frame based approach for peak to average power ratio reduction in ofdm a new method for reducing the peak to average power ratio papr in orthogonal frequency division multiplexing is proposed the new method called erasure pattern selection eps is based on the use of frame expansion for adding redundancy to the data part of the redundancy is removed by examining several patterns for erasing subcarriers and selecting the pattern that produces the lowest papr for transmission the residual redundancy in the data is exploited at the receiver to aid both the reconstruction of the erased data and correction of errors the implementation is aided with the incorporation of a projection onto convex sets pocs method in eps in order to select and assign the best values to the unused subcarriers and further reduce the papr complexity analysis and simulation results show that the pocs based eps method outperforms existing probabilistic methods while requiring lower overall complexity

improving upper bounds for the clique number by non valid inequalities the lovasz and lovasz schrijver bounds are well known upper bounds for the clique number of a graph based on the solution of semidefinite programming problems both bounds can be seen as obtained through a relaxation of a completely positive formulation of the maximum clique problem in this paper we propose to improve these bounds by adding inequalities based on independent sets which may be non valid in the sense that they may be violated by optimal solutions of the completely positive formulation some computational experiments have been performed over different classes of graphs and the results are promising

theoretical analysis and performance of ofdm signals in nonlinear awgn channels orthogonal frequency division multiplexing ofdm baseband signals may be modeled by complex gaussian processes with rayleigh envelope distribution and uniform phase distribution if the number of carriers is sufficiently large the output correlation function of instantaneous nonlinear amplifiers and the signal to distortion ratio can be derived and expressed in an easy way as a consequence the output spectrum and the bit error rate ber performance of ofdm systems in nonlinear additive white gaussian noise channels are predictable both for uncompensated amplitude modulation amplitude modulation am am and amplitude modulation pulse modulation am pm distortions and for ideal predistortion the aim of this work is to obtain the analytical expressions for the output correlation function of a nonlinear device and for the ber performance the results in closed form solutions are derived for am am and am pm curves approximated by bessel series expansion and for the ideal predistortion case

solving lift and project relaxations of binary integer programs we propose a method for optimizing the lift and project relaxations of binary integer programs introduced by lovasz and schrijver in particular we study both linear and semidefinite relaxations the key idea is a restructuring of the relaxations which isolates the complicating constraints and allows for a lagrangian approach we detail an enhanced subgradient method and discuss its efficient implementation computational results illustrate that our algorithm produces tight bounds more quickly than state of the art linear and semidefinite solvers

spectral collocation solutions to multiparameter mathieu s system our main aim is the accurate computation of a large number of specified eigenvalues and eigenvectors of mathieu s system as a multiparameter eigenvalue problem mep the reduced wave equation for small deflections is solved directly without approximations introduced by the classical mathieu functions we show how for moderate values of the cut off collocation parameter the qr algorithm and the arnoldi method may be applied successfully while for larger values the jacobi davidson method is the method of choice with respect to convergence accuracy and memory usage

a note on the backward errors for hermite eigenvalue problems we discuss the backward error analysis of the hermite eigenproblems three kinds of problems are included generalized eigenproblem matrix polynomial eigenproblem and multiparameter eigenproblem in the case of the approximate eigenvalue being real these problems have already been solved by higham and higham siam j matrix anal 20 1998 493 tisseur lin alg appl 309 2002 339 and hachstenbach and plestenjak lin alg appl 375 2003 63 this note as a complement of their results considers the complex case

on the distribution of the peak to average power ratio in ofdm signals the distribution of the peak to average power ratio papr in strictly band limited orthogonal frequency division multiplexing ofdm signals is studied assuming that the base band ofdm signal is characterized as a band limited complex gaussian process we first attempt to derive the exact distribution of the papr in the band limited ofdm signals since this distribution cannot be expressed in a closed form we further develop a simple closed form approximation based on the level crossing rate analysis comparisons of the proposed distributions with those obtained by computer simulations show good agreement and convergence with an increase in the number of subcarriers

iterative soft compensation for ofdm systems with clipping and superposition coded modulation this paper deals with the clipping method used in orthogonal frequency division multiplexing ofdm systems to reduce the peak to average power ratio papr an iterative soft compensation method is proposed to mitigate the clipping distortion which can outperform conventional treatments the impact of signaling schemes on the residual clipping noise power is studied via the symbol variance analysis it is found that superposition coded modulation scm can minimize the residual clipping noise power among all possible signaling schemes this indicates that scm based ofdm systems are more robust to clipping effect than other alternatives when soft compensation is applied it is also shown that a multi code scm scheme can further reduce the clipping effect and its overall performance can be quickly evaluated using a semi analytical evolution method numerical examples are provided to verify the analysis

