quantifying signals with power law correlations a comparative study of detrended fluctuation analysis and detrended moving average techniques detrended fluctuation analysis dfa and detrended moving average dma are two scaling analysis methods designed to quantify correlations in noisy nonstationary signals we systematically study the performance of different variants of the dma method when applied to artificially generated long range power law correlated signals with an a priori known scaling exponent alpha 0 and compare them with the dfa method we find that the scaling results obtained from different variants of the dma method strongly depend on the type of the moving average filter further we investigate the optimal scaling regime where the dfa and dma methods accurately quantify the scaling exponent alpha 0 and how this regime depends on the correlations in the signal finally we develop a three dimensional representation to determine how the stability of the scaling curves obtained from the dfa and dma methods depends on the scale of analysis the order of detrending and the order of the moving average we use as well as on the type of correlations in the signal

a novel constellation reshaping method for papr reduction of ofdm signals in this paper we propose a constellation reshaping method for peak to average power ratio papr reduction in orthogonal frequency division multiplexing ofdm systems the key idea of the proposed method is to generate a reshaped quadrature amplitude modulation r qam constellation in which the minimum distance of the r qam is the same as that of the traditional qam constellation when the novel r qam constellation is employed with the traditional partial transmit sequence pts and selected mapping slm methods in ofdm systems called as the r pts and r slm methods in this paper respectively the mean square errors between the constellations of the received data and each r qam rotated by different phase rotation factors are calculated at the receiver and the phase rotation factor with the minimum mean square error is selected to recover the original data without side information therefore the flexibility in phase rotation choice and the ability to avoid data rate loss make the r pts and r slm methods more suitable for good bit error rate performance in ofdm systems theoretical analysis and simulation results show that the r pts and r slm methods could provide the same papr reduction and bit error rate as those of the conventional pts and slm methods with perfect side information respectively

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

empirical mode decomposition and correlation properties of long daily ozone records sreceived 16 november 2004 revised manuscript received 17 march 2005 published 27 may 2005d correlations for daily data of total ozone column are investigated by detrended fluctuation analysis sdfad the removal of annual periodicity does not result in a background free signal for the tropical station mauna loa in order to identify the remaining quasiperiodic constituent the relatively new method of empirical mode decomposition semdd is tested we found that the so called intrinsic mode functions do not represent real signal components of the ozone time series their amplitude modulation is very sensitive to local changes such as random data removal or smoothing tests on synthetic data further corroborate the limitations of decomposing quasiperiodic signals from noise with emd nevertheless the emd algorithm helps to identify dominating frequencies in the time series which allows to separate fluctuations from the remaining background we demonstrate that dfa analysis for the cleaned mauna loa record yields scaling comparable to a mid latitude station

multifractal detrended cross correlation analysis for two nonstationary signals we propose a method called multifractal detrended cross correlation analysis to investigate the multifractal behaviors in the power law cross correlations between two time series or higher dimensional quantities recorded simultaneously which can be applied to diverse complex systems such as turbulence finance ecology physiology geophysics and so on the method is validated with cross correlated one and two dimensional binomial measures and multifractal random walks as an example we illustrate the method by analyzing two financial time series

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

sensitivity analysis of parametric weak vector equilibrium problems in this paper two implicit multifunction theorems are obtained then by using a set valued gap function and the results obtained we study the sensitivity analysis of the solution mapping for a parametric weak vector equilibrium problem and obtain an explicit expression for the contingent derivative of the solution mapping

fractionally integrated process with power law correlations in variables and magnitudes we propose a new stochastic process de ned by only two parameters 1 and 2 which generates power law correlations or anticorrelations in the variable increments and power law correlations in their magnitudes to account for empirical observations in a range of physical systems to demonstrate the utility of our process we consider the case with power law anticorrelations in the variable increments and power law correlations in their magnitudes to model scaling properties in heartbeat data the parameters 1 and 2 control separately the correlations in the increments and their magnitudes and we nd linear relations between each parameter and the corresponding correlation exponent

