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

a new approach to multipath correction of constant modulus signals an adaptive digital filtering algorithm that can compensate for both frequency selective multipath and interference on constant envelope modulated signals is presented the method exploits the fact that multipath reception and various interference sources generate incidental amplitude modulation on the received signal a class of so called constant modulus performance functions is developed which sense this am term but are insensitive to the angle modulation simple adaptive algorithms for finite impulse response fir digital filters are developed which employ a gradient search of the performance function one of the resulting algorithms is simulated for the example of an fm signal degraded by specular multipath propagation substantial improvements in noise power ratio npr are observed e g 25 db with moderately rapid convergence time these results are then extended to include tonal interference on a fm signal and intersymbol interference on a qpsk data signal

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

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

trellis coded constant envelope modulations with linear receivers we present two multilevel constant envelope continuous phase modulation cpm schemes with four dimensional 4 d trellis coding the receiver is composed of a simple quadrature demodulator followed by a symbol rate sampler and a viterbi decoder matched to the code trellis the first modulation is a quaternary cpm scheme whose phase transitions over a symbol interval are those of spl pi 4 shift quaternary phase shift keying qpsk the demodulator filter is optimized so as to minimize the combined effect of intersymbol interference isi and noise at the decision instants we use wei s 1987 16 state 4 d trellis code and redefine the set partitioning tree so as to maintain the same minimum distance between parallel transitions as in quadrature amplitude modulation qam signal sets the resulting modulation outperforms minimum shift keying msk by as much as 3 5 db in addition to reducing the 30 db signal bandwidth by 20 next we introduce an octonary 8 level cpm scheme whose phase transitions are those of spl pi 8 shift 8psk the same trellis code and receive filter optimization are also applied to this modulation which is shown to achieve better error rate performance than msk while saving some 60 of the transmitted signal bandwidth

nonparametric kernel algorithm for recovery of functions from noisy measurements with applications this note presents a kernel algorithm for recovery of a regression function from noisy data conditions are provided that assure pointwise convergence in the mean square and almost sure senses an application to a class of linear system identification problems is discussed

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

blind identification of fir systems driven by markov like input signals we propose a new algorithm for the blind identification and equalization of finite impulse response fir systems using the second order statistics of the received signal the new algorithm is set in the same context as the algorithms of tong et al 1994 and moulines et al 1995 however unlike those earlier approaches it is designed to allow correlated input signals specifically the algorithm accommodates finite memory sources and sources whose autocorrelation function decays exponentially numerical simulations compare the equalization performance of the new algorithm to those of tong and moulines it is shown that our algorithm yields consistently lower bit error rates at a wide variety of signal to noise ratios and at various equalizer lengths moreover the algorithm maintains this advantage even if it has no a priori information of source correlation or if source symbols are uncorrelated

blind channel estimation using the second order statistics asymptotic performance and limitations we consider the asymptotic performance and fundamental limitations of the class of blind estimators that use second order statistics an achievable lower bound of the asymptotic normalized mean square error anmse is derived it is shown that the achievable anmse is lower bounded by the condition number of the jacobian matrix of the correlation function with respect to the channel parameters it is shown next that the jacobian matrix is singular if and only if the subchannels share common conjugate reciprocal zeros this condition is different from the existing channel identification conditions asymptotic performance of some existing eigenstructure based algorithms is analyzed closed form expressions of anmse and their lower bounds are derived for the least squares ls and the subspace ss blind channel estimators when there are two subchannels asymptotic efficiency of ls ss algorithms is also evaluated showing that significant performance improvement is possible when the information of the source correlation is exploited

blind identification and source separation in 2 spl times 3 under determined mixtures under determined mixtures are characterized by the fact that they have more inputs than outputs or with the antenna array processing terminology more sources than sensors the problem addressed is that of identifying and inverting the mixture which obviously does not admit a linear inverse identification is carried out with the help of tensor canonical decompositions on the other hand the discrete distribution of the sources is utilized for performing the source extraction the under determined mixture being either known or unknown the results presented in this paper are limited to two dimensional 2 d mixtures of three sources

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

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

frequency offset estimation for unknown qam constellations we introduce a novel both gain and signal to noise ratio independent constellation unaware blind frequency offset estimation procedure for qam signals asymptotic performance analysis and numerical simulations show that the herein presented method outperforms a selected state of the art blind constellation unaware estimator especially for cross constellations

