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

a novel decomposition analysis of nonlinear distortion in ofdm transmitter systems in orthogonal frequency division multiplexing ofdm transmitter systems nonlinear distortion is a major impairment caused by power amplifier pa the distortion is constituted by numerous noise like inter modulation products imps although the overall behavior of nonlinear imp distortion has been well studied in large multi carrier contexts such as in ofdm the knowledge of individual imps and their quantitative interrelationships together with the derivation of behavioural knowledge and the predictability of consequences arising from such interrelationships is a fairly unexplored topic this is the subject of this paper the powers of the very numerous individual imps generated are analytically derived based on a bessel fourier pa behavioural model and it is proven that these powers have only a small number of distinct powers proven also is that the ratios of these power values are constants and that these constants are invariant with the particular pa s nonlinearity characteristics or operating point further it is proven that specific types of imps dominate nonlinear distortion effects finally it is shown that imp power spectra can be derived from a simple product of two polynomials which are quadrature functions of frequency and pa operating point respectively application possibilities for findings presented in this paper such as their potential to contribute efficiency improvements in ofdm system modulation fidelity calculations over 1100 times faster than conventional methods are also outlined in the conclusions

nonlinear equalization of hammerstein ofdm systems a practical orthogonal frequency division multiplexing ofdm system can generally be modelled by the hammerstein system that includes the nonlinear distortion effects of the high power amplifier hpa at transmitter in this contribution we advocate a novel nonlinear equalization scheme for ofdm hammerstein systems we model the nonlinear hpa which represents the static nonlinearity of the ofdm hammerstein channel by a b spline neural network and we develop a highly effective alternating least squares algorithm for estimating the parameters of the ofdm hammerstein channel including channel impulse response coefficients and the parameters of the b spline model moreover we also use another b spline neural network to model the inversion of the hpa s nonlinearity and the parameters of this inverting b spline model can easily be estimated using the standard least squares algorithm based on the pseudo training data obtained as a byproduct of the hammerstein channel identification equalization of the ofdm hammerstein channel can then be accomplished by the usual one tap linear equalization as well as the inverse b spline neural network model obtained the effectiveness of our nonlinear equalization scheme for ofdm hammerstein channels is demonstrated by simulation results

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

the extended sequentially drilled joint congruence transformation and its application in gaussian independent vector analysis independent vector analysis iva has emerged in recent years as an extension of independent component analysis ica into multiple sets of mixtures where the sources in each set are independent but may depend on sources in the other sets in a semiblind iva framework information regarding the probability distributions of the sources may be available giving rise to maximum likelihood ml separation in recent work we have shown that under the multivariate gaussian model with arbitrary temporal covariance matrices stationary or non stationary of the sources ml separation requires the solution of a sequentially drilled joint congruence sedjoco transformation of a set of matrices which is reminiscent of but different from classical joint diagonalization in this paper we extend our results to the iva problem showing how the ml solution for the gaussian model with arbitrary covariance and cross covariance matrices takes the form of an extended sedjoco solution we formulate the extended problem derive a condition for the existence of a solution and propose two iterative solution algorithms additionally we derive the induced cramer rao lower bound icrlb on the resulting interference to source ratios isr and demonstrate by simulation how the ml separation obtained by solving the extended sedjoco problem attains the icrlb asymptotically as opposed to other separation approaches which cannot exploit prior knowledge regarding the sources distributions

irreducible restrictions of representations of symmetric and alternating groups in small characteristics abstract building on reduction theorems and dimension bounds for symmetric groups obtained in our earlier work we classify the irreducible restrictions of representations of the symmetric and alternating groups to proper subgroups such a classification is known when the characteristic of the ground field is greater than 3 but the small characteristics cases require a substantially more delicate analysis and new ideas our results fit into the aschbacher scott program on maximal subgroups of finite classical groups

representations of the alternating group which are irreducible over subgroups let f be an algebraically closed field of characteristic p geq 0 and a n be the alternating group on n letters the main goal of this paper is to describe the pairs g e where e is an irreducible fa n module and g 3 the case p 0 has been treated by j saxl the problem is important for the classification of maximal subgroups in finite classical groups 2000 mathematical subject classification 20c20 20c30 20b35 20b20

