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

coded continuous phase modulation using ring convolutional codes rate 1 2 convolutional codes over the ring of integers modulo m are combined with m ary continuous phase modulation cpm schemes whose modulation indices are of the form h 1 m an m ary cpm scheme with h 1 m can be modeled by a continuous phase encoder cpe followed by a memoryless modulator mm where the cpe is linear over the ring of integers modulo m the fact that the convolutional code and the cpe are over the same algebra allows the state of the cpe to be fed back and used by the convolutional encoder a modified euclidean distance function that substantially simplifies the search for good codes has been derived and used to find new codes numerical results show that this approach consistently improves the performance as compared to coded schemes using binary convolutional codes with the same decoding complexity

coding cpfsk for differential demodulation a model is developed for finding codes for differentially demodulated continuous phase frequency shift keying with modulation index h 1 m where m is the size of the symbol alphabet the results of codes searches show that there is very little loss in squared euclidean distance when comparing differential codes with coherent codes

optimization of trellis coded tfm via matched codes a matched code is a convolutional code chosen in such a way that when combined with modulation with memory the resulting receiver for the coded modulation has the smallest possible number of states in the paper the matched coding technique is applied to coded tamed frequency modulation tfm schemes and a formal procedure is developed to find the best combination of a code and a modulation the optimization criterion is the maximum free euclidean distance for a given code rate and a given number of states in the viterbi receiver used for the coded modulation a search for the best codes was carried out for code rates 1 2 and 2 3 and for receivers with up to 256 and 64 states respectively good coding gains more than 7 db for rate 1 2 were achieved some of the best codes were catastrophic yet the coded modulation was not the codes obtained using the matched coding approach were in many cases better than those obtained using traditional optimization techniques

correlative encoded digital fm this paper gives a straightforward method of obtaining an explicit expression for the spectrum of a correlative encoded digital fm signal an investigation of the band occupancy for various encoding schemes with rectangular as well as raised cosine pulse shaping is carried out correlative encodings that are spectrally more efficient than minimum shift keying msk and that promise an improved error performance are shown in addition if a small degradation in error performance is tolerated substantial increases in band efficiency are possible for example with the polynomial 1 2d d 2 4 the signal is spectrally 47 percent more efficient than msk and with an snr performance degradation of only 1 1 db

noncoherently detected trellis coded partial response cpm on mobile radio channels a noncoherent receiver is proposed for partial response trellis coded continuous phase modulation tc cpm on interleaved flat rician fading channels by using a multiple symbol observation interval and a simple metric calculator the power efficiency is improved over a receiver that uses a single symbol observation interval performance bounds on the bit error probability are derived by defining a set of characteristic distances for cpm signals and showing that tc cpm is equivalent to a tcm scheme our results show that with the same observation length the proposed receiver is less than 0 5 db inferior to a coherent receiver for which perfect channel information is needed we also conclude that in terms of joint power bandwidth complexity 2rc is the best candidate for rate 1 2 tcm codes

combined coded multi h cpfsk signaling a continuous phase frequency shift keying cpfsk signaling technique is suggested that combines convolutional encoding and multi h signaling in contrast to regular multi h signaling this technique changes the modulation index in a preselected pattern in order to maximize the minimum euclidean distance a rate 1 2 convolutional encoder along with a 2 h quaternary cpfsk modulator which uses two fixed modulation indexes is considered minimum euclidean distances are calculated corresponding to the best encoder mapper combinations for different modulation index patterns at attractive pairs of modulation indexes numerical results obtained for encoder memory lengths of one and two are used to illustrate that the minimum euclidean distance of coded cpfsk signals can be significantly increased by combining with multi h signaling modulation index patterns which perform significantly better than regular multi h signals are determined an error event analysis over the additive white gaussian noise channel is carried out to investigate the actual error rate performance and to verify the theoretical results

eigenvalue bracketing for discrete and metric graphs abstract we develop eigenvalue estimates for the laplacians on discrete and metric graphs using various types of boundary conditions at the vertices of the metric graph via an explicit correspondence of the equilateral metric and discrete graph spectrum also in the exceptional values of the metric graph corresponding to the dirichlet spectrum we carry over these estimates from the metric graph laplacian to the discrete case we apply the results to covering graphs and present examples where the covering graph laplacians have spectral gaps

