an almost sure large deviation principle for the hopfield model we prove a large deviation principle for the finite dimensional marginals of the gibbs distribution of the macroscopic overlap parameters in the hopfield model in the case where the number of random patterns m as a function of the system size n satisfies lim sup m n n 0 in this case the rate function is independent of the disorder for almost all realizations of the patterns

convergence of the complex envelope of bandlimited ofdm signals orthogonal frequency division multiplexing ofdm systems have been used extensively in wireless communications in recent years thus there is significant interest in analyzing the properties of the transmitted signal in such systems in particular a large amount of work has focused on analyzing the variation of the complex envelope of the transmitted signal and on designing methods to minimize this variation in this paper it is established that the complex envelope of a bandlimited uncoded ofdm signal converges weakly to a gaussian random process as the number of subcarriers goes to infinity this shows that the properties of the ofdm signal will asymptotically approach those of a gaussian random process over any finite time interval the convergence proof is then extended to two important cases namely coded ofdm systems and systems with an unequal power allocation across subcarriers

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

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

models of degenerate fourier integral operators and radon transforms fourier integral operators whose lagrangians project with singularities arise frequently in many areas of analysis and geometry 3 5 9 10 18 20 however there are as yet few analytic tools available for their study and even their simplest regularity properties with respect to the singularities of the lagrangian are still obscure 4 5 13 16 in this paper we study a class of oscillatory integrals ta and fourier integral operators r which can be expected to model the higher order singularities of the lagrangian they have homogeneous polynomial phases in two variables of order n and indeed the case n 3 is the model for lagrangians which project with whitney folds 3 10 11 the main difficulty which sets the higher order degeneracy cases n 4 apart from the the lower ones n 2 3 is that the critical varieties which arise there are usually not smooth manifolds a systematic study of these oscillatory integrals was begun in 14 the main idea in that work was to treat the critical varieties as smooth manifolds away from a lower dimensional subvariety and to keep track of the distance to this lower dimensional subvariety to achieve this we introduced a method of stationary phase which exhibited clearly the dependence on the distance between critical points the method gave sharp bounds on the size of the kernel k x y of tat but no information on its phase and the resulting cancellations it does not seem possible to refine this approach to the phase level and this suggests looking instead for decompositions of the operators ta which can incorporate indirectly the required cancellations the main goal of this paper is to introduce such decompositions these decompositions which we will try to describe momentarily reflect the singular nature of the critical points and are powerful enough to yield sharp bounds for the above oscillatory integrals and radon transforms although the models under consideration are very

rigorous solution of the gardner problem we prove rigorously the well known result of gardner about the typical fractional volume of interactions between n spins which solve the problem of storing a given set of p random patterns the gardner formula for this volume in the limit n p p n is proven for all values of besides we prove a useful criterion for the factorisation of all correlation functions for a class of models of classical statistical mechanics

peak value estimation of bandlimited signals from their samples noise enhancement and a local characterization in the neighborhood of an extremum the paper addresses the problem of estimating the peak value of bandlimited signals from their samples with and without oversampling this problem has significant relevance to orthogonal frequency division multiplexing ofdm signal processing and system design in particular an upper bound on the peak value is established given the peak value of the samples and the oversampling rate moreover it is shown that the bounds are sharp for all practical rates by constructing bandlimited signals taking on this bound the proof also provides a local characterization of bandlimited signals in the neighborhood of an extremum a different analysis examines the effect of small errors in the samples it is shown that oversampling can provide robust recovery in the sense that small errors in the samples lead to small errors in the reconstructed signal again an upper bound is derived relating the peak error in the samples and the peak error in the signals furthermore both problems are shown to be coupled and put in a unifying context the bounds are compared and applied to problems concerning ofdm

gibbs states of the hopfield model with extensively many patterns we consider the hopfield model withm n n patterns wheren is the number of neurons we show that if is sufficiently small and the temperature sufficiently low then there exist disjoint gibbs states for each of the stored patterns almost surely with respect to the distribution of the random patterns this solves a provlem left open in previous work the key new ingredient is a self averaging result on the free energy functional this result has considerable additional interest and some consequences are discussed a similar result for the free energy of the sherrington kirkpatrick model is also given

the free energy of a class of hopfield models we show that in the limitp n 0 p n 0 the limit free energy of the hopfield model equals in probability the curie weiss free energy we prove also that the free energy of the hopfield model is self averaging for any finite

a balancing method for pmepr reduction in ofdm signals a relation is established between the strength of a binary code over the alphabet 1 1 and its ability to reduce peak to mean envelope power ratio pmepr in n subcarrier ofdm signals based on this relation a method is proposed to deterministically bound pmepr of such signals using coordinate wise multiplication by a balancing vector bv chosen from a code of given strength a practical probabilistic scheme considering a small number of candidate codewords is devised for this scheme estimates on the pmepr reduction achievable with arbitrary high probability are derived in particular the scheme provides for large n pmepr of lnn 2 01lnlnn with ln2 middot log2n 2 1 bits of redundancy the failure probability at most e n and testing n lnlnn candidate bvs finally several practical settings are considered for example for quaternary phase shift keying n 128 the scheme with 36 bits of redundancy 18 redundant subcarriers by testing only 4 bvs provides over 2 db pmepr reduction for any failure rate below 10 2 5

