birational automorphism groups and the movable cone theorem for calabi yau manifolds of wehler type via universal coxeter groups thanks to the theory of coxeter groups we produce the first family of calabi yau manifolds x of arbitrary dimension n for which rm bir x is infinite and the kawamata morrison movable cone conjecture is satisfied for this family the movable cone is explicitly described it s fractal nature is related to limit sets of kleinian groups and to the apollonian gasket then we produce explicit examples of biregular automorphisms with positive entropy on some calabi yau varieties

minimum probability of error for asynchronous gaussian multiple access channels consider a gaussian multiple access channel shared by k users who transmit asynchronously independent data streams by modulating a set of assigned signal waveforms the uncoded probability of error achievable by optimum multiuser detectors is investigated it is shown that the k user maximum likelihood sequence detector consists of a bank of single user matched filters followed by a viterbi algorithm whose complexity per binary decision is o 2 k the upper bound analysis of this detector follows an approach based on the decomposition of error sequences the issues of convergence and tightness of the bounds are examined and it is shown that the minimum multiuser error probability is equivalent in the iow noise region to that of a single user system with reduced power these results show that the proposed multiuser detectors afford important performance gains over conventional single user systems in which the signal constellation carries the entire burden of complexity required to achieve a given performance level

thermodynamics dimension and the weil petersson metric in this paper we study branched coverings of metrized simplicial trees f t t which arise from polynomial maps f c c with disconnected julia sets we show that the collection of all such trees up to scale forms a contractible space ptd compactifying the moduli space of polynomials of degree d that f records the asymptotic behavior of the multipliers of f and that any meromorphic family of polynomials over can be completed by a unique tree at its central fiber in the cubic case we give a combinatorial enumeration of the trees that arise and show that pt3 is itself a tree resume dans ce travail nous etudions des revetements ramifies d arbres metriques simpliciaux f t t qui sont obtenus a partir d applications polynomiales f c c possedant un ensemble de julia non connexe nous montrons que la collection de tous ces arbres a un facteur d echelle pres forme un espace contractile ptd qui compactifier l espace des modules des polynomes de degre d nous montrons aussi que f enrigistre le comportement asymptotique des multiplicateurs de f et que tout famille meromorphe de polynomes definis sur peut etre completee par un unique arbre comme sa fibre centrale dans le cas cubique nous donnons une enumeration combinatoire des arbres ainsi obtenus et montrons que pt3 est lui meme un arbre

on using perturbation analysis to do sensitivity analysis derivatives versus differences one use of perturbation analysis is to compute the derivative of a performance measure p with respect to a parameter theta for use in iterative optimization schemes to locate local maxima by driving the derivative to zero it has been pointed out that in stochastic approximation contexts there is an advantage in using derivatives as opposed to differences another use of perturbation analysis is just to do a sensitivity analysis with respect to a parameter without relation to any optimization the advantages of using differences rather than derivatives for sensitivity analysis are identified this prompts the use of noninfinitesimal perturbation analysis or other techniques whereby perturbation information can be obtained from a single run

partial correlation effects in direct sequence spread spectrum multiple access communication systems nearly all previous analytical results on the performance of direct sequence spread spectrum multiple access ds ssma communication systems are restricted to systems in which the period p of the signature sequence is equal to the number n of chips per data symbol in many applications however it is necessary to employ signature sequences whose period p is much larger than n thus successive n chip segments of the signature sequence are used to phase code the carrier during the transmission of successive data symbols the performance of such systems depends on the partial correlation properties of the signature sequences rather than the aperiodic correlation properties as in the case when n p in this paper we consider the performance of a ds ssma system for arbitrary values of p and n as special cases of our results we delermine the effects of partial correlation in three classes of systems those for which n p those for which n and p are relatively prime and those for which n is a divisor of p we also provide two methods for the design of sequences for systems for which n is a divisor of p

an analysis of nonlinear direct sequence correlators an analysis of the performance of nonlinear correlation reception of direct sequence signals in single and multiuser channels is presented the communications channel is modeled as containing non gaussian background noise and in some cases multiple access interference as well the error probability behavior is studied asymptotically as the lengths of the spreading codes increase without bound and conditions on the spreading sequences are obtained that assure asymptotic achievement of single user performance in a multiuser system a long spreading sequence approximation to the average error probability is also derived and this result is applied to the analysis of smooth limiting correlation receivers in impulsive channels simulation results are also provided to verify the analysis average bit error probabilities are computed by monte carlo simulations for linear hard limiting and smooth limiting correlation receivers in both single and two user impulsive channels the simulation results are compared to the error rates by asymptotic approximations for the smooth limiter and also to those from previous studies on linear and hard limiting correlators

