asymmetric perfectly matched layer for the absorption of waves the perfectly matched layer pml has become a standard for comparison in the techniques that have been developed to close the system of maxwell equations more generally wave equations when simulating an open system the original berenger pml formulation relies on a split version of maxwell equations with numerical electric and magnetic conductivities we present here an extension of this formulation which introduces counterparts of the electric and magnetic conductivities affecting the term which is spatially differentiated in the equations the phase velocity along each direction is also multiplied by an additional coefficient we show that under certain constraints on the additional numerical coefficients this medium does not generate any reflection at any angle or any frequency and is thus a perfectly matched layer technically it is a superset of berenger s pml to which it reduces for a specific set of parameters and like it it is anisotropic however unlike the pml it introduces some asymmetry in the absorption rate and is therefore labeled an apml for asymmetric perfectly matched layer we present here the numerical considerations that have led us to introduce such a medium as well as its theory several finite difference numerical implementations are derived in one two and three dimensions and the performance of the apml is contrasted with that of the pml in one and two dimensions using plane wave analysis we show that our apml implementations lead to higher absorption rates than the considered pml implementations although we have considered in this paper the finite difference discretization of maxwell like equations only the apml system of equations may be used with other discretization schemes such as finite elements and may be applied to other equations for applications beyond electromagnetics

exact ber analysis of ostbcs in spatially correlated mimo channels the bit error rate ber performance of orthogonal space time block codes stbcs in correlated multiple input multiple output mimo channels is studied we first derive closed form exact ber equations for pulse amplitude modulation quadrature amplitude modulation and phase shift keying constellations in a correlated rayleigh mimo channel the ber expressions can be easily evaluated without any numerical methods then we consider correlated mimo channels where the line of sight components exist and they suffer from shadowing namely correlated shadowed rician mimo channels for three practical channel scenarios the ber is analyzed and closed form ber equations are presented

matched filter bound for multipath rician fading channels this paper derives an infinite series and an integral for computing matched filter bounds for binary phase shift keying bpsk communications over a multipath rician fading channel of discrete or continuous dispersion based on the derived bound we compare intrinsic frequency diversity ifd gains for channels of different rician factors

m psk and m qam ber computation using signal space concepts in this paper we introduce a simple geometric approach that is based on signal space concepts to efficiently evaluate the performance of m ary phase shift keying m psk and m ary quadrature amplitude modulation m qam schemes over an additive white gaussian noise channel in particular new bit error rate approximations are derived and shown to be in excellent agreement with monte carlo simulation results

the asymptotic distribution of maxima of independent and identically distributed sums of correlated or non identical gamma random variables and its applications in this paper we show that the asymptotic probability density function pdf of the maxima of n independent and identically distributed i i d sums of independent non identically i n i d distributed gamma random variables rvs is a gumbel pdf using extreme value theory evt we will also show that the asymptotic pdf of the maxima of n i i d sums of correlated gamma rvs is a gumbel pdf some applications in wireless communication are discussed where the maxima of n i i d sums of correlated gamma rvs and maxima of n i i d sums of i n i d gamma rvs arise we discuss the utility of our results in the context of these applications

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

another look at the performance of mrc schemes in nakagami m fading channels with arbitrary parameters in this letter we take a close look at the performance of maximal ratio combining mrc schemes operating in a flat nakagami m fading environment with arbitrary fading parameters we derive an expression for the probability density function pdf of the output signal to noise ratio snr by expressing the moment generating function of the output snr in the form of multiple barnes type contour integrals by evaluating the inverse transform and converting the multiple contour integrals into infinite series we are able to derive an expression for the pdf of the output snr when the nakagami fading parameters along the diversity branches take on real and arbitrary values consequently the average bit error rate can now be expressed in terms of lauricella s multivariate hypergeometric function which can be easily evaluated numerically special cases of the main results reduce to known results in the literature the results which apply to independent as well as correlated diversity branches will be useful for predicting the system performances when the nakagami fading parameters are real and arbitrary

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

an extended fdtd scheme for the wave equation application to multiscale electromagnetic simulation abstract an algorithm for the application of the mesh refinement technique to finite difference calculation of the wave equation is presented via the introduction of a new extended fdtd scheme this scheme can be viewed as an extension of the yee scheme using a new set of variables relating to the direction of propagation of the waves along an axis because of this additional information this scheme allows a more natural implementation of the mesh refinement technique the extended scheme is presented for both a one dimensional and a multidimensional system the mesh refinement algorithm is given in one dimension and the performances are compared to other proposed schemes

