multiplexing is proposed to improve the performance of cofdm without sacrificing spectral efficiency since the channel suffers the frequency selective fading the received signal contains strong inter symbol interference isi to obtain the diversity and code gains an iterative receiving algorithm is presented by jointly using diversity combining interference cancellation and soft decoding the proposed iterative receiving algorithm properly decodes the information bits in the strong isi environment consequently all the subcarriers of fd cofdm participate in diversity so that the system can achieve full frequency diversity in most practical channels the new receiving algorithm is relatively simple compared to the maximum likelihood estimation algorithm and is therefore a better alternative to balance the algorithm complexity and system performance

a hybrid method for anisotropic elliptic problems based on the coupling of an asymptotic preserving method with the asymptotic limit model this paper presents a hybrid numerical method to solve efficiently a class of highly anisotropic elliptic problems the anisotropy is aligned with one coordinate axis and its strength is described by a parameter e 0 1 which can largely vary in the study domain our hybrid model is based on asymptotic techniques and couples spatially an asymptotic preserving model with its asymptotic limit model the latter being used in regions where the anisotropy parameter e is small adequate coupling conditions link the two models the aim of this hybrid procedure is to reduce the computational time for problems where the region of small e values extends over a significant part of the domain and this is due to the reduced complexity of the limit model

perturbation of spectral subspaces and solution of linear operator equations abstract let a and b be normal operators on a hilbert space let k a and k b be subsets of the complex plane at distance at least from each other let e be the spectral projector for a belonging to k a and let f be the spectral projector for b belonging to k b our main results are estimates of the form ef c e a b f in some special situations the constant c is as low as 1 as an application we prove for an absolute constant d that if the space is finite dimensional and if a and b are normal with a b d then the spectrum of b can be obtained from that of a multiplicities counted by moving each eigenvalue by at most our main results have equivalent formulations as statements about the operator equation aq qb s let a and b be normal operators on perhaps different hilbert spaces assume a k a and b k b where k a k b and are as before then we give estimates of the forms q c aq qb

discrete cosine transform in error control coding the authors define a new class of real number linear block codes using the discrete cosine transform dct they also show that a subclass with a bch like structure can be defined and therefore encoding decoding algorithms for bch codes can be applied a 16 10 dct code is given as an example

robustness analysis of the phase phase correlator to white impulsive noise with applications to autoregressive modeling using only the phase information and a relationship based on the gaussian hypergeometric function the phase phase correlator can be utilized to estimate the normalized cross correlation coefficient between two zero mean complex gaussian processes this estimator naturally introduces a certain robustness to white impulsive observation noise over the gaussian maximum likelihood estimator this correspondence examines the robustness of the phase phase correlator in the presence of uncorrelated impulsive noise we show that its asymptotic bias compares favorably to the robust schweppe type gm estimator with the huber function termed shgm at a cost of efficiency application of the ppc to autoregressive time series analysis is illustrated with a parametric spectral estimation example

efficient algorithms for burst error recovery using fft and other transform kernels we show that the problem of signal reconstruction from missing samples can be handled by using reconstruction algorithms similar to the reed solomon rs decoding techniques usually the rs algorithm is used for error detection and correction of samples in finite fields for the case of missing samples of a speech signal we work with samples in the field of real or complex numbers and we can use fft or some new transforms in the reconstruction algorithm dsp implementation and simulation results show that the proposed methods are better than the ones previously published in terms of the quality of recovered speech signal for a given complexity the burst error recovery method using the fft kernel is sensitive to quantization and additive noise like the other techniques however other proposed transform kernels are very robust in correcting bursts of errors with the presence of quantization and additive noise

analysis and design of short block ofdm spreading matrices for use on multipath fading channels we consider the use of block spreading in a multicarrier system to gain diversity advantage when employed over multipath fading channels the main idea is to split the full set of subcarriers into smaller blocks and spread the data symbols across these blocks via unitary spreading matrices in order to gain multipath diversity across each block at the receiver we pose the problem of designing the spreading matrix as a finite dimensional optimization problem in which the asymptotic error is minimized this formulation allows us to find explicit solutions for the optimal spreading matrices the performance is validated for the uncoded channel as well as for the coded channel employing turbo iterative decoding we further demonstrate that suboptimal linear complexity equalization strategies for spread orthogonal frequency division multiplexing ofdm do not gain any diversity advantage over traditional diagonal ofdm

an asymptotic preserving method for highly anisotropic elliptic equations based on a micro macro decomposition the concern of the present work is the introduction of a very efficient asymptotic preserving scheme for the resolution of highly anisotropic diffusion equations the characteristic features of this scheme are the uniform convergence with respect to the anisotropy parameter 0 e 1 the applicability on cartesian grids to cases of non uniform and non aligned anisotropy fields b and the simple extension to the case of a non constant anisotropy intensity 1 e the mathematical approach and the numerical scheme are different from those presented in the previous work p degond f deluzet a lozinski j narski c negulescu duality based asymptotic preserving method for highly anisotropic diffusion equations communications in mathematical sciences 10 1 2012 1 31 and its considerable advantages are pointed out

