continuous phase modulation part i full response signaling the continuous phase modulation cpm signaling scheme has gained interest in recent years because of its attractive spectral properties data symbol pulse shaping has previously been studied with regard to spectra for binary data and modulation index 0 5 in this paper these results have been extended to the m ary case where the pulse shaping is over a one symbol interval the so called full response systems results are given for modulation indexes of practical interest concerning both performance and spectrum comparisons are made with minimum shift keying msk and systems have been found which are significantly better in e b n 0 for a large signal to noise ratio snr without expanded bandwidth schemes with the same bit error probability as msk but with considerably smaller bandwidth have also been found significant improvement in both power and bandwidth are obtained by increasing the number of levels m from 2 to 4

mmse optimal approximation of continuous phase modulated signal as superposition of linearly modulated pulses the optimal linear modulation approximation of any m ary continuous phase modulated cpm signal under the minimum mean square error mmse criterion is presented in this paper with the introduction of the mmse signal component an m ary cpm signal is exactly represented as the superposition of a finite number of mmse incremental pulses resulting in the novel switched linear modulation cpm signal models then the mmse incremental pulse is further decomposed into a finite number of mmse pulse amplitude modulated pam pulses so that an m ary cpm signal is alternatively expressed as the superposition of a finite number of mmse pam components similar to the laurent representation advantageously these mmse pam components are mutually independent for any modulation index the optimal cpm signal approximation using lower order mmse incremental pulses or alternatively using a small number of mmse pam pulses is also made possible since the approximation error is minimized in the mmse sense finally examples of the mmse optimal cpm signal approximation and its comparison with the laurent approximation approach are given using raised cosine frequency pulse cpm schemes

numerical simulations for radiation hydrodynamics a finite difference scheme is proposed for two dimensional radiation hydrodynamical equations in the transport limit the scheme is of godunov type in which the set of time averaged flux needed in the scheme is calculated through riemann problems solved in the scheme flow signals are explicitly treated while radiation signals are implicitly treated flow fields and radiation fields are updated simultaneously an iterative approach is proposed to solve the set of nonlinear algebraic equations arising from the implicitness of the scheme the sweeping method used in the scheme significantly reduces the number of iterations or computer cpu time needed a new approach to further accelerate the convergence is proposed which further reduces the number of iterations needed by more than one order no matter how many cells radiation signals propagate in one time step only an extremely small number of iterations are needed in the scheme and each iteration costs only about 0 8 percent of computer cpu time which is needed for one time step of a second order accurate and fully explicit scheme two dimensional problems are treated through a dimensionally split technique therefore iterations for solving the set of algebraic equations are carried out only in each one dimensional sweep through numerical examples it is shown that the scheme keeps the principle advantages of godunov schemes for flow motion in the time scale of flow motion numerical results are the same as those obtained from a second order accurate and fully explicit scheme the acceleration of the convergence proposed in this paper may be directly applied to other hyperbolic systems

minimum euclidean distance for combinations of short rate 1 2 convolutional codes and cpfsk modulation continuous phase frequency shift keying cpfsk is a constant amplitude modulation method with good spectral sidelobe properties good error probability properties can be obtained with coherent maximum likelihood detection in this paper we study the euclidean distance properties of signals formed by a conventional rate 1 2 convolutional encoder followed by a binary or 4 level cpfsk modulator the minimum euclidean distance is calculated for these signal sets as a function of the modulation index and the observation interval length the optimum detector is discussed for rational modulation index values the best obtainable codes are found for the case of short rate 1 2 codes with binary or 4 level cpfsk modulation lists of the best codes are given among the results are that the noncatastrophic rate 1 2 convolutional codes with optimum free hamming distance do not in general give the best euclidean distance with cpfsk

frequency detectors for cpm signals frequency tracking loops are used in digital links to control the carrier frequency of the received signals a basic component in such loops is the frequency difference detector fdd this paper concentrates on a class of fdds for use with binary continuous phase modulation cpm their derivation is based on two ideas the maximum likelihood principle for parameter estimation and laurent s 1986 decomposition of a cpm signal into the sum of linearly modulated components the proposed fdds are suitable for digital implementation and their operation is independent of clock recovery analysis and simulation are employed to investigate tracking operation and acquisition capability of frequency control loops endowed with such fdds numerical examples are provided for modulation schemes of practical interest such as msk and gaussian msk the loop acquisition range is found to be fairly large about 0 5 1 0 times the bit rate

suboptimum detection of trellis coded cpm for transmission on bandwidth and power limited channels the authors consider a communication scheme based on continuous phase modulated cpm signals used in conjunction with trellis coded modulation tcm for transmission over a channel affected by gaussian noise and fading this scheme provides a power saving due to the coding gain of tcm and a reduced bandwidth occupancy due to the features of cpm signals moreover cpm provides constant envelope signals to keep the complexity of the receiver manageable and to be able to use interleaving deinterleaving techniques to spread the fade bursts suboptimal detection schemes must be used two such schemes based on coherent and noncoherent detection of cpm are considered their performance is evaluated by computing the computational cutoff rate of the discrete channel generated by cpm