s n energy selection combining for mpsk and 16 qam signaling in nakagami m and rician fading channels a signal plus noise s n energy selection diversity combining s n esc scheme for m ary phase shift keying mpsk in rayleigh fading channels is mathematically analyzed also the s n esc scheme for mpsk and 16 quadrature amplitude modulation 16 qam signaling in nakagami m and rician fading channels is studied by computer simulations the s n esc selects the branch with the maximum s n energy for detection the advantage of the s n esc scheme is that it requires no explicit channel estimation for diversity branch selection we show that the symbol error probability sep of the s n esc is the same as that of classical selection combining sc for mpsk signaling in independent and identically distributed i i d rayleigh fading channels also we show that the sep of a weighted s n esc scheme is the same as that of classical sc for mpsk signaling in independent and nonidentically distributed i n d rayleigh fading channels it is shown by computer simulations that the s n esc scheme provides a smaller sep than classical sc for mpsk signaling in nondispersive fading channels such as nakagami m fading channels with nakagami parameter m 1 and rician fading channels with rician parameter k 0 on the other hand the s n esc scheme is shown by computer simulations to have a larger sep than classical sc for 16 qam signaling in nakagami m and rician fading channels

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

on the snr penalty of mpsk with hybrid selection maximal ratio combining over i i d rayleigh fading channels closed form expressions that lower and upper bound the penalty of hybrid selection maximal ratio combining relative to maximal ratio combining mrc for m ary phase shift keying mpsk modulation are proved the bounds offer simple to evaluate explicit expressions and are typically within 0 6 db for hybrid systems with diversity order up to eight that use at least two branches yet are independent of signal to noise ratio snr contrary to conclusions conjectured in a previously published paper it is proved that the snr penalty is not a constant independent of snr it is also shown that previous estimates of the performance losses of selection diversity relative to mrc underestimate or lower bound the losses for mpsk modulation systems and that the true loss can be significantly larger than previously believed an upper bound to this loss is also obtained

effect of channel estimation error on qam systems with antenna diversity this paper studies the effect of channel estimation error and antenna diversity on multilevel quadrature amplitude modulation m qam systems over rayleigh fading channels based on the characteristic function method a general closed form bit error rate ber for m qam systems is presented the effect of the inaccurate channel estimation on the performance for pilot symbol assisted modulation m qam systems with antenna diversity is investigated simulation results for m qam m 4 16 64 256 etc show that the analytical method can accurately estimate the system performance moreover numerical results show that with the antenna diversity technique the ber performance improves significantly especially in perfect channel estimation cases it is also found that the channel estimation error limits the benefit of antenna diversity by increasing the length of the channel estimator and the amplitude of the pilot symbol more accurate channel estimation can be achieved so that the ber performance is improved

design and analysis of low complexity multi antenna relaying for ofdm based relay networks a class of low complexity multi antenna relaying schemes is proposed for orthogonal frequency division multiplexing based one way and two way relay networks in the proposed schemes two single antenna terminal nodes complete the data transfer in two time phases via a multi antenna amplify and forward relay without channel state information discrete fourier transform dft and inverse dft the relay signal processing consists of receive combining power scaling and transmit diversity where instantaneous time domain power scaling is proposed for power scaling and power based selection combining and cyclic delay combining are proposed for receive combining to leverage the performance only with time domain operations an approximation to the outage probability is also derived to predict the coded performance behavior under practical channel models it is shown by evaluating the outage probability and coded bit error rate that the proposed schemes outperform the conventional schemes of comparable complexity

virtual branch analysis of symbol error probability for hybrid selection maximal ratio combining in rayleigh fading we derive analytical expressions for the symbol error probability sep for a hybrid selection maximal ratio combining h s mrc diversity system in multipath fading wireless environments with h s mrc l out of n diversity branches are selected and combined using maximal ratio combining mrc we consider coherent detection of m ary phase shift keying mpsk and quadrature amplitude modulation mqam using h s mrc for the case of independent rayleigh fading with equal signal to noise ratio averaged over the fading the proposed problem is made analytically tractable by transforming the ordered physical diversity branches which are correlated into independent and identically distributed i i d virtual branches which results in a simple derivation of the sep for arbitrary l and n we further obtain a canonical structure for the sep of h s mrc as a weighted sum of the elementary seps which are the seps using mrc with i i d diversity branches in rayleigh fading or equivalently the seps of the nondiversity single branch system in nakagami fading whose closed form expressions are well known we present numerical examples illustrating that h s mrc even with l spl lt n can achieve a performance close to that of n branch mrc

a novel analytical method for maximum likelihood detection in mimo multiplexing systems this letter addresses the problem of symbol error probability sep analysis for maximum likelihood ml detection in multiple input multiple output mimo multiplexing systems a new analytical method is presented based on the total probability theorem the effects of imperfect channel estimation and power allocation scheme are investigated the accuracy of the proposed method is demonstrated by monte carlo simulations it is shown that the analytical results match quite well with the simulation ones irrespective of the signal to noise ratio snr

necessary and sufficient conditions for viability for semilinear differential inclusions given a set a in a banach space x we define the tangent set and the quasi tangent set to k atc g k concepts more general than the one of tangent vector introduced by bouligand 1930 and severi 1931 both notions prove very suitable in the study of viability problems referring to differential inclusions namely we establish several new necessary and even necessary and sufficient conditions for viability referring to both differential inclusions and semilinear evolution inclusions conditions expressed in terms of the tangency concepts introduced

