statistical mechanics of multiplex networks entropy and overlap there is growing interest in multiplex networks where individual nodes take part in several layers of networks simultaneously this is the case for example in social networks where each individual node has different kinds of social ties or transportation systems where each location is connected to another location by different types of transport many of these multiplexes are characterized by a significant overlap of the links in different layers in this paper we introduce a statistical mechanics framework to describe multiplex ensembles a multiplex is a system formed by n nodes and m layers of interactions where each node belongs to the m layers at the same time each layer ensuremath alpha is formed by a network g ensuremath alpha here we introduce the concept of correlated multiplex ensembles in which the existence of a link in one layer is correlated with the existence of a link in another layer this implies that a typical multiplex of the ensemble can have a significant overlap of the links in the different layers moreover we characterize microcanonical and canonical multiplex ensembles satisfying respectively hard and soft constraints and we discuss how to construct multiplexes in these ensembles finally we provide the expression for the entropy of these ensembles that can be useful to address different inference problems involving multiplexes

noncoherent capacity of underspread fading channels we derive bounds on the noncoherent capacity of wide sense stationary uncorrelated scattering wssus channels that are selective both in time and frequency and are underspread i e the product of the channel s delay spread and doppler spread is small the underspread assumption is satisfied by virtually all wireless communication channels for input signals that are peak constrained in time and frequency we obtain upper and lower bounds on capacity that are explicit in the channel s scattering function are accurate for a large range of bandwidth and allow to coarsely identify the capacity optimal bandwidth as a function of the peak power and the channel s scattering function we also obtain a closed form expression for the first order taylor series expansion of capacity in the infinite bandwidth limit and show that our bounds are tight in the wideband regime for input signals that are peak constrained in time only and hence allowed to be peaky in frequency we provide upper and lower bounds on the infinite bandwidth capacity our lower bound is closely related to a result by viterbi 1967 we find cases where the bounds coincide and hence the infinite bandwidth capacity is characterized exactly the analysis in this paper is based on a discrete time discrete frequency approximation of wssus time and frequency selective channels this discretization takes the underspread property of the channel explicitly into account

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

low complexity mimo multiuser receiver a joint antenna detection scheme for time varying channels this paper deals with the uplink of a wireless multiple input multiple output mimo communication system based on multicarrier mc code division multiple access cdma we focus on time varying channels for users moving at vehicular speeds the optimal maximum a posteriori map receiver for such a system is prohibitively complex and can be approximated using iterative linear minimum mean square error lmmse multiuser detection and parallel interference cancellation pic for time varying channels two lmmse filters for channel estimation and multiuser detection need to be computed at every time instant making implementation in a real time system difficult we develop a novel low complexity receiver that exploits the multiple antenna structure of the system and performs joint iterative multiuser detection and channel estimation our receiver algorithms are based on the krylov subspace method which solves a linear system with low complexity trading accuracy for efficiency the computational complexity of the channel estimator can be reduced by one order of magnitude for multiuser detection a pic scheme in the user space i e after the matched filter allows simultaneous detection of all users as well as drastic computational complexity reduction by more than one order of magnitude

interference resilient block spreading cdma with minimum mai sequence design code division multiple access cdma schemes based on block spreading implement the spreading of entire data blocks rather than single symbols thus achieving a higher robustness against the frequency selectivity of the channel and allowing the use of efficient modulation equalization schemes operating in the frequency domain fd in this paper we present a new block cdma b cdma system where a single cyclic prefix cp is used at the end of each spread block this provides a higher spectral efficiency with respect to existing schemes by observing that complete orthogonality among users is achievable only for half loaded systems on dispersive channels we introduce new criteria for the design of spreading and despreading sequences which aim at minimizing the mean square error at the output of the despreader for the equalization of the received signal we propose an iterative block decision feedback equalizer which iterates between equalization and decoding equalization filters are designed to minimize the mean square error and take into account the residual interference due to the nonorthogonality of the spreading sequences the performance of b cdma is evaluated in an uplink wireless scenario and compared to existing cdma schemes

blind channel estimation in orthogonally coded mimo ofdm systems a semidefinite relaxation approach a new blind channel estimation approach for orthogonally coded multiple input multiple output orthogonal frequency division multiplexing mimo ofdm systems is proposed the main idea of our technique is using specific properties of the orthogonal space time block codes ostbcs to estimate the finite impulse response fir channel parameters in the time domain instead of doing this in the frequency domain independently for each subcarrier this results in a substantially improved parsimony of the channel parametric model as compared to the direct per subcarrier channel estimation methods and allows coherent processing across the subcarriers it is shown that using the semidefinite relaxation sdr technique our channel estimation problem can be approximated as a convex semidefinite programming sdp problem and hence can be solved efficiently using modern convex optimization methods our simulations validate the performance and or computational complexity advantages of the proposed method as compared to some current state of the art blind mimo ofdm channel estimation methods

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

analysis of the response of a strongly nonlinear damped system using a differential transformation technique the differential transformation technique is applied to solve a nonlinear differential equation that describes the underdamped and the overdamped motion of a system subjected to external excitations numerical results are compared to those obtained by the runge kutta method to illustrate the preciseness and effectiveness of the proposed method

time variant channel estimation using discrete prolate spheroidal sequences we propose and analyze a low complexity channel estimator for a multiuser multicarrier code division multiple access mc cdma downlink in a time variant frequency selective channel mc cdma is based on orthogonal frequency division multiplexing ofdm the time variant channel is estimated individually for every flat fading subcarrier assuming small intercarrier interference the temporal variation of every subcarrier over the duration of a data block is upper bounded by the doppler bandwidth determined by the maximum velocity of the users slepian showed that time limited snapshots of bandlimited sequences span a low dimensional subspace this subspace is also spanned by discrete prolate spheroidal dps sequences we expand the time variant subcarrier coefficients in terms of orthogonal dps sequences we call slepian basis expansion this enables a time variant channel description that avoids the frequency leakage effect of the fourier basis expansion the square bias of the slepian basis expansion per subcarrier is three magnitudes smaller than the square bias of the fourier basis expansion we show simulation results for a fully loaded mc cdma downlink with classic linear minimum mean square error multiuser detection the users are moving with 19 4 m s using the slepian basis expansion channel estimator and a pilot ratio of only 2 we achieve a bit error rate performance as with perfect channel knowledge

