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

closed form expressions for the ber ser of ofdm systems with an integer time offset this paper provides a detailed mathematical analysis of the impact of integer time offsets on the performance of ofdm systems although a number of approximate expressions for the probability of error in ofdm systems with integer time offset can be found in the literature to the best of our knowledge this work is the first that provides exact expressions in particular we derive exact closed form expressions for the bit error rate ber and the symbol error rate ser of bpsk qpsk and 16 qam modulation for transmission over both awgn and rayleigh fading channels the effect of the fractional carrier frequency offset cfo is taken into consideration in the derivations this makes the derived expressions more useful in evaluating the probability of error for ofdm systems with cfo only especially in cases like 16 qam modulation for transmission over rayleigh fading channels where exact closed form expressions are not available for ofdm systems with a large number of subcarriers an approximate method for evaluating the ber ser is given finally numerical results are included to demonstrate the exactness of the derived expressions and the accuracy of the approximate method

optimal detection of digital data over the nonselective rayleigh fading channel with diversity reception based on the criterion of minimum symbol error probability an analysis is made of symbol by symbol detection of a sequence of digital data transmitted using linear suppressed carrier modulation over l independent diversity channels with awgn additive white gaussian noise and slow nonselective rayleigh fading the optimal receiver is derived but is found to be difficult to implement in practice because of its exponential growth in complexity as a function of sequence length suboptimal decision feedback approximations are then suggested which are linear and readily implementable and can be integrated as generalized differentially coherent receivers the exact bit error probabilities of these suboptimal receivers are obtained tight upper bounds on these error probabilities are also obtained which show simply how they behave as a function of signal to noise ratio and order of diversity a main conclusion of this work is that optimal data detection on a fading channel should be performed using mmse minimum mean squared error estimates of the quadrature amplitudes of the channel fading processes as a coherent reference

transverse vibrations of non homogeneous orthotropic rectangular plates of variable thickness a spline technique an analysis and numerical results are presented for free transverse vibrations of non homogeneous orthotropic rectangular plates of non uniform thickness and resting on an elastic foundation of winkler type on the basis of classical plate theory the non homogeneity of the plate material is assumed to arise due to the exponential variation in young s moduli and density along one direction following levy approach i e the two parallel edges are simply supported the fourth order differential equation governing the motion of such plates of exponentially varying thickness in one direction has been solved by using the quintic splines interpolation technique for three different combinations of clamped simply supported and free boundary conditions at the other two edges effect of the non homogeneity and elastic foundation together with other plate parameters such as orthotropy aspect ratio and thickness variation on the natural frequencies of vibration is illustrated for the first three modes of vibration normalized displacements are presented for specified plates for all the three boundary conditions

relation between bit and symbol error probabilities for fsk with ldi detection in m ary gray coded digital communication the bit error probability is usually approximated by the symbol error probability divided by the number of bits in a symbol this approximation is known to be excellent for phase shift keying with coherent detection at high signal to noise ratios and gaussian channel here it is illustrated that this approximation may also be good for m ary frequency shift keying with limiter discriminator integrator detection on gaussian rayleigh and rician channels

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

buckling of a conical thin shell with variable thickness under a dynamic loading this study considers the buckling of an elastic truncated conical shell having a meridional thickness expressed by an arbitrary function subject to a uniform external pressure which is a power function of time at first the fundamental relations and donnell type dynamic buckling equation of an elastic conical shell with variable thickness have been obtained then employing galerkin s method those equations have been reduced to a time dependent differential equation with variable coefficients finally applying the ritz type variational method the critical static and dynamic loads the corresponding wave numbers dynamic factor and critical stress impulse have been found analytically using the results thus obtained the effects of the thickness variations with a power or an exponential function the variation of the semi vertex angle and the variation of the power of time in the external pressure expression are studied through pertinent computations it is observed that these factors have appreciable effects on the critical parameters of the problem in the heading

a note on the equivalence of two heuristics to minimize total tardiness abstract over the last thirty years many researchers have studied single machine static and deterministic scheduling with the objective of minimizing total tardiness it has been established that the tardiness problem is np hard so it is unlikely that a polynomial time algorithm can be found for developing optimal solutions to this problem the modified due date rule mdd is generally considered to be an efficient heuristic that deals with the tardiness problem recently panwalkar et al have proposed the psk rule as effective in dealing with tardiness the purpose of this paper is to show that the psk rule is an implementation of the mdd rule furthermore the relationship between the mdd rule and the wi wilkeson and irwin rule is clarified