effect of mmse channel estimation on ber performance of orthogonal space time block codes in rayleigh fading channels we present a simple closed form expression for the ber of orthogonal space time block codes ostbcs with mmse channel estimation assuming pam and qam constellations and flat rayleigh block fading the ber expression is exact for a certain class of ostbcs and provides a very accurate approximation for other ostbcs

a novel extension to craig s q function formula and its application in dual branch egc performance analysis a novel identity for the gaussian q function of the sum of two non negative variables is introduced as an extension of craig s q function formula it is shown that this new identity provides a unified framework in the performance analysis of dual branch equal gain combining egc diversity similar to that of craig s q function formula for maximum ratio combining diversity then the performance of dual correlated branch egc in nakagami m fading is studied using this novel approach for coherent modulations with error probabilities in terms of the gaussian q function it is shown that the average error probability of the dual correlated branch egc in nakagami m fading is the same as the average error probability of a modeled single channel receiver in the same fading environment using this fact simple exact and approximate closed form expressions for this average error probability are derived the analytical results are verified and illustrated by numerical results and computer simulations

a viability theorem for set valued states in a hilbert space abstract applications in robust control problems and shape evolution motivate the mathematical interest in control problems whose states are compact possibly non convex sets rather than vectors this leads to evolutions in a basic set which can be supplied with a metric like the well established pompeiu hausdorff distance but it does not have an obvious linear structure this article extends differential inclusions with state constraints to compact valued states in a separable hilbert space h the focus is on sufficient conditions such that a given constraint set of compact subsets is viable a k a weakly invariant our main result extends the tangential criterion in the well known viability theorem usually for differential inclusions in a vector space to the metric space of non empty compact subsets of h

error probabilities of two dimensional m ary signaling in fading a new exact method for computing the average symbol error probability of two dimensional m ary signaling in slow fading is presented the method is generally applicable to polygonal decision regions the exact average symbol error rate of coherent 16 star qam is obtained and compared to that of 16 rectangular qam new results for optimum ring ratios of 16 star qam in additive white gaussian noise awgn and in slow fading are also given

equal gain transmission in multiple input multiple output wireless systems multiple input multiple output mimo wireless systems are of interest due to their ability to provide substantial gains in capacity and quality the paper proposes equal gain transmission egt to provide diversity advantage in mimo systems experiencing rayleigh fading the applications of egt with selection diversity combining equal gain combining and maximum ratio combining are addressed it is proven that systems using egt with any of these combining schemes achieve full diversity order when transmitting over a memoryless flat fading rayleigh matrix channel with independent entries since in practice full channel knowledge at the transmitter is difficult to realize a quantized version of egt is proposed an algorithm to construct a beamforming vector codebook that guarantees full diversity order is presented monte carlo simulation comparisons with various beamforming and combining systems illustrate the performance as a function of quantization

a new absorbing layer boundary condition for the wave equation a new absorbing boundary condition using an absorbing layer is presented for application to finite difference time domain fdtd calculation of the wave equation this algorithm is by construction a hybrid between the berenger perfectly matched layer pml algorithm and the one way sommerfeld algorithm the new prescription contains both of these earlier ones as particular cases and retains benefits from both numerical results indicate that the new algorithm provides absorbing rates superior to those of the pml algorithm

uncoded and coded performance of mfsk and dpsk in nakagami fading channels the author presents uncoded and coded performance results for noncoherent m ary frequency shift keying mfsk and differentially coherent binary phase shift keying dpsk in a slow nonselective nakagami m 1960 fading channel he gives simple expressions for the asymptotic slopes of probability of bit error for large signal to noise ratio and shows that the effective order of diversity compared to an uncoded rayleigh channel is the product of two parameters one for the channel and one for the code he also compares the uncoded nakagami m results to those of the rician channel in order to show performance differences between these two generalized fading channel models

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

impulse capture basins of sets under impulse control systems given a target contained in a constrained set and an impulse control system governing the evolutions of runs or executions that are hybrids of continuous and discrete evolutions this paper studies and provides several characterizations of the capture basin of the target viable in the constrained set it is the subset of initial runs from which start at least one run viable in the constrained set until it reaches the target in finite time it also provides algorithms and regulation rules governing the runs that reach the targets while obeying state constraints

error vector magnitude analysis in generalized fading with co channel interference in this paper we derive the data aided error vector magnitude evm in an interference limited system when both the desired channel and interferers experience independent and nonidentically distributed kappa mu shadowed fading then it is analytically shown that the evm is equal to the square root of number of interferers when the desired channel and interferers do not experience fading furthermore the evm is derived in the presence of interference and noise when the desired channel experiences kappa mu shadowed fading and the interferers experience independent and identical nakagami fading moreover using the properties of the special functions the derived evm expressions are also simplified for various special cases