adaptive quantization on a grassmann manifold for limited feedback beamforming systems in this paper we examine delay limited adaptive quantization on the grassmann manifold of 1 dimensional subspaces in n dimensional space due to strict delay limits vector quantization over multiple time instants cannot be applied to exploit the temporal correlation of the source signal instead a vector predictive quantizer is proposed that combines prediction and differential quantization algorithms to achieve an efficient quantization of the correlated grassmannian source the proposed predictor is based on adaptive finite impulse response filters to adjust to the temporal statistics of the source signal it is shown that the prediction error in the tangent space associated with the grassmann manifold behaves approximately gaussian provided its norm is sufficiently small the proposed quantization algorithm is applied to channel state information quantization in multi user beamforming wireless communication systems large throughput gains are demonstrated in comparison to memoryless quantization due to reduced multi user interference

lagrange vandermonde mui eliminating user codes for quasi synchronous cdma in unknown multipath a family of codes for low complexity quasi synchronous code division multiple access cdma systems is developed in order to eliminate multiuser interference mui completely in the presence of unknown and even rapidly varying multipath judiciously designed precomputable symbol periodic user codes which we term lagrange or vandermonde and the corresponding linear receivers offer a generalization of orthogonal frequency division multiplexing ofdm which are especially valuable when deep fading carrier frequency errors and doppler effects are present the flexibility inherent to the designed transceivers is exploited to derive transmission strategies that cope with major impairments of wireless cdma channels the symbol periodic code design is also generalized to include the class of aperiodic spreading and orthogonal multirate codes for variable bit rate users performance analysis and simulations results illustrate the advantages of the proposed scheme over competing alternatives

mui free receiver for a synchronous ds cdma system based on block spreading in the presence of frequency selective fading we discuss a synchronous direct sequence code division multiple access ds cdma system based on block spreading in the presence of frequency selective fading note that block spreading which is also known as chip interleaving refers to a spreading of a data block sequence which is obtained by dividing a data symbol sequence into consecutive blocks for such a system we develop a simple new receiver that completely removes the multiuser interference mui without using any channel information the mui free operation is obtained by the use of a shift orthogonal set of code sequences on which this receiver is based within the framework of the mui free receiver we further present a subspace deterministic blind single user channel estimation algorithm as a benchmark for the mui free receiver and the corresponding subspace deterministic blind single user channel estimation algorithm we consider the linear multiuser equalizer and the corresponding subspace deterministic blind multiuser channel estimation algorithm developed by liu and xu 1996 for a standard synchronous ds cdma system in the presence of frequency selective fading we show that the complexity of the mui free receiver using the corresponding subspace deterministic blind single user channel estimation algorithm is much smaller than the complexity of the linear multiuser equalizer using the corresponding subspace deterministic blind multiuser channel estimation algorithm we further show that the performance of the mui free receiver is comparable with the performance of the linear multiuser equalizer this is for the case in which the channels are known as well as for the case in which the channels are estimated with the corresponding subspace deterministic blind channel estimation algorithm

subspace based channel estimation for code division multiple access communication systems we consider the estimation of channel parameters for code division multiple access cdma communication systems operating over channels with either single or multiple propagation paths the multiuser channel estimation problem is decomposed into a series of single user problems through a subspace based approach by exploiting the eigenstructure of the received signal s sample correlation matrix the observation space can be partitioned into a signal subspace and a noise subspace without prior knowledge of the unknown parameters the channel estimate is formed by projecting a given user s spreading waveform into the estimated noise subspace and then either minimizing the likelihood or minimizing the euclidean norm of this projection both of these approaches yield algorithms which are near far resistant and do not require a preamble

a subspace method for signature waveform estimation in synchronous cdma systems synchronous code division multiple access cdma techniques possess intrinsic protection against co channel interference due to orthogonal codes employed and thus offers higher capacity than existing frequency division multiple access fdma or time division multiple access tdma systems in the presence of multipath however each signal is subject to frequency selective fading and the orthogonality condition does not necessarily hold leading to increased cross correlation in these scenarios multiuser detection need to be performed to suppress interference and recover the message symbols to implement such a technique explicit knowledge of the nonorthogonal signature waveforms of all users is required we propose a blind estimation scheme that provides closed form estimates of the signature waveforms by exploiting the structure information of the data output in particular we show that the subspace of the data matrix contains sufficient information for unique determination of the signature waveforms based on this observation a multiple signal classification music like algorithm is derived performance analysis of the new approach is also presented

time varying channel estimation using two dimensional channel orthogonalization and superimposed training in this correspondence a method is presented for estimating double selective channels using superimposed training st the estimator is based on a subspace projection of the time varying channel onto a set of two dimensional orthogonal functions these functions are formed via the outer product of the discrete prolate spheroidal basis vectors and the universal basis vectors this approach allows the channel to be expanded in both the time delay and time dimensions with the fewest parameters when incomplete channel statistics are given this correspondence also provides a theoretical performance analysis of the estimation algorithm and its corroboration via simulations it is shown that this new method provides an enhancement in channel estimation when compared with state of the art approaches