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

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

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

data aided and blind stochastic gradient algorithms for widely linear mmse mai suppression for ds cdma in this paper three novel stochastic gradient algorithms for adjustment of the widely linear wl minimum mean squared error mmse filter for multiple access interference mai suppression for direct sequence code division multiple access ds cdma are introduced and analyzed in particular we derive a data aided wl least mean square lms algorithm a blind wl minimum output energy moe algorithm and a wl blind lms blms algorithm we give analytical expressions for the steady state signal to interference plus noise ratios sinrs of the proposed wl algorithms and we also investigate their speed of convergence wherever possible comparisons with the corresponding linear adaptive algorithms are made both analytical considerations and simulations show in good agreement the superiority of the novel wl adaptive algorithms nevertheless all proposed wl algorithms require a slightly lower computational complexity than their linear counterparts

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

multichannel blind image deconvolution using the bussgang algorithm spatial and multiresolution approaches this work extends the bussgang blind equalization algorithm to the multichannel case with application to image deconvolution problems we address the restoration of images with poor spatial correlation as well as strongly correlated natural images the spatial nonlinearity employed in the final estimation step of the bussgang algorithm is developed according to the minimum mean square error criterion in the case of spatially uncorrelated images for spatially correlated images the nonlinearity design is rather conducted using a particular wavelet decomposition that detecting lines edges and higher order structures carries out a task analogous to those of the preattentive stage of the human visual system experimental results pertaining to restoration of motion blurred text images out of focus spiky images and blurred natural images are reported

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

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

computing the minimum phase filter using the ql factorization we investigate the ql factorization of a time invariant convolutive filtering matrix and show that this factorization not only provides the finite length equivalent to the minimum phase filter but also gives the associated all pass filter the convergence properties are analyzed and we derive the exact convergence rate and an upper bound for a simple single input single output system with filter length finally this upper bound is used to derive an approximation of the convergence rate for systems of arbitrary length implementation wise the method has the advantage of being numerically stable and straight forward to extend to the multiple input multiple output case furthermore due to the existence of fast ql factorization methods it is possible to compute the filters efficiently

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

identification of miso nonlinear regressions in the presence of a wide class of disturbances a nonparametric algorithm based on multiple fourier series for identification of miso multidimensional input single output systems is investigated it is shown that the algorithm converges for a wide class of noise

on the blind equalization of continuous phase modulated signals using the constant modulus criterion the use of the constant modulus cm criterion to achieve blind equalization of continuous phase modulated cpm signals is investigated in this paper solutions to the cm criterion are characterized it is shown that blind equalization using the cm criterion may be unsuccessful in the sense that the output of the equalizer does not necessarily coincides with a delayed and rotated version of the input signal an indeterminacy indeed remains and this residual indeterminacy is characterized as an application of our results a blind equalization criterion that allows us to eliminate the latter indeterminacy is proposed simulation results sustain theoretical claims and illustrate the attractive performance of the proposed criterion

multiple fourier series procedures for extraction of nonlinear regressions from noisy data three nonparametric procedures for the extraction of nonlinear regressions from noisy data are proposed the procedures are based on the dirichlet fejer and de la vallee poussin multiple kernels convergence properties are investigated in particular it is shown that the algorithms are convergent in the mean integrated square error sense the appropriate theorem establishes a relation between the order of kernels and the number of observations special attention is focused on the two dimensional case it is proved that the procedures attain the optimal rate of convergence which cannot be exceeded by any other nonparametric algorithm

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

super exponential methods for blind deconvolution a class of iterative methods for solving the blind deconvolution problem i e for recovering the input of an unknown possibly nonminimum phase linear system by observation of its output is presented these methods are universal do not require prior knowledge of the input distribution are computationally efficient and statistically stable and converge to the desired solution regardless of initialization at a very fast rate the effects of finite length of the data finite length of the equalizer and additive noise in the system on the attainable performance intersymbol interference are analyzed it is shown that in many cases of practical interest the performance of the proposed methods is far superior to linear prediction methods even for minimum phase systems recursive and sequential algorithms are also developed which allow real time implementation and adaptive equalization of time varying systems

