discontinuous galerkin methods for friedrichs systems i general theory this paper presents a unified analysis of discontinuous galerkin methods to approximate friedrichs systems an abstract set of conditions is identified at the continuous level to guarantee existence and uniqueness of the solution in a subspace of the graph of the differential operator then a general discontinuous galerkin method that weakly enforces boundary conditions and mildly penalizes interface jumps is proposed all the design constraints of the method are fully stated and an abstract error analysis in the spirit of strang s second lemma is presented finally the method is formulated locally using element fluxes and links with other formulations are discussed details are given for three examples namely advection reaction equations advection diffusion reaction equations and the maxwell equations in the so called elliptic regime

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

a matrix algebraic approach to linear parallel interference cancellation in cdma linear parallel interference cancellation pic schemes are described and analyzed using matrix algebra it is shown that the linear pic whether conventional or weighted can be seen as a linear matrix filter applied directly to the chip matched filtered received signal vector an expression for the exact bit error rate ber is obtained and conditions on the eigenvalues of the code correlation matrix and the weighting factors to ensure convergence are derived the close relationship between the linear multistage pic and the steepest descent method sdm for minimizing the mean squared error mse is demonstrated a modified weighted pic structure that resembles the sdm is suggested which approaches the minimum mse mmse detector rather than the decorrelator it is shown that for a k user system only k pic stages are required for the equivalent matrix filter to be identical to the the mmse filter for fewer stages techniques are devised for optimizing the choice of weights with respect to the mse one unique optimal choice of weights is found which will lead to the minimum achievable mse at the final stage simulation results show that a few stages are sufficient for near mmse performance

asymptotic multiuser efficiencies for decision directed multiuser detectors the asymptotic multiuser efficiencies ames are derived for various classes of decision directed multiuser detectors including multistage detectors and decision feedback detectors novel classes of soft decision multistage detectors are proposed and analyzed each class is specified in part by a soft decision nonlinearity such as a symmetric quantizer or a linear clipper closed form expressions for two user ames are derived for soft decision two stage detectors and can be used as a design criterion to optimize the soft decision nonlinearities for a special case of two synchronous users the soft decision two stage detector using an optimized linear clipper with either conventional or decorrelated tentative decisions is shown to achieve optimum ame upper and lower bounds on the ame are obtained for decision feedback detectors using either conventional or decorrelated tentative decisions it is demonstrated that decision directed multiuser detectors with conventional tentative decisions have low near far resistance compared to those with decorrelated tentative decisions

iterative methods for linear complementarity problems with upperbounds on primary variables this paper is concerned with iterative methods for the linear complementarity problem lcp of findingx and y in rn such thatc dx y 0 b x 0 andxt c dx y yt b x 0 whenb 0 this is the lcp m q withm l 0d t which is in turn equivalent to a linear variational inequality over a rectangle this type of problem arises for example from quadratic programming qp problems with upper and lower bounds ifd is symmetric and from multicommodity market equilibrium problems with institutional price controls imposed ifd is not necessarily symmetric iterative methods for the lcp m q with symmetricm are well developed and studied using qp applications for nonsymmetric cases withm being either an h matrix with positive diagonals or a z matrix there exists a robust iterative method with guaranteed convergence this paper extends this algorithm so that the lcp m q withm l 0d t which is neither symmetric nor an h matrix with positive diagonals nor a z matrix can be processed when onlyd notm satisfies such properties the case whered is nonsymmetric is explicitly discussed

breadth first maximum likelihood detection in multiuser cdma in this letter we derive a recursive additive metric for complexity constrained maximum likelihood detection for multiuser cdma using breadth first detection algorithms the metric requires linear filtering of the matched filtered received signal vector it is shown that a class of filters fulfilling certain requirements lead to identical performance

first order least squares method with weakly imposed boundary condition for convection dominated diffusion problems we present and analyze a first order least squares method for convection dominated diffusion problems which provides robust l 2 a priori error estimate for the scalar variable even if the given data f l 2 the novel theoretical approach is to rewrite the method in the framework of discontinuous petrov galerkin dpg method and then show numerical stability by using a key equation discovered by gopalakrishnan and qiu 2014 this new approach gives an alternative way to do numerical analysis for least squares methods for a large class of differential equations we also show that the condition number of the global matrix is independent of the diffusion coefficient a key feature of the method is that there is no stabilization parameter chosen empirically in addition dirichlet boundary condition is weakly imposed numerical experiments verify our theoretical results and in particular show our way of weakly imposing dirichlet boundary condition is essential to the design of least squares methods numerical solutions on subdomains away from interior layers or boundary layers have remarkable accuracy even on coarse meshes which are unstructured quasi uniform