predistorter for mimo system with nonlinear power amplifiers a multiple input multiple output mimo system with nonlinear power amplifiers pas is considered the nonlinear pas distort the transmitted signal causing performance degradation the common approach for the mitigation of nonlinear distortions is the linearization of each one of the pas in the mimo system separately we propose to apply a more generic approach in the form of a global linearization of the entire nonlinear mimo channel the aim of the global linearization is to reduce the nonlinear distortions seen at the receiver an iterative technique is proposed for the implementation of such a linearization the proposed technique improves the system performance including 1 power efficiency of the pas 2 quality of the received signal measured in terms of symbol error rate and 3 spectral purity of the transmitted signals

reduction of peak factor in orthogonal multicarrier modulation by amplitude limiting and coding a main disadvantage of orthogonal multicarrier modulation is that it exhibits a high peak to average power ratio papr because of this all circuits between the output of the modulator and the input of the demodulator must be linear within a large dynamic range to avoid distortions and spectral spreading it is therefore desirable to limit the papr of the multicarrier signal a method based on amplitude limiting and forward error correcting al fec coding is proposed for reduction of the papr the performance of the al fec is compared to two methods based on block coding specially constructed to reduce the papr the al fec is superior as compared to the existing methods moreover its practical realization is very simple for any number of carriers

a general framework for transmission with transceiver distortion and some applications a general theoretical framework is presented for analyzing information transmission over gaussian channels with memoryless transceiver distortion which encompasses various nonlinear distortion models including transmit side clipping receive side analog to digital conversion and others the framework is based on the so called generalized mutual information gmi and the analysis in particular benefits from the setup of gaussian codebook ensemble and nearest neighbor decoding for which it is established that the gmi takes a general form analogous to the channel capacity of undistorted gaussian channels with a reduced effective signal to noise ratio snr that depends on the nominal snr and the distortion model when applied to specific distortion models an array of results of engineering relevance is obtained for channels with transmit side distortion only it is shown that a conventional approach which treats the distorted signal as the sum of the original signal part and a uncorrelated distortion part achieves the gmi for channels with output quantization closed form expressions are obtained for the effective snr and the gmi and related optimization problems are formulated and solved for quantizer design finally super nyquist sampling is analyzed within the general framework and it is shown that sampling beyond the nyquist rate increases the gmi for all snr values for example with binary symmetric output quantization information rates exceeding one bit per channel use are achievable by sampling the output at four times the nyquist rate

an analysis of band limited communication systems from amplifier efficiency and distortion perspective considering growing concerns toward green communications not only their bandwidth efficiency but also their power consumption is expected to gain increasing importance for future communication systems a power amplifier pa is one of the most power consuming analog devices at the transmitter in communication systems and a precise estimation of the power consumption at the transmitter circuit requires the knowledge of its efficiency that depends on the distribution of input signal envelope and the amount of input back off in this paper we develop a simple analytical model that can be used for estimating achievable efficiency of a linear pa as well as the amount of resulting nonlinear distortion for a given modulated signal exclusively from its envelope distribution based on this model the trade off relationships between the efficiency and signal to distortion power ratio for several spectrally efficient linear modulations are examined it is also shown that in some special cases of gaussian input and memoryless nonlinearity pa models the results can be represented in simple closed form expressions

a novel trellis shaping design with both peak and average power reduction for ofdm systems a new trellis shaping design is proposed for reducing the peak to average power ratio of the bandlimited orthogonal frequency division multiplexing ofdm signals the approach is based on recursive minimization of the autocorrelation sidelobes of an ofdm data sequence a novel metric in conjunction with the viterbi algorithm is devised the performance of the trellis shaping depends on signal mapping strategy and the two types of mapping referred to as type i and type ii are proposed the type i mapping has no capability of reducing the average power but it can achieve a significant reduction of the peak to average power ratio on the other hand the type ii mapping is designed to achieve both peak and average power reduction the bit error probability of the system over an awgn channel is evaluated based on the simulations which confirms the effectiveness of the proposed scheme

