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

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

two sided bounds on the rate of convergence to a stable law we derive necessary and sufficient conditions for several characterizations of the rate of convergence of a sum of independent variables to a stable law the technique used is to obtain upper and lower bounds on the rate in terms of functions depending in a very simple way on the common underlying distribution this permits a general approach to the problem of rates of convergence

frames arising from irreducible solvable actions i abstract in this work we provide a unified method for the construction of reproducing systems arising from unitary irreducible representations of some solvable lie groups in contrast to other well known techniques such as the coorbit theory the generalized coorbit theory and other discretization schemes we make no assumption on the integrability or square integrability of the representations of interest moreover our scheme produces explicit constructions of frames with precise frame bounds as an illustration of the scope of our results we highlight that a large class of representations which naturally occur in wavelet theory and time frequency analysis is handled by our scheme for example the affine group the generalized heisenberg groups the shearlet groups solvable extensions of vector groups and various solvable extensions of non commutative nilpotent lie groups are a few examples of groups whose irreducible representations are handled by our method the class of representations studied in this work is described as follows let g be a simply connected connected completely solvable lie group with lie algebra g p m next let be an infinite dimensional unitary irreducible representation of g obtained by inducing a character from a closed normal subgroup p exp p of g additionally we assume that g p m m exp m is a closed subgroup of g d m is a fixed haar measure on the solvable lie group m and there exists a linear functional p such that the representation ind p g is realized as acting in l 2 m d m making no assumption on the integrability of we describe explicitly a discrete subset of g and a vector f l 2 m d m such that f is a tight frame for l 2 m d m we also construct compactly supported smooth functions s and discrete subsets g such that s is a frame for l 2 m d m

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

an econometric model of network formation with degree heterogeneity i introduce a model of undirected dyadic link formation which allows for assortative matching on observed agent characteristics homophily as well as unrestricted agent level heterogeneity in link surplus degree heterogeneity like in fixed effects panel data analyses the joint distribution of observed and unobserved agent level characteristics is left unrestricted two estimators for the common homophily parameter 0 are developed and their properties studied under an asymptotic sequence involving a single network growing large the first tetrad logit tl estimator conditions on a sufficient statistic for the degree heterogeneity the second joint maximum likelihood jml estimator treats the degree heterogeneity a i0 i 1 super n as additional incidental parameters to be estimated the tl estimate is consistent under both sparse and dense graph sequences whereas consistency of the jml estimate is shown only under dense graph sequences

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

high order moments and gaussianity of single carrier and ofdm signals this paper analyzes the high order moments of linearly modulated single carrier as well as orthogonal frequency division multiplexing ofdm signals assuming that the modulated symbols that form resulting continuous signal waveform are statistically independent for a single carrier case with the ideal low pass filter used for pulse shaping closed form expressions of the moments with up to the eighth order are derived the proposed approach is then extended to gaussianity assessment of ofdm signals we show how the moments of ofdm signals can approach to those of gaussian distribution as the number of subcarriers increases for a given modulation constraint on each subcarrier also reported is the peculiar nonstationary behavior of the fourth order moments in the case of bpsk modulated ofdm signals

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

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

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

gaussian approximation of suprema of empirical processes we develop a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of gaussian processes without taking the route of approximating empirical processes themselves in the sup norm we prove an abstract approximation theorem that is applicable to a wide variety of problems primarily in statistics especially the bound in the main approximation theorem is non asymptotic and the theorem does not require uniform boundedness of the class of functions the proof of the approximation theorem builds on a new coupling inequality for maxima of sums of random vectors the proof of which depends on an effective use of stein s method for normal approximation and some new empirical processes techniques we study applications of this approximation theorem to local empirical processes and series estimation in nonparametric regression where the classes of functions change with the sample size and are not donsker type importantly our new technique is able to prove the gaussian approximation for the supremum type statistics under considerably weak regularity conditions especially concerning the bandwidth and the number of series functions in those examples

