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

numerical solution of three dimensional volterra fredholm integral equations of the first and second kinds based on bernstein s approximation abstract a new and efficient method is presented for solving three dimensional volterra fredholm integral equations of the second kind 3d vfiek2 first kind 3d vfiek1 and even singular type of these equations here we discuss three variable bernstein polynomials and their properties this method has several advantages in reducing computational burden with good degree of accuracy furthermore we obtain an error bound for this method finally this method is applied to five examples to illustrate the accuracy and implementation of the method and this method is compared to already present methods numerical results show that the new method provides more efficient results in comparison with other methods

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

an iterative multistep kernel based method for nonlinear volterra integral and integro differential equations of fractional order abstract an iterative multistep kernel based method is proposed for the nonlinear volterra integral equations and nonlinear volterra integro differential equations of fractional order which can produce reliable globally smooth numerical solutions an error estimate of the positive definite kernel interpolation and the convergence and error analysis of the proposed iterative scheme are investigated here we focused on positive definite radial basis kernels and further a new and applicable shape parameter selection strategy is proposed the proposed multi step method set up and solve several small local problems instead of a single large problem which makes it suitable for problems with long time simulations in order to show the efficiency and versatility of the proposed method some numerical experiments are reported the comparison of the numerical results with the analytical solutions and the best reported results in the literature confirm the good accuracy and applicability of the proposed method

detecting ofdm signals in alpha stable noise this paper analyzes various receiver schemes for orthogonal frequency division multiplexing ofdm transmission in impulsive noise we consider rayleigh block fading and model the noise process by additive white symmetric stable noise aws sn we begin by discussing maximum likelihood ml detection performance of baseband ofdm though optimal the computational cost increases exponentially with the number of carriers alternatively one may evaluate soft estimates of the transmitted symbol block and employ carrier wise detection to lower computational complexity we analyze such schemes under the frameworks of m estimation and compressed sensing theory moving on we highlight important rules that ensure the passband aws sn process is converted to a baseband form suitable for the discussed schemes finally it is shown that linear passband to baseband conversion actually reduces the signal to noise ratio snr at the receiver and that all these rules may be avoided by applying an estimation scheme directly on the passband samples

solving a class of two dimensional linear and nonlinear volterra integral equations by the differential transform method in this paper we will give some results for developing the two dimensional differential transform tddt for double integrals then the tddt method will be developed for solving a class of two dimensional linear and nonlinear volterra integral equations we also give some examples to demonstrate the accuracy of the method

a computational method for solving a class of two dimensional volterra integral equations the use of the geometric series theorem together with schauder bases in certain banach spaces allows us to design a numerical algorithm in order to solve an important type of two dimensional linear integral equations a study of the convergence and error is presented here all the calculations can be easily implemented and the efficiency of this method will be shown with numerical results

bistable kinetic model driven by correlated noises steady state analysis a simple rule to obtain the fokker planck equation for a general one dimensional system driven by correlated gaussian white noises is proved by the functional method the fokker planck equation obtained in this paper is applied to the bistable kinetic model we find the following for the steady state 1 in the ensuremath alpha d parameter plane ensuremath alpha is the strength of the additive noise and d is the multiplicative noise strength the critical curve separating the unimodal and bimodal regions of the stationary probability distribution spd of the model is shown to be affected by ensuremath lambda the degree of correlation of the noises as ensuremath lambda is increased the area of the bimodal region in the ensuremath alpha d plane is contracted 2 when we take a point fixed in the ensuremath alpha d plane and increase ensuremath lambda the form of the spd changes from a bimodal to a unimodal structure 3 the positions of the extreme value of the spd of the model sensitively depend on the strength of the multiplicative noise and weakly depend on the additive noise strength 4 for ensuremath lambda 1 the case of perfectly correlated noises when the parameters ensuremath alpha and d take values in the neighborhood of the line ensuremath alpha d in the ensuremath alpha d plane the spd s corresponding to the points ensuremath alpha dg1 and ensuremath alpha d1 exhibit a very different shape of divergence therefore the ratio ensuremath alpha d 1 plays the role of a critical ratio

extrapolation method of iterated collocation solution for two dimensional nonlinear volterra integral equations in this paper we study the numerical solution of two dimensional nonlinear volterra integral equation by collocation and iterated collocation method asymptotic error expansion of iterated collocation solution is obtained using richardson s extrapolation we show that the accuracy of numerical solution in the iterated collocation method can be improved greatly some numerical examples are given to illustrate this theory

differential transform method for the system of two dimensional nonlinear volterra integro differential equations in this paper we develop the differential transform method dtm for solving a class of the system of two dimensional linear and nonlinear volterra integro differential equations of the second kind to this end we give some preliminary results of the differential transform and describe the method of this paper we also give some examples to demonstrate the accuracy of the presented method

on the use of cascade structure to correct impulsive noise in multicarrier systems we propose a new decoding algorithm based on a cascade structure for impulsive noise correction in multicarrier systems such as orthogonal frequency division multiplexing ofdm based systems this new cascade structure based algorithm has the advantage to lead on one hand to a reduced complexity implementation in an ofdm demodulator and on the other hand to overcome the lacks of other algorithms dedicated for impulsive noise correction to do so we start the derivation by investigating closed form analytical expressions of the a priori probabilities used in hypotheses tests that are necessary for the different steps needed for the execution of the cascade structure based decoding algorithm such closed form expressions for the a priori probabilities result in efficient setups of the threshold values used for the execution of the decoding algorithm furthermore we show that this cascade structure can be applied to efficiently cancel the impulsive noise in ofdm systems as the clipping event present in ofdm systems can be seen as an additive impulsive noise we prove that after introducing some minor modifications we can apply the proposed cascade structure to significantly reduce the peak to average power ratio papr level in such systems simulation results are given to illustrate the usefulness of the proposed algorithm results in practical ofdm based communication systems such as hiperlan 2

numerical approaches for systems of volterra fredholm integral equations in this work we introduce two numerical methods for solving systems of volterra fredholm integral equations in the nonlinear case we suggest a fixed point method where the iterations are perturbed in a suitable way according to a schauder basis in the banach space of continuous functions c a b 2 in the linear case we propose a collocation method based on a particular class of approximating functions in both methods convergence analysis and or low computational cost are analysed taking into account the properties of the basis under consideration numerical results confirm the theoretical study