computational experience with stable set relaxations we investigate relaxations for the maximum stable set problem based on the lovasz number vartheta g as an initial upper bound we strengthen this relaxation by adding two classes of cutting planes odd circuit and triangle inequalities we present computational results using this tighter model on many classes of graphs

exploring the relationship between max cut and stable set relaxations the max cut and stable set problems are two fundamental hard problems in combinatorial optimization it has been known for a long time that any instance of the stable set problem can be easily transformed into a max cut instance moreover laurent poljak rendl and others have shown that any convex set containing the cut polytope yields via a suitable projection a convex set containing the stable set polytope we review this work and then extend it in the following ways we show that the rounded version of certain positive semidefinite inequalities for the cut polytope imply via the same projection a surprisingly large variety of strong valid inequalities for the stable set polytope these include the clique odd hole odd antihole web and antiweb inequalities and various inequalities obtained from these via sequential lifting we also examine a less general class of inequalities for the cut polytope which we call odd clique inequalities and show that they are in general much less useful for generating valid inequalities for the stable set polytope as well as being of theoretical interest these results have algorithmic implications in particular we obtain as a by product a polynomial time separation algorithm for a class of inequalities which includes all web inequalities

clipping noise in ofdm based optical wireless communication systems in this paper the impact of clipping noise on optical wireless communication owc systems employing orthogonal frequency division multiplexing ofdm is investigated the two existing optical ofdm o ofdm transmission schemes asymmetrically clipped optical ofdm aco ofdm and direct current biased optical ofdm dco ofdm are studied time domain signal clipping generally results from direct current dc biasing and or from physical limitations of the transmitter front end these include insufficient forward biasing and the maximum power driving limit of the emitter the clipping noise can be modeled according to the bussgang theorem and the central limit theorem clt as attenuation of the data carrying subcarriers at the receiver and addition of zero mean complex valued gaussian noise analytical expressions for the attenuation factor and the clipping noise variance are determined in closed form and employed in the derivation of the electrical signal to noise ratio snr the validity of the model is verified through a monte carlo bit error ratio ber simulation finally the ber performance of aco ofdm with dco ofdm is compared for different clipping levels and multi level quadrature amplitude modulation m qam schemes

recursive clipping and filtering with bounded distortion for papr reduction repeated clipping and filtering rcf is a simple method for reducing the peak to average power ratio papr of the signal in the orthogonal frequency division modulation ofdm system we propose to modify rcf by limiting the distortion on each tone of the ofdm so that both low papr and low error can be achieved

connections between semidefinite relaxations of the max cut and stable set problems we describe links between a recently introduced semidefinite relaxation for the max cut problem and the well known semidefinite relaxation for the stable set problem underlying the lovasz s theta function it turns out that the connection between the convex bodies defining the semidefinite relaxations mimics the connection existing between the corresponding polyhedra we also show how the semidefinite relaxations can be combined with the classical linear relaxations in order to obtain tighter relaxations

solving airline crew scheduling problems by branch and cut the crew scheduling problem is one that has been studied almost continually for the past 40 years but all prior approaches have always approximated the problem of finding an optimal schedule for even the smallest of an airline s fleets the problem is especially important today since costs for flying personnel of major u s carriers have grown and now often exceed 1 3 billion a year and are the second largest item next to fuel cost of the total operating cost of major u s carriers thus even small percentage savings amount to substantial dollar amounts we present a branch and cut approach to solving to proven optimality large set partitioning problems arising within the airline industry we first provide some background related to this important application and then describe the approach for solving representative problems in this problem class the branch and cut solver generates cutting planes based on the underlying structure of the polytope defined by the convex hull of the feasible integer points and incorporates these cuts into a tree search algorithm that uses automatic reformulation procedures heuristics and linear programming technology to assist in the solution numerical experiments are reported for a sample of 68 large scale real world crew scheduling problems these problems include both pure set partitioning problems and set partitioning problems with side constraints these base constraints represent contractual labor requirements and have heretofore not been represented explicitly in the construction of crew schedules thus making it impossible to provide any measure of how far the obtained solution was from optimality an interesting result of obtaining less costly schedules is that the crews themselves are happier with the schedules because they spend more of their duty time flying than waiting on the ground