a posteriori error estimates for upwind finite volume schemes for nonlinear conservation laws in multi dimensions in this paper we shall derive a posteriori error estimates in the l 1 norm for upwind finite volume schemes for the discretization of nonlinear conservation laws on unstructured grids in multi dimensions this result is mainly based on some fundamental a priori error estimates published in a recent paper by c chainais hillairet the theoretical results are confirmed by numerical experiments

trellis termination of multi h cpm and the diophantine frobenius problem this paper presents a method for terminating the phase trellis in multi h continuous phase modulation cpm it is shown that tilted phase trellis for multi h cpm signals is periodic and enables the representation of the multi h cpm modulator as a cascade of a periodic recursive continuous phase encoder cpe and a phase modulator pm we then pose the problem of finding the minimum number of symbols that will terminate the phase trellis in a known state of the modulator and establish a connection of its solution to the diophantine frobenius problem fp analytical results are established for the existence of a terminating sequence and upper and lower bounds are derived on its length for arbitrary modulation parameters we show that the trellis terminating symbols and their quantity depends upon the initial state of the encoder the set of modulation indices the cpe memory order and the number of bits per modulated symbol it is shown that required overhead for trellis termination can be significant for schemes with integer modulation indices

convolutional coding combined with continuous phase modulation background theory and specific coding designs for combined coding modulation schemes utilizing convolutional codes and continuous phase modulation cpm are presented in this paper the case of r 1 2 coding onto a 4 ary cpm is emphasized with short constraint length codes presented for continuous phase fsk double raised cosine and triple raised cosine modulation coding buys several decibels of coding gain over the gaussian channel with an attendant increase of bandwidth performance comparisons in the power bandwidth tradeoff with other approaches are made

frequency domain equalization techniques for multi h continuous phase modulation two receiver architectures are presented for equalization of multi h continuous phase modulation cpm in the first approach the receiver front end is a matched filter bank which is derived from laurent decomposition of the signal a circulant matrix model derived for the samples of the matched filter is used to perform the equalization in frequency domain the second technique employs a receiver with a simple front end consisting of a low pass filter and a fractional sampler we also develop a circulant matrix model for the latter approach which relates the laurent pseudo symbols to each polyphase component at the output of the sampler a linear frequency domain equalizer fde is also proposed using this model in addition to providing the details of these approaches the paper proposes several simplifications applicable to each of the two cases and provides a detailed discussion on the performance complexity trade off bit error rate ber results are presented for the irig 106 aeronautical telemetry dual h cpm waveform

numerical approximation of entropy solutions for hyperbolic integro differential equations scalar hyperbolic integro differential equations arise as models for e g radiating or self gravitating fluid flow we present finite volume schemes on unstructured grids applied to the cauchy problem for such equations for a rather general class of integral operators we show convergence of the approximate solutions to a possibly discontinuous entropy solution of the problem for a specific model problem in radiative hydrodynamics we introduce a convergent fully discrete finite volume scheme under the assumption of sufficiently fast spatial decay of the entropy solution we can even establish the convergence rate h1 4 ln h where h denotes the grid parameter the convergence proofs rely on appropriate variants of the classical kruzhkov method for local balance laws together with a truncation technique to cope with the nonlocal character of the integral operator

a quasi optimum receiver for continuous phase modulation a simple receiver structure for any continuous phase modulation cpm scheme is introduced its front end is just the ordinary linear receiver followed by a subinterval sampler eliminating the need for the standard analog matched filters its design is based on the decomposition of the cpm signal in the walsh signal space this brings the hardware requirement to a minimum and near optimum performance can be easily obtained

a note on the convergence of the discontinuous galerkin method for a scalar hyperbolic equation a numerical example is presented which shows that the known l 2 error estimate left u u h right leqq ch k 1 2 left u right k 1 for the discontinuous galerkin method cannot be improved within the class of quasi uniform meshes not even for smooth exact solutions u

a decomposition approach to cpm it is shown that any continuous phase modulation cpm system can be decomposed into a continuous phase encoder and a memoryless modulator in such a way that the former is a linear modulo some integer p time invariant sequential circuit and the latter is also time invariant this decomposition is exploited to obtain alternative realizations of the continuous phase encoder and hence of cpm and also to obtain alternative forms of the optimum decoding algorithm when p is a prime p so that the encoder is linear over the finite field gf p it is shown that cascading it with an outside convolutional encoder is equivalent to a single convolutional encoder it is pointed out that the cascade of the modulator the waveform channel which it is assumed is characterized by additive white gaussian noise and the demodulator that operates over one symbol interval yield a discrete memoryless channel that can be studied without the distractions introduced by continuous phase encoding