hermitian symmetric dft codes a new class of complex dft codes we introduce a new class of real number codes derived from dft matrix hermitian symmetric dft hsdft codes we propose a new decoding algorithm based on coding theoretic as well as subspace based approach decoding of hsdft codes requires only real arithmetic operations and smaller dimension matrices compared to the decoding of the state of art real bch dft rbdft class of codes hsdft codes will also be shown to have more burst error correction capacity for a gauss markov source on a binary symmetric channel at lower to moderate bit error rates bers hsdft codes show better performance than rbdft codes and on a gilbert elliot channel hsdft codes consistently perform better than rbdft codes

redundancy the discrete fourier transform and impulse noise cancellation the relationship between the discrete fourier transform and error control codes is examined under certain conditions we show that discrete time sequences carry redundant information which then allow for the detection and correction of errors an application of this technique to impulse noise cancellation for pulse amplitude modulation transmission is described

a necessary condition on the location of pilot tones for maximizing the correction capacity in ofdm systems this paper presents a new view of the bose chaudhuri hocquengem bch code through the addition of some flexibility to the syndromes distribution in the transmitted sequence in order to get this flexibility we derive a necessary condition nc on the syndromes distribution for decoding bch codes which includes the already known hartmann tzeng proposition this nc is essentially deduced from the decoding process of bch code and is related to the locator polynomial and the requested constraints to guarantee a maximal error correction capacity the obtained results have the advantage to be applicable for any considered field finite or not furthermore we prove that when the correction capacity is equal to 2 or 3 the obtained nc becomes also sufficient this result is very useful in some practical transmission systems such as orthogonal frequency division multiplexing systems once the pilot tones considered in such systems verify the necessary and sufficient condition it becomes possible to both reduce the peak to average power rate and correct the impulse noise present in such multicarrier systems the usefulness of the presented analysis and the exploitation of the derived condition on the pilot tones distribution is illustrated by simulation results in the case of the hiperlan2 system

efficient techniques for impulsive noise cancellation in cgu sd systems in this paper we investigate the problem of impulsive noise cancellation in systems that use jointly overcomplete expansion representations namely the cyclic geometrically uniform cgu frame and sigma delta sd quantization we first describe the existing analogy between the cgu frames and reed solomn rs codes and how it can be exploited in order to reformulate the impulsive noise cancellation problem as the impulsive noise does by nature represent a sparse signal it fits the compressed sensing cs framework this is why we investigate how to remodel our impulsive noise cancellation in a cgu sd based system as a cs problem then we study the use and limitations of some existing cs recovery techniques namely smoothed l0 sl0 orthogonal matching pursuit omp compressive sampling matching pursuit cosamp and bayes based approach bba in order to overcome such limitations we propose how to improve such techniques and we show that their related improved versions namely improved sl0 i sl0 i omp and i cosamp and i bba efficiently cancel the impulsive noise of cgu sd systems and do lead to a quasi optimal performance simulation results are given to support our claims

a smooth transition model between kinetic and hydrodynamic equations this paper presents a model which provides a smooth transition between a kinetic and a hydrodynamic domain the idea is to use a buffer zone in which both hydrodynamics and kinetic equations will be solved the solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations we use an artificial connecting function which makes the equation on each domain degenerate at the end of the buffer zone thus no boundary condition is needed at the transition point consequently this model avoids the delicate issue of finding the interface condition in a typical domain decomposition method that couples a kinetic equation with hydrodynamic equations a simple kinetic scheme is developed to discretize our model and numerical examples are used to validate the method

block sparse impulsive noise reduction in ofdm systems a novel iterative bayesian approach using a novel block iterative bayesian algorithm block iba this paper presents a new impulsive noise reduction method for ofdm systems the method utilizes the guard band null subcarriers and data subcarriers for the impulsive noise estimation and cancellation unlike some other general ofdm transceivers which use time domain interleaving tdi to cancel impulsive noise we design a specific receiver for bursty impulsive noise channels that removes the delay due to tdi and saves memory space the block iba first estimates the variance and the transition matrix of markov chain model for the impulsive noise it then iteratively estimates the amplitudes and positions of the block sparse impulsive noise using the steepest ascent based expectation maximization em and optimally selects the nonzero elements of the block sparse impulsive noise by adaptive thresholding numerical experiments show that the proposed receiver outperforms existing receivers under the block sparse impulsive noise environment

improved coding theoretic and subspace based decoding algorithms for a wider class of dct and dst codes the decoding of a class of discrete cosine transform dct and discrete sine transform dst codes that are maximum distance separable codes mds is considered in this paper these class of codes are considered for error correction over real fields all the existing algebraic decoding algorithms are capable of decoding only a subclass of these codes which can be characterized into the bose chaudhuri hocquenghem bch form and fails to decode the remaining even though they are mds in this paper we propose a new generic algorithm along the lines of coding theoretic and subspace methods to decode the entire class of mds dct and dst codes the proposed subspace approaches are similar to popular esprit and music algorithms the proposed algorithms also perform significantly better than the existing algorithms on the bch like subclass a perturbation analysis is also presented to study the effect of various parameters on the error localization due to the quantization noise simulation results are presented to demonstrate the capability of proposed algorithms to decode the entire class and to perform significantly better on the bch like subclass than the existing algorithm under the influence of quantization noise