on the accuracy of the gaussian approximation for the evaluation of nonlinear effects in ofdm signals the almost gaussian nature of ofdm orthogonal frequency division multiplexing signals with high number of subcarriers n is widely employed to characterize nonlinearly distorted ofdm signals and to evaluate the corresponding performance in this paper we study the accuracy of the gaussian approach when evaluating nonlinear effects in ofdm signals with finite number of subcarriers showing the strengths and limitations of this approach it is shown that the decomposition in useful and self interference components is valid even for a reduced number of subcarriers the gaussian approximation of the nonlinear self interference at the subcarrier level is very accurate provided that n2 is high however the nonlinear distortion levels slightly lower than the ones obtained with the gaussian approximation with relative errors dropping with 1 n leading to somewhat pessimistic sir levels signal to interference ratio

maximum likelihood detection of nonlinearly distorted multicarrier symbols by iterative decoding this paper proposes a new method for decoding multicarrier symbols with severe nonlinear distortion the first part evaluates mutual information expressions for practical nonlinear models and shows the performance bounds for commonly used receiver structures then we derive the maximum likelihood ml sequence estimator which unfortunately has an exponential complexity due to the nonlinear distortion this extremely large complexity can be reduced with a simple algorithm that iteratively estimates the nonlinear distortion thereby reducing the exponential ml to the standard ml without nonlinear distortion the proposed method can be used to reduce the peak to average power ratio of multicarrier signals by clipping the transmit sequence it can also be used to correct any nonlinear distortion present in transmitter receiver amplifiers that are operating close to saturation

asymptotically compatible schemes and applications to robust discretization of nonlocal models many problems in nature being characterized by a parameter are of interest both with a fixed parameter value and with the parameter approaching an asymptotic limit numerical schemes that are convergent in both regimes offer robust discretizations which can be highly desirable in practice the asymptotically compatible schemes studied in this paper meet such objectives for a class of parametrized problems an abstract mathematical framework is established rigorously here together with applications to the numerical solution of both nonlocal models and their local limits in particular the framework can be applied to nonlocal diffusion models and a general state based peridynamic system parametrized by the horizon radius recent findings have exposed the risks associated with some discretizations of nonlocal models when the horizon radius is proportional to the discretization parameter thus it is desirable to develop asymptotically compatible schemes for such models so as to offer robust numerical dis

frequency independent and frequency dependent nonlinear models of twt amplifiers simple two parameter formulas are presented for the functions involved in the amplitude phase and the quadrature nonlinear models of a twt amplifier and are shown to fit measured data very well also a closed form expression is derived for the output signal of a twt amplifier excited by two phase modulated carriers and an expression containing a single integral is given when more than two such earriers are involved finally a frequencydependent quadrature model is proposed whose parameters are obtainable from single tone measurements

a partially decoupled rls algorithm for volterra filters in this correspondence we consider a partially decoupled variation of the rls algorithm it is based on a constrained optimization of the cumulative filter error using the higher order sets of filter weights to improve on the performance of the lower order weight sets whose values are already established from this constrained optimization a recursive algorithm is developed whose form closely resembles the standard volterra rls algorithm but with structural differences that arise from eliminating the dependence of the lower order weight sets on the higher order weight sets while retaining the dependence of the higher order weights on the lower order weights the resulting algorithm while suboptimal requires less computational effort than the fully coupled version converges to steady state in the same amount of time and is shown by example not to exhibit a substantial degradation in performance

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

spectral precoding for constant envelope ofdm spectrally precoded orthogonal frequency division multiplexing ofdm and constant envelope ofdm ce ofdm are two modified ofdm formats that enhance the signaling features of ofdm while allowing for the efficient implementation by discrete fourier transform and the insertion of guard intervals to counteract channel dispersion the spectrally precoded ofdm signal provides very small power spectral sidelobes decaying asymptotically as f 2j 2 with j integer valued design parameter thereby suppressing sidelobe powers effectively and achieving higher spectral efficiency than nonprecoded rectangularly pulsed ofdm which has power spectral sidelobes decaying asymptotically as f 2 the ce ofdm signal exhibits a unity peak to average power ratio and thus enables the efficient use of transmitter s power amplifier in this paper a specific ce ofdm block signaling format is proposed to incorporate spectral precoding with an aim to suppressing sidelobe powers more effectively than conventional nonprecoded ce ofdm the general constraint on spectral precoding is developed to ensure that the power spectral sidelobes of the spectrally precoded ce ofdm block signal with arbitrary data statistics decay asymptotically as f 2j 2 some spectral codes previously found for spectrally precoded ofdm are shown to meet the constraint and thus suited for spectrally precoded ce ofdm specifically spectral performance is analyzed for the spectrally precoded ce ofdm block signal with independent and identically distributed data to illustrate the prevailing spectral advantage the corresponding receiver is also developed to demodulate the spectrally precoded ce ofdm block signal over dispersive channels