orthogonal space time block code over time varying flat fading channels channel estimation detection and performance analysis this paper studies the channel estimation detection and performance analysis of mobile wireless communication systems employing space time block codes stbc where the channels exhibit flat rayleigh fading with a significant amount of doppler spread pilot symbol assisted modulation psam is developed to estimate the channels the performance of the channel estimation is evaluated maximum likelihood ml detection is first formulated a linear detector called the symmetric linear sl detector is proposed an interference cancellation ic detector is also developed to improve the performance of the sl detector we derive the closed form analytical expressions for the bit error rate ber or symbol error rate ser of pilot sequence assisted stbc with binary phase shift keying psk quaternary psk 16 quadrature amplitude modulation qam and 64 qam when the sl and ic detectors are used some important design issues in the pilot sequence assisted stbc systems including the selection of pilot spacing and interpolator size are discussed simulation results are presented that verify our analytical results the tradeoffs between the performance and complexity for ml sl and ic detection are also discussed

an exact performance analysis of mrc ostbc over generalized fading channels a unified analytical framework for evaluating the performance of maximal ratio combining mrc and orthogonal space time block coding ostbc over generalized fading channels is presented the basic motivation for developing such a framework pertains to analyzing the distribution of a sum of squared random variables rvs belonging to different families of fading distributions following a novel analytical approach stemming from the definition of a common moment generating function mgf model for these families of distributions the probability density function pdf and the cumulative distribution function cdf of a general sum of squared rvs are expressed by simple infinite gamma series expansions based on these expressions the capacity and error probability of mrc ostbc over generalized fading channels is thoroughly studied the developed theory is used to evaluate the performance of ostbc for a mixed nakagami m rice fading model and novel analytical results are presented the accuracy of the derived expressions is validated by extensive monte carlo simulations

viability for nonautonomous semilinear differential equations abstract let x be a reflexive banach space a d a x x the infinitesimal generator of a compact c0 semigroup s t x x t 0 d a locally closed subset in x and t x f t x a function on a b d which is locally integrably bounded measurable with respect to t and continuous with respect to x the main result of the paper is t heorem under the general assumptions above a necessary and sufficient condition in order that for each a b dthere exists at least one mild solutionu t dof du dt t au t f t u t satisfyingu is the tangency condition below there is a negligible subset z of a b such that for eacht a b zand eachx d lim inf h 0 1 h d s h x hf t x d 0

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

on the error probability of binary and m ary signals in nakagami m fading channels in this letter we present new closed form formulas for the exact average symbol error rate ser of binary and m ary signals over nakagami m fading channels with arbitrary fading index m using the well known moment generating function based analysis approach we express the average ser in terms of the higher transcendental functions such as the gauss hypergeometric function appell hypergeometric function or lauricella function the results are generally applicable to arbitrary real valued m furthermore with the aid of reduction formulas of hypergeometric functions we show previously published results for rayleigh fading m 1 as special cases of our expressions

signaling constellations for fading channels the performance of various coherent 8 ary and 16 ary modulations in additive white gaussian noise awgn and slowly fading channels are analyzed new expressions for the exact symbol error rates ser in fading with diversity combining are derived for any two dimensional signaling format having polygonal decision boundaries maximal ratio combining equal gain combining and selection combining are considered the ser formulas obtained make it possible for the first time to optimize parameters of various constellations precisely and to determine which constellation has the lowest probability of error for example a star constellation such as that specified in the ccitt v 29 standard can be improved by adjusting the amplitude ratios of the points in the constellation to save about 0 63 db power in awgn without sacrificing the phase error tolerance while maintaining the same error rate the sensitivity of each constellation to phase error is presented and comparisons are made six 8 ary signal sets and 11 16 ary signal sets are examined using the new symbol error probability formulas to determine best signal sets for fading channels

a new formula for the ber of binary modulations with dual branch selection over generalized k error performance is one of the main performance measures and the derivation of its closed form expression has proved to be quite involved for certain communication systems operating over composite fading channels in this letter a unified closed form expression applicable to different binary modulation schemes for the bit error rate of dual branch selection diversity based systems undergoing independent but not necessarily identically distributed generalized k fading is derived in terms of the extended generalized bivariate meijer g function

