reply to comments on reactive energies impedance and q factor of radiating structures the merit of this comment is the fact that the procedure to arrive at the expressions 18 and 19 introduced for the first time in 1 is indeed very simple and easy to explain in my view the main step is the choice of 10 and 11 this choice does have a lot of pros it is not only the most intuitive one possible on top it yields the correct energies in the limit for frequencies going to zero the charge distribution is linked to the electric energy and the current distribution to the magnetic energy

constellation rotated vector ofdm and its performance analysis over rayleigh fading channels although the single antenna vector ofdm vofdm proposed by xia shows performance robust to channel spectral nulls it does not necessarily attain full diversity for multi path fading channels it is known that the degradation in diversity order is sometimes rescued by the rotation of constellation a simple application of constellation rotation to the v ofdm system does not however improve its performance in this paper we discuss the sub channel spectral structure of the v ofdm signal and give upper bounds on its pair wise error probability over multi path rayleigh fading channels and propose a novel constellation rotated v ofdm crv ofdm with improved diversity to this end we design rotation angles for sub channel symbols to minimize upper bounds on ber simulation results show that the proposed crv ofdm attains diversity order min m p for the vector length m and the number of paths p as the results for ber 10 4 crv ofdm improves the performance of v ofdm by 2 db for both bpsk and qpsk modulation when m is 2 and for m 4 the improvement factor is about 1 3 db we also discuss the effects of m on the transmitter and receiver complexities and on the peak to averate power ratio finally we compare several methods for rotational angle determination

structural optimization a new dual method using mixed variables a new and powerful mathematical programming method is described which is capable of solving a broad class of structural optimization problems the method employs mixed direct reciprocal design variables in order to get conservative first order approximations to the objective function and to the constraints by this approach the primary optimization problem is replaced with a sequence of explicit subproblems each subproblem being convex and separable it can be efficiently solved by using a dual formulation an attractive feature of the new method lies in its inherent tendency to generate a sequence of steadily improving feasible designs examples of application to real life aerospace structures are offered to demonstrate the power and generality of the approach presented

on improved bounds on the decoding error probability of block codes over interleaved fading channels with applications to turbo like codes we derive here improved upper bounds on the decoding error probability of block codes which are transmitted over fully interleaved rician fading channels coherently detected and maximum likelihood ml decoded we assume that the fading coefficients during each symbol are statistically independent due to a perfect channel interleaver and that perfect estimates of these fading coefficients are provided to the receiver the improved upper bounds on the block and bit error probabilities are derived for fully interleaved fading channels with various orders of space diversity and are found by generalizing some previously introduced upper bounds for the binary input additive white gaussian nose awgn channel the advantage of these bounds over the ubiquitous union bound is demonstrated for some ensembles of turbo codes and low density parity check ldpc codes and it is especially pronounced in a portion of the rate region exceeding the cutoff rate our generalization of the duman and salehi bound duman and salehi 1998 duman 1998 which is based on certain variations of gallager s 1965 bounding technique is demonstrated to be the tightest reported upper bound we therefore apply it to calculate numerically upper bounds on the thresholds of some ensembles of turbo like codes referring to the optimal ml decoding for certain ensembles of uniformly interleaved turbo codes the upper bounds derived here also indicate good match with computer simulation results of efficient iterative decoding algorithms

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

new closed form bounds on the performance of coding in correlated rayleigh fading new simple bounds are presented for the probability of error in a binary hypothesis test for communications using diversity signaling in correlated rayleigh fading the bounds are developed in the context of pairwise error event probabilities in decoding an error correction code a long standing conjecture regarding the form of worst case error events in exponentially correlated rayleigh fading is also proven the utility of the results is illustrated by their application to transfer function bounds on the probability of bit error for a system using a convolutional code the closed form transfer function bounds are shown to be tighter than previously developed transfer function bounds for communications in exponentially correlated rayleigh fading

a unified approach for parameter identification of inelastic material models in the frame of the finite element method this work is concerned with identification of parameters for inelastic material models in order to account for possible non uniformness of stress and strain distributions the identification is performed in the frame of the finite element method in particular linearization procedures are described in a systematic manner for the case of complex material models within a geometric linear theory this unified approach allows one to apply the newton method for solving the associated direct problem and to apply gradient based methods for solving the associated inverse problem which is considered as an optimization problem two numerical examples demonstrate the versatility of our approach firstly we consider cooks membrane problem based on simulated data for re identification of material parameters for a viscoplastic power law furthermore material data for j2 flow theory are determined based on experimental data obtained by a grating method for a compact specimen and we will investigate the results by using different starting values and stochastic perturbation of the experimental data

