theoretical analysis and performance of ofdm signals in nonlinear awgn channels orthogonal frequency division multiplexing ofdm baseband signals may be modeled by complex gaussian processes with rayleigh envelope distribution and uniform phase distribution if the number of carriers is sufficiently large the output correlation function of instantaneous nonlinear amplifiers and the signal to distortion ratio can be derived and expressed in an easy way as a consequence the output spectrum and the bit error rate ber performance of ofdm systems in nonlinear additive white gaussian noise channels are predictable both for uncompensated amplitude modulation amplitude modulation am am and amplitude modulation pulse modulation am pm distortions and for ideal predistortion the aim of this work is to obtain the analytical expressions for the output correlation function of a nonlinear device and for the ber performance the results in closed form solutions are derived for am am and am pm curves approximated by bessel series expansion and for the ideal predistortion case

a novel decomposition analysis of nonlinear distortion in ofdm transmitter systems in orthogonal frequency division multiplexing ofdm transmitter systems nonlinear distortion is a major impairment caused by power amplifier pa the distortion is constituted by numerous noise like inter modulation products imps although the overall behavior of nonlinear imp distortion has been well studied in large multi carrier contexts such as in ofdm the knowledge of individual imps and their quantitative interrelationships together with the derivation of behavioural knowledge and the predictability of consequences arising from such interrelationships is a fairly unexplored topic this is the subject of this paper the powers of the very numerous individual imps generated are analytically derived based on a bessel fourier pa behavioural model and it is proven that these powers have only a small number of distinct powers proven also is that the ratios of these power values are constants and that these constants are invariant with the particular pa s nonlinearity characteristics or operating point further it is proven that specific types of imps dominate nonlinear distortion effects finally it is shown that imp power spectra can be derived from a simple product of two polynomials which are quadrature functions of frequency and pa operating point respectively application possibilities for findings presented in this paper such as their potential to contribute efficiency improvements in ofdm system modulation fidelity calculations over 1100 times faster than conventional methods are also outlined in the conclusions

on actor critic algorithms in this article we propose and analyze a class of actor critic algorithms these are two time scale algorithms in which the critic uses temporal difference learning with a linearly parameterized approximation architecture and the actor is updated in an approximate gradient direction based on information provided by the critic we show that the features for the critic should ideally span a subspace prescribed by the choice of parameterization of the actor we study actor critic algorithms for markov decision processes with polish state and action spaces we state and prove two results regarding their convergence

solute transport in highly heterogeneous aquifers the paper deals with the transport of nonreactive solute in heterogeneous formations with prescribed statistical properties of the hydraulic log conductivity y ln k available solutions obtained from perturbation methods are limited to first and second order solutions valid only for small values of the log conductivity variance 2y published numerical investigations give comparative results with finite values of 2y but some discrepancies among the results generate doubts about the capability of numerical methods to capture high order effects for media with large variance values when these large 2y values are encountered in natural formations the related nonlinear effects could be significant in the velocity statistics and in the overall dispersion process the nonlinearity consequences are here investigated in two dimensional isotropic porous media by the monte carlo technique coupled with a finite element analysis the analysis includes 2y values from 0 05 to 4 enhancing the relevance of the nonlinear effects in the dispersion tensor solution to dissipate the doubts related to the numerical approach the accuracy of the solutions was defined by checking the influence of the factors which can affect the solution and by giving an estimation of the related errors the numerical results confirm the validity of the first order and second order analyses when 2y 0 the second order solution captures the nonlinear effects in a small range of log conductivity variance close to zero the nonlinear terms neglected in the first order formulation for higher 2y values give 1 late travel time longitudinal dispersion values greater than the linear solution 2 notably non gaussian distribution of the lagrangian velocity and particle displacements and 3 travel times to approach the asymptotic fickian regime longer than those obtained using the linear solution