constant envelope ofdm this paper describes a transformation technique aimed at solving the peak to average power ratio papr problem associated with ofdm orthogonal frequency division multiplexing constant envelope ofdm ce ofdm transforms the ofdm signal by way of phase modulation to a signal designed for efficient power amplification at the receiver the inverse transformation phase demodulation is applied prior to the conventional ofdm demodulator the performance of ce ofdm is analyzed in additive white gaussian noise awgn and fading channels ce ofdm is shown to achieve good performance in dense multipath with the use of cyclic prefix transmission in conjunction with a frequency domain equalizer fde by way of computer simulation and hardware realization ce ofdm is shown to compare favorably to conventional ofdm

on the power amplifier nonlinearity in mimo transmit beamforming systems in this paper single carrier multiple input multiple output mimo transmit beamforming tb systems in the presence of high power amplifier hpa nonlinearity are investigated specifically due to the suboptimality of the conventional maximal ratio transmission maximal ratio combining mrt mrc under hpa nonlinearity we propose the optimal tb scheme with the optimal beamforming weight vector and combining vector for mimo systems with nonlinear hpas moreover an alternative suboptimal but much simpler tb scheme namely quantized equal gain transmission qegt is proposed the latter profits from the property that the elements of the beamforming weight vector have the same constant modulus the performance of the proposed optimal tb scheme and qegt mrc technique in the presence of the hpa nonlinearity is evaluated in terms of the average symbol error probability and mutual information with the gaussian input considering the transmission over uncorrelated quasi static frequency flat rayleigh fading channels numerical results are provided and show the effects on the performance of several system parameters namely the hpa parameters numbers of antennas quadrature amplitude modulation modulation order number of pilot symbols and cardinality of the beamforming weight vector codebook for qegt

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

rf power amplifier linearization through amplitude and phase predistortion this paper presents a novel technique for power amplifier linearization in digital microwave radio systems the proposed technique is based on the use of a predistortion circuit whose am am and am pm responses are separately implemented as polynomial approximations of the respective responses of the ideal linearizer the proposed scheme is shown to attain superior performance in comparison with other well known predistortion structures such as those based on the cancellation of third or fifth order distortion with no substantial aggravation in implementation complexity

reduction of the envelope fluctuations of multi carrier modulations using adaptive neural fuzzy inference systems in this paper a novel scheme for reducing the envelope fluctuations in multi carrier signals applying adaptive neural fuzzy inference systems anfis is proposed and analyzed once trained with signals with very low envelope fluctuations such as those obtained by the active constellation expansion approximate gradient project ace agp algorithm anfis approximately reaches a similar reduction as with ace agp for multi carrier signals without the complexity and the large convergence time of conventional ace agp we show that our approach is less complex than other previous schemes and with better performance

complex valued b spline neural networks for modeling and inverting hammerstein systems many communication signal processing applications involve modeling and inverting complex valued cv hammerstein systems we develop a new cv b spline neural network approach for efficient identification of the cv hammerstein system and effective inversion of the estimated cv hammerstein model in particular the cv nonlinear static function in the hammerstein system is represented using the tensor product from two univariate b spline neural networks an efficient alternating least squares estimation method is adopted for identifying the cv linear dynamic model s coefficients and the cv b spline neural network s weights which yields the closed form solutions for both the linear dynamic model s coefficients and the b spline neural network s weights and this estimation process is guaranteed to converge very fast to a unique minimum solution furthermore an accurate inversion of the cv hammerstein system can readily be obtained using the estimated model in particular the inversion of the cv nonlinear static function in the hammerstein system can be calculated effectively using a gaussian newton algorithm which naturally incorporates the efficient de boor algorithm with both the b spline curve and first order derivative recursions the effectiveness of our approach is demonstrated using the application to equalization of hammerstein channels