symbol to symbol performance evaluation of densely populated asynchronous ds cdma in gaussian and impulsive noise environments a fourier bessel series approach this letter considers the well established poisson impulse noise model with a random amplitude area distributed according to the spl epsiv mixture gaussian probability density function this model is used to develop fast converging truncated fourier bessel fb series expressions required to evaluate accurately the performance of a binary phase shift keying bpsk modulation scheme as part of a densely populated asynchronous direct sequence code division multiple access a ds cdma configuration the average error probability of the correlation receiver is easily and quickly obtained here even for the case of a large number of users k 100 unlike earlier attempts in this area in which the use of other analysis approaches e g closed form approach or taylor series expansion approach could not exceed the limit of k 2 and k 24 in an spl epsiv mixture impulsive and or gaussian noise environment respectively

performance of noncoherent direct sequence spread spectrum communications over specular multipath fading channels the performance of coherent direct sequence spread spectrum communications over specular multipath fading channels is investigated the average probability of error of the correlation receiver is derived for an arbitrary number of paths with deterministic or random gain coefficients the gain coefficients delays and phase angles of any two distinct paths are modeled as mutually independent random variables numerical results for several values of the system and channel parameters are presented

error probability for direct sequence spread spectrum multiple access communications part i upper and lower bounds upper and lower bounds on the average probability of error are obtained for direct sequence spread spectrum multipleaccess communications systems with additive white gaussian noise channels the bounds which are developed from convexity properties of the error probability function are valid for systems in which the maximum multiple access interference does not exceed the desired signal and the signature sequence period is equal to the duration of the data pulse the tightness of the bounds is examined for systems with a small number of simultaneously active transmitters this is accomplished by comparisons of the upper and lower bounds for several values of the system parameters the bounds are also compared with an approximation based on the signal to noise ratio and with the chernoff upper bound

spread spectrum multiple access performance of orthogonal codes linear receivers this paper analyzes a direct sequence spread spectrum multiple access ssma communication system which assigns a set of m orthogonal sequences to each user with all direct sequence ssma systems k users share a channel by phase modulating their transmissions with signature sequences however the users of our system transmit log 2 m bits of information sequence this contrasts classical ssma schemes which use a pair of antipodal sequences and transmit 1 bit sequence in this paper we assume that the channel noise is a combination of additive white gaussian noise awgn and multiple access interference we employ the optimum single user demodulator for orthogonal signals in gaussian noise the multiple user performance of this receiver is analyzed we obtain approximations for the multiuser probability of error by using a gaussian approximation for the multiple access interference we also obtain an upper bound on the exact probability by using characteristic functions our ssma system is well suited for application at the lower radio frequencies therefore a companion paper describes a realistic model for low frequency radio noise modifies the receiver to include a zero memory nonlinearity and studies the performance of the nonlinear receiver

bit error rate evaluation for spread spectrum multiple access systems a unified method for approximating and bounding the average bit error probability for spread spectrum multiple access communication systems is presented various forms of direct sequence spreadspectrum modulation are considered including binary phase shift keying quadriphase shift keying and minimum shift keying the analysis of the multiple access interference makes use of a number of moments sufficent to evaluate the error probability with a high degree of accuracy a computationally efficient algorithm for computing the moments is also given the subsequent transformation from the moments to the average bit error probability is carried out by means of gauss type numerical integration formulas it is shown that the same approach can be exploited for evaluating two classes of upper and lower bounds on the bit error rate finally some results and comparisons are reported