absence of self averaging of the order parameter in the sherrington kirkpatrick model we prove that if n is the sherrington kirkpatrick sk hamiltonian and the quantity bar q n n 1 sum left langle s l right rangle h 2 converges in the variance to a nonrandom limit asn then the mean free energy of the model converges to the expression obtained by sk since this expression is known not to be correct in the low temperature region our result implies the non self averaging of the order parameter of the sk model this fact is an important ingredient of the parisi theory which is widely believed to be exact we also prove that the variance of the free energy of the sk model converges to zero asn i e the free energy has the self averaging property

peak to average power control via tone reservation in general orthonormal transmission systems in this paper we study the tone reservation method for reducing the peak to average power ratio papr in general orthonormal transmission systems we prove that strong solvability where the peak value of the transmit signal has to be bounded by a constant times the energy of the information symbols is equivalent to weak solvability where the peak value of the transmit signal has to be only bounded further we show that in the case where the papr problem is not weakly solvable almost all information sequences lead to an unbounded transmit signal

optimal tone reservation for cdma systems in this paper we analytically analyze the tone reservation method for the reduction of the peak to average power ratio papr in code division multiple access systems that employ the walsh functions we find the best possible reduction of the papr and give one optimal information set that achieves this reduction interestingly when using more than one information carrier the smallest possible extension constant is independent of the size of the information set and has the value sqrt 2 we further show that the minimal extension constant can also be achieved with finite compensation sets and illustrate the findings with a numerical example for certain special cases we are also able to provide results for the system of complex exponentials which is employed in orthogonal frequency division multiplexing

about the ergodic regime in the analogical hopfield neural networks moments of the partition function in this paper we introduce and exploit the real replica approach for a minimal generalization of the hopfield model by assuming the learned patterns to be distributed according to a standard unit gaussian we consider the high storage case when the number of patterns linearly diverges with the number of neurons we study the infinite volume behavior of the normalized momenta of the partition function we find a region in the parameter space where the free energy density in the infinite volume limit self averages around its annealed approximation as well as the entropy and the internal energy density moreover we evaluate the corrections to their extensive counterparts with respect to their annealed expressions the fluctuations of properly introduced overlaps which act as order parameters are also discussed

asymptotic limits in peak envelope power reduction by redundant coding in orthogonal frequency division multiplex modulation this paper uses some computational results to show that the peak envelope power pep of orthogonal frequency division multiplex ofdm waveforms can be reduced very substantially by coding to select only those messages with low peak factor as valid codewords in the scheme it is shown that the asymptotic limit of the pep is between two and three and that only four bits of redundancy are necessary to limit the pep to within 10 of this optimum value as the number of carriers becomes large

on the computation and reduction of the peak to average power ratio in multicarrier communications for any code c defined over an equal energy constellation it is first shown that at any time instance the problem of determining codewords of c with high peak to average power ratios papr in a multicarrier communication system is intimately related to the problem of minimum distance decoding of c subsequently a method is proposed for computing the papr by minimum distance decoding of c at many points of time moreover an upper bound on the error between this computed value and the true one is derived analogous results are established for codes defined over arbitrary signal constellations as an application of this computational method an approach for reducing the papr of c proposed by jones and wilkinson 1996 is revisited this approach is based on introducing a specific phase shift to each coordinate of all the codewords where phase shifts are independent of the codewords and known both to the transmitter and the receiver we optimize the phase shifts offline by applying our method for computing the papr for the coding scenario proposed by the etsi bran standardization committee reductions of order 4 5 db can be freely obtained using the computed phase shifts examples are provided showing that most of the gain is preserved when the computed optimal phase shifts are rounded to quantenary phase shift keying psk 8 psk and 16 psk type phase shifts

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

asymptotic performance analysis and successive selected mapping for par reduction in ofdm one major drawback of orthogonal frequency division multiplexing ofdm systems is the high peak to average power ratio par of the transmit signal in order to overcome this problem selected mapping slm is a well known method for par reduction in this paper asymptotic performance analysis of slm is carried out and a bound on the maximum tolerable par values is derived starting with the analysis of gaussian signalling at nyquist rate it is also shown that these theoretic results can be applied for qam signalling at any oversampling rate based on the idea to distinguish between tolerable and nontolerable par values a novel variant of slm is derived namely successive slm sslm with this approach it is possible to significantly decrease the average number of assessed signal candidates and the average number of required side information bits per ofdm frame as long as the threshold of tolerable par values is larger than the critical par for nyquist sampled signals as a rule of thumb less than 2 71 euler s number candidates and less than 2 57 bits of side information are required on average

more on the distance distribution of bch codes we derive a new estimate for the error term in the binomial approximation to the distance distribution of bch codes this is an improvement on the earlier bounds by kasami fujiwara lin 1985 vladuts skorobogatov 1991 and krasikov litsyn 1995