a practical analysis of performance optimization in ostbc based nonlinear mimo ofdm systems this paper presents a practical performance analysis of an orthogonal space time block code ostbc based multiple input multiple output mimo orthogonal frequency division multiplexing ofdm system in the presence of nonlinear power amplifiers pas the equivalent single input single output siso scalar model is introduced and this then is used to construct a model for the nonlinear mimo ofdm system based on an unique inter modulation product imp analysis it is shown how the receiver signal to noise ratio snr may be derived to a polynomial based function of the system operating point it is also shown that expressions for the asymptotical behavior of this snr when the linear and highly nonlinear pa operations are applied may also be derived based on these derivations it is further shown that the optimal system operating point which corresponds to the maximum receiver snr and sep lower bound can be identified and be derived to a polynomial based expression additionally a general expression for the different integral expressions of sep for the phase shift keying psk and quadrature amplitude modulation qam signals is found by means of these analytical results it was found possible to advance analytical explanations of observed behaviour in simulations and also to provide a practical analysis of performance optimization of nonlinear mimo ofdm systems

sequence detection in nonlinear channels a convenient alternative to analog predistortion a new maximum likelihood sequence detection receiver for spectrally efficient linear modulations on bandlimited bandpass nonlinear channels is proposed the receiver is based on oversampling the received signal corrupted by noise and nonlinear distortion contrary to other solutions in the literature in the proposed technique there is no need for a bank of matched filters and the receiver front end reduces to a single lowpass filter for a given peak power level a performance gain can be achieved over more traditional approaches to transmission on nonlinear channels such as those based on predistortion if a moderate spectral expansion is allowed to analyze the receiver performance the concept of distance spectrum is employed since the minimum distance alone cannot account for a reliable performance evaluation both analysis and simulation are carried out for realistic narrowband nonlinear channels possibly employing reduced state sequence detection appreciable gain margins are confirmed to be possible in these realistic cases

on the use of cascade structure to correct impulsive noise in multicarrier systems we propose a new decoding algorithm based on a cascade structure for impulsive noise correction in multicarrier systems such as orthogonal frequency division multiplexing ofdm based systems this new cascade structure based algorithm has the advantage to lead on one hand to a reduced complexity implementation in an ofdm demodulator and on the other hand to overcome the lacks of other algorithms dedicated for impulsive noise correction to do so we start the derivation by investigating closed form analytical expressions of the a priori probabilities used in hypotheses tests that are necessary for the different steps needed for the execution of the cascade structure based decoding algorithm such closed form expressions for the a priori probabilities result in efficient setups of the threshold values used for the execution of the decoding algorithm furthermore we show that this cascade structure can be applied to efficiently cancel the impulsive noise in ofdm systems as the clipping event present in ofdm systems can be seen as an additive impulsive noise we prove that after introducing some minor modifications we can apply the proposed cascade structure to significantly reduce the peak to average power ratio papr level in such systems simulation results are given to illustrate the usefulness of the proposed algorithm results in practical ofdm based communication systems such as hiperlan 2

performance analysis for ofdm signals with peak cancellation peak cancellation pc is known as one of the simplest peak to average power ratio papr reduction techniques that are applicable to various communications standards the salient advantage of pc is its ease of hardware implementation but it induces in band distortion and out of band radiation in order to restrict the amount of distortion within an acceptable level it is critical to carefully design the cancelling pulses as well as the envelope threshold over which pc is applied in most studies however they are determined empirically through computer simulations this paper thus focuses on a rigorous theoretical analysis of pc applied to band limited orthogonal frequency division multiplexing ofdm signals and discusses its validity and limitation for practical applications based on the level crossing rate approximation of the peak distribution we derive a closed form expression for the achievable signal to distortion power ratio sdr we also analyze the adjacent channel leakage ratio aclr as well as error vector magnitude evm with which the symbol error rate ser over an additive white gaussian noise awgn channel is obtained all the theoretical results developed in this work are compared with those based on the corresponding computer simulations to justify our analytical approach it thus serves as a useful and accurate tool for designing cancelling pulses as well as the threshold level for given specific system requirements such as sdr or evm and aclr

irreducible restrictions of representations of symmetric groups in small characteristics reduction theorems we study irreducible restrictions of modules over symmetric groups to subgroups we get reduction results which substantially restrict the classes of subgroups and modules for which this is possible such results are known when the characteristic of the ground field is greater than 3 but the small characteristics cases require a substantially more delicate analysis and new ideas this work fits into the aschbacher scott program on maximal subgroups of finite classical groups

