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

asymptotic models for curved rods derived from nonlinear elasticity by gamma convergence we study the problem of the rigorous derivation of one dimensional models for a thin curved beam starting from three dimensional nonlinear elasticity we describe the limiting models obtained for different scalings of the energy in particular we prove that the limit functional corresponding to higher scalings coincides with the one derived by dimension reduction starting from linearized elasticity finally we also address the case of thin elastic rings

on the commutability of homogenization and linearization in finite elasticity we consider a family of non convex integral functionals frac 1 h 2 int omega w x varepsilon rm id h nabla g x rm d x quad g in w 1 p omega mathbb r n where w is a caratheodory function periodic in its first variable and non degenerate in its second we prove under suitable conditions that the limits corresponding to linearization h 0 and homogenization varepsilon rightarrow 0 commute provided w is minimal at the identity and admits a quadratic taylor expansion at the identity moreover we show that the homogenized integrand which is determined by a multi cell homogenization formula has a quadratic taylor expansion with a quadratic term that is given by the homogenization of the second variation of w

derivation of homogenized euler lagrange equations for von karman rods in this paper we study the effects of simultaneous homogenization and dimension reduction in the context of convergence of stationary points for thin nonhomogeneous rods under the assumption of the von karman scaling assuming stationarity conditions for a sequence of deformations close to a rigid body motion we prove that the corresponding sequences of scaled displacements and twist functions converge to a limit point which is the stationary point of the homogenized von karman rod model the analogous result holds true for the von karman plate model

a strictly contractive peaceman rachford splitting method with logarithmic quadratic proximal regularization for convex programming recently a strictly contractive peaceman rachford splitting method prsm was proposed for a separable convex minimization model whose variables are subject to some linear constraints and two additional generic constraints in general the strictly contractive prsm requires to solve two constrained minimization subproblems at each iteration in this paper we consider the case where the additional constraints on variables are positive orthants and apply the well developed logarithmic quadratic proximal lqp regularization to regularize the subproblems of the strictly contractive prsm a new algorithm in combination with the strictly contractive prsm and the lqp regularization is thus proposed the new algorithm only needs to solve two unconstrained subproblems at each iteration an inexact version allowing the unconstrained subproblems to be solved approximately subject to certain inexactness criterion is also studied we prove the global convergence and establish a worst case convergence rate measured

a hierarchy of plate models derived from nonlinear elasticity by gamma convergence we derive a hierarchy of plate models from three dimensional nonlinear elasticity by convergence what distinguishes the different limit models is the scaling of the elastic energy per unit volume h where h is the thickness of the plate this is in turn related to the strength of the applied force h membrane theory derived earlier by le dret and raoult corresponds to 0 nonlinear bending theory to 2 von karman theory to 3 4 and linearized vk theory to 3 intermediate values of lead to certain theories with constraints a key ingredient in the proof is a generalization to higher derivatives of our rigidity result 29 which states that for maps v 0 1 3 3 the l2 distance of v from a single rotation is bounded by a multiple of the l2 distance from the set so 3 of all rotations

solving a class of optimum multiuser detection problems with polynomial complexity we identify a class of optimum multiuser detection problems which can be solved with polynomial complexity in the number of users the identification is based on transforming a quadratic 0 1 programming problem into an equivalent problem in graph theory for a synchronous direct sequence code division multiple access cdma system the result translates to designing a set of pseudorandom codes with the property that the cross correlation between every pair of codes in the set over one symbol period is nonpositive we give two sets of codes with good correlation properties that fall within this class finally we derive a bound on the cardinality of a signal set in an n dimensional space having the property that the cross correlation between every pair of signals in the set is nonpositive

saint venant s problem and semi inverse solutions in nonlinear elasticity saint venant s problem consists in finding elastic deformations of an infinite prismatic body taking given values for the cross sectional resultants of force and moment using the center manifold approach we show that all deformations having sufficiently small bounded strains lie on a finite dimensional manifold in particular the flow on this manifold is described by a set of equations having exactly the form of the classical rod equations moreover the set of semi inverse solutions can be analyzed locally

a block alternating likelihood maximization approach to multiuser detection in this paper we address the maximum likelihood ml multiuser detection problem for asynchronous code division multiple access cdma systems with multiple receiver antennas in frequency selective fading environments multiuser ml detection mld in this case provides attractive symbol error performance but it requires the solution of a large scale combinatorial optimization problem to deal with the computational complexity of this problem we propose an efficient approximation method based on a block alternating likelihood maximization balm principle the idea behind balm is to decompose the large scale mld problem into smaller subproblems assuming binary or quaternary phase shift keying bpsk or qpsk which are often employed in cdma the combinatorial subproblems are then accurately and efficiently approximated by the semidefinite relaxation sdr algorithm an algorithm that has been recently shown to lead to quasi ml performance in synchronous cdma scenarios simulation results indicate that this balm detector provides close to optimal bit error rate ber performance the balm principle is quite flexible and we demonstrate this flexibility by extending balm to multicarrier mc multiuser systems by exploiting the special signal correlation structure of mc systems we develop a variation of balm in which dynamic programming dp is used to solve the subproblems it is shown using simulations that the ber performance of this dp based balm detector is as promising as that of the sdr based balm detector