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

gibbs states of the hopfield model in the regime of perfect memory we study the thermodynamic properties of the hopfield model of an autoassociative memory ifn denotes the number of neurons andm n the number of stored patterns we prove the following results ifm n 0 asn then there exists an infinite number of infinite volume gibbs measures for all temperaturest 1 concentrated on spin configurations that have overlap with exactly one specific pattern moreover the measures induced on the overlap parameters are dirac measures concentrated on a single point and the gibbs measures on spin configurations are products of bernoulli measures ifm n asn for small enough we show that for temperaturest smaller than somet 1 the induced measures can have support only on a disjoint union of balls around the previous points but we cannot construct the infinite volume measures through convergent sequences of measures

peak power reduction of ofdm signals with sign adjustment it has recently been shown that significant reduction in the peak to mean envelope power pmepr can be obtained by altering the sign of each subcarrier in a multicarrier system with n subcarriers however finding the best sign not only requires a search over 2n possible signs but also may lead to a substantial rate loss for small size constellations in this paper we first propose a greedy algorithm to choose the signs based on p norm minimization and prove that the resulting pmepr is guaranteed to be less than c log n where c is a constant independent of n for any n this approach has lower complexity in each iteration compared to the derandomization approach of while achieving similar pmepr reduction we further improve the performance of the proposed algorithm by enlarging the search space using pruning simulation results show that pmepr of a multicarrier signal with 128 subcarriers can be reduced to within 1 6 db of the pmepr of a single carrier system in the second part of the paper we address the rate loss by proposing a block coding scheme in which only one sign vector is chosen for k different modulating vectors the sign vector can be computed using the greedy algorithm in n iterations we show that the multi symbol encoding approach can reduce the rate loss by a factor of k while achieving the pmepr of c logkn i e only logarithmic growth in k simulation results show that the rate loss can be made smaller than 10 at the cost of only 1 db increase in the resulting pmepr for a system with 128 subcarriers

optimality condition for selected mapping in ofdm it is well known that orthogonal frequency division multiplexing ofdm transmission is spectrally efficient but power inefficient due to the large peak to average power ratio par of the ofdm signal selected mapping slm is a promising par reduction technique that is distortionless and has good par reducing capability in slm the phases of the frequency domain ofdm subsymbols are first rotated before the inverse fourier transform is applied thus an equivalent representation of the ofdm signal can be obtained the one with the lowest par from among m such representations is retained and transmitted in place of the original ofdm signal in this paper we investigate the optimum design of the phase rotation table so that the complementary cumulative distribution function ccdf of the par of the slm ofdm signal is minimized for any given m we prove that if the phases denoted by random variable phi are independently and identically distributed i i d with e ejphi 0 then optimum slm performance can be achieved

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

representing group codes as permutation codes given an abstract group spl gscr an n dimensional orthogonal matrix representation g of spl gscr and an initial vector x spl isin r sup n slepian defined the group code generated by the representation g to be the set of vectors gx if g is a group of permutation matrices the set gx is called a permutation code for permutation codes a stack algorithm decoder exists that in the presence of low noise produces the maximum likelihood estimate of the transmitted vector by using far fewer computations than the standard decoder in this correspondence a new concept of equivalence of codes of different dimensions is presented which is weaker than the usual definition of equivalent codes we show that every group code is weakly equivalent to a permutation code and we discuss the minimal degree of this permutation code

singular and maximal radon transforms analysis and geometry part 2 geometric theory 8 curvature introduction 8 1 three notions of curvature 8 2 theorems 8 3 examples 9 curvature some details 9 1 the exponential representation 9 2 diffeomorphism invariance 9 3 curvature condition cy 9 4 two lemmas 9 5 double fibration formulation 10 equivalence of curvature conditions 10 1 invariant submanifolds and deficient lie algebras 10 2 vanishing jacobians 10 3 construction of invariant submanifolds

capacity of the hopfield model for a given if neurons deviating from the memorized patterns are allowed we constructively show that if and only if all stored patterns are fixed points of the hopfield model if neurons are allowed with then where is the distribution function of the normal distribution the result obtained by amit and co workers only formally coincides with the latter case which indicates that the replica trick approach to the capacity of the hopfield model is only valid in the case