reed solomon and simplex codes for peak to average power ratio reduction in ofdm new schemes for peak to average power ratio reduction in orthogonal frequency division multiplexing ofdm systems are proposed reed solomon rs and simplex codes are employed to create a number of candidates from which the best are selected thereby in contrast to existing approaches the codes are arranged over a number of ofdm frames rather than over the carriers hence a combination of the principles of multiple signal representation with selection as done in selected mapping and the use of channel coding is present in particular in multiple antenna transmission the proposed schemes do not cause any additional delay but due to the utilization of the dimension space additional gains can be achieved moreover the schemes are very flexible due to the selection step any criterion of optimality can be taken into account besides multiple antenna transmission packet transmission is briefly considered which moreover covers the appealing similarities with incremental redundancy check schemes in automatic repeat request arq applications and with decoding of codes transmitted over the erasure channel the performance of the schemes is using some approximations derived analytically and is covered by numerical results that are in very good agreement with the theory significant gains can be achieved with these very flexible and versatile methods

generalized bounds on the crest factor distribution of ofdm signals with applications to code design in this paper generalized bounds on the crest factor cf distribution in orthogonal frequency division multiplexing ofdm transmission for both independent and dependent subcarriers are derived here the latter situation represents the coded case for independent subcarriers a general path for bounding practical constellations is provided moreover a complete characterization of their asymptotic behavior is devised and discussed the results are shown to carry over to the spherical constellations improving on recent results for dependent subcarriers the focus is mainly on binary codes where bounds on the cf distribution are obtained in terms of the distance distributions and their duals the asymptotic behavior of codes is analyzed and it is shown that the upper bound on the effective crest factor of a large class of bose chaudhuri hocquenghem bch codes behaves asymptotically as radiclogn finally two applications of the results to code design are presented first fixed phase shifts on the subcarriers for all codewords are used and an algorithm to calculate the phase shifts is designed that way it is proved that the effective cf of any binary code can be scaled to be of order radiclogn for large n without sacrificing on rate furthermore the same approach is applied to calculation of the phases of redundant subcarriers for each codeword it is shown by simulations that the values can be effectively chosen so that the cf is significantly reduced with nonexponential complexity

optimization of sndr for amplitude limited nonlinearities many components used in communication systems are nonlinear and have a peak power or peak amplitude constraint nonlinearity generates distortions and thus signal to noise and distortion ratio sndr is an appropriate performance measure in this paper we are interested in finding the nonlinear mapping that maximizes the sndr subject to the peak amplitude constraint the answer is a soft limiter with gain calculated based on the noise power and the probability density function of the input amplitude we also investigate a bounding relationship between the sndr and capacity of the nonlinear channel the results of this paper can be applied for efficient transmission of high peak to average power ratio signals or for optimal linearization of nonlinear devices

performance analysis of deliberately clipped ofdm signals we analyze the performance of the clipped orthogonal frequency division multiplexing ofdm system in terms of peak power reduction capability and degradation of channel capacity the clipping is performed on the baseband ofdm signals with and without oversampling followed by the ideal low pass filter first the effect of the envelope clipping on the peak to average power ratio papr and the instantaneous power of the band limited ofdm signal is studied we then discuss the channel capacity of the oversampled and clipped ofdm signals over the additive white gaussian noise and ideally interleaved rayleigh fading channels the capacity is calculated based on the assumption that the distortion terms caused by the clipping are gaussian it is shown that the snr penalty due to the clipping can be considerably alleviated by using optimal coding and reducing the information data rate the results are justified by the simulation results using near optimal turbo codes

cones of matrices and set functions and 0 1 optimization it has been recognized recently that to represent a polyhedron as the projection of a higher dimensional but simpler polyhedron is a powerful tool in polyhedral combinatorics a general method is developed to construct higher dimensional polyhedra or in some cases convex sets whose projection approximates the convex hull of 0 1 valued solutions of a system of linear inequalities an important feature of these approximations is that one can optimize any linear objective function over them in polynomial time in the special case of the vertex packing polytope a sequence of systems of inequalities is obtained such that the first system already includes clique odd hole odd antihole wheel and orthogonality constraints in particular for perfect and many other graphs this first system gives the vertex packing polytope for various classes of graphs including t perfect graphs it follows that the stable set polytope is the projection of a polytope with a polynomial number of facets an extension o