cdma multiuser detection a nonlinear programming approach the optimum receiver to detect the bits of multiple code division multiple access cdma users has an exponential complexity in the number of active users in the system consequently many suboptimum receivers have been developed to achieve good performance with less complexity we take the approach of approximating the solution of the optimum multiuser detection problem omud using nonlinear programming relaxations first we observe that some popular suboptimum receivers indeed correspond to relaxations of the optimal detection problem in particular one proposed approximation method yields to iterative solutions which correspond to previously proposed heuristic nonlinear detectors using a nonlinear programming approach we identify the convergence properties of these iterative detectors secondly we propose a relaxation that yields a receiver which we call the generalized minimum mean squared error detector we give a simple iterative implementation of the detector its performance is evaluated and comparisons to other suboptimum detection schemes are given

a theorem on geometric rigidity and the derivation of nonlinear plate theory from three dimensional elasticity the energy functional of nonlinear plate theory is a curvature functional for surfaces rst proposed on physical grounds by g kirchhoff in 1850 we show that it arises as a 0 limit of three dimensional nonlinear elasticity theory as the thickness of a plate goes to zero a key ingredient in the proof is a sharp rigidity estimate for maps v v u r n u r n we show that the l 2 distance of rv from a single rotation matrix is bounded by a multiple of the l 2 distance from

near optimum tree search detection schemes for bit synchronous multiuser cdma systems over gaussian and two path rayleigh fading channels simple reduced tree search detection schemes of the breadth first type are applied to suboptimal joint multiuser detection in bit synchronous code division multiple access cdma systems over both gaussian and two path rayleigh fading channels it is pointed out that in contrast to the case of the optimal multiuser detector the choice of the receiver filter severely influences the performance of suboptimal multiuser detectors simulation results supported by analysis show that breadth first tree search algorithms using a decorrelating noise whitening receiver filter perform better than similar receivers which solely use a matched filter mf for virtually all nonsingular spreading code sets studied most of the code sets are randomly generated the m and t algorithm detectors based on decorrelating noise whitening filter wf outputs can achieve near optimum performance at a very low complexity compared to the optimal detector although the proposed detectors are more complex than some known suboptimum detectors furthermore the use of combining techniques is considered for a two path rayleigh fading channel and a semi synchronous cdma structure is proposed it is shown that if maximum ratio combining mrc is employed the decorrelating noise wf still exists the corresponding suboptimal combining detector with a decorrelating noise wf outperforms a similar noncombining detector

a maximum likelihood digital receiver using coordinate ascent and the discrete wavelet transform in this paper a maximum likelihood ml method is presented for joint estimation of amplitude phase time delay and data symbols in a single user direct sequence spread spectrum communication system since maximization of the likelihood function is analytically intractable a novel coordinate ascent algorithm is used to obtain sequential updates of the data symbols and all unknown nuisance parameters the novelty of the algorithm is due to the use of a multiresolution expansion of the received signal and the use of polynomial rooting in the complex plane in place of a line search over the signal delay parameter the multiresolution structure of the algorithm is exploited to reduce sensitivity to impulsive noise via wavelet thresholding computer simulations of the single user system show that the algorithm has fast convergence and comparison with theoretical lower bounds establishes that the algorithm achieves nearly optimal error performance

a new approach to greedy multiuser detection we propose a new suboptimum multiuser detector for synchronous and asynchronous multiuser communications in this approach a greedy strategy is used to maximize the cost function the maximum likelihood ml metric the coefficients of the ml metric are utilized as weights indicating in which order bits can be estimated the complexity of the algorithm is approximately k sup 2 log k per bit where k is the number of users we analyze the performance of the greedy multiuser detection in the additive white gaussian noise channel as well as in the frequency nonselective rayleigh fading channel and compare it with the optimum detector and several suboptimum schemes such as conventional successive interference cancellation decorrelator sequential and multistage detectors the proposed greedy approach considerably outperforms these suboptimum schemes especially for moderate and high loads in low and moderate signal to noise ratio regions the results show that when there is a significant imbalance in the values of the coefficients of the ml metric due to moderate to high noise fading and asynchronous transmission near optimum performance is achieved by the greedy detection

