cyclic spectral analysis of continuous phase modulated signals continuous phase modulated cpm signals play a prominent role in modern communication systems due to their desirable constant modulus property and the ability to control their power and bandwidth efficiencies popular cpm signals include the classical minimum shift keyed msk signal the lrec family of signals also known as continuous phase frequency shift keyed cpfsk signals and gaussian msk which is used in state of the art gsm and pcs mobile communication systems cpm signals like virtually all man made communication signals are known to exhibit cyclostationarity which implies that their probabilistic parameters such as mean second moment and higher order cumulants are almost periodic functions of time a novel representation of cpm signals as a sum of pam signals is presented for both integer and noninteger modulation index cases then the nth order cyclostationarity properties of binary cpm signals are derived in terms of nth order temporal and spectral moment and cumulant functions moreover the case of m ary cpm signals is briefly addressed the results are illustrated with simulations involving msk lrec and gmsk signals

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

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

generalized synchronization via the differential primitive element abstract generalized synchronization gs in nonlinear systems appears when the states of one system through a functional mapping are equal to states of another this mapping can be obtained if there exists a differential primitive element which generates a differential transcendence basis we introduce a new definition of gs in nonlinear systems using the concept of differential primitive element in this contribution we investigate the gs problem when we have strictly different nonlinear systems and we consider that for both the slave and master systems only some states are available from measurements the first component of the mapping is called differential primitive element and in general is defined by means of a linear combination of the known states and the inputs of the system furthermore we design a new dynamical feedback controller able to achieve complete synchronization in the coordinate transformation systems and gs in the original coordinates these particular forms of gs are illustrated with numerical results of well known chaotic benchmark systems

linear receivers for correlatively coded msk in this paper we show that many spectrally efficient modified msk schemes termed generalized msk although not representable as oqpsk may nevertheless be suboptimally demodulated using an i q receiver with a proper choice of carrier phase offset correlatively coded msk schemes with i q receivers are studied and it is concluded that duobinary msk and 1 2d d 2 4 msk represent good performance bandwidth tradeoffs among first and second order correlative coding polynomial schemes the optimal design of these receivers are considered subject to the constraint of a finite duration impulse response especially for asymptotic cases of arbitrarily small and large snr filter design based on a zero intersymbol interference constraint for pam based approximations of the signals is also considered the optimized linear i q receivers for 1 d 2 msk and 1 d 2 4 msk are presented these receivers are only 0 28 and 1 24 db poorer than the optimal viterbi receivers at high snr

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

symmetric tensor representations quasimodular forms and weak jacobi forms abstract we establish a correspondence between vector valued modular forms with respect to a symmetric tensor representation and quasimodular forms this is carried out by first obtaining an explicit isomorphism between the space of vector valued modular forms with respect to a symmetric tensor representation and the space of finite sequences of modular forms of certain type this isomorphism uses rankin cohen brackets and extends a result of kuga and shimura who considered the case of vector valued modular forms of weight two we also obtain a correspondence between such vector valued modular forms and weak jacobi forms

signal interception in non gaussian noise the interception of weak signals in nongaussian noise is discussed the spectral correlation property exhibited by all cyclostationary signals is exploited to synthesize multi cycle and single cycle detectors which assure a superior tolerance as compared to radiometric techniques to one of the most challenging problems in interception namely accommodating unknown and changing noise level and interference activity the proposed detectors perform a maximum likelihood estimate of the noise level and use the estimate to form the detection statistic to obtain some analytical information about the performance of the multi cycle and single cycle detectors the deflection which is a useful measure of the output signal to noise ratio especially appropriate for weak signal snr interception has been evaluated the receiver operating characteristics carried out via computer simulation confirm the superiority of the proposed cycle detector with respect to the traditional radiometer

asymptotic performance analysis of cyclic detectors the paper deals with the analytical evaluation of the asymptotic detection and false alarm probabilities of multicycle and single cycle detectors operating in additive white gaussian noise with unknown and nonrandom spectral level which are based on the cyclostationarity properties of the signal to be intercepted the receiver operating characteristics are derived by using the asymptotic complex normality and the covariance expression of the sample average estimator of the cyclic covariance in an observed discrete time series a numerical example for interception of a binary phase shift keying signal is considered

optimization of linear receivers for data communication signals the optimization of receivers constrained to consist of a linear filter and level slicer is considered for general data communication signals in additive white gaussian noise special consideration is given to the two limiting cases of arbitrarily low and high signal to noise ratios snrs the low snr case results in an average matched filter receiver the high snr filter is shown to be the solution to a specific nonlinear mathematical problem with a simple geometric interpretation an efficient algorithm is developed to solve the problem the results are illustrated for a duobinary minimum shift keyed signal observed over an interval of three symbol period duration