time dependent hurst exponent in financial time series abstract we calculate the hurst exponent h t of several time series by dynamical implementation of a recently proposed scaling technique the detrending moving average dma in order to assess the accuracy of the technique we calculate the exponent h t for artificial series simulating monofractal brownian paths with assigned hurst exponents h we next calculate the exponent h t for the return of high frequency tick by tick sampled every minute series of the german market we find a much more pronounced time variability in the local scaling exponent of financial series compared to the artificial ones the dma algorithm allows the calculation of the exponent h t without any a priori assumption on the stochastic process and on the probability distribution function of the random variables as happens for example in the case of the kitagawa grid and the extended kalmann filtering methods the present technique examines the local scaling exponent h t around a given instant of time this is a significant advance with respect to the standard wavelet transform or to the higher order power spectrum technique which instead operate on the global properties of the series by legendre or fourier transform of qth order moments

second order contingent derivatives of set valued mappings with application to set valued optimization abstract in this paper a family of parameterized set valued optimization problems whose constraint set depends on a parameter are considered some calculus rules are obtained for calculating the second order contingent derivatives of the composition and sum of two set valued mappings then by using these calculus rules some results concerning second order sensitivity analysis are established and an explicit expression for the second order contingent derivative of the weak perturbation mapping in the set valued optimization problems is obtained

a flexible peak to average power ratio reduction scheme for ofdm systems by the adaptive projected subgradient method one of the main issues of the orthogonal frequency division multiplexing ofdm modulation is the high peak to average power ratio papr of the transmitted signal which adversely affects the complexity of power amplifiers in this paper we consider transmitters that reduce the papr by slightly disturbing the symbols in carriers used to transmit information and by sending dummy symbols i e symbols not conveying information in unused carriers the optimal choice of the data and dummy symbols is determined by the solution of a convex optimization problem to reduce the papr with low complexity we apply a modified version of the adaptive projected subgradient method to a sequence of convex cost functions closely related to the original optimization problem the resulting algorithm achieves near optimal papr in practical scenarios generalizes existing algorithms based on polyak s method and can easily handle multiple constraints

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

vector equilibrium problem and vector optimization this paper examines the vector equilibrium model based on a vector cost consideration this is a generalization of the well known wardrop traffic equilibrium principle where road users choose paths based on just a single cost the concept of parametric equilibria is introduced and used to establish relations with parametric complementarity and variational inequality problems relations with some vector optimization problems via scalarization techniques are given under appropriate conditions some solution methods for solving vector equilibrium problems are also discussed

a novel low complexity precoded ofdm system with reduced papr the computational complexity and peak to average power ratio papr of conventional precoded orthogonal frequency division multiplexing ofdm systems can be reduced using a t ofdm precoded system based on the walsh hadamard matrix the present paper proposes a novel precoding scheme for further reducing the computational complexity and papr of t ofdm in the proposed scheme the precoding matrix is combined with an inverse discrete fourier transform to construct a new transform matrix at the transmitter notably the transform matrix is both unitary and circulant with each column being a perfect gaussian integer sequence containing just four non zero elements of pm 1 pm j a low complexity receiver is additionally constructed for the proposed precoding scheme a closed form expression is derived for the bit error rate ber in t ofdm and the proposed precoding scheme under frequency selective fading channels the simulation results for the ber are shown to be in good agreement with the mathematical derivations in addition it is demonstrated that t ofdm and the proposed scheme have an equivalent ber performance when their precoding matrices are designed in such a way as to obtain full frequency diversity however the proposed scheme has a better papr performance and a lower computational complexity than t ofdm

weak sharp solutions of variational inequalities xuexiang huang pointed out that the statement on line 5 of page 184 of p marcotte and d zhu siam j optim 9 1999 pp 179 189 is invalid and supplied an alternative proof of the inequality that appears on line 10 here is a simple proof of this result due to an anonymous referee the substitution starts at line 4 and ends at line 11