stabilized hp finite element methods for first order hyperbolic problems we analyze the hp version of the streamline diffusion finite element method sdfem and of the discontinuous galerkin finite element method dgfem for first order linear hyperbolic problems for both methods we derive new error estimates on general finite element meshes which are sharp in the mesh width h and in the spectral order p of the method assuming that the stabilization parameter is o h p for piecewise analytic solutions exponential convergence is established on quadrilateral meshes for the dgfem we admit very general irregular meshes and for the sdfem we allow meshes which contain hanging nodes numerical experiments confirm the theoretical results

an optimal order error estimate for the discontinuous galerkin method in this paper a new approach is developed for analyzing the discontinuous galerkin method for hyperbolic equations for a model problem in r2 the method is shown to converge at a rate 0 hn l when applied with nth degree polynomial approxi mations over a semiuniform triangulation assuming sufficient regularity in the solution

new results on the spectral analysis of multi h cpm signals this paper deals with the spectral analysis of multi h continuous phase modulation cpm signals a new solution to the problem is obtained by identifying an inner hidden markov model in the cpm signal which can be accomplished by expressing the modulator as the cascade of a sequential machine sm and a bank of pam modulators an in depth study of the resulting markov chain shows that it is both cyclostationary and reducible and proper tools are identified to address these peculiarities as a result the multi h cpm spectrum is expressed as a combination of fourier transforms of portions of a cpm signal thus allowing an efficient numerical evaluation through fast fourier transforms ffts

pam decomposition of m ary multi h cpm it is known that any multilevel continuous phase modulated cpm signal with a single modulation index can be exactly represented by a sum of pulse amplitude modulated pam waveforms in this paper we show how multi h cpm signals can also be represented in this manner the decomposition is presented in general terms as a function of the alphabet size modulation indexes and phase pulse of the cpm scheme the number of pulses required to exactly construct the signal is shown to increase over that previously given for single h schemes this increase is in proportion to the number of modulation indexes we propose an approximation which significantly reduces the number of signal pulses and which minimizes the mean squared error for an arbitrary set of modulation indexes we show that this approximation can have two objectives 1 to reduce the number of pulses in the same manner as has been proposed for single h schemes and or 2 to reduce the number of multi h pulses we also show the conditions where this latter objective is most practical we compare this minimum mean squared error approximation with another method which was recently proposed for cpm we also give numerical results on detection performance which demonstrate the practicality of the proposed approximation

exact and approximate construction of digital phase modulations by superposition of amplitude modulated pulses amp minimum shift keying and offset qpsk are two well known modulations which can be interpreted as a set of time phase shifted am pulses we show in this paper that any constant amplitude binary phase modulation can also be expressed as a sum of a finite number of time limited amplitude modulated pulses amp decomposition new methods for computing autocorrelation and power frequency spectrum are derived which give very simple results for half integer index modulations we also show that the signal can be built with good accuracy using only one optimized pulse main pulse this synthesis is particularly satisfactory for modulations that have good spectral characteristics and or low index

linear diophantine constrained intra fix for frequency domain equalization of multi h cpm this paper considers the problem of constructing a symbol block to generate a cyclic multi h continuous phase modulated cpm signal so as to permit frequency domain equalization fde at the receiver like single h cpm the memory inherent in a multi h cpm waveform requires the use of an additional segment called an intra fix in each transmitted block the intra fix forces the transmitter state machine to regress to the state it had at the start of the block the constraints on the symbols of the intra fix which ensure above condition are shown to be a set of linear diophantine equations ldes three different methods are proposed for finding the symbols of the intra fix such that the length of the intra fix is minimized the last two methods connect the problem of intra fix insertion to the problem of trellis termination of the tilted phase this connection enables us to state and justify that existing bounds established on the length of the terminating sequence are effective for the length of the intra fix we observe that multi h cpm schemes typically require a shorter intra fix as compared to single h cpm schemes having similar modulation parameters we apply the proposed procedure to a dual h cpm scheme

iterative multisymbol noncoherent reception of coded cpfsk a system involving the multisymbol noncoherent reception of coded continuous phase frequency shift keying is developed optimized and analyzed unlike coherent systems the modulation index of the waveform does not need to be rational with a small denominator and the oscillator only needs to be stable for the duration of a small block of symbols the achievable performance over awgn and rayleigh block fading channels is determined by computing the average mutual information which is the capacity of a channel using the given modulation format and receiver architecture under the constraint of uniformly distributed input symbols the code rate and modulation index are jointly optimized with respect to average mutual information under a bandwidth constraint for binary and quaternary signaling the information theoretic results are corroborated by bit error rate curves generated using a standardized turbo code in conjunction with iterative demodulation and decoding it is shown that while more robust than a system with coherent reception the proposed system offers superior energy efficiency compared with conventional single symbol noncoherent reception

iterative decoding of serially concatenated cpm in fading channels with noisy channel state information we use the sum product algorithm spa to propose a reduced complexity detector for serially concatenated continuous phase modulated sccpm signals with noisy channel state information csi at the receiver two channel effects phase noise pn and flat fading are tackled using the statistical model and associated factor graph fg of the problem although optimal performance is not assured due to the loopy nature of the fg as well as simplifying assumptions made in the algorithm development simulations show that very significant performance gains are possible and the gap between systems with noiseless and noisy csi can be reduced to about 1 db using the proposed methods the increase in complexity compared to the conventional decoder which treats csi estimates as if they were equal to their true values is small