visibility graph similarity a new measure of generalized synchronization in coupled dynamic systems abstract synchronization is defined as interdependencies among coupled dynamic systems in most coupled systems the intrinsic and internal variants and the interdependencies among their subsystems are not accessible therefore in order to quantify the interdependencies among the coupled systems attempts have been made through measuring the synchronization between their outputs represented mostly as time series in this paper a new method called visibility graph similarity vgs is presented as a method of measuring generalized synchronization first each time series is reconstructed as a trajectory in a state space next a distance time series dts is created from a sequence of relative distances of the states to a reference state subsequently a visibility graph vg is constructed using dts then a sequence of degrees of the vg called degree sequence ds is obtained correlation of the dss of two coupled systems is called vgs and is presented as a measurement of similarity of dynamics of the coupled systems the synchronization measurement performance of the vgs is compared with synchronization likelihood sl and the classical cross correlation method using two identical and non identical models of two coupled henon map over the entire time domain also it is compared with sl for tracing temporal synchronization using both models it is shown that vgs provides a more accurate measure of the overall synchronization compared with sl it is more reliable for measuring weak couplings compared with the cross correlation method moreover vgs uses fewer parameters and detects the temporal synchronization sooner than the sl

simple cpm receivers based on a switched linear modulation model based on a switched linear modulation model recently developed for continuous phase modulated cpm signal representation and approximation and incorporated with new phase state symbol definitions three simple cpm receivers are proposed in this letter their performance simulation results and complexity comparison are given using a quaternary 2rc raised cosine frequency pulse cpm scheme

on time reversibility and the uniqueness of moving average representations for non gaussian stationary time series a recent result by findley 1986 on the uniqueness of moving average representations for non gaussian time series is shown to establish a conjecture by weiss 1975 on the time reversibility of general linear processes 1988 biometrika trust

a new interpretation of the average matched filter for msk type receivers the minimum mean square error approximation to a generalized minimum shift keying msk signal using an offset quadrature phase shift keying waveform with an elementary pulse g t is considered it is shown that the optimum shape of g t gamma t coincides with the average pulse of the generalized msk signal therefore gamma t is the impulse response of the corresponding average matched fiber

estimating correlation dimension from a chaotic time series when does plateau onset occur abstract suppose that a dynamical system has a chaotic attractor a with a correlation dimension d 2 a common technique to probe the system is by measuring a single scalar function of the system state and reconstructing the dynamics in an m dimensional space using the delay coordinate technique the estimated correlation dimension of the reconstructed attractor typically increases with m and reaches a plateau on which the dimension estimate is relatively constant for a range of large enough m values the plateaued dimension value is then assumed to be an estimate of d 2 for the attractor in the original full phase space in this paper we first present rigorous results which state that for a long enough data string with low enough noise the plateau onset occurs at m ceil d 2 where ceil d 2 standing for ceiling of d 2 is the smallest integer greater than or equal to d 2 we then numerical examples illustrating the theoretical prediction in addition we discuss new findings showing how practical factors such as a lack of data and observational noise can produce results that may seem to be inconsistent with the theoretically predicted plateau onset at m ceil d 2

two channel likelihood detectors for arbitrary linear channel distortion this paper derives likelihood and generalized likelihood detection test statistics for a set of two channel problems this set includes additive gaussian and non gaussian noise known signals signals with unknown deterministic parameters signals with unknown statistical parameters and signals completely unknown the set also includes arbitrary linear channel distortion which is a generalization of time delay frequency shift and multipath simple expressions are obtained for the test statistic in the weak signal limit for additive non gaussian noise the ambiguity function is derived under the assumption of white gaussian noise with the signal completely unknown generalizations of the ambiguity function are derived and are used to construct detection statistics for other signal problems