novel adaptive nonlinear predistorters based on the direct learning algorithm the adaptive nonlinear predistorter is an effective technique to compensate for the nonlinear distortion existing in digital communication and control systems however available adaptive nonlinear predistorters using indirect learning are sensitive to measurement noise and do not perform optimally other available types are either slow to converge complicated in structure and computationally expensive or do not consider the memory effects in nonlinear systems such as a high power amplifier hpa in this paper we first propose several novel adaptive nonlinear predistorters based on direct learning algorithms the nonlinear filtered x rls nfxrls algorithm the nonlinear adjoint lms nalms algorithm and the nonlinear adjoint rls narls algorithm using these new learning algorithms we design adaptive nonlinear predistorters for an hpa with memory effects or for an hpa following a linear system because of the direct learning algorithm these novel adaptive predistorters outperform nonlinear predistorters that are based on the indirect learning method in the sense of normalized mean square error nmse bit error rate ber and spectral regrowth moreover our developed adaptive nonlinear predistorters are computationally efficient and or converge rapidly when compared to other adaptive nonlinear predistorters that use direct learning and furthermore can be easily implemented we further simplify our proposed algorithms by exploring the robustness of our proposed algorithm as well as by examining the statistical properties of what we call the instantaneous equivalent linear iel filter simulation results confirm the effectiveness of our proposed algorithms

performance of combined trellis coded modulation and nonlinear cancellation the performance of nonlinear cancellation schemes is limited by the accuracy of tentative decisions this correspondence analyzes the performance of combined trellis coded modulation and nonlinear cancellation a scheme is proposed to make use of the redundancy of the code it is shown that performance close to optimum can be achieved with this scheme

optimal volterra kernel estimation algorithms for a nonlinear communication system for psk and qam inputs a fifth order volterra kernel estimation algorithm which is optimal in the least mean square error sense for a bandpass nonlinear system is derived the algorithm is based on some characteristics of i i d circularly symmetric zero mean complex valued gaussian random variables the proposed algorithm can be used to identify a nonlinear system under uniformly i i d rectangular m qam input and under uniformly i i d m psk input m spl ges 4 with modest modification the same approach has been used to derive an optimal volterra kernel estimation algorithm up to the third order however in some cases a third order model is not of high enough order to capture the nonlinear system characteristics a simulation example is given to show the necessity of deriving a fifth order volterra kernel estimation algorithm and to test for the correctness of the algorithm

identification of certain time varying nonlinear wiener and hammerstein systems the problem of identification and tracking of time varying nonlinear systems is addressed in particular the wiener system that consists of a dynamic time varying linear part followed by a fixed nonlinearity and the hammerstein system in which the order of these two blocks is reversed are studied the extended kalman filter ekf algorithm is applied it is also shown that this algorithm can be reformulated in terms of a nonlinear minimization problem with a quadratic inequality constraint in order to ensure exponential stability resulting in the algorithm cekf as indicated by means of numerical examples this latter algorithm is less sensitive to the chosen initialization than the ekf the proposed algorithms depend on certain second order statistics that may be unknown in a typical scenario a method for estimation of these quantities is proposed it is demonstrated that the suggested algorithms can be successfully applied to the problem of acoustic echo cancelation

a constructive peridynamic kernel for elasticity abstract different kernel formulations have been proposed and used for bond based peridynamic models of elastic materials while all such kernels produce results that in the limit of the nonlocal region horizon going to zero while grid spacing relative to the horizon size is constant converge not all converge to the classical solution here we introduce a constructive path to arriving at a peridynamic kernel for 1d 2d and 3d elasticity we focus on the particular one point gauss quadrature method of spatial discretization and study the convergence properties of different kernels with respect to the classical local model for dynamic elasticity in 1d where exact representation of geometry is possible we analyze the influence of two ways of imposing boundary conditions and of the skin effect on the solution we show that similar to the diffusion case the peridynamic kernel derived based on physical principles for dynamic elasticity is the only one whose convergence to the classical solution does not depend on the fineness of the discretization grid relative to the nonlocal region size the results presented demonstrate that special care must be taken when claiming validation of peridynamic results by specific comparisons with classical local model solutions