canonical space time processing for wireless communications a canonical space time characterization of mobile wireless channels is introduced in terms of a fixed basis that is independent of the true channel parameters the basis captures the essential degrees of freedom in the received signal using discrete multipath delays doppler shifts and directions of arrival doa the canonical representation provides a robust representation of the propagation dynamics and eliminates the need for estimating delay doppler and doa parameters of different multipaths furthermore it furnishes a natural framework for designing low complexity space time receivers single user receivers based on the canonical channel representation are developed and analyzed it is demonstrated that the resulting canonical space time receivers deliver near optimal performance at substantially reduced complexity compared to existing designs

structural measures for multiplex networks many real world complex systems consist of a set of elementary units connected by relationships of different kinds all such systems are better described in terms of multiplex networks where the links at each layer represent a different type of interaction between the same set of nodes rather than in terms of single layer networks in this paper we present a general framework to describe and study multiplex networks whose links are either unweighted or weighted in particular we propose a series of measures to characterize the multiplexicity of the systems in terms of i basic node and link properties such as the node degree and the edge overlap and reinforcement ii local properties such as the clustering coefficient and the transitivity and iii global properties related to the navigability of the multiplex across the different layers the measures we introduce are validated on a genuinely multiplex data set of indonesian terrorists where information among 78 individuals are recorded with respect to mutual trust common operations exchanged communications and business relationships

measuring the dissimilarity of multiplex networks an empirical study of international trade networks abstract in recent years multiplex networks are becoming a research focus in the domain of complex networks discovering significant correlations between layers in multiplex networks can provide an insight to their structures in this study we propose some methods to measure the dissimilarities of different layers in directed and weighted multiplex networks the dissimilarity is defined on two levels node level and layer level the node dissimilarity is computed based on the distance of the probability distribution of its link weights vectors in different layers and the layer level dissimilarity is the weighted sum of the nodes dissimilarities furthermore the dissimilarity is disintegrated into the connection based dissimilarity and the weight based dissimilarity which represent the topological structure changes and the link weight changes respectively the proposed methods are applied to international trade networks

design and analysis of mmse pilot aided cyclic prefixed block transmissions for doubly selective channels this paper considers affine cyclic prefixed block based pilot aided transmission pat over the single antenna doubly selective channel where the channel is assumed to obey a complex exponential basis expansion model first a tight lower bound on the mean squared error mse of pilot aided channel estimates is derived along with necessary and sufficient conditions on the pilot data pattern that achieves this bound from these conditions novel minimum mse mmse pat schemes are proposed and upper lower bounds on their ergodic achievable rates are derived a pilot data power allocation technique is also developed a high snr asymptotic analysis of the ergodic achievable rate of affine mmse pat is then performed which suggests that the channel s spreading parameters should be taken into account when choosing among affine mmse pat schemes specifically we establish that multicarrier mmse pat achieves higher rates than single carrier mmse pat when the channel s delay spread dominates its doppler spread and vice versa

roast rapid orthogonal approximate slepian transform in this paper we provide a rapid orthogonal approximate slepian transform roast for the discrete vector that one obtains when collecting a finite set of uniform samples from a baseband analog signal the roast offers an orthogonal projection which is an approximation to the orthogonal projection onto the leading discrete prolate spheroidal sequence dpss vectors also known as slepian basis vectors as such the roast is guaranteed to accurately and compactly represent not only oversampled bandlimited signals but also the leading dpss vectors themselves moreover the subspace angle between the roast subspace and the corresponding dpss subspace can be made arbitrarily small the complexity of computing the representation of a signal using the roast is comparable to the fast fourier tranform which is much less than the complexity of using the dpss basis vectors we also give non asymptotic results to guarantee that the proposed basis not only provides a very high degree of approximation accuracy in a mean squared error sense for bandlimited sample vectors but also that it can provide high quality approximations of all sampled sinusoids within the band of interest

random walk centrality in interconnected multilayer networks abstract real world complex systems exhibit multiple levels of relationships in many cases they require to be modeled as interconnected multilayer networks characterizing interactions of several types simultaneously it is of crucial importance in many fields from economics to biology and from urban planning to social sciences to identify the most or the less influent nodes in a network using centrality measures however defining the centrality of actors in interconnected complex networks is not trivial in this paper we rely on the tensorial formalism recently proposed to characterize and investigate this kind of complex topologies and extend two well known random walk centrality measures the random walk betweenness and closeness centrality to interconnected multilayer networks for each of the measures we provide analytical expressions that completely agree with numerically results

taylor series method for solving a class of nonlinear singular boundary value problems arising in applied science abstract taylor series method is applied to a class of nonlinear singular boundary value problems without requiring any specific technique in handling the singularity at the origin for the problems with exponential nonlinearity a variable transformation is introduced to accelerate the convergence of the solution by converting this exponential nonlinearity into a polynomial nonlinearity the efficiency and applicability of the algorithm are assessed and tested on several problems arising in applied science pade approximants are used to verify that the series solutions to these problems converge within the boundaries an error analysis is presented and the results show that the analytical approximate solutions obtained are highly accurate

mc cdma performance evaluation over a multipath fading channel using the characteristic function method this letter presents an efficient and accurate performance evaluation method for binary mc cdma systems with deterministic signature sequences this method is based on a formulation of the characteristic function and does not resort to any assumption on the statistical or spectral behavior of the interference the accuracy of the gaussian approximation method is also considered

analytical study of vibrating systems with strong non linearities by employing saw tooth time transformations abstract a special saw tooth temporal transformation technique is formulated it is simple enough to allow analytical computation of strongly non linear free and forced dynamic responses but at the same time can be applied to the analysis of general classes of non linear problems

a multi step differential transform method and application to non chaotic or chaotic systems the differential transform method dtm is an analytical and numerical method for solving a wide variety of differential equations and usually gets the solution in a series form in this paper we propose a reliable new algorithm of dtm namely multi step dtm which will increase the interval of convergence for the series solution the multi step dtm is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations this new algorithm is applied to lotka volterra chen and lorenz systems then a comparative study between the new algorithm multi step dtm classical dtm and the classical runge kutta method is presented the results demonstrate reliability and efficiency of the algorithm developed