multiresolution transmission of the correlation modes between bivariate time series based on complex network theory abstract this study introduces an approach to study the multiscale transmission characteristics of the correlation modes between bivariate time series the correlation between the bivariate time series fluctuates over time the transmission among the correlation modes exhibits a multiscale phenomenon which provides richer information to investigate the multiscale transmission of the correlation modes this paper describes a hybrid model integrating wavelet analysis and complex network theory to decompose and reconstruct the original bivariate time series into sequences in a joint time frequency domain and defined the correlation modes at each time frequency domain we chose the crude oil spot and futures prices as the sample data the empirical results indicate that the main duration of volatility 32 64 days for the strongly positive correlation between the crude oil spot price and the futures price provides more useful information for investors moreover the weighted degree weighted indegree and weighted outdegree of the correlation modes follow power law distributions the correlation fluctuation strengthens the extent of persistence over the long term whereas persistence weakens over the short and medium term the primary correlation modes dominating the transmission process and the major intermediary modes in the transmission process are clustered both in the short and long term

on joint source and channel coding using trellis coded cpm analytical bounds on the channel distortion joint source and channel coding jscc using trellis coded quantization tcq in conjunction with trellis coded continuous phase modulation cpm is studied the channel is assumed to be the additive white gaussian noise awgn channel analytical bounds on the channel distortion for the investigated systems with maximum likelihood sequence detection mlsd are developed the bounds are based on the transfer function technique which was modified and generalized to include continuous amplitude discrete time signals for a memoryless uniform source the constructed bounds for the investigated systems are shown to be asymptotically tight for increasing channel signal to noise ratio snr values for a memoryless nonuniform source the constructed bounds are not as tight as the one for the uniform source however it still can be used as an indication to how the system performs it is concluded that the minimum euclidean distance of the system alone is not enough to evaluate the performance of the considered systems the number of error events having minimum euclidean distance and the total distortion caused by those error events also affect the asymptotic performance this work provides an analysis tool for the investigated systems the analysis method is very general it may be applied to any trellis based jscc schemes

an adaptive higher order method for solving the radiation transport equation on unstructured grids a new class of solution methods based on a short characteristics approach embedded in the finite element framework for the solution of the radiation transport equation is developed and tested the order of convergence and the error to runtime ratio are determined in numerical tests furthermore the efficiency of the scheme is demonstrated in the case of a challenging problem from the field of solar physics a quantitative comparison with other methods based either on the characteristics or on the finite element approach is carried out this emphasizes the efficiency and accuracy of our method two different adaptation mechanisms are studied grid adaptation and local variation of the order of the scheme

an adaptive mesh refinement algorithm for the radiative transport equation the discrete ordinates form of the radiative transport equation rte is spatially discretized and solved using an adaptive mesh refinement amr algorithm this technique permits local grid refinement to minimize spatial discretization error of the rte an error estimator is applied to define regions for local grid refinement overlapping refined grids are recursively placed in these regions and the rte is then solved over the entire domain the procedure continues until the spatial discretization error has been reduced to a sufficient level the following aspects of the algorithm are discussed error estimation grid generation communication between refined levels and solution sequencing this initial formulation employs the step scheme and is valid for absorbing and isotropically scattering media in two dimensional enclosures the utility of the algorithm is tested by comparing the convergence characteristics and accuracy to those of the standard single grid algorithm for two simple benchmark problems the amr algorithm maintains the convergence characteristics of the standard single grid algorithm but it does not provide any efficiency gains due to a lack of disparate spatial scales in a third more localized problem however the amr algorithm demonstrates significant memory and cpu time reductions

pam decomposition of ternary cpm with duobinary encoding in this paper we investigate the pulse amplitude modulation pam decomposition and the spectral efficiency of duobinary continuous phase modulation cpm where duo binary cpm represents a ternary cpm whose symbols are generated using a duobinary encoder we show that this precoder ensures a higher spectral efficiency compared with binary cpm and we propose a pam decomposition characterized by the presence of a single main pulse and by uncorrelated pseudo symbols for a half integer modulation index value for this ternary cpm we show that shaped offset quadrature phase shift keying belongs to this cpm family and we provide a new reduced complexity trellis detector capable of reaching identical performance as the one introduced by perrins as well as new linear detectors

an analysis of the discontinuous galerkin method for a scalar hyperbolic equation we prove lp stability and error estimates for the discontinuous galerkin method when applied to a scalar linear hyperbolic equation on a convex polygonal plane domain using finite element analysis techniques we obtain l2 estimates that are valid on an arbitrary locally regular triangulation of the domain and for an arbitrary degree of polynomials lp estimates for p 2 are restricted to either a uniform or piecewise uniform triangulation and to polynomials of not higher than first degree the latter estimates are proved by combining finite difference and finite element analysis techniques