a multiresolution approach for texture synthesis using the circular harmonic functions in this paper an unsupervised model based texture reproduction technique is described in accordance with the julesz s 1962 conjecture the statistical properties of the prototype up to the second order are copied in order to generate a synthetic texture perceptually indistinguishable from the given sample however this task is accomplished using a hybrid approach which operates partially in the spatial domain and partially in a multiresolution domain the latter employed is the circular harmonic function chf domain since it has been proven to be well suited for mimicking the behavior of the human visual system hvs this approach allows for a wide range of textures typologies obtaining synthetic textures that better match the prototype with respect to the ones obtained using techniques based on the julesz s conjecture operating only in the spatial domain and to dramatically reduce the computational complexity of similar methods operating only in the multiresolution domain

generalized app detection of continuous phase modulation over unknown isi channels techniques for computing soft information in the presence of unknown intersymbol interference are presented with a particular focus on iterative detection of serially concatenated continuous phase modulation the techniques are centered around the recursive least squares algorithm thus enabling unsupervised detection in particular we employ bidirectional estimation

repetitive control system a new type servo system for periodic exogenous signals a control scheme called repetitive control is proposed in which the controlled variables follow periodic reference commands a high accuracy asymptotic tracking property is achieved by implementing a model that generates the periodic signals of period l into the closed loop system sufficient conditions for the stability of repetitive control systems and modified repetitive control systems are derived by applying the small gain theorem and the stability theorem for time lag systems synthesis algorithms are presented by both the state space approach and the factorization approach in the former approach the technique of the kalman filter and perfect regulation is utilized while coprime factorization over the matrix ring of proper stable rational functions and the solution of the hankel norm approximation are used in the latter one

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

discrete time linear optimal multi periodic repetitive control a benchmark tracking solution the use of optimal control tracking methodologies for the development of feedback control schemes for arbitrary discrete time linear systems is considered for the special case when the demand signal is multi periodic i e can be expressed as a finite sum of periodic signals of different but known frequencies by embedding the reference signal into plant dynamics the problem is reduced to a classical linear quadratic control problem which yields an explicit formula for a globally stabilizing tracking controller asymptotic perfect tracking is guaranteed by the presence of the familiar internal model of the demand signal dynamics within the control structure transfer function analysis of the controller indicates that it consists of an inner state feedback loop plus an error actuated forward path control element containing the internal model

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

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

blind channel equalization with colored sources based on second order statistics a linear prediction approach we consider the blind equalization and estimation of single user multichannel models from the second order statistics of the channel output when the channel input statistics are colored but known by exploiting certain results from linear prediction theory we generalize the algorithm of tong et al 1994 which was derived under the assumption of a white transmitted sequence in particular we show that all one needs to estimate the channel to within an unitary scaling constant and thus to find its equalizers is a that a standard channel matrix have full column rank and b a vector of the input signal and its delays have positive definite lag zero autocorrelation an algorithm is provided to determine the equalizer under these conditions we argue that because this algorithm makes explicit use of the input statistics the equalizers thus obtained should outperform those obtained by other methods that neither require nor exploit the knowledge of the input statistics simulation results are provided to verify this fact

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

on system identification by nonparametric function fitting a new nonparametric algorithm for function fitting is proposed and its application to a broad class of system identification problems is discussed

generalized serial msk modulation a generalized form of the serial msk gsmsk modem is presented the impulse response of the conversion filter required to produce a gsmsk signal whose upward phase trellis arms have an arbitrary curvature is derived analysis is presented which shows that the proposed modem does not have intersymbol interference and that the ber performance is that of an antipodal signal set numerical results are shown for a particular trellis curvature

decision feedback detectors for soqpsk we consider highly simplified decision feedback detectors for shaped offset quadrature phase shift keying soqpsk a highly bandwidth efficient and popular constant envelope modulation in particular we show that the state complexity can be reduced to a minimal level two states with asymptotically optimum performance as demonstrated by performance analysis and confirmed by computer simulations the complexity reduction is achieved by a novel manipulation of the differential encoder and the soqpsk precoder which are both part of the transmission model for soqpsk we give two possible architectures for achieving this complexity reduction the pulse amplitude modulation pam technique and the pulse truncation pt technique we also formulate these detectors for coherent and noncoherent detection the resulting family of detectors makes use of recent advances in soqpsk technology based on a continuous phase modulation cpm interpretation of soqpsk the proposed simplifications are significant because they minimize the complexity of trellis based soqpsk detectors which have become available only in recent years because trellis based soqpsk detectors are 1 2 db superior to the widely deployed family of symbol by symbol soqpsk detectors the proposed two state detectors offer the simplest means of achieving these performance gains thus these simple detection schemes are applicable in settings where high performance and low complexity are needed to meet restrictions on power consumption and cost