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

intrinsic ultracontractivity and the dirichlet laplacian we show that if d x y 0 x 1 f x y 1 where f is negative upper semicontinuous and bounded below then the semigroup associated with the dirichlet laplacian on d is intrinsically ultracontractive analogs in higher dimensions are proved we construct domains of infinite area with this property

performance bounds for ds ssma communications with complex signature sequences a unified performance analysis of direct sequence spread spectrum multiple access ds ssma communications with deterministic complex signature sequences is presented the probability density function pdf of the multiple user interference is determined using a round down and round up procedure on the pdf arbitrarily tight lower and upper bounds on the probability of bit error pbe are obtained results based on the gaussian approximation method are also presented it is shown that complex sequences can yield better pbe performance than binary sequences using complex sequences the number of signature sequences that have good auto and cross correlation properties is greatly enlarged new users employing complex or binary signature sequences can be added to existing systems with graceful performance degradation

calculating hausdorff dimension of julia sets and kleinian limit sets we present a new algorithm for efficiently computing the hausdorff dimension of sets x invariant under conformal expanding dynamical systems by locating the periodic points of period up to n we construct approximations s n which converge to dim x super exponentially fast in n this method can be used to give rigorous estimates for important examples including hyperbolic julia sets and limit sets of schottky and quasifuchsian groups

counting problems in apollonian packings an apollonian circle packing is a classical construction which is made by repeatedly inscribing circles into the triangular interstices in a descartes configuration of four mutually tangent circles remarkably if the original four circles have integer curvature all of the circles in the packing will have integer curvature making the packings of interest from a number theoretic point of view many of the natural arithmetic problems have required new and sophisticated tools to solve them the reason for this difficulty is that the study of apollonian packings reduces to the study of a subgroup of gl4 z which is thin in a sense that we describe in this article and arithmetic problems involving thin groups have only recently become approachable in broad generality in this article we report on what is currently known about apollonian packings in which all circles have integer curvature and how these results are obtained this survey is also meant to illustrate how to treat arithmetic problems related to other thin groups

optimal phases for a family of quadriphase cdma sequences signature sequences with good even even and odd or polyphase correlations are crucial for asynchronous code division multiple access cdma when the data sequence is random the even and odd or polyphase correlations are equally important however for most known signature sequences only their even correlations were analyzed it appears that determining the odd or the polyphase correlations is generally a very hard problem since the odd or the polyphase correlations depend on the phases of the signature sequences sole 1989 boztas hammons and kumar 1992 found a family of quadriphase sequences that are asymptotically optimal these sequences gain a factor spl radic 2 in terms of their maximum periodic even correlations when compared with the best possible binary phase shift keying bpsk sequences we find the optimal phases of these sequences the optimality is in the sense that at these phases the mean square values of the even odd and the polyphase correlations are minimal and achieve the welch 1974 bound equality simultaneously furthermore we show that at these phases the average user interference of these sequences is always smaller than that of the ideal random signature sequences comprehensive analytical and numerical results show that good phase sequences can offer a nonnegligible amount of gain over bad phase sequences at modest and high signal to noise ratios

interference modeling in a direct sequence spread spectrum packet radio network a technique for characterizing multiuser interference and background noise in a direct sequence spread spectrum network is introduced and packet error probabilities are calculated the multiuser interference over a packet in the network is modeled as a compound gaussian multivariate random variable for moderate to large values of the processing gain the conditional variance is dependent on the number of users and their interference powers the method works for any interference with statistics of the block interference having a spherically symmetric distribution the best performance results in terms of the expected total interference power are obtained for the case of a large number of interferers with comparable interference powers as the number of interferers approaches infinity the performance is the same as that for gaussian noise for a small number of interferers the block error probability curve is broader than that for gaussian noise for small values of snr the probability of error is smaller than that corresponding to gaussian noise and for large values of snr it is larger modifications to the basic direct sequence scheme that improve performance in the case of one strong interferer are suggested

ultracontractivity and the heat kernel for schrodinger operators and dirichlet laplacians abstract abstract connections between integral kernels of positivity preserving semigroups and suitable lp contractivity properties are established then these questions are studied for the semigroups generated by v and h the dirichlet laplacian for an open connected region as an application under a suitable hypothesis sobolev estimates are proved valid up to of the form x c 0 x h k 2 where 0 is the unique positive l2 eigenfunction of h

performance of binary and quaternary direct sequence spread spectrum multiple access systems with random signature sequences the performance of synchronous and asynchronous binary and quaternary with and without offset direct sequence spread spectrum multiple access ds ssma communication systems using random signature sequences and arbitrary chip waveforms is investigated the average probability of error at the output of the correlation receiver is evaluated using a characteristic function approach for these systems numerical results are presented that illustrate performance comparisons between systems using random and deterministic signature sequences synchronous and asynchronous systems systems with rectangular or sinewave chip waveforms and binary and quaternary systems with the same data rates and bandwidth in all cases the accuracy of the gaussian approximation is also examined

