average rate of downlink heterogeneous cellular networks over generalized fading channels a stochastic geometry approach in this paper we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks the framework leverages recent application of stochastic geometry to other cell interference modeling and analysis the heterogeneous cellular network is modeled as the superposition of many tiers of base stations bss having different transmit power density path loss exponent fading parameters and distribution and unequal biasing for flexible tier association a long term averaged maximum biased received power tier association is considered the positions of the bss in each tier are modeled as points of an independent poisson point process ppp under these assumptions we introduce a new analytical methodology to evaluate the average rate which avoids the computation of the coverage probability pcov and needs only the moment generating function mgf of the aggregate interference at the probe mobile terminal the distinguishable characteristic of our analytical methodology consists in providing a tractable and numerically efficient framework that is applicable to general fading distributions including composite fading channels with small and mid scale fluctuations in addition our method can efficiently handle correlated log normal shadowing with little increase of the computational complexity the proposed mgf based approach needs the computation of either a single or a two fold numerical integral thus reducing the complexity of pcov based frameworks which require for general fading distributions the computation of a four fold integral

on a generalization of mittag leffler function and its properties abstract let s and z be complex variables s the gamma function and s s s for any complex the generalized pochhammer symbol the principal aim of the paper is to investigate the function e q z n 0 q n n z n n where c re 0 re 0 re 0 and q 0 1 n this is a generalization of the exponential function exp z the confluent hypergeometric function z the mittag leffler function e z the wiman s function e z and the function e z defined by prabhakar for the function e q z its various properties including usual differentiation and integration laplace transforms euler beta transforms mellin transforms whittaker transforms generalised hypergeometric series form mellin barnes integral representation with their several special cases are obtained and its relationship with laguerre polynomials fox h function and wright hypergeometric function is also established

choice of specific interpolation points in quadrature formula for integrals containing bessel functions a method for calculation of integrals containing bessel functions is suggested which based on linear interpolation applied to the function entering the integral along with the bessel function a specific choice of interpolation points allows excluding the contribution into integral of all interpolation points besides the first one the study of errors leads to determination of bounds of the considered integral

numerical evaluation of spherical bessel transforms via fast fourier transforms the purpose of this article is to describe a new fast fourier transform fft method for calculating spherical bessel transforms the method is based on an expansion representation of the spherical bessel functions in terms of sine and cosine trigonometric functions multiplied by polynomials in inverse powers of the argument of the bessel function 11 the method should be of value in algorithms in which frequent calculations of spherical bessel transforms are required at many values of the transform variables which is frequently the situation in time dependent scattering calculations the method makes use of ffts for which the computing time for each transform scales as nlog n where n is the number of quadrature points rather than the n2 scaling of ordinary numerical quadratures also the explicit evaluation of the spherical bessel functions is not required in the method the method differs from that given in the work of j d talman 2 33 and a e siegmon 4 in the work of talman 2 33 and siegman 4 a change to logarithmic variables is required to recast the integral transform as a convolution integral which is then evaluated by fft procedures however as pointed out by talman this makes the step size ar increase proportionally with r and renders the method unsuitable for functions of an oscillatory nature in particular the oscillatory nature of the function is lost in the increasing mesh intervals in essence the talman siegman method is excellent for bound state wave functions but it is not

structure of the liquid vapor interface using a gaussian column model with a variable interaction range abstract we study properties of the liquid vapor interface using an exactly solvable model consisting of a one dimensional array of columns whose interaction is of variable range and quadratic in the height difference between columns in the limit of infinitely long ranged intercolumn interactions the classical mean field description of the interface is exact there is an intrinsic interface profile of finite width and all pair correlations are short ranged however for realistic short ranged interactions the model is equivalent to the capillary wave model of buff lovett and stillinger here we find long ranged pair correlations parallel to the interface of precisely the form deduced by wertheim the interface profile now depends on system size and strength of an external gravitational field the interface width diverges as the field tends to zero in an infinite system explicit expressions for the pair correlation are inverted to yield the direct correlation function in the interfacial region

outage probability of diversity systems over generalized fading channels outage probability is an important performance measure of communication systems operating over fading channels relying on a simple and accurate algorithm for the numerical inversion of the laplace transforms of cumulative distribution functions we develop a moment generating function based numerical technique for the outage probability evaluation of maximal ratio combining mrc and postdetection equal gain combining egc in generalized fading channels for which the fading in each diversity path need not be independent identically distributed nor even distributed according to the same family of distributions the method is then extended to coherent egc but only for the case of nakagami m fading channels the mathematical formalism is illustrated by applying the method to some selected numerical examples of interest showing the impact of the power delay profile and the fading correlation on the outage probability of mrc and egc systems

an algorithm for the numerical evaluation of the hankel and abel transforms a procedure for the efficient numerical evaluation of the hankel and abel transforms is proposed the abel transform is reduced to a convolution which is evaluated in part analytically and in part with an fft the hankel transform is obtained by following the abel transform with an fft

technical report an mgf based unified framework to determine the joint statistics of partial sums of ordered i n d random variables the joint statistics of partial sums of ordered random variables rvs are often needed for the accurate performance characterization of a wide variety of wireless communication systems a unified analytical framework to determine the joint statistics of partial sums of ordered independent and identically distributed i i d random variables was recently presented however the identical distribution assumption may not be valid in several real world applications with this motivation in mind we consider in this paper the more general case in which the random variables are independent but not necessarily identically distributed i n d more specifically we extend the previous analysis and introduce a new more general unified analytical framework to determine the joint statistics of partial sums of ordered i n d rvs our mathematical formalism is illustrated with an application on the exact performance analysis of the capture probability of generalized selection combining gsc based rake receivers operating over frequency selective fading channels with a non uniform power delay profile we also discussed a couple of other sample applications of the generic results presented in this work