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

an alternative expression for the symbol error probability of mpsk in the presence of i q unbalance this letter provides a new expression for the probability of the phase angle between two vectors perturbed by gaussian noise with in phase quadrature phase i q unbalance in order to simplify the analysis of the error probabilities of m ary phase shift keying mpsk the error probabilities symbol error rates or bit error rates for mpsk with i q balance or unbalance can be presented straightforwardly from the derived expression because the newly derived result is provided in terms of the conventional first order gaussian q function and the joint gaussian q function with a correlation coefficient dependent on m it readily allows rapid evaluation for various cases of practical interest

global minimax approximations and bounds for the gaussian q function by sums of exponentials this paper presents a novel systematic methodology to obtain new simple and tight approximations lower bounds and upper bounds for the gaussian q function and functions thereof in the form of a weighted sum of exponential functions they are based on minimizing the maximum absolute or relative error resulting in globally uniform error functions with equalized extrema in particular we construct sets of equations that describe the behaviour of the targeted error functions and solve them numerically in order to find the optimized sets of coefficients for the sum of exponentials this also allows for establishing a trade off between absolute and relative error by controlling weights assigned to the error functions extrema we further extend the proposed procedure to derive approximations and bounds for any polynomial of the q function which in turn allows approximating and bounding many functions of the q function that meet the taylor series conditions and consider the integer powers of the q function as a special case in the numerical results other known approximations of the same and different forms as well as those obtained directly from quadrature rules are compared with the proposed approximations and bounds to demonstrate that they achieve increasingly better accuracy in terms of the global error thus requiring significantly lower number of sum terms to achieve the same level of accuracy than any reference approach of the same form

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

minimization of antenna quality factor optimal currents on arbitrarily shaped radiators with respect to the minimum quality factor are found using a simple and efficient procedure the solution starts with a reformulation of the problem of minimizing quality factor q as an alternative so called dual problem taking advantage of modal decomposition and group theory it is shown that the dual problem can easily be solved and always results in minimal quality factor q moreover the optimization procedure is generalized to minimize quality factor q for embedded antennas with respect to the arbitrarily weighted radiation patterns or with prescribed magnitude of the electric and magnetic near fields the obtained numerical results are compatible with previous results based on the composition of modal currents convex optimization and quasi static approximations however using the methodology in this paper the class of solvable problems is significantly extended

improved upper bounds on the ml decoding error probability of parallel and serial concatenated turbo codes via their ensemble distance spectrum the ensemble performance of parallel and serial concatenated turbo codes is considered where the ensemble is generated by a uniform choice of the interleaver and of the component codes taken from the set of time varying recursive systematic convolutional codes following the derivation of the input output weight enumeration functions of the ensembles of random parallel and serial concatenated turbo codes the tangential sphere upper bound is employed to provide improved upper bounds on the block and bit error probabilities of these ensembles of codes for the binary input additive white gaussian noise awgn channel based on coherent detection of equi energy antipodal signals and maximum likelihood decoding the influence of the interleaver length and the memory length of the component codes is investigated the improved bounding technique proposed here is compared to the conventional union bound and to a alternative bounding technique by duman and salehi 1998 which incorporates modified gallager bounds the advantage of the derived bounds is demonstrated for a variety of parallel and serial concatenated coding schemes with either fixed or random recursive systematic convolutional component codes and it is especially pronounced in the region exceeding the cutoff rate where the performance of turbo codes is most appealing these upper bounds are also compared to simulation results of the iterative decoding algorithm

error probability for coherent and differential psk over arbitrary rician fading channels with multiple cochannel interferers this paper discusses the performance of communication systems using binary coherent and differential phase shift keyed psk modulation in correlated rician fading channels with diversity reception the presence of multiple rician faded cochannel users which may have arbitrary and nonidentical parameters is modeled exactly exact bit error probability bep expressions are derived via the moment generating functions mgfs of the relevant decision statistics which are obtained through coherent detection with maximum ratio combining for coherent psk modulation and differential detection with equal gain combining egc for differential modulation evaluating the exact expressions requires a complexity that is exponential in the number of interferers to avoid this potentially time consuming operation we derive two low complexity approximate methods each for coherent and differential modulation formats which are more accurate than the traditional gaussian approximation approach two new and interesting results of this analysis are 1 unlike in the case of rayleigh fading channels increasing correlation between diversity branches may lead to better performance in rician fading channels and 2 the phase distribution of the line of sight or static fading components of the desired user has a significant influence on the bep performance in correlated diversity channels