channel estimation in wireless ofdm systems with irregular pilot distribution this paper addresses pilot assisted channel estimation for wireless orthogonal frequency division multiplexing ofdm systems with irregular pilot arrangements using nonuniform sampling techniques we propose a novel channel estimator that is based on conjugate gradient iterations and features very low computational complexity we investigate the impact of the pilot arrangement on the channel estimation mean square error and we provide a heuristic stopping criterion for early termination of the conjugate gradient iterations one dimensional and two dimensional channel estimator implementations and applications of our method to multiple antenna and multiuser ofdm systems are discussed extensive numerical simulations corroborate that the proposed method performs similarly to computationally much more expensive minimum mean square error estimators

robust precoding with bayesian error modeling for limited feedback mu miso systems we consider the robust precoder design for multiuser multiple input single output mu miso systems where the channel state information csi is fed back from the single antenna receivers to the centralized transmitter equipped with multiple antennas we propose to compress the feedback data by projecting the channel estimates onto a vector basis known at the receivers and the transmitter and quantizing the resulting coefficients the channel estimator and the basis for the rank reduction are jointly optimized by minimizing the mean square error mse between the true and the rank reduced csi expressions for the conditional mean and the conditional covariance of the channel are derived which are necessary for the robust precoder design these expressions take into account the following sources of error channel estimation truncation for rank reduction quantization and feedback channel delay as an example for the robust problem formulation vector precoding vp is designed based on the expectation of the mse conditioned on the fed back csi our results show that robust precoding based on fed back csi clearly outperforms conventional precoding designs which do not take into account the errors in the csi

multi access interference suppression in canonical space time coordinates a decentralized approach we propose a decentralized space time multiuser detection scheme based on the notion of canonical space time coordinates cstcs for representing the received signal the cstc representation provides a natural framework for decentralized multi access interference mai suppression in lower dimensional subspaces that results in complexity reduction relative to existing chip rate filtering schemes the framework is based on a partitioning of the signal space into active and inactive cstcs the active cstcs contain the signal of the desired user facilitate maximal diversity exploitation and minimal complexity interference suppression the inactive cstcs only contain mai and can be included progressively to attain a desired level of mai suppression at the cost of increased complexity we develop cstc based linear coherent multiuser detectors using the linearly constrained minimum variance lcmv criterion we characterize the set of inactive coordinates and analyze the performance of the lcmv receiver as a function of the number of inactive cstcs channel estimation and detector sensitivity to channel estimation errors are discussed we demonstrate that the low complexity adaptive receivers designed via the cstc framework are more robust to channel estimation errors than existing chip domain filtering schemes

averaging method using generalized harmonic functions for strongly non linear oscillators abstract an averaging method in which generalized harmonic functions are used is applied to study the approximate solutions of the strongly non linear oscillators g x e x and g x ef x t where g x is an arbitrary non linear function the method gives the approximate solutions in terms of generalized harmonic functions these functions are also periodic and are exact solutions of strongly non linear differential equations some phenomena considered include limit cycles of strongly non linear autonomous oscillators and steady state response of strongly non linear oscillators subject to weak harmonic excitation the procedure is simple and easy to apply

bounds on the interchannel interference of ofdm in time varying impairments in this article tight and universal bounds have been derived for the interchannel interference ici of an orthogonal frequency division multiplexing ofdm signal resulting from doppler spread the universal bound depends only on the product of the maximum doppler frequency and the ofdm symbol duration the tight bound also depends on the variance of the doppler spectrum compared with the exact ici expressions derived by other researchers these bounds are easier to evaluate and can provide useful insight

tensor decompositions and applications this survey provides an overview of higher order tensor decompositions their applications and available software a tensor is a multidimensional or n way array decompositions of higher order tensors i e n way arrays with n geq 3 have applications in psycho metrics chemometrics signal processing numerical linear algebra computer vision numerical analysis data mining neuroscience graph analysis and elsewhere two particular tensor decompositions can be considered to be higher order extensions of the matrix singular value decomposition candecomp parafac cp decomposes a tensor as a sum of rank one tensors and the tucker decomposition is a higher order form of principal component analysis there are many other tensor decompositions including indscal parafac2 candelinc dedicom and paratuck2 as well as nonnegative variants of all of the above the n way toolbox tensor toolbox and multilinear engine are examples of software packages for working with tensors

time frequency transfer function calculus symbolic calculus of linear time varying systems linear operators based on a generalized underspread theory we introduce a generalized concept of underspread linear time varying systems linear operators which contains a previous definition as a special case we show that an existing approximate transfer function calculus symbolic calculus can be extended to this wider and practically more relevant class of underspread operators as a mathematical underpinning of this calculus we establish explicit bounds on various error quantities associated with it the transfer function calculus provides a theoretical basis for various methods recently proposed for nonstationary signal processing and it has important implications in the theory of time varying power spectra

convolutional spreading cdma and comparison with the ds cdma with rake receiver for synchronous downlink direct sequence code division multiple access ds cdma we introduce a cyclic prefix cp based convolutional spreading cdma cs cdma cp scheme employing zero correlation zone zcz codes which gives a class of multiuser interference mui free cdma schemes including suehiro s cdma and block spreading bs cdma as special cases we show that cs cdma cp employing appropriately selected binary and ternary zcz codes have good user capacity peak to average power ratio papr and transmission power loss compared with previously proposed bs cdma schemes by simulation we show the effect of papr to its bit error rate ber performance when nonlinear amplifiers are used and also compare its ber performance with the conventional ds cdma scheme employing a rake receiver

application of a differential transformation method to strongly nonlinear damped q difference equations the theory of approximate solution lacks research on the area of nonlinear q difference equations this article explores the possibility of using the differential transformation method to find an approximate solution for strongly nonlinear damped q difference equations the time response of the nonlinear equation is presented under different parameter conditions and the results are then compared with those derived from the numerical method to verify the accuracy of the proposed method