vector variational inequality as a tool for studying vector optimization problems the paper aims to show that a vector variational inequality can be an useful tool for studying a vector optimization problem

novel low complexity slm schemes for papr reduction in ofdm systems selected mapping slm schemes are commonly employed to reduce the peak to average power ratio papr in orthogonal frequency division multiplexing ofdm systems it has been shown that the computational complexity of the traditional slm scheme can be substantially reduced by adopting conversion vectors obtained by using the inverse fast fourier transform ifft of the phase rotation vectors in place of the conventional ifft operations c l wang and y ouyang low complexity selected mapping schemes for peak to average power ratio reduction in ofdm systems ieee trans signal process vol 53 no 12 pp 4652 4660 dec 2005 to ensure that the elements of these phase rotation vectors have an equal magnitude conversion vectors should have the form of a perfect sequence this paper presents three novel classes of perfect sequence each of which comprises certain base vectors and their cyclically shifted versions three novel low complexity slm schemes are then proposed based upon the unique structures of these perfect sequences it is shown that while the papr reduction performances of the proposed schemes are marginally poorer than that of the traditional slm scheme the three schemes achieve a substantially lower computational complexity

power law correlated processes with asymmetric distributions motivated by the fact that many physical systems display sid power law correlations together with siid an asymmetry in the probability distribution we propose a stochastic process that can model both properties the process depends on only two parameters where one controls the scaling exponent of the power law correlations and the other controls the degree of asymmetry in the distributions leaving the correlations unaffected we apply the process to air humidity data and find that the statistical properties of the process are in a good agreement with those observed in the data

a low complexity pts based radix fft method for papr reduction in ofdm systems a low complexity partial transmit sequence pts technique for reducing the peak to average power ratio papr of an orthogonal frequency division multiplexing ofdm signal is presented signals at the middle stages of an point radix fft using decimation in frequency dif or decimation in time dit are considered for pts subblocking we show that dif has a lower multiplicative complexity than dit for similar papr reduction a higher radix based fft achieves better papr reduction per stage with less multiplicative complexity compared with a lower radix fft we further reduce the computational complexity by proposing a new technique called decomposition pts d pts subblocking where subblocks are assigned through different stages of the transform this new technique reduces the multiplicative complexity while providing papr reduction similar to other techniques such as original pts o pts moreover it has lower additive complexity

differential and sensitivity properties of gap functions for minty vector variational inequalities the purpose of this paper is to investigate differential properties of a class of set valued maps and gap functions involving minty vector variational inequalities relationships between their contingent derivatives are discussed an explicit expression of the contingent derivative for the class of set valued maps is established optimality conditions of solutions for minty vector variational inequalities are obtained

cross correlations between volume change and price change in finance one usually deals not with prices but with growth rates r defined as the difference in logarithm between two consecutive prices here we consider not the trading volume but rather the volume growth rate r the difference in logarithm between two consecutive values of trading volume to this end we use several methods to analyze the properties of volume changes r and their relationship to price changes r we analyze 14 981 daily recordings of the standard and poor s s p 500 index over the 59 year period 1950 2009 and find power law cross correlations between r and r by using detrended cross correlation analysis dcca we introduce a joint stochastic process that models these cross correlations motivated by the relationship between r and r we estimate the tail exponent of the probability density function p r r 1 for both the s p 500 index as well as the collection of 1819 constituents of the new york stock exchange composite index on 17 july 2009 as a new method to estimate we calculate the time intervals q between events where r q we demonstrate that q the average of q obeys q q we find 3 furthermore by aggregating all q values of 28 global financial indices we also observe an approximate inverse cubic law