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

bit error probability for coherent m ary psk systems a simple technique for evaluating the bit error probability of coherent m ary phase shift keying psk with any bit mapping is proposed closed form expressions are given in terms of error functions for half and quadrant plane probabilities in the decision space avoiding the numerical evaluation of complicated integrals that occurs in the direct method bit error probability expressions for m ary psk with gray natural binary and folded binary bit mappings are derived

the foster reactance theorem for antennas and radiation q the calculation of antenna q has been an interesting and a controversial topic for years we first give a rigorous study of antenna q by introducing a complete description of the complex power balance relation for an antenna system using the complex poynting theorem we have shown that the antenna is essentially equivalent to a one port lossy network the foster reactance theorem is usually stated for a lossless network the main purpose of this paper is to determine whether the foster reactance theorem holds for antennas by making use of a complex frequency domain version of the poynting theorem we have shown that the foster reactance theorem is valid for an antenna finally the foster reactance theorem for the antenna has been applied to demonstrate the widely held assumption q spl ap 1 b provided q spl gt 1 where b stands for the fractional bandwidth of an arbitrary antenna

efficient computation of erfc x for large arguments a new infinite series representation for the error function is developed it is especially suitable for computing erfc x for large x for instance for any x spl ges 4 the error function can be evaluated with a relative error less than 10 sup 10 by using only eight terms similarly the error function can be evaluated with a relative error less than 8 spl times 10 sup 7 for any x spl ges 2 using just six terms an analytical bound is derived to show that the total error due to series truncation and undersampling rapidly decreases as x increases comparisons with two other series are provided

average of product of two gaussian q functions and its application to performance analysis in nakagami fading the average of the product of two gaussian q functions having arguments as different scaled versions of the same nakagami distributed fading gain magnitude is derived in closed form both the cases when 1 the fading parameter is an integer and 2 the fading parameter is an odd multiple of one half are considered the results are applied to evaluating in closed form a the symbol error probability sep of rectangular quadrature amplitude modulation with maximal ratio combining in independent nakagami fading and b the outage probability of a two user synchronous code division multiple access system having signal to noise ratio snr imbalance among users in nakagami fading it is found in application a that with increase in the degree of fading the robustness to decision distance imbalance between in phase and quadrature signals increases in addition there exists an optimum decision distance ratio at which the sep has a minimum in application b we find that the outage probability increases sharply with snr imbalance factor at low snr imbalance and tends to reach saturation as the imbalance increases

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 fast algorithm for learning a ranking function from large scale data sets we consider the problem of learning a ranking function that maximizes a generalization of the wilcoxon mann whitney statistic on the training data relying on an e accurate approximation for the error function we reduce the computational complexity of each iteration of a conjugate gradient algorithm for learning ranking functions from o m2 to o m where m is the number of training samples experiments on public benchmarks for ordinal regression and collaborative filtering indicate that the proposed algorithm is as accurate as the best available methods in terms of ranking accuracy when the algorithms are trained on the same data however since it is several orders of magnitude faster than the current state of the art approaches it is able to leverage much larger training data sets

versatile accurate and analytically tractable approximation for the gaussian q function the existing approximations for the gaussian q function have been developed bearing in mind applications that require high estimation accuracies e g derivation of the error probability for digital modulation schemes unfortunately the associated mathematical expressions are too complex to be easily employed in many other analytical studies even if they do not require such a high accuracy this letter proposes a simple yet accurate mathematical approximation to the gaussian q function when compared to other existing approximations the proposed model provides an adequate balance between accuracy and analytical tractability its simplicity enables its application over a wider range of analytical studies at reasonable accuracy levels as an illustrative example the proposed approximation is employed to obtain a new and simple closed form expression for the probability of detection of an energy detector under rayleigh fading channels

analytical results for size topology correlations in 2d disk and cellular packings random tilings or packings in the plane are characterized by a size distribution of individual elements domains and by the statistics of neighbor relations between the domains most systems occurring in nature or technology have a unimodal distribution of both areas and number of neighbors empirically strong correlations between these distributions have been observed and formulated as universal laws using only the local correlation free granocentric model approach with no free parameters we construct accurate analytical descriptions for disk crystallization size topology correlations and lemaitre s law

