deformed algebras from elliptic sl n algebras we extend to the case the results that we previously obtained on the construction of algebras from the elliptic algebra the elliptic algebra at the critical level c n has an extended center containing trace like operators t z families of poisson structures indexed by n n 1 2 integers defining q deformations of the algebra are constructed the operators t z also close an exchange algebra when for it becomes abelian when in addition p qnh where h is a non zero integer the poisson structures obtained in these classical limits contain different q deformed algebras depending on the parity of h characterizing the exchange structures at p qnh as new algebras

the drinfeld realization of the elliptic quantum group bq λ a2 2 we construct a realization of the l operator satisfying the rll relation of the face type elliptic quantum group bq a2 2 the construction is based on the elliptic analog of the drinfeld currents of uq a2 2 which forms the elliptic algebra uq p a2 2 we give a realization of the elliptic currents e z f z and k z as a tensor product of the drinfeld currents of uq a2 2 and a heisenberg algebra in the level one representation we also give a free field realization of the elliptic currents applying these results we derive a free field realization of the uq p a2 2 analog of the bq a2 2 intertwining operators the resultant operators coincide with those of the vertex operators in the dilute al model which is known to be a rsos restriction of the a2 2 face model

dynamical centers for the elliptic quantum algebra we identify generating functionals that satisfy dynamical exchange relations with the lax matrices defining the face type elliptic quantum algebra when the central charge takes the two possible values these generating functionals are constructed as quadratic trace like objects in terms of the lax matrices the obtained structures are characterized as dynamical centers i e the centrality property is deformed by dynamical shifts for these values the functionals define genuine abelian subalgebras of

an elliptic algebra and the fusion rsos model we introduce an elliptic algebra with and present its free boson representation at generic level k we show that this algebra governs a structure of the space of states in the k fusion rsos model specified by a pair of positive integers r k or equivalently a q deformation of the coset conformal field theory extending the work by lukyanov and pugai corresponding to the case k 1 we give a full set of screening operators for k 1 the algebra has two interesting degeneration limits p 0 and p 1 the former limit yields the quantum affine algebra whereas the latter yields the algebra the scaling limit of the elliptic algebra using this correspondence we also obtain the highest component of two types of vertex operators which can be regarded as q deformations of the primary fields in the coset conformal field theory

a class of partition functions associated with e_ tau eta gl_3 by izergin korepin analysis recently a class of partition functions associated with higher rank rational and trigonometric integrable models were introduced by foda and manabe we use the dynamical r matrix of the elliptic quantum group e gl3 to introduce an elliptic analog of the partition functions associated with e gl3 we investigate the partition functions of foda manabe type by developing a nested version of the elliptic izergin korepin analysis and present the explicit forms as symmetrization of multivariable elliptic functions we show that special cases are essentially the elliptic weight functions introduced in the works by rimanyi tarasov and varchenko konno and felder rimanyi and varchenko

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

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

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

on the general ber expression of one and two dimensional amplitude modulations quadrature amplitude modulation qam is an attractive technique to achieve high rate transmission without increasing the bandwidth a great deal of attention has been devoted to the study of bit error rate ber performance of qam and approximate expressions for the bit error probability of qam have been developed in many places in the literature however the exact and general ber expression of qam with an arbitrary constellation size has not been derived yet we provide an exact and general closed form expression of the ber for one dimensional and two dimensional amplitude modulations i e pam and qam under an additive white gaussian noise awgn channel when gray code bit mapping is employed the provided ber expressions offer a convenient way to evaluate the performance of pam and qam systems for various cases of practical interest moreover simple approximations can be found from our expressions which are the same as the well known approximations if only the dominant terms are considered

note on coherent states and adiabatic connections curvatures we give a possible generalization to the example in the paper of zanardi and rasetti phys lett a 264 94 1999 for this explicit forms of adiabatic connection curvature etc are given we also discuss the possibility of another generalization of their model

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

exact pairwise error probability of space time codes we describe a simple technique for the numerical calculation within any desired degree of accuracy of the pairwise error probability pep of space time codes over fading channels this method applies also to the calculation of e q spl radic spl xi for any nonnegative random variable spl xi whose moment generating function spl phi sub spl xi s e exp s spl xi is known its application to the multiple antenna independent rayleigh fading channel and to the rayleigh block fading channel is discussed and illustrated by two simple examples