iterative learning control using optimal feedback and feedforward actions an algorithm for iterative learning control is developed on the basis of an optimization principle which has been used previously to derive gradient type algorithms the new algorithm has numerous benefits which include realization in terms of riccati feedback and feedforward components this realization also has the advantage of implicitly ensuring automatic step size selection and hence guaranteeing convergence without the need for empirical choice of parameters the algorithm is expressed as a very general norm optimization problem in a hilbert space setting and hence in principle can be used for both continuous and discrete time systems a basic relationship with almost singular optimal control is outlined the theoretical results are illustrated by simulation studies which highlight the dependence of the speed of convergence on parameters chosen to represent the norm of the signals appearing in the optimization problem

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

differentially coherent detection of binary partial response continuous phase modulation with index 0 5 the performance of binary partial response continuous phase modulation with index 0 5 using a differentially coherent receiver depends on the choice of the receiver filter an optimum mmse design method for this filter is presented the receiver filter is equivalent to the cascade of a matched filter and an equalizer in order to reduce inherent intersymbol interference isi it is shown that performance degradation with respect to that of the differential binary phase shift keying bpsk system is due to inherent isi contained in the signal and also to noise enhancement and correlation caused by the receiver filter the bit error probability on the gaussian channel is calculated by assuming that isi is gaussian the gaussian minimum shift keying msk signal is used for illustration

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

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

on optimal global rate of convergence of some nonparametric identification procedures a study of orthogonal series procedures for function fitting motivated by an interest in nonparametric identification of linear dynamic systems is reported it is shown that the procedures attain the optimal rate of convergence for the fourier and the walsh orthonormal systems these rates cannot be exceeded by any method of estimation this is the first analytical result giving a clear answer to the question of which orthonormal system is the best one for the purpose of system identification

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

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

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

bussgang zero crossing equalization an integrated hos sos approach an integrated higher order statistics hos and second order statistics sos based equalization technique is presented as an extension of the bussgang equalization algorithm this extension allows one to simultaneously take account of the statistical knowledge about the data source as done in the conventional hos approaches and in particular by bussgang like equalization algorithms such as super exponential constant modulus etc and the spectral redundancy usually present in pulse amplitude modulation pam and quadrature amplitude modulation qam modulated signals exploited by sos based approaches the technique presented employs a new form of sos equalization that naturally integrates into the bussgang scheme it is based on a zero crossing zc property of the received signal when it is passed through a suitable filter the novel equalization scheme is presented in a bayesian estimation framework after illustration of the general bussgang paradigm and of the principles of the zc approach from simulated experiments results show that the extended bussgang zc equalizer not only outperforms conventional bussgang equalizers but is also robust to situations where hos and sos approaches individually fail

multi periodic repetitive control system a lyapunov stability analysis for mimo systems a multi input multi output mimo repetitive control problem of tracking and disturbance rejection is considered when both reference and disturbance signals are finite linear combinations of periodic but not necessarily sinusoidal signals lyapunov stability analyses under a positive real condition and a natural relaxation and exponential stability under a strict positive real condition are provided together with bounds on the induced l 2 and rms gains of the closed loop system it is shown that similar lyapunov stability results apply when the plant is a positive real state delay system extension of the analyses to a class of non linear systems is discussed and indicates a good degree of robustness in the design

carrier frequency estimation for transmissions over selective channels this paper deals with carrier frequency estimation for burst transmissions over frequency selective channels three estimation schemes are proposed all based on the use of known training sequences the first scheme employs an arbitrary sequence and provides joint maximum likelihood ml estimates of the carrier frequency and the channel response its implementation complexity is relatively high but its accuracy achieves the cramer rao bound the second scheme is still based on the ml criterion but the training sequence is periodic which helps to reduce the computational load the third scheme also employs periodic sequences but its structure comes from heuristic reasoning theoretical analysis and simulations are employed to assess the performance of the three schemes