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

stochastic time frequency analysis using the analytic signal why the complementary distribution matters we challenge the perception that we live in a proper world where complex random signals can always be assumed to be proper also called circularly symmetric rather we stress the fact that the analytic signal constructed from a nonstationary real signal is in general improper which means that its complementary correlation function is nonzero we explore the consequences of this finding in the context of stochastic time frequency analysis in cohen s class there the analytic signal plays a prominent role because it reduces interference terms however the usual time frequency representation tfr based on the analytic signal gives only an incomplete signal description it must be augmented by a complementary tfr whose properties we develop in detail we show why it is still advantageous to use the pair of standard and complementary tfrs of the analytic signal rather than the tfr of the corresponding real signal

the role of spectral correlation in design and performance analysis of synchronizers the popular class of synchronizers that consist of a quadratic nonlinearity followed by a phase lock loop is investigated and it is shown that the optimum design of the quadratic transformation is characterized in terms of a spectral correlation function for the signal to be synchronized to it is also shown that the snr performance of this quadratic transformation and the mean square phase jitter of the phaselock loop are both characterized in terms of spectral correlation functions the conditions under which the optimum quadratic transformations for symbol synchronization of bpsk qpsk sqpsk and msk and for carrier synchronization of bpsk reduce to the well known matched filter squarer are identified in addition the well known zeromean square phase jitter condition is generalized from pam to all synchronizable signals and is characterized in terms of the spectral correlation function the low snr maximum likelihood synchronizer for all quadratically synchronizable signals is characterized in terms of a multiplicity of maximum snr quadratic spectral line generators a closed form implementation in terms of a matched filter squarer and symbol rate synchronized averager is obtained for bpsk and qpsk signals

cyclic statistic estimators with uncertain cycle frequencies for almost cyclostationary processes sufficient conditions are derived such that estimates of the second order cyclic probabilistic functions with estimated cycle frequencies are mean square consistent and asymptotically complex normal cyclic conjugate autocorrelation functions and cyclic conjugate spectra are considered under the derived conditions asymptotically as the data record length approaches infinity the estimates of cyclic statistics with estimated cycle frequencies have the same complex normal distribution as the case of exactly known cycle frequencies the results are applied to the detection of a moving cyclostationary source in the presence of strong doppler effect and for low values of snr

a low complexity iterative phase noise tracker for bit interleaved coded cpm signals in awgn this paper considers iterative detection of bit interleaved coded continuous phase modulation in the presence of both phase noise pn and additive white gaussian noise awgn the proposed receiver iterates between a detection module and an estimation module the detection module operates according to the sum product algorithm and the factor graph framework in order to perform coherent maximum a posteriori bit detection in awgn using a pn estimate provided by the estimation module the latter module which results from the expectation maximization algorithm for maximum likelihood estimation of the unknown pn samples is implemented as a smoothing phase locked loop that uses soft decisions provided by the detector the separation between the detection and the estimation modules allows the use of an off the shelf coherent bit detector the technique is further characterized by a very low computational complexity a small error performance degradation and a small number of overhead symbols

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

application of higher order spectral analysis to cubically nonlinear system identification in this study digital higher order spectral analysis and frequency domain volterra system models are utilized to yield a practical methodology for the identification of weakly nonlinear time invariant systems up to third order the primary focus is on consideration of random excitation of nonlinear systems and thus the approach makes extensive use of higher order spectral analysis to determine the frequency domain volterra kernels which correspond to linear quadratic and cubic transfer functions although the volterra model is nonlinear in terms of its input it is linear in terms of its unknown transfer functions thus a least squares approach is used to determine the optimal in a least squares sense set of linear quadratic and cubic transfer functions of particular practical note is the fact that the approach of this paper is valid for non gaussian as well as gaussian random excitation it may also be utilized for multitone inputs the complexity of the problem addressed in this paper arises from two principal causes 1 the necessity to work in a 3d frequency space to describe cubically nonlinear systems and 2 the necessity to characterize the non gaussian random excitation by computing higher order spectral moments up to sixth order a detailed description of the approach used to determine the nonlinear transfer functions including considerations necessary for digital implementation is presented

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

receivers with widely linear processing for frequency selective channels we propose several equalization schemes based on widely linear processing wlp the received signal and its complex conjugate are separately filtered and the results are linearly combined it is shown that wlp yields a gain in performance if the noiseless received signal can be interpreted as the convolution of a real valued data sequence and an equivalent complex valued intersymbol interference channel impulse response such a model applies to e g amplitude shift keying offset quadrature amplitude modulation and binary minimum shift keying type modulation we consider receivers without and with decision feedback finite impulse response filters are derived for these structures which are optimum with respect to the zero forcing and minimum mean squared error mmse criteria respectively in the mmse case adaptive algorithms for filter adjustment are given infinite filter orders are investigated in order to obtain analytical performance results furthermore suboptimum trellis based detection with widely linear preprocessing is briefly discussed it is demonstrated analytically and by numerical examples that widely linear schemes may outperform conventional schemes significantly depending on the considered application