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

a new lift and project operator abstract in this paper we analyze the strength of split cuts in a lift and project framework we first observe that the lovasz schrijver and sherali adams lift and project operator hierarchies can be viewed as applying specific 0 1 split cuts to an appropriate extended formulation and demonstrate how to strengthen these hierarchies using additional split cuts more precisely we define a new operator that adds all 0 1 split cuts to the extended formulation for 0 1 mixed integer sets with k binary variables this new operator is guaranteed to obtain the integer hull in k 2 steps compared to k steps for the lovasz schrijver or the sherali adams operator we also present computational results on the stable set problem with our new operator

integer based constellation shaping method for papr reduction in ofdm systems in this paper the problem of reducing the peak to average power ratio papr in an orthogonal frequency division multiplexing system is considered we design a cubic constellation called the hadamard constellation whose boundary is along the bases defined by the hadamard matrix in the transform domain then we further reduce the papr by applying the selective mapping technique the encoding method following the method introduced in the work of kwok is derived from a decomposition known as the smith normal form this new technique offers a papr that is significantly lower than those of the best known techniques without any loss in terms of energy and or spectral efficiency and without any side information being transmitted moreover it has a low computational complexity

antiweb wheel inequalities and their separation problems over the stable set polytopes a stable set in a graph g is a set of pairwise nonadjacent vertices the problem of finding a maximum weight stable set is one of the most basic hard problems an important approach to this problem is to formulate it as the problem of optimizing a linear function over the convex hull stab g of incidence vectors of stable sets since it is impossible unless co to obtain a concise characterization of stab g as the solution set of a system of linear inequalities it is a more realistic goal to find large classes of valid inequalities with the property that the corresponding separation problem given a point x find if possible an inequality in the class that x violates is efficiently solvable some known large classes of separable inequalities are the trivial edge cycle and wheel inequalities in this paper we give a polynomial time separation algorithm for the t antiweb inequalities of trotter we then introduce an even larger class in fact a sequence of classes of valid inequalities called t antiweb s wheel inequalities this class is a common generalization of the t antiweb inequalities and the wheel inequalities we also give efficient separation algorithms for them

an analytical approach to the calculation of evm in clipped multi carrier signals error vector magnitude evm is an important figure of merit in many communication systems in this work an analytical approach to the calculation of evm in clipped multi carrier signals is proposed in contrast to previous work the evm in this work is calculated with no simplifying model e g a gaussian assumption the expression is given in a form of a power series based on the derived expressions for evm bounds on the maximal achievable rate are derived

eigenvalues pseudospectrum and structured perturbations we investigate the behavior of eigenvalues under structured perturbations we show that for many common structures such as complex symmetric toeplitz symmetric toeplitz circulant and others the structured condition number is equal to the unstructured condition number for normwise perturbations and prove similar results for real perturbations an exception are complex skewsymmetric matrices we also investigate componentwise complex and real perturbations here hermitian and skew hermitian matrices are exceptional for real perturbations furthermore we characterize the structured complex and real pseudospectrum for a number of structures and show that often there is little or no significant difference to the usual unstructured pseudospectrum

ellipsoidal relaxations of the stable set problem theory and algorithms a new exact approach to the stable set problem is presented which attempts to avoid the pitfalls of existing approaches based on linear and semidefinite programming the method begins by constructing an ellipsoid that contains the stable set polytope and has the property that the upper bound obtained by optimizing over it is equal to the lovasz theta number this ellipsoid can then be used to construct useful convex relaxations of the stable set problem which can be embedded within a branch and bound framework extensive computational results are given which indicate the potential of the approach

the boolean quadric polytope some characteristics facets and relatives we study unconstrained quadratic zero one programming problems havingn variables from a polyhedral point of view by considering the boolean quadric polytope qpn inn n 1 2 dimensions that results from the linearization of the quadratic form we show that qpn has a diameter of one descriptively identify three families of facets of qpn and show that qpn is symmetric in the sense that all facets of qpn can be obtained from those that contain the origin by way of a mapping the naive linear programming relaxation qpnlp of qpn is shown to possess the trubin property and its extreme points are shown to be 0 1 2 1 valued furthermore o n3 facet defining inequalities of qpn suffice to cut off all fractional vertices of qpnlp whereas the family of facets described by us has at least o 3n members the problem is also studied for sparse quadratic forms i e when several or many coefficients are zero and conditions are given for the previous results to carry over to this case polynomially solvable problem instances are discussed and it is shown that the known polynomiality result for the maximization of nonnegative quadratic forms can be obtained by simply rounding the solution to the linear programming relaxation in the case that the graph induced by the nonzero coefficients of the quadratic form is series parallel a complete linear description of the associated boolean quadric polytope is given the relationship of the boolean quadric polytope associated to sparse quadratic forms with the vertex packing polytope is discussed as well

