design of reduced rank mmse multiuser detectors using random matrix methods reduced rank minimum mean squared error mmse multiuser detectors using asymptotic weights have been shown to reduce receiver complexity while maintaining good performance in long sequence code division multiple access cdma systems in this paper we consider the design of reduced rank mmse receivers in a general framework which includes fading single and multiantenna receivers as well as direct sequence cdma ds cdma and multicarrier cdma both uplink and downlink in all these cases random matrix results are used to obtain explicit expressions for the asymptotic eigenvalue moments of the interference autocorrelation matrix and for the asymptotic weights used in the reduced rank receiver

a deterministic equivalent for the analysis of correlated mimo multiple access channels in this article novel deterministic equivalents for the stieltjes transform and the shannon transform of a class of large dimensional random matrices are provided these results are used to characterize the ergodic rate region of multiple antenna multiple access channels when each point to point propagation channel is modelled according to the kronecker model specifically an approximation of all rates achieved within the ergodic rate region is derived and an approximation of the linear precoders that achieve the boundary of the rate region as well as an iterative water filling algorithm to obtain these precoders are provided an original feature of this work is that the proposed deterministic equivalents are proved valid even for strong correlation patterns at both communication sides the above results are validated by monte carlo simulations

quasiconvexity in 3 manifold groups in this paper we study strongly quasiconvex subgroups in a finitely generated 3 manifold group pi 1 m we prove that if m is a compact orientable 3 manifold that does not have a summand supporting the sol geometry in its sphere disc decomposition then a finitely generated subgroup h le pi 1 m has finite height if and only if h is strongly quasiconvex on the other hand if m has a summand supporting the sol geometry in its sphere disc decomposition then pi 1 m contains finitely generated finite height subgroups which are not strongly quasiconvex we also characterize strongly quasiconvex subgroups of graph manifold groups by using their finite height their morse elements and their actions on the bass serre tree of pi 1 m this result strengthens analogous results in right angled artin groups and mapping class groups finally we characterize hyperbolic strongly quasiconvex subgroups of a finitely generated 3 manifold group pi 1 m by using their undistortedness property and their morse elements

aggregation and estimation for low order periodic arma models the aggregated time series resulting from summing over the seasons of a seasonal time series which is assumed to follow either an ar 1 or arma 1 1 model having periodic seasonal parameters is shown to follow an arma 1 1 model parameter estimation for such models is investigated analytically and via simulation significant gain in parameter estimation efficiency at the aggregated level is demonstrated when the seasonal data and their model is utilized rather than the aggregated annual data and their model

eigenvalue distributions of sums and products of large random matrices via incremental matrix expansions this paper uses an incremental matrix expansion approach to derive asymptotic eigenvalue distributions a e d s of sums and products of large random matrices we show that the result can be derived directly as a consequence of two common assumptions and matches the results obtained from using and transforms in free probability theory we also give a direct derivation of the a e d of the sum of certain random matrices which are not free this is used to determine the asymptotic signal to interference ratio of a multiuser code division multiple access cdma system with a minimum mean square error linear receiver

asymptotic performance of linear receivers in mimo fading channels linear receivers are an attractive low complexity alternative to optimal processing for multiple antenna multiple input multiple output mimo communications in this paper we characterize the information theoretic performance of mimo linear receivers in two different asymptotic regimes for fixed number of antennas we investigate the limit of error probability in the high signal to noise ratio snr regime in terms of the diversity multiplexing tradeoff dmt following this we characterize the error probability for fixed snr in the regime of large but finite number of antennas as far as the dmt is concerned we report a negative result we show that both linear zero forcing zf and linear minimum mean square error mmse receivers achieve the same dmt which is largely suboptimal even in the case where outer coding and deacircnot coding is performed across the antennas we also provide an apacircnot proximate quantitative analysis of the markedly different behavior of the mmse and zf receivers at finite rate and nonasymptotic snr and show that while the zf receiver achieves poor diversity at any finite rate the mmse receiver error curve slope flattens out progressively as the coding rate increases when snr is fixed and the number of antennas becomes large we show that the mutual information at the output of an mmse or zf linear receiver has fluctuations that converge in distribution to a gaussian random variable whose mean and variance can be characterized in closed form this analysis extends to the linear reacircnot ceiver case a well known result previously obtained for the optimal receiver simulations reveal that the asymptotic analysis captures accurately the outage behavior of systems even with a moderate number of antennas

acylindrical hyperbolicity of groups acting on trees we provide new examples of acylindrically hyperbolic groups arising from actions on simplicial trees in particular we consider amalgamated products and hnn extensions one relator groups automorphism groups of polynomial algebras 3 manifold groups and graph products acylindrical hyperbolicity is then used to obtain some results about the algebraic structure analytic properties and measure equivalence rigidity of groups from these classes

streamflow simulation a nonparametric approach in this paper kernel estimates of the joint and conditional probability density functions are used to generate synthetic streamflow sequences streamflow is assumed to be a markov process with time dependence characterized by a multivariate probability density function kernel methods are used to estimate this multivariate density function simulation proceeds by sequentially resampling from the conditional density function derived from the kernel estimate of the underlying multivariate probability density function this is a nonparametric method for the synthesis of streamflow that is data driven and avoids prior assumptions as to the form of dependence e g linear or nonlinear and the form of the probability density functions e g gaussian we show using synthetic examples with known underlying models that the nonparametric method presented is more flexible than the conventional models used in stochastic hydrology and is capable of reproducing both linear and nonlinear dependence the effectiveness of this model is illustrated through its application to simulation of monthly streamflow from the beaver river in utah

nonparametric density estimation prediction and regression for markov sequences abstract let xi be a stationary markov sequence having a transition probability density function f y x giving the pdf of x i 1 xi x in this study nonparametric density and regression techniques are employed to infer f y x and m x e x i 1 xi x it is seen that under certain regularity and markovian assumptions the asymptotic convergence rate of the nonparametric estimator mn x to the predictor m x is the same as it would have been had the xi s been independently and identically distributed and this rate is optimal in a certain sense consistency can be maintained after differentiability and even the markovian assumptions are abandoned computational and modeling ramifications are explored i claim that my methodology offers an interesting alternative to the popular arma approach

estimation of arma models with seasonal parameters the yule walker equations for arma p q models with periodic parameters are derived from which moment estimates can be obtained specifically for the case of arma p 1 models the periodic autoregressive parameters can be found by solving a system of linear equations while the periodic moving average parameters satisfy a system of equations which can be solved iteratively particular examples are given and comparisons are made between the proposed moment estimates and estimates given previously

limit laws for random matrices and free products in earlier articles we studied a kind of probability theory in the framework of operator algebras with the tensor product replaced by the free product we prove here that free random variables naturally arise as limits of random matrices and that wigner s semicircle law is a consequence of the central limit theorem for free random variables in this way we obtain a non commutative limit distribution of a general gaussian random matrix as an operator in a certain operator algebra wigner s law being given by the trace of the spectral measure of the selfadjoint component of this operator

asymptotic analysis of lmmse multiuser receivers for multi signature multicarrier cdma in rayleigh fading this paper considers a multicarrier mc code division multiple access system where each user employs multiple signatures the receiver is linear and minimizes the mean square error of the data estimate both multiple user and single user systems are considered as well as single and multiple signatures per user in each case an asymptotic analysis is used to derive the output signal to interference plus noise ratio sinr as a function of the system loading the noise power and the fading properties of the channel asymptotic in this case means that the number of independent subcarriers and number of signatures per user each tends to infinity with fixed ratio the associated bit error rate ber is evaluated for binary phase shift keying symbols simulations show that the asymptotic sinrs and bers derived in each case are accurate for realistic finite systems

a non gaussian multicomponent model for river flow in order to model satisfactorily sharp rises and slow decreases appearing in any pure runoff time series with a small enough time base exponentially decaying recession and base flow terms are first subtracted from total runoff the remaining part is deseasonalized by a truncated fourier series multiplicator and then modeled as a second order markov stationary series the use of non gaussian distributions allows the modeling of zero contributions which correspond to dry spells an example has been optimized and simulated and the observed and simulated series have been compared even on hydrologically interesting properties such as return periods which were not modeled explicitly the results were satisfactory

physical basis of stochastic models of annual flows the main objective of this paper is to demonstrate that annual streamflow time series can be represented by autoregressive and moving average arma processes the method follows the conceptual representation of a watershed given by fiering 1967

asymptotic analysis of optimum and suboptimum cdma downlink mmse receivers in this paper we investigate the performance of two linear receivers for code division multiple access cdma downlink transmissions over frequency selective channels the users having possibly different powers the optimum minimum mean square error mmse receiver is first considered because this receiver requires the knowledge of the code vectors attributed to all the users within the cell when these vectors are time varying its use may be unrealistic in the forward link a classical suboptimum receiver consisting in a chip rate equalizer followed by a despreading with the code of the user of interest is therefore studied and compared to the optimum mmse receiver performance of both receivers is assessed through the signal to interference plus noise ratio sinr at their outputs the analytical expressions of these sinrs depend in a rather nonexplicit way on the codes allocated to the users of the cell and are therefore not informative this difficulty is dealt with by modeling the users code matrix by a random matrix because the code matrices used in the forward link are usually isometric the code matrix is assumed to be extracted from a haar distributed random unitary matrix the behavior of the sinrs is studied when the spreading factor and the number of users converge to spl infin at the same rate using certain results of the free probability theory we establish the fact that the sinrs converge almost surely toward quantities that depend only on the complex amplitudes of propagation channel paths we then use the expressions of these sinr limits to discuss the influence of the various parameters on the performance of the receivers

mmse analysis of certain large isometric random precoded systems linear precoding consists in multiplying by an n spl times k matrix a k dimensional vector obtained by serial to parallel conversion of a symbol sequence to be transmitted in this paper new tools borrowed from the so called free probability theory are introduced for the purpose of analyzing the performance of minimum mean square error mmse receivers for certain large random isometric precoded systems on fading channels the isometric condition represents the case of precoding matrices with orthonormal columns it is shown in this contribution that the signal to interference plus noise ratio sinr at the equalizer output converges almost surely to a deterministic value depending on the probability distribution of the channel coefficients when n spl rarr spl infin and k n spl rarr spl alpha spl les 1 these asymptotic results are used to analyze the impact of orthogonal spreading as well as to optimally balance the redundancy introduced between linear precoding versus classical convolutional coding while preserving a simple mmse equalization scheme at the receiver

commensurability of groups quasi isometric to raags let g be a right angled artin group with defining graph gamma and let h be a finitely generated group quasi isometric to g we show if g satisfies that 1 its outer automorphism group is finite 2 gamma does not contain any induced 4 cycles 3 gamma is star rigid then h is commensurable to g we show condition 2 is sharp in the sense that if gamma contains an induced 4 cycle then there exists an h quasi isometric to g but not commensurable to g moreover one can drop condition 1 if h is a uniform lattice acting on the universal cover of the salvetti complex of g as a consequence we obtain a conjugation theorem for such uniform lattices the ingredients of the proof include a blow up building construction in huang and kleiner duke math j 167 3 537 602 2018 https doi org 10 1215 00127094 2017 0042 and a haglund wise style combination theorem for certain class of special cube complexes however in most of our cases relative hyperbolicity is absent so we need new ingredients for the combination theorem

no eigenvalues outside the support of the limiting spectral distribution of large dimensional sample covariance matrices let b n 1 n t n 1 2 x n x n t n 1 2 where x n is n times n with i i d complex standardized entries having finite fourth moment and t n 1 2 is a hermitian square root of the nonnegative definite hermitian matrix t n it is known that as n to infty if n n converges to a positive number and the empirical distribution of the eigenvalues of t n converges to a proper probability distribution then the empirical distribution of the eigenvalues of b n converges a s to a nonrandom limit in this paper we prove that under certain conditions on the eigenvalues of t n for any closed interval outside the support of the limit with probability 1 there will be no eigenvalues in this interval for all n sufficiently large

a nearest neighbor bootstrap for resampling hydrologic time series a nonparametric method for resampling scalar or vector valued time series is introduced multivariate nearest neighbor probability density estimation provides the basis for the resampling scheme developed the motivation for this work comes from a desire to preserve the dependence structure of the time series while bootstrapping resampling it with replacement the method is data driven and is preferred where the investigator is uncomfortable with prior assumptions as to the form e g linear or nonlinear of dependence and the form of the probability density function e g gaussian such prior assumptions are often made in an ad hoc manner for analyzing hydrologic data connections of the nearest neighbor bootstrap to markov processes as well as its utility in a general monte carlo setting are discussed applications to resampling monthly streamflow and some synthetic data are presented the method is shown to be effective with time series generated by linear and nonlinear autoregressive models the utility of the method for resampling monthly streamflow sequences with asymmetric and bimodal marginal probability densities is also demonstrated

modeling water table fluctuations by means of a stochastic differential equation the combined system of soil water and shallow groundwater is modeled with simple mass balance equations assuming equilibrium soil moisture conditions this results in an ordinary but nonlinear differential equation of water table depth at a single location if errors in model inputs errors due to model assumptions and parameter uncertainty are lumped and modeled as a wide band noise process a stochastic differential equation sde results a solution for the stationary probability density function is given through use of the fokker planck equation for the nonstationary case where the model inputs are given as daily time series sample functions of water table depth soil saturation and drainage discharge can be simulated by numerically solving the sde these sample functions can be used for designing drainage systems and to perform risk analyses the parameters and noise statistics of the sde are calibrated on time series of water table depths by embedding the sde in a kaiman filter algorithm and using the filter innovations in a filter type maximum likelihood criterion the stochastic model is calibrated and validated at two locations a peat soil with a very shallow water table and a loamy sand soil with a moderately shallow water table it is shown in both cases that sample functions simulated with the sde are able to reproduce a wide range of statistics of water table depth despite its unrealistic assumption of constant inputs the stationary solution derived from the fokker planck equation gives good results for the peat soil most likely because the characteristic response time of the water table is very small

unified large system analysis of mmse and adaptive least squares receivers for a class of random matrix channels we present a unified large system analysis of linear receivers for a class of random matrix channels the technique unifies the analysis of both the minimum mean squared error mmse receiver and the adaptive least squares als receiver and also uses a common approach for both random independent identically distributed i i d and random orthogonal precoding we derive expressions for the asymptotic signal to interference plus noise ratio sinr of the mmse receiver and both the transient and steady state sinr of the als receiver trained using either i i d data sequences or orthogonal training sequences the results are in terms of key system parameters and allow for arbitrary distributions of the power of each of the data streams and the eigenvalues of the channel correlation matrix in the case of the als receiver we allow a diagonal loading constant and an arbitrary data windowing function for i i d training sequences and no diagonal loading we give a fundamental relationship between the transient steady state sinr of the als and the mmse receivers we demonstrate that for a particular ratio of receive to transmit dimensions and window shape all channels which have the same mmse sinr have an identical transient als sinr response we demonstrate several applications of the results including an optimization of information throughput with respect to training sequence length in coded block transmission

a mixed gamma arma 1 1 model for river flow time series in this paper we consider a time series model which can easily be used for simulating stationary river flow sequences with high skewness and the long term correlation structure of an arma 1 1 model the model is fitted to monthly streamflows taken from a river in malaysia the simulated data bear a close resemblance to the historical sequence in terms of the mean variance skewness and autocorrelation coefficients

a stochastic streamflow model based on physical principles based on hydrologic arguments a stochastic model for discretized streamflow from rainfall is proposed in the form of an averaged filtered poisson process fpp using a two component description with excess precipitation and drainage as inputs to the surface and subsurface flow systems simplified models are presented for the physical processes the mean variance and covariance function of discretized streamflow are computed in terms of the first and second moments of excess precipitation and drainage which are derived analytically the behavior of the stochastic properties of streamflow is evaluated for various soil types basin travel times and effective initial soil water contents where there is an intuitive feeling for the interaction of physical characteristics and stochastic properties such as the mean the model appears to produce qualitatively correct results prediction of stochastic properties is limited by the selection of an effective initial soil moisture value

signature optimization for cdma with limited feedback we study the performance of joint signature receiver optimization for direct sequence code division multiple access ds cdma with limited feedback the receiver for a particular user selects the signature from a signature codebook and relays the corresponding b index bits to the transmitter over a noiseless channel we study the performance of a random vector quantization rvq scheme in which the codebook entries are independent and isotropically distributed assuming the interfering signatures are independent and have independent and identically distributed i i d elements we evaluate the received signal to interference plus noise ratio sinr in the large system limit as the number of users processing gain and feedback bits b all tend to infinity with fixed ratios this sinr is evaluated for both the matched filter and linear minimum mean squared error mmse receivers furthermore we show that this large system sinr is the maximum that can be achieved over any sequence of codebooks numerical results show that with the mmse receiver one feedback bit per signature coefficient achieves close to single user performance we also consider a less complex and suboptimal reduced rank signature optimization scheme in which the user s signature is constrained to lie in a lower dimensional subspace the optimal subspace coefficients are scalar quantized and relayed to the transmitter the large system performance of the quantized reduced rank scheme can be approximated and numerical results show that it performs in the vicinity of the rvq bound finally we extend our analysis to the scenario in which a subset of users optimize their signatures in the presence of random interference

space time modeling of water table depth using a regionalized time series model and the kalman filter the spatiotemporal variation of shallow water table depth is modeled with a regionalized version of an autoregressive exogenous arx time series model the arx model relates the temporal variation of the water table depth at a single location to a time series of precipitation surplus the arx model is calibrated first at locations where time series of water table depth are available arx parameters at nonvisited locations are estimated through geostatistical interpolation using auxiliary information resulting in a regionalized arx model or rarx model the parameters of the geostatistical model are estimated by embedding the rarx model in a space time kalman filter and minimization of a maximum likelihood criterion built from the filter innovations the resulting state estimator can be used for optimal space time prediction of water table depth network optimization and space time conditional simulation

asymptotic performance of mmse receivers for large systems using random matrix theory random matrix theory is used to derive the limit and asymptotic distribution of signal to interference plus noise ratio sir for a class of suboptimal minimum mean square error mmse receivers applied to large random systems with unequal power users we prove that the limiting sir converges to a deterministic value when k and n go to infinity with lim k n y being a positive constant where k is the number of users and n is the number of degrees of freedom we also prove that the sir of each particular user is asymptotically gaussian for large n and derive the closed form expressions of the variance for the sir variable under real spreading and complex spreading channel environments it is revealed that for a given k n pair under certain mild conditions the variance of the sir for complex spreading channels is half of that for the corresponding real spreading channels since the suboptimal mmse receiver becomes optimal for the case when the users are equally powered our results show that the conjecture made by tse and zeitouni for the complex spreading case is not affirmative we also derive the asymptotic distribution for sir in decibels which provides better description when n is small numerical results and computer simulations are provided to evaluate the accuracy of various limiting and asymptotic results obtained in this paper

conceptual stochastic modeling of seasonal runoff using autoregressive moving average models and different scales of aggregation the statistical and phenomenological aspects of the runoff process observed on different scales of aggregation are taken as a priori information for the conceptually based stochastic modeling of seasonal runoff runoff is considered as the sum of two groundwater components with over year and subannual response lag and of a purely random component representing the direct runoff this scheme is equivalent to a linear system with two parallel linear reservoirs plus a zero lag linear channel the system output is the runoff and the input is the effective rainfall considered proportional to the direct runoff assuming the effective rainfall as a non gaussian periodic independent process and considering nonseasonal groundwater parameters this conceptualization leads to an autoregressive and moving average 2 2 stochastic process with periodic independent residual stochastic model parameters are directly related to the linear system coefficients and the effective rainfall structure can be determined from the estimated model residual in order to obtain parameter estimates consistent with the conceptual constraints two estimation stages on an annual and a seasonal basis and an iterative procedure are needed the model was applied to a number of time series of monthly streamflows in the apennine regions of italy with promising results

good lattice constellations for both rayleigh fading and gaussian channels recent work on lattices matched to the rayleigh fading channel has shown how to construct good signal constellations with high spectral efficiency we present a new family of lattice constellations based on complex algebraic number fields which have good performance on rayleigh fading channels some of these lattices also present a reasonable packing density and thus may be used at the same time over a gaussian channel conversely we show that particular versions of the best lattice packings d sub 4 e sub 6 e sub 8 k sub 12 spl lambda sub 16 spl lambda sub 24 constructed from totally complex algebraic cyclotomic fields present better performance over the rayleigh fading channel the practical interest in such signal constellations rises from the need to transmit information at high rates over both terrestrial and satellite links some further results in algebraic number theory related to ideals and their factorization are presented and the decoding algorithm used with these lattice constellations are illustrated together with practical results

calibration of transfer function noise models to sparsely or irregularly observed time series a method is presented to calibrate transfer function noise tfn models operating at the same frequency as the input auxiliary variables to sparsely or irregularly observed time series of the output target variable once calibrated the tfn models can be used to predict or simulate the output variable at the same frequency as the input variable consequently the method provides a useful tool for filling in gaps of irregularly or sparsely observed hydrological time series although generic and suitable for any type of time series the method is described through the modeling of a time series of groundwater head data with precipitation surplus precipitation minus potential evapotranspiration as input variable first the tfn model is written in vector notation yielding the state equation of a linear discrete stochastic system subsequently the state equation is embedded in a kalman filter algorithm the kalman filter is then combined with a maximum likelihood criterion to obtain estimates of the parameters of the tfn model for small time steps e g 1 day while using sparsely e g two times a month or even irregularly observed time series of groundwater head data the method is illustrated using subsets of time series of groundwater head data with varying regular and irregular observation intervals

cross validation of multivariate densities abstract in recent years the focus of study in smoothing parameter selection for kernel density estimation has been on the univariate case while multivariate kernel density estimation has been largely neglected in part this may be due to the perception that calibrating multivariate densities is substantially more difficult in this article we explicitly derive and compare multivariate versions of the bootstrap method of taylor the least squares cross validation method developed by bowman and rudemo and a biased cross validation method similar to that of scott and terrell for multivariate kernel estimation using the product kernel estimator the theoretical behavior of these cross validation algorithms is shown to improve surprisingly as the dimension increases approaching the best rate of o n 1 2 simulation studies suggest that the new biased cross validation method performs quite well and with reasonable variability as compared to the other two methods bivariate examples with heart disease

hyperbolic structures on 3 manifolds i deformation of acylindrical manifolds this is the first in a series of papers showing that haken manifolds have hyperbolic structures this first was published the second two have existed only in preprint form and later preprints were never completed this eprint is only an approximation to the published version which is the definitive form for part i and is provided for convenience only all references and quotations should be taken from the published version since the theorem numbering is different and not all corrections have been incorporated into the present version parts ii and iii will be made available as eprints shortly

quasi isometric classification of graph manifold groups we show that the fundamental groups of any two closed irreducible nongeometric graph manifolds are quasi isometric we also classify the quasi isometry types of fundamental groups of graph manifolds with boundary in terms of certain finite twocolored graphs a corollary is the quasi isometric classification of artin groups whose presentation graphs are trees in particular any two right angled artin groups whose presentation graphs are trees of diameter greater than 2 are quasi isometric further this quasi isometry class does not include any other right angled artin groups a finitely generated group can be considered geometrically when endowed with a word metric up to quasi isometric equivalence such metrics are unique in this article only finitely generated groups are considered given a collection of groups g gromov 11 proposed the fundamental questions of identifying which groups are quasi isometric to those in g rigidity and which groups in g are quasi isometric to each other classification in this article we focus on the classification question for graph manifold groups and right angled artin groups a compact 3 manifold m is called geometric if m m admits a geometric structure in the sense of thurston i e a complete locally homogeneous riemannian metric of finite volume thurston s geometrization conjecture see 29 17 21 23 22 provides that every irreducible 3 manifold of zero euler characteristic i e with boundary consisting only of tori and klein bottles admits a decomposition along tori and klein bottles into geometric pieces the minimal such decomposition being called the geometric decomposition there is a considerable literature on quasi isometric rigidity and classification of 3 manifold groups the rigidity results can be briefly summarized in the following form

spectral efficiency of cdma with random spreading the cdma channel with randomly and independently chosen spreading sequences accurately models the situation where pseudonoise sequences span many symbol periods furthermore its analysis provides a comparison baseline for cdma channels with deterministic signature waveforms spanning one symbol period we analyze the spectral efficiency total capacity per chip as a function of the number of users spreading gain and signal to noise ratio and we quantify the loss in efficiency relative to an optimally chosen set of signature sequences and relative to multiaccess with no spreading white gaussian background noise and equal power synchronous users are assumed the following receivers are analyzed a optimal joint processing b single user matched filtering c decorrelation and d mmse linear processing

asymptotic behavior of random vandermonde matrices with entries on the unit circle analytical methods for finding moments of random vandermonde matrices with entries on the unit circle are developed vandermonde matrices play an important role in signal processing and wireless applications such as direction of arrival estimation precoding and sparse sampling theory just to name a few within this framework we extend classical freeness results on random matrices with independent and identically distributed i i d entries and show that vandermonde structured matrices can be treated in the same vein with different tools we focus on various types of matrices such as vandermonde matrices with and without uniform phase distributions as well as generalized vandermonde matrices in each case we provide explicit expressions of the moments of the associated gram matrix as well as more advanced models involving the vandermonde matrix comparisons with classical i i d random matrix theory are provided and deconvolution results are discussed we review some applications of the results to the fields of signal processing and wireless communications

output mai distributions of linear mmse multiuser receivers in ds cdma systems multiple access interference mai in a code division multiple access cdma system plays an important role in performance analysis and characterization of fundamental system limits we study the behavior of the output mai of the minimum mean square error mmse receiver employed in the uplink of a direct sequence ds cdma system we focus on imperfect power controlled systems with random spreading and establish that in a synchronous system 1 the output mai of the mmse receiver is asymptotically gaussian and 2 for almost every realization of the signatures and received powers the conditional distribution of the output mai converges weakly to the same gaussian distribution as in the unconditional case we also extend our study to asynchronous systems and establish the gaussian nature of the output interference these results indicate that in a large system the output interference is approximately gaussian and the performance of the mmse receiver is robust to the randomness of the signatures and received powers the gaussianity justifies the use of single user gaussian codes for cdma systems with linear mmse receivers and implies that from the viewpoints of detection and channel capacity signal to interference ratio sir is the key parameter that governs the performance of the mmse receiver in a cdma system

physical basis of time series models for water table depths the relationship between precipitation excess and water table depth can be described by empirical time series models such as transfer function noise models autoregressive exogenous variable models arx and threshold autoregressive self exciting open loop models in this paper these models are interpreted in terms of the water balance of a soil column a physically based arx model is used to predict the effect of an intervention on the water table dynamics at two locations it is shown that the physically based arx model predicts the effect of interventions reasonably well

asymptotic performance of successive interference cancellation in the context of linear precoded ofdm systems recent results on the asymptotic empirical eigenvalue distribution of random matrices have enabled the study of the asymptotic limits of linear precoded orthogonal frequency division multiplexing systems with minimum mean square error mmse equalization in this letter we extend these results to the mmse successive interference cancellation detector and quantify the nonlinearity gain for certain type of precoding matrices

spectral efficiency of multicarrier cdma we analyze the spectral efficiency sum rate per subcarrier of randomly spread synchronous multicarrier code division multiple access mc cdma subject to frequency selective fading in the asymptotic regime of number of users and bandwidth going to infinity with a constant ratio both uplink and downlink are considered either conditioned on the subcarrier fading coefficients for nonergodic channels or unconditioned thereon for ergodic channels the following receivers are analyzed a jointly optimum receiver b linear minimum mean square error mmse receiver c decorrelator and d single user matched filter

on the quantitative quasi isometry problem transport of poincare inequalities and different types of quasi isometric distortion growth abstract we consider a quantitative form of the quasi isometry problem we discuss several arguments which lead us to a number of results and bounds of quasi isometric distortion comparison of volumes connectivity etc then we study the transport of poincare constants by quasi isometries and we give sharp lower and upper bounds for the homotopy distortion growth for a certain class of hyperbolic metric spaces a quotient of a heintze group r r n by z n we also prove the linear distortion growth between hyperbolic space h n n 3 and a tree

thick metric spaces relative hyperbolicity and quasi isometric rigidity we study the geometry of non relatively hyperbolic groups generalizing a result of schwartz any quasi isometric image of a non relatively hyperbolic space in a relatively hyperbolic space is contained in a bounded neighborhood of a single peripheral subgroup this implies that a group being relatively hyperbolic with non relatively hyperbolic peripheral subgroups is a quasi isometry invariant as an application artin groups are relatively hyperbolic if and only if freely decomposable we also introduce a new quasi isometry invariant of metric spaces called metrically thick which is sufficient for a metric space to be non hyperbolic relative to any non trivial collection of subsets thick finitely generated groups include mapping class groups of most surfaces outer automorphism groups of most free groups certain artin groups and others non uniform lattices in higher rank semisimple lie groups are thick and hence non relatively hyperbolic in contrast with rank one which provided the motivating examples of relatively hyperbolic groups mapping class groups are the first examples of non relatively hyperbolic groups having cut points in any asymptotic cone resolving several questions of drutu and sapir about the structure of relatively hyperbolic groups outside of group theory teichmuller spaces for surfaces of sufficiently large complexity are thick with respect to the weil peterson metric in contrast with brock farb s hyperbolicity result in low complexity

asymptotic theorems for the product of certain structured random matrices and their application to analysis of asynchronous cdma this paper consists of two parts in the first part asymptotic theorems about the product of certain structured random matrices are developed by means of the moment convergence theorem mct and the free probability theory this product of random matrices is a generalization of the product of a sample covariance matrix and an arbitrary hermitian matrix in the second part the theoretical results obtained in the first part are applied to analyze a randomly spread asynchronous direct sequence code division multiple access ds cdma system with both the number of users k and the number of chips per symbol n approaching infinity but the ratio k n kept as a finite constant two levels of asynchronism are considered one is symbol asynchronous but chip synchronous and the other is chip asynchronous asymptotic spectral distribution asd of cross correlation matrix and asymptotic spectral efficiency are investigated conditions under which cdma systems with various synchronism levels synchronous and two levels of asynchronism have the same performance are also established

randomized isometric linear dispersion space time block coding for the df relay channel this paper presents a randomized linear dispersion space time block code for decode and forward synchronous relays the coding matrices are obtained as a set of columns or rows of randomly generated haar distributed unitary matrices with respect to independent and identically distributed i i d generated codes this particular isometric structure reduces the intersymbol interference generated within each relay the gain over i i d codes in terms of spectral efficiency is analyzed for both the lmmse and the ml receivers under the assumption of frequency flat quasi static fading in this setting the spectral efficiency is a random quantity since it depends on the random coding matrices however it is proven that the spectral efficiency converges in probability to a deterministic quantity when the dimensions of the matrices tend to infinity while keeping constant their ratio i e the coding rate consequently when the random coding matrices are large enough the presented system behaves as a deterministic one this result is achieved by means of the rectangular r transform a powerful tool of free probability theory which allows determining the distribution of the singular values of a sum of rectangular matrices

locally weighted regression an approach to regression analysis by local fitting abstract locally weighted regression or loess is a way of estimating a regression surface through a multivariate smoothing procedure fitting a function of the independent variables locally and in a moving fashion analogous to how a moving average is computed for a time series with local fitting we can estimate a much wider class of regression surfaces than with the usual classes of parametric functions such as polynomials the goal of this article is to show through applications how loess can be used for three purposes data exploration diagnostic checking of parametric models and providing a nonparametric regression surface along the way the following methodology is introduced a a multivariate smoothing procedure that is an extension of univariate locally weighted regression b statistical procedures that are analogous to those used in the least squares fitting of parametric functions c several graphical methods that are useful tools for understanding loess estimates and checking the a

disaggregation procedures for generating serially correlated flow vectors the structure of disaggregation models places severe constraints on the feasible values of the lagged covariance of generated flow vectors a new and simple class of disaggregation models is presented which employ the valencia schaake disaggregation model structure but allow the models innovations to be serially correlated these models can reproduce 1 the covariance matrix of the disaggregated flows 2 their covariance with the upper level flows and 3 reasonable approximations to the lag one covariance of the disaggregated flow vectors given the constraints imposed by a disaggregation approach the mejia rousselle disaggregation model is shown in general to fail to reproduce the anticipated variances and covariances of the disaggregated flows because the model and its parameter estimators are not self consistent the paper closes with a discussion of practical modeling considerations and of staged disaggregation procedures which reduce the size of multisite multiseason models

mimo channel modeling and the principle of maximum entropy we devise theoretical grounds for constructing channel models for multiple input multiple output mimo systems based on information theoretic tools the paper provides a general method to derive a channel model which is consistent with one s state of knowledge the framework we give here has already been fruitfully explored with success in the context of bayesian spectrum analysis and parameter estimation for each channel model we conduct an asymptotic analysis in the number of antennas of the achievable transmission rate using tools from random matrix theory a central limit theorem is provided on the asymptotic behavior of the mutual information and validated in the finite case by simulations the results are useful both in terms of designing a system based on criteria such as quality of service and in optimizing transmissions in multiuser networks

a characterization of cocompact hyperbolic and finite volume hyperbolic groups in dimension three we show that a cocompact hyperbolic group in dimension 3 is char acterized by certain properties of its word metric which depend only on the group structure and not on any action on hyperbolic space we prove a similar theorem for finite volume hyperbolic groups in dimension 3 a group g is called cocompact hyperbolic of dimension n if and only if it can act isometrically properly discontinuously and cocompactly on hyperbolic space h proper discontinuity implies that the action has at most finite kernel our main result states that a group g is cocompact hyperbolic of dimension 3 if and only if it has a finite generating set c and associated cayley graph f r cr c such that the word metric on t is comparable in the large quasi isometric with the standard hyperbolic metric on h3 we have a similar result for finite volume hyperbolic groups in dimension 3 we believe that our results generalize to all dimensions at least in the cocompact case our result for groups of finite volume employs a different metric space instead of the cayley graph with word metric we use an augmented cayley graph associated with a group g and a finite family of euclidean subgroups of g we prove that the group acts isometrically and properly discontinuously on h3 with orbit space of finite volume if and only if the augmented cayley graph is quasi isometric with h3 precise definitions of all of these terms will appear in 2 the proof of the cocompact case appears in 3 the proof of the finite volume case appears in 4 our results are similar to a result of gromov gl but without the added assumption that the group be the fundamental group of a convex path space there are other results on the classification of groups up to quasi isometry in g2 in particular a group is quasi isometric to e if and only if there is a subgroup z of finite index it would be interesting to know which groups are quasi isometric to the 3 dimensional geometries h2 x e1 solv and psl 2 r gromov s work on groups with polynomial growth g3 bk implies that a group is quasi isometric to nil if and only if it has a subgroup of finite index which is the fundamental group of a compact nil 3 orbifold notice that all compact

bootstrapping in nonparametric regression local adaptive smoothing and confidence bands abstract the operation of the bootstrap in the context of nonparametric regression is considered bootstrap samples are taken from estimated residuals to study the distribution of a suitably recentered kernel estimator the application of this principle to the problem of local adaptive choice of bandwidth and to the construction of confidence bands is investigated and compared with a direct method based on asymptotic means and variances the technique of the bootstrap is to replace any occurrence of the unknown distribution in the definition of the statistical function of interest by the empirical distribution function of the observed errors in a regression context these errors are not directly observed although their role can be played by the residuals from the fitted model in this article the fitted model is a kernel nonparametric regression estimator since nonparametric smoothing is involved an additional difficulty is created by the bias incurred in smoothing this bias however can be estimated

asymptotic spectral efficiency of multiuser multisignature cdma in frequency selective channels this paper presents an asymptotic analysis of multisignature code division multiple access cdma in the presence of frequency selective channels we characterize the sum spectral efficiency and spectral efficiency regions for both the optimal and linear minimum mean squared error mmse multiuser receivers both independent and identically distributed i i d signatures and isometric signatures which are orthogonal at each transmitter are considered our results are asymptotic as the number of signatures per user and processing gain both tend to infinity with fixed ratio the spectral efficiency of the mmse receiver is determined from the asymptotic output signal to interference plus noise ratio sinr for isometric signatures our results rely on approximating certain covariance matrices with unitarily invariant matrices that are asymptotically free this approximation is shown to be very accurate through comparison with both simulation and an incremental signature analysis which can be used to compute asymptotic moments also a novel proof of the convergence of the empirical spectral distribution of the signal correlation matrix is presented from these results we derive the optimal coding spreading tradeoff which maximizes the mmse spectral efficiency for the case of a single user with multiple i i d signatures simulation studies demonstrate that the asymptotic results accurately predict the performance of finite size systems of interest the resulting expressions are used to highlight and infer properties of the multisignature cdma system including the benefit of orthogonal relative to i i d signatures and the tradeoff between spectral efficiency and the versatility of providing a variable data rate service through multiple signatures

groups quasi isometric to right angled artin groups we characterize groups quasi isometric to a right angled artin group raag g with finite outer automorphism group in particular all such groups admit a geometric action on a cat 0 cube complex that has an equivariant fibering over the davis building of g this characterization will be used in forthcoming work of the first author to give a commensurability classification of the groups quasi isometric to certain raags

tarso modeling of water table depths threshold autoregressive self exciting open loop tarso models are fitted to six time series of water table depths with precipitation excess as input variable basically these models are nonlinear in structure because they incorporate several regimes which are separated by so called thresholds for each well a subset tarso ss tarso model is selected using a bayes information criterion bic ss tarso models are used to simulate realizations of water table depths with lengths of 30 years from which characteristics such as durations of exceedance are computed the simulation performance of the fitted ss tarso models is compared with results obtained from transfer function noise tfn models dynamic regression dr models and with a physical descriptive model called swatre extended with additional autoregressive moving average arma processes for the noise swatre arma as compared to the linear tfn and dr models the ss tarso models perform better because they incorporate several regimes these regimes are the result of different soil layers or drainage levels furthermore it is interesting that ss tarso models show a good relative performance as compared to the swatre arma models a possible reason may be that inputs of swatre are uncertain

constellations matched to the rayleigh fading channel we introduce a new technique for designing signal sets matched to the rayleigh fading channel in particular we look for n dimensional n spl ges 2 lattices whose structure provides nth order diversity our approach is based on a geometric formulation of the design problem which in turn can be solved by using a number geometric approach specifically a suitable upper bound on the pairwise error probability makes the design problem tantamount to the determination of what is called a critical lattice of the body s x x sub 1 spl middot spl middot spl middot x sub n spl isin r sup n spl pi sub i 1 sup n x sub i spl les 1 the lattices among which we search for an optimal solution are the standard embeddings in r sup n of the number ring of some totally real number field of degree n over q simulation results confirm that this approach yields lattices with considerable coding gains

asymptotic performance analysis of blind minimum output energy receivers for large ds cdma systems the random matrix theory is used to analyze the asymptotic performance of the blind minimum output energy moe receiver in direct sequence code division multiple access ds cdma systems in the presence of unknown multipath channel under the condition that the spreading factor and the number of users go to infinity with the same rate as a special case the asymptotic properties of the blind capon receiver are also studied and the conditions of convergence of the signal to interference plus noise ratio sinr of this receiver to that of the optimal minimum mean square error mmse receiver are discussed in particular it is shown that the sinr performances of the capon and mmse receivers are nearly identical in the uplink scenario while the performance of the capon receiver may be considerably inferior to that of the mmse receiver in the downlink transmission case as the performance of the capon receiver is closely related to the performance of the capon channel estimator the asymptotic properties of the latter estimator are also studied and the conditions of convergence of the capon channel estimate to a scaled version of the channel vector of the user of interest are obtained

quasi isometries preserve the geometric decomposition of haken manifolds we prove quasi isometry invariance of the canonical decomposition for fundamental groups of haken 3 manifolds with zero euler characteristic we show that groups quasi isometric to haken manifold groups with nontrivial canonical decomposition are finite extensions of haken orbifold groups as a by product we describe all 2 dimensional quasi flats in the universal covers of non geometric haken manifolds

blind channel estimation in mimo ofdm systems with multiuser interference this paper proposes a blind channel estimation method in the context of a multiuser orthogonal frequency domain multiplexing ofdm system where each user transmits utilizing all available subcarriers a linear nonredundant block precoding scheme is applied at the input of the ofdm system the precoding spreads the symbols of each user over all subcarriers thus increasing multipath diversity at the same time it introduces a structure to the transmitted symbols which is exploited at the receiver to estimate the channel in a blind fashion the proposed channel estimation approach employs computationally simple cross correlation operations and yields the channel up to a diagonal ambiguity it does not require channel length information and is not sensitive to additive stationary noise the precoding does not increase transmission power and maintains even distribution of power between ofdm blocks a general description of precoding matrices is provided as well as analytical expressions of symbol error probability and signal to interference ratio which could be used to obtain optimum precoding schemes

periodic gamma autoregressive processes for operational hydrology a number of models have been suggested for hydrologic time series in general and streamflow series in particular most of them are normal autoregressive ar of order 1 with either constant or periodic parameters since generally hydrologic time series are nonnormal skewed transformations have been suggested to make the series approximately normal a new class of univariate models is proposed herein which incorporates skewed and correlation properties within the model structure without the necessity of transformations such models assume a gamma marginal distribution and a constant or periodic autoregressive structure the models may be additive gamma multiplicative gamma or a mixed model which incorporates properties of both additive and multiplicative models the gamma models were tested and compared in relation to transformed normal ar models by computer simulation studies based on five weekly streamflow series with samples varying from 35 to 40 years of record the results show that the new class of gamma models compares favorably with respect to the normal models in reproducing the basic statistics usually analyzed for streamflow simulation it is expected that the proposed gamma models will be of interest to other researchers for further developments and applications to hydrologic and geophysical time series

sum rate optimal multicode cdma systems an equivalence result in this paper the sum rate of a multicode code division multiple access cdma system with asymmetric power users is maximized given a processing gain and the power profile of users unlike the sum rate maximization for a single code cdma system the optimization requires the joint optimal distribution of each user s power to its multiple data streams as well as the optimal design of signature sequences the crucial step is to establish an equivalence of the multicode cdma system to restricted frequency division multiple access fdma and time division multiple access tdma systems the cdma system has upper limits on the numbers of multicodes of users whereas the fdma system has upper limits on the bandwidths and the tdma system has upper limits on the duty cycles of users the equivalence facilitates the complete characterization of the maximum sum rate of the multicode cdma system and also provides new insights into single and multicode cdma systems in terms of the parameters of the equivalent fdma and tdma systems

simple polynomial detectors for cdma downlink transmissions on frequency selective channels in code division multiple access cdma transmissions computing the multiuser minimum mean squared error mmse detector coefficients requires the inversion of the covariance matrix associated to the received vector signal an operation usually difficult to implement when the spreading factor and the number of users are large it is therefore interesting to approximate the inverse by a matrix polynomial in this correspondence means for computing the polynomial coefficients are proposed in the context of cdma downlink transmissions on frequency selective channels the users having possibly different powers derivations are made in the asymptotic regime where the spreading factor and the number of users grow toward infinity at the same rate results pertaining to the mathematics of large random matrices and in particular to free probability theory are used spreading matrices are modeled as isometric random matrices spreading vectors orthonormality is a natural assumption in downlink and also as random matrices with independent and identically distributed i i d elements