a space time code design for cpm diversity order and coding gain sufficient conditions are derived under which m ary partial and full response continuous phase modulation cpm space time st codes will attain both full spatial diversity and optimal coding gain general code construction rules are desirable due to the nonlinearity and inherent memory of the cpm signals which makes manual design or computer search difficult using a linear decomposition of cpm signals with tilted phase we identify a rank criterion for m ary partial and full response cpm that specifies the set of allowable modulation indices we also propose a coding gain design criterion optimization of the coding gain for cpm st codes is shown to depend on the cpm frequency phase shaping pulse modulation index and codewords the modulation indices and phase shaping functions that improve the coding gain are specified finally optimization of coding gain for st cpm and orthogonal st cpm codewords is discussed

detection and source location of weak cyclostationary signals simplifications of the maximum likelihood receiver the problem of dual receiver interception of low snr signals which includes detection of the presence of a particular signal type and location of its source is considered in particular source location based on time difference of arrival tdoa measurements is examined and the low snr maximum likelihood receiver for joint detection and tdoa estimation is taken as a starting point by explicitly revealing the way in which this receiver exploits the spectral correlation properties of the cyclostationary signal several partial implementations with optimality properties of their own are proposed these greatly simplified implementations which require only a one dimensional search over the tdoa parameter are shown by simulation to perform competitively with the relatively complicated maximum likelihood receiver which requires a two or three dimensional search for phase shift keyed psk signals

l2 orthogonal st code design for cpm non linear modulations like the continuous phase modulation cpm with its constant envelope property have been appealing for energy efficient communication systems in parallel linear orthogonal space time block codes stbc have emerged as a simple way of achieving spectral efficiency by full diversity and simple decoupled maximum likelihood decoding however linear codes rely on pointwise orthogonality which leads to a well known degradation of data rate for more than two antennas in this paper we introduce the concept of l2 orthogonality for non linear space time codes stc our approach generalizes code design based on pointwise orthogonality namely we are able to derive new codes with the same advantages as pointwise orthogonal stbc i e low decoding complexity and diversity gain at the same time we are no longer limited by the restrictions of pointwise orthogonal codes i e the reduction in data rate actually we show how to construct full rate codes for any arbitrary number of transmit antennas more precisely a family of codes for continuous phase modulation cpm is detailed the l2 orthogonality of these codes is ensured by a bank of phase correction functions which maintains the phase continuity but also introduces frequency offsets we prove that these codes achieve full diversity and have full rate moreover these codes don t put any restriction on the cpm parameters

the cumulant theory of cyclostationary time series ii development and applications for pt i see ibid vol 42 no 12 p 3387 3408 1994 the development of the theory of nonlinear processing of cyclostationary time series that is initiated in part i is continued a new type of cumulant for complex valued variables is introduced and used to generalize the temporal and spectral moments and cumulants for cyclostationary time series from real valued to complex valued time series the relations between the temporal and spectral moments and cumulants at the inputs and outputs of several signal processing operations are determined formulas for the temporal and spectral cumulants of complex valued pulse amplitude modulated time series are derived estimators for the temporal moments and cumulants and for the cyclic polyspectra are presented and their properties are discussed the performance of these estimators is illustrated by several computer simulation examples for pulse amplitude modulated time series the theory is applied to the problems of weak signal detection and interference tolerant time delay estimation

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

fourth order spectra of gaussian amplitude modulated sinusoids propagating underwater signals are sometimes amplitude modulated by the medium or other physical effects since this is a multiplicative phenomenon the resulting spectrum is a convolution of the spectra of the modulation and the desired signal a new method based on the spectrum of a special case of the fourth order cumulant is proposed to extract the desired signal it is shown that the special case of the fourth order cumulant is independent of the covariance of a gaussian modulating function and therefore it can extract the desired signal even when the modulating process is gaussian white noise convergence equations are derived which show that the fourth order cumulant and its special case will converge to their asymptotic forms as the data length increases the spectrum of the special case of the fourth order cumulant is also derived at the output of a low pass filter to demonstrate these theoretical results an experiment was conducted a sinusoid was modulated by white gaussian noise and transmitted through the water and received on an omnidirectional hydrophone the second order spectrum the spectrum of the special case of the fourth order moment and the spectrum of the special case of the fourth order cumulant were estimated from the filtered data the experiment corroborated the theoretical results by showing that the second order spectrum could not extract the sinusoidal frequency but the spectrum of the special case of the fourth order moment and the spectrum of the special case of the fourth order cumulant could simulations are included which further corroborate the theoretical results

