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

exactly solvable potentials and the concept of shape invariance the author analyses the relationship between shape invariance and exactly solvable potentials using earlier results he shows that all actually known shape invariant potentials with a single parameter can be recovered quite simply extension to the case of shape invariant potentials with two parameters as well as to non shape invariant but exactly solvable potentials are also possible

on the bivariate nakagami m cumulative distribution function closed form expression and applications in this paper we derive exact closed form expressions for the bivariate nakagami m cumulative distribution function cdf with positive integer fading severity index m in terms of a class of hypergeometric functions particularly we show that the bivariate nakagami m cdf can be expressed as a finite sum of elementary functions and bivariate confluent hypergeometric 3 functions direct applications which arise from the proposed closed form expression are the outage probability op analysis of a dual branch selection combiner in correlated nakagami m fading or the calculation of the level crossing rate lcr and average fade duration afd of a sampled nakagami m fading envelope

algebraic shape invariant potentials in two steps the simplified algebraic structure of the shape invariance condition in two steps is developed by imposing an extra relation on the two superpotentials of the corresponding two step potentials this simplified version of potential algebra is found to be similar to that of the shape invariance condition in one step the solvable potentials of shape invariance in two steps with a translation change of parameters a1 a0 are shown to possess such a simplified version of potential algebra the condition under which the potential algebra of shape invariance in more than two steps becomes simplified is also discussed

on multivariate rayleigh and exponential distributions in this paper expressions for multivariate rayleigh and exponential probability density functions pdfs generated from correlated gaussian random variables are presented we first obtain a general integral form of the pdfs and then study the case when the complex gaussian generating vector is circular we consider two specific circular cases the exchangeable case when the variates are evenly correlated and the exponentially correlated case expressions for the multivariate pdf in these cases are obtained in integral form as well as in the form of a series of products of univariate pdfs we also derive a general expression for the multivariate exponential characteristic function cf in terms of determinants in the exchangeable and exponentially correlated cases cf expressions are obtained in the form of a series of products of univariate gamma cfs the cf of the sum of exponential variates in these cases is obtained in closed form finally the bivariate case is presented mentioning its main features while the integral forms of the multivariate pdfs provide a general analytical framework the series and determinant expressions for the exponential cfs and the series expressions for the pdfs can serve as a useful tool in the performance analysis of digital modulation over correlated rayleigh fading channels using diversity combining

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

a two level atom coupled to a two dimensional supersymmetric and shape invariant system models a class of bound state problems which represents the coupling of a two level atom with a two dimensional supersymmetric system involving two shape invariant potentials is introduced we study two models with different coupling hamiltonians

gazeau klauder coherent states for trigonometric rosen morse potential the gazeau klauder coherent states for the trigonometric rosen morse potential are constructed it is shown that the resolution of unity temporal stability and action identity conditions are satisfied for the coherent states the mandel parameter is also calculated for the weighting distribution function corresponding to the coherent states

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

three level coupled systems and parasupersymmetric shape invariance a class of bound state problems which represents the coupling of a three level atom with a two dimensional system involving two shape invariant potentials is introduced we consider second order parasupersymmetric quantum mechanical models and using an algebraic formulation for shape invariant potential systems resolve the eigenvalue problem for these coupled systems considering two possible kinds for the coupling hamiltonian linear and nonlinear in the potential ladder operators an application is given for a couple of shape invariant potentials harmonic oscillator morse potentials

a weighted queue based model for correlated rayleigh and rician fading channels a new channel model for binary additive noise communication channel with memory called weighted queue based channel wqbc is introduced the proposed wqbc generalizes the conventional queue based channel qbc such that each queue cell has a different contribution to the noise process i e the queue cells are selected with different probabilities suitably selecting the modeling function the generalization introduced by the wqbc does not increase the number of modelling parameters required compared to the qbc the statistical and information theoretical properties of the new model are derived the wqbc and the qbc are compared in terms of capacity and the accuracy in modeling a family of hard decision frequency shift keying demodulated correlated rayleigh and rician fading channels it is observed that the wqbc requires a much smaller markovian memory than the qbc to achieve the same capacity and provides a very good approximation of the fading channels as the qbc for a wide range of channel conditions