fuzzy multiplication semigroup the notion of fuzzy multiplication semigroup is introduced using fuzzy ideal in a fuzzy multiplication semigroup with identity i every fuzzy ideal with sup property whose radical is prime is primary and ii every primary fuzzy ideal with sup property is some power of its fuzzy radical conditions i and ii are also found to be sufficient for a commutative semigroup with identity and satisfying some other conditions to be a fuzzy multiplication semigroup

prime fuzzy ideals in rings abstract in this paper give a characterization of prime fuzzy ideals we introduce weakly completely prime fuzzy ideals and establish a relation between completely prime fuzzy ideals and weakly completely prime fuzzy ideals

discontinuous galerkin methods for friedrichs systems part iii multifield theories with partial coercivity this paper is the third and last part of a work attempting to give a unified analysis of discontinuous galerkin methods the purpose of this paper is to extend the framework that has been developed in part ii for two field friedrichs systems associated with second order pdes we now consider two field friedrichs systems with partial l 2 coercivity and three field friedrichs systems with an even weaker l 2 coercivity hypothesis in particular this work generalizes the discontinuous galerkin methods of part ii to compressible and incompressible linear continuum mechanics we also show how the stabilizing parameters of the method must be set when the two field friedrichs system is composed of terms that may be of different magnitude thus accounting for instance for advection diffusion equations at high peclet numbers

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

friedrichs systems in a hilbert space framework solvability and multiplicity abstract the friedrichs 1958 theory of positive symmetric systems of first order partial differential equations encompasses many standard equations of mathematical physics irrespective of their type this theory was recast in an abstract hilbert space setting by ern guermond and caplain 2007 and by antonic and burazin 2010 in this work we make a further step presenting a purely operator theoretic description of abstract friedrichs systems and proving that any pair of abstract friedrichs operators admits bijective extensions with a signed boundary map moreover we provide sufficient and necessary conditions for existence of infinitely many such pairs of spaces and by the universal operator extension theory grubb 1968 we get a complete identification of all such pairs which we illustrate on two concrete one dimensional examples

mimo detection by lagrangian dual maximum likelihood relaxation reinterpreting regularized lattice decoding this paper considers lattice decoding for multi input multi output mimo detection under pam constellations a key aspect of lattice decoding is that it relaxes the symbol bound constraints in the optimal maximum likelihood ml detector for faster implementations it is known that such a symbol bound relaxation may lead to a damaging effect on the system performance for this reason regularization was proposed to mitigate the out of bound symbol effects in lattice decoding however minimum mean square error mmse regularization is the only method of choice for regularization in the present literature we propose a systematic regularization optimization approach considering a lagrangian dual relaxation ldr of the ml detection problem as it turns out the proposed ldr formulation is to find the best diagonally regularized lattice decoder to approximate the ml detector and all diagonal regularizations including the mmse regularization can be subsumed under the ldr formalism we show that for the 2 pam case strong duality holds between the ldr and ml problems also for general pam we prove that the ldr problem yields a duality gap no worse than that of the well known semidefinite relaxation method to physically realize the proposed ldr the projected subgradient method is employed to handle the ldr problem so that the best regularization can be found the resultant method can physically be viewed as an adaptive symbol bound control wherein regularized lattice decoding is recursively performed to correct the decision simulation results show that the proposed ldr approach can outperform the conventional mmse based lattice decoding approach

applications of convex optimization in signal processing and digital communication in the last two decades the mathematical programming community has witnessed some spectacular advances in interior point methods and robust optimization these advances have recently started to significantly impact various fields of applied sciences and engineering where computational efficiency is essential this paper focuses on two such fields digital signal processing and communication in the past the widely used optimization methods in both fields had been the gradient descent or least squares methods both of which are known to suffer from the usual headaches of stepsize selection algorithm initialization and local minima with the recent advances in conic and robust optimization the opportunity is ripe to use the newly developed interior point optimization techniques and highly efficient software tools to help advance the fields of signal processing and digital communication this paper surveys recent successes of applying interior point and robust optimization to solve some core problems in these two fields the successful applications considered in this paper include adaptive filtering robust beamforming design and analysis of multi user communication system channel equalization decoding and detection throughout our emphasis is on how to exploit the hidden convexity convex reformulation of semi infinite constraints analysis of convergence complexity and performance as well as efficient practical implementation