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

asymptotic performance of hybrid selection maximal ratio combining over fading channels in this letter we study the asymptotic performance of hybrid selection maximal ratio combining hs mrc and postdetection hs equal gain combining hs egc over generalized fading channels for large average signal to noise ratios asnrs by evaluating the asymptotic moment generating function of the hs mrc output snr at high asnr we derive the diversity and coding gains for hs mrc for a large class of modulation formats and versatile fading conditions including different types of fading channels and nonidentical snr statistics across diversity branches our analytical results reveal that the diversity gains of hs mrc and hs egc are equivalent to that of mrc and the difference in the coding gains for different modulation formats is manifested in terms of a modulation factor defined in this letter some new analytical results about effects of the number of combined branches for hs mrc and noncoherent combining loss of hs egc are also provided

space time power optimization of variable rate space time block codes based on successive interference cancellation based on a zero forcing with successive interference cancellation zfsic method we construct variable rate space time block codes stbcs for two three and four transmit antennas in rayleigh fading channels considering the error propagation effect in the zfsic scheme we analyze the bit error rate ber and optimize the transmit power so that the average ber is minimized unlike the approach based on zero forcing zf the method adopted in this paper can construct variable rate stbcs even when the receive antennas are fewer than the transmit antennas in addition to improve the bers further we propose space time power optimization numerical results show that the codes presented in this paper provide much lower bers compared with the codes developed by kim and tarokh

continued fraction absorbing boundary conditions for convex polygonal domains continued fraction absorbing boundary conditions cfabcs are highly effective boundary conditions for modelling wave absorption into unbounded domains they are based on rational approximation of the exact dispersion relationship and were originally developed for straight computational boundaries in this paper cfabcs are extended to the more general case of polygonal computational domains the key to the current development is the surprising link found between the cfabcs and the complex co ordinate stretching of perfectly matched layers pmls this link facilitates the extension of cfabcs to oblique corners and thus to polygonal domains it is shown that the proposed cfabcs are easy to implement expected to perform better than pmls and are effective for general polygonal computational domains in addition to the derivation of cfabcs a novel explicit time stepping scheme is developed for efficient numerical implementation numerical examples presented in the paper illustrate that effective absorption is attained with a negligible increase in the computational cost for the interior domain although this paper focuses on wave propagation its theoretical development can be easily extended to the more general class of problems where the governing differential equation is second order in space with constant coefficients copyright 2005 john wiley sons ltd

a general method for calculating error probabilities over fading channels signal fading is a ubiquitous problem in mobile and wireless communications in digital systems fading results in bit errors and evaluating the average error rate under fairly general fading models and multichannel reception is often required predominantly to date most researchers perform the averaging using the probability density function method or the moment generating function mgf method this paper presents a third method called the characteristic function chf method for calculating the average error rates and outage performance of a broad class of coherent differentially coherent and noncoherent communication systems with or without diversity reception in a myriad of fading environments unlike the mgf technique the proposed chf method based on parseval s theorem enables us to unify the average error rate analysis of different modulation formats and all commonly used predetection diversity techniques i e maximal ratio combining equal gain combining selection diversity and switched diversity within a single common framework the chf method also lends itself to the averaging of the conditional error probability involving the complementary incomplete gamma function and the confluent hypergeometric function over fading amplitudes which heretofore resisted to a simple form as an aside we show some previous results as special cases of our unified framework

a useful integral for wireless communication theory and its application to rectangular signaling constellation error rates a useful integral representing the average over rayleigh fading of the product of two gaussian q functions is solved in closed form a closed form solution for the symbol error probability of general rectangular quadrature amplitude modulation in rayleigh fading is derived

feedback spreading control laws for semilinear distributed parameter systems the paper shows for the first time that a feedback spreading control law for semilinear distributed parameter systems with compact linear operator can be provided by a selection procedure which involves both the dynamics of the system and the property to be spread in the case of affine dependence upon the control a minimum energy feedback spreading control law will be derived by using a parametrized constrained optimization technique along with some facts of set valued analysis

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

viability in a non local population model structured by size and spatial position abstract motivated conceptually by multiscale models of cancer cell migration the focus is on a broad class of set valued population models structured both physiologically and spatially for time dependent sets of constraints given sufficient conditions are provided such that every permitted density function initializes at least one admissible weak solution this result about viability a k a weak invariance concerns non local hyperbolic differential inclusions of first order with memory and with one boundary condition for the minimal value of the scalar structure parameter

the n fold convolution of a finite mixture of densities abstract in this paper the probability density function of the n fold convolution of a finite mixture of densities is obtained the new density is again a finite mixture of densities in this way the formula recently given by ma n y ma a comment on on the distribution of ma and king applied mathematics and computation 218 2011 202 203 for a two fold convolution is interpreted and extended and a correct expression for the formula provided by nadarajah s nadarajah on the distribution of ma and king applied mathematics and computation 189 2007 732 733 is given several relevant examples are provided including the convolution for the generalized exponential sum distribution

a trivariate nakagami m distribution with arbitrary covariance matrix and applications to generalized selection diversity receivers this paper deals with a trivariate nakagami m distribution derived from the diagonal elements of a wishart matrix for this distribution infinite series representations for its probability density and cumulative distribution functions are derived having an arbitrary covariance matrix and integer order fading parameters moreover upper bounds on the error resulting from truncating the infinite series are obtained based on the derived formulas the performance of triple branch generalized selection combining gsc receivers is analyzed for this type of receivers the outage and the average bit error probability for a variety of modulation schemes are analytically obtained the performance of gsc receivers is compared to that of conventional selection and maximal ratio diversity schemes in order to check the accuracy and convergence of the derived formulas various performance evaluation results are presented and compared to equivalent simulation ones