ucht based complex sequences for asynchronous cdma system the use of orthogonal spreading codes has attracted much attention due to their ability to suppress interference from other users compared with the nonorthogonal sequences in the synchronous case in this paper new sets of orthogonal sequences derived from the unified complex hadamard transforms uchts are investigated various correlation properties of the sequences are mathematically derived and analyzed it is shown that some ucht sequences provide better autocorrelation properties than orthogonal walsh hadamard sequences performance comparisons between ucht sequences gold small set of kasami and m sequences show that some ucht sequences outperform these well known spreading sequences under simulation of systems in the presence of multiple access interference and additive white gaussian noise

hausdorff dimension and conformal dynamics iii computation of dimension this paper presents an eigenvalue algorithm for accurately computing the hausdorff dimension of limit sets of kleinian groups and julia sets of rational maps the algorithm is applied to schottky groups quadratic polynomials and blaschke products yielding both numerical and theoretical results dimension graphs are presented for a the family of fuchsian groups generated by reflections in 3 symmetric geodesics b the family of polynomials f c z z 2 c c 1 1 2 and c the family of rational maps f t z z t 1 z t 0 1 we also calculate h dim 1 305688 for the apollonian gasket and h dim j f 1 3934 for douady s rabbit where f z z 2 c satisfies f 3 0 0

bit to bit error dependence in slotted ds ssma packet systems with random signature sequences a technique is developed to find an accurate approximation to the probability of data bit error and the probability of packet success in a direct sequence spread spectrum multiple access ds ssma packet radio system with random signature sequences an improved gaussian approximation to the probability of data bit error is performed packet performance is analyzed by using the theory of moment spaces to gain insight into the effect of bit to bit error dependence caused by interfering signal relative delays and phases which are assumed constant over the duration of a desired packet numerical results show that if no error control exists in the desired packet or if block error control is used when multiple access interference is high the error dependence increases the average probability of packet success beyond that predicted by models which use independent bit errors however when block error control is used and the multiple access interference is low the bit error dependencies cause a reduction in packet error performance

computationally efficient bounds for the performance of direct sequence spread spectrum multiple access communications systems in jamming environments an approach for calculating upper and lower bounds for the probability of error for asynchronous multiple access spread spectrum communication systems using deterministic codes is presented the techniques is then generalized to include multiple tone jamming the approach utilizes the cumulative distribution function of individual interference terms the computational complexity of the technique is calculated to the polynomial like results showing the multiple access performance of gold codes of lengths 31 and 127 in the presence of jamming are shown the fact that this computational technique gives upper and lower bounds is rigorously proved using the riemann stieltjes integral

optimum multiuser asymptotic efficiency the degradation in bit error rate due to the presence of multiple access interference in a white gaussian channel can be measured by the multiuser asymptotic efficiency defined as the ratio between the snr required to achieve the same uncoded bit error rate in the absence of interfering users and the actual snr in this paper the asymptotic efficiency of the optimum multiuser demodulator a bank of matched filters followed by a viterbi algorithm is investigated and compared to that of the conventional single user matched filter receiver the computation of the optimum asymptotic efficiency of any given user is equivalent to the minimization of the euclidean distance between any pair of multiuser signals which differ in at least one of the symbols of that user it is shown that the optimum multiuser efficiency of asynchronous systems is nonzero with probability 1 and therefore the optimum demodulator does not become multiple access limited in contrast to the single user receiver a class of signal constellations with moderate cross correlation requirements is shown to achieve unit optimum multiuser efficiencies and hence to be equivalent to orthogonal signal sets from the viewpoint of performance of the optimum multiuser detector

error probability for direct sequence spread spectrum multiple access communications part ii approximations approximations are obtained for the average probability of error in an asynchronous direct sequence spread spectrum multiple access communications system both binary and quaternary systems are considered and the chip waveforms are allowed to be arbitrary time limited waveforms with time duration equal to the inverse of the chip rate the approximation is based on the integration of the characteristic function of the multiple access interference the amount of computation required to evaluate this approximation grows only linearly with the product of the number of simultaneous transmitters and the number of chips per bit the accuracy of the approximation is extremely good in most cases but it can be improved if necessary by an application of a series expansion numerical results are presented for specific chip waveforms and signature sequences