decision feedback sequence estimation for continuous phase modulation on a linear multipath channel an approach to reduced complexity detection of partial response continuous phase modulation cpm on a linear multipath channel is presented the method referred to as decision feedback sequence estimation dfse is based on a conventional viterbi algorithm va using a reduced state trellis combined with decision feedback df by varying the number of states in the va the receiver structure can be changed gradually from a df receiver to the optimal maximum likelihood sequence estimator mlse in this way different tradeoffs between performance and complexity can be obtained results on the receiver performance based on minimum distance calculations and bit error rate simulations are given for gaussian minimum shift keying modulation on typical mobile radio channels it is shown that for channels with a long memory a significant complexity reduction can be achieved at the cost of a moderate degradation in performance

standard and goal oriented adaptive mesh refinement applied to radiation transport on 2d unstructured triangular meshes standard and goal oriented adaptive mesh refinement amr techniques are presented for the linear boltzmann transport equation a posteriori error estimates are employed to drive the amr process and are based on angular moment information rather than on directional information leading to direction independent adapted meshes an error estimate based on a two mesh approach and a jump based error indicator are compared for various test problems in addition to the standard amr approach where the global error in the solution is diminished a goal oriented amr procedure is devised and aims at reducing the error in user specified quantities of interest the quantities of interest are functionals of the solution and may include for instance point wise flux values or average reaction rates in a subdomain a high order up to order 4 discontinuous galerkin technique with standard upwinding is employed for the spatial discretization the discrete ordinates method is used to treat the angular variable

a new finite series expansion of continuous phase modulated waveforms the laurent decomposition expresses any binary single h continuous phase modulated cpm signal as the summation of a finite number of pulse amplitude modulated pam waveforms and the resulting signal space is so constructed that the waveform can usually be synthesized with a reasonable degree of accuracy by using only the ldquomainrdquo component pulse this derivation has been very useful for reduced complexity demodulation of binary cpm signals subsequent to laurent s work it was shown that commensurate expressions could be obtained for multilevel and multi h cpm but with an exponential increase in the total number of pam component pulses in the signal representation in this paper we show that by expressing a cpm signal in its equivalent binary multi form we can derive a generalization of laurent s result for the general class of such waveforms that use noninteger modulation indices in this new signal representation there is a clearly identifiable data dependent ldquomainrdquo expansion pulse during each symbol interval which carries most of the signal energy as in the laurent decomposition the number of terms in this decomposition is only dependent on the cpm signal memory

catastrophic continuous phase modulation schemes and their noncatastrophic equivalents continuous phase modulation cpm schemes are bandwidth and energy efficient constant envelope modulation schemes that can be viewed as a continuous phase encoder cpe followed by a memoryless modulator mm where the cpe is of convolutional type it is observed that cpm schemes can be catastrophic in the sense that pairs of input sequences that differ in an infinite number of positions can be mapped into pairs of signals with finite euclidean distance this can happen in spite of the fact that the cpe is never catastrophic when considered as a stand alone convolutional encoder the necessary and sufficient condition for a general cpm scheme to be catastrophic is given each member of the two major families of cpm schemes namely the lrec and the lrc has been classified as a catastrophic or noncatastrophic scheme for the catastrophic schemes the probability that a catastrophic event occurs is determined a canonical precoder which transforms each scheme of both families into an equivalent noncatastrophic scheme is derived the equivalent noncatastrophic scheme has the same number of states as the original one moreover it has the property that if two input sequences differ in the ith position the corresponding output signals have nonzero euclidean distance in the ith interval

a new performance bound for pam based cpm detectors it is well understood that the pulse amplitude modulation pam representation of continuous phase modulation cpm can lead to reduced complexity detectors with near optimum performance it has recently been shown that the pam representation also extends to cpm schemes with multiple modulation indexes multi h cpm in this paper we present a detector for multi h cpm which is based on the pam representation we also give an exact expression for the pairwise error probability for the entire class of pam based cpm detectors single and multi h optimal and reduced complexity over the additive white gaussian noise awgn channel and show that this bound is tighter than the previously published bound for approximate pam based detectors in arriving at this expression we show that pam based detectors for cpm are a special case of the broad class of mismatched cpm detectors we also show that the metrics for pam based detectors accumulate distance in a different manner than metrics for other cpm detectors these distance properties are especially useful in applications with greatly reduced trellis sizes we give thorough examples of the analysis for different single and multi h signaling schemes we also apply the new bound in comparing the performance of pam based detectors with other reduced complexity detectors for cpm