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

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

linear diversity analyses for m psk in rician fading channels symbol and bit error rates of m ary differentially encoded differentially decoded phase shift keying mdpsk and coherent m ary phase shift keying m psk over slow flat rician fading channels are derived when linear diversity combining is applied to combat degradation due to fading these closed form solutions are general enough to cover several cases of nondiversity additive white gaussian noise the nonfading mode rayleigh fading mixtures of rayleigh and rician fading the mixed mode and rician fading the results presented here can also be applied to predict the error rate performance when recent transmit diversity techniques are employed the solutions for the nonuniform fading profile are included as well error probabilities are graphically displayed for both modulation schemes

analytical matched filter bound for m qam hierarchical constellations with diversity reception in multipath rayleigh fading channels in this paper we derive matched filter bound mfb expressions for the performance of hierarchical quadrature amplitude modulations m hqam over time discrete multipath rayleigh fading environments with diversity the expressions are valid for multipath environments where different paths and antennas can be correlated since hierarchical constellations are usually employed to achieve unequal bit error protection the mfb expressions are given in terms of the individual bit error rate ber for the different bit streams although typically the mfb is obtained assuming slow time varying channels fast varying channels are also considered in this paper

free vibration analysis of orthotropic rectangular plates with variable thickness and general boundary conditions a discrete method is developed for analyzing the free vibration problem of orthotropic rectangular plates with variable thickness the green function which is obtained by transforming the differential equations into integral equations and using numerical integration is used to establish the characteristic equation of the free vibration the effects of the aspect ratios boundary conditions the variation of the thickness on the frequencies are considered by comparing the numerical results obtained by the present method with the those previously published the efficiency and accuracy of the present method are investigated the frequency parameters are obtained for the orthotropic plates with general boundary conditions and variable thickness in one or two directions the model shapes are given for some of the square plates with three kinds of thickness variations

a new dominance rule to minimize total weighted tardiness with unequal release dates abstract we present a new dominance rule by considering the time dependent orderings between each pair of jobs for the single machine total weighted tardiness problem with release dates the proposed dominance rule provides a sufficient condition for local optimality therefore if any sequence violates the dominance rule then switching the violating jobs either lowers the total weighted tardiness or leaves it unchanged we introduce an algorithm based on the dominance rule which is compared to a number of competing heuristics for a set of randomly generated problems our computational results indicate that the proposed algorithm dominates the competing algorithms in all runs therefore it can improve the upper bounding scheme in any enumerative algorithm the proposed time dependent local dominance rule is also implemented in two local search algorithms to guide these algorithms to the areas that will most likely contain the good solutions

a branch and bound algorithm for the total weighted tardiness problem this paper presents a new branch and bound algorithm for the single machine total weighted tardiness problem it obtains lower bounds using a lagrangian relaxation approach with subproblems that are total weighted completion time problems the well known subgradient optimization technique is replaced by a multiplier adjustment method that leads to an extremely fast bound calculation the method incorporates various devices for checking dynamic programming dominance in the search tree extensive computational results for problems with up to 50 jobs show the superiority of the algorithm over existing methods

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

error analysis for nonuniform signaling over rayleigh fading channels we investigate the error performance of a communication system where a nonuniform memoryless binary source is transmitted via gray mapped m ary phase shift keying or quadrature amplitude modulation over memoryless rayleigh fading channels and demodulated via optimal maximum a posteriori detection using recently derived upper and lower bounds on the probability of a general union of events which are tight and can be efficiently computed the system symbol error p sub s and bit error p sub b rates are evaluated for a wide range of channel conditions since for nonuniform signaling gray mapping is not necessarily optimal for minimizing p sub s or p sub b as was recently shown by takahara et al we also evaluate the system performance under the map obtained by takahara et al and compare it with a gray mapped system