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

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

completeness of coherent states associated with self similar potentials and ramanujan s integral extension of the beta function a decomposition of identity is given as a complex integral over the coherent states associated with a class of shape invariant self similar potentials there is a remarkable connection between these coherent states and ramanujan s integral extension of the beta function

analysis of switched diversity systems on generalized fading channels the performances of switched diversity systems operating on generalized nakagami fading channels are analyzed using a discrete time model the average bit error rate ber of binary noncoherent frequency shift keying ncfsk on slow nonselective nakagami fading channels is derived closed form expressions that can be used to determine optimum switching thresholds in a minimum error rate sense are also derived in addition the use of optimum fixed thresholds is considered it is found that a considerable amount of diversity gain can be obtained using an optimum fixed rather than adaptive switching threshold results are obtained for both independent and correlated nakagami fading branch signals the effects of fading severity and the correlation coefficient on both the ber and on the optimum switching threshold are investigated it is shown that useful diversity gain can be obtained with power correlation coefficients as high as 0 9 when the fading is strong the results for a rayleigh channel are obtained and presented as a special case of generalized fading 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

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

new series representation for the trivariate non central chi squared distribution this paper derives a new infinite series representation for the trivariate non central chi squared distribution when the underlying correlated gaussian variables have a tridiagonal form of an inverse covariance matrix the joint probability density function is derived using miller s approach and dougall s identity moreover the trivariate cumulative distribution function cdf and characteristic function chf are also derived finally the bivariate non central chi squared distribution and some known forms are shown to be special cases of the more general distribution however the derivation of non central chi squared distribution for an arbitrary covariance matrix seems intractable via miller s approach two applications of the newly derived results are provided for performance analysis of multiple input multiple output mimo systems with transmit antenna selection over a correlated rician fading environment some numerical results are also presented to verify the accuracy of the analytical expressions

linear interference cancellation in cdma based on iterative techniques for linear equation systems it has previously been shown that well known iterations for solving a set of linear equations correspond to linear interference cancellation structures here we suggest applying a block wise iteration that consists of an outer and an inner iteration the outer iteration used is the gauss seidel gs method while for the inner iteration we study direct matrix inversion the jacobi over relaxation iteration and the conjugate gradient iteration when a true inner iteration is used this approach allows for a timely derivation of the acceleration parameters required by advanced iterations the block iteration is based on a symbol level implementation which leads to the same detection delay profile for both parallel and serial structures at the expense of differences in the amount of serial processing required this is discussed in some detail and quantified for comparison the performance of the detectors is studied via computer simulations where it is found that the block approach can provide significantly faster convergence leading to improved detection delay over the simpler gs iteration the improvements are obtained at the expense of an increase in the required serial processing speed

performance of bicm sc and bicm ofdm systems with diversity reception in non gaussian noise and interference in this paper we present a general mathematical framework for performance analysis of single carrier sc and orthogonal frequency division multiplexing ofdm systems employing popular bit interleaved coded modulation bicm and multiple receive antennas the proposed analysis is applicable to bicm systems impaired by general types of fading including rayleigh ricean nakagami m nakagami q and weibull fading and general types of noise and interference with finite moments such as additive white gaussian noise awgn additive correlated gaussian noise gaussian mixture noise co channel interference narrowband interference and ultra wideband interference we present an approximate upper bound for the bit error rate ber and an accurate closed form approximation for the asymptotic ber at high signal to noise ratios for viterbi decoding with the standard euclidean distance branch metric for the standard rate 1 2 convolutional code the proposed approximate upper bound and the asymptotic approximation become tight at bers of 10 6 and 10 12 respectively however if the code is punctured to higher rates e g 2 3 or 3 4 the asymptotic approximation also becomes tight at a ber of 10 6 exploiting the asymptotic ber approximation we show that the diversity gain of bicm systems only depends on the free distance of the code the type of fading and the number of receive antennas but not on the type of noise in contrast their coding gain strongly depends on the noise moments our asymptotic analysis shows that as long as the standard euclidean distance branch metric is used for viterbi decoding bicm systems optimized for awgn are also optimum for any other type of noise and interference with finite moments

