fuzzy modal analysis prediction of experimental behaviours abstract the objective of this paper is to numerically predict the modal behaviours of a two plate steel structure defined with variable parameters and to validate this prediction experimentally first the test structure in which geometrical and material variability has been identified is studied using a fuzzy finite element method this method named paem allows the fuzzy numerical eigenfrequencies and eigenvectors to be calculated second the test structure is analyzed experimentally to quantify the possible variation of the eigensolutions modal behaviours and to build the experimental fuzzy sets finally the fuzzy numerical quantities are compared with the experimental quantities to highlight the efficiency of our non deterministic model for predicting the behavioural modifications of the test structure

performance of generalized multicarrier ds cdma over nakagami m fading channels a class of generalized multicarrier direct sequence code division multiple access mc ds cdma schemes is defined and its performance is considered over multipath nakagami m fading channels the spacing between two adjacent subcarriers of the generalized mc ds cdma is a variable allowing us to gain insight into the effects of the spacing on the bit error rate ber performance of mc ds cdma systems this generalized mc ds cdma scheme includes the subclasses of multitone ds cdma and orthogonal mc ds cdma as special cases we present a unified analytical framework for determining the exact average ber of the generalized mc ds cdma system over generalized multipath nakagami m 1960 fading channels the optimum spacing of the mc ds cdma system required for achieving the minimum ber is investigated and the ber performance of the system having optimum spacing is evaluated the resultant ber is compared with that of both multitone ds cdma and orthogonal mc ds cdma

correction of mismatched l values in bicm receivers in this work we analyze the problem of correction of the reliability metrics l values in bit interleaved coded modulation bicm receivers first we propose a method for finding the linear correction factors that minimize the probability of error of a maximum likelihood decoder that uses the corrected l values to this end we use the efficient approximation of the pairwise error probability in the domain of the cumulant generating functions cgf of the l values and conclude that the optimal correction factors are equal to the twice of value of the saddlepoint of the cgf next a simple extension of the proposed method to the non linear correction is presented we provide numerical examples demonstrating improvements attainable with the proposed method comparing it to the competitive solutions

performance analysis of coded modulation with generalized selection combining in rayleigh fading we consider coded modulation with generalized selection combining gsc for bandwidth efficient coded modulation over rayleigh fading channels our results show that reception diversity with generalized selection combining can conveniently trade off system complexity versus performance we provide a number of new results by calculating the cutoff rate and by deriving analytical upper bounds on symbol interleaved trellis coded modulation tcm and bit interleaved coded modulation bicm with gsc all are verified by simulation we show that our new bounds on tcm with gsc which includes maximum ratio combining and selection combining as special cases are tighter than the previously derived bounds a new asymptotic analysis on the pairwise error probability which can be used as a guideline for designing coded modulation over gsc channels is also given finally we show that bicm with iterative decoding bicm id can achieve significant coding gain over conventional coded modulation in a multiple receiving antenna channel

error probability analysis of bit interleaved coded modulation this correspondence presents a simple method to accurately compute the error probability of bit interleaved coded modulation bicm thanks to the binary input output symmetric bios nature of the channel the pairwise error probability pep is equal to the tail probability of a sum of random variables with a particular distribution this probability is in turn computed with a saddlepoint approximation its precision is numerically validated for coded transmission over standard gaussian noise and fully interleaved fading channels for both convolutional and turbo like codes

ser of threshold based hybrid selection maximal ratio combining in correlated nakagami fading the average symbol error rate of threshold based hybrid selection maximal ratio combining t hs mrc with correlated nakagami m fading channels is obtained for positive integer values of fading parameter m for a special correlation structure an accurate approximate analysis of t hs mrc in arbitrarily correlated nakagami m fading channels is presented by using a green matrix approximation the derivation allows different m ary linear modulation schemes we illustrate our methodology using m ary phase shift keying as an example

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

exact evaluation of maximal ratio and equal gain diversity receivers for m ary qam on nakagami fading channels exact integral expressions are derived for calculating the symbol error rate ser of multilevel quadrature amplitude modulation mqam in conjunction with l fold antenna diversity on arbitrary nakagami fading channel both maximal ratio combining mrc in independent and correlated fading and equal gain combining egc predetection in independent fading diversity techniques have been considered exact closed form ser expressions for two restricted nakagami fading cases mrc reception are also derived an exact analysis of egc for mqam has not been reported previously despite its practical interest remarkably the exact ser integrals can also be replaced by a finite series approximation formula a useful procedure for computing the confluent hypergeometric series is also presented

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

maximum entropy approach for modeling random uncertainties in transient elastodynamics a new approach is presented for analyzing random uncertainties in dynamical systems this approach consists of modeling random uncertainties by a nonparametric model allowing transient responses of mechanical systems submitted to impulsive loads to be predicted in the context of linear structural dynamics the information used does not require the description of the local parameters of the mechanical model the probability model is deduced from the use of the entropy optimization principle whose available information is constituted of the algebraic properties related to the generalized mass damping and stiffness matrices which have to be positive definite symmetric matrices and the knowledge of these matrices for the mean reduced matrix model an explicit construction and representation of the probability model have been obtained and are very well suited to algebraic calculus and to monte carlo numerical simulation in order to compute the transient responses of structures submitted to impulsive loads the fundamental properties related to the convergence of the stochastic solution with respect to the dimension of the random reduced matrix model are analyzed finally an example is presented