very simple tight bounds on the q function we present new lower and upper bounds on the gaussian q function unified in a single and simple algebraic expression which contains only two exponential terms with a constant and a rational coefficient respectively lower and upper bounding properties are obtained from such unified expression by selecting the coefficients accordingly despite the remarkable simplicity the bounds are found to be as tight as multi term alternatives obtained e g from the exponential 2 and jensen cotes 3 families of bounds a corollary result is that the n th integer power of q x can also be tightly bounded both below and above with only n 1 algebraic terms in addition to offering remarkable accuracy and mathematical tractability combined the new bounds are very consistent in which both lower and upper counterparts are similarly tight over the entire domain

probability density function of reliability metrics in bicm with arbitrary modulation closed form through algorithmic approach in the popular bit interleaved coded modulation bicm the output of the channel encoder and the input of the modulator are separated by a bit level interleaver from the decoder s point of view the modulator the transmission channel and the demodulator calculating bits reliability metrics become a memoryless bicm channel with binary inputs and real outputs in unfaded channels the bicm channel s outputs reliability metrics are known to be gaussian for binary or quaternary phase shift keying but their probability density function pdf is not known for higher order modulation we fill this gap by presenting an algorithmic method to calculate closed form expressions for the pdf of reliability metrics in bicm with arbitrary modulation and bits to symbol mapping when the so called max log approximation is applied such probabilistic description of bicm channel is useful to analyze from an information theoretic point of view any bicm constellation mapping design

jensen cotes upper and lower bounds on the gaussian q function and related functions we present new families of lower and upper bounds on q functions first we consider the craig form of the gaussian q function q x and shown that its integrand phi thetas x can be partitioned into a pair of complementary convex and concave segments this property is then exploited in conjunction with the jensen inequality and the newton cotes quadrature rule to produce a complete family of upper and lower bounds on q x which can be made arbitrarily tight by finer segmentation the basic idea is then utilized to derive families of upper and lower bounds also for the squared gaussian q function q2 x the 2d joint gaussian q function q x y p and the generalized marcum q function qm x y the bounds are shown to be tighter than alternatives found in the literature and in some cases the lower bounds provided find no equivalent in current literature the generality of the principle is the elegant point of the method and the resulting jensen cotes bounds are easy to implement and evaluate since only elementary transcendental functions are involved as an example of application to the analysis of communication systems we consider the bit error rates ber s of decode and forward df cooperative relaying schemes with coherent and differential phase shift keying psk modulations which have been shown to have an intricate dependence on the gaussian q function complicated by crossproducts irrational functional arguments and multiple numerical integrations in that example the bounds substantially reduce the complexity required to evaluate the expressions retaining tightness despite multiple numerical integrations with infinite limits

the nonlinear programming method of wilson han and powell with an augmented lagrangian type line search function the paper represents an outcome of an extensive comparative study of nonlinear optimization algorithms this study indicates that quadratic approximation methods which are characterized by solving a sequence of quadratic subproblems recursively belong to the most efficient and reliable nonlinear programming algorithms available at present the purpose of this paper is to analyse the theoretical convergence properties and to investigate the numerical performance in more detail in part 1 the exactl 1 penalty function of han and powell is replaced by a differentiable augmented lagrange function for the line search computation to the able to prove the global convergence and to show that the steplength one is chosen in the neighbourhood of a solution in part 2 the quadratic subproblem is exchanged by a linear least squares problem to improve the efficiency and to test the dependence of the performance from different solution methods for the quadratic or least squares subproblems

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 stabilization procedure by line search computation for first order approximation strategies in structural optimization the paper is concerned with first order approximation methods to solve non linear optimization problems as they arise in structural optimization a modification of the original method of moving asymptotes mma is presented to prevent oscillation or divergence by incorporating a line search into the global iteration algorithm in this line search a merit function of augmented lagrangian type is decreased by using a backtracking strategy a proof is presented to show the descent property of the proposed merit function for mma numerical examples demonstrate how the new technique stabilizes the iteration process

the method of moving asymptotes a new method for structural optimization a new method for non linear programming in general and structural optimization in particular is presented in each step of the iterative process a strictly convex approximating subproblem is generated and solved the generation of these subproblems is controlled by so called moving asymptotes which may both stabilize and speed up the convergence of the general process

sep performance of coherent mpsk over fading channels in the presence of phase quadrature error and i q gain mismatch this letter presents a joint approach to the symbol error probability sep of coherent m ary phase shift keying in a situation where the phase error quadrature error and in phase quadrature i q gain mismatch problems take place all concurrently over an additive white gaussian noise and arbitrary fading channel a set of equations that characterizes the conditional sep on an instantaneous fading signal to noise ratio is derived in the form of the craig representation

evaluation of the exact union bound for trellis coded modulations over fading channels an analytical technique is presented for computing the exact union bound on the average bit error probability of trellis coded modulation schemes over rayleigh rician or shadowed rician fading channels to this end an integral expression is derived for the pairwise error event probability pep existing bounds can be obtained as special cases of this expression it turns out that a gauss chebyshev quadrature rule offers excellent accuracy for this integral by extension the exact union bound i e the weighted sum of an exact peps of a code can readily be evaluated this method has the same complexity as the union chernoff bound and a few examples are given to show its application