exact ber analysis of distributed alamouti s code for cooperative diversity networks we analyze the bit error rate ber performance of the distributed alamouti s code for cooperative diversity networks consisting of a source two relays and a destination node over rayleigh fading channels it is assumed that the relays adopt the amplify and forward protocol firstly assuming the existence of the direct path component from the source to the destination we derive the exact ber expression in a one integral form for m pulse amplitude modulation pam and m quadrature amplitude modulation qam constellations we also present a series expansion of a very accurate ber approximation which does not require any numerical calculation and we prove this series is convergent secondly considering the system where the direct path component does not exist we obtain the exact ber expression in a one integral form and a series expansion of the exact ber expression numerical results confirm that the two exact ber expressions in a one integral form perfectly match the simulation results and the two series expressions of ber are very accurate even with a small truncation window

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

energy detection of unknown signals in fading and diversity reception a comprehensive performance analysis of the energy detector over fading channels with single antenna reception or with antenna diversity reception is developed for the no diversity case and for the maximal ratio combining mrc diversity case with either nakagami m or rician fading expressions for the probability of detection are derived by using the moment generating function mgf method and probability density function pdf method the former which avoids some difficulties of the latter uses a contour integral representation of the marcum q function for the equal gain combining egc diversity case with nakagami m fading expressions for the probability of detection are derived for the cases l 2 3 4 and l 4 where l is the number of diversity branches for the selection combining sc diversity with nakagami m fading expressions for the probability of detection are derived for the cases l 2 and l 2 a discussion on the comparison between mgf and pdf methods is presented we also derive several series truncation error bounds that allow series termination with a finite number of terms for a given figure of accuracy these results help quantify and understand the achievable improvement in the energy detector s performance with diversity reception numerical and simulation results are also provided

non equilibrium critical behaviour on fractal lattices a simple one component surface reaction model exhibiting a critical point has been studied on deterministic fractal lattices with fractal dimension 1 df 2 results from time dependent simulations show a change in the value of the critical exponents with df two of the exponents interpolate very nicely between the values in one and two dimensions

infinite series representations of the bivariate rayleigh and nakagami m distributions despite the usefulness of the bivariate correlated nakagami m cumulative distribution function cdf in communications systems analysis an infinite series for the computation of this function is not known in this letter an infinite series representation of the bivariate cdf is derived bounds on the error resulting from truncation of the infinite series are also derived

on the multivariate nakagami m distribution with exponential correlation capitalizing on the proof of a theorem presented by l e blumenson and k s miller see ann math statist vol 34 p 903 10 1963 we propose a useful closed formula for the exponentially correlated n variate nakagami m probability density function moreover an infinite series approach for the corresponding cumulative distribution function is presented bounds on the error resulting from the truncation of the infinite series are also derived finally in order to check the accuracy of the proposed formulation numerical results are presented

approximate ser of h s mrc in nakagami fading with arbitrary branch power correlation an accurate approximation to the average symbol error rate of hybrid selection maximal ratio combining h s mrc in correlated nakagami m fading with positive integer values of m is obtained by using a green s matrix approximation this approach is valid for different m ary linear modulation schemes we illustrate our methodology using m ary phase shift keying as an example

path integrals for quantum algebras and the classical limit coherent states path integral formalism for the simplest quantum algebras q oscillator suq 2 and suq 1 1 is introduced in the classical limit canonical structure is derived with a modified symplectic and riemannian metric non constant deformation induced curvature for the phase spaces is obtained

tsallis based variational method for finding approximate wave functions abstract we introduce trial functions of a form that maximizes a tsallis information measure and use them in conjunction with the variational approach of cooper dawson and shepard cds that is based upon supersymmetry ideas

error probability of interleaved mc cdma systems with mrc receiver and correlated nakagami m fading channels the performance of an interleaved multicarrier code division multiple access system with a maximal ratio combining receiver is studied with the help of the characteristic function of correlated nakagami m random variables computer simulations are used to demonstrate the accuracy of the analysis based on the analytical results with an exhaustive search of different subcarrier interleaving schemes the optimal subcarrier interleaver which provides the minimum bit error rate ber can be achieved compared to a random interleaver the optimal subcarrier interleaver offers significant performance improvement