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

performance analysis of transmit beamforming for miso systems with imperfect feedback in this paper we analyze the performance of transmit beamforming on multiple antenna rayleigh fading channels with imperfect channel feedback we characterize the feedback imperfections in terms of noisy channel estimation feedback delay and finite rate channel quantization we develop a general framework that is valid for an arbitrary two dimensional linear modulation to capture the aforementioned imperfections and derive the symbol and bit error probability expressions for both m psk and m ary rectangular qam constellations with gray code mapping we show that the proposed analytical formulation is valid for a frequency domain duplexing system with without finite rate channel quantization and a time domain duplexing system we validate the accuracy of the analysis through simulations and assess the relative effects of channel estimation inaccuracy feedback delay and finite rate quantization on the symbol and bit error performances for various constellations

eigenvalue bounds of structures with uncertain but bounded parameters many analysis and design problems in engineering and science involve uncertainty to varying degrees this paper is concerned with the structural vibration problem involving uncertain material or geometric parameters specified as bounds on these parameters this produces interval stiffness and mass matrices and the problem is transformed into a generalized interval eigenvalue problem in interval mathematics however tighter bounds on the eigenvalues may be obtained by using the formulation of the structural dynamic problem often the stiffness and mass matrices can be formed as a non negative decomposition in the uncertain structural parameters in this case the eigenvalue bounds may be obtained from the parameter vertex solutions even more efficiently using interval extension from interval mathematics the generalized interval eigenvalue problem may be divided into two generalized eigenvalue problems for real symmetric matrix pairs the parameter vertex solution algorithm is compared with deif s solution the eigenvalue inclusion principle and the interval perturbation method in numerical examples

on the information loss of the max log approximation in bicm systems we present a comprehensive study of the information rate loss of the max log approximation for m ary pulse amplitude modulation pam in a bit interleaved coded modulation bicm system it is widely assumed that the calculation of l values using the max log approximation leads to an information loss we prove that this assumption is correct for all m pam constellations and labelings with the exception of a symmetric 4 pam constellation labeled with a gray code we also show that for max log l values the bicm generalized mutual information gmi which is an achievable rate for a standard bicm decoder is too pessimistic in particular it is proved that the so called harmonized gmi which can be seen as the sum of bit level gmis is achievable without any modifications to the decoder we then study how bit level channel symmetrization and mixing affect the mi and the gmi for max log l values our results show that these operations which are often used when analyzing bicm systems preserve the gmi however this is not necessarily the case when the mi is considered necessary and sufficient conditions under which these operations preserve the mi are provided

analysis of inequality and residual flow procedures and an iterative scheme for free surface seepage an efficient block overrelaxation algorithm is presented for the solution of the steady state dam seepage problem the formulation of alt is used in conjunction with a finite element method on a fixed mesh to obtain a finite dimensional problem which is then solved by the algorithm some similarities of the formulation and the residual flow method of desai are also discussed numerical results are compared with results of other authors

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

higher order failure probability calculation using nonlinear approximations use of approximations for calculating the structural failure probability under uncertainties is a necessary aspect but efficient use of suitable approximations at different stages of reliability prediction and design makes this valuable tool practical for many large scale structures the objective of this paper is to address the modern approximation concepts and their utility in structural reliability estimation emphasis is placed on building the higher order approximations using intervening variables to closely represent the nonlinear limit state functions the most probable failure point mpp search can be carried either in x space or u space for a wide variety of random variable distributions several test problems with highly nonlinear performance functions are used to demonstrate the accuracy of the proposed method

performance analysis for bicm transmission over gaussian mixture noise fading channels bit interleaved coded modulation bicm has been adopted in many systems and standards for spectrally efficient coded transmission the analytical evaluation of bicm performance parameters in particular bit error rate ber has received considerable attention in the recent past in this paper we derive ber approximations for bicm transmission over general fading channels impaired by gaussian mixture noise gmn to this end we build upon the saddlepoint approximation of the pairwise error probability pep and a recently established approximation for the probability density function pdf of bit wise reliability metrics for nonfading additive white gaussian noise awgn channels we extend this pdf approximation to the case of gmn and obtain closed form expressions for its laplace transform for fading gmn channels the latter allows us to express the pep and thus ber via the saddlepoint approximation for the special case of fading awgn channels the presented approximations are closed form since the saddlepoint is well approximated by 1 2 for bicm decoding furthermore we derive closed form pep expressions also for gmn channels in the high signal to noise ratio regime and establish the diversity and coding gain for bicm transmission over fading gmn channels selected numerical results for the ber of convolutional coded bicm highlight the usefulness of the proposed approximations and the differences between awgn and gmn channels

matrix variate distributions for probabilistic structural dynamics matrix variate distributions are proposed to quantify uncertainty in the mass stiffness and damping matrices arising in linear structural dynamics the proposed approach is based on the so called wishart random matrices it is assumed that the mean of the system matrices are known a new optimal wishart distribution is proposed to model the random system matrices the optimal wishart distribution is such that the mean of the matrix and its inverse produce minimum deviations from their respective deterministic values the method proposed here gives a simple nonparametric approach for uncertainty quantification and propagation for complex aerospace structural systems the new method is illustrated using a numerical example it is shown that wishart random matrices can be used to model uncertainty across a wide range of excitation frequencies

fuzzy finite element method for frequency response function analysis of uncertain structures a concept is presented for incorporating fuzzy uncertainties in dynamic e nite element analyses of uncertain structures the objective is twofold the e rst goal is to clarify and extend the classical fuzzy e nite element ffe method as it was introduced for static analyses the shortcomings of the classical approach are described and an extension to a generalized approach is proposed this generalized approach is proven to be a more realistic and therefore more reliable concept for taking uncertainty into account the second goal is to illustrate the applicability of the method for dynamic analyses the classical and the generalized approach are compared using an eigenvalue analysis of a simple numerical example the ffe method is also applied to the calculation of the total envelope frequency response function frf using the modal superposition principle this method requires safe approximations of the individual mode envelope frequency response functions for this purpose a number of safe approximate optimization strategies are introduced the numerical example shows that useful results are obtained using this ffe approach for frf calculations

approximating the llr distribution for a class of soft output mimo detectors we present approximations of the llr distribution for a class of fixed complexity soft output mimo detectors such as the optimal soft detector and the soft output via partial marginalization detector more specifically in a mimo awgn setting we approximate the llr distribution conditioned on the transmitted signal and the channel matrix with a gaussian mixture model gmm our main results consist of an analytical expression of the gmm model including the number of modes and their corresponding parameters and a proof that in the limit of high snr this llr distribution converges in probability towards a unique gaussian distribution