blind equalization and multiuser detection in dispersive cdma channels the problem of blind demodulation of multiuser information symbols in a high rate code division multiple access cdma network in the presence of both multiple access interference mai and intersymbol interference isi is considered the dispersive cdma channel is first cast into a multiple input multiple output mimo signal model framework by applying the theory of blind mimo channel identification and equalization it is then shown that under certain conditions the multiuser information symbols can be recovered without any prior knowledge of the channel or the users signature waveforms including the desired user s signature waveform although the algorithmic complexity of such an approach is prohibitively high however in practice the signature waveform of the user of interest is always available at the receiver it is shown that by incorporating this knowledge the impulse response of each user s dispersive channel can be identified using a subspace method it is further shown that based on the identified signal subspace parameters and the channel response two linear detectors that are capable of suppressing both mai and isi i e a zero forcing detector and a minimum mean square error mmse detector can be constructed in closed form at almost no extra computational cost data detection can then be furnished by applying these linear detectors obtained blindly to the received signal the major contribution of this paper is the development of these subspace based blind techniques for joint suppression of mai and isi in the dispersive cdma channels

polynomial spline approximation of clarke s model we investigate polynomial spline approximation of stationary random processes on a uniform grid applied to clarke s model of time variations of path amplitudes in multipath fading channels with doppler scattering the integral mean square error mse for optimal and interpolation splines is presented as a series of spectral moments the optimal splines outperform the interpolation splines however as the sampling factor increases the optimal and interpolation splines of even order tend to provide the same accuracy to build such splines the process to be approximated needs to be known for all time which is impractical local splines on the other hand may be used where the process is known only over a finite interval we first consider local splines with quasioptimal spline coefficients then we derive optimal spline coefficients and investigate the error for different sets of samples used for calculating the spline coefficients in practice approximation with a low processing delay is of interest we investigate local spline extrapolation with a zero processing delay the results of our investigation show that local spline approximation is attractive for implementation from viewpoints of both low processing delay and small approximation error the error can be very close to the minimum error provided by optimal splines thus local splines can be effectively used for channel estimation in multipath fast fading channels

a distributional theory for asymptotic expansions the purpose of this chapter is to present the distributional theory of asymptotic expansions for functions of one variable this chapter and the next where the multidimensional expansions are studied are the central part of the book

improvement of a krylov bogoliubov method that uses jacobi elliptic functions abstract an improved version of a krylov bogoliubov method that gives the approximate solution of the non linear cubic oscillator x c 1 x c 3 x 3 ef x x dot 0 in terms of jacobi elliptic functions is described compact general expressions are given for the time derivatives of the amplitude and phase similar to those obtained by the usual krylov bogoliubov method which gives the approximate solution in terms of circular functions these expressions are especially simple for quasilinear c3 0 and quasi pure cubic c1 0 oscillators two types of cubic oscillators have been used as examples the linear damped oscillator f x x dot x dot and the van der pol oscillator f x x dot x 2 x dot the approximate solutions of these quasilinear and quasi pure cubic oscillators are simple and accurate the influence of the non linearity on the rate of variation of the amplitude of these two types of cubic oscillators was also studied

exploring complex networks through random walks most real complex networks such as protein interactions social contacts and the internet are only partially known and available to us while the process of exploring such networks in many cases resembles a random walk it becomes a key issue to investigate and characterize how effectively the nodes and edges of such networks can be covered by different strategies at the same time it is critically important to infer how well can topological measurements such as the average node degree and average clustering coefficient be estimated during such network explorations the present article addresses these problems by considering random barabasi albert ba and geographical network models with varying connectivity explored by three types of random walks traditional preferential to untracked edges and preferential to unvisited nodes a series of relevant results are obtained including the fact that networks of the three studied models with the same size and average node degree allow similar node and edge coverage efficiency the identification of linear scaling with the size of the network of the random walk step at which a given percentage of the nodes edges is covered and the critical result that the estimation of the averaged node degree and clustering coefficient by random walks on ba networks often leads to heavily biased results many are the theoretical and practical implications of such results

analysis of axial vibration of compound bars by differential transformation method although there are solutions for the axial vibration of compound bars i e bars of different cross section connected in mechanical series this note is to illustrate another solution the primary objective is to analyze this problem by a relatively new technique originated in 1986 and known as the differential transformation dt method the numerical solutions are compared with classical exact solution and other studies in the literature the accuracy simplicity and effectiveness of the dt approach are demonstrated

statistics of cycles how loopy is your network we study the distribution of cycles of length h in large networks of size n 1 and find it to be an excellent ergodic estimator even in the extreme inhomogeneous case of scale free networks the distribution is sharply peaked around a characteristic cycle length h n our results suggest that h and the exponent might usefully characterize broad families of networks in addition to an exact counting of cycles in hierarchical nets we present a monte carlo sampling algorithm for approximately locating h and reliably determining our empirical results indicate that for small random scale free nets of degree exponent 1 1 and grows as the nets become larger

sharp estimates for the personalized multiplex pagerank abstract pagerank can be understood as the stationary distribution of a markov chain that occurs in a two layer network with the same set of nodes in both layers the physical layer and the teleportation layer in this paper we present some bounds for the extension of this two layer approach to multiplex networks establishing sharp estimates for this multiplex pagerank and locating the possible values of the personalized pagerank for each node of a network several examples are shown to compare the values obtained for both algorithms the classic and the two layer pagerank

exploring complex networks by walking on them we carry out a comparative study of the problem of a walker searching several typical complex networks the search efficiency is evaluated for various strategies having no knowledge of the global properties of the underlying networks and the optimal path between any two given nodes it is found that the best search strategy is the self avoiding random walk the preferentially self avoiding random walk does not help in improving the search efficiency further in return topological information of the underlying networks may be drawn by comparing the results of the different search strategies

simulation models with correct statistical properties for rayleigh fading channels in this paper new sum of sinusoids statistical simulation models are proposed for rayleigh fading channels these new models employ random path gain random initial phase and conditional random doppler frequency for all individual sinusoids it is shown that the autocorrelations and cross correlations of the quadrature components and the autocorrelation of the complex envelope of the new simulators match the desired ones exactly even if the number of sinusoids is as small as a single digit integer moreover the probability density functions of the envelope and phase the level crossing rate the average fade duration and the autocorrelation of the squared fading envelope which contains fourth order statistics of the new simulators asymptotically approach the correct ones as the number of sinusoids approaches infinity while good convergence is achieved even when the number of sinusoids is as small as eight the new simulators can be directly used to generate multiple uncorrelated fading waveforms for frequency selective fading channels multiple input multiple output channels and diversity combining scenarios statistical properties of one of the new simulators are evaluated by numerical results finding good agreements

on the design of comb spectrum code for multiple access scheme a new methodology that applies frequency orthogonality to the spreading code design has been presented the main purpose is to reduce the receiver complexity of the cyclic prefix code division multiple access cp cdma over the downlink channel and to enable parallel transmission over the uplink channel the receiver complexity has been found for requiring full band fft and ifft calculations in the channel equalizer to handle this problem we developed the comb spectrum codes organized in frequency orthogonal groups in each of which the codes have time correlation orthogonality for the downlink channel the reduction of complexity in signal processing of a cscdma receiver is due to that the separation of groups is simple and each separated group is in the form of a narrower bandwidth cp cdma thus the full band fft and ifft can be replaced by the partial fft and partial ifft as shown in this proposed approach for the uplink channel we assign the code groups to different users to form a group division multiple access gdma for enabling an independent channel equalization of each user at base station the theoretical analysis and the simulation results agree well with each other and both confirm the effectiveness of this approach

space time block coding for doubly selective channels in this paper we present a new space time block code for time and frequency selective doubly selective channels it can be interpreted as the extension of the alamouti code to doubly selective channels and relies on a joint time frequency reversal of the transmitted sequences under certain channel conditions the proposed space time block code belongs to the class that achieves full spatial delay and doppler diversity using a maximum likelihood ml receiver as well as a linear zero forcing lzf or linear minimum mean squared error lmmse receiver for realistic doubly selective channels a real valued linear data model is presented for which different receiver structures can be developed

optimum receivers and low dimensional spreaded modulation for multiuser space time communications the jointly optimum receiver is obtained for multi user communications in a frequency nonselective rayleigh fading channel with n sub t transmit antennas per user and n sub r receive antennas based on a general analysis of quadratic receivers in zero mean complex gaussian vectors asymptotically tight expressions for high signal to noise ratio snr for the pairwise error probabilities are derived subsequently it is shown that n sub t dimensional single user signaling suffices to provide full diversity order n n sub t n sub r for all the users in other words the presence of other users does not increase the minimum dimension required beyond what is needed for the single user space time channel for the special case of low rank code division multiple access cdma signaling with n sub t 1 and provided the signatures of any two users are linearly independent it is shown that the error probability of a k user system asymptotically approaches single user like performance for every user remarkably therefore an increase in the number of users and hence an increase in the aggregate spectral efficiency does not require the users to transmit with more power to achieve single user like performance asymptotically a signal design algorithm is proposed to illustrate this point and examples are given these results are then generalized to the multiple transmit antenna case a new n sub t 1 dimensional signaling strategy is proposed for the multiuser channel that leverages existing single user space time signal designs while ensuring full diversity order and single user like performance asymptotically for every user

channel estimation for ofdma uplink a hybrid of linear and bem interpolation approach we consider the channel estimation for the subband orthogonal frequency division multiple access ofdma uplink the channel for each subband is modeled by combing the linear and fourier basis expansion functions based on this mode a two dimensional interpolation approach is proposed for the channel estimation which is carefully investigated in terms of estimation error and pilot placement

on doubly selective channel estimation using superimposed training and discrete prolate spheroidal sequences channel estimation and data detection for frequency selective time varying channels are considered using superimposed training we employ a discrete prolate spheroidal basis expansion model dps bem to describe the time varying channel a periodic nonrandom training sequence is arithmetically added superimposed at low power to the information sequence at the transmitter before modulation and transmission therefore there is no loss in data transmission rate compared to time multiplexed tm training we first estimate the channel using dps bem and only the first order statistics of the observations in this estimator the unknown information sequence acts as interference resulting in a poor signal to noise and interference ratio snir for channel estimation we then apply a data dependent superimposed training sequence to either totally or partially cancel out the effects of the unknown information sequence at the receiver on channel estimation in total cancellation at certain frequencies the information bearing components are nulled to compensate for this information loss we investigate a partially data dependent pdd superimposed training scheme where a tradeoff is made between interference cancellation and frequency integrity design of certain parameters for pdd superimposed training is also investigated finally a deterministic maximum likelihood dml approach is used iteratively to enhance channel estimation and data detection computer simulation examples show that the proposed approaches are competitive with the conventional tm training without incurring data rate loss

chip interleaved block spread code division multiple access a novel multiuser interference mui free code division multiple access cdma transceiver for frequency selective multipath channels is developed relying on chip interleaving and zero padded transmissions orthogonality among different users spreading codes is maintained at the receiver even after frequency selective propagation as a result deterministic multiuser separation with low complexity code matched filtering becomes possible without loss of maximum likelihood optimality in addition to mui free reception the proposed system guarantees channel irrespective symbol detection and achieves high bandwidth efficiency by increasing the symbol block size filling the zero gaps with known symbols allows for perfectly constant modulus transmissions important variants of the proposed transceivers are derived to include cyclic prefixed transmissions and various redundant or nonredundant precoding alternatives semi blind channel estimation algorithms are also discussed simulation results demonstrate improved performance of the proposed system relative to competing alternatives

application of the differential transformation method to the solution of a damped system with high nonlinearity abstract this paper employs the differential transformation method to investigate the response of a damped system with high nonlinearity the accuracy and validity of the proposed method are demonstrated through its application to the solution of a dynamic system with various values of power form nonlinearity the numerical results indicate that the amplitude decays more rapidly at higher values of nonlinearity particularly at higher values of the damping coefficient it is shown that the current results are in excellent agreement with those provided by the runge kutta method therefore the method presented in this study provides an effective scheme for determining the solutions of a damped vibration problem with high nonlinearity

inverse methods for reconstruction of channel taps in ofdm systems we describe a novel pilot aided method for estimation of doubly selective wireless channels in ofdm systems we compute the first few fourier coefficients of each channel tap from the pilot information we then estimate the bem coefficients of the channel taps from their respective fourier coefficients using a recently developed inverse reconstruction method for a system with l channel taps the proposed method uses o l log l operations and o l memory per ofdm symbol we validate our method by simulating a system conforming to the ieee 802 16e standard

on circularity circularity is an assumption that was originally introduced for the definition of the probability distribution function of complex normal vectors however this concept can be extended in various ways for nonnormal vectors the first purpose of the paper is to introduce and compare some possible definitions of circularity from these definitions it is also possible to introduce the concept of circular signals and to study whether or not the spectral representation of stationary signals introduces circular components therefore the relationships between circularity and stationarity are analyzed in detail finally the theory of linear mean square estimation for complex signals exhibits some connections with circularity and it is shown that without this assumption the estimation theory must be reformulated

nondata aided joint channel estimation and equalization for ofdm systems in very rapidly varying mobile channels this paper is concerned with the challenging and timely problem of joint channel estimation and equalization for orthogonal frequency division multiplexing ofdm systems in the presence of frequency selective and very rapidly time varying channels the resulting algorithm is based on the space alternating generalized expectation maximization maximum a posteriori probability sage map technique which is particularly well suited to multicarrier signal formats the algorithm is implemented in the time domain which enables one to use the gaussian approximation of the transmitted ofdm samples consequently the averaging process of the nonpilot data symbols becomes analytically possible resulting in a feasible and computationally efficient channel estimation algorithm leading to a receiver structure that yields also an equalized output from which the data symbols are detected with excellent symbol error rate ser performance based on this gaussian approximation the exact bayesian cramer rao lower bound crlb as well as the convergence rate of the algorithm are derived analytically to reduce the computational complexity of the algorithm discrete legendre orthogonal basis functions are employed to represent the rapidly time varying fading channel it is shown that depending on the normalized doppler frequency only a small number of expansion coefficients is sufficient to approximate the channel very well and there is no need to know the correlation function of the input signal the computational complexity of the algorithm is shown to be o nl per detected data symbol and per sage map algorithm cycle where is the number of ofdm subcarriers and is the number of multipath components

two dimensional differential transform for partial differential equations the differential transform is a numerical method for solving differential equations in this paper we present the definition and operation of the two dimensional differential transform a distinctive feature of the differential transform is its ability to solve linear and nonlinear differential equations partial differential equation of parabolic hyperbolic elliptic and nonlinear types can be solved by the differential transform we demonstrate that the differential transform is a feasible tool for obtaining the analytic form solutions of linear and nonlinear partial differential equation

a unified analysis for coded ds cdma with equal gain chip combining in the downlink of ofdm systems this paper presents a novel unified analysis for the bit error rate in the downlink of convolutionally coded and single user detected multicarrier code division multiple access cdma multicarrier direct sequence cdma time and frequency domain spreading cdma and orthogonal frequency division multiple access performance is analyzed under the assumption of hadamard spreading codes equal gain chip combining and a highly correlated frequency selective rayleigh fading channel closed form expressions are presented for the cumulative distribution function probability distribution function and moment generating function for the signal to noise plus interference ratio after despreading the presented results assume error free channel estimates a perfectly synchronized receiver and are found to reasonably well agree with simulation results

orthogonal multiple access over time and frequency selective channels suppression of multiuser interference mui and mitigation of time and frequency selective doubly selective channel effects constitute major challenges in the design of third generation wireless mobile systems relying on a basis expansion model bem for doubly selective channels we develop a channel independent block spreading scheme that preserves mutual orthogonality among single cell users at the receiver this alleviates the need for complex multiuser detection and enables separation of the desired user by a simple code matched channel independent block despreading scheme that is maximum likelihood ml optimal under the bem plus white gaussian noise assumption on the channel in addition each user achieves the maximum delay doppler diversity for gaussian distributed bem coefficients issues like links with existing multiuser transceivers existence user efficiency special cases backward compatibility with direct sequence code division multiple access ds cdma and error control coding are briefly discussed

discrete multiple tone modulation with coset coding for the spectrally shaped channel a discrete approach to multiple tone modulation is developed for digital communication channels with arbitrary intersymbol interference isi and additive gaussian noise multiple tone modulation is achieved through the concatenation of a finite block length modulator based on discrete fourier transform dft code vectors and high gain coset or trellis codes symbol blocks from an inverse dft idft are cyclically extended to generate isi free channel output symbols that decompose the channel into a group of orthogonal and independent parallel subchannels asymptotic performance of this system is derived and examples of asymptotic and finite block length coding gain performance for several channels are evaluated at different values of bits per sample this discrete multiple tone technique is linear in both the modulation and the demodulation and is free from the effects of error propagation that often afflict systems employing bandwidth optimized decision feedback plus coset codes

