optimal phase control for equal gain transmission in mimo systems with scalar quantization complexity and algorithms the complexity of the optimal phase control problem in wireless mimo systems with scalar feedback quantization and equal gain transmission is studied the problem is shown to be np hard when the number of receive antennas grows linearly with the number of transmit antennas for the case where the number of receive antennas is constant the problem can be solved in polynomial time an optimal algorithm is explicitly constructed for practical purposes a low complexity algorithm based on local search is presented simulation results show that its performance is nearly optimal

discrete riemann surfaces and the ising model we define a new theory of discrete riemann surfaces and present its basic results the key idea is to consider not only a cellular decomposition of a surface but the union with its dual discrete holomorphy is defined by a straightforward discretisation of the cauchy riemann equation a lot of classical results in riemann theory have a discrete counterpart hodge star harmonicity hodge theorem weyl s lemma cauchy integral formula existence of holomorphic forms with prescribed holonomies giving a geometrical meaning to the construction on a riemann surface we define a notion of criticality on which we prove a continuous limit theorem we investigate its connection with criticality in the ising model we set up a dirac equation on a discrete universal spin structure and we prove that the existence of a dirac spinor is equivalent to criticality

probability of error for equal gain combiners over rayleigh channels some closed form solutions the probability of error of a general equal gain combiner eg in closed form is not available in the literature by formulating the problem in the framework of signal detection and evaluating the probability of error directly from the characteristic function cf of the signal at the combiner output we obtain closed form solutions for the probability of error of the eg combiner with two or three branches operating over a rayleigh fading channel

infinite series representations associated with the bivariate rician distribution and their applications analytical expressions for the evaluation of the bivariate rician cumulative distribution function cdf the covariance and the characteristic function chf are not known despite their usefulness in wireless communications systems analysis in this letter motivated by the ability of the rician model to describe fading in wireless communications we derive infinite series representations for the probability density function the cdf the covariance and the chf of two correlated rician random variables it is shown that the presented infinite series expressions converge rapidly and can be efficiently used to study several performance criteria for dual diversity receivers operating over correlated rician fading channels

conformal invariance of domino tiling let u be a multiply connected region in r 2 with smooth boundary let p be a polyomino in z 2 approximating u as 0 we show that for certain boundary conditions on p the height distribution on a random domino tiling dimer covering of p is conformally invariant in the limit as tends to 0 in the sense that the distribution of heights of boundary components or rather the difference of the heights from their mean values only depends on the conformal type of u the mean height is not strictly conformally invariant but transforms analytically under conformal mappings in a simple way the mean height and all the moments are explicitly evaluated

the dirichlet problem for orthodiagonal maps abstract we prove that the discrete harmonic function corresponding to smooth dirichlet boundary conditions on orthodiagonal maps that is plane graphs having quadrilateral faces with orthogonal diagonals converges to its continuous counterpart as the mesh size goes to 0 this provides a convergence statement for discrete holomorphic functions similar to the one obtained by chelkak and smirnov 4 for isoradial graphs we observe that by the double circle packing theorem 3 any finite simple 3 connected planar map admits an orthodiagonal representation our result improves the work of skopenkov 41 and werness 47 by dropping all regularity assumptions required in their work and providing effective bounds in particular no bound on the vertex degrees is required thus the result can be applied to models of random planar maps that with high probability admit orthodiagonal representation with mesh size tending to 0 in a companion paper 21 we show that this can be done for the discrete mating of trees random map model of duplantier gwynne miller and sheffield 15 25

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

moments based approach to the performance analysis of equal gain diversity in nakagami m fading in this letter an alternative moments based approach for the performance analysis of an l branch predetection equal gain combiner egc over independent or correlated nakagami m fading channels is presented exact closed form expressions are derived for the moments of the egc output signal to noise ratio snr while the corresponding moment generating function mgf is accurately approximated with the aid of pade spl acute approximants theory important performance criteria are studied the average output snr which is expressed in closed form both for independent and correlative fading and for arbitrary system parameters the average symbol error probability for several coherent noncoherent and multilevel modulation schemes and the outage probability which are both accurately approximated using the well known mgf approach the proposed mathematical analysis is illustrated by various numerical results and computer simulations have been performed to verify the validity and the accuracy of the theoretical approach