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

tight analytical and asymptotic upper bound for the ber and fer of linear codes over exponentially correlated generalized fading channels in this paper the upper bound and asymptotical approximation for the bit error rate ber as well as for the frame error rate of linear block codes under maximum likelihood decoding operating over exponentially correlated ec generalized fading channels are proposed particularly our analysis takes the convolutional codes as an example and three different fading scenarios are considered namely rice nakagami m and weibull fading such scenarios have a common property that is spherically invariant random process sirp our analysis relies on the derivation of new lower bounds per each eigenvalue since the ber as well as the fer expressions are written in terms of the pairwise error probability which by its turn depends on the eigenvalues of the channel covariance matrix based on that the upper bounds and asymptotic expressions of the considered metrics subject to the three above fading models are derived which show to be tighter than the previous results published elsewhere in the literature especially for the high signal to noise ratio regions

dual diversity over correlated log normal fading channels a great deal of attention has been devoted in the literature to studying the bit error rate ber performance of diversity combining systems in the presence of rayleigh rice and nagakami m fading by comparison the literature is relatively sparse in comparable analyses over log normal channels which typically characterize shadowing from indoor obstacles and moving human bodies one reason for this disparity stems from the difficulty in evaluating the exact average ber when log normal variates are involved using for example the moment generating function mgf approach due to the inability of expressing the mgf itself in a simple closed form since it is possible to evaluate the marginal and joint statistical moments as well as the cumulative distribution function cdf associated with a log normal distribution in closed form we rather focus here on other performance measures namely average combined output signal to noise ratio amount of fading and outage probability the first two performance measures depend only on the moments whereas the outage probability depends solely on the cdf closed form expressions in terms of known functions single integral representations or upper and lower bounds are obtained for these measures corresponding to maximal ratio combining selection combining and switch and stay combining schemes allowing for the possibility of correlation between the two branches numerical evaluations of these expressions illustrating the performances of each individual diversity type as well as comparisons among them are also presented

chernoff type bounds for the gaussian error function we study single term exponential type bounds also known as chernoff type bounds on the gaussian error function this type of bound is analytically the simplest such that the performance metrics in most fading channel models can be expressed in a concise closed form we derive the conditions for a general single term exponential function to be an upper or lower bound on the gaussian error function we prove that there exists no tighter single term exponential upper bound beyond the chernoff bound employing a factor of one half regarding the lower bound we prove that the single term exponential lower bound of this letter outperforms previous work numerical results show that the tightness of our lower bound is comparable to that of previous work employing eight exponential terms

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

envelope and phase distribution of two correlated gaussian variables probability density functions pdf s are derived for the phase and amplitude envelope of the complex gain x jy j radic 1 where x and y are two correlated non zero mean gaussian random variables the pdf of the amplitude is derived as an infinite series but reduces to a closed form expression when the means are zero the classical rayleigh and rician pdf s turn out to be special cases of the derived pdf this pdf is used to analyze the error performance of non coherent binary frequency shift keying bfsk with in phase quadrature i q imbalance over an additive white gaussian noise awgn channel the resulting bit error rate ber expression is derived as an infinite series the analytical expressions are validated by simulation and the i q imbalance related performance degradation is quantified convergence of the pdf series and the ber series is established

the evaluation of error probabilities for intersymbol and cochannel interference an efficient series that can be used to calculate the probability of error in a binary symmetric channel with intersymbol interference and additive noise is derived the series is derived by representing the noise complementary probability distribution function by an exact or approximate fourier series bounds on the accuracy of the estimate are derived for gaussian noise examples show that only a small numerical effort may be required to compute error probabilities of interest using the series applications to both finite and infinite intersymbol interference systems are discussed a similar technique is used to derive series representations for the probability of error of additive noise channels with cochannel interference or with combined intersymbol and cochannel interferences the accuracy of the results is bounded for gaussian noise