the spillover effects between natural gas and crude oil markets the correlation network analysis based on multi scale approach abstract this paper proposes a new compound model to investigate the dynamic linkage mechanism between the natural gas and crude oil markets from the multi scale perspective in the proposed model two main steps are involved multi scale analysis and network research based on the bivariate empirical mode decomposition bemd and fine to coarse algorithm the multi scale analysis ensures the relationship between price fluctuations can be studied under three different time scales which corresponding to market disequilibrium significant events and long term trend by integrating the grey correlation degree and coarse gaining algorithm the network research reveals the dynamic spillover effects of the two markets at different time scales to capture the different linked characteristic in different periods the sample data of henry hub and wti spot prices from 1997 to 2017 is divided into three periods we transfer the daily correlations between the price fluctuations with specific time scale into the correlation patterns and establish the network based on their transmission relations the crucial correlation patterns and the significant transmission relations are revealed by some network indicators and the proposed approach in this paper can be applied to other field of research

decomposition of m ary cpm signals into pam waveforms it is widely known that minimum shift keying msk may be seen as a pam signaling scheme and that the same is true albeit approximately with msk like modulations it is also known perhaps not so widely that any binary continuous phase modulated cpm signal may be exactly decomposed into the sum of a few pam waveforms in this paper we show that this property extends to multilevel cpm signaling features of a pam decomposition are discussed as a function of the alphabet size the modulation index and the frequency response of the system it is found that especially with signaling schemes with a long memory the decomposition has so many terms that it becomes unmanageable for these cases an approximation is proposed with a limited number of terms

the role of fluctuating modes of autocorrelation in crude oil prices abstract autocorrelation exists in the crude oil price due to price inertia the cobweb theorem model errors etc many researchers have studied the fluctuation of the crude oil price but few have focused on the autocorrelation fluctuation in crude oil prices exploring the fluctuating rules of autocorrelation can aid in understanding the fluctuating mechanism of crude oil prices to study the role of fluctuating modes of autocorrelation in crude oil prices which have time series characteristics this study selected international crude oil spot prices as sample data to employ the methods of statistical physics the fluctuating modes of autocorrelation were defined by the autocorrelation coefficient symbolization and a coarse graining process we set the modes as nodes and the transformation between modes as edges the fluctuating mode weight network of autocorrelation was then built thus the study of autocorrelation fluctuation was transformed to a network study then certain aspects such as the statistical properties the small world behavior and the transmission medium in the network could be analyzed using complex network theory and analytical methods the periodicity of the fluctuation was calculated using a spectral analysis method this study not only describes the fluctuation of the time series more precisely than other methods but also provides ideas for methods of studying the fluctuation of univariate autocorrelations

main memory triangle computations for very large sparse power law graphs finding counting and or listing triangles three vertices with three edges in massive graphs are natural fundamental problems which have recently received much attention because of their importance in complex network analysis here we provide a detailed survey of proposed main memory solutions to these problems in a unified way we note that previous authors have paid surprisingly little attention to space complexity of main memory solutions despite its both fundamental and practical interest we therefore detail space complexities of known algorithms and discuss their implications we also present new algorithms which are time optimal for triangle listing and beats previous algorithms concerning space needs they have the additional advantage of performing better on power law graphs which we also detail we finally show with an experimental study that these two algorithms perform very well in practice allowing us to handle cases which were previously out of reach

the pam decomposition of cpm signals with integer modulation index this article presents the solution for decomposing continuous phase modulated cpm signals with integer modulation index into pulse amplitude modulated components the notion of main complex pulse is also introduced a simplified demodulator for cpm signals with integer modulation index is proposed as an application example and simulation results using a quaternary 2 raised cosine rc scheme are given

inverse transport calculations in optical imaging with subspace optimization algorithms inverse boundary value problems for the radiative transport equation play an important role in optics based medical imaging techniques such as diffuse optical tomography dot and fluorescence optical tomography fot despite the rapid progress in the mathematical theory and numerical computation of these inverse problems in recent years developing robust and efficient reconstruction algorithms remains a challenging task and an active research topic we propose here a robust reconstruction method that is based on subspace minimization techniques the method splits the unknown transport solution or a functional of it into low frequency and high frequency components and uses singular value decomposition to analytically recover part of low frequency information minimization is then applied to recover part of the high frequency components of the unknowns we present some numerical simulations with synthetic data to demonstrate the performance of the proposed algorithm

a class of reduced complexity viterbi detectors for partial response continuous phase modulation partial response continuous phase modulation cpm gives constant envelope digital modulation schemes with excellent power spectra both narrow main lobe and low spectral tails can be achieved when these signals are detected in an optimum coherent maximum likelihood sequence detector viterbi detector power efficient schemes can also be designed sometimes at the expense of receiver complexity this paper describes a general class of simple viterbi detectors with reduced complexity compared to the optimum case the key idea is that the approximate receiver is based on a less complex cpm scheme than the transmitted scheme the asymptotically optimum reduced complexity receiver is found for a variety of transmitted schemes and various complexity reduction factors for a specific class of receivers and modulation indexes a new distance measure is introduced for the performance analysis smooth schemes based on raised cosine pulses are analyzed and simulated for the case of simplified reception a graceful performance degradation occurs with the reduction of complexity