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

on p blocks of symmetric and alternating groups with all irreducible brauer characters of prime power degree abstract we classify all p blocks of the symmetric and alternating groups where all irreducible p brauer characters are of prime power degree as well as the p blocks of these groups where all p brauer characters are of p power degree this is an extension and a block refinement of an earlier result where all irreducible p brauer characters were assumed to be of p power degree

representations of the general linear groups which are irreducible over subgroups we classify all triples g v h such that sl n q leq g leq gl n q v is a representation of g of dimension greater than one over an algebraically closed field bbb f of characteristic prime to q and h is a proper subgroup of g such that the restriction v downarrow h is irreducible this problem is a natural part of the aschbacher scott program on maximal subgroups in finite classical groups

convergence adaptive refinement and scaling in 1d peridynamics we introduce here adaptive refinement algorithms for the non local method peridynamics which was proposed in j mech phys solids 2000 48 175 209 as a reformulation of classical elasticity for discontinuities and long range forces we use scaling of the micromodulus and horizon and discuss the particular features of adaptivity in peridynamics for which multiscale modeling and grid refinement are closely connected we discuss three types of numerical convergence for peridynamics and obtain uniform convergence to the classical solutions of static and dynamic elasticity problems in 1d in the limit of the horizon going to zero continuous micromoduli lead to optimal rates of convergence independent of the grid used while discontinuous micromoduli produce optimal rates of convergence only for uniform grids examples for static and dynamic elasticity problems in 1d are shown the relative error for the static and dynamic solutions obtained using adaptive refinement are significantly lower than those obtained using uniform refinement for the same number of nodes copyright 2008 john wiley sons ltd

surjective word maps and burnside s p aq b theorem we prove surjectivity of certain word maps on finite non abelian simple groups more precisely we prove the following if n is a product of two prime powers then the word map x y mapsto x ny n is surjective on every finite non abelian simple group if n is an odd integer then the word map x y z mapsto x ny nz n is surjective on every finite quasisimple group these generalize classical theorems of burnside and feit thompson we also prove asymptotic results about the surjectivity of the word map x y mapsto x ny n that depend on the number of prime factors of the integer n

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

performance of volterra and mlsd receivers for nonlinear band limited satellite systems this paper evaluates the performance of volterra equalizers and maximum likelihood sequence detection mlsd receivers for compensation of signal distortion in nonlinear band limited satellite systems in addition the performance of a receiver with a fractionally spaced equalizer followed by a volterra equalizer is studied fse volterra equalizer for the equalizers adaptation of the equalizer weights is considered including a multiple step lms algorithm which improves the convergence characteristics two mlsd receiver structures are considered the optimum receiver consisting of a matched filter bank followed by a viterbi 1967 detector and a suboptimum receiver consisting of a single receiver filter followed by a viterbi detector the performance of the mlsd receivers is then compared to that of the equalizers

cancellation of nonlinearities in bandpass qam systems an orthogonalized input output characterization of nonlinear bandpass quadrature amplitude modulation systems with memory is developed the orthogonal expansion is used with a nonlinear canceller structure to counteract the effect of nonlinear distortion introduced by high power amplifiers at the transmitter it is shown through simulations that when the transmitted symbols are known at the canceller relatively simple structures can eliminate the effect of the nonlinearity even when the transmitted symbols are not known at the canceller the improvement in performance with the nonlinear canceller with respect to a linear receiver is significant

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

a morphing approach to couple state based peridynamics with classical continuum mechanics abstract a local nonlocal coupling technique called the morphing method is developed to couple classical continuum mechanics with state based peridynamics state based peridynamics which enables the description of cracks that appear and propagate spontaneously is applied to the key domain of a structure where damage and fracture are considered to have non negligible effects in the rest of the structure classical continuum mechanics is used to reduce computational costs and to simultaneously satisfy solution accuracy and boundary conditions both models are glued by the proposed morphing method in the transition region the morphing method creates a balance between the stiffness tensors of classical continuum mechanics and the weighted coefficients of state based peridynamics through the equivalent energy density of both models linearization of state based peridynamics is derived by taylor approximations based on vector operations the discrete formulation of coupled models is also described two dimensional numerical examples illustrate the validity and accuracy of the proposed technique it is shown that the morphing method originally developed for bond based peridynamics can be successfully extended to state based peridynamics through the original developments presented here