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

a new multistage detector for synchronous cdma communications in this paper we develop a new multistage detector to approach the optimal solution of the detection problem in a synchronous code division multiple access cdma system the transformation modifies the diagonal elements of the hessian matrix of the quadratic likelihood function and brings the continuous minimum of the transformed function as close to the optimal solution as possible the computational complexity is essentially linear with the number of users except that a few computations of a quadratic function are needed

a variational inference framework for soft in soft out detection in multiple access channels we propose a unified framework for deriving and studying soft in soft out siso detection in multiple access channels using the concept of variational inference the proposed framework may be used in multiple access interference mai intersymbol interference isi and multiple input multiple output mimo channels without loss of generality we will focus our attention on turbo multiuser detection to facilitate a more concrete discussion it is shown that with some loss of optimality variational inference avoids the exponential complexity of a posteriori probability app detection by optimizing a closely related but much more manageable objective function called variational free energy in addition to its systematic appeal there are several other advantages to this viewpoint first of all it provides unified and rigorous justifications for numerous detectors that were proposed on radically different grounds and facilitates convenient joint detection and decoding utilizing the turbo principle when error control codes are incorporated second efficient joint parameter estimation and data detection is possible via the variational expectation maximization em algorithm such that the detrimental effect of inaccurate channel knowledge at the receiver may be dealt with systematically we are also able to extend bpsk based siso detection schemes to arbitrary square qam constellations in a rigorous manner using a variational argument

layered tabu search algorithm for large mimo detection and a lower bound on ml performance in this letter we are concerned with low complexity detection in large multiple input multiple output mimo systems with tens of transmit receive antennas our new contributions in this letter are two fold first we propose a low complexity algorithm for large mimo detection based on a layered low complexity local neighborhood search second we obtain a lower bound on the maximum likelihood ml bit error performance using the local neighborhood search the advantages of the proposed ml lower bound are i it is easily obtained for mimo systems with large number of antennas because of the inherent low complexity of the search algorithm ii it is tight at moderate to high snrs and iii it can be tightened at low snrs by increasing the number of symbols in the neighborhood definition the proposed detection algorithm based on the layered local neighborhood search achieves bit error performances which are quite close to this lower bound for large number of antennas and higher order qam

fuzzy ideals and fuzzy prime ideals of a ring abstract besides obtaining certain ring theoretic analogues some peculiarities of the fuzzy setting are also discussed in particular a study of i the conditions under which a given fuzzy ideal can or cannot be expressed as a union of two proper fuzzy ideals ii the algebraic nature of images and preimages of fuzzy prime ideals under homomorphisms and iii the ring of all the fuzzy cosets of a fuzzy prime fuzzy maximal ideal is carried out

a unified discontinuous petrov galerkin method and its analysis for friedrichs systems we propose a unified discontinuous petrov galerkin dpg framework with optimal test functions for friedrichs like systems which embrace a large class of elliptic parabolic and hyperbolic partial differential equations pdes the well posedness i e existence uniqueness and stability of the dpg solution is established on a single abstract dpg formulation and two abstract dpg methods corresponding to two different but equivalent norms are devised we then apply the single dpg framework to several linear ized pdes including but not limited to scalar transport laplace diffusion convection diffusion convection diffusion reaction linear ized continuum mechanics e g linear ized elasticity a version of linearized navier stokes equations etc time domain acoustics and a version of the maxwell s equations the results show that we not only recover several existing dpg methods but also discover new dpg methods for both pdes currently considered in the dpg community and new ones as

fuzzy maximal radical and primary ideals of a ring we introduce the concepts of fuzzy maximal ideal the fuzzy radical of a fuzzy ideal and fuzzy primary ideal of a ring we show that a fuzzy left right ideal a of a ring r is a fuzzy maximal ideal if and only a 0 1 and a x r a x a 0 is a maximal left right ideal of r we also show that a fuzzy ideal a of a commutative ring r with unity is a fuzzy primary ideal of r if and only a 0 1 a is two valued and a is a primary ideal of r