reduced complexity approach to iterative detection of coded soqpsk we develop a reduced complexity approach for the detection of coded shaped offset quadrature phase shift keying soqpsk a highly bandwidth efficient and popular constant envelope modulation the complexity savings result from viewing the signal as a continuous phase modulation cpm we give a simple and convenient closed form expression for a recursive binary to ternary precoder for soqpsk the recursive nature of this formulation is necessary in serially concatenated systems where soqpsk serves as the inner code we show that the proposed detectors are optimal in the full response case and are near optimal in the partial response case due to some additional complexity reducing approximations in all cases the proposed detectors achieve large coding gains for serially concatenated coded soqpsk these gains are similar to those reported recently by li and simon which were obtained using a more complicated cross correlated trellis coded quadrature modulation xtcqm interpretation

low complexity decoders for constant envelope digital modulations digital angle modulations having input symbol memory can be demodulated using maximum likelihood sequence estimation mlse or viterbi decoding the demodulation of the more bandwidth efficient of these can require a large number of computations in this paper lower complexity decoding approaches are presented these decoders use a predetermined processing order and a reduced number of survivor signals s at every time nt processing is performed on the signal sequences using metrics likelihoods obtained by a matched filter bank similar to that needed for mlse the decoders can achieve asymptotic optimality of error rate while being computationally faster and simpler than mlse for many modulations in addition error rate performance can be traded for complexity reduction expected performance has been verified for representative modulations

a system theory approach to decompose cpm signals into pam waveforms in 1986 laurent showed that binary continuous phase modulated cpm signals can be decomposed into pulse amplitude modulated pam waveforms this result later extended to multilevel cpm signals by mengali and morelli has attracted much attention especially for the design of simplified receivers the paper proceeds from the premise that the decomposition into pam waveforms is not unique and follows a systemtheory approach that leads to a natural formulation first the cpm modulator is represented by a nonlinear part encoder followed by a linear part bank of pam modulators the two parts are then rearranged with the aim of obtaining real valued continuous pam waveforms and to reduce their number several classes of decompositions arise with this approach each of which admits an infinite number of different decompositions of the same cpm signal among which the laurent and mengalimorelli results appear as special cases throughout the paper a systematic use is made of the kronecker product which appears to be the natural tool for dealing with cpm decompositions and for expressing results in a very simple form

nonlinear multipulse block coding of cpfsk signals a nonlinear multipulse block coding technique is proposed to improve cpfsk signaling formats the coding technique is developed to prevent merging events with lower distances by separating the respective paths in the time domain coded schemes are constructed with constant h 2 h and trellis coded cpfsk signals the spectral variations and the performance bandwidth tradeoffs of the proposed coded signals are found and compared to those without coding it is concluded from the numerical results that the proposed coding technique can significantly improve the performance bandwidth tradeoff of many cpfsk signaling formats particularly at lower bandwidths

woven coded cpfsk with hierarchical code structure we introduce hierarchical woven coded continuous phase frequency shift keying hierarchical wccpfsk as the serial concatenation of different outer convolutional codes and inner cpfsk we compare it to wccpfsk with identical outer convolutional codes with the proposed code combinations hierarchical wccpfsk achieves superior decoding capability simulations show that it performs better at medium snrs

orthogonal space time block coding for continuous phase modulation with frequency domain equalization in this letter an orthogonal space time st block coding stbc technique for continuous phase modulation cpm is proposed and combined with a frequency domain equalizer fde to obtain high performance gains over frequency selective channels the new method maintains the constant envelope and phase continuity of the cpm waveforms perfectly by using appropriate tail symbols during the addition of cyclic prefix and interblock transitions and therefore has no negative impact on the spectral efficiency because the stcoded cpm blocks remain orthogonal fde is applied as in the case of single antenna transmissions without any increase in the computational load simulations corroborate the performance improvement offered by stbc while also preserving the desired bandwidth efficiency of cpm

orthogonalization by principal components applied to cpm the orthonormal basis for the space spanned by a given signal set can be chosen in many different ways however when the basis is truncated to fewer dimensions the quality of the approximated signals differs depending on the choice of the original basis we study two energy related quality measures and show that the optimal lower dimensional approximation is given by the principal components pc method which is also a simple and efficient alternative to gram schmidt techniques in addition we derive and bound the average decrease in squared euclidean distances over one symbol interval caused by the pc method this measure is relevant in serially concatenated continuous phase modulation where a manifold of signal pairs contributes to the bit error rate for low to medium signal to noise ratios by a numerical evaluation we find that for this measure the decrease is lower than that of a previous method by j huber and w liu see ieee j select areas commun vol 7 p 1437 49 1989 finally we compare the minimum squared euclidean distance for error events which is relevant for uncoded cpm systems here the loss with the pc method is generally larger than with huber and liu s method although examples of the opposite exist

pam representation of ternary cpm this letter considers the pulse amplitude modulation pam representation of continuous phase modulation cpm with a ternary data alphabet this technique is applied to the problem of constructing reduced complexity detectors with near optimum performance the usefulness of this approach is demonstrated using the ternary cpm variant known as shaped offset quadrature phase shift keying soqpsk