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

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

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

exact symbol error probability analysis for orthogonal space time block codes two and higher dimensional constellations cases exact expressions are obtained for the symbol error probability of orthogonal space time block codes at the output of the coherent maximum likelihood decoder in the general case of arbitrary input signal constellation and code such expressions are derived for the cases of both deterministic fixed and random rayleigh ricean fading channels and both the two and higher dimensional constellations

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

the elliptic algebra and the drinfeld realization of the elliptic quantum group by using the elliptic analogue of the drinfeld currents in the elliptic algebra we construct a l operator which satisfies the rll relations characterizing the face type elliptic quantum group for this purpose we introduce a set of new currents k j v 1 leq j leq n in as in the n 2 case we find a structure of as a certain tensor product of and a heisenberg algebra in the level one representation we give a free field realization of the currents in using the coalgebra structure of and the above tensor structure we derive a free field realization of the analogue of intertwining operators the resultant operators coincide with those of the vertex operators in the a n 1 1 type face model

time optimal cnot between indirectly coupled qubits in a linear ising chain we give analytical solutions for the time optimal synthesis of entangling gates between indirectly coupled qubits 1 and 3 in a linear spin chain of three qubits subject to an ising hamiltonian interaction with a symmetric coupling j plus a local magnetic field acting on the intermediate qubit the energy available is fixed but we relax the standard assumption of instantaneous unitary operations acting on single qubits the time required for performing an entangling gate which is equivalent modulo local unitary operations to the cnot 1 3 between the indirectly coupled qubits 1 and 3 is i e faster than a previous estimate based on a similar hamiltonian and the assumption of local unitaries with zero time cost furthermore performing a simple walsh hadamard rotation in the hilbert space of qubit 3 shows that the time optimal synthesis of the cnot 1 3 which acts as the identity when the control qubit 1 is in the state 0 while if the control qubit is in the state 1 the target qubit 3 is flipped as also requires the same time t

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

a squaring method to simplify the decoding of orthogonal space time block codes we present a squaring method to simplify the decoding of orthogonal space time block codes in a wireless communication system with an arbitrary number of transmit and receive antennas using this squaring method a closed form expression of signal to noise ratio after space time decoding is also derived it gives the same decoding performance as the maximum likelihood ratio decoding while it shows much lower complexity

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

a unified approach for calculating error rates of linearly modulated signals over generalized fading channels we present a unified analytical framework to determine the exact average symbol error rate ser of linearly modulated signals over generalized fading channels the results are applicable to systems employing coherent demodulation with maximal ratio combining multichannel reception the analyses assume independent fading paths which are not necessarily identically distributed in all cases the proposed approach leads to an expression of the average ser involving a single finite range integral which can be easily computed numerically in addition as special cases ser expressions for single channel reception are obtained these expressions reduce to well known solutions give alternative often simpler expressions for previous results or provide new formulas that are either closed form expressions or simple to compute numerically

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

accurate error rate performance analysis of ofdm on frequency selective nakagami m fading channels error rates of orthogonal frequency division multiplexing ofdm signals in multipath slow fading nakagami m fading channels are considered the exact probability density function of a sum of nakagami m random phase vectors is used to derive a closed form expression for the error rates of ofdm signals the precise error rate analysis is extended to a system using multichannel reception with maximal ratio combining an asymptotic error rate analysis is also provided for a two tap channel with finite values of nakagami m fading parameters our analysis and numerical results show that the asymptotic error rate performance of an ofdm signal is similar to that of a single carrier signal transmitted over a rayleigh fading channel on the other hand our analysis further shows that a frequency selective channel that can be represented by two constant taps has similar asymptotic error rate performance to that of a one sided gaussian fading channel it is observed that depending on the number of channel taps the error rate performance does not necessarily improve with increasing nakagami m fading parameters