the boundary value problem for discrete analytic functions abstract this paper is on further development of discrete complex analysis introduced by r isaacs j ferrand r duffin and c mercat we consider a graph lying in the complex plane and having quadrilateral faces a function on the vertices is called discrete analytic if for each face the difference quotients along the two diagonals are equal we prove that the dirichlet boundary value problem for the real part of a discrete analytic function has a unique solution in the case when each face has orthogonal diagonals we prove that this solution uniformly converges to a harmonic function in the scaling limit this solves a problem of s smirnov from 2010 this was proved earlier by r courant k friedrichs h lewy and l lusternik for square lattices by d chelkak s smirnov and implicitly by p g ciarlet p a raviart for rhombic lattices in particular our result implies uniform convergence of the finite element method on delaunay triangulations this solves a problem of a bobenko from 2011 the methodology is based on energy estimates inspired by alternating current network theory

a fourier based method for approximating the joint detection probability in mimo communications we propose a numerically efficient technique to approximate the joint detection probability of a coherent multiple input multiple output mimo receiver in the presence of inter symbol interference isi and additive white gaussian noise awgn this technique approximates the probability of detection by numerically integrating the product of the characteristic function cf of the received filtered signal with the fourier transform of the multi dimension decision region naturally the accuracy of the approximation is dependent on the number of points in the numerical integration the proposed method selects the number of points to integrate over by deriving bounds on the approximation error as such a reduction of up to 1 100th of the number points can be achieved when comparing with existing single input single output siso techniques simulation results demonstrate that the proposed method is highly accurate with the calculated errors being well within the bounded approximation error in addition the results are closely matched with those obtained using the monte carlo simulations with a typical error less than 10 4 while requiring only a fraction of the computation time

conformal invariance in random cluster models i holmorphic fermions in the ising model we construct discrete holomorphic observables in the ising model at criticality and show that they have conformally covariant scaling limits as mesh of the lattice tends to zero in the sequel those observables are used to construct conformally invariant scaling limits of interfaces though ising model is often cited as a classical example of conformal invariance it seems that ours is the first paper where it is actually established

microdiversity on rician fading channels formats coherent phase shift keying cpsk and noncoherent frequency shift keying ncfsk results using both maximal ratio combining mrc and selection diversity combining sc are presented for comparison our results show that from a feasibility and practical tradeoffs point of view the performance of an eg combiner may be as good as that of a mr combiner the effects of gain unbalance between branches of the eg combiner on the probability distribution of snr and on the bit error rates are also investigated the rician fading model may be used to model both the microcellular environment and the mobile satellite fading channel hence the results of this paper may be useful in both of these areas furthermore in the development of the analysis we present an efficient method for computing the distribution of sums of rich random variables this may be useful for other problems involving rician fading the suitability of modeling a rician fading environment by a properly chosen nakagami model is examined a formula for determining the corresponding values of rician parameter k and nakagami parameter m is also assessed

deterministic linear combining receivers for random fading channels in this paper linear combining receivers with deterministic weights are considered for a communication system employing receive diversity in flat rician fading we propose two receiver structures 1 a modified maximum likelihood ml receiver in which detection is performed by maximizing the likelihood function of the combined received signal 2 a deterministic maximal ratio combining mrc receiver which uses the same structure as that of an mrc receiver but with deterministic weights the deterministic weight vector is chosen such that it minimizes the union bound on the symbol error probability methods of computing this deterministic weight vector are presented the error performance of the receivers is numerically compared with that of the square law combining receiver and the equal gain combining egc receiver which requires more complex phase estimation rather than using fixed deterministic weights numerical results show that in the case of phase shift keying the egc receiver performs better than the modified ml receiver which has the same performance as that of the deterministic mrc receiver but the performance gap decreases with increase of the rician k factor it is also seen that in the case of orthogonal frequency shift keying the modified ml and deterministic mrc receivers outperform the square law combining receiver

gaussian class multivariate weibull distributions theory and applications in fading channels ascertaining on the suitability of the weibull distribution to model fading channels a theoretical framework for a class of multivariate weibull distributions originated from gaussian random processes is introduced and analyzed novel analytical expressions for the joint probability density function pdf moment generating function mgf and cumulative distribution function cdf are derived for the bivariate distribution of this class with not necessarily identical fading parameters and average powers two specific distributions with arbitrary number of correlated variates are considered and studied with exponential and with constant correlation where their pdfs are introduced both cases assume equal average fading powers but not necessarily identical fading parameters for the multivariate weibull distribution with exponential correlation useful corresponding formulas as for the bivariate case are derived the presented theoretical results are applied to analyze the performance of several diversity receivers employed with selection equal gain and maximal ratio combining mrc techniques operating over correlated weibull fading channels for these diversity receivers several useful performance criteria such as the moments of the output signal to noise ratio snr including average output snr and amount of fading and outage probability are analytically derived moreover the average symbol error probability for several coherent and noncoherent modulation schemes is studied using the mgf approach the proposed mathematical analysis is complemented by various evaluation results showing the effects of the fading severity as well as the fading correlation on the diversity receivers performance