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

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

an analysis on neural dynamics with saturated sigmoidal functions we propose a unified approach to study the relation between the set of saturated attractors and the set of system parameters of the hopfield model linsker s model and the dynamic link network dln which use saturated sigmoidal functions in its dynamics of the state or weight the key point for this approach is to rigorously derive a necessary and sufficient condition to test whether a given saturated state in the hopfield model or weight vector in linsker s model and the dln is stable or not for any given set of system parameters and used this to determine the complete regime in the parameter space over which the given state or weight is stable our approach allows us to give an exact characterization between the parameters and the capacity in the hopfield model to generalize our previous results on linsker s network and the dln to have a better understanding of the underlying mechanism among these models the method reported here could be adopted to analyze a variety of models in the field of the neural networks

on the peak to mean envelope power ratio of phase shifted binary codes the peak to mean envelope power ratio pmepr of a code employed in orthogonal frequency division multiplexing ofdm systems can be reduced by permuting its coordinates and by rotating each coordinate by a fixed phase shift motivated by some previous designs of phase shifts using suboptimal methods the following question is considered in this paper for a given binary code how much pmepr reduction can be achieved when the phase shifts are taken from a 2h ary phase shift keying 2h psk constellation a lower bound on the achievable pmepr is established which is related to the covering radius of the binary code generally speaking the achievable region of the pmepr shrinks as the covering radius of the binary code decreases the bound is then applied to some well understood codes including nonredundant bpsk signaling bch codes and their duals reed muller codes and convolutional codes it is demonstrated that most presumably not optimal phase shift designs from the literature attain or approach our bound

on multicarrier signals where the pmepr of a random codeword is asymptotically logn multicarrier signals exhibit a large peak to mean envelope power ratio pmepr in this correspondence without using a gaussian assumption we derive lower and upper probability bounds for the pmepr distribution when the number of subcarriers n is large even though the worst case pmepr is of the order of n the main result is that the pmepr of a random codeword c c sub 1 c sub n is logn with probability approaching one asymptotically for the following three general cases i c sub i s are independent and identically distributed i i d chosen from a complex quadrature amplitude modulation qam constellation in which the real and imaginary part of c sub i each has i i d and even distribution not necessarily uniform ii c sub i s are i i d chosen from a phase shift keying psk constellation where the distribution over the constellation points is invariant under spl pi 2 rotation and iii c is chosen uniformly from a complex sphere of dimension n based on this result it is proved that asymptotically the varshamov gilbert vg bound remains the same for codes with pmepr of less than logn chosen from qam psk constellations

near shannon limit and low peak to average power ratio turbo block coded ofdm in this paper we present an advanced solution for the long standing problem of large peak to average power ratio papr in orthogonal frequency division multiplexing ofdm systems although the design of low papr codewords has been extensively studied and the existence of asymptotically good codes with low papr is also proven still no code has been constructed to satisfy all requirements the main goal of the paper is to develop a coding scheme that not only generates low papr codewords but it also performs relatively close to the shannon limit we achieve this goal by implementing a time frequency turbo block coded ofdm in this scheme we design the frequency domain component to have a tightly bounded papr the time domain component code is designed to obtain good performance while the decoding algorithm has reasonable complexity through comparative performance evaluation we show that utilizing the proposed method we achieve considerable improvement in terms of papr while we slightly loose the performance compared to capacity achieving codes with similar overall block length

polyphase codes for uplink ofdm cdma systems we propose a ofdm cdma system that employs polyphase codes to support variable spreading factors a systematic approach for constructing the polyphase code sequences of variable spreading factors is developed polyphase codes exhibit better auto and cross correlation properties than hadamard codes when employed in ofdm cdma systems polyphase codes result in certain structured multiple access interference mai caused by multipath analytical and numerical results show that ofdm cdma systems employing polyphase codes have better papr performance than those using hadamard codes the ber performance of the ofdm cdma system using polyphase codes is evaluated by numerical results and compared to that of the ofdm cdma system using hadamard codes with and without clipping

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

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

radon transforms and finite type conditions the purpose of this paper is to study averaging operators of radon transform type we shall formulate suitable finite type conditions and prove lp sobolev and lplq estimates the results will be essentially sharp for operators associated with families of curves in the plane let xc and t be smooth manifolds dimx3 nl dim2 nr and let m be a submanifold in xc x t with conormal bundle n m we denote by t the codimension of m we shall always assume that the projections lry m x and 7rt m 42 are surjective with rank dirx nl rank dr9 nr this in particular implies that n m c t x o x t o where 0 refers to the zero sections in t x and t 2 respectively this is the usual assumption for the canonical relation associated with lagrangian distributions arising as kernels of fourier integral operators the assumptions on dirx d7rt imply that for fixed x e x y e 2 the sets amx y e t x y e mi m x ye2x x y em i