closest point search in lattices in this semitutorial paper a comprehensive survey of closest point search methods for lattices without a regular structure is presented the existing search strategies are described in a unified framework and differences between them are elucidated an efficient closest point search algorithm based on the schnorr euchner 1995 variation of the pohst 1981 method is implemented given an arbitrary point x spl isin spl ropf sup m and a generator matrix for a lattice spl lambda the algorithm computes the point of spl lambda that is closest to x the algorithm is shown to be substantially faster than other known methods by means of a theoretical comparison with the kannan 1983 1987 algorithm and an experimental comparison with the pohst 1981 algorithm and its variants such as the viterbo boutros see ibid vol 45 p 1639 42 1999 decoder modifications of the algorithm are developed to solve a number of related search problems for lattices such as finding a shortest vector determining the kissing number computing the voronoi 1908 relevant vectors and finding a korkine zolotareff 1873 reduced basis

quasi maximum likelihood multiuser detection using semi definite relaxation with application to synchronous cdma the maximum likelihood ml multiuser detector is well known to exhibit better bit error rate ber performance than many other multiuser detectors unfortunately ml detection mld is a nondeterministic polynomial time hard np hard problem for which there is no known algorithm that can find the optimal solution with polynomial time complexity in the number of users in this paper a polynomial time approximation method called semi definite sd relaxation is applied to the mld problem with antipodal data transmission sd relaxation is an accurate approximation method for certain np hard problems the sd relaxation ml sdr ml detector is efficient in that its complexity is of the order of k3 5 where k is the number of users we illustrate the potential of the sdr ml detector by showing that some existing detectors such as the decorrelator and the linear minimum mean square error detector can be interpreted as degenerate forms of the sdr ml detector simulation results indicate that the ber performance of the sdr ml detector is better than that of these existing detectors and is close to that of the true ml detector even when the cross correlations between users are strong or the near far effect is significant

heterogeneous thin films of martensitic materials we study the effective behavior of heterogeneous thin films with three competing length scales the film thickness and the length scales of heterogeneity and material microstructure we start with three dimensional nonhomogeneous nonlinear elasticity enhanced with an interfacial energy of the van der waals type and derive the effective energy density as all length scales tend to zero with given limiting ratios we do not require any a priori selection of asymptotic expansion or ansatz in deriving our results depending on the dominating length scale the effective energy density can be identified by three procedures averaging homogenization and thin film limit we apply our theory to martensitic materials with multi well energy density and use a model example to show that the shape memory behavior can crucially depend on the ratios of these length scales we comment on the effective conductivity of linear composites and also on multilayers made of shape memory and elastic materials

an interior point method for semidefinite programming we propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices

the slowest descent method and its application to sequence estimation a new approach to sequence estimation is proposed and its performance is analyzed for a number of channels of practical interest the proposed approach termed the slowest descent method comprises as a special case the zero forcing equalizer for intersymbol interference channels and the decorrelator for the multiuser detection problem the latter two methods quantize the unconstrained sequence that maximizes the likelihood function the proposed method can be viewed as a generalization of these two methods in two ways first the unconstrained maximization is extended to nonquadratic log likelihood functions second the decorrelator estimate can be refined by comparing its likelihood to a set of discrete valued sequences along mutually orthogonal lines of the least decrease in the likelihood function the gradient descent method for iterative computation of the line of least likelihood decrease i e slowest likelihood descent and its relationship to the expectation maximization em algorithm for unconstrained likelihood maximization is discussed the slowest descent method is shown to provide a performance comparable to maximum likelihood for a number of channels these problems can be described by either quadratic or nonquadratic log likelihood functions

space alternating generalized expectation maximization algorithm the expectation maximization em method can facilitate maximizing likelihood functions that arise in statistical estimation problems in the classical em paradigm one iteratively maximizes the conditional log likelihood of a single unobservable complete data space rather than maximizing the intractable likelihood function for the measured or incomplete data em algorithms update all parameters simultaneously which has two drawbacks 1 slow convergence and 2 difficult maximization steps due to coupling when smoothness penalties are used the paper describes the space alternating generalized em sage method which updates the parameters sequentially by alternating between several small hidden data spaces defined by the algorithm designer the authors prove that the sequence of estimates monotonically increases the penalized likelihood objective derive asymptotic convergence rates and provide sufficient conditions for monotone convergence in norm two signal processing applications illustrate the method estimation of superimposed signals in gaussian noise and image reconstruction from poisson measurements in both applications the sage algorithms easily accommodate smoothness penalties and converge faster than the em algorithms