far field filtering operators for suppression of reflections from artificial boundaries the concern of this paper is the treatment of far field artificial boundaries for first order hyperbolic systems where the aim is to suppress nonphysical reflections of outgoing waves we construct far field filtering operators of two types 1 slowing down operators and 2 damping operators the operators are activated in anarrow sponge layer near the far field boundary and have the following properties a the operators act only on the outgoing part of the solution leaving the incoming part unharmed b the passage of waves across the modified layer is reflection free and c the implementation of the operators amounts to a small modification of the governing equations in the far field in either case the treatment of the boundary itself is greatly simplified since the outgoing waves either do not reach the boundary or have practically zero strength when they do well posedness of the modified equations and stability of the discretization scheme are established we also show that such reflection

optimizing the perfectly matched layer the berenger perfectly matched layer or pml 4 3 is used in computational electromagnetism as a sponge layer to terminate finite element approximations of scattering problems an infinite perfectly matched layer creates no reflection for incident waves of any frequency or any incident direction and the waves decay exponentially in magnitude into the layer this property is lost when the layer is truncated since the truncation boundary generates a reflected wave discretization of the differential equations further changes the reflection coefficient of the layer in this talk we shall describe the pml in the simple case of a two dimensional electromagnetic problem the first part of this abstract is expository we shall show how to derive the layer using a change of variable approach 5 9 6 after this derivation we describe some new analysis to show the effects of truncating and discretizing the pml 9 we end by showing how to compute an optimal layer and make some remarks about pml for the full maxwell system

asymptotic analysis and tight performance bounds of diversity receptions over beckmann fading channels with arbitrary correlation prior results on exact error rates and outage probabilities of diversity receptions over arbitrarily correlated fading channels involve intractable nested integrals which makes the performance analyses challenging to carry out in this paper we derive asymptotic expressions and asymptotically tight bounds for error rates and outage probabilities of diversity receptions including maximal ratio combining selection combining and equal gain combining over arbitrarily correlated beckmann fading channels these new asymptotic performance expressions reveal insights into the diversity systems over arbitrarily correlated beckmann fading channels and the accuracy of the asymptotic performance expressions is explicitly quantified by the performance bounds using these analytical tools one can assess the performance of the diversity reception systems over arbitrarily correlated beckmann fading channels without resorting to time consuming monte carlo simulation or numerical multifold integration

error rates for nakagami m fading multichannel reception of binary and m ary signals this paper derives new closed form formulas for the error probabilities of single and multichannel communications in rayleigh and nakagami m 1960 fading closed form solutions to three generic trigonometric integrals are presented as part of the main result providing a unified method for the derivation of exact closed form average symbol error probability expressions for binary and m ary signals with l independent channel diversity reception both selection diversity and maximal ratio combining mrc techniques are considered the results are generally applicable for arbitrary two dimensional signal constellations that have polygonal decision regions operating in a slow nakagami m fading environments with positive integer fading severity index mrc with generically correlated fading is also considered the new expressions are applicable in many cases of practical interest the closed form expressions derived for a single channel reception case can be extended to provide an approximation for the error rates of binary and m ary signals that employ an equal gain combining diversity receiver

a unified approach to the probability of error for noncoherent and differentially coherent modulations over generalized fading channels we present a unified approach to determine the exact bit error rate ber of noncoherent and differentially coherent modulations with single and multichannel reception over additive white gaussian noise and generalized fading channels the multichannel reception results assume independent fading in the channels and are applicable to systems that employ post detection equal gain combining our approach relies on an alternate form of the marcum q function and leads to expressions of the ber involving a single finite range integral which can be readily evaluated numerically aside from unifying the past results the new approach also allows for a more general solution to the problem in that it includes many situations that in the past defied a simple solution the best example of this occurs for multichannel reception where the fading on each channel need not be identically distributed nor even distributed according to the same family of distributions

on the error probability of linearly modulated signals on rayleigh frequency flat fading channels consideration is given to optimal detection of linearly modulated signals subject to multiplicative rayleigh distributed distortion and additive white gaussian noise for coherent detection regenerated amplitude and phase references are employed at the receiver to compensate for amplitude and phase deviations from the correct values a system model is formulated under the assumption of perfect symbol timing and in the absence of intersymbol interference producing a final additive noise term applied just before the detection which contains the effects of the original additive and multiplicative distortions and of the errors in the phase and amplitude references by determining the probability density function of this final noise term for arbitrary types of linear modulation it is possible to perform exact calculations of error probabilities