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

universal l p improving for averages along polynomial curves in low dimensions we prove sharp lp lq estimates for averaging operators along general polynomial curves in two and three dimensions these operators are translation invariant given by convolution with the so called affine arclength measure of the curve and we obtain universal bounds over the class of curves given by polynomials of bounded degree our method relies on a geometric inequality for general vector polynomials together with a combinatorial argument due to m christ almost sharp lorentz space estimates are obtained as well

the complex envelope of a bandlimited ofdm signal converges weakly to a gaussian random process orthogonal frequency division multiplexing ofdm systems have been used extensively in wireless communications applications in recent years thus there is significant interest in analyzing the properties of the transmitted signal in such systems in particular a large amount of recent work has focused on analyzing the variation of the complex envelope of the transmitted signal and on designing methods to minimize this variation in this paper it is established that the complex envelope of a bandlimited uncoded ofdm signal converges weakly to a gaussian random process as the number of subcarriers goes to infinity this establishes that the properties of the ofdm signal will asymptotically approach those of a gaussian random process over any finite time interval the symbol length in a bandlimited ofdm system will eventually exceed any finite time interval as the number of subcarriers approaches infinity however practical interest is in how asymptotic approximations apply for a finite number of carriers and hence the convergence proof is reasonable motivation for considering how the extremal value theory of gaussian random processes might provide accurate approximations for the distribution of the peak to mean envelope power ratio pmepr of practical ofdm systems indeed numerical results are presented that indicate that the resulting simple expressions are accurate for a wide range of the distribution for moderate numbers of subcarriers the important extensions of the analytical and numerical results to coded ofdm systems as well as systems with unequal power allocation across subcarriers are also presented

synthesis of power efficient multitone signals with flat amplitude spectrum it is shown that generally any binary or polyphase sequence belonging to a pair of complementary sequences can be used to construct the initial phases of tones forming a multitone signal with the crest factor less than or equal to 6 db the previously proposed shapiro rudin sequences are representatives of a much larger family of binary golay complementary sequences numerical investigations show that the values of the crest factors obtained by applying complementary sequences binary or polyphase are between 5 and 6 db regardless of the number of tones

free energy and some sample path properties of a random walk with random potential we study the asymptotic behavior of the free energy for a model defined by sinai of one dimensional random walk with random potential in particular we obtain a central limit theorem and a strong law of large numbers for this free energy we use some results on the free energy to study some sample path properties of this random walk which are related respectively to its recurrence and localization some exponents describing the recurrence and localization are found

self averaging in a class of generalized hopfield models we prove the almost sure convergence to zero of the fluctuations of the free energy in a class of disordered mean field spin systems that generalize the hopfield model in two ways i multi spin interactions are permitted and ii the random variables xi imu describing the patterns can have arbitrary distributions with mean zero and finite 4 epsilon th moments the number of patterns m is allowed to be an arbitrary multiple of the system size this generalizes a previous result of bovier gayrard and picco for the standard hopfield model and improves a result of feng and tirozzi that required m to be a finite constant note that the convergence of the mean of the free energy is not proven

the distribution of the partition function of the hopfield model with finite number of patterns we derive the leading term in the large n asymptotic expansion of the partition function of the hopfield model with finite number of patterns we show that this leading order term is deterministic in the high temperature region in the low temperature region and at the critical point it is random with the distribution governed by normal or iterated exponential distributions

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

a necessary condition for waveforms with better papr than ofdm this paper establishes a necessary condition that must be satisfied by the modulation waveforms of any generalized waveforms for multicarrier gwmc system with better peak to average power ratio papr than conventional orthogonal frequency division multiplexing ofdm gwmc systems include in particular all classical multicarrier modulation systems as a consequence we show that ofdm has the best papr performance over all gwmc systems that do not satisfy this necessary condition we also identify an infinite family of gwmc systems with the same papr performance as ofdm to illustrate our results we present the simulations of the papr behavior for different gwmc systems including some with better papr performance than ofdm

uniform estimates for the x ray transform restricted to polynomial curves abstract we establish near optimal mixed norm estimates for the x ray transform restricted to polynomial curves with a weight that is a power of the affine arclength the bounds that we establish depend only on the spatial dimension and the degree of the polynomial some of our results are new even in the well curved case

on the design of multidimensional signal sets for ofdm systems an orthogonal frequency division multiplexing ofdm system operating over a wireless communication channel effectively forms a number of parallel frequency nonselective fading channels thereby obviating the need for complex equalization and thus greatly simplifying equalization decoding however the ofdm system also exhibits two weaknesses relative to its single carrier counterparts 1 the diversity achieved by the ofdm system can be less than a single carrier system employing the same error control code in a signaling environment rich in diversity and 2 the baseband transmitted signal can exhibit significant amplitude fluctuation over time thereby precluding efficient transmit amplifier operation in this paper nonstandard multidimensional signal sets matched to the ofdm framework are prescribed that address both of these issues the proposed signal sets are chosen to maximize the diversity achieved by an uncoded system under a constraint to control the peak to mean envelope power ratio pmepr of the baseband transmitted waveform the cost of employing the proposed signal sets is an increase in decoding complexity as essentially a small amount of controlled equalization has been added to the receiver thus the resulting system can be viewed as a hybrid between an ofdm system and a standard single carrier system numerical results are presented which suggest that 1 the system can provide an attractive alternative to a standard ofdm system in terms of required average transmitted snr versus receiver complexity and 2 the system yields a modest reduction in pmepr versus a standard ofdm system