new exact closed form pdf of the sum of nakagami m random variables with applications an exact closed form expression is developed for the probability density function pdf of the sum of independent but not necessarily identically distributed nakagami m random variables by utilizing the newly developed pdf and the associated developments new exact expressions of the bit error probability are presented for predetection equal gain combining diversity

some notes on the fourier transform methods for error rate analysis of equal gain combining transform techniques based on moment generating functions mgfs and characteristic functions chfs have recently provided efficient analytical tools for the performance evaluation of digital communication systems over fading channels more recently the convolution theorem of the fourier transform has been employed to obtain unified expressions for the average error probabilities of equal gain combining egc diversity reception in terms of the chfs of the branches amplitude gains in this paper we prove that these expressions include redundant terms furthermore simpler analytical expressions for the average error rates of egc diversity reception can be obtained when the convolutional theorem of the sine and cosine transforms are used instead of the conventional fourier transform

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

improper signaling for symbol error rate minimization in k user interference channel the rate maximization for the k user interference channels ics has been investigated extensively in the literature however the practical problem of minimizing the error probability with given signal modulations and or data rates of the users is less studied in this paper by utilizing additional degrees of freedom from the improper signaling versus the conventional proper signaling we seek to optimize the precoding matrices for the k user single input single output siso ics to minimize pair wise error probability pep and symbol error rate ser with two proposed algorithms respectively compared with conventional proper signaling and other state of the art improper signaling designs our proposed improper signaling schemes achieve notable error rate improvement in siso ics under both the additive white gaussian noise awgn and cellular system setups with or without channel coding our study provides another viewpoint for optimizing transmissions in ics and further justifies the practical benefit of improper signaling in interference limited communication systems

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

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

unified graph based multi fluid model for gas liquid pipeline flows we present a novel model of transient multiphase flow for gas liquid mixtures in long pipelines the study develops a general flexible formulation of a one dimensional flow for complex multiphase mixtures in the presence of slip and mass exchange multi fluid and drift flux approaches are combined the multi fluid model governs the momentum balance for the fluids and drift flux correlations are used for modelling of the slip between individual components a tree like graph is introduced to describe the hierarchy of fluids and components within the mixture the numerical implementation for an arbitrary number of components is based on the extension of the semi implicit method for pressure linked equations imbalances of equations are selected as criteria for iteration convergence specific corrections are discussed including those proposed for the equilibrium gas release model

on the distribution of the sum of nakagami m random variables in this paper we investigate the classical problem of finding the probability density function pdf of the sum of nakagami m random variables exact infinite series representations are derived for the sum of three and four identically and independently distributed i i d nakagami m random variables and subsequently it is extended to the sum of general number of random variables a useful pattern emerged as a result of these extensions and a new fourier transform pair that involves parabolic cylinder function and gauss hypergeometric function is obtained bounds on the error resulting from truncation of the infinite series of pdfs are also presented these pdfs are used to analyze the performance of dual triple and quadruple branch predetection equal gain combining egc receivers over nakagami m fading environment furthermore a hypergeometric relation is derived as a result of those derivations subsequently the analysis is extended to the case of l branch egc receiver performance as well selected simulation plots are provided to compare the results with the approximate results available in the literature and to illustrate the validity of the formulation

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

performance of dual diversity predetection egc in correlated rayleigh fading with unequal branch snrs the bit error probability bep for coherent detection of binary signals with dual diversity predetection equal gain combining is derived using the beaulieu 1991 series in particular we consider a correlated rayleigh fading channel with unequal branch signal to noise ratios the bep expression is in terms of the power correlation coefficient of the branches is easy to compute and depicts clearly the effect of correlated fading on the error performance