the role of am to pm conversion in memoryless nonlinear systems a generalized proof is presented that am to pm conversion can only degrade never improve the intermodulation noise performance of memoryless nonlinear systems with random input signals having even probability density functions and a measure of degradation is defined it is also shown for such signals that am to pm conversion causes a deterministic constant phase shift to be added to the argument of the signal component at the output but has no other effect on its phase this class of inputs includes one or the sum of several psk signals as well as large ensembles that can be modeled as gaussian noise the latter are dealt with by using bussgang s theorem on input output cross correlation in the proof bussgang s theorem is extended to the complex case to include phase as well as amplitude nonlinearities yielding a complex version of the theorem for gaussian inputs it is shown that the undistorted signal and the intermodulation noise at the output of such systems are uncorrelated

the steiner connectivity problem the steiner connectivity problem has the same significance for line planning in public transport as the steiner tree problem for telecommunication network design it consists in finding a minimum cost set of elementary paths to connect a subset of nodes in an undirected graph and is therefore a generalization of the steiner tree problem we propose an extended directed cut formulation for the problem which is in comparison to the canonical undirected cut formulation provably strong implying e g a class of facet defining steiner partition inequalities since a direct application of this formulation is computationally intractable for large instances we develop a partial projection method to produce a strong relaxation in the space of canonical variables that approximates the extended formulation we also investigate the separation of steiner partition inequalities and give computational evidence that these inequalities essentially close the gap between undirected and extended directed cut formulation using these techniques large steiner connectivity problems with up to 900 nodes can be solved within reasonable optimality gaps of typically less than five percent

a theoretical characterization of nonlinear distortion effects in ofdm systems this paper presents a theoretical characterization of nonlinear distortion effects in orthogonal frequency division multiplexing ofdm transmission systems in the theoretical framework developed it is shown that the effects on the decision variables of the in band distortion introduced by a bandpass memoryless nonlinearity can be described by means of a complex gain and an additive gaussian term with zero mean and suitable variance analytical expressions for gain and variance are given the conditions which allow this description are emphasized and discussed as a consequence a completely analytical procedure to evaluate error probability is also obtained and illustrated using ofdm discrete multitone modulation dmt systems with rectangular pulse shaping for the soft envelope limiter nonlinearity a closed form is derived a comparison with simulation results is carried out to verify the accuracy of this method

semidefinite programming relaxations for graph coloring and maximal clique problems the semidefinite programming formulation of the lovasz theta number does not only give one of the best polynomial simultaneous bounds on the chromatic number g or the clique number g of a graph but also leads to heuristics for graph coloring and extracting large cliques this semidefinite programming formulation can be tightened toward either g or g by adding several types of cutting planes we explore several such strengthenings and show that some of them can be computed with the same effort as the theta number we also investigate computational simplifications for graphs with rich automorphism groups

frame theoretic analysis of dft codes with erasures discrete fourier transform dft codes have been used as joint source channel codes in order to provide robustness against channel errors and erasures this paper presents a frame theoretic analysis of lowpass dft codes with erasures first it is shown that such codes make a special class of frames then the message reconstructions by the frame theoretic signal space projection and coding theoretic syndrome decoding of erasures are analyzed and their equivalence is proved the error performance of lowpass dft codes is analyzed using the frame theory the analysis helps in classifying the subframes of a dft frame into several classes this classification leads to the development of packetization criteria in order to guarantee minimum mean square reconstruction error and thus to minimize the effect of the quantization error simulation results substantiate the presented theory and the proposed packetization schemes

structured backward error for palindromic polynomial eigenvalue problems a detailed structured backward error analysis for four kinds of palindromic polynomial eigenvalue problems ppep left sum ell 0 d a ell lambda ell right x 0 quad a d ell varepsilon a ell star quad rm for ell 0 1 ldots lfloor d 2 rfloor is one of the two actions transpose and conjugate transpose and varepsilon in pm 1 each of them has its application background with the case star taking transpose and e 1 attracting a great deal of attention lately because of its application in the fast train modeling computable formulas and bounds for the structured backward errors are obtained the analysis reveals distinctive features of ppep from general polynomial eigenvalue problems pep investigated by tisseur linear algebra appl 309 339 361 2000 and by liu and wang appl math comput 165 405 417 2005