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

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

an mgf based performance analysis of generalized selection combining over rayleigh fading channels using the notion of the spacing between ordered exponential random variables a performance analysis of the generalized selection combining gsc diversity scheme over rayleigh fading channels is presented and compared with that of the conventional maximal ratio combining and selection combining schemes starting with the moment generating function mgf of the gsc output signal to noise ratio snr we derive closed form expressions for the average combined snr outage probability and average error probability of a wide variety of modulation schemes operating over independently identically distributed i i d diversity paths because of their simple form these expressions readily allow numerical evaluation for cases of practical interest the results are also extended to the case of non i i d diversity paths

error probability performance prediction for multichannel reception of linearly modulated coherent systems on fading channels this paper provides a framework for the analysis of error rate performance of maximal ratio combining multichannel reception of coherent linearly modulated systems over frequency selective fading channels expressions for the error probability are developed and the special cases for which closed form or acceptable efficient numerical solutions are possible are delineated a new efficient and accurate recursive method for the ricean fading main resolved path case is presented for coherent quadrature amplitude modulation constellations the effect of automatic gain control error on analysis of modulation schemes is demonstrated finally numerical examples based on the maritime high data rate channel model are provided to demonstrate the usefulness of the framework

the elliptic quantum algebra u_ q hbox scriptsize p widehat sl_n and its vertex operators we construct a realization of the elliptic quantum algebra for any given level k in terms of free boson fields and their twisted partners it can be considered as the elliptic deformation of the wakimoto realization of the quantum affine algebra we also construct a family of screening currents which commute with the currents of up to total q differences and we give explicit twisted expressions for the type i and type ii vertex operators of by twisting the known results of the type i vertex operators of the quantum affine algebra and the new results of the type ii vertex operators of we obtained in this paper

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

error probability for orthogonal space time block code diversity system using rectangular qam transmission over rayleigh fading channels in this paper theoretical symbol error probability sep expressions are derived for orthogonal space time block code ostbc diversity systems employing arbitrary rectangular m qam transmission over flat rayleigh fading channels independent fading between diversity channels is assumed channel average powers may be distinctive identical or mixed with both the rectangular m qam results are extended to square m qam m pam and binary antipodal signaling all derived expressions are in elementary forms without complicated high order transcendental functions and unevaluated integrals and hence are strictly exact and can be readily simulated by the computer moreover it is shown that mixed rayleigh fading results can be readily extended to various nakagami m fading results a four transmit antenna system with a half rate ostbc for 16 qam signaling is used to demonstrate that the theoretical result is in excellent agreement with the monte carlo simulated result from simulation curves it is shown that under the independent channel fading condition channels with identical powers have better error rate performance than channels with distinctive powers

space time block codes a maximum snr approach in tarokh et al 1999 space time block codes were introduced to obtain coded diversity for a multiple antenna communication system in this work we cast space time codes in an optimal signal to noise ratio snr framework and show that they achieve the maximum snr and in fact they correspond to a generalized maximal ratio combiner the maximum snr framework also helps in calculating the distribution of the snr and in deriving explicit expressions for bit error rates we bring out the connection between the theory of amicable orthogonal designs and space time codes based on this we give a much simpler proof to one of the main theorems on space time codes for complex symbols we present a rate 1 2 code for complex symbols which has a smaller delay than the code already known we also present another rate 3 4 code which is simpler than the one already known in the sense it does not involve additions or multiplications we also point out the connection between generalized real designs and generalized orthogonal designs

performance analysis of multibranch switched diversity systems we investigate the performance of multibranch switched diversity systems specifically we first derive generic formulas for the cumulative distribution function probability density function and moment generating function of the combined signal power for both switch and stay combining ssc and switch and examine combining sec schemes we then capitalize on these expressions to obtain closed form expressions for the outage probability and average error rate for various practical communication scenarios of interest as a byproduct of our analysis we prove that for ssc with identically distributed and uniformly correlated branches increasing the number of branches to more than two does not improve the performance but the performance can be different in the case the branches are not identically distributed and or not uniformly correlated we also show that in general the sec performance improves with additional branches the mathematical formalism is illustrated with a number of selected numerical examples

isoholonomic problems and some applications we study the problem of finding the shortest loops with a given holonomy we show that the solutions are the trajectories of particles in yang mills potentials theorem 4 or equivalently the projections of kaluza klein geodesics theorem 2 applications to quantum mechanics berry s phase sect 3 and the optimal control of deformable bodies sect 6 are touched upon

error probability performance of l branch diversity reception of mqam in rayleigh fading new exact expressions involving hypergeometric functions are derived for the symbol error rate ser of m ary quadrature amplitude modulation mqam for l branch diversity reception in rayleigh fading and additive white gaussian noise awgn the diversity combining techniques considered are maximum ratio combining mrc and selection combining sc mrc with identical channels and dissimilar channels are analyzed

error rates for rayleigh fading multichannel reception of mpsk signals this paper provides a new closed form expression for calculating the probability that an mpsk signal will lie in a particular decision region when received over n independent and identically distributed rayleigh fading channels corrupted by additive white gaussian noise this expression is applied to provide a unified method to derive the exact symbol error rate and bit error rate for mpsk signals considering n channel diversity reception the n channel diversity reception techniques considered are maximal ratio combining mrc and selection combining mrc with identical channels and dissimilar channels is considered the results for mrc can be extended to provide an approximation for the error rates of mpsk under equal gain combining

exact solutions of the isoholonomic problem and the optimal control problem in holonomic quantum computation the isoholonomic problem in a homogeneous bundle is formulated and solved exactly the problem takes a form of a boundary value problem of a variational equation the solution is applied to the optimal control problem in holonomic quantum computer we provide a prescription to construct an optimal controller for an arbitrary unitary gate and apply it to a k dimensional unitary gate which operates on an n dimensional hilbert space with n 2k our construction is applied to several important unitary gates such as the hadamard gate the cnot gate and the two qubit discrete fourier transformation gate controllers for these gates are explicitly constructed

towards a cladistics of double yangians and elliptic algebras a self contained description of algebraic structures obtained by combinations of various limit procedures applied to vertex and face sl 2 elliptic quantum affine algebras is given new double yangian structures of dynamical type are defined connections between these structures are established a number of them take the form of twist like actions these are conjectured to be evaluations of universal twists

parametrization of semi dynamical quantum reflection algebra we construct sets of structure matrices for the semi dynamical reflection algebra solving the yang baxter type consistency equations extended by the action of an automorphism of the auxiliary space these solutions are parametrized by dynamical conjugation matrices drinfel d twist representations and quantum non dynamical r matrices they yield factorized forms for the monodromy matrices

time optimal quantum evolution of mixed states we present a general formalism based on the variational principle for finding the time optimal quantum evolution of mixed states governed by a master equation when the hamiltonian and the lindblad operators are subject to certain constraints the problem may be reduced to solving first a fundamental equation which can be written down once the constraints are specified for the hamiltonian and then solving the constraints and the master equation for the lindblad and the density operators as an application of our formalism we study a simple one qubit model where the optimal lindblad operators can be simulated by a tunable coupling with an ancillary qubit

symmetric functions and wavefunctions of xxz type six vertex models and elliptic felderhof models by izergin korepin analysis we present a method to analyze the wavefunctions of six vertex models by extending the izergin korepin analysis originally developed for domain wall boundary partition functions first we apply the method to the case of the basic wavefunctions of the xxz type six vertex model by giving the izergin korepin characterization of the wavefunctions we show that these wavefunctions can be expressed as multiparameter deformations of the quantum group deformed grothendieck polynomials as a second example we show that the izergin korepin analysis is effective for analysis of the wavefunctions for a triangular boundary and present the explicit forms of the symmetric functions representing these wavefunctions as a third example we apply the method to the elliptic felderhof model which is a face type version and an elliptic extension of the trigonometric felderhof model we show that the wavefunctions can be expressed as one parameter deformations of an elliptic analog of the vandermonde determinant and elliptic symmetric functions we present a method to analyze the wavefunctions of six vertex models by extending the izergin korepin analysis originally developed for domain wall boundary partition functions first we apply the method to the case of the basic wavefunctions of the xxz type six vertex model by giving the izergin korepin characterization of the wavefunctions we show that these wavefunctions can be expressed as multiparameter deformations of the quantum group deformed grothendieck polynomials as a second example we show that the izergin korepin analysis is effective for analysis of the wavefunctions for a triangular boundary and present the explicit forms of the symmetric functions representing these wavefunctions as a third example we apply the method to the elliptic felderhof model which is a face type version and an

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

free field approach to the dilute al models we construct a free field realization of vertex operators of the dilute al models along with the felder complex for l 3 we also study an e8 structure in terms of the deformed virasoro currents

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

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

quantal phase factors accompanying adiabatic changes a quantal system in an eigenstate slowly transported round a circuit c by varying parameters r in its hamiltonian r will acquire a geometrical phase factor exp i c in addition to the familiar dynamical phase factor an explicit general formula for c is derived in terms of the spectrum and eigenstates of r over a surface spanning c if c lies near a degeneracy of c takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy as an illustration c is calculated for spinning particles in slowly changing magnetic fields although the sign reversal of spinors on rotation is a special case the effect is predicted to occur for bosons as well as fermions and a method for observing it is proposed it is shown that the aharonov bohm effect can be interpreted as a geometrical phase factor

free field construction for the abf models in regime ii the wakimoto construction for the quantum affine algebra u q widehat mathfrak s mathfrak l 2 admits a reduction to the q deformed parafermion algebras we interpret the latter theory as a free field realization of the andrews baxter forrester models in regime ii we give multi particle form factors of some local operators on the lattice and compute their scaling limit where the models are described by a massive field theory with mathbb z k symmetric minimal scattering matrices

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

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

optimal transmitter eigen beamforming and space time block coding based on channel correlations optimal transmitter designs obeying the water filling principle are well documented and widely applied when the propagation channel is deterministically known and regularly updated at the transmitter because channel state information csi may be costly or impossible to acquire in rapidly varying wireless environments we develop in this paper statistical water filling approaches for stationary random fading channels these approaches require only knowledge of the channel correlations that do not necessitate frequent updates and can be easily acquired applied to a multiple transmit antenna paradigm our optimal transmitter design turns out to be an eigen beamformer with multiple beams pointing to orthogonal directions along the eigenvectors of the channel s correlation matrix and with proper power loading across the beams the optimality pertains to minimizing a tight bound on the symbol error rate the resulting loaded eigen beamforming outperforms not only the equal power allocation across all antennas but also the conventional beamformer that transmits the available power along the strongest direction coupled with orthogonal space time block codes two dimensional 2 d eigen beamforming emerges as a more attractive choice than conventional one dimensional 1 d beamforming with uniformly better performance without rate reduction and without complexity increase

the elliptic algebra and the deformation of wn algebra after reviewing the recent results on the drinfeld realization of the face type elliptic quantum group b q sl n by the elliptic algebra u q p sl n we investigate a fusion of the vertex operators of u q p sl n the basic generating functions j z 1 j n 1 of the deformed w n algebra are derived explicitly

geometrical phases for the g 4 2 grassmannian manifold we generalize the usual abelian berry phase generated for example in a system with two nondegenerate states to the case of a system with two doubly degenerate energy eigenspaces the parametric manifold describing the space of states of the first case is formally given by the g 2 1 grassmannian manifold while for the generalized system it is given by the g 4 2 one for the latter manifold which exhibits a much richer structure than its abelian counterpart we calculate the connection components the field strength and the associated geometrical phases that evolve nontrivially both of the degenerate eigenspaces a simple atomic model is proposed for their physical implementation

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

on the vertex operators of the elliptic quantum algebra uq p sl2 k a realization of the elliptic quantum algebra uq p sl2 for any given level k is constructed in terms of three free boson fields and their accompanying twisted partners it can be viewed as the elliptic deformation of the wakimoto realization two screening currents are constructed they commute or anticommute with uq p sl2 modulo total q differences the free field realization for two types of vertex operators nominated as the type i and the type ii vertex operators is presented the twisted version of the two types of vertex operators are also obtained they all play crucial roles in calculating correlation functions

bootstrap equations and correlation functions for the heisenberg xyz antiferromagnet we present two kinds of integral solutions to the quantum knizhnik zamolodchikov equations for the 2n point correlation functions of the heisenberg xyz antiferromagnet our first integral solution can be obtained from those for the cyclic sos model by using the vertex face correspondence by the construction the sum with respect to the local height variables k0 k1 k2n of the cyclic sos model remains other than the n fold integral in the first solution in order to perform these summations we improve this to find the second integral solution of r 1 n fold integral for r 1 where r is a parameter of the xyz model furthermore we discuss the relations among our formula lashkevich pugai s formula and that of shiraishi