serially concatenated continuous phase modulation with convolutional codes over rings in this paper we investigate serially concatenated continuous phase modulation sccpm with convolutional codes cc over rings the transmitted signals are disturbed by additive white gaussian noise the properties for systems with both infinite and finite block lengths are investigated for an infinite length system we check the convergence threshold using the extrinsic information transfer chart for a finite length system we use union bound techniques to estimate the error floors in the union bound analysis we consider both the order and the position of nonzero permuted symbols a simple method for determining a cpm error event through the sum of the input symbol sequence is shown thus we can determine if the output symbol sequence of an error event in the ring cc can form an error event in cpm two properties concerning the interleaver gain ig are investigated a recursive search algorithm for the maximal ig is shown compared with previous sccpm with a binary cc the proposed system shows an improvement concerning the convergence threshold or error floors

trellis codes for 4 ary continuous phase frequency shift keying the approach of morales moreno and pasupathy 1988 is extended for the design of trellis codes for 4 ary continuous phase frequency shift keying cpfsk with modulation index h 1 2 the criterion for comparison of codes is the maximum free euclidean distance for a given rate and the number of states of the signal space code for the same number of states of the signal space code these codes improve the free euclidean distance by up to 1 25 db over previously published results finally the implementation of the combined coding and modulation system is discussed

finding the multipath propagation of multivariable crude oil prices using a wavelet based network approach the globalization and regionalization of crude oil trade inevitably give rise to the difference of crude oil prices the understanding of the pattern of the crude oil prices mutual propagation is essential for analyzing the development of global oil trade previous research has focused mainly on the fuzzy long or short term one to one propagation of bivariate oil prices generally ignoring various patterns of periodical multivariate propagation this study presents a wavelet based network approach to help uncover the multipath propagation of multivariable crude oil prices in a joint time frequency period the weekly oil spot prices of the opec member states from june 1999 to march 2011 are adopted as the sample data first we used wavelet analysis to find different subseries based on an optimal decomposing scale to describe the periodical feature of the original oil price time series second a complex network model was constructed based on an optimal threshold selection to describe the structural feature of multivariable oil prices third bayesian network analysis bna was conducted to find the probability causal relationship based on periodical structural features to describe the various patterns of periodical multivariable propagation finally the significance of the leading and intermediary oil prices is discussed these findings are beneficial for the implementation of periodical target oriented pricing policies and investment strategies

serially concatenated continuous phase modulation with iterative decoding serially concatenated and interleaved continuous phase modulation cpm with iterative decoding is investigated an a posteriori probability app algorithm for cpm is developed based on the classic app algorithm for channel codes the system is analyzed through upper bounds on the average bit error probability for coded and interleaved minimum shift keying the weight spectrum is computed resulting in a transfer function bound this is cumbersome for a general cpm system instead only the most significant error events contributing to the weight spectrum are identified simulations show that firstly these events give a satisfactory view of system performance when equal outer codes are used and secondly that remarkably good performance can be obtained for some simple systems finally power spectral densities and bandwidths are computed allowing for a bandwidth performanee comparison of different combinations

reduced complexity detection and phase synchronization of cpm signals based on an extension of laurent 1986 decomposition of continuous phase modulation cpm signals into a sum of linearly modulated components we derive a class of reduced complexity maximum likelihood ml coherent detection and closed loop phase synchronization schemes the complexity of the resulting detection schemes expressed in terms of the number of matched filters and states of a viterbi algorithm is significantly reduced with respect to that of optimal coherent receivers with negligible performance loss this result extends a known one valid for the binary case to multilevel cpm the proposed synchronization schemes do not require an increased number of matched filters and are perfectly suitable to be used in conjunction with these receivers based on the phase locked loop pll equivalent linear model a method for optimizing the parameters of digital second order pll s is presented numerical examples based on theoretical analysis and computer simulation are provided for two specific formats in the cpm class tamed frequency modulation tfm and a quaternary raised cosine rc modulation

design of coded cpfsk modulation systems for bandwidth and energy efficiency consideration is given to the problems related to the design of m ary continuous phase frequency shift keying cpfsk systems with modulation index h j m combined with eternal rate r binary convolution encoders the following questions are raised and answered 1 how should different encoder modulator systems be compared and how can comparable systems be recognized from the system parameters i e m h and r 2 what are the limits on the information rate per unit bandwidth versus signal to noise ratio when reliable transmission is required 3 how does one choose the system parameters m h and r when the overall system has to achieve a specified performance and 4 how does one design the external rate r binary convolutional encoder to put in front of the m ary cpfsk modulation system with h j m a simple approximation for the bandwidth of a cpfsk signal is given and shown to be sufficiently accurate for system design purposes the design of the external convolutional encoder is carried out in a novel way that leads to fewer states in the combined encoder modulator system and thus yields improved performance for a given demodulation decoding complexity compared to previous approaches for the design of coded cpfsk systems

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed