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

global target aggregation and state agreement of nonlinear multi agent systems with switching topologies in this paper we discuss coordination problems of a group of autonomous agents including the target aggregation to a convex set and the state agreement the aggregation of the whole agent group consisting of leaders informed agents and followers to a given set is investigated with switching interconnection topologies described by the connectivity assumptions on the joint topology in the time interval t for any time t and then the state agreement problem is studied in a similar way an approach based on set stability and limit set analysis is given to study the multi agent convergence problems with the help of graph theory and convex analysis coordination conditions are obtained in some important cases and the results show that simple local rules can make the networked agents with first order nonlinear individual dynamics achieve desired collective behaviors

rank revealing qr factorizations abstract an algorithm is presented for computing a column permutation pi and a qr factorization a pi qr of an m by n m or n matrix a such that a possible rank deficiency of a will be revealed in the triangular factor r having a small lower right block for low rank deficient matrices the algorithm is guaranteed to reveal the rank of a and the cost is only slightly more than the cost of one regular qr factorization a posteriori upper and lower bounds on the singular values of a are derived and can be used to infer the numerical rank of a keywords qr factorization rank deficient matrices least squares computation subset selection rank singular values

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

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

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

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

distributed continuous time convex optimization on weight balanced digraphs this technical note studies the continuous time distributed optimization of a sum of convex functions over directed graphs contrary to what is known in the consensus literature where the same dynamics works for both undirected and directed scenarios we show that the consensus based dynamics that solves the continuous time distributed optimization problem for undirected graphs fails to converge when transcribed to the directed setting this study sets the basis for the design of an alternative distributed dynamics which we show is guaranteed to converge on any strongly connected weight balanced digraph to the set of minimizers of a sum of convex differentiable functions with globally lipschitz gradients our technical approach combines notions of invariance and cocoercivity with the positive definiteness properties of graph matrices to establish the results

maximizing bilinear forms subject to linear constraints abstract we present methods for maximizing a bilinear form x t ay x y or its absolute value subject to linear constraints the constraints are either of the form c x d g y h or of the form c x e r d g y e r h where r d and r h represent the column spaces of matrices d and h we also show how to compute the angle between two subspaces of r m subject to these types of linear constraints and how to compute linearly constrained canonical correlations and the corresponding canonical vectors

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

continuous time penalty methods for nash equilibrium seeking of a nonsmooth generalized noncooperative game in this paper we propose centralized and distributed continuous time penalty methods to find a nash equilibrium for a generalized noncooperative game with shared inequality and equality constraints and private inequality constraints that depend on the player itself by using the l 1 penalty function we prove that the equilibrium of a differential inclusion is a normalized nash equilibrium of the original generalized noncooperative game and the centralized differential inclusion exponentially converges to the unique normalized nash equilibrium of a strongly monotone game suppose that the players can communicate with their neighboring players only and the communication topology can be represented by a connected undirected graph based on a leader following consensus scheme and singular perturbation techniques we propose distributed algorithms by using the exact l 1 penalty function and the continuously differentiable squared l 2 penalty function respectively the squared l 2 penalty function method works for games with smooth constraints and the exact l 2 penalty function works for certain scenarios the proposed two distributed algorithms converge to an neighborhood of the unique normalized nash equilibrium and an neighborhood of an approximated nash equilibrium respectively with being a positive constant for each 0 and each initial condition there exists an varepsilon such that for each 0 varepsilon varepsilon the convergence can be guaranteed where varepsilon is a parameter in the algorithm

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

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

approximate projected consensus for convex intersection computation convergence analysis and critical error angle in this paper we study an approximate projected consensus algorithm for a network to cooperatively compute the intersection of convex sets where each set corresponds to one network node instead of assuming exact convex projection that each node can compute we allow each node to compute an approximate projection with respect to its own set after receiving the approximate projection information nodes update their states by weighted averaging with the neighbors over a directed and time varying communication graph the approximate projections are related to projection angle errors which introduces state dependent disturbance in the iterative algorithm projection accuracy conditions are presented for the considered algorithm to converge the results indicate how much projection accuracy is required to ensure global consensus to a point in the intersection set when the communication graph is uniformly jointly strongly connected in addition we show that pi 4 is a critical angle for the error of the projection approximation to ensure the boundedness finally the results are illustrated by simulations

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

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

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

distributed optimization for linear multiagent systems edge and node based adaptive designs this paper studies the distributed optimization problem for continuous time multiagent systems with general linear dynamics the objective is to cooperatively optimize a team performance function formed by a sum of convex local objective functions each agent utilizes only local interaction and the gradient of its own local objective function to achieve the cooperative goal a couple of fully distributed optimal algorithms are designed first an edge based adaptive algorithm is developed for linear multiagent systems with a class of convex local objective functions then a node based adaptive algorithm is constructed to solve the distributed optimization problem for a class of agents satisfying the bounded input bounded state stable property sufficient conditions are given to ensure that all agents reach a consensus while minimizing the team performance function finally numerical examples are provided to illustrate the theoretical results

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

canonical analysis relative to a closed subspace first a maximum coefficient notion between two real closed hilbertian subspaces relative to a third one is given many examples illustrate the study when the third subspace is trivial or not then a relative canonical analysis between two closed subspaces relative to a third one is introduced it leads to relative or partial association measures and allows a notion of relative information between subspaces

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

second order leader following consensus of nonlinear multi agent systems via pinning control abstract without assuming that the interaction diagraph is strongly connected or contains a directed spanning tree this paper studies the second order leader following consensus problem of nonlinear multi agent systems with general network topologies based on graph theory matrix theory and lasalle s invariance principle a pinning control algorithm is proposed to achieve leader following consensus in a network of agents with nonlinear second order dynamics furthermore a pinning consensus protocol is developed for coupled double integrators with a constant reference velocity in particular this paper addresses what kind of agents and how many agents should be pinned and establishes some sufficient conditions to guarantee that all agents asymptotically follow the virtual leader numerical simulations are given to verify the theoretical analysis

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

constrained consensus and optimization in multi agent networks we present distributed algorithms that can be used by multiple agents to align their estimates with a particular value over a network with time varying connectivity our framework is general in that this value can represent a consensus value among multiple agents or an optimal solution of an optimization problem where the global objective function is a combination of local agent objective functions our main focus is on constrained problems where the estimates of each agent are restricted to lie in different convex sets to highlight the effects of constraints we first consider a constrained consensus problem and present a distributed projected consensus algorithm in which agents combine their local averaging operation with projection on their individual constraint sets this algorithm can be viewed as a version of an alternating projection method with weights that are varying over time and across agents we establish convergence and convergence rate results for the projected consensus algorithm we next study a constrained optimization problem for optimizing the sum of local objective functions of the agents subject to the intersection of their local constraint sets we present a distributed projected subgradient algorithm which involves each agent performing a local averaging operation taking a subgradient step to minimize its own objective function and projecting on its constraint set we show that with an appropriately selected stepsize rule the agent estimates generated by this algorithm converge to the same optimal solution for the cases when the weights are constant and equal and when the weights are time varying but all agents have the same constraint set

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

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

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

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

a generalization of the eckart young mirsky matrix approximation theorem abstract the eckart young mirsky theorem solves the problem of approximating a matrix by one of lower rank however the approximation generally differs from the original in all its elements in this paper it is shown how to obtain a best approximation of lower rank in which a specified set of columns of the matrix remains fixed the paper concludes with some applications of the generalization

gossip algorithms for convex consensus optimization over networks in many applications nodes in a network desire not only a consensus but an optimal one to date a family of subgradient algorithms have been proposed to solve this problem under general convexity assumptions this technical note shows that for the scalar case and by assuming a bit more novel non gradient based algorithms with appealing features can be constructed specifically we develop pairwise equalizing pe and pairwise bisectioning pb two gossip algorithms that solve unconstrained separable convex consensus optimization problems over undirected networks with time varying topologies where each local function is strictly convex continuously differentiable and has a minimizer we show that pe and pb are easy to implement bypass limitations of the subgradient algorithms and produce switched nonlinear networked dynamical systems that admit a common lyapunov function and asymptotically converge moreover pe generalizes the well known pairwise averaging and randomized gossip algorithm while pb relaxes a requirement of pe allowing nodes to never share their local functions

canonical correlation analysis with linear constraints abstract we develop canonical correlation analysis by imposing linear constraints upon parameters corresponding to two sets of variables the results of our method which we call canolc are shown in terms of projection operators both orthogonal and oblique further calc correspondence analysis with linear constraints turns out to be a special case of canolc

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

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

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

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

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

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

agreeing asynchronously this paper formulates and solves a version of the widely studied vicsek consensus problem in which each member of a group of n 1 agents independently updates its heading at times determined by its own clock it is not assumed that the agents clocks are synchronized or that the ldquoeventrdquo times between which any one agent updates its heading are evenly spaced nor is it assumed that heading updates must occur instantaneously using the concept of ldquoanalytic synchronizationrdquo together with several key results concerned with properties of ldquocompositionsrdquo of directed graphs it is shown that the conditions under which a consensus is achieved are essentially the same as those applicable in the synchronous case provided the notion of an agent s neighbor between its event times is appropriately defined however in sharp contrast with the synchronous case where for analysis an n dimensional state space model is adequate for the asynchronous version of the problem a 2n dimensional state space model is required it is explained how to analyze this model despite the fact that unlike the synchronous case the stochastic matrices involved do not have all positive diagonal entries

distributed adaptive convex optimization on directed graphs via continuous time algorithms this note considers the distributed optimization problem on directed graphs with nonconvex local objective functions and the unknown network connectivity a new adaptive algorithm is proposed to minimize a differentiable global objective function by introducing dynamic coupling gains and updating the coupling gains using relative information of system states the nonconvexity of local objective functions unknown network connectivity and the uncertain dynamics caused by locally lipschitz gradients are tackled concurrently consequently the global asymptotic convergence is established when the global objective function is strongly convex and the gradients of local objective functions are only locally lipschitz when the communication graph is strongly connected and weight balanced the algorithm is independent of any global information then the algorithm is naturally extended to unbalanced directed graphs by using the left eigenvector of the laplacian matrix associated with the zero eigenvalue several numerical simulations are presented to verify the results

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

perturbation analysis of the canonical correlations of matrix pairs abstract we present a perturbation analysis of the canonical correlations of matrix pairs absolute perturbation bounds for normwise as well as componentwise perturbations are derived we demonstrate by way of examples that small relative perturbation of a matrix pair does not necessarily imply small relative perturbation in its canonical correlations and we identify a class of matrix pairs for which good relative perturbation bounds can be derived under certain conditions

reaching an optimal consensus dynamical systems that compute intersections of convex sets in this paper multi agent systems minimizing a sum of objective functions where each component is only known to a particular node is considered for continuous time dynamics with time varying interconnection topologies assuming that each node can observe a convex solution set of its optimization component and the intersection of all such sets is nonempty the considered optimization problem is converted to an intersection computation problem by a simple distributed control rule the considered multi agent system with continuous time dynamics achieves not only a consensus but also an optimal agreement within the optimal solution set of the overall optimization objective directed and bidirectional communications are studied respectively and connectivity conditions are given to ensure a global optimal consensus in this way the corresponding intersection computation problem is solved by the proposed decentralized continuous time algorithm we establish several important properties of the distance functions with respect to the global optimal solution set and a class of invariant sets with the help of convex and non smooth analysis

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

distributed finite time tracking of multiple non identical second order nonlinear systems with settling time estimation this paper investigates the distributed finite time consensus tracking problem for a group of autonomous agents modeled by multiple non identical second order nonlinear systems first a class of distributed finite time protocols are proposed based on the relative position and relative velocity measurements by providing a topology dependent lyapunov function it is shown that distributed consensus tracking can be achieved in finite time under the condition that the nonlinear errors between the leader and the followers are bounded then a new class of observer based algorithms are designed to solve the finite time consensus tracking problem without using relative velocity measurements the main contribution of this paper is that by computing the value of the lyapunov function at the initial point the finite settling time can be theoretically estimated for second order multi agent systems with the proposed control protocols finally the effectiveness of the analytical results is illustrated by an application in low earth orbit spacecraft formation flying

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

lyapunov stability theory of nonsmooth systems this paper develops nonsmooth lyapunov stability theory and lasalle s invariance principle for a class of nonsmooth lipschitz continuous lyapunov functions and absolutely continuous state trajectories computable tests based on filipov s differential inclusion and clarke s generalized gradient are derived the primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control

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