error probabilities for binary direct sequence spread spectrum communications with random signature sequences binary direct sequence spread spectrum multiple access communications an additive white gaussian noise channel and a coherent correlation receiver are considered an expression for the output of the receiver is obtained for the case of random signature sequences and the corresponding characteristic function is determined the expression is used to study the density function of the multiple access interference and to determine arbitrarily tight upper and lower bounds on the average probability of error the bounds which are obtained without making a gaussian approximation are compared to results obtained using a gaussian approximation the effects of transmitter power the length of the signature sequences and the number of interfering transmitters are illustrated each transmitter is assumed to have the same power although the general approach can accommodate the case of transmitters with unequal powers

performance of ds ssma communications in impulsive channels part i linear correlation receivers the performance of digital linear correlation receivers is studied in a multiuser environment there are assumed to be two types of sources interfering with data transmission multiple access interference and additive channel noise which is attributed to impulsive noise sources in the environment the contribution of multiple access interference is examined by considering k asynchronous users transmitting simultaneously over a linear channel using the binary psk direct sequence spreadspectrum multiple access ds ssma technique alternatively the effects of the non gaussian impulsive channel in such a system are studied by modeling the samples of noise after front end filtering errorprobability performance under these conditions is compared to that for additive white gaussian noise awgn channels due to computational complexity exact analysis is limited here to systems utilizing short spreading sequences computationally simple methods are proposed for approximating the average error probability when the length of the signature sequences is large furthermore some asymptotic results are obtained for the case of infinitely long sequences in all cases performance variation is examined as the shape of the noise density varies with snr held constant the results of this analysis indicate that the presence of impulsive noise can cause significant performance degradation over that predicted from an awgn model even when the total noise power does not increase

an asymptotic analysis of band limited ds ssma communication systems a new asymptotic analysis is presented to establish whether or not commonly used techniques to approximate the performance of direct sequence spread spectrum multiple access ds ssma systems still apply when the systems are strictly band limited the results apply to any linear data modulation and spreading scheme the interference components including the interchip interference ici of a linear receiver output are shown to be asymptotically jointly gaussian random variables conditioned on the phases and delays of the interfering signals expressions for the error probabilities of band limited systems are also developed from this result

sharp constants related to the triangle inequality in lorentz spaces we study the lorentz spaces lp s r in the range 1 p s for which the standard functional f p s 0 t1 pf t s dt t 1 s is only a quasi norm we find the optimal constant in the triangle inequality for this quasi norm which leads us to consider the following decomposition norm f p s inf

all finitely generated kleinian groups of small hausdorff dimension are classical schottky groups this is the second part of our works on the hausdorff dimension of schottky groups hou in geom topol 14 473 519 2010 in this paper we prove that there exists a universal positive number lambda 0 such that up to a finite index any finitely generated non elementary kleinian group with a limit set of hausdorff dimension lambda is a classical schottky group the proof relies on our previous works in hou geom topol 14 473 519 2010 j differ geom 57 173 195 2001 which provide the foundation for the general result of this paper our results can also be considered as a converse to the well known theorem of doyle acta math 160 249 284 1988 and phillips sarnak acta math 155 173 241 1985

imaginary cones and limit roots of infinite coxeter groups let w s be an infinite coxeter system to each geometric representation of w is associated a root system while a root system lives in the positive side of the isotropic cone of its associated bilinear form an imaginary cone lives in the negative side of the isotropic cone precisely on the isotropic cone between root systems and imaginary cones lives the set e of limit points of the directions of roots in this article we study the close relations of the imaginary cone with the set e which leads to new fundamental results about the structure of geometric representations of infinite coxeter groups in particular we show that the w action on e is minimal and faithful and that e and the imaginary cone can be approximated arbitrarily well by sets of limit roots and imaginary cones of universal root subsystems of w i e root systems for coxeter groups without braid relations the free object for coxeter groups finally we discuss open questions as well as the possible relevance of our framework in other areas such as geometric group theory

dynamics of kaleidoscopic maps abstract first we introduce a certain class of piecewise affine elliptic rotation maps on t 2 called the kaleidoscopic maps and describe its importance and then we concentrate our efforts on a special case when the rotation angle of a kaleidoscopic map is n n z for the special case we answer the conjectures regarding the periodicity and the singularity structure of such kaleidoscopic dynamics in the process we prove the partial riddling of the regular orbits that gives rise to the classification of periodic sets and estimate the hausdorff dimension of the singular set finally we study the dynamics of such kaleidoscopic maps restricted within the singular set and answer conjectures concerning the chaos the local chaos and the ergodicity with respect to the normalized hausdorff measure of the singular set