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

extended supersymmetry for the bound states of the generalized hulthen potential hierarchy using the associated hypergeometric differential equation we analytically solve the bound states corresponding to a hierarchy of the radial potential v0 e r 1 e r c e r 1 e r 2 as a generalization of the hulth n potential then an analytic solution corresponding to a special case for which the parameter c is expected to be in terms of l l 1 is also derived meanwhile without introducing a superpotential and in the framework of supersymmetric quantum mechanics it is shown that these bound states can be calculated by two different algebraic methods based on these two approaches it is noted that the bound states realize an extended supersymmetry structure

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

mobile communication systems in the presence of fading shadowing noise and interference in this paper the effects of interference on composite fading environments where multipath fading coexists with shadowing are investigated based on some mathematical convenient expressions for the sum of squared cal k distributed random variables which are derived for the first time important statistical metrics for the signal to interference and noise ratio sinr are studied for various cases including non identical identical and fully correlated statistics furthermore our analysis is extended to multi channel receivers and in particular to selection diversity sd receivers investigating two distinct cases namely signal to noise ratio based and sinr based sd for all scenarios simplified expressions are also provided for the interference limited case where the influence of thermal noise is ignored the derived expressions are used to analyze the performance in terms of the average bit error probability abep and the outage probability op of such systems operating over composite fading environments a high snr analysis is also presented for the op and the abep giving a clear physical insight of the system s performance in terms of the diversity and coding gains the analysis is accompanied by numerical evaluated results clearly demonstrating the usefulness of the proposed theoretical framework

performance of dual selection combiners over correlated nakagami m fading with different fading parameters this letter presents infinite series expressions for the outage probability the probability density function the average error probability for binary modulations and the average signal to noise ratio of dual selection combiners over correlated fading with arbitrary fading parameters at each input of the combiner the outage probability is calculated for both thermal noise and interference limited scenarios the results obtained for the outage probabilities specified for identical fading parameters at both branches of the combiner are contrasted with the results of other studies in the literature

novel simple representations for gaussian class multivariate distributions with generalized correlation novel single integral representations for the multivariate probability density functions and cumulative distribution functions of gaussian class distributions rayleigh rician weibull nakagami m and generalized rician are derived the solutions are expressed in terms of well known functions which are available in common mathematical software the marginal random variables are not necessarily identically distributed as is the case for some past solutions a generalized correlation structure based on a special linear transformation of independent gaussian random variables is used in this study the advantage of the new representation is that only a single integral computation is needed to compute an n dimensional distribution

linear estimation of correlated data in wireless sensor networks with optimum power allocation and analog modulation in this paper we study the energy efficient distributed estimation problem for a wireless sensor network where a physical phenomena that produces correlated data is sensed by a set of spatially distributed sensor nodes and the resulting noisy observations are transmitted to a fusion center via noise corrupted channels we assume a gaussian network model where i the data samples being sensed at different sensors have a correlated gaussian distribution and the correlation matrix is known at the fusion center ii the links between the local sensors and the fusion center are subject to fading and additive white gaussian noise awgn and the fading gains are known at the fusion center and iii the central node uses the squared error distortion metric we consider two different distortion criteria i individual distortion constraints at each node and ii average mean square error distortion constraint across the network we determine the achievable power distortion regions under each distortion constraint taking the delay constraint into account we investigate the performance of an uncoded transmission strategy where the noisy observations are only scaled and transmitted to the fusion center at the fusion center two different estimators are considered i the best linear unbiased estimator blue that does not require knowledge of the correlation matrix and ii the minimum mean square error mmse estimator that exploits the correlations for each estimation method we determine the optimal power allocation that results in a minimum total transmission power while satisfying some distortion level for the estimate under both distortion criteria the numerical comparisons between the two schemes indicate that the mmse estimator requires less power to attain the same distortion provided by the blue and this performance gap becomes more dramatic as correlations between the observations increase furthermore comparisons between power distortion region achieved by the theoretically optimum system and that achieved by the uncoded system indicate that the performance gap between the two systems becomes small for low levels of correlation between the sensor observations if observations at all sensor nodes are uncorrelated the uncoded system with mmse estimator attains the theoretically optimum system performance

on first order markov modeling for the rayleigh fading channel previous models for the received signal amplitude of the flat fading channel that use first order finite state markov chains are examined the stochastic properties of a proposed first order model based on these models are examined the limitations of using an information theoretic metric which is sometimes used to justify a first order markov chain as a sufficient model for very slowly fading channels are discussed a simple method of qualitatively comparing autocorrelation functions is instead proposed the usefulness of the first order markov chain in representing the flat fading channel is examined by looking at two specific problems in wireless system applications that represent two disparate cases the first case involves analysis over a short duration of time relative to the inverse of the normalized doppler frequency while the second involves analysis over a long duration of time contrary to previous reports the results indicate that first order markov chains are not generally suitable for very slowly fading channels rather first order markov chains can be suitable for very slowly fading applications which require analysis over only a short duration of time

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

new simplest exact forms for the 3 d and 4 d multivariate rayleigh pdfs with applications to antenna array geometries determining tractable analytical expressions for the probability density functions pdfs of correlated rayleigh random variables i e the multivariate rayleigh joint pdf is a longstanding problem in wireless communications recent results have reported simpler forms for the 3 d and 4 d rayleigh joint pdfs yet the new solutions are still mathematically complex new representations for the general 3 d rayleigh and the general 4 d rayleigh fading pdfs are derived an advantage of the new representations is that only a single integral computation is needed to compute the 3 d rayleigh pdf and only double integral computation is needed for the 4 d rayleigh pdf where the integrals are proper and definite on 0 pi and 0 2 pi respectively the new expressions for the 3 d and 4 d rayleigh pdfs are used to determine several special best placements in the 2 d plane for three and four antennas closed form solutions are found for three antennas with two or three independent antenna pairs and four antennas with four or five independent antenna pairs

more on the q oscillator algebra and q orthogonal polynomials properties of certain q orthogonal polynomials are connected to the q oscillator algebra the wall and q laguerre polynomials are shown to arise as matrix elements of q exponentials of the generators in a representation of this algebra a realization is presented where the continuous q hermite polynomials form a basis of the representation space various identities are interpreted within this model in particular the connection formula between the continuous big q hermite and the continuous q hermite polynomials is thus obtained and two generating functions for these last polynomials are derived algebraically

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

algebraic nature of shape invariant and self similar potentials self similar potentials generalize the concept of shape invariance which was originally introduced to explore exactly solvable potentials in quantum mechanics in this paper it is shown that the previously introduced algebraic approach to the latter can be generalized to the former the infinite lie algebras introduced in this context are shown to be closely related to the q algebras the associated coherent states are investigated

on a one parameter family of q exponential functions we examine the properties of a family of q exponential functions which depend on an extra parameter these functions have a well defined meaning for both the 0 1 cases if only it is shown that any two members of this family with different values of the parameter are related to each other by a fourier gauss transformation

an algebraic q deformed form for shape invariant systems a quantum deformed theory applicable to all shape invariant bound state systems is introduced by defining q deformed ladder operators we show that these new ladder operators satisfy new q deformed commutation relations in this context we construct an alternative q deformed model that preserves the shape invariance property presented by the primary system q deformed generalizations of morse scarf and coulomb potentials are given as examples