low complexity ml detectors for generalized spatial modulation systems spatial modulation sm combined with spatial multiplexing is a newly developed transmission scheme in multiple input multiple output mimo systems the resultant system referred to as generalized sm gsm can use the maximum likelihood ml detector jointly detecting the antenna subset as index and symbol vector as known the ml detector can achieve optimum performance however its computational complexity can be prohibitively high when the dimension of the gsm system is large in this paper we propose new methods to solve the problem the main idea is to split the detection into two stages one for the as index and the other for the symbol vector for the detection of the as index we develop two methods referred to as gaussian approximation and qr projection once the as index is detected conventional low complexity ml detectors can be applied for the detection of the symbol vector the diversity order for the proposed methods are further analyzed and an enhanced method is also proposed to achieve near optimum performance finally the proposed methods are extended to conduct soft detection of gsm systems simulations show that our methods significantly outperform existing ones while the detection complexity remains similar

fuzzy modal parameters abstract in order to identify modal parameters with uncertain experimental data a non deterministic identification method based on fuzzy formalism is proposed the aim is to provide a degree of confidence in the modal parameters identified

a numerical algorithm for the solution of signorini problems in this paper we propose a new iterative algorithm for the solution of a certain class of signorini problems such problems arise in the modelling of a variety of physical phenomena and usually involve the determination of an unknown free boundary here we describe a way of locating the free boundary directly and provide a proof that the algorithm converges when used with analytic methods the advantage of this algorithm is that it can be used in conjunction with any numerical method with minimal development of extra code we demonstrate its application with the boundary element method to some physical problems in both two and three dimensions

a fuzzy finite element procedure for the calculation of uncertain frequency response functions of damped structures part 2 numerical case studies this work introduces a numerical algorithm to calculate frequency response functions of damped finite element models with fuzzy uncertain parameters part 1 of this paper focusses on the numerical procedure for the solution of the underlying interval finite element problem based on the undamped procedure and the principle of rayleigh damping part 2 of this paper illustrates the applicability of the methodology through four case studies the concepts of the interval and the fuzzy finite element frequency response function analysis are illustrated for different types of uncertainties the obtained results are compared with the results of monte carlo simulations

statistics of vibration energy flow in randomly parametered trusses the problem of determining the ensemble averages of vibration energy flow in harmonically driven trusses with random parameter variations is considered the mass elasticity damping and length of the truss members are modelled as random variables the uncertainty associated with member lengths result in randomness in truss geometry four different linear damping models for truss members namely strain rate dependent viscous hysteretic models and velocity dependent viscous hysteretic models are considered the analysis employs random dynamic stiffness matrices and monte carlo simulation procedures a comparison of the ensemble averages of subsystem energies obtained using this approach and those using statistical energy analysis sea formalism is also made the energy coefficient matrix arising in sea studies is determined using the direct dynamic stiffness matrix approach the paper illustrates the relative importance of alternative damping models and alternative sources of system randomness on the behavior of spectra of subsystem vibration energies in a 13 member truss the uncertainties in randomness in truss geometry and the choice of damping model are shown to significantly affect the energy statistics

constellation labeling for linear encoders this paper investigates optimal constellation labeling in the context of the edge profile a constellation s edge profile lists the minimum distance edge for each binary symbol error the paper introduces the symmetric ultracomposite su labeling structure and shows that this structure provides undominated edge profiles for 2 sup n psk 2 sup n pam and 2 sup 2n point square qam the su structure is a generalization of the commonly used reflected binary gray code with the proper choice of basis vectors su labeling can support either set partition or gray code labeling of 2 sup n psk 2 sup n pam and 2 sup 2n point square qam notably there are gray code and set partition labelings that do not have the su structure these labelings yield inferior edge profiles the su structure does not apply to cross constellations however for any standard cross constellation with 32 or more points a quasi su labeling structure can approximate the su structure with the correct choice of basis quasi su labelings produce quasi gray labelings however the quasi su structure cannot support set partition labeling in fact the quasi su structure provides a better edge profile than standard set partition labeling thus for cross constellations there is a choice between edge profile optimality and the group structure provided by set partitioning here the correct choice depends on whether the encoder trellis has parallel branches

optimal transmitter eigen beamforming and space time block coding based on channel mean feedback optimal transmitter designs obeying the water filling principle are well documented they are widely applied when the propagation channel is deterministically known and regularly updated at the transmitter because channel state information is impossible to be known perfectly at the transmitter in practical wireless systems we design in this paper an optimal multiantenna transmitter based on the knowledge of mean values of the underlying channels our optimal transmitter design turns out to be an eigen beamformer with multiple beams pointing to orthogonal directions along the eigenvectors of the correlation matrix of the estimated channel at the transmitter and with proper power loading across beams the optimality pertains to minimizing an upper bound on the symbol error rate which leads to better performance than maximizing the expected signal to noise ratio snr at the receiver coupled with orthogonal space time block codes two directional eigen beamforming emerges as a more attractive choice than conventional one directional beamforming with uniformly improved performance without rate reduction and without essential increase in complexity with multiple receive antennas and reasonably good feedback quality the two directional eigen beamformer is also capable of achieving the best possible performance in a large range of transmit power to noise ratios without a rate penalty