related aspects of positivity in riemannian geometry pour une variete de riemann on etudie le lien entre le point 0 du l 2 spectre le plus proche de zero pour l extension de friedrich d un operateur semi defini symetrique et le taux exponentiel de transition d un operateur de markoff conservant la positivite

hausdorff dimension and conformal dynamics i strong convergence of kleinian groups this paper investigates the behavior of the hausdorff dimensions of the limit sets n and of a sequence of kleinian groups n where m h is geometrically finite we show if n strongly then a mn h 3 n is geometrically finite for all n 0 b n in the hausdorff topology and c h dim n h dim if h dim 1 on the other hand we give examples showing the dimension can vary discontinuously under strong limits when h dim 1 continuity can be recovered by requiring that accidental parabolics converge radially similar results hold for higher dimensional manifolds applications are given to quasifuchsian groups and their limits

direct sequence spread spectrum multiple access communications with random signature sequences a large deviations analysis a direct sequence spread spectrum multiple access bit error probability analysis is developed using large deviations theory let m denote the number of interfering spread spectrum signals and let n denote the signature sequence length then the large deviations limit is as n to infinity with m fixed a tight asymptotic expression for the bit error probability is proven and in addition recent large deviations results with the importance sampling monte carlo estimation technique are applied to obtain accurate and computationally efficient estimates of the bit error probability for finite values of m and n the large deviations point of view is compared also to the conventional asymptotics of central limit theory and the associated gaussian approximation the gaussian approximation is accurate and the ratio m n is moderately large and all signals have roughly equal power in the near far situation however the gaussian approximation is quite poor in contrast large deviations techniques are more accurate in the near far situation and it is here that these methods provide some important practical insight

a simple accurate method to calculate spread spectrum multiple access error probabilities the exact calculation of error probabilities for direct sequence spread spectrum multiple access ds ssma systems has been addressed in the literature the exact calculation is computationally difficult so emphasis has been on approximations and bounds one particularly attractive approximation is to just use a signal to noise ratio in a gaussian approximation the standard approximation unfortunately that approximation is not generally accurate enough an improved gaussian approximation with good accuracy has recently been presented the author derives an accurate gaussian approximation which is also computationally very simple

performance evaluation for band limited ds cdma systems based on simplified improved gaussian approximation the standard gaussian approximation sga for error analysis of direct sequence code division multiple access ds cdma systems is very optimistic in many cases improved gaussian approximation iga is a technique that produces accurate error probabilities but is still computationally intensive simplified iga siga has complexity similar to that of sga and at the same time provides sufficient accuracy in this paper we consider siga for ds cdma systems employing random sequences in a band limited scenario the validity of iga for band limited systems is established in a rigorous mathematical sense then a key parameter in siga is derived via a frequency domain approach applications to a number of typical chip waveforms including the popular sinc and raised cosine pulses are investigated performance comparison with iga based lower and upper bounds shows that siga yields very accurate probability of error

a characterization of multiple access interference in generalized quadriphase spread spectrum communications a proposition that is useful for studying multiple access interference mai in generalized quadriphase spread spectrum systems is established the proposition provides the conditional density functions and the conditional cumulative distribution functions of random variables that characterize the mai it is shown that these characterizing random variables converge almost surely to the true mai the proposition provides a method to study the effect of the chip waveform on the performance of the system and provides a means for the design and analysis of spectrally efficient systems with continuous phase or m ary phase shift keyed modulation the proposition allows the evaluation of the average error probability with arbitrary accuracy without making a gaussian approximation for the mai and is also useful for studying systems that send data in packets where the delays of the interferers are often fixed for the duration of a packet for illustration the proposition is applied to computing the average error probability of generalized quadriphase direct sequence spread spectrum multiple access communication systems with various chip waveforms and offset parameters corresponding to commonly used modulation schemes

bit error probabilities of multicode direct sequence spread spectrum multiple access systems many techniques for calculating bit error probabilities beps of direct sequence spread spectrum multiple access systems ds ssma have been reported among them are the following three techniques 1 the standard gaussian approximation 2 the improved gaussian approximation 3 and the simplified improved gaussian approximation we extend these techniques to derive the beps of multicode ds ssma systems we assess the three techniques by comparing their results with the result of computer simulation