space time code design for cpfsk modulation over frequency nonselective fading channels we derive a novel space time code stc design criterion for continuous phase frequency shift keying cpfsk over frequency nonselective fading channels our derivation is based on a specific matrix that is related to the input symbols of the cpfsk modulators with this code design criterion we propose a simple interleaved space time encoding scheme for cpfsk modulation over frequency nonselective correlated fading channels to exploit potential temporal and spatial diversity advantages such an encoding scheme consists of a ring convolutional encoder and a spatial encoder between which a convolutional interleaver is placed a decoding algorithm that generates symbol metrics for the viterbi decoder of convolutional codes from the spatial modulation trellis is examined simulation results confirm that the advantages of the combination of the interleaved convolutional encoding for temporal diversity and the spatial encoding for spatial diversity are promising for various system parameters

generalized synchronization of chaos in directionally coupled chaotic systems synchronization of chaotic systems is frequently taken to mean actual equality of the variables of the coupled systems as they evolve in time we explore a generalization of this condition which equates dynamical variables from one subsystem with a function of the variables of another subsystem this means that synchronization implies a collapse of the overall evolution onto a subspace of the system attractor in full space we explore this idea in systems where a response system bold y ital t is driven with the output of a driving system bold x ital t but there is no feedback to the driver we lose generality but gain tractability with this restriction to investigate the existence of the synchronization condition bold y ital t phi bold x ital t we introduce the idea of mutual false nearest neighbors to determine when closeness in response space implies closeness in driving space the synchronization condition also implies that the response dynamics is determined by the drive alone and we provide tests for this as well examples are drawn from computer simulations on various known cases of synchronization and on data from nonlinear electrical circuits determining the presence of generalized synchronization will be quite important when one has only scalarmore observations from the drive and from the response systems since the use of time delay or other embedding methods will produce imperfect coordinates in which strict equality of the synchronized variables is unlikely to transpire less

the first nyquist criterion applied to coherent receiver design for generalised msk signals a simple procedure for designing the post detection filter of an msk type receiver for continuous phase modulation with modulation index h 0 5 generalized msk signals is proposed the criterion descends from a useful general representation of this class of signals the frequency response of the baseband receiver filter is analytically optimized in closed form whatever the modulation pulse shaping of the transmitted signal and signal to noise ratio at the receiver the criterion is pointed out through a significant exact representation of generalized msk signals whatever the modulation pulse shaping waveform which is assumed to be included in a time range equal to lt t symbol time the main part of intersymbol interference as appears from the representation of the cpm signal is cancelled by applying the nyquist criterion to the most significant function among those describing the signal structure the numerical results obtained show a performance improvement with respect to the averaged matched filter amf criterion and are very close to the results reported in the literature deriving from more complex design criteria the suitability of the design criterion is also tested in the presence of interferers showing a significant advantage of the proposed filter when considering adjacent channel interference

space time coded systems using continuous phase modulation we develop space time trellis coded stc schemes using continuous phase modulation cpm we employ the rimoldi model of cpm to create a decomposed model of stc cpm the decomposition separates the coding from the modulation the space time encoding and the inherent cpm encoding is combined into a single trellis encoder on the ring of integers modulo this is followed by a bank of memoryless modulators the model allows the search for good space time codes to take into account the inherent encoding of the modulation

second order blind separation of first and second order cyclostationary sources application to am fsk cpfsk and deterministic sources most of the second order so and higher order ho blind source separation bss methods developed this last decade aim at blindly separating statistically independent sources that are assumed zero mean stationary and ergodic nevertheless in many situations of practical interest such as in radiocommunications contexts the sources are nonstationary and very often cyclostationary digital modulations the behavior of the current so and fourth order fo cumulant based bss methods in the presence of cyclostationary sources has been analyzed recently in a previous paper by ferre spl acute ol and chevalier assuming zero mean sources however some cyclostationary sources used in practical situations are not zero mean but have a first order fio cyclostationarity property which is in particular the case for some amplitude modulated am signals and for some nonlinearly modulated digital sources such as frequency shift keying fsk or some continuous phase frequency shift keying cpfsk sources for such sources the results presented in the previous paper by ferre spl acute ol and chevalier no longer hold and the purpose of this paper is to analyze the behavior and to propose adaptations of the current so bss methods for sources that are both fio and so cyclostationary and cyclo ergodic an extension for deterministic sources is also proposed in the paper