an infinite series for the computation of the complementary probability distribution function of a sum of independent random variables and its application to the sum of rayleigh random variables the properties of the series are studied for both bounded and unbounded random variables the technique is used to find efficient series for computation of the distributions of sums of uniform random variables and sums of rayleigh random variables a useful closed form expression for the characteristic function of a rayleigh random variable is presented and an efficient method for computing a confluent hypergeometric function is given an infinite series for the probability density function of a sum of independent random variables is also derived the inversion of characteristic functions a trapezoidal rule for numerical integration and the sampling theorem in the frequency domain are related to and interpreted in terms of the results

error probability bounds for bit interleaved space time trellis coding over block fading channels in this correspondence we investigate the error probability bounds of a bit interleaved space time trellis coding bisttc scheme which concatenates bit interleaved coded modulation bicm with a space time trellis code sttc we focus on general block fading channels wherein each data packet or frame spans a number of independent fading blocks bicm applied to such channel environments can effectively exploit both time and frequency selectivity while a sttc maximizes the spacial diversity order the exact pairwise error probability pep and weight enumeration function wef of bisttc are used to evaluate the error bound due to the concatenation of an outer error correction code ecc and a sttc the overall wef of bisttc is obtained by combining the wef of the outer code with that of the sttc through an uniform interleaver the main challenge here is to compute the wef of a sttc for block fading channels with reasonable complexity we rely on constructing a composite state transition matrix based on a number of single step virtual trellises each corresponding to an independent fading block within a frame we discuss how this approach reduces storage and computational requirements in the bound analysis compared to the existing method of obtaining the state transition matrix through accumulation of single step transition matrices the derived bound is applicable to both spatially uncorrelated and correlated channels as well as to both flat and frequency selective block fading channels the bound is shown to provide a reasonably close estimate of the simulated performance based on the turbo equalizer like iterative processing of soft information between the sttc decoder and the ecc decoder

a closed form expression for the exact ber of generalized pam and qam constellations we derive an explicit closed form expression for the exact bit error rate ber computation of generalized hierarchical m ary pulse amplitude modulations over additive white gaussian noise awgn and fading channels this expression can also be used to obtain the exact ber of generalized hierarchical quadrature amplitude modulations square and rectangular for the awgn case these expressions are in the form of a weighted sum of complementary error functions and are solely dependent on the constellation size m the carrier to noise ratio and a constellation parameter which controls the relative message importance

an evaluation of the integral of the product of the error function and the normal probability density with application to the bivariate normal integral abstract this paper derives the value of the integral of the product of the error function and the normal probability density as a series of the hermite polynomial and the normalized incomplete gamma function this expression is beneficial and can be used for evaluating the bivariate normal integral as a series expansion this expansion is a good alternative to the well known tetrachoric series when the correlation coefficient is large in absolute value

joint multiuser detection of multidimensional constellations over fading channels we investigate the error performance of multidimensional constellations in the multiple access and broadcast channels more specifically we provide closed form expressions for the pairwise error probability pep of the joint maximum likelihood detection for multiuser signaling in the presence of additive white gaussian noise and rayleigh fading arbitrary numbers of users and multidimensional signal sets are assumed while the provided formula for the pep is a function of the dimension wise distances of the multidimensional constellation furthermore a useful upper bound on the average symbol error probability is also obtained through the union bound the analysis is applied to the sparse code multiple access systems the analytical results are validated successfully through simulations and show their importance in the multidimensional constellation design

on the functional relation between quality factor and fractional bandwidth the functional relation between the fractional bandwidth and the quality factor of a radiating system is investigated in this communication several widely used definitions of the quality factor are compared with two examples of rlc circuits that serve as a simplified model of a single resonant antenna tuned to its resonance it is demonstrated that for a first order system only the quality factor based on differentiation of the input impedance has unique proportionality to the fractional bandwidth whereas e g the classical definition of the quality factor i e the ratio of the stored energy to the lost energy per one cycle is not uniquely proportional to the fractional bandwidth in addition it is shown that for higher order systems the quality factor based on differentiation of the input impedance ceases to be uniquely related to the fractional bandwidth

upper bounds on the symbol error probability of mpsk with phase error using pawula f function iv this letter presents an alternative derivation of the case iv of pawula f function and an approximation for the corresponding probability density function pdf in the presence of the tikhonov distributed phase error the pdf of case iv is used to obtain new upper bounds for the conditional and average symbol error probabilities of m ary phase shift keying with phase error over additive white gaussian noise channels numerical results demonstrate the validity of the upper bounds