an efficient technique for evaluating direct sequence spread spectrum multiple access communications a technique is presented for obtaining bounds on the average probability of error for direct sequence spread spectrum multiple access ds ssma communications the technique is of interest because it yields arbitrarily right bounds involves a small amount of computation avoids numerical integrations and applies to many types of detection as an illustration the technique is applied to binary ds ssma communications an additive white gaussian noise channel and a coherent correlation receiver it is assumed that all the signature sequences are deterministic each transmitter is assumed to have the same power although the approach can accommodate the case of transmitters with unequal powers expressions are given for the density functions of the random variables that model the multiple access interference these expressions are used to obtain arbitrarily tight upper and lower bounds on the average probability of error without making a gaussian approximation or performing numerical integrations to incorporate the effects of multiple access interference

the dirichlet heat kernel in inner uniform domains local results compact domains and non symmetric forms abstract this paper provides sharp dirichlet heat kernel estimates in inner uniform domains including bounded inner uniform domains in the context of certain possibly non symmetric bilinear forms resembling dirichlet forms for instance the results apply to the dirichlet heat kernel associated with a uniformly elliptic divergence form operator with symmetric second order part and bounded measurable real coefficients in inner uniform domains in r n the results are applicable to any convex domain to the complement of any convex domain and to more exotic examples such as the interior and exterior of the snowflake

global integrability of supertemperatures let d be a lipschitz domain or a john domain in mathbb r n with n ge 2 we study the global integrability of nonnegative supertemperatures on the cylinder d times 0 t we show that the integrability depends on the lower estimate of the green function for the dirichlet laplacian on d in particular if d is a c 1 domain then every nonnegative supertemperature on d times 0 t is l p integrable over d times 0 t prime for any 0 t prime t provided 0 p n 2 n 1 the bound n 2 n 1 is sharp

precise analysis of bit error probability for asynchronous multicode ds cdma systems a precise bit error probability bep analysis method is derived for a multicode direct sequence code division multiple access ds cdma system in an additive white gaussian noise channel the method is applicable to a multicode ds cdma system with an arbitrary number of multiple code sequences and any selection of multiple code sequences the precise method gives results that discriminate the effect of the selection of different multiple code sequences on the bep whereas gaussian approximations gas do not thus the new method can be used to select the best multicode set for a given system a task that cannot be achieved using gas a two step analytical procedure enables deriving an explicit compact form for the cf of the receiver decision statistic in a ds cdma system with an arbitrary number of multiple code sequences and for any selection of multiple code sequences

strange objects in the complex plane julia sets are examined as examples of strange objects which arise in the study of long time properties of simple dynamical systems technically they are the closure of the set of unstable cycles of analytic maps physically they are sets of points which lead to chaotic behavior the mapf z z2 p is analyzed for smallp where the julia set is a closed curve and for largep where the julia set is completely disconnected in both cases the hausdorff dimension is calculated in perturbation theory and numerically an expression for the rate at which points escape from the neighborhood of the julia set is derived and tested in a numerical simulation of the escape

an optimal signal design for band limited asynchronous ds cdma communications an optimal signal design for band limited asynchronous direct sequence code division multiple access ds cdma communications with aperiodic random spreading sequences and a conventional matched filter receiver is considered in an additive white gaussian noise awgn channel with bandwidth defined in the strict sense two optimization problems are solved under finite bandwidth and zero interchip interference constraints first a chip waveform optimization is performed given the system bandwidth the data symbol transmission rate and the processing gain a technique to characterize a band limited chip waveform with a finite number of parameters is developed and it is used to derive optimum chip waveforms which minimize the effect of multiple access interference mai for any energy and delay profile of users next a joint optimization of the processing gain and the chip waveform is performed given the system bandwidth and the data symbol transmission rate a sufficient condition for a system to have lower average probability of bit error for any energy profile is found and it is used to derive some design strategies it is shown that the flat spectrum pulse with the processing gain leading to zero excess bandwidth results in the minimum average probability of bit error design examples and numerical results are also provided