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

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

synchronized chaos and other coherent states for two coupled neurons abstract the parametrized time discrete dynamics of two recurrently coupled chaotic neurons is investigated basic dynamical features of this system are demonstrated for symmetric couplings of identical neurons periodic as well as chaotic orbits constrained to a manifold m of synchronized states are observed parameter domains for locally stable synchronization manifolds m are determined by numerical simulations in addition to the synchronized dynamics there often co exist periodic quasiperiodic and even chaotic attractors representing different kinds of non synchronous coherent dynamics simulation results for selected sets of parameters are presented and synchronization conditions for systems with non identical neurons are derived also these more general systems inherit the above mentioned dynamical properties

polyspectrum modeling using linear or quadratic filters the polyspectrum modeling problem using linear or quadratic filters is investigated in the linear case it is shown that if the output pth order cumulant function of a filter driven by a white noise is of finite extent then the filter necessarily has a finite extent impulse response it is proved that every factorable polyspectrum with a non gaussian white noise can also be modeled with a quadratic filter driven by a gaussian white noise it is shown that if the quadratic filter has a finite extent impulse response then the output pth order cumulant function is of finite extent and if the output pth order cumulant function of a quadratic filter is of finite extent then the impulse response may or may not be of finite extent it is shown that there exist finite and infinite extent pth order cumulant functions that are not factorable but can be modeled with quadratic filters

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

elliptic genera and quantum field theory it is shown that in elliptic cohomology as recently formulated in the mathematical literature the supercharge of the supersymmetric nonlinear signa model plays a role similar to the role of the dirac operator ink theory this leads to several insights concerning both elliptic cohomology and string theory some of the relevant calculations have been done previously by schellekens and warner in a different context

non data aided estimation of the modulation index of continuous phase modulations in this paper a new non data aided estimator of the modulation index of continuous phase modulated cpm signals is proposed it is based on the observation that the inverse of the index is the smallest positive real number a cpm signal should be raised to in order to generate a sinusoid of period 2t where t is the symbol period the asymptotic behavior of the estimator is studied if n is the sample size the estimation error is shown to converge to a non gaussian distribution at a rate of 1 n simulation results sustain the conclusions of the theoretical asymptotic analysis

generalized synchronization of chaos in electronic circuit experiments abstract two examples of one way coupled electronic circuits displaying generalized synchronization of chaos are considered in one of them the dynamics of both the response and the driving systems represent a double scroll chaos oscillator in another example the double scroll oscillator is driven by an electronic analog of the mackey glass system to detect the generalized synchronization an auxiliary response system that is a replica of the original one is used in these systems we have discovered two types of generalized synchronization namely a strong and a weak synchronization which correspond to the existence of a smooth and a nonsmooth map from the trajectories of the driving attractor to the trajectories of the response system respectively

moments and polyspectra of the discrete time random telegraph signal the random telegraph signal rts is an ordered signal which means that the explicit expression of the moment functions requires that the time instants appearing in these moments are put in an increasing order this property greatly complicates the calculation of higher order polyspectra fourier transforms of moments this article presents an extension to the discrete time dt case of a method already known in continuous time this extension exhibits new problems which makes the calculation even more difficult these difficulties are analyzed and the structure of trispectrum is discussed in detail

noncoherent sequence detection of continuous phase modulations in this paper noncoherent sequence detection proposed in a companion paper by colavolpe and raheli see ibid vol 47 no 9 p 1376 85 1999 is extended to the case of continuous phase modulations cpms the results in the companion paper on linear modulations with intersymbol interference isi are used here because a cpm signal is mathematically equivalent to a sum of isi affected linearly modulated components according to the laurent decomposition the proposed suboptimal detection schemes have a performance which approaches that of coherent detection with acceptable complexity allow for time varying phase models and compare favorably with previously proposed solutions

lag synchronization of structurally nonequivalent chaotic systems with time delays abstract in this paper we investigate the synchronization of a class of structurally nonequivalent chaotic systems with time delays the nonequivalence could be parameter mismatches differences in the time delays or more complicated nonequivalent structures we give a unified approach via unidirectional and impulsive control to them achieving lag synchronization then we apply this method to typical time delay chaotic systems mackey glass and ikeda models the corresponding estimations are given lastly we compare the results with existing results

signal interception a unifying theoretical framework for feature detection the unifying framework of the spectral correlation theory of cyclostationary signals is used to present a broad treatment of weak random signal detection for interception purposes the relationships among a variety of previously proposed ad hoc detectors optimum detectors and newly proposed detectors are established the spectral correlation plane approach to the interception problem is put forth as especially promising for detection classification and estimation in particularly difficult environments involving unknown and changing noise levels and interference activity a fundamental drawback of the popular radiometric methods in such environments is explained