nonlinear channel equalization with gaussian processes for regression we propose gaussian processes for regression gpr as a novel nonlinear equalizer for digital communications receivers gpr s main advantage compared to previous nonlinear estimation approaches lies on their capability to optimize the kernel hyperparameters by maximum likelihood which improves its performance significantly for short training sequences besides gpr can be understood as a nonlinear minimum mean square error estimator a standard criterion for training equalizers that trades off the inversion of the channel and the amplification of the noise in the experiment section we show that the gpr based equalizer clearly outperforms support vector machine and kernel adaline approaches exhibiting outstanding results for short training sequences

on restrictions of modular spin representations of symmetric and alternating groups let f be an algebraically closed field of characteristic p and h be an almost simple group or a central extension of an almost simple group an important problem in representation theory is to classify the subgroups g of h and fh modules v such that the restriction v g is irreducible for example this problem is a natural part of the program of describing maximal subgroups in finite classical groups in this paper we investigate the case of the problem where h is the schur s double cover n or s n

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

conditioning analysis of nonlocal integral operators in fractional sobolev spaces we study the conditioning of nonlocal integral operators with singular and integrable kernels in fractional sobolev spaces these operators are used for instance in peridynamics formulation and nonlocal diffusion in one dimension 1d we present sharp quantification of the extremal eigenvalues in all three parameters size of nonlocality mesh size and regularity of the fractional sobolev space we accomplish sharpness both rigorously and numerically for the minimal eigenvalue we obtain sharpness analytically by using a nonlocal characterization of sobolev spaces we verify this estimate by exploiting the toeplitz property of the stiffness matrix however the analytical approach fails to give sharp quantification of the maximal eigenvalue hence in 1d we take an algebraic approach by directly working with the stiffness matrix entries which have complicated expressions due to all three parameters we systematically characterize the nonzero entries and dramatically simplify their expressions by u

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

representations of the alternating group which are irreducible over subgroups ii nsf dms 1161094 dms 0901241 dms 1201374 humboldt foundation simons foundation 204181 simons foundation fellowship 305247

analysis and approximation of nonlocal diffusion problems with volume constraints a recently developed nonlocal vector calculus is exploited to provide a variational analysis for a general class of nonlocal diffusion problems described by a linear integral equation on bounded domains in mbrn the nonlocal vector calculus also enables striking analogies to be drawn between the nonlocal model and classical models for diffusion including a notion of nonlocal flux the ubiquity of the nonlocal operator in applications is illustrated by a number of examples ranging from continuum mechanics to graph theory in particular it is shown that fractional laplacian and fractional derivative models for anomalous diffusion are special cases of the nonlocal model for diffusion that we consider the numerous applications elucidate different interpretations of the operator and the associated governing equations for example a probabilistic perspective explains that the nonlocal spatial operator appearing in our model corresponds to the infinitesimal generator for a symmetric jump process sufficie

variational theory and domain decomposition for nonlocal problems abstract in this article we present the first results on domain decomposition methods for nonlocal operators we present a nonlocal variational formulation for these operators and establish the well posedness of associated boundary value problems proving a nonlocal poincare inequality to determine the conditioning of the discretized operator we prove a spectral equivalence which leads to a mesh size independent upper bound for the condition number of the stiffness matrix we then introduce a nonlocal two domain variational formulation utilizing nonlocal transmission conditions and prove equivalence with the single domain formulation a nonlocal schur complement is introduced we establish condition number bounds for the nonlocal stiffness and schur complement matrices supporting numerical experiments demonstrating the conditioning of the nonlocal one and two domain problems are presented

continuous and discontinuous finite element methods for a peridynamics model of mechanics in contrast to classical partial differential equation models the recently developed peridynamic nonlocal continuum model for solid mechanics is an integro differential equation that does not involve spatial derivatives of the displacement field as a result the peridynamic model admits solutions having jump discontinuities so that it has been successfully applied to fracture problems the peridynamic model features a horizon which is a length scale that determines the extent of the nonlocal interactions based on a variational formulation continuous and discontinuous galerkin finite element methods are developed for the peridynamic model discontinuous discretizations are conforming for the model without the need to account for fluxes across element edges through a series of simple one dimensional computational experiments we investigate the convergence behavior of the finite element approximations and compare the results with theoretical estimates one issue addressed is the effect of the relative sizes of the horizon and the grid for problems with smooth solutions we find that continuous and discontinuous piecewise linear approximations result in the same accuracy as that obtained by continuous piecewise linear approximations for classical models piecewise constant approximations are less robust and require the grid size to be small with respect to the horizon we then study problems having solutions containing jump discontinuities for which we find that continuous approximations are not appropriate whereas discontinuous approximations can result in the same convergence behavior as that seen for smooth solutions in case a grid point is placed at the locations of the jump discontinuities such results are directly obtained in the general case we show that such results can be obtained through a simple automated abrupt local refinement of elements containing the discontinuity in order to reduce the number of degrees of freedom while preserving accuracy we also briefly consider a hybrid discretization which combines continuous discretizations in regions where the solution is smooth with discontinuous discretizations in small regions surrounding the jump discontinuities