large deviation principles for the hopfield model and the kac hopfield model we study the kac version of the hopfield model and prove a lebowitz penrose theorem for the distribution of the overlap parameters at the same time we prove a large deviation principle for the standard hopfield model with infinitely many patterns

fourier integral operators with cusp singularities we study the boundedness properties on lebesgue and sobolev spaces of fourier integral operators associated with canonical relations such that at least one of the projections is a simple whitney cusp in the process we obtain decay estimates for oscillatory integral operators whose symplectic relations have the same singular structure such singularities occur generically for averages over lines and curves in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i on l 2 we show that the operators lose 1 3 derivative to obtain sharp results off of l 2 we need to impose an additional transversality condition satisfied by many geometric averaging operators which leads to the notion of a strong cusp these estimates can be further improved if we impose curvature conditions on the cusp surface one application is the l 2 comp l 2 1 6 loc and l 12 7 comp l 2 loc boundedness of restrictions of the x ray transform on inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i to four dimensional families of lines satisfying a natural curvature and torsion condition

existence of codes with constant pmepr and related design recently several coding methods have been proposed to reduce the high peak to mean envelope ratio pmepr of multicarrier signals it has also been shown that with probability one the pmepr of any random codeword chosen from a symmetric quadrature amplitude modulation phase shift keying qam psk constellation is logn for large n where n is the number of subcarriers therefore the question is how much reduction beyond logn can one asymptotically achieve with coding and what is the price in terms of the rate loss in this paper by optimally choosing the sign of each subcarrier we prove the existence of q ary codes of constant pmepr for sufficiently large n and with a rate loss of at most log sub q 2 we also obtain a varsharmov gilbert type upper bound on the rate of a code given its minimum hamming distance with constant pmepr for large n since ours is an existence result we also study the problem of designing signs for pmepr reduction motivated by a derandomization algorithm suggested by spencer we propose a deterministic and efficient algorithm to design signs such that the pmepr of the resulting codeword is less than clogn for any n where c is a constant independent of n for symmetric q ary constellations this algorithm constructs a code with rate 1 log sub q 2 and with pmepr of clogn with simple encoding and decoding simulation results for our algorithm are presented

peak to average power ratio in high order ofdm the problem of peak to average power ratio papr of high order orthogonal frequency division modulation ofdm is considered using results on level crossing of random processes an upper bound on the probability that the papr of an ofdm signal will exceed a given value is derived numerical computations are used to show that this bound is tight for low pass ofdm systems the central limit theorem is used to find an asymptotic expression for the bound when the number of carriers n grows to infinity the central limit theorem is also used to find an asymptotic expression for another bound that is based on the envelope of the ofdm signal and is tighter for bandpass systems it is shown that effectively the papr grows as 2lnn and not linearly with n and by developing a lower bound on the probability that the papr of an ofdm signal will exceed a given value it is shown that asymptotically most ofdm symbols have a papr close to 2lnn some approaches to coping with the papr problem are discussed in light of the obtained results

first and second passage times of rayleigh processes corresp the first and second passage times of a stationary rayleigh process r t a are discussed r t a represents the envelope of a stationary random process consisting of a sinusoidal signal of amplitude and frequency f 0 plus stationary gaussian noise of unit variance having a narrow band power spectral density which is symmetrical about f 0 approximate integral equations are developed whose solutions yield approximate probability densities concerning the first and second passage times of r t a the resulting probability functions are presented in graphs for the case when the power spectral density of the noise is gaussian related results concerning the approximate distribution function of the absolute minimum or absolute maximum of r t a in the closed interval 0 tau are also presented the exact probability densities are expressed in the form of an infinite series of multiple integrals

on the phase sequence set of slm ofdm scheme for a crest factor reduction the crest factor distribution of orthogonal frequency division multiplexing ofdm symbol sequences is evaluated and it is shown that ofdm symbol sequences with a short period are expected to have a high crest factor the crest factor relationship between two input symbol sequences hamming distance d apart is also derived using these two results two criteria are proposed for a phase sequence set of the selected mapping slm ofdm scheme and suggest the rows of the cyclic hadamard matrix constructed from an m sequence as a near optimal phase sequence set of the slm ofdm scheme

a limit law on the distance distribution of binary codes an approximation is given of the distance distribution of a binary code by the binomial distribution with an exponentially decreasing error term specifically the upper bound of the relative error term between the normalized distance distribution of a binary code and the binomial distribution has been asymptotically improved in particular the bound becomes exponentially small for large distances in families of codes with small sigma and rate 0 5 the approach used was based on an integral representation of krawtchouk polynomials examples of interest are bch codes of primitive length duals of irreducible cyclic codes and preparata codes