perturbation theory for homogeneous polynomial eigenvalue problems we consider polynomial eigenvalue problems p a alpha beta x 0 in which the matrix polynomial is homogeneous in the eigenvalue alpha beta uc2 in this framework infinite eigenvalues are on the same footing as finite eigenvalues we view the problem in projective spaces to avoid normalization of the eigenpairs we show that a polynomial eigenvalue problem is well posed when its eigenvalues are simple we define the condition numbers of a simple eigenvalue alpha beta and a corresponding eigenvector x and show that the distance to the nearest ill posed problem is equal to the reciprocal of the condition number of the eigenvector x we describe a bihomogeneous newton method for the solution of the homogeneous polynomial eigenvalue problem homogeneous pep

mimo ofdm with nonlinear power amplifiers the influence of nonlinear power amplifiers pas on the performance of multiple input multiple output mimo orthogonal frequency division multiplexing ofdm systems is investigated a full mimo scheme with transmitters tx precoding and receivers rx decoding is considered it is shown under assumption of high order ofdm and frequency selective channel that the ratio between the useful signal and the nonlinear distortions is proportional to the number of tx antennas i e the influence of the nonlinear distortions decreases as the number of tx antennas increases the distortion reduction factor drf is proposed as a performance metric for mimo ofdm systems with nonlinear pas a general formula for signal to distortion and noise ratio is obtained for the nonlinear pa with memory described by the wiener hammerstein wh model special cases of mimo such as maximum ratio transmission mrt and maximum ratio combining mrc are considered a full agreement between the theoretical and simulation results is obtained the main contribution of this paper is in a statement that tx processing reduces the effect of nonlinear distortions this is obtained by novel approach for analysis of the mimo ofdm systems with nonlinear pas with memory

regularization methods for semidefinite programming we introduce a new class of algorithms for solving linear semidefinite programming sdp problems our approach is based on classical tools from convex optimization such as quadratic regularization and augmented lagrangian techniques we study the theoretical properties and we show that practical implementations behave very well on some instances of sdp having a large number of constraints we also show that the boundary point method from povh rendl and wiegele computing 78 2006 pp 277 286 is an instance of this class

single symbol ml decoding for orthogonal and quasi orthogonal stbc in clipped mimo ofdm systems using a clipping noise model with gaussian approximation an efficient way to reduce the peak to average power ratio papr in ofdm systems is clipping after the clipping in an mimo ofdm system the additive noise may not be white in this paper we develop fast single symbol ml decoding algorithms for orthogonal space time block codes ostbc and linearly transformed quasi orthogonal space time block codes qostbc in clipped mimo ofdm systems by using a clipping noise model with gaussian approximation by using the statistics of the clipping distortions our newly developed fast ml decoding algorithms improve the performance for clipped mimo ofdm systems with ostbc and qostbc while the decoding complexities are not increased simulation results are presented to illustrate the improvement

on the optimum multicarrier performance with memoryless nonlinearities it is widely recognized that orthogonal frequency division multiplexing ofdm signals are very prone to nonlinear distortion effects which can lead to significant performance degradation however recent results have showed that nonlinear distortion effects do not necessarily mean performance degradation and can actually lead to performance improvements relative to conventional linear ofdm schemes in this paper we consider the effects of bandpass memoryless nonlinear devices on ofdm signals and study the optimum asymptotic performance for both nondispersive channels and severely time dispersive channels we present analytical methods for obtaining the euclidean distance between two ofdm signals that are subjected to different nonlinear characteristics these results are then employed for obtaining the average asymptotic gain relative to conventional linear ofdm schemes in nondispersive channels and the gain distribution for severely time dispersive channels with rayleigh distributed fading on the different multipath components our analytical results which are shown to be very accurate indicate that the optimum detection of ofdm schemes with strong nonlinear distortion effects allows significant gains when compared with conventional linear ofdm schemes

numerical computation of an analytic singular value decomposition of a matrix valued function this paper extends the singular value decomposition to a path of matricese t an analytic singular value decomposition of a path of matricese t is an analytic path of factorizationse t x t s t y t t wherex t andy t are orthogonal ands t is diagonal to maintain differentiability the diagonal entries ofs t are allowed to be either positive or negative and to appear in any order this paper investigates existence and uniqueness of analytic svd s and develops an algorithm for computing them we show that a real analytic pathe t always admits a real analytic svd a full rank smooth pathe t with distinct singular values admits a smooth svd we derive a differential equation for the left factor develop euler like and extrapolated euler like numerical methods for approximating an analytic svd and prove that the euler like method converges