linear interference cancellation in cdma based on iterative techniques for linear equation systems it has previously been shown that well known iterations for solving a set of linear equations correspond to linear interference cancellation structures here we suggest applying a block wise iteration that consists of an outer and an inner iteration the outer iteration used is the gauss seidel gs method while for the inner iteration we study direct matrix inversion the jacobi over relaxation iteration and the conjugate gradient iteration when a true inner iteration is used this approach allows for a timely derivation of the acceleration parameters required by advanced iterations the block iteration is based on a symbol level implementation which leads to the same detection delay profile for both parallel and serial structures at the expense of differences in the amount of serial processing required this is discussed in some detail and quantified for comparison the performance of the detectors is studied via computer simulations where it is found that the block approach can provide significantly faster convergence leading to improved detection delay over the simpler gs iteration the improvements are obtained at the expense of an increase in the required serial processing speed

multidomain spectral method for the helically reduced wave equation we consider the 2 1 and 3 1 scalar wave equations reduced via a helical killing field respectively referred to as the 2 dimensional and 3 dimensional helically reduced wave equation hrwe the hrwe serves as the fundamental model for the mixed type pde arising in the periodic standing wave psw approximation to binary inspiral we present a method for solving the equation based on domain decomposition and spectral approximation beyond describing such a numerical method for solving strictly linear hrwe we also present results for a nonlinear scalar model of binary inspiral the psw approximation has already been theoretically and numerically studied in the context of the post minkowskian gravitational field with numerical simulations carried out via the eigenspectral method despite its name the eigenspectral technique does feature a finite difference component and is lower order accurate we intend to apply the numerical method described here to the theoretically well developed post minkowski psw formalism with the twin goals of spectral accuracy and the coordinate flexibility afforded by global spectral interpolation

asymptotically optimal nonlinear mmse multiuser detection based on multivariate gaussian approximation in this paper a class of nonlinear minimum mean squared error multiuser detectors is derived based on a multivariate gaussian approximation of the multiple access interference for large systems this approach leads to expressions identical to those describing the probabilistic data association pda detector thus providing an alternative analytical justification for this structure a simplification to the pda detector based on approximating the covariance matrix of the multivariate gaussian distribution is suggested resulting in a soft interference cancellation scheme corresponding multiuser soft input soft output detectors delivering extrinsic log likelihood ratios are derived for application in iterative multiuser decoders finally a large system performance analysis is conducted for the simplified pda showing that the bit error rate ber performance of this detector can be accurately predicted and related to the replica method analysis for the optimal detector methods from statistical neurodynamics are shown to provide a closely related alternative large system prediction numerical results demonstrate that for large systems the ber is accurately predicted by the analysis and found to be close to optimal performance

a tent pitching scheme motivated by friedrichs theory certain friedrichs systems can be posed on hilbert spaces normed with a graph norm functions in such spaces arising from advective problems are found to have traces with a weak continuity property at points where the inflow and outflow boundaries meet motivated by this continuity property an explicit space time finite element scheme of the tent pitching type with spaces that conform to the continuity property is designed numerical results for a model one dimensional wave propagation problem are presented

discontinuous galerkin methods for advection diffusion reaction problems we apply the weighted residual approach recently introduced in f brezzi et al comput methods appl mech engrg 195 2006 pp 3293 3310 to derive discontinuous galerkin formulations for advection diffusion reaction problems we devise the basic ingredients to ensure stability and optimal error estimates in suitable norms and propose two new methods

blind identification equalization using deterministic maximum likelihood and a partial prior on the input a semi deterministic maximum likelihood dml approach is presented to solve the joint blind channel identification and blind symbol estimation problem for single input multiple output systems a partial prior on the symbols is incorporated into the criterion which improves the estimation accuracy and brings robustness toward poor channel diversity conditions at the same time this method introduces fewer local minima than the use of a full prior statistical ml in the absence of noise the proposed batch algorithm estimates perfectly the channel and symbols with a finite number of samples based on these considerations an adaptive implementation of this algorithm is proposed it presents some desirable properties including low complexity robustness to channel overestimation and high convergence rate