bit error probabilities mdpsk over the nonselective rayleigh fading channel with diversity reception data transmission using m ary differential phase shift keying mdpsk over the nonselective rayleigh fading channel with diversity reception is considered while previous studies on error probability mostly assume no fading fluctuation the author considers exclusively the case in which the fading process fluctuates from one symbol interval to the next exact bit error probability results for 2 4 and 8 dpsk as well as tight upper bounds are derived some applications of the results are discussed

a recursive algorithm for the exact ber computation of generalized hierarchical qam constellations hierarchical constellations offer a different degree of protection to the transmitted messages according to their relative importance as such they find interesting application in digital video broadcasting systems as well as wireless multimedia services although a great deal of attention has been devoted in the literature to the study of the bit error rate ber performance of uniform quadrature amplitude modulation qam constellations very few results were published on the ber performance of hierarchical qam constellations we obtain exact and generic expressions in m for the ber of the generalized hierarchical m pam pulse amplitude modulation constellations over additive white gaussian noise awgn and fading channels we also show how these expressions can be extended to generalized hierarchical m qam constellations 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 because of their generic nature these new expressions readily allow numerical evaluation for various cases of practical interest

on convexity of error rates in digital communications convexity properties of error rates of a class of decoders including the maximum likelihood min distance one as a special case are studied for arbitrary constellations bit mapping and coding earlier results obtained for the additive white gaussian noise channel are extended to a wide class of noise densities including unimodal and spherically invariant noise under these broad conditions symbol and bit error rates are shown to be convex functions of the signal to noise ratio snr in the high snr regime with an explicitly determined threshold which depends only on the constellation dimensionality and minimum distance thus enabling an application of the powerful tools of convex optimization to such digital communication systems in a rigorous way it is the decreasing nature of the noise power density around the decision region boundaries that ensures the convexity of symbol error rates in the general case the known high low snr bounds of the convexity concavity regions are tightened and no further improvement is shown to be possible in general the high snr bound fits closely into the channel coding theorem all codes including capacity achieving ones whose decision regions include the hardened noise spheres from the noise sphere hardening argument in the channel coding theorem satisfy this high snr requirement and thus has convex error rates in both snr and noise power we conjecture that all capacity achieving codes have convex error rates convexity properties in signal amplitude and noise power are also investigated some applications of the results are discussed in particular it is shown that fading is convexity preserving and is never good in low dimensions under spherically invariant noise which may also include any linear diversity combining

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

the error performance of gray encoded qpsk and 8 psk schemes in a fading channel with cochannel interference closed form ber bit error rate expressions are derived for gray encoded qpsk quadrature phase shift keying and 8 psk schemes using coherent detection in a slow rayleigh fading narrowband channel with fading cochannel interference earlier work has been limited to deriving the approximate ber using the canonical stein 1961 receiver concept the symbol error rate ser for the qpsk scheme is also derived the desired signal and the cochannel interferer are both psk signals modulated by different baseband pulses with identical signaling rate

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

error rates of the maximum likelihood detector for arbitrary constellations convex concave behavior and applications motivated by a recent surge of interest in convex optimization techniques convexity concavity properties of error rates of the maximum likelihood detector operating in the awgn channel are studied and extended to frequency flat slow fading channels generic conditions are identified under which the symbol error rate ser is convex concave for arbitrary multidimensional constellations in particular the ser is convex in snr for any one and two dimensional constellation and also in higher dimensions at high snr pairwise error probability and bit error rate are shown to be convex at high snr for arbitrary constellations and bit mapping universal bounds for the ser first and second derivatives are obtained which hold for arbitrary constellations and are tight for some of them applications of the results are discussed which include optimum power allocation in spatial multiplexing systems optimum power time sharing to decrease or increase jamming problem error rate an implication for fading channels fading is never good in low dimensions and optimization of a unitary precoded ofdm system for example the error rate bounds of a unitary precoded ofdm system with qpsk modulation which reveal the best and worst precoding are extended to arbitrary constellations which may also include coding the reported results also apply to the interference channel under gaussian approximation to the bit error rate when it can be expressed or approximated as a nonnegative linear combination of individual symbol error rates and to coded systems

transverse vibrations of an orthotropic rectangular plate of linearly varying thickness and with a free edge fil bambill diana virginia consejo nacional de investigaciones cientificas y tecnicas centro cientifico tecnologico conicet bahia blanca argentina universidad nacional del sur departamento de ingenieria argentina