nonparametric algorithm for input signals identification in static distributed parameter systems in this correspondence a nonparametric algorithm for identification of input signals in linear static distributed parameter systems is proposed and investigated integral mean square convergence of the algorithm is proved for an infinite number of point measurements of the system state the algorithm is a generalized version of the one recently proposed by rutkowski 10 for nonparametric function fitting and in a common area the presented results are complementary

modified cramer rao bounds for continuous phase modulated signals we consider the estimation of signal amplitude time offset and the parameters of a polynomial phase signal from a continuous phase modulated cpm signal that contains both unknown data symbols and known pilot symbols transformation of the polynomial phase signal into an orthogonal basis allows us to derive the modified cramer rao bounds mcrb for the problem of vector parameter estimation in closed form numerical results demonstrate that the achievable estimation accuracy significantly depends on the burst structure and highlight the need for properly designed pilot sequences since our bounds are easy to evaluate they can aid the design of pilot and burst configuration for cpm systems

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

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

on optimum detection of linearly filtered cpm signals a novel structure of the mlse receiver for linearly filtered cpm continuous phase modulation signals is derived it is shown that the correlator bank required in the works of svensson 1987 can equivalently be replaced by a reduced correlator bank preceded by a linear filter with impulse response h t channel matched filter the reduced correlator bank only incorporates characteristics of the cpm signals and is independent of the channel impulse response this implies that the complexity of the modified correlator bank depends only linearly on the channel filter impulse response length the proposed receiver structure permits considerable complexity reduction when compared to the currently known solution

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

nonparametric fitting of multivariate functions a nonparametric algorithm based on the multiple fejer s sum for fitting of multivariate functions is proposed the mean square error convergence and the speed of convergence are investigated

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

design and analysis of feedforward symbol timing estimators based on the conditional maximum likelihood principle this paper presents a general feedforward symbol timing estimation framework based on the conditional maximum likelihood principle the proposed timing estimator presents reduced implementation complexity and is obtained by performing an approximation on the fourier series expansion of the conditional maximum likelihood function the proposed algorithm is applied to linear modulations and two commonly used continuous phase modulations minimum shift keying msk and gaussian msk gmsk for the linear modulations it is shown both analytically and via simulations that the performance of the proposed estimator is very close to the conditional crb and modified crb for signal to noise ratios snrs in the range snr spl les 30 db furthermore the proposed estimator is shown to be asymptotically equivalent to the classic square law nonlinearity estimator under certain conditions in the case of msk and gmsk modulations although the proposed algorithm reaches the conditional crb at certain snrs however the conditional crb is quite far away from the modified crb and there exists an alternative algorithm whose performance comes closer to the modified crb therefore the proposed estimator is more suitable for linear modulations than for msk and gmsk modulations

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

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

new modulation techniques for low cost power and bandwidth efficient satellite earth stations new power and bandwidth efficient modulation techniques named intersymbol interference and jitter free ijf qpsk and ijf oqpsk are presented the properties of the ijf qpsk and ijf oqpsk signals in linear and nonlinear earth station satellite systems are studied a finite state markov chain model is used to calculate power spectra of hard limited ijf qpsk and ijf oqpsk the model provides insights into the spectral spreading action of the ideal hard limiter on the ijf qpsk and ijf oqpsk signals experimental simulation and theoretical results are in good agreement the results indicate that the ijf oqpsk modulated signal exhibits much less spectrum spreading than qpsk oqpsk and msk the error probability p e performance of ijf qpsk and ijfoqpsk in an additive white gaussian noise and adjacent channel interference environment is evaluated the results show that the p e performance of the ijf oqpsk is superior to that of qpsk oqpsk and msk in narrow band nonlinear channels

adaptive rejection of multi periodic disturbances for a class of linear systems abstractthis paper deals with adaptive rejection of general multi periodic disturbances for a class of linear systems via output feedback the multi periodic disturbance is a superposition of several general periodic disturbances assume that all periods of the multi periodic disturbance are known a method of estimating the multi periodic disturbance and its derivatives is presented which can ensure these estimate errors converge to zero based on these estimation methods we present a new adaptive control method for disturbance rejection which guarantees that in the closed loop system all the signals are bounded and the output converges to zero a simulation example is presented to verify the effectiveness of the control scheme