lovasz schrijver sdp operator near perfect graphs and near bipartite graphs we study the lovasz schrijver lift and project operator mathrm text ls ls based on the cone of symmetric positive semidefinite matrices applied to the fractional stable set polytope of graphs the problem of obtaining a combinatorial characterization of graphs for which the mathrm text ls ls operator generates the stable set polytope in one step has been open since 1990 we call these graphs mathrm text ls ls perfect in the current contribution we pursue a full combinatorial characterization of mathrm text ls ls perfect graphs and make progress towards such a characterization by establishing a new close relationship among mathrm text ls ls perfect graphs near bipartite graphs and a newly introduced concept of full support perfect graphs

a class of nonlinear signal processing schemes for bandwidth efficient ofdm transmission with low envelope fluctuation this work presents a wide class of digital signal processing schemes for orthogonal frequency division multiplexing ofdm transmission which combine a nonlinear operation in the time domain and a linear filtering operation in the frequency domain the ultimate goal of these schemes is to reduce the envelope fluctuation of ordinary ofdm while keeping its high spectral efficiency and allowing a low cost power efficient implementation an appropriate statistical model concerning the transmitted frequency domain blocks is developed which is derived from well established results on gaussian stochastic processes distorted by memoryless nonlinearities this model can be employed for performance evaluation by analytical means with highly accurate results whenever the corresponding conventional ofdm signals exhibit quasi gaussian characteristics cases where the signal processing scheme is repeatedly used in an iterative way are treated through an extension of the proposed statistical modeling a set of numerical results is presented and discussed so as to show the practical interest of both the proposed schemes and the analytical methods for evaluation of their performance for the sake of comparisons this paper includes numerical results concerning the partial transmit sequence technique which is an alternative peak to mean envelope power ratio reducing technique of higher complexity often recommended due to its distortionless nature the superior performance complexity tradeoffs through the proposed class of nonlinear signal processing schemes is emphasized

backward error condition numbers and pseudospectra for the multiparameter eigenvalue problem we define and evaluate the normwise backward error and condition numbers for the multiparameter eigenvalue problem mep the pseudospectrum for the mep is defined and characterized we show that the distance from a right definite mep to the closest non right definite mep is related to the smallest unbounded pseudospectrum some numerical results are given

finite dimensional multiparameter spectral theory the nonderogatory case abstract a completeness theorem for nonderogatory eigenvalues of multiparameter systems is proved in a finite dimensional setting also a basis for the second root subspace of a simple eigenvalue is given weakly elliptic multiparameter systems are introduced it is shown that simple real eigenvalues of such systems are nonderogatory

strong lift and project cutting planes for the stable set problem a great deal of research has been focusing since the early seventies on finding strong relaxations for the stable set problem polyhedral combinatorics techniques have been at first developed to strengthen the natural linear formulation afterward strong semidefinite programming relaxations have been deeply investigated nevertheless the resulting integer programming ip algorithms cannot be regarded as being quite successful in practice as most of the relaxations give rise to one out of two extreme situations either provide weak bounds at low computational cost or give good bounds sometimes excellent but too demanding to compute in this paper we present a method to bridge such a gap in particular a new lift and project relaxation is obtained by a problem specific variant of the lifting operator m k k by lovasz and schrijver combined with benders decomposition this yields strong cutting planes generated by solving a cut generating linear program an extensive computational experience shows that embedding these cuts in a branch and cut framework significantly reduces the size of the enumeration trees as well as the cpu times with respect to state of the art ip algorithms

an application of the lovasz schrijver m k k operator to the stable set problem although the lift and project operators of lovasz and schrijver have been the subject of intense study their m k k operator has received little attention we consider an application of this operator to the stable set problem we begin with an initial linear programming lp relaxation consisting of clique and non negativity inequalities and then apply the operator to obtain a stronger extended lp relaxation we discuss theoretical properties of the resulting relaxation describe the issues that must be overcome to obtain an effective practical implementation and give extensive computational results remarkably the upper bounds obtained are sometimes stronger than those obtained with semidefinite programming techniques