doubly selective channel estimation using exponential basis models and subblock tracking three versions of a novel adaptive channel estimation approach exploiting the over sampled complex exponential basis expansion model ce bem is presented for doubly selective channels where we track the bem coefficients rather than the channel tap gains since the time varying nature of the channel is well captured in the ce bem by the known exponential basis functions the time variations of the unknown bem coefficients are likely much slower than those of the channel and thus more convenient to track we propose a subblockwise tracking scheme for the bem coefficients using time multiplexed tm periodically transmitted training symbols three adaptive algorithms including a kalman filtering scheme based on an assumed autoregressive ar model of the bem coefficients and two recursive least squares rls schemes not requiring any model for the bem coefficients are investigated for bem coefficient tracking simulation examples illustrate the superior performance of our approach over several existing doubly selective channel estimators

minimum energy band limited predictor with dynamic subspace selection for time variant flat fading channels in this paper we develop and analyze the basic methodology for minimum energy me band limited prediction of sampled time variant flat fading channels this predictor is based on a subspace spanned by time concentrated and band limited sequences the time concentration of these sequences is matched to the length of the observation interval and the band limitation is determined by the support of the doppler power spectral density of the fading process slepian showed that discrete prolate spheroidal dps sequences can be used to calculate the me band limited continuation of a finite sequence we utilize this property to perform channel prediction we generalize the concept of time concentrated and band limited sequences to a band limiting region consisting of disjoint intervals for a fading process with constant spectrum over its possibly discontiguous support we prove that the me band limited predictor is identical to a reduced rank maximum likelihood predictor which is a close approximation of a wiener predictor in current cellular communication systems the time selective fading process is highly oversampled the essential dimension of the subspace spanned by time concentrated and band limited sequences is in the order of two to five only the prediction error mainly depends on the support of the doppler spectrum we exploit this fact to propose low complexity time variant flat fading channel predictors using dynamically selected predefined subspaces the subspace selection is based on a probabilistic bound on the reconstruction error we compare the performance of the me band limited predictor with a predictor based on complex exponentials for a prediction horizon of one eights of a wavelength the numerical simulation results show that the me band limited predictor with dynamic subspace selection performs better than or similar to a predictor based on complex exponentials with perfectly known frequencies for a prediction horizons of three eights of a wavelength the performance of the me band limited predictor approaches that of a wiener predictor with perfectly known doppler bandwidth

fundamental limits of linear equalizers diversity capacity and complexity linear equalizers les have been widely adopted for practical systems due to their low computational complexity however it is also well known that les provide inferior performance relative to a maximum likelihood equalizer mle or other near mles because les usually cannot collect the diversity order enabled by the transmitter and at the same time they lose mutual information more importantly unlike mle or near mles the performance of les has not been well quantified this hinders more general applications of les in wireless systems in this paper we reveal a fundamental link between a channel parameter orthogonality deficiency od of the channel matrix and the diversity and capacity of les we identify that when the od of channel matrix has an upper bound strictly less than 1 the same diversity order as that of mles is collected by les and the outage capacity loss relative to mles is also a constant over signal to noise ratio snr these results can be applied to designing a framework for hybrid equalizers furthermore by studying the statistical properties of the od and comparing the complexity of different equalizers we show that hybrid equalizers can trade off between performance and complexity by tuning the channel matrix od the theoretical analysis is corroborated by computer simulations

frequency selective fading channel estimation with a polynomial time varying channel model a rectangular windowed least squares estimator using a polynomial model of the time varying channel taps is proposed for estimating the impulse response of a frequency selective fading channel this method provides a significant improvement in mean square identification error msie over the conventional least mean squares lms and the exponentially weighted recursive least squares ew rls algorithms without a polynomial model a detailed study of the effects of channel parameters such as the fading rate and the signal to noise ratio on the proposed method is carried out the performance of the method depends on the window size of the least squares estimator and the polynomial order being used algorithms to obtain the approximately optimal window size and polynomial order are proposed and are shown to perform well

low complexity equalization of time varying channels with precoding this correspondence deals with time varying tv single input multiple output simo channels which are both frequency selective due to high data rate and time selective due to mobility a complex exponential basis expansion model ce bem is used to model the channel we consider a block transmission system where on the transmit side a precoder is employed to enable the maximum available diversity for a ce bem channel after direct decoding on the receive side the resulting channel resembles a finite impulse response fir filter on both block and symbol level we therefore propose an equalizer that bears a structure analogous to the effective channel in comparison with a standard block minimum mean square error decision feedback equalizer bmmse dfe that involves the inversion of a large size matrix the proposed parametric equalizer renders a similar performance but at a lower computational cost if there are multiple outputs present another contribution of this correspondence is a semiblind algorithm to estimate this equalizer when the channel state information is not available the equalizer taps and the information symbol estimates are refined recursively by means of normalized least mean squares nlms adaptation

low complexity equalization for doubly selective channels modeled by a basis expansion we propose a novel equalization method for doubly selective wireless channels whose taps are represented by an arbitrary basis expansion model bem we view such a channel in the time domain as a sum of product convolution operators created from the basis functions and the bem coefficients equivalently a frequency domain channel can be represented as a sum of convolution products the product convolution representation provides a low complexity memory efficient way to apply the channel matrix to a vector we compute a regularized solution of a linear system involving the channel matrix by means of the gmres and the lsqr algorithms which utilize the product convolution structure without ever explicitly creating the channel matrix our method applies to all cyclic prefix transmissions in an ofdm transmission with k subcarriers each iteration of gmres or lsqr requires only o k k flops and o k memory additionally we further accelerate convergence of both gmres and lsqr by using the single tap equalizer as a preconditioner we validate our method with numerical simulations of a wimax like system ieee 802 16e in channels with significant delay and doppler spreads the proposed equalizer achieves bers comparable to those of mmse equalization and noticeably outperforms low complexity equalizers using an approximation by a banded matrix in the frequency domain with preconditioning the lowest bers are obtained within 3 16 iterations our approach does not use any statistical information about the wireless channel