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

on fuzzy ideals and fuzzy bi ideals in semigroups abstract in this paper we give some properties of fuzzy ideals and fuzzy bi ideals of semigroups and characterize semigroups that are left duo left simple and semilattices of subsemigroups in terms of fuzzy ideals and fuzzy bi ideals

a new c0 discontinuous galerkin method for kirchhoff plates abstract a general framework of constructing c 0 discontinuous galerkin cdg methods is developed for solving the kirchhoff plate bending problem following some ideas in castillo et al 2000 10 and cockburn 2003 12 the numerical traces are determined based on a discrete stability identity which lead to a class of stable cdg methods a stable cdg method called the lcdg method is particularly interesting in our study it can be viewed as an extension to fourth order problems of the ldg method studied in castillo et al 2000 10 and cockburn 2003 12 for this method optimal order error estimates in certain broken energy norm and h 1 norm are established some numerical results are reported confirming the theoretical convergence orders

heat equation as a friedrichs system abstract inspired by recent advances in the theory of friedrichs symmetric positive systems we apply newly developed results to the heat equation by showing how the intrinsic theory of ern guermond and caplain 2007 can be used in order to get a well posedness result for the dirichlet initial boundary value problem we also demonstrate the application of the two field theory with partial coercivity of ern and guermond 2008 originally developed for elliptic problems and also discuss different possibilities for the construction of the appropriate boundary operator

on some properties of quadratic programs with a convex quadratic constraint in this paper we consider the problem of minimizing a possibly nonconvex quadratic function with a quadratic constraint we point out some new properties of the problem in particular in the first part of the paper we show that i given a kkt point that is not a global minimizer it is easy to find a better feasible point ii strict complementarity holds at the local nonglobal minimizer in the second part of this paper we show that the original constrained problem is equivalent to the unconstrained minimization of a piecewise quartic merit function using the unconstrained formulation we give in the nonconvex case a new second order necessary condition for global minimizers in the third part of this paper algorithmic applications of the preceding results are briefly outlined and some preliminary numerical experiments are reported

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

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

fuzzy semiprime ideals in semigroups abstract in this paper we shall introduce the notion of fuzzy semiprimality in a semigroup which is an extension of semiprimality in it and characterize a semigroup that is a semilattice of simple semigroups in terms of fuzzy semiprimality

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

designing low complexity near optimal multiple symbol detectors for impulse radio uwb systems multiple symbol detection has recently caught attention in ultrawideband uwb communications because of its high performance without requiring explicit channel estimation in this context the generalized likelihood ratio test glrt for multiple symbol detection problem is developed to jointly detect multiple symbols which exhibits considerable error performance improvement over transmitted reference transmissions methods unfortunately the glrt is a boolean quadratic programming bqp problem which is generally nondeterministic polynomial hard np hard in this paper we propose two near optimal detectors with polynomial complexity the first detector performs semidefinite relaxation to approximately solve the bqp problem called sdp msd the second detector is based on a sphere based relaxation of the bqp problem we refer to this as modified unconstrained relaxation multiple symbol detector mur msd both detectors achieve near optimal performance while the sdp msd performs slightly better than the mur msd at the price of higher computational complexity furthermore the mur msd can be treated as a further nontight relaxation of sdp msd simulations are utilized to validate our findings and to demonstrate performance robustness to multiaccess interference

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

complex friedrichs systems and applications recently there has been a significant development of the abstract theory of friedrichs systems in hilbert spaces ern a guermond j l and caplain g commun partial differ equations 32 317 341 2007 and antonic n and burazin k commun partial differ equations 35 1690 1715 2010 and its applications to specific problems in mathematical physics however these applications were essentially restricted to real systems we check that the already developed theory of abstract friedrichs systems can be adjusted to the complex setting with some necessary modifications which allows for applications to partial differential equations with complex coefficients we also provide examples where the involved hilbert space is not the space of square integrable functions as it was the case in previous studies but rather its closed subspace or the space hs rd cr for real s this setting appears to be suitable for particular systems of partial differential equations such as the dirac system the di

discontinuous galerkin methods for friedrichs systems part ii second order elliptic pdes this paper is the second part of a work attempting to give a unified analysis of discontinuous galerkin methods the setting under scrutiny is that of friedrichs systems endowed with a particular 2 times 2 structure in which one unknown can be eliminated to yield a system of second order elliptic like pdes for the remaining unknown a general discontinuous galerkin method for approximating such systems is proposed and analyzed the key feature is that the unknown that can be eliminated at the continuous level can also be eliminated at the discrete level by solving local problems all the design constraints on the boundary operators that weakly enforce boundary conditions and on the interface operators that penalize interface jumps are fully stated examples are given for advection diffusion reaction linear continuum mechanics and a simplified version of the magnetohydrodynamics equations comparisons with well known discontinuous galerkin approximations for the poisson equation are presented