effect of trends on detrended fluctuation analysis scaling behavior we find that crossovers result from the competition between the scaling of the noise and the apparent scaling of the trend we study how the characteristics of these crossovers depend on i the slope of the linear trend ii the amplitude and period of the periodic trend iii the amplitude and power of the power law trend and iv the length as well as the correlation properties of the noise surprisingly we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws i e long range power law dependence of the position of the crossover on the parameters of the trends we show that the dfa result of noise with a trend can be exactly determined by the superposition of the separate results of the dfa on the noise and on the trend assuming that the noise and the trend are not correlated if this superposition rule is not followed this is an indication that the noise and the superposed trend are not independent so that removing the trend could lead to changes in the correlation properties of the noise in addition we show how to use dfa appropriately to minimize the effects of trends how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation or if the crossover is due to a trend without any transition in the dynamical properties of the noise

on the generalized vector variational inequality problem abstract in this paper we study vector variational inequalities with set valued mappings the concept of c x pseudomonotone mapping is introduced by employing the fan lemma we establish several existence results the new results extend and unify existence results of vector variational inequalities for single valued operators under the banach space setting

detecting long range correlations with detrended fluctuation analysis abstract we examine the detrended fluctuation analysis dfa which is a well established method for the detection of long range correlations in time series we show that deviations from scaling which appear at small time scales become stronger in higher orders of dfa and suggest a modified dfa method to remove them the improvement is necessary especially for short records that are affected by non stationarities furthermore we describe how crossovers in the correlation behavior can be detected reliably and determined quantitatively and show how several types of trends in the data affect the different orders of dfa

wavelet analysis and synthesis of fractional brownian motion fractional brownian motion fbm offers a convenient modeling for nonstationary stochastic processes with long term dependencies and 1 f type spectral behavior over wide ranges of frequencies statistical self similarity is an essential feature of fbm and makes natural the use of wavelets for both its analysis and its synthesis a detailed second order analysis is carried out for wavelet coefficients of fbm it reveals a stationary structure at each scale and a power law behavior of the coefficients variance from which the fractal dimension of fbm can be estimated conditions for using orthonormal wavelet decompositions as approximate whitening filters are discussed consequences of discretization are considered and some connections between the wavelet point of view and previous approaches based on length measurements analysis or dyadic interpolation synthesis are briefly pointed out

a hybrid detrending method for fractional gaussian noise abstract determining trend and implementing detrending operations are important steps in data analysis yet there is neither precise definition of trend nor any logical algorithm for extracting it in this paper we propose a hybrid detrending method hdm which is based on the empirical mode decomposition emd and the detrended fluctuation analysis dfa our method can remove the polynomial and sinusoidal trends from the fractional gaussian noise fgn background we illustrate the method by selected examples from artificial time series and climate data in comparison with existing frequency domain based detrending methods our method is a posteriori the trend defined by our method is only derived from the data further our method also preserves the scaling behavior of the original signals

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

low complexity papr reduction scheme without side information for ofdm systems this paper proposes a novel peak to average power ratio papr reduction scheme that requires no side information in orthogonal frequency division multiplexing ofdm systems unlike the selective mapping slm or the partial transmit sequence pts scheme the proposed scheme deals with post inverse fast fourier transform ifft symbols and thus requires only a single ifft processor in the transmitter compared to other conventional schemes implemented with a single ifft processor such as the circularly shifted phase sequences csps or the optimised circularly shifted phase sequences ocsps method the proposed scheme achieves an even lower complexity since only phase rotation and cyclic shifting of ofdm symbols are performed more importantly the proposed scheme significantly outperforms the csps and the ocsps methods in reducing papr as shown in simulation results an added benefit of the proposed scheme is that it employs a linear receiver such as a maximal likelihood ml detector a minimum mean square error mmse estimator or a zero forcing zf estimator to demap quadrature amplitude modulation qam symbols especially the ml detector demaps the qam symbols with no side information simulation results also show that the bit error rate ber of the proposed scheme has no loss when the ml detector the zf or the mmse estimator is used with hard decision compared to that of the conventional ofdm system without any papr reduction scheme over rayleigh fading channel