symbol error probability and bit error probability for optimum combining with mpsk modulation new expressions are derived for the exact symbol error probability and bit error probability for optimum combining with multiple phase shift keying the expressions are for any numbers of equal power cochannel interferers and receive branches it is assumed that the aggregate interference and noise is gaussian and that both the desired signal and interference are subject to flat rayleigh fading the new expressions have low computational complexity as they contain only a single integral form with finite limits and finite integrand

some new efficient methods to solve the n 1 ri ϵti scheduling problem abstract in this paper we prove a sufficient condition for local optimality to solve the n 1 r i t i scheduling problem which is known to be np hard we then define a new dominant subset of schedules on the basis of this condition and propose several new approximate algorithms to construct schedules belonging to this subset numerical experiments enable us to compare them with classical approximate algorithms

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

accurate evaluation for mdpsk with noncoherent diversity the error probability analysis of m ary differential phase shift keying signals with noncoherent diversity combining over general fading channels is not available in the literature except for some simple cases the difficulty lies in the philosophy which attempts to explicitly determine the phase distribution expressions of the received signal and this often leads to a mathematically intractable issue in this paper we take a novel approach by formulating the phase distribution in terms of joint moment generating functions of the real and imaginary parts of the decision variable at the receiver output we further derive fast convergent techniques for two dimensional 2 d inverse laplace transform enabling us to accurately evaluate the phase distribution the error probability formulas thus obtained involve a twofold integral which can be efficiently evaluated by using our algorithms developed on the basis of the 2 d trapezoidal summation and gauss chebyshev quadrature the new technique is very general taking into account the effects of arbitrary diversity order symbol alphabet size m and arbitrary diversity branches correlation numerical results are also presented for illustration

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

probability of bit error for mpsk modulation with diversity reception in rayleigh fading and log normal shadowing channel in an additive white gaussian noise channel subject to rayleigh fading and log normal shadowing consideration is given to diversity reception with k port macroscopic selection and l branch microscopic maximal ratio combining and analytical expressions are derived for upper and lower bounds on the bit error probabilities for bpsk qpsk 8 psk and 16 psk modulations the derived expressions can be evaluated at any location in the serving cell error probability can be calculated by averaging over all possible locations within the serving cell by evaluating these bounds numerical results for the following cases are presented without diversity reception microdiversity combining macrodiversity selection and simultaneous use of macrodiversity selection and microdiversity combining for symmetrical arrangement of macrodiversity ports against the lognormal shadowing error probability at the equidistant point gives upper bounds on the error probabilities for most of the area in the serving cell error probability at the equidistant point is a good estimate of the error probability obtained by averaging over all possible locations in the cell

minimizing total tardiness on a single machine with unequal release dates this study addresses the problem of minimizing total tardiness on a single machine with unequal release dates dominance properties established in previous literatures and herein are adopted to develop branch and bound and heuristic procedures computational experiments were conducted to evaluate the approaches the results revealed that the branch and bound algorithm is efficient in solving hard problems and easy problems that involve up to 50 and 500 jobs respectively the computational effectiveness of the heuristic is also reported

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

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

exact error rate analysis of diversity 16 qam with channel estimation error the bit error rate ber performance of multilevel quadrature amplitude modulation with pilot symbol assisted modulation channel estimation in static and rayleigh fading channels is derived both for single branch reception and maximal ratio combining diversity receiver systems the effects of noise and estimator decorrelation on the received ber are examined the high sensitivity of diversity systems to channel estimation error is investigated and quantified the influence of the pilot symbol interpolation filter windowing is also considered

degrees of freedom in adaptive modulation a unified view we examine adaptive modulation schemes for flat fading channels where the data rate transmit power and instantaneous ber are varied to maximize spectral efficiency subject to an average power and ber constraint both continuous rate and discrete rate adaptation are considered as well as average and instantaneous ber constraints we find the general form of power ber and data rate adaptation that maximizes spectral efficiency for a large class of modulation techniques and fading distributions the optimal adaptation of these parameters is to increase the power and data rate and decrease the ber as the channel quality improves surprisingly little spectral efficiency is lost when the power or rate is constrained to be constant hence the spectral efficiency of adaptive modulation is relatively insensitive to which degrees of freedom are adapted

rayleigh s optimization concept and the use of sinusoidal co ordinate functions the present note reports some numerical experiments performed on the determination of the fundamental frequency vibration of a rectangular plate with three simply supported edges while the fourth is free the optimization parameter is contained in the argument of the sinusoidal terms of a truncated fourier series

exact ber computation of generalized hierarchical psk constellations we obtain in this paper generic expressions in m for the exact bit error rate of the generalized hierarchical 2 4 spl middot spl middot spl middot m phase shift keyed constellations over additive white gaussian noise awgn and fading channels for the awgn case these expressions are in the form of a weighted sum of pawula f 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 the mathematical expressions are illustrated with some select numerical examples

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

computing and bounding the first order marcum q function a geometric approach a geometric interpretation of the first order marcum q function q a b is introduced as the probability that a complex gaussian random variable with real mean a takes on values outside of a disk co b of radius b centered at the origin o this interpretation engenders a fruitful approach for deriving new representations and tight upper and lower bounds on q a b the new representations obtained involve finite range integrals with pure exponential integrands they are shown to be simpler and more robust than their counterparts in the literature the new bounds obtained include the generic exponential bounds which involve an arbitrarily large number of exponential functions and the simple erfc bounds which involve just a few erfc functions together with exponential functions in some cases the new generic exponential bounds approach the exact value of q a b as the number of exponential terms involved increases these generic exponential bounds evaluated with only two terms and the new simple erfc bounds are much tighter than the existing exponential bounds in most cases especially when the arguments a and b are large thus in many applications requiring further analytical manipulations of q a b these new bounds can lead to some closed form results which are better than the results available so far

ber criterion and codebook construction for finite rate precoded spatial multiplexing with linear receivers precoded spatial multiplexing systems with rate limited feedback have been studied recently based on various precoder selection criteria instead of those based on indirect performance indicators we in this paper propose a new criterion directly based on the exact bit error rate ber that is applicable to systems with linear receivers and rectangular square quadrature amplitude modulation constellations the ber criterion outperforms any other alternative in terms of optimizing the ber performance for an uncoded system with linear receivers we then develop a precoder codebook construction method based on the generalized lloyd algorithm from the vector quantization literature this construction is not directly based on the ber criterion hence it is suboptimal in the ber sense however relative to those currently available our newfound codebooks improve considerably various minimum distances between any pair of codewords of the codebook finally we analyze the ber optimal precoder in the asymptotic case with infinite rate feedback that amounts to perfect channel knowledge at the transmitter the infinite rate optimal precoder based on the ber criterion is drastically different from the counterparts with other criteria and it leads to a benchmark performance for finite rate precoded spatial multiplexing systems we observe from numerical results that the ber performance of finite rate feedback with suboptimal codebooks approaches quickly the benchmark performance of infinite rate feedback this suggests that i the number of feedback bits in practical systems need not be large and ii the room for performance improvement via further codebook optimization shrinks quickly as the codebook size increases

bounds and approximations for rapid evaluation of coherent mpsk error probabilities the error probability for mpsk detection is expressed here as a sum of a familiar upper bound approximation and a correction term which is well suited for numerical integration an asymptotic expansion of the correction term is derived from which simple and extremely tight upper and lower bounds are obtained relative errors in using these bounds and approximations of them are graphed for cases of practical interest

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

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

a symbol by symbol channel estimation receiver for space time block coded systems and its performance analysis on the nonselective rayleigh fading channel we present a symbol by symbol channel estimation receiver for an orthogonal space time block coded system and derive its analytical performance on a slow nonselective rayleigh fading channel exact closed form expressions for its bit error probability bep performance for m ary phase shift keying modulations are obtained which enable us to theoretically predict the actual performance achievable under practical conditions with channel estimation error our bep expressions show explicitly the dependence of bep on the mean square error of the channel estimates which in turn depend on the channel fading model and the channel estimator used tight upper bounds are presented that show more clearly the dependence of the bep on various system parameters simulation results using various fading models are obtained to demonstrate the validity of the analysis