constrained maximum likelihood detection in cdma the detection strategy usually denoted optimal multiuser detection is equivalent to the solution of a 0 1 constrained maximum likelihood ml problem a problem which is known to be np hard in contrast the unconstrained ml problem can be solved quite easily and is known as the decorrelating detector in this paper we consider the constrained ml problem where the solution vector is restricted to lie within a closed convex set ccs such a design criterion leads to detector structures which are ml under the constraint assumption a close relationship between a sphere constrained ml detector and the well known minimum mean square error detector is found and verified an iterative algorithm for solving a ccs constraint problem is derived based on results in linear variational inequality theory special cases of this algorithm subject to a box constraint are found to correspond to known nonlinear successive and parallel interference cancellation structures using a clipped soft decision for making tentative decisions while a weighted linear parallel interference canceler with signal dependent weights arises from the sphere constraint convergence issues are investigated and an efficient implementation is suggested the bit error rate performance is studied via computer simulations and the expected performance improvements over unconstrained ml are verified

iterative multiuser receivers for cdma channels an em based approach maximum likelihood detection for the multiuser code division multiple access cdma channel is prohibitively complex this paper considers new iterative multiuser receivers based on the expectation maximization em algorithm and related more powerful space alternating algorithms the latter algorithms include the sage algorithm and a new missing parameter space alternating algorithm that alternately updates individual parameter components or treats them as probabilistic missing data application of these em based algorithms to the problem of discrete parameter estimation i e data detection in the gaussian multiple access channel leads to a variety of convergent receiver structures that incorporate soft decision feedback for interference cancellation and or sequential updating of iterative bit estimates convergence and performance analyses are based on well known properties of the em algorithm and on numerical simulation

rate of convergence analysis of decomposition methods based on the proximal method of multipliers for convex minimization this paper presents two classes of decomposition algorithms based on the proximal method of multipliers pmm introduced in the mid 1970s by rockafellar for convex minimization we first show that

polynomial complexity optimal detection of certain multiple access systems it is demonstrated that optimal multiple user detection in a linear multiple access system with identical crosscorrelations requires only spl oscr klogk operations instead of the worst case o 2 sup k a simple optimal detection algorithm is given which when generalized has a complexity that is exponential not in the number of users but in the number of unique crosscorrelation values

image restoration based on the minimized surface regularization abstract we propose an image restoration model based on the minimized surface regularization the proposed model closely relates to the classical smoothing rof model rudin et al 1992 we deduce two different conjugation forms via coupling the gradient operator with the smoothing parameter or not and then provide the existence of the minimizer in the continuous setting in order to efficiently solving the proposed model we employ the primal dual method by reformulating the proposed model as a min max problem relying on the convex conjugation the convergence of the algorithm is provided as well numerical implementations mainly emphasize the effectiveness of the proposed method by comparing it to other two well known methods in terms of the cpu time and restoration quality

semidefinite relaxation based multiuser detection for m ary psk multiuser systems because of the powerful symbol error performance of multiuser maximum likelihood ml detection recently there has been much interest in seeking effective ways of approximating multiuser ml detection mld with affordable computational costs it has been illustrated that for the synchronous code division multiple access cdma scenario the so called semidefinite relaxation sdr algorithm can accurately and efficiently approximate multiuser mld this sdr mld algorithm however can only handle binary and quadratic phase shift keying psk symbol constellations in this sequel we propose an extended sdr algorithm for mld with m ary psk mpsk constellations for the synchronous cdma scenario the proposed sdr algorithm provides an attractive polynomial time complexity order of k sup 3 5 where k is the number of users simulation results indicate that the proposed detector provides improved symbol error performance compared with several commonly used multiuser detectors

iterative space time processing for multiuser detection in multipath cdma channels space time processing and multiuser detection are two promising techniques for combating multipath distortion and multiple access interference in code division multiple access cdma systems to overcome the computational burden that rises very quickly with increasing numbers of users and receive antennas in applying such techniques iterative implementations of several space time multiuser detection algorithms are considered here these algorithms include iterative linear space time multiuser detection cholesky iterative decorrelating decision feedback space time multiuser detection multistage interference canceling space time multiuser detection and expectation maximization em based iterative space time multiuser detection a new space time multiuser receiver structure that allows for efficient implementation of iterative processing is also introduced fully exploiting various types of diversity through joint space time processing and multiuser detection brings substantial gain over single receiver antenna or single user based methods it is shown that iterative implementation of linear and nonlinear space time multiuser detection schemes discussed in this paper realizes this substantial gain and approaches the optimum performance with reasonable complexity among the iterative space time multiuser receivers considered in this paper the em based sage iterative space time multiuser receiver introduced here achieves the best performance with excellent convergence properties