a new construction of 64 qam golay complementary sequences in this correspondence we present a new construction for 64 qam golay sequences of length n 2 sup m for integer m the peak envelope power pep of 64 qam golay sequences is shown to be bounded by 4 66n the new construction of 64 qam golay sequences of length n 2 sup m is based on our earlier construction of new offsets of 16 qam golay sequences which are also presented here the total number of offsets of 64 qam golay sequences is 496 for m 2 808 for m 3 and 976 for m 4 obtained by computer search we also computed the pep distribution for 64 qam golay sequences for m 2 m 3 and m 4

papr analysis as a ratio of two random variables application to multicarrier systems with low subcarriers number the distribution of the peak to average power ratio papr of multicarrier systems is studied in the context of signals featuring low subcarriers number considering the mean power of the signal as a random variable a general cumulative distribution function of the papr is suggested we show that the new formulation is valid not only for low subcarriers number but also for larger subcarriers number thus an asymptotic analysis using a large subcarriers number proves a perfect concordance between the suggested approach and the state of the art derivations only valid for large subcarriers number all the theoretical developments are supported through simulations and we discuss the case of oversampled signals as well

the adaptive interpolation method a simple scheme to prove replica formulas in bayesian inference in recent years important progress has been achieved towards proving the validity of the replica predictions for the asymptotic mutual information or free energy in bayesian inference problems the proof techniques that have emerged appear to be quite general despite they have been worked out on a case by case basis unfortunately a common point between all these schemes is their relatively high level of technicality we present a new proof scheme that is quite straightforward with respect to the previous ones we call it the adaptive interpolation method because it can be seen as an extension of the interpolation method developped by guerra and toninelli in the context of spin glasses with an interpolation path that is adaptive in order to illustrate our method we show how to prove the replica formula for three non trivial inference problems the first one is symmetric rank one matrix estimation or factorisation which is the simplest problem considered here and the one for which the method is presented in full details then we generalize to symmetric tensor estimation and random linear estimation we believe that the present method has a much wider range of applicability and also sheds new insights on the reasons for the validity of replica formulas in bayesian inference

on the peak to average power of ofdm signals based on oversampling orthogonal frequency division multiplexing ofdm introduces large amplitude variations in time which can result in significant signal distortion in the presence of nonlinear amplifiers we introduce a new bound for the peak of the continuous envelope of an ofdm signal based on the maximum of its corresponding oversampled sequence it is shown to be very tight as the oversampling rate increases the bound is then used to derive a closed form probability upper bound for the complementary cumulative distribution function of the peak to mean envelope power ratio of uncoded ofdm signals for sufficiently large numbers of subcarriers as another application of the bound for oversampled sequences we propose tight relative error bounds for computation of the peak power using two main methods the oversampled inverse fast fourier transform and the method introduced for coded systems based on minimum distance decoding of the code

uniform lxp lx rq improving for dilated averages over polynomial curves abstract numerous authors have considered the problem of determining the lebesgue space mapping properties of the operator a given by convolution with affine arc length measure on some polynomial curve in euclidean space essentially a takes weighted averages over translates of the curve in this paper a variant of this problem is discussed where averages over both translates and dilates of a fixed curve are considered the sharp range of estimates for the resulting operator is obtained in all dimensions except for an endpoint the techniques used are redolent of those previously applied in the study of a in particular the arguments are based upon the refinement method of christ although a significant adaptation of this method is required to fully understand the additional smoothing afforded by averaging over dilates

a low complexity time domain linear symbol combining technique for papr reduction in ofdm systems high peak to average power ratio papr is a particular disadvantage of orthogonal frequency division multiplexing ofdm systems and can significantly degrade the power efficiency at the transmitter the aim of this paper is to propose a post inverse fast fourier transform ifft papr reduction method based on intelligent linear symbol combining with the objective to minimize the papr at the transmitter unlike the methods so far reported in the literature the proposed method has a relatively low complexity and does not require external randomization sequences this paper will also investigate the impact of the proposed method on the system s bit error rate ber performance and provide a closed form analytical expression that takes into account the ber dependency on the side information bits and multiblock combination it will be shown that the proposed technique can provide significant papr reductions at manageable levels of signal processing requirements while the ber degradation is relatively small

the replica symmetric solution without replica trick for the hopfield model we derive the saddle point equations for the order parameters of the hopfield model in the case of replica symmetry without using the replica trick but assuming that the edwards anderson parameter is a self averaging quantity

a new construction of 16 qam near complementary sequences we present a new 16 qam near complementary sequence construction where the length of the sequences is n 2m the 16 qam near complementary sequences are constructed by nonlinear offsets but the peak to mean envelope power ratio bounds for these 16 qam near complementary sequences is as low as 2 4 the number of newly constructed 16 qam near complementary sequences is m 2 4m 1

peak to average power ratio of good codes for gaussian channel consider a problem of forward error correction for the additive white gaussian noise awgn channel for finite blocklength codes the backoff from the channel capacity is inversely proportional to the square root of the blocklength in this paper it is shown that the codes achieving this tradeoff must necessarily have peak to average power ratio papr proportional to logarithm of the blocklength this is extended to codes approaching capacity slower and to papr measured at the output of an orthogonal frequency division multiplex ing modulator as a by product the convergence of smith s amplitude constrained awgn capacity to shannon s classical formula is characterized in the regime of large amplitudes this converse type result builds upon recent contributions in the study of empirical output distributions of good channel codes

l p improving bounds for averages along curves we establish local l p l q mapping properties for averages on curves the exponents are sharp except for endpoints let n 2 and let m1 and m2 be two smooth n 1 dimensional manifolds 1 each containing a preferred origin 0m1 and 0m2 we shall abuse notation and write 0 for both 0m1 and 0m2 for the purposes of integration we shall place a smooth riemannian metric on m1 and m2 although the exact choice of this metric will not be relevant all our considerations shall be local to the origin 0 we are interested in the local l p improving properties of averaging operators on curves before we give the rigorous description of these operators let us first give an informal discussion informally we assume that we have a smooth assignment x2 7 x2 taking points in m2 to curves in m1 with a corresponding dual assignment x1 x1 taking points in m1 to curves in m2 such that x1 x2 x2 1 we then form the operator r taking functions 2 on m1 to functions on m2 defined

upper bounds on the statistical distribution of the crest factor in ofdm transmission this article analyzes the crest factor behavior of an orthogonal frequency division multiplexing ofdm modem the behavior is characterized in terms of the complementary distribution function of the crest factor cdfc the cdfc is a key parameter of ofdm systems for example it provides limits on achievable information rates several approximations have been developed in the literature so far but no true upper bounds dependent on the different constellations that are used in ofdm modulation have been derived a new approach is given providing upper bounds that substitute for time consuming simulations

blind estimation of ofdm carrier frequency offset via oversampling blind deterministic estimation of the orthogonal frequency division multiplexing ofdm frequency offset via oversampling is proposed in this paper this method utilizes the intrinsic phase shift of neighboring sample points incurred by the frequency offset that is common among all subcarriers the proposed method is data efficient it requires only a single ofdm symbol to achieve reliable estimation hence making it more suitable to systems with stringent delay requirement and mobility induced channel variation the proposed scheme is devised to perfectly retrieve frequency offset in the absence of noise quite remarkably we show that in the presence of channel noise this intuitive scheme is indeed the maximum likelihood estimate of the carrier frequency offset the possible presence of virtual carriers are also accommodated in the system model and some interesting observations are obtained the cramer rao lower bound is derived for the oversampling based signal model and we show through numerical simulation that the proposed algorithm is efficient practical issues such as identifiability the front end filter bandwidth and the possible presence of correlated noises are also carefully addressed

on the achievable information rate with peak power limited orthogonal frequency division multiplexing this paper addresses the problem of determining the statistical distribution of the peak to average power ratio par of orthogonal frequency division multiplexing ofdm transmit signals in practice transmission systems are amplitude limited thus the large peak values of ofdm signals are clipped and nonlinear distortion follows in order to avoid the resulting degradations i e spectral widening and increased bit error rate a systematic construction of ofdm signals without large peaks is desired the paper provides new results on the par distribution and hence on the achievable information rate with ofdm signals that are peak limited in particular it is shown that in the case of phase shift keying psk subcarrier modulation the frequently applied model of gaussian data coefficients is not appropriate by solving an integral equation new analytic expressions for the par and the achievable information rate are derived comparison with simulation results confirms that the new model is accurate for all ranges of practical interest

an approximation to the weight distribution of binary primitive bch codes with designed distances 9 and 11 corresp recently kasami em et al presented a linear programming approach to the weight distribution of binary linear codes 2 their approach to compute upper and lower bounds on the weight distribution of binary primitive bch codes of length 2 m 1 with m geq 8 and designed distance 2t 1 with 4 leq t leq 5 is improved from these results the relative deviation of the number of codewords of weight j leq 2 m 1 from the binomial distribution 2 mt left stackrel 2 m 1 j right is shown to be less than 1 percent for the following cases 1 t 4 j geq 2t 1 and m geq 16 2 t 4 j geq 2t 3 and 10 leq m leq 15 3 t 4 j geq 2t 5 and 8 leq m leq 9 4 t 5 j geq 2t 1 and m geq 20 5 t 5 j geq 2t 3 and 12 leq m leq 19 6 t 5 j geq 2t 5 and 10 leq m leq 11 7 t 5 j geq 2t 7 and m 9 8 t 5 j geq 2t 9 and m 8