laurent s representation of binary digital continuous phase modulated signals with modulation index 1 2 revisited in order to simplify modulator and demodulator structures the composition of binary continuous phase modulations cpms by the linear superposition of impulses as developed by laurent 1986 is advantageous based on differential encoding of the binary data sequence a novel cpm modulator concept for modulation index 1 2 is presented

a high performance reduced complexity gmsk demodulator a four state adaptive maximum likelihood sequence estimation mlse gaussian minimum shift keying gmsk demodulator for modulation bt 0 3 on awgn channels is analyzed and simulated this demodulator uses the linear representation of gmsk signals and achieves near optimum ber performance the channel impulse response used in the mlse demodulator is initialized to the highest energy component in the linear representation and then adapted in a decision directed mode to offset any performance losses incurred by initially ignoring other lower energy and time varying components in the linear representation the number of mlse states is reduced to two at about 0 1 db performance loss by implementing a whitening matched filter which concentrates most of the gmsk pulse energy in its two leading samples

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

on circularity circularity is an assumption that was originally introduced for the definition of the probability distribution function of complex normal vectors however this concept can be extended in various ways for nonnormal vectors the first purpose of the paper is to introduce and compare some possible definitions of circularity from these definitions it is also possible to introduce the concept of circular signals and to study whether or not the spectral representation of stationary signals introduces circular components therefore the relationships between circularity and stationarity are analyzed in detail finally the theory of linear mean square estimation for complex signals exhibits some connections with circularity and it is shown that without this assumption the estimation theory must be reformulated

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

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

blind equalization for correlated input symbols a bussgang approach this paper addresses the problem of blind equalization in the case of correlated input symbols and it shows how the knowledge of the symbol sequence probability distribution can be directly incorporated in a bussgang blind equalization scheme numerical results pertaining to both linear and nonlinear modulation schemes show that a significant improvement in equalization performance is obtained by exploiting the symbol sequence probability distribution using the approach herein described

prerecorded history of a system as an experimental tool to control chaos we present experimental results of synchronizing the current state of a chaotic system with its prerecorded history this is achieved by a small self controlling feedback perturbation in the form of the difference between the current state of the system and its past dynamics the perturbation transforms an unpredictable chaotic behavior into a predictable chaotic or periodic motion via stabilization of unstable aperiodic or periodic orbits of the strange attractor one advantage of the method is its robustness against noise furthermore it does not require any analytical knowledge of the system dynamics and can be simply implemented in experiment by a purely analog technique the experimental results are supported by a numerical analysis of the conditional lyapunov exponents and other characteristics of the model equations

on the principal domain of the discrete bispectrum of a stationary signal the paper presents a simplifying yet general approach to determining the symmetry structure of a bispectrum the principal domain pd of the bispectrum and its region of positive support are derived in a way that illuminates the controversy surrounding the triangle in the pd which is called the outer triangle ot by hinich and wolinsky 1988 where the bispectrum is zero for a stationary random sampled process that is not aliased the basic statistical issues of testing for nonzero bispectral structure are reviewed

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

polyspectra of ordered signals polyspectra are related to fourier transforms of moment or cumulant functions of any order of random signals they play an important role in many problems of signal analysis and processing however there are only a few statistical models giving explicitly the expression of polyspectra ordered signals are signals for which the explicit expression of the moment functions requires that the time instants appearing in these moments are put in an increasing order there are many examples of such signals the best known being the random telegraph signal constructed from a poisson process some of these examples are presented and analyzed the origin of the ordering structure is related with the point that real time is an oriented variable making a difference between past and future this especially appears in markov processes the calculation of polyspectra is difficult because ordering is not adapted to fourier analysis by an appropriate grouping of various terms the explicit expression of spectral moment functions is obtained it shows in particular that many ordered signals present a normal density on the normal manifolds of the frequency domain and another contribution on the stationary manifold that is explicitly calculated the analysis of the structure of this expression allows us to discuss some relationships with normal distribution central limit theorem and time reversibility

frequency domain glr detection of a second order cyclostationary signal over fading channels cyclostationary processes exhibit a form of frequency diversity based on that we show that a digital waveform with symbol period t can be asymptotically represented as a rank 1 frequency domain vector process which exhibits uncorrelation at different frequencies inside the nyquist spectral support of 1 t by resorting to the fast fourier transform fft this formulation obviates the need of estimating a cumbersome covariance matrix to characterize the likelihood function we then derive the generalized likelihood ratio test glrt for the detection of a cyclostationary signal in unknown white noise without the need of a assuming a synchronized receiver this provides a sound theoretical basis for the exploitation of the cyclostationary feature and highlights an explicit link with classical square timing recovery schemes which appear implicitly in the core of the glrt moreover to avoid the well known sensitivity of cyclostationary based detection schemes to frequency selective fading channels a parametric channel model based on a lower bound on the coherence bandwidth is adopted and incorporated into the glrt by exploiting the rank 1 structure of small spectral covariance matrices the obtained detector outperforms the classical spectral correlation magnitude detector