equal gain diversity receiver performance in wireless channels performance analysis of equal gain combining egc diversity systems is notoriously difficult only more so given that the closed form probability density function pdf of the egc output is only available for dual diversity combining in rayleigh fading a powerful frequency domain approach is therefore developed in which the average error rate integral is transformed into the frequency domain using parseval s theorem such a transformation eliminates the need for computing or approximating the egc output pdf which is unknown but instead requires the knowledge of the corresponding characteristic function which is readily available the frequency domain method also circumvents the need to perform multiple fold convolution integral operations usually encountered in the calculation of the pdf of the sum of the received signal amplitudes we then derive integral expressions for the average symbol error rate of an arbitrary two dimensional signaling scheme with egc reception in rayleigh rician nakagami m 1960 and nakagami q fading channels for practically important cases of second and third order diversity systems in nakagami fading both coherent and noncoherent detection methods for binary signaling are analyzed using the appell hypergeometric function a number of closed form solutions are derived in which the results put forward by zhang see ibid vol 45 p 270 73 1997 are shown to be special cases

on the distribution function of the generalized beckmann random variable and its applications in communications the beckmann distribution has a wide range of applications in radio frequency communications free space optical fso communications and underwater wireless optical communications uwoc however the cumulative distribution function cdf of the beckmann random variable rv does not have a closed form expression which makes it challenging to derive analytical solutions for the outage probability of systems involving beckmann rvs in this paper we study the generalized beckmann distribution which includes the beckmann rayleigh rician nakagami m hoyt kappa mu eta mu single sided gaussian and the beaulieu xie distributions as special cases three approaches are proposed to estimate the cdf of the generalized beckmann distribution including closed form upper and lower cdf bounds single fold integration based on the closed form characteristic function and a left tail cdf approximation we compare the three approaches in terms of the ranges of applications and the computation time complexity based on the new cdf estimation techniques one can efficiently evaluate the outage probabilities of pointing error limited fso systems uwoc systems and maximum ratio combining over arbitrarily correlated generalized beckmann channels

nagumo type condition for partial differential inclusions on etudie un probleme de la forme x t ax t g xc h x o x 0 k t o t x t k ou a est un operateur elliptique et k n est pas necessairement compact on trouve des conditions tangentielles de type nagumo

error vector magnitude analysis of fading simo channels relying on mrc reception we analytically characterize the data aided error vector magnitude evm performance of a single input multiple output simo communication system relying on maximal ratio combining mrc having either independent or correlated branches that are nonidentically distributed in particular exact closed form expressions are derived for the evm in eta text mu fading and kappa w mu shadowed fading channels and these expressions are validated by simulations the derived expressions are expressed in terms of lauricella s function of the fourth kind f d n which can be easily computed furthermore we have simplified the derived expressions for various special cases such as independent and identically distributed branches rayleigh fading nakagami m fading and kappa text mu fading additionally a parametric study of the evm performance of the wireless system is presented

unknown bounds on performance in nakagami channels optimum performance of communication in nakagami channels is reexamined with novel functionals of m gamma distribution analyses of signal interference and of coherent binary detection are greatly simplified the general error rate formula holds for coherent and noncoherent detection of psk or fsk signals a lower bound on error rates is established for some diversity systems

noncoherent diversity reception over nakagami fading channels a method for computing the average bit error probability of binary differential phase shift keying dpsk and frequency shift keying fsk signals transmitted over nakagami asymptotically slow fading channels with postdetection diversity reception is presented to extend previously published results the previously published results apply only for maximum ratio combining i e with predetection combining where phase coherency is necessary the results for postdetection combining are derived with the explicit expressions for the most practical cases of independent channels and particular cases of correlated channels

viability theorems for a class of differential operator inclusions abstract this paper discusses the following viability problem of a differential inclusion x t ax t f x t x 0 x0 k t 0 x t k where k is a compact subset of a banach space x a is the infinitesimal generator of a compact differentiable semigroup of bounded linear operators on x and f k x is upper semicontinuous with compact convex values we show that a natural tanegential condition is necessary and sufficient for the existence of a global solution to this problem

m ary symbol error outage over nakagami m fading channels in shadowing environments this letter addresses the problem of finding a tractable expression for the symbol error outage seo in flat nakagami m fading and shadowing channels we deal with m ary phase shift keying m psk and quadrature amplitude modulation m qam which extends our previous results on bpsk signaling we propose a new tight approximation of the symbol error probability sep holding for m psk and m qam signals which is accurate over all signal to noise ratios snrs of interest we derive a new generic expression for the inverse sep which facilitates the derivation of a tight approximation of the seo in a lognormal shadowing environment

feedback spreading control under speed constraints this paper is concerned with the control of spread in semilinear parabolic systems it first introduces a formula in order to measure the speed of a spread then feedback spreading control laws under speed constraints are studied by a set valued approach the optimality of such laws is examined in the case in which the system is affine dependent upon the control

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

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

the performance of binary transmission in slow nakagami fading channels with mrc diversity this letter presents equations which describe an average weighted spectrum of errors and average block error probabilities for noncoherent frequency shift keying ncfsk used in d branch maximal ratio combining mrc diversity in independent very slow nonselective nakagami fading channels the average is formed over the instantaneous receiver signal to noise ratio snr after combining the analysis is limited to additive gaussian noise

optimized nonuniform psk for multiclass traffic and its application to space time block codes we construct nonuniform phase shift keying psk constellations that provide unequal error protection for multiclass traffic such as compressed voice and video data then closed form expressions expression for the exact bit error rate ber of the nonuniform psk constellations is derived in multiple receive antenna systems over rayleigh fading channels based on this ber analysis we optimize the nonuniform psk constellations such that the bers of all the bits of each class are equalized or such that the total transmission power is minimized subject to the average ber constraints in particular we demonstrate that even for transmitting single class traffic the optimized nonuniform psk constellations can be better than the conventional uniform psk finally we extend the nonuniform psk constellations to space time coded communications systems with multiple transmit and multiple receive antennas

asymptotically exact performance bounds of af multi hop relaying over nakagami fading a new class of upper bounds on the end to end signal to noise ratio snr of channel assisted amplify and forward af multi hop n 2 relay networks is presented it is the half harmonic mean of the minimum of the first p 0 hop snrs and the minimum of the remaining n p hop snrs the parameter p varies between 0 to n and may be chosen to provide the tightest bound the closed form cumulative distribution function and moment generating function are derived for independent and non identically distributed rayleigh fading and for independent and identically distributed nakagami m fading where m is an integer the resulting outage probability and the average symbol error rate bounds are asymptotically exact the asymptotic exactness holds for any 0 p n as applications two cases of multi hop multi branch relay networks i the best branch selection and ii maximal ratio combining reception are treated numerical results are provided to verify the comparative performance against the existing bounds

asymptotic maximum order statistic for sir in kappa mu shadowed fading using tools from extreme value theory evt it is proved that when the user signal and the interferer signals undergo independent and non identically distributed i n i d kappa mu shadowed fading the limiting distribution of the maximum of l independent and identically distributed i i d signal to interference ratio sir random variables rvs is a frechet distribution it is observed that this limiting distribution is close to the true distribution of maximum for maximum sir evaluated over moderate l furthermore moments of the maximum rv is shown to converge to the moments of the frechet rv in addition the rate of convergence of the actual distribution of the maximum to the frechet distribution is derived and analyzed for different kappa and mu parameters finally results from the stochastic ordering are used to analyze the variation in the limiting distribution with respect to the variation in source fading parameters these results are then used to derive upper bound for the rate in full array selection fas schemes for the antenna selection and the asymptotic outage probability and the ergodic rate in maximum sum capacity msc scheduling systems

feedback spreading controls for semilinear parabolic systems abstract distributed biophysical processes usually involve spreads in space e g pollution desertification in vegetation dynamics etc in this paper based on the fact that spreadability of a distributed system reduces to a monotonicity problem we show how feedback spreading control laws can be determined in semilinear parabolic systems in case of affine dependence upon the control the use of a technique which combines saddle points and contraction mapping theorem yields a minimum energy feedback spreading control law a mathematical example is examined in order to illustrate the derived results

performance of mrc diversity systems for the detection of signals with nakagami fading bit error rate ber is analyzed theoretically for diversity reception in nakagami fading environment using an m branch maximal ratio combiner mrc coherent and incoherent reception of frequency shift keying fsk are considered using the multiple branch diversity system for both identical and different diversity branch fading parameters the effect of correlation is also considered for the dual diversity case the results are extended to include coherent phase shift keying cpsk and differential phase shift keying dpsk

quadratic forms in random variables theory and applications textbook for a one semester graduate course for students specializing in mathematical statistics or in multivariate analysis or reference for theoretical as well as applied statisticians confines its discussion to quadratic forms and second degree polynomials in real normal random vectors and matr

closed form statistics for the sum of squared nakagami m variates and its applications we present closed form expressions for the probability density function pdf and the cumulative distribution function cdf of the sum of non identical squared nakagami m random variables rvs with integer order fading parameters as it is shown they can be written as a weighted sum of erlang pdfs and cdfs respectively while the analysis includes both independent and correlated sums of rvs the proposed formulation significantly improves previously published results which are either in the form of infinite sums or higher order derivatives of the fading parameter m the obtained formulas can be applied to the performance analysis of diversity combining receivers operating over nakagami m fading channels

tangent sets viability for differential inclusions and applications abstract let x be a real banach space let a d a x x be a given operator k a nonempty and possible non open subset in d a f k x a given multi function in this lecture we consider the differential inclusion u t a u t f u t with a a 0 b a linear and c a nonlinear and in each one of these cases we give a short survey of the most important and very recent necessary and sufficient conditions for viability expressed in terms of tangent sets and a quasi tangent sets to k at a given point k concepts recently introduced by the authors from a rather long list of applications we confined ourselves only to solutions in moving sets a comparison result for a reaction diffusion system a comparison result for a nonlinear diffusion inclusion and a sufficient condition for null controllability

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

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