higher order effects on flow and transport in randomly heterogeneous porous media advective solute transport in nonuniform geologic media is generally nonlocal and non fickian neuman 1993 cushman and ginn 1993 in statistically homogeneous log conductivity fields under uniform mean flow the transport is expected to become asymptotically local and fickian at late time during the earlier preasymptotic regime macrodispersivity a measure of the rate at which a plume spreads is expected to vary with solute residence time a first order linear in the natural log hydraulic conductivity variance 2 analysis of this variation has been performed by dagan 1984 1987 1988 he found that when local dispersion is neglected the longitudinal macrodispersivity increases monotonically from zero toward a constant asymptote however the transverse macrodispersivity first increases from zero to a peak value then decreases monotonically toward zero the first order asymptotic analyses by winter 1982 gelhar and axness 1983 and winter et al 1984 also yield zero transverse macrodispersivity when local dispersion is disregarded

solute transport in three dimensional heterogeneous media with a gaussian covariance of log hydraulic conductivity the analytical solutions for the velocity covariance uij one particle displacement covariance xij and the macrodispersivity tensor ij defined as 0 5 dxij dt were derived in three dimensional heterogeneous media a gaussian covariance function gcf of logarithmic hydraulic conductivity log k was used assuming uniform mean flow and first order approximation in log conductivity variance where is the magnitude of the mean flow velocity based on these solutions the time dependent ensemble averages of the second spatial moments zij aij aij 0 xij rij and the effective dispersivity tensor ij defined as 0 5 d aij dt were evaluated for a finite line source either normal or parallel to where aij 0 is the initial value of the second spatial moment of a plume aij and rij is the plume centroid covariance the results obtained in this study were compared with previous results for an exponential covariance function ecf it was found that in a stationary log k field the spreading of a solute plume depends not only on the variance and integral scale of the log k field but also on the shape of its covariance function the more strongly correlated the hydraulic conductivities at short separation distances are the faster zii and ii grow at early time also the earlier that ii approaches its asymptote or peak and the higher the peak is the larger the negative transverse dispersivity more importantly the ergodic limits for gcf are reached faster than those for ecf as the initial size of a plume increases the ergodic limit x11 for gcf is slightly larger than that for ecf but x22 and x33 are significantly smaller than those for ecf even though the asymptotic ii for gcf is the same with that for ecf

analytical modeling of mimo ofdm system in the presence of nonlinear power amplifier with memory in this paper the effects of nonlinear high power amplifier hpa with memory on multi input multi output mimo orthogonal frequency division multiplexing ofdm system are analyzed and a theoretical framework is proposed the memory effects are represented by generalized memory polynomial gmp model moreover we derive an analytical formulation with infinite nonlinearity order and infinite memory length the channel is assumed mimo frequency selective and it is modeled as a linear dispersive channel with uniform power profile we show that the decision variables of the nonlinearity distortion can be modeled by the complex attenuation and zero mean additive noise model the analytical expressions for complex attenuation mean and variance of nonlinear noise are derived and ser of mimo ofdm system using hpa with memory is presented excellent agreement between the analytical results and numerical simulations is observed that verifies the accuracy and efficiency of the proposed method

event based optimization of markov systems recent research indicates that markov decision processes mdps and perturbation analysis pa based optimization can be derived easily from two fundamental performance sensitivity formulas with this sensitivity point of view an event based optimization approach including event based sensitivity analysis and event based policy iteration was proposed via an example by x r cao discrete event dyn syst theory appl vol 15 pp 169 197 2005 this approach utilizes the special feature of a system and illustrates how the potentials can be aggregated using the special feature the approach applies to many practical problems that do not fit well the standard mdp formulation this note provides a mathematical formulation and proves the main results for this approach

simulation based optimization of markov reward processes this paper proposes a simulation based algorithm for optimizing the average reward in a finite state markov reward process that depends on a set of parameters as a special case the method applies to markov decision processes where optimization takes place within a parametrized set of policies the algorithm relies on the regenerative structure of finite state markov processes involves the simulation of a single sample path and can be implemented online a convergence result with probability 1 is provided

the influence of pore scale dispersion on concentration statistical moments in transport through heterogeneous aquifers transport of an inert solute in a heterogeneous aquifer is governed by two mechanisms advection by the random velocity field v x and pore scale dispersion of coefficients ddij the velocity field is assumed to be stationary and of constant mean u and of correlation scale i much larger than the pore scale d it is assumed that ddij diju are constant the relative effect of the two mechanisms is quantified by the peclet numbers peij u ddij i dij which as a rule are much larger than unity the main aim of the study is to determine the impact of finite though high pe on c and c2 the concentration mean and variance respectively the solution derived in the past for pe is reconsidered first by assuming a normal x probability density function p d f closed form solutions are obtained for c and c2 recasting the problem in an eulerian framework leads to the same results if certain closure conditions are adopted the concentration moments for a finite pe are derived subsequently in a lagrangean framework the pore scale dispersion is viewed as a brownian motion type of displacement xd of solute subparticles of scale smaller than d added to the advective displacements x by adopting again a normal p d f for the latter explicit expressions for c and c2 are obtained in terms of quadratures over the joint p d f of advective two particles trajectories while the influence of high pe on c is generally small it has a significant impact on c2 simple results are obtained for a small v0 for which trajectories are fully correlated in particular the concentration coefficient of variation at the center tends to a constant value for large time comparison of the present solution obtained in terms of a quadrature with the monte carlo simulations of graham and mclaughlin 1989 shows a very good agreement

conditional estimation of solute travel time in heterogeneous formations impact of transmissivity measurements solute transport through heterogeneous formations is modeled by the travel time approach i e the time it takes a solute particle to travel from the source to a control plane due to uncertainty is a random variable characterized by its cumulative probability density function g this function is used by regulatory agencies in pollution site assessment the main aim of the present study is to examine the impact of data namely measured transmissivities upon g and reduction of uncertainty this is achieved for two dimensional steady flow of average uniform head gradient by using a lagrangian approach developed in the past dagan 1982 1984 1989 rubin 1990 1991 the impact of data is seen in conditioning on measured values and in estimation of parameters characterizing flow and formation properties the approach is illustrated by a simulation based on synthetic data the results show how uncertainty is reduced by increasing the density of measurements for a control plane sufficiently far from the source

performance analysis of linear precoded mu mimo ofdm systems with nonlinear power amplifiers and correlated channel in this paper we investigate the effect of power amplifier pa nonlinearity on a multi user multiple input multiple output orthogonal frequency division multiplexing mu mimo ofdm system where the base station bs uses linear precoding to transmit data for single antenna users through a correlated channel the signal to distortion interference and noise ratio is derived for any order of pa nonlinearity our analysis shows that a correlated channel can result in correlated distortions at the output of pas which increase the received distortion power of users approximations for the ergodic achievable rate of the users are provided when the bs transmits data through a correlated channel using maximum ratio transmission or zero forcing precodings and number of bs antennas and users are large also closed form approximations for the ergodic achievable sum rate of the system are provided when the channel is not correlated the simulation results agree with the derived approximations even when the number of transmit antennas and users are relatively small the approximations can be used to find the achievable sum rate maximizing number of users or transmit power of the system

a practical analysis of performance optimization in ostbc based nonlinear mimo ofdm systems this paper presents a practical performance analysis of an orthogonal space time block code ostbc based multiple input multiple output mimo orthogonal frequency division multiplexing ofdm system in the presence of nonlinear power amplifiers pas the equivalent single input single output siso scalar model is introduced and this then is used to construct a model for the nonlinear mimo ofdm system based on an unique inter modulation product imp analysis it is shown how the receiver signal to noise ratio snr may be derived to a polynomial based function of the system operating point it is also shown that expressions for the asymptotical behavior of this snr when the linear and highly nonlinear pa operations are applied may also be derived based on these derivations it is further shown that the optimal system operating point which corresponds to the maximum receiver snr and sep lower bound can be identified and be derived to a polynomial based expression additionally a general expression for the different integral expressions of sep for the phase shift keying psk and quadrature amplitude modulation qam signals is found by means of these analytical results it was found possible to advance analytical explanations of observed behaviour in simulations and also to provide a practical analysis of performance optimization of nonlinear mimo ofdm systems

stochastic optimization of regenerative systems using infinitesimal perturbation analysis we consider the problem of optimizing the steady state mean of a controlled regenerative process using a stochastic optimization algorithm driven by infinitesimal perturbation analysis ipa derivative estimates we derive ipa derivative estimates for our problem and prove almost sure convergence of the algorithm the generality of our formulation should encompass a wide variety of practical systems we illustrate our framework and results via several examples

optimization of queues using an infinitesimal perturbation analysis based stochastic algorithm with general update times convergence with probability one of a stochastic optimization algorithm for a single server queue is proved the parameter to be optimized is updated using an infinitesimal perturbation analysis estimate of the gradient of the performance measure and the updates are performed at general times first an algorithm in which the parameter is updated before each customer begins service is considered then it is shown how this analysis can be extended to an algorithm that updates at certain stopping times the analysis suggests that the sample path behavior of the algorithm is similar to that of an algorithm that updates at the start of every busy period

effect of smooth nonlinear distortion on ofdm symbol error rate nonlinear distortion of ofdm signals can significantly increase the receiver symbol error rate ser currently distortion analyses rely on simulation not yielding insight into the problem or apply to specific nonlinearities only in this letter general analytic results are presented on the errors resulting from distortion the results are applicable to smooth nonlinear distortion of an ofdm signal which is the most common distortion simple analytical expressions are derived which allows a designer to determine the ser before performing simulations further it is shown that the error on each ofdm subcarrier is approximately equally large

the n th order bias optimality for multichain markov decision processes in this paper we propose a new approach to the theory of finite multichain markov decision processes mdps with different performance optimization criteria we first propose the concept of nth order bias then using the average reward and bias difference formulas derived in this paper we develop an optimization theory for finite mdps that covers a complete spectrum from average optimality bias optimality to all high order bias optimality in a unified way the approach is simple direct natural and intuitive it depends neither on laurent series expansion nor on discounted mdps we also propose one phase policy iteration algorithms for bias and high order bias optimal policies which are more efficient than the two phase algorithms in the literature furthermore we derive high order bias optimality equations this research is a part of our effort in developing sensitivity based learning and optimization theory

adaptive estimation of the log fluctuating conductivity from tracer data at the cape cod site an adaptive estimation scheme is used to obtain the integral scale and variance of the log fluctuating conductivity at the cape cod site based on the fast fourier transform stochastic model of deng et al 1993 and a kalmanlike filter the filter incorporates prior estimates of the unknown parameters with tracer moment data to adaptively obtain improved estimates as the tracer evolves the results show that significant improvement in the prior estimates of the conductivity can lead to substantial improvement in the ability to predict plume movement the structure of the covariance function of the log fluctuating conductivity can be identified from the robustness of the estimation both the longitudinal and transverse spatial moment data are important to the estimation

dynamic range and other fundamentals of the complex bessel function series approximation model for memoryless nonlinear devices an explanation is given of the application of the complex bessel function series approximation model of the memoryless amplitude and phase characteristics of nonlinear devices confusion had arisen because of the choice of a value of a parameter in the approximating expression the practice had been to choose this simply as though it was just an arbitrary constant which scales the input or as an optimizing parameter in the effort to get a best fit of the approximation to the measured data by examining the derivation of the particular approximation a determining and important link between this parameter and the desired operating dynamic range of the nonlinear characteristic being approximated is shown how values for this parameter are calculated in terms of input overdrive relative to device saturation is also shown in examining the origin of the approximating expressions an alternative and simpler derivation to that given by j c fuenzalida et al 1973 is presented that is based on the work of m j eric et al 1972

a solute flux approach to transport in heterogeneous formations 1 the general framework it is common to represent solute tranport in heterogeneous formations in terms of the resident concentration c x t regarded as a random space function the present study investigates the alternative representation by q the solute mass flux at a point of a control plane normal to the mean flow this representation is appropriate for many field applications in which the variable of interest is the mass of solute discharged through a control surface a general framework to compute the statistical moments of q and of the associated total solute discharge q and mass m is established with x the direction of the mean flow a solute particle is crossing the control plane at y z and at the travel arrival time the associated expected solute flux value is proportional to the joint probability density function pdf g1 of and whereas the variance of q is shown to depend on the joint pdf g2 of the same variables for two particles in turn the statistical moments of and depend on those of the velocity components through a system of stochastic ordinary differential equations for a steady velocity field and neglecting the effect of pore scale dispersion a major simplification of the problem results in the independence of the random variables and as a consequence the pdf of and can be derived independently of a few approximate approaches to derive the statistical moments of and are outlined these methods will be explored in paper 2 in order to effectively derive the variances of the total solute discharge and mass while paper 3 will deal with the nonlinear effect of the velocity variance upon the moments of and

actor critic type learning algorithms for markov decision processes algorithms for learning the optimal policy of a markov decision process mdp based on simulated transitions are formulated and analyzed these are variants of the well known actor critic or adaptive critic algorithm in the artificial intelligence literature distributed asynchronous implementations are considered the analysis involves two time scale stochastic approximations

convergence of parameter sensitivity estimates in a stochastic experiment to reduce the error in estimating the gradient parameter sensitivity of an unknown function is of great importance in stochastic optimization problems three kinds of parameter sensitivity estimates using the monte carlo method are discussed in this paper the estimates depend on the number of replications n and the change in parameter delta d the convergence properties as n rightarrow infty and delta d rightarrow 0 for these estimates are obtained the result explains many theoretical and practical issues in the study of discrete event dynamic systems as well as continuous dynamic systems by the monte carlo method it is proved that an estimate based on averaging the gradients calculated along each sample path by a perturbation of the path is much better than the other estimates if the output functions are uniformly differentiable with probability one w p 1 it is also concluded that in computer simulations one should always choose the same seed for both d and d delta d in estimating the parameter sensitivity combining the results in this paper with existing stochastic approximation algorithms may yield algorithms with faster convergence

characterization of aquifer heterogeneity using indicator variables for solute concentrations 1 a new approach to the use of tracer test concentration data for inference of the parameters characterizing the hydraulic conductivity heterogeneity is introduced rather than using concentration data directly the concentrations are transformed into indicator variables whose time dependent mean and covariance structure in a control plane orthogonal to the mean flow direction are developed in terms of the log conductivity variance vertical and horizontal correlation lengths and the mean flow velocity parameter values can be inferred by comparison of the theoretical indicator moments with field measurements the approach is found to have several advantages over the direct use of concentrations these include 1 insensitivity of the indicator covariance to the log conductivity variance allowing for independent determination of the integral scale in isotropic media and 2 less susceptibility to measurement errors or interference from ambient groundwater concentrations also because the indicator records only the first concentration detect it is more efficient than methods such as travel time moment analysis which require the entire breakthrough record

eulerian lagrangian approach for modeling of flow and transport in heterogeneous geological formations this paper presents a new eulerian lagrangian method for modeling flow and transport of passive solutes in heterogeneous porous formations the physically plausible random velocity fields are generated by a geostatistical based model the ability of the method to correctly reproduce the velocity field statistics and to satisfy mass balance is tested and demonstrated for the case of two dimensional flow the method is found particularly useful in dealing with large fields where numerical fixed grid methods such as finite difference or finite elements become very demanding from a computational point of view the transport problem is solved in a lagrangian framework by the particle tracking approach which uses a suitable grid refinement to correctly handle the velocity fluctuation at any a priori defined resolution the new method is employed to compute the probability distribution functions of the concentration and travel times and to investigate the limitations of existing methods for predicting concentrations

potential based online policy iteration algorithms for markov decision processes performance potentials play a crucial role in performance sensitivity analysis and policy iteration of markov decision processes the potentials can be estimated on a single sample path of a markov process in this paper we propose two potential based online policy iteration algorithms for performance optimization of markov systems the algorithms are based on online estimation of potentials and stochastic approximation we prove that with these two algorithms the optimal policy can be attained after a finite number of iterations a simulation example is given to illustrate the main ideas and the convergence rates of the algorithms