partially decoupled volterra filters formulation and lms adaptation the adaptation of volterra filters by one particular method the method of least mean squares lms while easily implemented is complicated by the fact that upper hounds for the values of step sizes employed by a parallel update lms scheme are difficult to obtain in this paper we propose a modification of the volterra filter in which the filter weights of a given order are optimized independently of those weights of higher order using this approach we then solve the minimum mean square error mmse filtering problem as a series of constrained optimization problems which produce a partially decoupled normal equation for the volterra filter from this normal equation we are able to develop an adaptation routine that uses the principles of partial decoupling that is similar in form to the volterra lms algorithm but with important structural differences that allow a straightforward derivation of bounds on the algorithm s step sizes these bounds can be shown to depend on the respective diagonal blocks of the volterra autocorrelation matrix this produces a reliable set of design guidelines that allow more rapid convergence of the lower order weight sets

a class of signal processing schemes for reducing the envelope fluctuations of cdma signals in this paper we present a class of nonlinear signal processing schemes to reduce the envelope fluctuations in the downlink transmission within code division multiple access cdma systems these schemes are compatible with conventional cdma receivers since they just require some modifications at the transmitter side the proposed transmitter structure includes a nonlinear operation in the time domain followed by a linear frequency domain filtering operation we also include a semi analytical statistical characterization of the transmitted signals which takes advantage of the gaussian like nature of cdma signals with a high number of users this characterization is used for an analytical performance evaluation of the proposed techniques a set of performance results is presented showing that we can reduce significantly the envelope fluctuations of the transmitted signals while maintaining the spectral occupation of the corresponding conventional cdma signals moreover the performance degradation due to the nonlinear distortion effects on the transmitted signals can be kept relatively low

analysis and comparison of different approximations to nonlocal diffusion and linear peridynamic equations we consider the numerical solution of nonlocal constrained value problems associated with linear nonlocal diffusion and nonlocal peridynamic models two classes of discretization methods are presen

iterative cancellation of non linear distortion noise in digital communication systems in this paper an iterative receiver that performs non linear distortion noise cancellation is presented the performance is assessed for time division multiple access tdma orthogonal frequency division multiple access ofdma and single carrier frequency division multiple access sc fdma waveforms even though a return link setup is considered the receiver is equally applicable in the forward link taking into account the differences in the data multiplexing and the channel analytical modeling of the received electrical signal to noise ratio snr is carried out for ofdma with one iteration of non linear distortion noise cancellation the performance is assessed in terms of power efficiency and spectral efficiency where the total degradation td of the received snr in a non linear channel is minimized the modulation formats of the dvb rcs2 satellite return link standard and a respective non linear channel have been used ofdma shows the highest power efficiency gain of 1 1 2 5 db with 2 iterations of non linear noise cancellation across the different modulation orders in sc fdma the gain is in the range of 0 3 1 1 db while gains of 0 1 0 8 db and 0 2 1 9 db are presented in tdma with 20 roll off and 5 roll off respectively

passive detection of correlated subspace signals in two mimo channels in this paper we consider a two channel multiple input multiple output passive detection problem in which there is a surveillance array and a reference array the reference array is known to carry a linear combination of broadband noise and a subspace signal of known dimension but unknown basis the question is whether the surveillance channel carries a linear combination of broadband noise and a subspace signal of the same dimension but unknown basis which is correlated with the subspace signal in the reference channel we consider a second order detection problem where these subspace signals are structured by an unknown but common p dimensional random vector of symbols transmitted from sources of opportunity and then received through unknown m times p matrices at each of the m element arrays the noises in each channel have spatial correlation models ranging from arbitrarily correlated to independent with identical variances we provide a unified framework to derive the generalized likelihood ratio test for these different noise models in the most general case of arbitrary noise covariance matrices the test statistic is a monotone function of canonical correlations between the reference and surveillance channels