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

approximation to stable law by the lindeberg principle abstract by the lindeberg principle we develop in this paper an approximation to one dimensional possibly asymmetric stable distributions with 0 2 in the smooth wasserstein distance it is the first time that the general stable central limit theorem is proved by the lindeberg principle and that this theorem with 0 1 is proved by a new method other than fourier analysis our main tools are a taylor like expansion and a kolmogorov forward equation

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

central limit theorems and bootstrap in high dimensions this paper derives central limit and bootstrap theorems for probabilities that sums of centered high dimensional random vectors hit hyperrectangles and sparsely convex sets specifically we derive gaussian and bootstrap approximations for probabilities p n 1 2 ni 1xi a p n 1 2 i 1nxi a where x1 xnx1 xn are independent random vectors in rprp and aa is a hyperrectangle or more generally a sparsely convex set and show that the approximation error converges to zero even if p pn p pn as n n and p np n in particular pp can be as large as o ecnc o ecnc for some constants c c 0c c 0 the result holds uniformly over all hyperrectangles or more generally sparsely convex sets and does not require any restriction on the correlation structure among coordinates of xixi sparsely convex sets are sets that can be represented as intersections of many convex sets whose indicator functions depend only on a small subset of their arguments with hyperrectangles being a special case

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

peak power and bandwidth efficient linear modulation in portable wireless communication systems power consumption is of major concern traditional modulation and coding schemes have been designed from the standpoint of minimizing average power however for linear power amplifiers needed for spectrally efficient modulation formats amplifier efficiency and hence power consumption are determined by the peak power of the transmitted signal this paper looks into modulation formats which minimize peak power and retain high spectral efficiency peak power is broken into a sum in terms of decibels of average power and a peak to average power ratio and a variety of modulation formats are evaluated in terms of peak power efficiency in both a gaussian noise and rayleigh fading channel a generalized phase shift keying psk modulation format is developed and shown to offer superior peak power efficiency relative to that of commonly used linear modulation formats two schemes are presented for reducing the peak to average power ratio of various modulation formats first data translation codes are used to avoid data sequences which cause large peaks in the transmitted signal this approach was found to be most productive in quadrature amplitude modulation qam formats finally an adaptive peak suppression algorithm is presented which further reduces the peak to average power ratios of the psk and generalized psk formats the peak suppression algorithm is also applicable to spl pi 4 qpsk and was found to improve peak power efficiency of that format by about 1 25 db over a rayleigh fading channel

near constant envelope trellis shaping for psk signaling in this paper we propose a powerful trellis shaping for peak to average power ratio par reduction of pulse shaped phase shift keying psk systems the proposed approach consists of 1 memory extension of trellis shaping encoder for capturing the full effect of pulse shaping filter impulse response and 2 simple branch metrics that quantify envelope fluctuation of the filter output simulation results demonstrate that achieving near constant envelope is possible even if a pulse shaping filter with a roll off factor as low as 0 1 is employed furthermore due to the circular nature of the resulting signal trajectory the proposed system also exhibits a robustness against sampling timing jitter at the receiver

anisotropic local laws for random matrices we develop a new method for deriving local laws for a large class of random matrices it is applicable to many matrix models built from sums and products of deterministic or independent random matrices in particular it may be used to obtain local laws for matrix ensembles that are anisotropic in the sense that their resolvents are well approximated by deterministic matrices that are not multiples of the identity for definiteness we present the method for sample covariance matrices of the form open image in new window where t is deterministic and x is random with independent entries we prove that with high probability the resolvent of q is close to a deterministic matrix with an optimal error bound and down to optimal spectral scales as an application we prove the edge universality of q by establishing the tracy widom airy statistics of the eigenvalues of q near the soft edges this result applies in the single cut and multi cut cases further applications include the distribution of the eigenvectors and an analysis of the outliers and bbp type phase transitions in finite rank deformations they will appear elsewhere we also apply our method to wigner matrices whose entries have arbitrary expectation i e we consider w a where w is a wigner matrix and a a hermitian deterministic matrix we prove the anisotropic local law for w a and use it to establish edge universality