the selberg zeta function for convex co compact schottky groups we give a new upper bound on the selberg zeta function for a convex co compact schottky group acting on the hyperbolic space n 1 in strips parallel to the imaginary axis the zeta function is bounded by exp c s where is the dimension of the limit set of the group this bound is more precise than the optimal global bound exp c s n 1 and it gives new bounds on the number of resonances scattering poles of n 1 the proof of this result is based on the application of holomorphic l2 techniques to the study of the determinants of the ruelle transfer operators and on the quasi self similarity of limit sets we also study this problem numerically and provide evidence that the bound may be optimal our motivation comes from molecular dynamics and we consider n 1 as the simplest model of quantum chaotic scattering

the asymptotic distribution of circles in the orbits of kleinian groups let mathcal p be a locally finite circle packing in the plane invariant under a non elementary kleinian group and with finitely many orbits when is geometrically finite we construct an explicit borel measure on which describes the asymptotic distribution of small circles in mathcal p assuming that either the critical exponent of is strictly bigger than 1 or mathcal p does not contain an infinite bouquet of tangent circles glued at a parabolic fixed point of our construction also works for mathcal p invariant under a geometrically infinite group provided admits a finite bowen margulis sullivan measure and the skinning size of mathcal p is finite some concrete circle packings to which our result applies include apollonian circle packings sierpinski curves schottky dances etc

a simple and accurate method of probability of bit error analysis for asynchronous band limited ds cdma systems this paper considers probability of bit error p sub e analysis in asynchronous band limited direct sequence code division multiple access ds cdma systems it presents a simple and accurate method of p sub e analysis the proposed method can serve as an attractive alternative to the only two techniques currently available for band limited systems the standard gaussian approximation sga and the characteristic function method the former is prone to inaccuracy while the latter large computational complexity the method generalizes the simplified improved gaussian approximation siga derived previously for rectangular pulses this paper also outlines a generalization of another method referred to as the improved gaussian approximation iga numerical examples demonstrate the far greater accuracy of the generalized siga with respect to the sga the examples consider the is 95 and square root raised cosine sqrt rc pulses as well as uniform and nonuniform received power conditions

performance of ds ssma communications in impulsive channels ii hard limiting correlation receivers for pt i see ibid vol com 35 no 11 p 1179 88 1987 in part i it was demonstrated that impulsive channel noise can be a serious detriment to the performance of direct sequence spread spectrum multiple access ds ssma communications when conventional linear correlation reception is used here a hard limiting correlator as an alternative for reception of multiple access transmission in impulsive channels is considered for k asynchronous binary psk ds ssma users sharing a linear channel corrupted by impulsive noise that is modeled at the output of the front end filter of the receiver techniques are developed for analyzing bit error probabilities of this hard limiting receiver by exact computation for short spreading sequences by approximation for longer spreading sequences and by asymptotic limits for infinitely long spreading sequences performance is compared to that of the linear correlator under a variety of conditions showing that hard limiting correlation reception can offer substantial improvement over conventional systems in impulsive channels however the linear receiver is more effective against multiple access noise only and so a tradeoff emerges between rejection of impulsive noise and rejection of multiple access interference

ber performance of bandlimited ds cdma systems in nakagami fading accurate average bit error rate analysis of asynchronous bandlimited binary direct sequence code division multiple access ds cdma systems in nakagami m fading is studied the fading is assumed to be flat and slow the spectrum raised cosine src and beaulieu tan damen btd pulse shapes are employed a new method which combines the characteristic function cf method with the improved gaussian approximation ga is proposed for evaluating the ber of bandlimited ds cdma a substantial computational complexity reduction is achieved the well known standard ga holtzman s simplified improved ga and improved holtzman s ga methods are also considered the accuracies of the approximation methods are assessed using monte carlo simulation for a system employing a deterministic sequence for the desired user and random sequences for the active interfering users a cf method is employed to derive precise ber results the new btd pulse outperforms the src pulse in all situations

complex spreading sequences with a wide range of correlation properties this paper presents a new family of complex valued pseudo random sequences for use in coded multiple access communication systems the family offers a very wide range of values for both auto correlation ac and cross correlation cc functions allowing great flexibility in the selection of characteristics of sequence sets based on the measure described in this paper for the mean square aperiodic ac and cc values of a set of sequences the correlation properties of sets of these sequences are compared to well known sequence sets and it is shown that sets from the new family of sequences have superior qualities tables of parameters for various sequence sets are presented to enable the construction and comparison of sets from this new family