analysis of mean field annealing in substactive interference cancellation in this contribution we derive the cost function corresponding to the linear complexity subtractive interference cancellation with tangent hyperbolic tentative decisions we use the cost function to analyse the fix points of solving the subtractive interference cancellation equations the analysis show that we can control the slope of the tangent hyperbolic functions so that the corresponding cost function is convex we also show that increasing the slope can make the cost non convex going from the convex regime into the non convex regime we prove that the bifurcation of the fix points for non singular signal correlation matrices consist of the fix point of interest together with a saddle node bifurcation this proves that tracking the solution from low slopes with a convex cost gradually increasing to higher slopes with non convex cost can bring us to the best solution being very close to the optimal determined by enumeration this tracking is the idea behind annealing we show monte carlo studies with a substantial signal to noise ratio gain compared to not using annealing we also show how annealing can be used to increase capacity at a given target bit error rate in fact this capacity gain is the same obtained by improved parallel interference cancellation making us believe that the latter includes a mechanism to avoid local minima similar to annealing

on prime and primary fuzzy ideals and their radicals abstract the merits and demerits of various definitions of prime and primary fuzzy ideals are discussed and new definitions are suggested it is shown that the new definitions are more satisfactory the nil radical is defined as against the prime radical of a fuzzy ideal some theorems regarding the nil radical are proved it is shown that the two radicals coincide when the grade membership lattice is totally ordered

symbol error rate performance of box relaxation decoders in massive mimo the maximum likelihood ml decoder for symbol detection in large multiple input multiple output wireless communication systems is typically computationally prohibitive in this paper we study a popular and practical alternative namely the box relaxation optimization bro decoder which is a natural convex relaxation of the ml for independent identically distributed real gaussian channels with additive gaussian noise we obtain exact asymptotic expressions for the symbol error rate ser of the bro the formulas are particularly simple they yield useful insights and they allow accurate comparisons to the matched filter bound mfb and to linear decoders such as zero forcing and linear minimum mean square error for binary phase shift keying signals the ser performance of the bro is within 3 db of the mfb for square systems and it approaches the mfb as the number of receive antennas grows large compared to the number of transmit antennas our analysis further characterizes the empirical density function of the solution of the bro and shows that error events for any fixed number of symbols are asymptotically independent the fundamental tool behind the analysis is the convex gaussian min max theorem

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

a domain decomposition method for solving the three dimensional time harmonic maxwell equations discretized by discontinuous galerkin methods we present here a domain decomposition method for solving the three dimensional time harmonic maxwell equations discretized by a discontinuous galerkin method in order to allow the treatment of irregularly shaped geometries the discontinuous galerkin method is formulated on unstructured tetrahedral meshes the domain decomposition strategy takes the form of a schwarz type algorithm where a continuity condition on the incoming characteristic variables is imposed at the interfaces between neighboring subdomains a multifrontal sparse direct solver is used at the subdomain level the resulting domain decomposition strategy can be viewed as a hybrid iterative direct solution method for the large sparse and complex coefficients algebraic system resulting from the discretization of the time harmonic maxwell equations by a discontinuous galerkin method

discrete functional analysis tools for discontinuous galerkin methods with application to the incompressible navier stokes equations two discrete functional analysis tools are established for spaces of piecewise polynomial functions on general meshes i a discrete counterpart of the continuous sobolev embeddings in both hilbertian and non hilbertian settings ii a compactness result for bounded sequences in a suitable discontinuous galerkin norm together with a weak convergence property for some discrete gradients the proofs rely on techniques inspired by the finite volume literature which differ from those commonly used in finite element analysis the discrete functional analysis tools are used to prove the convergence of discontinuous galerkin approximations of the steady incompressible navier stokes equations two discrete convective trilinear forms are proposed a non conservative one relying on temam s device to control the kinetic energy balance and a conservative one based on a nonstandard modification of the pressure

solution of the time harmonic maxwell equations using discontinuous galerkin methods we present numerical results concerning the solution of the time harmonic maxwell equations discretized by discontinuous galerkin methods in particular a numerical study of the convergence which compares different strategies proposed in the literature for the elliptic maxwell equations is performed in the two dimensional case