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

extrapolation method for solving two dimensional volterral integral equations of the second kind abstract in this paper we propose a numerical quadrature method for solving two dimensional linear and nonlinear volterra integral equations firstly we generalize one dimensional quadrature formula to two dimensional case and its corresponding error asymptotic expansion based on the quadrature formula and the error expansion we next construct an iterative scheme and extrapolation algorithm the numerical solution of any point can be calculated by iterative scheme and the error accuracy and convergence order of the numerical solution are further improved by extrapolation algorithm using the extrapolation algorithm we can improve the convergence order from o h 0 2 to o h 0 3 or even o h 0 4 since the numerical solution of each point is obtained by assignment operation and iteration the computational complexity can be greatly reduced finally four numerical examples are given to illustrate the effectiveness of the method

comments on solving a class of two dimensional linear and nonlinear volterra integral equations by the differential transform method tari et al a tari m y rahimi s shahmorad f talati solving a class of two dimensional linear and nonlinear volterra integral equations by the differential transform method j comput appl math 228 2009 70 76 presented some fundamental properties of tdtm for the kernel functions in two dimensional volterra integral equations here we suggest simple proofs of those fundamental properties by using the basic properties of tdtm furthermore we present some fundamental properties of tdtm for the kernel functions of a quotient type in two dimensional volterra integral equations numerical illustrations are demonstrated to show the effectiveness of the tdtm for solving two dimensional volterra integral equations

an integral equation describing an asexual population in a changing environment in this paper we establish the existence of a travelling wave solution to an intrinsically nonlinear differential integral equation arising from the mathematical modelling of an asexual reproduction process the techniques used are fixed point theorems and asymptotic analysis the proofs although abstract give a hint on how to obtain the solutions numerically

anticipating regime shifts in gene expression the case of an autoactivating positive feedback loop considerable evidence suggests that anticipating sudden shifts from one state to another in bistable dynamical systems is a challenging task examples include ecosystems financial markets and complex diseases in this paper we investigate the effects of additive multiplicative and cross correlated stochastic perturbations on determining the regime shifts in a bistable gene regulatory system which gives rise to two distinct states of low and high concentrations of protein we obtain the stationary probability density and mean first passage time of the system we show that increasing the additive multiplicative noise intensity induces a regime shift from a low high to a high low protein concentration state however an increase in the cross correlation intensity always induces regime shifts from a high to a low protein concentration state for both bifurcation induced often called the tipping point and noise induced called stochastic switching regime shifts we further explore the robustness of recently developed critical down based early warning signal ews indicators e g rising variance and lag 1 autocorrelation on our simulated time series data we identify that using ews indicators prediction of an impending bifurcation induced regime shift is relatively easier than that of a noise induced regime shift in the considered system moreover the success of ews indicators also strongly depends upon the nature of the noise

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

a generalization of discrete gronwall inequality and its application to weakly singular volterra integral equation of the second kind this paper presents a new discrete gronwall inequality using the inequality we prove convergence and error estimate of the numerical solutions of the second weakly singular volterra integral equation where discrete equation is derived by novot s quadrature formula

numerical solution of a class of two dimensional nonlinear volterra integral equations using legendre polynomials in this paper a method for finding an approximate solution of a class of two dimensional nonlinear volterra integral equations is discussed the properties of two dimensional shifted legendre functions are presented the operational matrices of integration and product together with the collocation points are utilized to reduce the solution of the integral equation to the solution of a system of nonlinear algebraic equations some results concerning the error analysis are obtained we also consider the application of the method to the solution of certain partial differential equations illustrative examples are included to demonstrate the validity and applicability of the technique

new approach to solve two dimensional fredholm integral equations abstract in this paper we present an efficient iterative method based on quadrature formula to solve two dimensional nonlinear fredholm integral equations we investigate the convergence analysis of the proposed method the error estimation is given in terms of uniform and partial modulus of continuity in addition we show the numerical stability analysis of the method with respect to the choice of the first iteration finally some numerical experiments confirm the theoretical results and illustrate the accuracy of 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

two dimensional triangular functions and their applications to nonlinear 2d volterra fredholm integral equations two dimensional orthogonal triangular functions 2d tfs are presented as a new set of basis functions for expanding 2d functions their properties are determined and an operational matrix for integration obtained furthermore 2d tfs are used to approximate solutions of nonlinear two dimensional integral equations by a direct method since this approach does not need integration all calculations can be easily implemented and several advantages in reducing computational burdens arise finally the efficiency of this method will be shown by comparison with some numerical results

a new algorithm for the solution of nonlinear two dimensional volterra integro differential equations of high order abstract in this manuscript a new numerical approach is developed for approximating the solution of the one dimensional and two dimensional volterra integro differential equations 2d vides of high order new operational matrices of integration based on shifted jacobi polynomials are presented and used in combination with the collocation method to convert the 2d vide into a system of algebraic equations in addition the convergence analysis of the suggested approach is investigated the efficiency of the algorithm is demonstrated by means of several examples and the results are compared with those given using other numerical schemes