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

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

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

performance of l independent and dual correlated selection combiners in hoyt fading channels performance of an l independent branch and a dual correlated branch selection combining sc receivers are analyzed over hoyt fading channels exact analytical expressions for the probability density function pdf moments and outage probability of the combiner output signal to noise ratio snr and average bit error rate for binary coherent and non coherent modulations are obtained for each type of sc receiver upper bounds on the truncation errors of pdf expressions containing infinite series are obtained too numerical and simulation results are plotted and the effect of l and correlation on the performance is studied and compared with available results

performance of equal gain combining with quantized phases in rayleigh fading channels in this paper we analyze the error probability of equal gain combining with quantized channel phase compensation for binary phase shift keying signalling over rayleigh fading channels the probability density and characteristic functions of the combined signal amplitude are derived and used to compute the analytic expressions for the bit error probability in dependance of the number of quantization levels l the number of diversity branches nr and the average received signal to noise ratio the analysis is utilized to outline the trade off between nr and l and to compare the performance with non coherent binary frequency shift keying and differential binary phase shift keying schemes under diversity reception

rhombic embeddings of planar quad graphs given a finite or infinite planar graph all of whose faces have degree 4 we study embeddings in the plane in which all edges have length 1 that is in which every face is a rhombus we give a necessary and sucient condition for the existence of such an embedding as well as a description of the set of all such embeddings r etant donne un graphe planaire fini ou infini dont toutes les faces sont de degre 4 onetudie ses plongements dans le plan dont toutes les aretes sont de longueur 1 c estdire dont toutes les faces sont des losanges on donne une condition necessaire et susante pour l existence d un tel plongement et on decrit l ensemble de ces plongements

uniform spanning forests we study uniform spanning forest measures on infinite graphs which are weak limits of uniform spanning tree measures from finite subgraphs these limits can be taken with free fsf or wired wsf boundary conditions pemantle proved that the free and wired spanning forests coincide in z d and that they give a single tree iff d 4 in the present work we extend pemantle s alternative to general graphs and exhibit further connections of uniform spanning forests to random walks potential theory invariant percolation and amenability the uniform spanning forest model is related to random cluster models in statistical physics but because of the preceding connections its analysis can be carried further among our results are the following the fsf and wsf in a graph g coincide iff all harmonic dirichlet functions on g are constant the tail fields of the wsf and the fsf are trivial on any graph on any cayley graph that is not a finite extension of z all component trees of the wsf have one end this is new in z d for d 5 on any tree as well as on any graph with spectral radius less than 1 a s all components of the wsf are recurrent the basic topology of the free and the wired uniform spanning forest measures on lattices in hyperbolic space h d is analyzed a cayley graph is amenable iff for all e 0 the union of the wsf and bernoulli percolation with parameter e is connected harmonic measure from infinity is shown to exist on any recurrent proper planar graph with finite codegrees we also present numerous open problems and conjectures

performance analysis of triple selection diversity over exponentially correlated nakagami m fading channels an approach to the performance analysis of a triple selection diversity system over exponentially correlated nakagami m fading channels is presented closed form expressions of converged sums for both outage and average error probabilities are derived numerical results are presented to point out the effect of the fading correlation the fading severity as well as the improvement achieved by the triple selection combining compared with the corresponding dual diversity case

analysis of equal gain diversity on nakagami fading channels an infinite series for the complementary probability distribution function cdf of the signal to noise ratio snr at the output of l branch equal gain eg diversity combiners in nakagami 1960 fading channels is derived the bit error rate for a matched filter receiver is analyzed for the l branch eg combiner and different fading parameters both coherent phase shift keying cpsk and differential coherent phase shift keying dcpsk are considered the effects of gain unbalance between branches on the probability distribution of the snr and on the bit error rates are investigated bit error rate results are also obtained for coherent and noncoherent reception of frequency shift keying fsk the effects of gain unbalances on fsk modulations are also investigated bit error rates for eg combining on rayleigh fading channels are obtained for l 2 these results are presented as a special case of the more generalized nakagami fading model

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

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

probability of error calculation of ofdm systems with frequency offset orthogonal frequency division multiplexing ofdm is sensitive to the carrier frequency offset cfo which destroys orthogonality and causes intercarrier interference ici previously two methods were available for the analysis of the resultant degradation in performance firstly the statistical average of the ici could be used as a performance measure secondly the bit error rate ber caused by cfo could be approximated by assuming the ici to be gaussian however a more precise analysis of the performance i e ber or ser degradation is desirable in this letter we propose a precise numerical technique for calculating the effect of the cfo on the ber or symbol error in an ofdm system the subcarriers can be modulated with binary phase shift keying bpsk quaternary phase shift keying qpsk or 16 ary quadrature amplitude modulation 16 qam used in many ofdm applications the bpsk case is solved using a series due to beaulieu 1990 for the qpsk and 16 qam cases we use an infinite series expression for the error function in order to express the average probability of error in terms of the two dimensional characteristic function of the ici

infinite series representations of the trivariate and quadrivariate rayleigh distribution and their applications few theoretical results are known about the joint distribution of three or more arbitrarily correlated rayleigh random variables rvs consequently theoretical performance results are unknown for three and four branch equal gain combining egc selection combining sc and generalized sc gsc in correlated rayleigh fading this paper redresses this gap by deriving new infinite series representations for the joint probability density function pdf and the joint cumulative distribution function cdf of three and four correlated rayleigh rvs bounds on the error resulting from truncating the infinite series are derived a classical approach due to miller is used to derive our results unfortunately miller s approach cannot be extended to more than four variates and in fact the quadrivariate case considered in this paper appears to be the most general result possible for brevity we treat only a limited number of applications in this paper the new pdf and cdf expressions are used to derive the outage probability of three branch sc the moments of the egc output signal to noise ratio snr and the moment generating function of the gsc 2 3 output snr in arbitrarily correlated rayleigh fading a novel application of bonferroni s inequalities allows new outage bounds for multibranch sc in arbitrarily correlated rayleigh channels

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

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

further results on the beaulieu series a frequent problem in digital communications is the computation of the probability density function pdf and cumulative distribution function cdf given the characteristic function chf of a random variable rv this problem arises in signal detection equalizer performance equal gain diversity combining intersymbol interference and elsewhere often it is impossible to analytically invert the chf to get the pdf and cdf in closed form beaulieu 1990 1991 has derived an infinite series for the cdf of a sum of rvs that has been widely used we rederive his series using the gil pelaez 1951 inversion formula and the poisson sum formula this derivation has several advantages including both the bridging of the well known sampling theorem with beaulieu s series and yielding a simple expression for calculating the truncation error term it is also shown that the pdf and cdf can be computed directly using a discrete fourier transform

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

universality in the 2d ising model and conformal invariance of fermionic observables it is widely believed that the celebrated 2d ising model at criticality has a universal and conformally invariant scaling limit which is used in deriving many of its properties however no mathematical proof has ever been given and even physics arguments support a priori weaker mobius invariance we introduce discrete holomorphic fermions for the 2d ising model at criticality on a large family of planar graphs we show that on bounded domains with appropriate boundary conditions those have universal and conformally invariant scaling limits thus proving the universality and conformal invariance conjectures

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

the bivariate generalized κ κ g distribution and its application to diversity receivers the correlated bivariate generalized k kg distribution with not necessarily identical shaping and scaling parameters is introduced and studied this composite distribution is convenient for modeling multipath shadowing correlated fading environments when the correlations between the signal envelopes and their powers are different generic infinite series expressions are derived for the probability density function pdf the cumulative distribution function cdf and the joint moments assuming identical shaping parameters simpler expressions for the pdf cdf and the characteristic function cf are provided while the joint moments are derived in closed form furthermore the pdfs of the product and ratio of two correlated kg random variables are obtained capitalizing on these theoretical expressions for the statistical characteristics of the correlated kg distribution the performance analysis of various diversity reception techniques such as maximal ratio combining mrc equal gain combining egc and selection diversity sd over bivariate kg fading channels is presented for the sd the outage probability is studied while for the mrc and egc the average bit error probability is obtained the proposed analysis is accompanied by numerical results clearly demonstrating the usefulness of the theoretical approach as well as the appropriateness of the kg distribution to model multipath shadowing fading channels

the laplacian and dirac operators on critical planar graphs on a periodic planar graph whose edge weights satisfy a certain simple geometric condition the discrete laplacian and dirac operators have the property that their determinants and inverses only depend on the local geometry of the graph we obtain explicit expressions for the logarithms of the normalized determinants as well as the inverses of these operators we relate the logarithm of the determinants to the volume plus mean curvature of an associated hyperbolic ideal polyhedron in the associated dimer and spanning tree models for which the determinants of the dirac operator and the laplacian respectively play the role of the partition function this allows us to compute the entropy and correlations in terms of the local geometry in addition we define a continuous family of special discrete holomorphic functions which via convolutions gives a general process for constructing discrete holomorphic functions and discrete harmonic functions on critical planar graphs

computing the distribution of sums of random sine waves and of rayleigh distributed random variables by saddle point integration the method of saddle point integration is applied to calculating the cumulative distribution of sums of independent random variables that either have a rayleigh distribution or are sine waves with independently random phases in the presence of gaussian random noise

discrete complex analysis on isoradial graphs abstract we study discrete complex analysis and potential theory on a large family of planar graphs the so called isoradial ones along with discrete analogues of several classical results we prove uniform convergence of discrete harmonic measures green s functions and poisson kernels to their continuous counterparts among other applications the results can be used to establish universality of the critical ising and other lattice models

an approximate linearized riemann solver for a two fluid model an approximate linearized riemann solver is presented for the numerical simulation of two phase flows this new solver is based on a linearization of nonconservative products and uses an extension of roe s approximate riemann solver the scheme is applied to shock tube problem and to a standard test for two fluid codes

performance analysis of predetection egc in exponentially correlated nakagami m fading channel using a gil palaez lemma based approach we derive a general expression for the bit error rate of a predetection equal gain combining receiver for coherent binary phase shift keying modulation in exponentially correlated nakagami m fading channel for an arbitrary number of branches the obtained expressions are different for even and odd numbers of branches numerical results have been corroborated with simulations

asymptotic performance of energy detector in fading and diversity reception missed detection probability expressions for energy detectors often involve infinite series and do not provide quick insights into the effects of operating conditions to overcome these limitations we develop novel asymptotic analyses by proposing an approximate probability density function pdf of a random variable beta which in general can characterize fading channels in diverse operating conditions the coefficients of the proposed approximate pdf of beta are obtained by matching the coefficients of the approximate pdf s series expansion or coefficients of the approximate pdf s moment generating function mgf with those of the exact pdf or mgf of beta by using the proposed approximation a unified closed form asymptotic missed detection probability is derived its usefulness is then demonstrated for fading channels without and with antenna diversity for cooperative detection and in co channel interference for each case the sensing gain which reveals the effect of the operating conditions on the detection performance is determined explicitly furthermore the asymptotic complementary area under the receiver operating characteristic curve an alternative performance metric is derived and found to reveal the sensing gain numerical results verify the accuracy of our derived asymptotic expressions over a wider signal to noise ratio snr range compared to the existing asymptotic solution which is accurate only for high snrs

mathematical structure of the black oil model for petroleum reservoir simulation this model incorporates compressibility and general mass transfer between phases it consists of the conditions of thermodynamic equilibrium an equation of state for the volume balance between the fluidand the rock void darcy s law for the volumetric flow rates and component conservation equations these relations are manipulated to form a pressure equation and a modified system of component conservation equations it is shown that the pressure equation is parabolic and that in the absence of diffusive forces such as capillary pressure and mixing the component conservation equations are hyperbolic subject to technical conditions on the relative permeabilities this sequential formulation of the flow equations forms types of wave structures that occur for the system

effects of fading and partial band noise jamming on a fast fh bfsk acquisition receiver with noise normalization combination we present the performance analysis of a fast frequency hopped fh binary orthogonal frequency shift keying acquisition receiver for communication against adverse environments the receiver employs noncoherent noise normalized matched filtered mf correlation detection for rapid acquisition in the search mode our analysis includes four types of communication environments namely additive white gaussian noise awgn channel awgn channel with partial band noise jamming fading channels and fading channels with partial band noise jamming the considered fading channels include nakagami m rician and rayleigh amplitude models based on beaulieu s see ibid vol 38 no 9 p 1463 1990 convergent series approach efficient analytical formulas are developed for performance evaluation example performance results for various environments are presented in terms of two acquisition probabilities namely the detection probability and the false alarm probability of the noise normalized mf detector it is analytically shown that with a short mf correlation length and with a sufficiently large ratio of signal power to noise power the fast fh diversity combining yields noticeable performance improvement for environments with strong fading when the mf correlation is lengthened this improvement tends to fade away and the diversity combining results in performance loss

ber performance of dual predetection egc in correlative nakagami m fading in this letter an approach to the evaluation of the error performance in dual predetection equal gain combining egc systems over correlated nakagami m fading channels is presented deriving an infinite series representation for the characteristic function of the sum of two correlated nakagami m variables a closed form formula is extracted for binary phase shift keying and coherent binary frequency shift keying while several other modulation schemes are studied capitalizing on a parsevals s theorem based approach previously published numerical results and simulations are also presented to illustrate the proposed mathematical analysis and to point out the effect of the input signal to noise ratio unbalancing the fading severity and the fading correlation on the system s error performance

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