an mgf based unified framework to determine the joint statistics of partial sums of ordered random variables order statistics find applications in various areas of communications and signal processing in this paper we introduce an unified analytical framework to determine the joint statistics of partial sums of ordered random variables rvs with the proposed approach we can systematically derive the joint statistics of any partial sums of ordered statistics in terms of the moment generating function mgf and the probability density function pdf our mgf based approach applies not only when all the k ordered rvs are involved but also when only the ks ks k best rvs are considered in addition we present the closed form expressions for the exponential rv special case these results apply to the performance analysis of various wireless communication systems over fading channels

correlation functions in the two dimensional gaussian column model of the interface in a weak external field calculations of the correlation functions c and ccond for the two dimensional gaussian column model of the interface in a weak gravitational field g to 0 indicate the universality of the parametrisation of the direct correlation function c found for the sos model by stecki ciach and dudowicz 1986 the representations of the conditional correlation function ccond are slightly different in these two models

a smooth nonparametric estimator of a quantile function abstract a smooth alternative to the conventional sample quantile function as a nonparametric estimator of a population quantile function is proposed the proposed estimator is essentially a kernel type of estimator and has the same asymptotic distribution as the conventional sample quantile the mean squared convergence rate of the proposed estimator is also estimated monte carlo studies are conducted to compare the proposed estimator with the sample quantile and the estimator proposed by kaigh and lachenbruch the feasibility of using bootstrap techniques to estimate the optimal window width for the proposed estimator is also considered

on the distribution of a studentized quantile la variance asymptotique du quantile d echantillon depend de la valeur de la densite de population et du quantile de la population on considere l estimateur de siddiqui bloch gastwinth

a class of generalised multiple hypergeometric series arising in physical and quantum chemical applications the multivariable hypergeometric function nf x1 xn considered recently by niukkanen 1984 is a straightforward generalisation of certain well known hypergeometric functions of n variables indeed it provides a unification of the generalised hypergeometric function pfq of one variable appell and kampe de feriet functions of two variables and lauricella functions of n variables as well as of many other hypergeometric series which arise naturally in physical and quantum chemical applications the author derives several interesting properties of this multivariable hypergeometric function including for example many which were not given by niukkanen as useful consequences of substantially more general results available in the literature

discontinuity of the magnetization in one dimensional 1 x y 2 ising and potts models results from percolation theory are used to study phase transitions in one dimensional ising and q state potts models with couplings of the asymptotic form j sub x y approx const absolute value x y sup 2 for translation invariant systems with well defined lim sub x infinity x sup 2 j sub x j sup possibly o or infinity we establish 1 there is no long range order at inverse temperatures beta with beta j sup less than or equal to1 2 if beta j sup q then by sufficiently increasing j sub 1 the spontaneous magnetization m is made positive 3 in models with 0 j sup infinity the magnetization is discontinuous at the transition point as originally predicted by thouless and obeys m beta sub c less than or equal to 1 beta sub c j sup sup 1 2 4 for ising q 2 models with j sup infinity it is noted that the correlation function decays as beta approx c beta absolute value x y sup 2 whenever beta beta sub c points 1 3 are deduced from previous percolation results by utilizing the fortuin kasteleyn representation which also yields other results of independent interest relating potts models with different values of q

the discrete gaussian chain with 1 r n interactions exact results we show that the discrete gaussian chain with interactionv r 1 r2 1 4 is self dual at the dual temperaturek b t 1 we calculate the height height correlation function and find that the system is rough a duality relation is established for the temperature dependent correlation function exponent we also consider interactionsv r 1 rn and show that absence of a phase transition for 2 n 3 implies absence of a phase transition for 1 n 2 all these results have their counterparts in a linear system of charges interacting through a potential which is asymptotically logarithmic forn 2 or power law like forn 2

asymptotic behaviour of correlation functions and the interfacial tension in the two dimensional sos model of an interface in zero external field the modified direct correlation functions ccond and csym are studied for a two dimensional sos system m infinity in a zero external field g identical to 0 the asymptotic limit w to infinity of the interface width w m 1 pi is considered in particular also in connection with the yvon triezenberg zwanzig ytz formula for the interfacial tension gamma and with its modification obtained by ciach et al 1987 the successive contributions to the interfacial tension gamma resulting from various terms of the derived relations are computed and discussed in the asymptotic limit w to infinity the interfacial tensions obtained from the ytz formula and from the ciach formula agree with each other and with gamma calculated earlier by evans 1979 and extrapolated to g 0 by stecki and dudowicz 1985

some combinatorial properties of jack symmetric functions if 1 l n then write 2 n or 1 n if p is another partition then write p c j if pi 6 for all i i e if the diagram of 1 contains the diagram of p if ipl ii 1 then write p 2 1 reverse lexicographic order if either j i or the first nonvanishing difference e pi is positive for instance writing 2 1 i for ai i it 5 5 41 32 5 311 221 2111 11111 finally write p i if ipl lal and p1 pl2 pli a1 a2 li for all i macdonald m p 63 call the partial ordering the natural ordering but we will call it the dominance ordering let x x x2 be an infinite set of indeterminates as in mi we

unified framework for the effective rate analysis of wireless communication systems over miso fading channels this paper proposes a unified framework for the effective rate analysis over arbitrary correlated and not necessarily identical multiple input single output miso fading channels which uses the moment generating function mgf based approach and h transform representation the proposed framework has the potential to simplify the cumbersome analysis procedure compared with the probability density function based approach moreover the effective rates over two specific fading scenarios are investigated namely independent but not necessarily identical distributed i n i d miso hyper fox s h fading channels and arbitrary correlated generalized k fading channels the exact analytical representations for these two scenarios are also presented by substituting corresponding parameters the effective rates in various practical fading scenarios such as rayleigh nakagami m weibull gamma and generalized k fading channels are readily available in addition asymptotic approximations are provided for the proposed h transform and mgf based approach as well as for the effective rate over i n i d miso hyper fox s h fading channels simulations under various fading scenarios are also presented which support the validity of the proposed method

one dimensional models with 1 r2 interactions the critical behaviour of a general discrete one dimensional model with inverse square interactions is discussed using renormalisation group methods

on the efficient simulation of the distribution of the sum of gamma gamma variates with application to the outage probability evaluation over fading channels the gamma gamma distribution has recently emerged in a number of applications ranging from modeling scattering and reverberation in sonar and radar systems to modeling atmospheric turbulence in wireless optical channels in this respect assessing the outage probability achieved by some diversity techniques over this kind of channels is of major practical importance in many circumstances this is related to the difficult question of analyzing the statistics of a sum of gamma gamma random variables answering this question is not a simple matter this is essentially because outage probabilities encountered in practice are often very small and hence the use of classical monte carlo methods is not a reasonable choice this lies behind the main motivation of this paper in particular this paper proposes a new approach to estimate the left tail of the sum of gamma gamma variates more specifically we propose robust importance sampling schemes that efficiently evaluates the outage probability of diversity receivers over gamma gamma fading channels the proposed estimators satisfy the well known bounded relative error criterion for both maximum ratio combining and equal gain combining cases we show the accuracy and the efficiency of our approach compared with naive monte carlo via some selected numerical simulations

approximation for bessel functions and their application in the computation of hankel transforms we present rational approximations of the bessel functions jv x v 0 1 10 which can be used to simplify the computation of the hankel transform to the computation of two fourier transforms

constrained smoothing of histograms and scatterplots with simulated annealing histogram and scatterplot models are often required for statistical inference in the field of petroleum engineering stochastic simulation algorithms require among other statistics a model for the histogram of the petrophysical attribute porosity permeability being simulated often this model is taken to be the deciustered distribution of the sample data when there are many data say greater than l 000 this histogram may be reasonably informed most often however the sample histogram shows multiple sawtoothlike spikes that are not representative of the entire population the sample histogram must be smoothed a simulated annealing based procedure is proposed for smoothing one variable univariate histograms and two variable scatterplots bivariate histograms the smoothed histograms are constrained to the sample mean variance specified quantiles and a measure of smoothness in the bivariate case the distribution must be consistent with both marginal histograms and can be additionally cons

capacity of mrc on correlated rician fading channels a new exact explicit expression is derived for the ergodic capacity of maximal ratio combining mrc schemes over arbitrarily correlated rician fading channels this is used to study the effects of channel correlation on the ergodic capacity numerical results reveal that both the phase and the magnitude of correlation have an impact on the ergodic capacity of rician fading channels this is in contrast to correlated rayleigh fading where the phase of the correlation has no effect on the ergodic capacity it is also observed that negatively correlated branches in rician fading may lead to an increase in ergodic capacity beyond that obtained by uncorrelated branches

on the calculation of the incomplete mgf with applications to wireless communications the incomplete moment generating function imgf has paramount relevance in communication theory since it appears in a plethora of scenarios when analyzing the performance of communication systems we here present a general method for calculating the imgf of any arbitrary fading distribution then we provide exact closed form expressions for the imgf of the very general kappa mu shadowed fading model which includes the popular kappa mu eta mu rician shadowed and other classical models as particular cases we illustrate the practical applicability of this result by analyzing several scenarios of interest in wireless communications 1 physical layer security in the presence of an eavesdropper 2 outage probability analysis with interference and background noise 3 channel capacity with side information at the transmitter and the receiver and 4 average bit error rate with adaptive modulation when the fading on the desired link can be modeled by any of the aforementioned distributions

fast hankel transform by fast sine and cosine transforms the mellin connection the hankel transform of a function by means of a direct mellin approach requires sampling on an exponential grid which has the disadvantage of coarsely undersampling the tail of the function a novel modified hankel transform procedure that does not require exponential sampling is presented the algorithm proceeds via a three step mellin approach to yield a decomposition of the hankel transform into a sine a cosine and an inversion transform which can be implemented by means of fast sine and cosine transforms

tsallis scaling and the long range ising chain a transfer matrix approach a numerically efficient transfer matrix tm approach is introduced to investigate the long range ising spin chain results obtained within this procedure are primarily used to verify the tsallis scaling hypothesis for long range systems with an ensuremath alpha power law decay of the interaction constants both in the extensive ensuremath alpha g1 and nonextensive ensuremath alpha l1 regimes results for finite size systems taking into account all interactions between spins up to 24 sites apart show that the conjecture is satisfied with a very good precision less than 0 004 for all temperature intervals this tm procedure is further used to investigate several other thermodynamic and critical properties of this system and it may also be extended to similar one dimensional long range systems

secrecy capacity analysis over kappa mu fading channels theory and applications in this paper we consider the transmission of confidential information over a kappa mu fading channel in the presence of an eavesdropper who also experiences kappa mu fading in particular we obtain novel analytical solutions for the probability of strictly positive secrecy capacity spsc and a lower bound of secure outage probability sop l for independent and non identically distributed channel coefficients without parameter constraints we also provide a closed form expression for the probability of spsc when the mu parameter is assumed to take positive integer values monte carlo simulations are performed to verify the derived results the versatility of the kappa mu fading model means that the results presented in this paper can be used to determine the probability of spsc and sop l for a large number of other fading scenarios such as rayleigh rice nakagami n nakagami m one sided gaussian and mixtures of these common fading models in addition due to the duality of the analysis of secrecy capacity and co channel interference cci the results presented here will have immediate applicability in the analysis of outage probability in wireless systems affected by cci and background noise bn to demonstrate the efficacy of the novel formulations proposed here we use the derived equations to provide a useful insight into the probability of spsc and sop l for a range of emerging wireless applications such as cellular device to device peer to peer vehicle to vehicle and body centric communications using data obtained from real channel measurements

two dimensional sir epidemics with long range infection we extend a recent study of susceptible infected removed epidemic processes with long range infection referred to as i in the following from 1 dimensional lattices to lattices in two dimensions as in i we use hashing to simulate very large lattices for which finite size effects can be neglected in spite of the assumed power law p x x 2 for the probability that a site can infect another site a distance vector x apart as in i we present detailed results for the critical case for the supercritical case with 2 and for the supercritical case with 0 2 for the latter we verify the stretched exponential growth of the infected cluster with time predicted by m biskup for 2 we find generic power laws with dependent exponents in the supercritical phase but no kosterlitz thouless kt like critical point as in 1 d instead of diverging exponentially with the distance from the critical point the correlation length increases with an inverse power as in an ordinary critical point finally we study the dependence of the critical exponents on in the regime 0 2 and compare with field theoretic predictions in particular we discuss in detail whether the critical behavior for slightly less than 2 is in the short range universality class as conjectured recently by f linder et al as in i we also consider a modified version of the model where only some of the contacts are long range the others being between nearest neighbors if the number of the latter reaches the percolation threshold the critical behavior is changed but the supercritical behavior stays qualitatively the same

the critical behaviour of the long range potts chain from the largest cluster probability distribution abstract we present the numerical study of the one dimensional potts model with power law decaying ferromagnetic interactions the largest cluster probability distribution is obtained by monte carlo simulations using the swendsen wang cluster algorithm with cumulative probabilities the finite size scaling analysis of the largest cluster is used to derive the critical behaviour in the non classical regime of this model for various values of q

kernel quantile estimators abstract for an estimator of quantiles the efficiency of the sample quantile can be improved by considering linear combinations of order statistics that is l estimators a variety of such methods have appeared in the literature an important aspect of this article is that asymptotically several of these are shown to be kernel estimators with a guassian kernel and the bandwidths are identified it is seen that some implicit choices of the smoothing parameter are asymptotically suboptimal in addition the theory of this article suggests a method for choosing the smoothing parameter how much reliance should be placed on the theoretical results is investigated through a simulation study over a variety of distributions little consistent difference is found between various estimators an important conclusion made during the theoretical analysis is that all of these estimators usually provide only modest improvement over the sample quantile the results indicate that even if one knew the best estimator

solving 1d plasmas and 2d boundary problems using jack polynomials and functional relations the general one dimensional log sine gas is defined by restricting the positive and negative charges of a two dimensional coulomb gas to live on a circle depending on charge constrannts this problem is equivalent to different boundary field theories we study the electrically neutral case which is equivalent to a two dimensional free boson with an impurity cosine potential we use two different methods a perturbative one based on jack symmetric functions and a nonperturbative one based on the thermodynamic bethe ansatz and functional relations the first method allows us to find an explicit series expression for all coefficients in the virial expansion of the free energy and the experimentally measurable conductance some results for correlation functions are also presented the second method gives an expression for the full free energy which yields a surprising fluctuation dissipation relation between the conductance and the free energy

dual algorithms for fast calculation of the fourier bessel transform this paper presents a new procedure for the fast calculation of the fourier bessel transform the computation is performed in a dual mode and involves two matched algorithms the first of which provides the lower order components while the second yields intermediate and higher order samples of the transform the first algorithm is based on the fourier selection summation fss method derived in a previous study while the second relies on the bessel function large argument asymptotic expansion it is shown that the dual procedure constructed along these lines requires a computation time which is about four times that needed by a single n point fast fourier transform

smooth optimum kernel estimators of densities regression curves and modes several criteria concerning the choice of kernels for the nonparametric estimation of functions and their derivatives are discussed a specific optimality criterion is described which applies to kernels of compact support and of different orders of smoothness the solutions of the corresponding variational problems are explicitly given many kernels discussed previously are obtained as special cases

the one dimensional potts model with long range interactions a renormalization group approach the one dimensional q state potts model with ferromagnetic pair interactions which decay with the distance r as is considered we calculate through a real space renormalization group technique using kadanoff blocks of length b the critical temperature and the correlation length critical exponent as a function of for different values of q some of the very few known rigorous results for general q are reproduced by our approach several asymptotic behaviours are derived analytically for q 2 3 in the limit we also obtain extrapolated critical temperatures for arbitrary values of and for q 2 3 4 which we believe approximate the exact ones well except in the region near furthermore the use of another extrapolation procedure suitable only in the vicinity of led us to conjecture that the exact critical temperature is the same for any value of q we also verify that which is consistent with a recent conjecture of tsallis

an algorithm for computing general integer order hankel transforms a tomographic image reconstruction algorithm that we have been studying requires the nth order hankel transform for the nth function in a series where n varies over a set of integers unfortunately most previously proposed algorithms have either dealt with only zeroth order transforms or cannot be applied conveniently to our problem we propose an algorithm for computing general integer order hankel transforms the algorithm takes samples of equally spaced input functions and gives equally spaced samples of the transforms

a unified approach to computing error probabilities of diversity combining schemes over correlated fading channels the average bit error rate performance of one stage and two stage diversity combining schemes operating over correlated fading channels is investigated two channel models that can significantly simplify the performance analysis are considered in particular a linear correlation channel model having equal branch variances can be decorrelated at the receiver so that the branches become independent it is shown that in general employing diversity combining schemes for decorrelated or orthogonalized branches can recover some of the diversity gain lost due to the branch correlations this is observed for example for the case of hybrid selection maximum ratio combining operating over decorrelated and orthogonalized non zero mean gaussian fading channels furthermore a fading amplitude channel model is proposed assuming vector norm superposition of the impinging plane waves this channel model is well suited for the performance analysis of maximum ratio and equal gain combining schemes operating over correlated fading channels finally the average bit error rates of several diversity combining schemes are evaluated analytically using the prony approximation method as well as using computer simulation

exact sinr statistics in the presence of heterogeneous interferers we derive new results for the higher order moments of signal to interference plus noise ratio sinr in the presence of an arbitrary poisson point process ppp based heterogeneous interference field the analysis leverages on a moment generating function mgf methodology which only requires the statistics of intended signal and aggregate interference thus eliminating the need for the exact distribution of sinr we extend the existing results on interference statistics by deriving a generalized closed form expression of the interference mgf considering nakagami m fading channels with exclusion region in certain special cases explicit expressions for the averages of different functions of sinr are found which also lead to closed form solutions for the probability distributions of aggregate interference reciprocal and signal to interference ratio we prove that in such cases the effect of total ppp based interference power on useful transmission is mathematically equivalent to the severe fluctuations from a one sided gaussian fading channel as an application example the proposed methodology is used together with stochastic geometry theory to characterize the average sinr and rate in heterogeneous cellular networks the validity of our analytical derivations is confirmed via monte carlo simulations for various system settings we show that with cellular network densification there exists a tradeoff between the average sinr and rate performance

algorithms to numerically evaluate the hankel transform abstract the efficient and accurate evaluation of the hankel transform is required in a number of applications this paper reviews a number of algorithms that have only recently been exposed in the literature results of a comparative study of some useful algorithms are presented it is found that the performance of all algorithms depends on the type of function to be transformed the projection based methods provide acceptable accuracy with better efficiency than numerical quadrature

fast hankel transform algorithm the hankel or fourier bessel transform is an important computational tool for optics acoustics and geophysics it may be computed by a combination of an abel transform which maps an axisymmetric two dimensional function into a line integral projection and a one dimensional fourier transform this paper presents a hankel transform algorithm using a fast linear time abel transform followed by an fft

symbol error rate of mpsk over egk channels perturbed by a dominant additive laplacian noise the laplacian noise has received much attention during the recent years since it affects many communication systems we consider in this paper the probability of error of an m ary phase shift keying psk constellation operating over a generalized fading channel in presence of a dominant additive laplacian noise in this context the decision regions of the receiver are determined using the maximum likelihood and the minimum distance detectors once the decision regions are extracted the resulting symbol error rate expressions are computed and averaged over an extended generalized k fading distribution generic closed form expressions of the conditional and the average probability of error are obtained in terms of the fox s h function simplifications for some special cases of fading are presented and the resulting formulas end up being often expressed in terms of well known elementary functions finally the mathematical formalism is validated using some selected analytical based numerical results as well as monte carlo simulation based results

performance analysis of generalized selection combining in generalized correlated nakagami m fading the exact performance of selection combining hybrid selection maximal ratio combining h s mrc and threshold based h s mrc in correlated nakagami m fading for positive integer values of fading parameter m is analyzed for a particular correlation structure this correlation model though not general is much more general than the equal correlation case and includes equal correlation as a special case the symbol error rate and outage probability of the three combining schemes are obtained by transforming the correlated branch gains into a set of conditionally independent branch gains numerical and simulation results show excellent agreement with theoretical results

accurate computation of the mgf of the lognormal distribution and its application to sum of lognormals sums of lognormal random variables rvs are of wide interest in wireless communications and other areas of science and engineering since the distribution of lognormal sums is not log normal and does not have a closed form analytical expression many approximations and bounds have been developed this paper develops two computational methods for the moment generating function mgf or the characteristic function chf of a single lognormal rv the first method uses classical complex integration techniques based on steepest descent integration the saddle point of the integrand is explicitly expressed by the lambert function the steepest descent optimal contour and two closely related closed form contours are derived a simple integration rule e g the midpoint rule along any of these contours computes the mgf chf with high accuracy the second approach uses a variation on the trapezoidal rule due to ooura and mori importantly the cumulative distribution function of lognormal sums is derived as an alternating series and convergence acceleration via the epsilon algorithm is used to reduce in some cases the computational load by a factor of 106 overall accuracy levels of 13 to 15 significant digits are readily achievable

one dimensional ising spin glass model with long range interactions an ising chain with hamiltonian h j sigma i j epsilon ijsisj mod i j mod 1 sigma 2 is considered where the epsilon ij are independent random variables according to kotliar et al 1983 this model has a phrase transition with non mean field exponents when 1 3 sigma 1 and mean field exponents beyond the upper critical value of sigma 1 3 by means of an epsilon expansion about the lower critical value of sigma 1 the model is shown to be replica symmetric as epsilon to 0 and it is speculated that this result holds for 1 3 sigma 1

physical layer security for multiple antenna systems a unified approach secrecy capacity is a fundamental information theoretic performance metric to predict the maximum data rate of reliable communication while the intended message is not revealed to the eavesdropper motivated by this consideration in this paper a unified communication theoretic framework for the analysis of the probability of nonzero secrecy capacity the secrecy outage probability and the secrecy capacity of multiple antenna systems over fading channels is proposed specifically a powerful frequency domain approach is first developed in which the integrals involved in the evaluation of the probability of nonzero secrecy capacity and secrecy outage probability are transformed into the frequency domain by employing parseval s theorem a generic approach for the evaluation of the asymptotic secrecy outage probability at high signal to noise ratio snr region is also introduced thus providing useful insight as to the parameters affecting the secrecy performance finally a unified numerical approach for computing the average secrecy capacity of multiple antenna systems under arbitrary fading environments is developed the proposed framework is general enough to accommodate any well known multiantenna transmission technique and fading model finally the secrecy performance of several multiple antenna system setups is assessed in the presence of generalized fading conditions and arbitrary antenna correlation while various numerical and computer simulation results are shown and compared to substantiate the proposed mathematical analysis

reexamination of the long range potts model a multicanonical approach we investigate the critical behavior of the one dimensional q state potts model with long range lr interaction 1 r d sigma using a multicanonical algorithm the recursion scheme initially proposed by berg is improved so as to make it suitable for a large class of lr models with unequally spaced energy levels the choice of an efficient predictor and a reliable convergence criterion is discussed we obtain transition temperatures in the first order regime which are in far better agreement with mean field predictions than in previous monte carlo studies by relying on the location of spinodal points and resorting to scaling arguments we determine the threshold value sigma c q separating the first and second order regimes to two digit precision within the range 3 leq q leq 9 we offer convincing numerical evidence supporting sigma c q 1 0 for all q by virtue of an unusual finite size effect namely finite size scaling predicts a continuous transition in the thermodynamic limit despite the first order nature of the transition at finite size a qualitative account in terms of correlation lengths is provided finally we find the crossover between the lr and short range regimes to occur inside a narrow window 1 0 sigma 1 2 thus lending strong support to sak s scenario

simple and accurate methods for outage analysis in cellular mobile radio systems a unified approach two unified expressions for computing the refined outage criterion which considers the receiver noise in cellular mobile radio systems are derived using the laplace and fourier inversion formulas since these expressions do not impose any restrictions on the signal statistics while being easy to program they provide a powerful tool for outage analysis over generalized fading channels we also assess compatibility and applicability of previously published approaches that treat noise as cochannel interference noise limited model or consider a minimum detectable receiver signal threshold and receiver noise the outage probability in an interference limited case can be evaluated directly by setting the minimum power threshold to zero the analysis of correlated interferers is presented results are also developed for a random number of interferers several new closed form expressions for the outage probability are also derived some previous studies have suggested approximating rician desired signal statistics by a nakagami m 1960 model with positive integer fading severity index to circumvent the difficulty in evaluating the outage in rician fading the suitability of this approximation is examined by comparing the outage performance under these two fading conditions surprisingly some basic results for nakagami m channel have been overlooked which has led to misleadingly optimistic results with the nakagami m approximation model however similar approximation for the interferer signals is valid

h transforms for wireless communication the h transforms are integral transforms that involve fox s h functions as kernels a large variety of integral transforms can be put into particular forms of the h transform since h functions subsume most of the known special functions including meijer s g functions in this paper we embody the h transform theory into a unifying framework for modeling and analysis in wireless communication first we systematize the use of elementary identities and properties of the h transform by introducing operations on parameter sequences of h functions we then put forth h fading and degree 2 irregular h fading to model radio propagation under composite specular and or inhomogeneous conditions the h fading describes composite effects of multipath fading and shadowing as a single h variate including most of typical models such as rayleigh nakagami m weibull alpha mu n ast nakagami m generalized k fading and weibull gamma fading as its special cases as a new class of h variates called the degree zeta irregular h variate the degree 2 irregular h fading characterizes specular and or inhomogeneous radio propagation in which the multipath component consists of a strong specularly reflected or line of sight los wave as well as unequal power or correlated in phase and quadrature scattered waves this fading includes a variety of typical models such as rician nakagami q kappa mu eta mu rician los gamma and kappa mu los gamma fading as its special cases finally we develop a unifying h transform analysis for the amount of fading error probability channel capacity and error exponent in wireless communication using the new systematic language of transcendental h functions by virtue of two essential operations called mellin and convolution operations involved in the mellin transform and mellin convolution of two h functions the h transforms for these performance measures culminate in h functions using the algebraic asymptotic expansions of the h transform we further analyze the error probability and capacity at high and low signal to noise ratios in a unified fashion

effective capacity of l_p norm diversity receivers over generalized fading channels under adaptive transmission schemes this paper presents novel moment generating function mgf and characteristic function chf based frameworks for the ec performance analysis of a generic l p norm diversity combining scheme under adaptive transmission policies the considered system operates over generalized fading channels a maximum delay constraint and under various channel state information csi conditions depending upon the operational csi four policies are studied namely i constant power with optimal rate adaptation ora ii optimal power and rate adaptation opra iii channel inversion with fixed rate cifr and iv truncated cifr tifr the l p norm diversity is a generic diversity structure which includes as special cases various well known diversity schemes such as equal gain combining egc maximal ratio combining mrc and amplify and forward af relaying under the ora and opra policies we derive single integral expressions for evaluating the ec of l p norm diversity reception directly from the mgf or the incomplete mgf of the signal to noise ratio snr at the receiver respectively for the ec performance evaluation of the egc and af relaying systems operating under the opra policy a chf based approach which is computationally more efficient as compared to the mgf based approach is further presented it is shown that the ec for the cifr and tifr policies can be directly evaluated from the mgf or the chf of the snr at the receiver respectively for the ora policy a novel analytical approach for the asymptotic ec performance analysis is also developed and evaluated revealing how important system operation parameters affect the overall system performance the mathematical formalism is validated with selected numerical and equivalent simulation performance evaluation results thus confirming the correctness of the proposed analytical methodology

boundary bound states and boundary bootstrap in the sine gordon model with dirichlet boundary conditions we present a complete study of boundary bound states and related boundary s matrices for the sine gordon model with dirichlet boundary conditions our approach is based partly on the bootstrap procedure and partly on the explicit solution of the inhomogeneous xxz model with boundary magnetic field and solution of the boundary thirring model we identify boundary bound states with new boundary strings in the bethe ansatz the boundary energy is also computed

multiple multiindex mittag leffler functions and relations to generalized fractional calculus the classical mittag leer m l functions have already proved their eciency as solutions of fractional order differential and integral equations and thus have become important elements of the fractional calculus theory and applications in this paper we introduce analogues of these functions depending on two sets of multiple m tuple m 2i s an integer indices the hint for this comes from a paper by dzrbashjan izv an arm ssr 13 3 1960 21 63 related to the case m 2 we study the basic properties and the relations of the multiindex m l functions with the operators of the generalized fractional calculus corresponding generalized operators of integration and dierention of the so called gelfond leontiev type as well as borel laplace type integral transforms are also introduced and studied c 2000 elsevier science b v all rights reserved msc 26a33 33c60 33e30 44a15 44a30

simultaneous calculation of fourier bessel transforms up to order n abstract in many practical applications it is necessary to calculate the first n fourier bessel transforms this paper describes procedures allowing the simultaneous evaluation of these transforms the calculation involves a basic one dimensional fourier transform repeated selection of suitable fourier components followed by successive evaluation of fourier series coefficients determination of l samples of the first n fourier bessel transforms requires of the order of 2 ln log 2 n operations and this number is comparable to the operation count corresponding to a two dimensional discrete fourier transform

a unified mgf based capacity analysis of diversity combiners over generalized fading channels unified exact ergodic capacity results for l branch coherent diversity combiners including equal gain combining egc and maximal ratio combining mrc are not known this paper develops a novel generic framework for the capacity analysis of l branch egc mrc over generalized fading channels the framework is used to derive new results for the gamma shadowed generalized nakagami m fading model which can be a suitable model for the fading environments encountered by high frequency 60 ghz and above communications the mathematical formalism is illustrated with some selected numerical and simulation results confirming the correctness of our newly proposed framework

integrable structure of conformal field theory ii q operator and ddv equation this paper is a direct continuation of 1 where we began the study of the integrable structures in conformal field theory we show here how to construct the operators bf q pm lambda which act in the highest weight virasoro module and commute for different values of the parameter these operators appear to be the cft analogs of the q matrix of baxter 2 in particular they satisfy baxter s famous t q equation we also show that under natural assumptions about analytic properties of the operators as the functions of the baxter s relation allows one to derive the nonlinear integral equations of destri de vega ddv 3 for the eigenvalues of the q operators we then use the ddv equation to obtain the asymptotic expansions of the q operators at large it is remarkable that unlike the expansions of the t operators of 1 the asymptotic series for q contains the dual nonlocal integrals of motion along with the local ones we also discuss an intriguing relation between the vacuum eigenvalues of the q operators and the stationary transport properties in the boundary sine gordon model on this basis we propose a number of new exact results about finite voltage charge transport through the point contact in the quantum hall system

evaluation of bessel function integrals with algebraic singularities abstract a new method for the numerical evaluation of 1 0 1 x x j v ax dx is proposed where a are given constants and j is the bessel function of the first kind and of order it is assumed that f is a smooth function the method is based on approximation of the function f by a polynomial given in the form of a linear combination of the shifted jacobi polynomials r k and on the use of chebyshev series expansion for the function j ax

product of two envelopes taken from alpha mu kappa mu and eta mu distributions this paper presents exact novel formulations for the probability density function and cumulative distribution function for the product of two independent and non identically distributed alpha mu kappa mu and eta mu variates the expressions are given in terms of both 1 generalized fox h function and 2 easily computable series expansions the formulations derived can be directly used to explore the performance of a number of wireless communication processes including multihop systems cascaded channels radar communications multiple input multiple output links and others due to the high flexibility of the above mentioned distributions the results presented here comprise a substantial number of useful product distributions as application examples performance metrics for the cascaded fading channel are derived the validity of the expressions is confirmed via monte carlo simulation it is noteworthy that because any composite multipath shadowing fading model is obtained as a particular case of the product of two fading variables the results given here provide a plethora of composite multipath shadowing fading scenarios

the exact distribution of the sum of stable random variables abstract the exact distribution of the sum of any number of independent stable random variables is derived the probability density function of the exact distribution turns out to be sum of two multivariate h functions computational issues and a data application are discussed

mixed order phase transition of the contact process near multiple junctions we have studied the phase transition of the contact process near a multiple junction of m semi infinite chains by monte carlo simulations as opposed to the continuous transitions of the translationally invariant m 2 and semi infinite m 1 system the local order parameter is found to be discontinuous for m 2 furthermore the temporal correlation length diverges algebraically as the critical point is approached but with different exponents on the two sides of the transition in the active phase the estimate is compatible with the bulk value while in the inactive phase it exceeds the bulk value and increases with m the unusual local critical behavior is explained by a scaling theory with an irrelevant variable which becomes dangerous in the inactive phase quenched spatial disorder is found to make the transition continuous in agreement with earlier renormalization group results

a kernel type estimator of a quantile function from right censored data abstract based on right censored data from a lifetime distribution f 0 a kernel type estimator of the quantile function qo p inf t f 0 t p 0 p 1 is proposed the estimator is defined by which is smoother than the usual product limit quantile function where denotes the product limit estimator of f 0 from the censored sample under the random censorship model and general conditions on hn k and f 0 it is shown that qn p is strongly consistent in addition an approximation to qn is shown to be asymptotically equivalent to qn with probability one a small monte carlo simulation study shows that for several values of the bandwidth hn qn performs better than in the sense of estimated mean squared errors an optimal bandwidth hn may be estimated by bootstrap methods in some cases the procedure is illustrated by an application to data from a mechanical switch life test

a novel unified expression for the capacity and bit error probability of wireless communication systems over generalized fading channels analysis of the average binary error probabilities abep and average capacity ac of wireless communications systems over generalized fading channels have been considered separately in past years this paper introduces a novel moment generating function mgf based unified expression for the abep and ac of single and multiple link communications with maximal ratio combining in addition this paper proposes the hyper fox s h fading model as a unified fading distribution of a majority of the well known generalized fading environments as such the authors offer a generic unified performance expression that can be easily calculated and that is applicable to a wide variety of fading scenarios the mathematical formulism is illustrated with some selected numerical examples that validate the correctness of the authors newly derived results

regularity properties and pathologies of position space renormalization group transformations scope and limitations of gibbsian theory we reconsider the conceptual foundations of the renormalization group rg formalism and prove some rigorous theorems on the regularity properties and possible pathologies of the rg map our main results apply to local in position space rg maps acting on systems of bounded spins compact single spin space regarding regularity we show that the rg map defined on a suitable space of interactions formal hamiltonians is always single valued and lipschitz continuous on its domain of definition this rules out a recently proposed scenario for the rg description of first order phase transitions on the pathological side we make rigorous some arguments of griffiths pearce and israel and prove in several cases that the renormalized measure is not a gibbs measure for any reasonable interaction this means that the rg map is ill defined and that the conventional rg description of first order phase transitions is not universally valid for decimation or kadanoff transformations applied to the ising model in dimension d 3 these pathologies occur in a full neighborhood 0 h e of the low temperature part of the first order phase transition surface for block averaging transformations applied to the ising model in dimension d 2 the pathologies occur at low temperatures for arbitrary magnetic field strength pathologies may also occur in the critical region for ising models in dimension d 4 we discuss the heuristic and numerical evidence on rg pathologies in the light of our rigorous theorems in addition we discuss critically the concept of gibbs measure which is at the heart of present day classical statistical mechanics we provide a careful and we hope pedagogical overview of the theory of gibbsian measures as well as the less familiar non gibbsian measures emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations we give a rather complete catalogue of the known examples of such occurrences the main message of this paper is that despite a well established tradition gibbsiannessshould not be taken for granted

a note on the estimation of a distribution function and quantiles by a kernel method there has recently been extensive work on the estimation by kernel methods of probability densities and their derivatives for a review see wertz 1978 for estimating the cumulative distribution function the empirical distribution function f is in a sense already quite smooth although it is known that further smoothing can be an advantage the object of the present note is to report briefly an investigation of kernel estimation applied to distribution function and quantiles further details are available from the author for independent and identically distributed random variables x1 x the usual kernel estimator of the density f is

roughening behavior of a one dimensional crystal surface with inverse square potential abstract the discrete gaussian chain with inverse square potential which models a one dimensional crystal surface is studied by monte carlo methods the system is found to undergo a roughening transition and the temperature dependent correlation function exponent t is shown to be discontinous at the critical point these results can be transposed to the metal insulator transition of a one dimensional plasma of logarithmically interacting charges

statistical analysis and characterization of the indoor propagation channel this paper presents statistical analysis of data obtained by measuring narrowband path loss at dect digital enhanced cordless telecommunications frequency 1 89 ghz in an indoor environment specific goodness of fit tests are applied to the data the tests assess whether the data generating source belongs to a known family of random variables results obtained support that local path loss distribution can be represented as weibull or nakagami in most environments the close resemblance between such distributions and rice distribution with rayleigh as a special case confirms that rice rayleigh description of fading can be applied to indoor environments that similarity leads to a general simple approximate expression for the cumulative distribution function of the signal to interference ratio the expression can be used without limitations to the number and the parameters of the rice interferers

a hankel transform approach to tomographic image reconstruction a relatively unexplored algorithm is developed for reconstructing a two dimensional image from a finite set of its sampled projections the algorithm referred to as the hankel transform reconstruction htr algorithm is polar coordinate based the algorithm expands the polar form fourier transform f r theta of an image into a fourier series in theta calculates the appropriately ordered hankel transform of the coefficients of this series giving the coefficients for the fourier series of the polar form image f p phi resolves this series giving a polar form reconstruction and interpolates this reconstruction to a rectilinear grid the htr algorithm is outlined and it is shown that its performance compares favorably to the popular convolution backprojection algorithm

a law of the logarithm for kernel quantile density estimators received february 1992 revised february 1993 1this manuscript was prepared using computer facilities supported in part by nsf grants dms 89 05292 dms 87 03942 dms 86 01732 and dms 84 04941 and by the university of chicago block fund ams 1991 subject classifications primary 60f15 secondary 62g05 62g30

the bootstrap to smooth or not to smooth summary the bootstrap and smoothed bootstrap are considered as alternative methods of estimating properties of unknown distributions such as the sampling error of parameter estimates criteria are developed for determining whether it is advantageous to use the smoothed bootstrap rather than the standard bootstrap key steps in the argument leading to these criteria include the study of the estimation of linear functionals of distributions and the approximation of general functionals by linear functionals consideration of an example the estimation of the standard error in the variance stabilized sample correlation coefficient elucidates previously published simulation results and also illustrates the use of computer algebraic manipulation as a useful technique in asymptotic statistics finally the various approximations used are vindicated by a simulation study

fast nth order hankel transform algorithm an nth order hankel transform also called fourier bessel transform algorithm designed for many analytically defined functions is presented this algorithm is not restricted to order zero as such it provides greater generality than many others the traditional difficulty in the evaluation of hankel transforms the presence of bessel functions in the kernel of the integral transform is eliminated in this new hankel transform algorithm the algorithm presented is composed of a fast linear time nth order chebyshev transform followed by a fast fourier transform

relative deficiency of kernel type estimators of quantiles in this paper the asymptotic relative deficiency of the sample q quantile with respect to kernel type estimators of the q quantile is evaluated the comparison is based on the mean square errors of the estimators the result suggests a purely analytic measure of performance within the class of kernels it is notable that a similar situation occurs when kernel estimators of a distribution function are studied

evaluating infinite integrals involving bessel functions of arbitrary order abstract the evaluation of intergrals of the form i n 0 x j n x d x is considered in the past the method of dividing an oscillatory integral at its zeros forming a sequence of partial sums and using extrapolation to accelerate convergence has been found to be the most efficient technique available where the oscillation is due to a trigonometric function or a bessel function of order n 0 1 here we compare various extrapolation techniques as well as choices of endpoints in dividing the integral and establish the most efficient method for evaluating infinite integrals involving bessel functions of any order n not just zero or one we also outline a simple but very effective technique for calculating bessel function zeros