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

the cumulant theory of cyclostationary time series i foundation the problem of characterizing the sine wave components in the output of a polynomial nonlinear system with a cyclostationary random time series input is investigated the concept of a pure nth order sine wave is introduced and it is shown that pure nth order sine wave strengths in the output time series are given by scaled fourier coefficients of the polyperiodic temporal cumulant of the input time series the higher order moments and cumulants of narrowband spectral components of time series are defined and then idealized to the case of infinitesimal bandwidth such spectral moments and cumulants are shown to be characterized by the fourier transforms of the temporal moments and cumulants of the time series it is established that the temporal and spectral cumulants have certain mathematical and practical advantages over their moment counterparts to put the contributions of the paper in perspective a uniquely comprehensive historical survey that traces the development of the ideas of temporal and spectral cumulants from their inception is provided

trispectral analysis of stationary random time series this paper investigates the statistical properties of the trispectrum the trispectrum is the fourier transform of the fourth order joint lagged cumulant of a zero mean stationary random time series a complete representation of the principal domain of the trispectrum derived from its inherent symmetries is detailed the large sample variance for a consistent estimator of the trispectrum is presented and used in the development of the fourth order generalizations of the bispectrum based hinich tests of gaussianity and linearity a test for stationarity is developed using an amended version of the trispectrum based test of gaussianity an arithmetic frame averaging procedure is used to compute consistent trispectral estimates for a zero mean bandlimited real valued stationary random process the trispectral based tests are applied to time series of ship noise recorded by a sonobouy in the eastern atlantic ocean

a general procedure for the derivation of principal domains of higher order spectra a general procedure to determine the principal domain i e nonredundant region of computation of any higher order spectrum is presented using the bispectrum as an example the procedure is then applied to derive the principal domain of the trispectrum of a real valued stationary time series these results are easily extended to compute the principal domains of other higher order spectra

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

modeling and synchronizing chaotic systems from time series data the problem of obtaining ordinary differential equations ode s from chaotic time series data is addressed the vector fields for the ode s are polynomials constructed from a basis set that is orthonormal on the data the method for constructing the model is similar to the integration of ode s using adams predictor corrector integration the method is compared to the usual euler model and is shown to be accurate for much larger sampling intervals in addition the method used to construct the model is capable of determining the optimal polynomial vector field for the given data finally we demonstrate that it is possible to synchronize in the sense of fujisaka and yamada prog theor phys 69 32 1983 as well as pecora and carroll phys rev lett 64 821 1990 phys rev a 44 2374 1991 the model to a time series synchronization is used as a nontrivial test to determine how close the model vector field is to the true vector field implications and possible applications of synchronization are discussed

supplementary proof for exact and approximate construction of digital phase modulations by superposition of amp by p a laurent in this letter we supplement the derivation in laurent s paper by mathematically proving that combining binary continuous phase modulation cpm signals in different bit durations results in the decomposed cpm expression consisting of a set of continuous amplitude modulated pulse functions

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

minimal pam decompositions of cpm signals with separable phase this letter proposes a new pulse amplitude modulation decomposition of continuous phase modulation cpm signals under the constraint of phase response separability the separability condition is met by a broad class of cpm signals including full response signals we show that the proposed decomposition has minimal cardinality of n sub c l m 1 where m is the alphabet size and l is the cpm memory length the cardinality increases linearly with l while previous proposed decompositions have cardinalities m sup l m sup l 1 which grow exponentially with l

ergodicity and fourth order spectral moments relationships between ergodicity and structures of fourth order spectral moments are investigated in particular it is shown that second order ergodicity of a random process is directly related to the distribution of these moments on the normal manifolds of the frequency domain this result is illustrated by various examples

serially concatenated space time convolutional codes and continuous phase modulation this paper addresses space time convolutional code design using continuous phase modulation cpm the possibility of constructing full diversity space time codes is investigated a linear modulation approximation to cpm is done using the gram schmidt orthogonalization transform the cpm signal is generated as a vector with finite energy in a different euclidean space a serially concatenated cpm construction is considered in searching channel codes which are able to exploit maximum diversity design criteria based on the encoding scheme are derived for an arbitrary number of transmit antennas the investigations are done for a quasi static rayleigh fading channel