on an alleged philosophers stone concerning variational principles with subsidiary conditions in general the lagrange multiplier method lmm is used to incorporate subsidiary conditions into variational principles the lagrange multipliers represent an additional field of independent variables the attempt to satisfy subsidiary conditions without employing additional independent unknowns has led to the development of simplified variational principles svp they are characterized by expressing lagrange multipliers in terms of original field variables by means of the euler lagrange equations for the multipliers providing their physical interpretation in the first part of the theoretical investigation systems with infinitely many degrees of freedom are studied it is shown that the euler lagrange equations of a lmm based on a modification of the principle of minimum of potential energy pmipe do not hold unconditionally that is for arbitrary subsidiary conditions for the corresponding svp the second part of the theoretical investigation is concerned with systems with a finite number of degrees of freedom the finite element method fem is employed to discuss and compare the characteristics of the lmm and of the corresponding svp contrary to the former the latter are found to be problem dependent several shortcomings of the svp are listed including the possibility of obtaining an infinite sequence of singular coefficient matrices in the process of a systematic mesh refinement consequently convergence of finite element solutions to the true solution in the limit of finite element representations is not guaranteed the theoretical findings are corroborated by the results of a detailed numerical study

finite element formulation of unilateral boundary conditions for unsaturated flow in porous continua this paper presents the numerical resolution of unilateral boundary conditions able to effectively model several problems of unsaturated flow as those involving rainfall infiltration and seepage faces besides the penalty technique we also consider the novel regularization of these conditions by means of the more effective augmented lagrangian method the performance of the so obtained finite element method is carefully investigated in terms of accuracy and ill conditioning effects including comparisons with analytical solutions and a complete identification of the analogies with the problem of frictionless contact in this way we provide a priori estimates of optimal and admissible ranges for the penalty coefficient as functions of permeability and spatial discretization the proposed method and the estimated coefficient ranges are validated in further numerical examples involving the propagation of a wetting front due to rainfall and the partial saturation of an aged concrete dam these applications show that the proposed regularizations do not induce any detrimental effect on solution accuracy and on convergence rate of the employed newton raphson method hence the present approach should be preferred to the commonly used iterative switching between the imposed flow and the imposed pressure conditions which often leads to spurious oscillations and convergence failures

distribution of max log metrics for qam based bicm in fading channels in this letter we derive closed form expressions for the probability density functions pdfs of the bits reliability metrics l values in bit interleaved coded modulation bicm transmission over fully interleaved fading channels the expressions are valid for the relevant case of quadrature amplitude modulation qam with gray mapping when the metrics are calculated via the so called max log approximation using the developed expressions the performance of coded bicm transmissions is efficiently evaluated i e without resorting to otherwise required two dimensional numerical integration the bicm capacity for different fading channels and constellation sizes is also evaluated

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

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

an analytical method for approximate performance evaluation of binary linear block codes an analytical method for approximate performance evaluation of binary linear block codes using an additive white gaussian noise channel model with binary phase shift keying modulation is presented we focus on the probability density function of the bit log likelihood ratio llr which is expressed in terms of the gram charlier series expansion this expansion requires knowledge of the statistical moments of the bit llr we introduce an analytical method for calculating these moments this is based on some recursive calculations involving certain weight enumerating functions of the code it is proved that the approximation can be as accurate as desired if we use enough terms in the gram charlier series expansion numerical results are provided for some examples which demonstrate close agreement with simulation results

accurate error rate performance analysis of ofdm on frequency selective nakagami m fading channels error rates of orthogonal frequency division multiplexing ofdm signals in multipath slow fading nakagami m fading channels are considered the exact probability density function of a sum of nakagami m random phase vectors is used to derive a closed form expression for the error rates of ofdm signals the precise error rate analysis is extended to a system using multichannel reception with maximal ratio combining an asymptotic error rate analysis is also provided for a two tap channel with finite values of nakagami m fading parameters our analysis and numerical results show that the asymptotic error rate performance of an ofdm signal is similar to that of a single carrier signal transmitted over a rayleigh fading channel on the other hand our analysis further shows that a frequency selective channel that can be represented by two constant taps has similar asymptotic error rate performance to that of a one sided gaussian fading channel it is observed that depending on the number of channel taps the error rate performance does not necessarily improve with increasing nakagami m fading parameters

a complete method for efficient fuzzy modal analysis the objective of this paper is to determine both the fuzzy eigenvalues and eigenvectors of a finite element model defined with fuzzy parameters the proposed method introduces the concepts of mode shape pairing and the functional dependence of eigensolutions with respect to design parameters high order approximations are then introduced to limit the computational cost associated with variability management numerical test cases are used to highlight the abilities of this method to predict behaviour modifications due to variations in the physical parameters

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

error probability performance prediction for multichannel reception of linearly modulated coherent systems on fading channels this paper provides a framework for the analysis of error rate performance of maximal ratio combining multichannel reception of coherent linearly modulated systems over frequency selective fading channels expressions for the error probability are developed and the special cases for which closed form or acceptable efficient numerical solutions are possible are delineated a new efficient and accurate recursive method for the ricean fading main resolved path case is presented for coherent quadrature amplitude modulation constellations the effect of automatic gain control error on analysis of modulation schemes is demonstrated finally numerical examples based on the maritime high data rate channel model are provided to demonstrate the usefulness of the framework

error probability for orthogonal space time block code diversity system using rectangular qam transmission over rayleigh fading channels in this paper theoretical symbol error probability sep expressions are derived for orthogonal space time block code ostbc diversity systems employing arbitrary rectangular m qam transmission over flat rayleigh fading channels independent fading between diversity channels is assumed channel average powers may be distinctive identical or mixed with both the rectangular m qam results are extended to square m qam m pam and binary antipodal signaling all derived expressions are in elementary forms without complicated high order transcendental functions and unevaluated integrals and hence are strictly exact and can be readily simulated by the computer moreover it is shown that mixed rayleigh fading results can be readily extended to various nakagami m fading results a four transmit antenna system with a half rate ostbc for 16 qam signaling is used to demonstrate that the theoretical result is in excellent agreement with the monte carlo simulated result from simulation curves it is shown that under the independent channel fading condition channels with identical powers have better error rate performance than channels with distinctive powers

performance analysis of multibranch switched diversity systems we investigate the performance of multibranch switched diversity systems specifically we first derive generic formulas for the cumulative distribution function probability density function and moment generating function of the combined signal power for both switch and stay combining ssc and switch and examine combining sec schemes we then capitalize on these expressions to obtain closed form expressions for the outage probability and average error rate for various practical communication scenarios of interest as a byproduct of our analysis we prove that for ssc with identically distributed and uniformly correlated branches increasing the number of branches to more than two does not improve the performance but the performance can be different in the case the branches are not identically distributed and or not uniformly correlated we also show that in general the sec performance improves with additional branches the mathematical formalism is illustrated with a number of selected numerical examples

constellation mappings for two dimensional signaling of nonuniform sources the design of two dimensional constellation mappings for the transmission of binary nonuniform memoryless sources over additive white gaussian noise channels using standard m ary psk and qam modulation schemes is investigated the main application of this problem is the incorporation of an adaptive mapping assignment in modem devices that employ fixed psk qam modulation schemes for the transmission of heterogenous data such as multimedia information containing various levels of nonuniformity in general the optimal mapping depends on both the probability distribution of the input signals and the signal to noise ratio snr in the channel in addition to the geometry of the signal constellation we show that constellation mappings which follow the objective of minimizing the average symbol energy and given this maximizing the decoding probability of the most likely signals can yield symbol error rate and bit error rate performance that is substantially better than gray encoding maps gains as high as 3 5 db in snr e sub b n sub 0 are obtained for highly nonuniform sources finally we note that the mappings techniques result in nonzero mean constellations and briefly consider their performances when they are converted to zero mean constellations by shifting in this case we observe that the shifted zero mean gray map outperforms our shifted maps for small to medium sized constellations m spl les 32 but not for larger sizes

a survey of non probabilistic uncertainty treatment in finite element analysis the objective of this paper is to critically review the emerging non probabilistic approaches for uncertainty treatment in finite element analysis the paper discusses general theoretical and practical aspects of both the interval and fuzzy finite element analysis first the applicability of the non probabilistic concepts for numerical uncertainty analysis is discussed from a theoretical viewpoint the necessary conditions for a useful application of the non probabilistic concepts are determined and are proven to be complementary rather than competitive to the classical probabilistic approach the second part of the paper focuses on numerical aspects of the interval finite element method it describes two principal strategies for the implementation i e the anti optimisation and the interval arithmetic approach and gives a state of the art of the interval finite element algorithms available from literature it is shown how the application of the interval arithmetic approach to the classical finite element procedure can result in a severe overestimation of the uncertainty on the output and the main sources of this conservatism are identified a numerical example in the final part of the paper illustrates the capabilities of the different strategies on an eigenfrequency analysis of a built up benchmark structure

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

on the performance analysis of space time codes in quasi static rayleigh fading channels in this paper we analyze the performance of space time codes by deriving a new approximation of the frame error probabilities for space time trellis coded modulations over quasi static rayleigh fading channels we take advantage of two techniques the modified bounding technique and the limiting before averaging technique to tighten the upper bound in addition we establish a theorem that enables us to reduce the computation and memory needed to calculate the frame error rate fer approximation the newly derived approximation is very tight requires only the distance spectrum of the space time code and can be computed through single numerical integration numerical results exhibit that the new approximation is much closer to the simulation results than other existing bounds are especially in the case of one receive antenna

stochastic reduced basis methods stochastic reduced basis methods for solving large scale linear random algebraic systems of equations such as those obtained by discretizing linear stochastic partial differential equations in space time and the random dimension are introduced the fundamental idea employed is to represent the system response using a linear combination of stochastic basis vectors with undetermined deterministic coefficients or random functions we present a theoretical justification for employing basis vectors spanning the preconditioned stochastic krylov subspace to approximate the response process subsequently variants of the bubnov galerkin scheme are employed to compute the undetermined coefficients which allow explicit expressions for the response quantities to be derived we also examine some theoretical properties of the projection scheme and procedures for computing the response statistics numerical studies are presented for static and dynamic analysis of stochastic structural systems we demonstrate that significant improvements over the neumann expansion scheme as well as other relevant techniques in the literature can be achieved

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

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

an analytical approach for performance evaluation of bicm transmission over nakagami m fading channels bit interleaved coded modulation bicm has established itself as a quasi standard for bandwidth and power efficient wireless communication in this paper we present an analytical approach to evaluate the performance of bicm transmission over frequency flat fading additive white gaussian noise channels the statistic of the fading envelope is modeled as nakagami m distributed which spans a wide range of practical multipath fading scenarios through adjustment of the m parameter for this setup we derive approximations for the bit error rate ber and cutoff rate of bicm different from previously proposed methods our analysis is valid for general quadrature amplitude modulation and phase shift keying signal constellations and arbitrary bit to symbol mapping rules and it results in simple closed form expressions the key idea is to use well chosen subsets of signal points to approximate the probability density function of reliability metrics used for decoding this approximation is accurate for signal to noise ratio regions of interest for bicm systems with moderate coding complexity such as e g convolutional coded bicm systems based on this approximation we also derive an asymptotic ber expression which reveals the diversity order and coding gain of bicm the usefulness of the proposed analytical approach is validated through numerical and simulation results for a number of bicm transmission examples

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

a new formulation of signorini s type for seepage problems with free surfaces a new variational inequality formulation for seepage problems with free surfaces is presented in which a boundary condition of signorini s type is prescribed over the potential seepage surfaces this makes the singularity of seepage points eliminated and the location of seepage points determined easily compared to other variational formulations the proposed formulation can effectively overcome the mesh dependency and significantly improve the numerical stability a very challenging engineering example with complicated geometry aid strong inhomogeneity is investigated in detail

on the asymptotic performance of bit wise decoders for coded modulation two decoder structures for coded modulation over the gaussian channel are studied 1 the maximum likelihood symbol wise decoder and 2 the suboptimal bit wise decoder based on the bit interleaved coded modulation paradigm we consider a 16 ary quadrature amplitude constellation labeled with a gray labeling it is shown that the asymptotic loss in terms of pairwise error probability for any two codewords caused by the bit wise decoder is bounded by 1 25 db the analysis also shows that the asymptotic loss is zero for a wide range of linear codes including all rate 1 2 convolutional codes

calculating frequency response functions for uncertain systems using complex affine analysis this paper is concerned with the effect of parametric uncertainty upon the response of mechanical systems two uncertainty propagation techniques are employed and compared against a benchmark based upon randomly scanning input parameter ranges the first technique complex interval analysis is computationally very efficient but suffers from the issue of dependency which may result in large overestimation of the system response the second technique namely complex affine analysis is presented here for the first time and it keeps track of variable dependencies throughout the calculation thus limiting overestimation albeit at some computational expense the methods are demonstrated on the problem of calculation of the frequency response functions of a simple lumped mass system with uncertain parameters for purposes of transparency of the presented ideas although these ideas are equally applicable to more complex systems it transpired that the complex affine analysis performed significantly better than its interval counterpart

ser and outage of threshold based hybrid selection maximal ratio combining over generalized fading channels the average symbol error rate and outage probability of threshold based hybrid selection maximal ratio combining t hs mrc in generalized fading environments are analyzed a t hs mrc combiner chooses the combined branches according to a predetermined normalized threshold and the strength of the instantaneous signal to noise ratio snr of each branch therefore the number of combined branches is a random variable rather than a fixed number as in conventional hybrid selection maximal ratio combining h s mrc using the moment generating function method a unified analysis of t hs mrc over various slow and frequency nonselective fading channels is presented both independent identically distributed and independent nonidentically distributed diversity branches are considered the derivation allows different m ary linear modulation schemes the theory is illustrated using coherent m ary phase shift keying in nakagami m fading as an example it is shown that previous published results are incorrect

on the quantification of damping model uncertainty abstract the characterization of uncertainty in the damping forces in a vibrating structure is of significant interest in structural dynamics the most common approach is to use a viscous damping matrix with uncertain coefficients the viscous damping is not the only damping model within the scope of linear analysis any model which makes the energy dissipation functional non negative is a possible candidate for a valid damping model there are many functional forms which can be used as damping models in this paper two approaches are proposed to quantify such model form uncertainty associated with the use of the viscous damping model not only the model parameters the first approach is based on an ensemble of equivalent damping functions and the second approach is based on the random matrix theory the results obtained from the two methods are compared using numerical examples it was observed that the random matrix theory can be used to quantify damping model uncertainty in some cases

optimal alphabets and binary labelings for bicm at low snr optimal binary labelings input distributions and input alphabets are analyzed for the so called bit interleaved coded modulation bicm capacity paying special attention to the low signal to noise ratio snr regime for 8 ary pulse amplitude modulation pam and for 0 75 bit symbol the folded binary code results in a higher capacity than the binary reflected gray code brgc and the natural binary code nbc the 1 db gap between the additive white gaussian noise awgn capacity and the bicm capacity with the brgc can be almost completely removed if the input symbol distribution is properly selected first order asymptotics of the bicm capacity for arbitrary input alphabets and distributions dimensions mean variance and binary labeling are developed these asymptotics are used to define first order optimal foo constellations for bicm i e constellations that make bicm achieve the shannon limit 1 59 db it is shown that the eb n0 required for reliable transmission at asymptotically low rates in bicm can be as high as infinity that for uniform input distributions and 8 pam there are only 72 classes of binary labelings with a different first order asymptotic behavior and that this number is reduced to only 26 for 8 ary phase shift keying psk a general answer to the question of foo constellations for bicm is also given using the hadamard transform it is found that for uniform input distributions a constellation for bicm is foo if and only if it is a linear projection of a hypercube a constellation based on pam or quadrature amplitude modulation input alphabets is foo if and only if they are labeled by the nbc if the constellation is based on psk input alphabets instead it can never be foo if the input alphabet has more than four points regardless of the labeling

gray coding for multilevel constellations in gaussian noise the problem of finding the optimal labeling bit to symbol mapping of multilevel coherent phase shift keying psk pulse amplitude modulation pam and quadrature amplitude modulation qam constellations with respect to minimizing the bit error probability bep over a gaussian channel is addressed we show that using the binary reflected gray code brgc to label the signal constellation results in the lowest possible bep for high enough signal energy to noise ratios and analyze what is high enough in this sense it turns out that the brgc is optimal for psk and pam systems whenever the target bep is at most a few percent which covers most systems of practical interest new and simple closed form expressions are presented for the bep of psk pam and qam using the brgc

high dimensional model representation method for fuzzy structural dynamics abstract uncertainty propagation in multi parameter complex structures possess significant computational challenges this paper investigates the possibility of using the high dimensional model representation hdmr approach when uncertain system parameters are modeled using fuzzy variables in particular the application of hdmr is proposed for fuzzy finite element analysis of linear dynamical systems the hdmr expansion is an efficient formulation for high dimensional mapping in complex systems if the higher order variable correlations are weak thereby permitting the input output relationship behavior to be captured by the terms of low order the computational effort to determine the expansion functions using the cut method scales polynomically with the number of variables rather than exponentially this logic is based on the fundamental assumption underlying the hdmr representation that only low order correlations among the input variables are likely to have significant impacts upon the outputs for most high dimensional complex systems the proposed method is first illustrated for multi parameter nonlinear mathematical test functions with fuzzy variables the method is then integrated with a commercial finite element software adina modal analysis of a simplified aircraft wing with fuzzy parameters has been used to illustrate the generality of the proposed approach in the numerical examples triangular membership functions have been used and the results have been validated against direct monte carlo simulations it is shown that using the proposed hdmr approach the number of finite element function calls can be reduced without significantly compromising the accuracy

on the error probability of linearly modulated signals on frequency flat ricean rayleigh and awgn channels the method used in aghamohammadi and meyr 1990 for finding the error probability of linearly modulated signals on rayleigh frequency flat fading channels has been applied to the more general case of ricean fading a signal received on a fading channel is subject to a multiplicative distortion md and to the usual additive noise following a compensation of the md the signal provided to the detector may be thought to include only a single additive distortion term final noise which comprises the effects of the original additive noise the md and the error in md compensation an exact expression for the probability density function of the final noise is derived this allows calculation of error probability for arbitrary types of linear modulations results for many cases of interest are presented furthermore as special cases of ricean fading error probability for rayleigh fading and non fading channels are obtained which either match the results or complete the approximate derivations formerly known from the literature

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

on the difference of two chi square variates with application to outage probability computation an expression for the cumulative distribution function evaluated at zero of the difference of two chi square variates with different number of degrees of freedom is derived and applied to the outage probability computation of cellular mobile radio systems in fading channels in particular a generic result is developed for this probability which takes on several forms the simplest of which is a single integral with finite limits and an integrand composed of elementary exponential and trigonometric functions the results are applicable to cellular systems that are subject to independent identically distributed i i d interfering signals and that employ maximal ratio combining reception over i i d diversity paths various fading channel models are assumed for the desired signal and interferers for each desired signal interferer combination the outage probability is expressed in closed form in terms of a set of parameters that characterize the particular scenario a tabulation of these various scenarios and their associated parameters for channels of practical interest is included

dual form of discontinuous deformation analysis abstract discontinuous deformation analysis dda is a numerical method for analyzing dynamic behaviors of an assemblage of distinct blocks with the block displacements as the basic variables the contact conditions are approximately satisfied by the open close iteration which needs to fix or remove repeatedly the virtual springs between blocks in contact the results from dda are strongly dependent upon stiffness of these virtual springs excessively hard or soft springs all incur numerical problems this is believed to be the biggest obstacle to more extensive application of dda to avoid the introduction of virtual springs huge efforts have been made with little progress related to low efficiency in solution in this study the contact forces instead of the block displacements are taken as the basic variables stemming from the equations of momentum conservation of each block the block displacements can be expressed in terms of the contact forces acting on the block from the contact conditions a finite dimensional quasi variational inequality is derived with the contact forces as the independent variables on the basis of the projection contraction algorithm for the standard finite dimensional variational inequalities an iteration algorithm called the compatibility iteration is designed for the quasi variational inequality the main processes can be highly parallelized with no need to assemble the global stiffness matrix a number of numerical tests including those very challenging suggest that the proposed procedure has reached practical level in accuracy robustness and efficiency and the goal to abandon completely virtual springs has been reached

some new twists to problems involving the gaussian probability integral using an alternate form of the gaussian probability integral discovered a number of years ago it is shown that the solution to a number of previously considered communication problems can be simplified and in some cases made more accurate i e exact rather than bounded these problems include the evaluation of 1 the bit error probability of uncoded phase shift keying psk with costas loop tracking 2 word error probability of antipodal modulation in the presence of fading 3 bit error probability of coded m ary psk mpsk over the memoryless fading channel with given channel state information 4 conditional symbol error probability of mpsk in the presence of carrier synchronization error and 5 the average error probability for the binary additive white gaussian noise awgn intersymbol interference channel also obtained is a generalization of this new alternate form to the case of a two dimensional gaussian probability integral with arbitrary correlation which can be used to evaluate the symbol error probability of mpsk with i q unbalance

high snr asymptotics of mutual information for discrete constellations with applications to bicm asymptotic expressions of the mutual information between any discrete input and the corresponding output of the scalar additive white gaussian noise channel are presented in the limit as the signal to noise ratio snr tends to infinity asymptotic expressions of the symbol error probability sep and the minimum mean square error mmse achieved by estimating the channel input given the channel output are also developed it is shown that for any input distribution the conditional entropy of the channel input given the output mmse and sep have an asymptotic behavior proportional to the gaussian q function the argument of the q function depends only on the minimum euclidean distance med of the constellation and the snr and the proportionality constants are functions of the med and the probabilities of the pairs of constellation points at med the developed expressions are then generalized to study the high snr behavior of the generalized mutual information gmi for bit interleaved coded modulation bicm by means of these asymptotic expressions the long standing conjecture that gray codes are the binary labelings that maximize the bicm gmi at high snr is proven it is further shown that for any equally spaced constellation whose size is a power of two there always exists an anti gray code giving the lowest bicm gmi at high snr

seepage flow with free surface in fracture networks 1 crystalline rocks are often heterogeneous geological materials that contain numerous fractures of various attitudes and scales although considerable advances have been made in simulation of fluid flow through fractured media our knowledge of seepage flow with free surfaces in fracture networks remains to be an outstanding issue in this paper the partial differential equations pdes defined on the whole fracture network domain are formulated for free surface seepage flow problems by an extension of darcy s law a variational inequality vi formulation is then presented and the proof of the equivalence between the pde and vi formulations is given since the boundary conditions involving the flux components in the pde formulation become the natural conditions in the vi formulation the difficulty of choosing the trial functions for numerical solutions is significantly reduced and the locations of seepage points can be easily determined on the basis of the discrete vi the corresponding numerical procedure for unconfined seepage analysis of discrete fracture network has been developed the results from three typical examples demonstrate the validity and capability of the procedure for unconfined seepage problems involving complicated fracture networks

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

error rate of quadrature subbranch hybrid selection maximal ratio combining in rayleigh fading the symbol error rate ser of a quadrature subbranch hybrid selection maximal ratio combining qbhs mrc scheme for 1 d modulations in rayleigh fading is examined at the receiver n diversity branches are split into 2n in phase and quadrature subbranches traditional hybrid selection maximal ratio combining h s mrc is then applied over the 2n subbranches m ary pulse amplitude modulation including coherent binary phase shift keying with qbhs mrc is studied the ser performances of qbhs mrc and h s mrc are compared results show that qbhs mrc systems outperform traditional h s mrc systems

optimal transmitter eigen beamforming and space time block coding based on channel correlations optimal transmitter designs obeying the water filling principle are well documented and widely applied when the propagation channel is deterministically known and regularly updated at the transmitter because channel state information csi may be costly or impossible to acquire in rapidly varying wireless environments we develop in this paper statistical water filling approaches for stationary random fading channels these approaches require only knowledge of the channel correlations that do not necessitate frequent updates and can be easily acquired applied to a multiple transmit antenna paradigm our optimal transmitter design turns out to be an eigen beamformer with multiple beams pointing to orthogonal directions along the eigenvectors of the channel s correlation matrix and with proper power loading across the beams the optimality pertains to minimizing a tight bound on the symbol error rate the resulting loaded eigen beamforming outperforms not only the equal power allocation across all antennas but also the conventional beamformer that transmits the available power along the strongest direction coupled with orthogonal space time block codes two dimensional 2 d eigen beamforming emerges as a more attractive choice than conventional one dimensional 1 d beamforming with uniformly better performance without rate reduction and without complexity increase

random matrix theory for modeling uncertainties in computational mechanics this paper deals with data uncertainties and model uncertainties issues in computational mechanics if data uncertainties can be modeled by parametric probabilistic methods for a given mean model a nonparametric probabilistic approach can be used for modeling model uncertainties the first part is devoted to random matrix theory for which we summarize previous published results and for which two new ensembles of random matrices useful for the nonparametric models are introduced in a second part the nonparametric probabilistic approach of random uncertainties is presented for linear dynamical systems and for nonlinear dynamical systems constituted of a linear part with additional localized nonlinearities in a third part a new method is proposed for estimating the parameters of the nonparametric approach from experiments finally examples with experimental comparisons are given

the component mode transformation method a fast implementation of fuzzy arithmetic for uncertainty management in structural dynamics abstract the study of mechanical systems with uncertain parameters is of increasing importance in the analysis and in the design of structures because an adequate description of these uncertainties is necessary to provide a reliable forecasting model in order to update or evaluate an uncertain model different methods have been proposed but many of these such as the monte carlo simulation or the transformation method require multiple sequential evaluations of the model moreover to cover an adequate portion of the uncertain parameter space the number of necessary evaluations of the model grows exponentially with the number of uncertain parameters leading often to a large number of runs the proposed methodology deals with uncertain parameters that are modeled by the use of fuzzy numbers and the transformation method is applied to characterize the dynamic behavior of the structure in order to reduce the order of magnitude of the computational time a reduction of the model dimension obtained through a component mode synthesis is performed advantages and drawbacks of the proposed method are discussed together with an application to the study of the dynamics of a beam

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

exact error probability analysis of rectangular qam for single and multichannel reception in nakagami m fading channels in this contribution we derive exact closed form expressions for the average symbol error probability sep of arbitrary rectangular quadrature amplitude modulation qam for single and multichannel diversity reception over independent but not necessarily identically distributed nakagami m fading channels the diversity branches may hence exhibit identical or distinctive power levels and their associated nakagami indexes need not be the same our work extends previous results pertaining to nondiversity reception of m ary rectangular qam over rayleigh fading channels and multichannel reception of m ary square qam over nakagami m fading channels for a given number l of diversity branches and a corresponding set of arbitrary real valued nakagami indexes not less than 1 2 our sep results are expressed in terms of gauss s hypergeometric function 2f1 and lauricella s multivariate hypergeometric function fd l of l variables both of which can be efficiently evaluated using standard numerical softwares

llr compression for bicm systems using large constellations digital video broadcasting dvb c2 and other modern communication standards increase diversity by means of a symbol level interleaver that spans over several codewords de interleaving at the receiver requires a large memory which has a significant impact on the implementation cost in this paper we propose a technique that reduces the de interleaver memory size by quantizing log likelihood ratios with bit specific quantizers and compressing the quantized output we can significantly reduce the memory size with a negligible increase in computational complexity both the quantizer and compressor are designed via a gmi based maximization procedure for a typical dvb c2 scenario numerical results show that the proposed solution enables a memory saving up to 30

new bounds of pairwise error probability for space time codes in rayleigh fading channels in this paper we present new upper and lower bounds of the pairwise error probabilities pep for space time codes over rayleigh channels with independent fading in support of this we derive a new expression of the pep using alternative form of the gaussian tail function which is very simple and descriptive the new bounds are very accurate and suitable for easy estimation and application to the performance analysis based on distance spectrum according to numerical examples they turn out to be much closer to the exact pep than other existing bounds in addition they help to envision the behavior of the space time codes for the cases with more than one receiveing antennas

the transformation method for the simulation and analysis of systems with uncertain parameters in this paper the transformation method is introduced as a powerful approach for both the simulation and the analysis of systems with uncertain model parameters based on the concept of cuts the method represents a special implementation of fuzzy arithmetic that avoids the well known effect of overestimation which usually arises when fuzzy arithmetic is reduced to interval computation systems with uncertain model parameters can thus be simulated without any artificial widening of the simulation results as a by product of the implementation scheme the transformation method also provides a measure of influence to quantitatively analyze the uncertain system with respect to the effect of each uncertain model parameter on the overall uncertainty of the model output by this a special kind of sensitivity analysis can be defined on the basis of fuzzy arithmetic finally to show the efficiency of the transformation method the method is applied to the simulation and analysis of a model for the friction interface between the sliding surfaces of a bolted joint connection

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

a new uncertainty analysis for the transformation method in this paper a new uncertainty analysis for the transformation method tm is proposed as a practical implementation of fuzzy arithmetic the tm is a convenient tool for the simulation and analysis of systems with uncertain parameters that are expressed by fuzzy numbers the proposed uncertainty analysis and the sensitivity analysis of the tm complete each other in providing some quantification of the relationship between the uncertainties of the system input and the system output the computation of gain factors is proposed which allows the estimation of the absolute and relative measures of uncertainty these measures allow the quantification of the influence of the uncertainty of the input on the uncertainty of the output