boundary condition varying circle billiards and gratings the dirichlet singularity waves in a two dimensional domain with robin mixed boundary conditions that vary smoothly along the boundary exhibit unexpected phenomena if the variation includes a d point where the boundary condition is dirichlet vanishing wavefunction a variety of arguments indicate that the system is singular for a circle billiard the boundary condition fails to determine a discrete set of levels so the spectrum is continuous for a diffraction grating defined by periodically varying boundary conditions on the edge of a half plane the phase of a diffracted beam amplitude remains undetermined in both cases the wavefunction on the boundary has a singularity at a d point described by the polylogarithm function

trend function hypothesis testing in the presence of serial correlation in this paper test statistics are proposed that can be used to test hypotheses about the parameters of the deterministic trend function of a univariate time series the tests are valid in the presence of general forms of serial correlation in the errors and can be used without having to estimate the serial correlation parameters either parametrically or nonparametrically the tests are valid for i 0 and i 1 errors trend functions that are permitted include general linear polynomial trend functions that may have breaks at either known or unknown locations asymptotic distributions are derived and consistency of the tests is established the general results are applied to a model with a simple linear trend a local asymptotic analysis is used to compute asymptotic size and power of the tests for this example size is well controlled and is relatively unaffected by the variance of the initial condition asymptotic power curves are computed for the simple linear trend model and are compared to existing tests it is shown that the new tests have nontrivial asymptotic power a simulation study shows that the asymptotic approximations are adequate for sample sizes typically used in economics the tests are used to construct confidence intervals for average gnp growth rates for eight industrialized countries using post war data

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

self adjoint extensions of the laplace beltrami operator and unitaries at the boundary abstract we construct in this article a class of closed semi bounded quadratic forms on the space of square integrable functions over a smooth riemannian manifold with smooth compact boundary each of these quadratic forms specifies a semi bounded self adjoint extension of the laplace beltrami operator these quadratic forms are based on the lagrange boundary form on the manifold and a family of domains parametrized by a suitable class of unitary operators on the boundary that will be called admissible the corresponding quadratic forms are semi bounded below and closable finally the representing operators correspond to semi bounded self adjoint extensions of the laplace beltrami operator this family of extensions is compared with results existing in the literature and various examples and applications are discussed

uniform distance and error probability properties of tcm schemes the class of uniform trellis coded modulation tcm techniques is defined and simple explicit conditions for uniformity are derived uniformity is shown to depend on the metric properties of the two subconstellations resulting from the first step in set partitioning as well as on the assignment of binary labels to channel symbols the uniform distance property and uniform error property which are both derived from uniformity but are not equivalent are discussed the derived concepts are extended to encompass transmission over a not necessarily gaussian memoryless channel in which the metric used for detection may not be maximum likelihood an appropriate distance measure is defined that generalizes the euclidean distance it is proved that uniformity of a tcm scheme can also be defined under this new distance the results obtained are shown to hold for channels with phase offset or independent amplitude only fading examples are included to illustrate the applicability of the results

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

unit memory codes for continuous phase modulation in an awgn channel the combination of unit memory codes and continuous phase modulation in an additive white gaussian noise channel is considered our motivation is based on the fact that when rouanne and costello s 1988 free distance lower bound is applied to unit memory codes an improved lower bound is obtained specific constructions are considered for 4 level modulation schemes with full response and weak partial response heuristic design rules are used for defining the subsets of codes within which an exhaustive search is conducted the coding gains of the best codes within these subsets are better than those of best previously known multi memory codes

heteroskedasticity autocorrelation robust standard errors using the bartlett kernel without truncation in this paper we analyze heteroskedasticity autocorrelation hac robust tests constructed using the bartlett kernel without truncation we show that while such an hac estimator is not consistent asymptotically valid testing is still possible we show that tests using the bartlett kernel without truncation are exactly equivalent to recent hac robust tests proposed by kiefer vogelsang and bunzel 2000 econometrica 68 pp 695 714

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

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

on the minimum euclidean distance for a class of signal space codes the minimum euclidean distance for a class of constant envelope phase modulation codes is studied bandwidth and power efficient signals with continuous phase are considered the information carrying phase varies piecewise linearly and the slopes are cyclically changed for successive symbol time intervals yielding the so called multi h signals it has previously been shown that this class of signals contains bandwidth and power efficient signals when coherent maximum likelihood sequence detection is used bounds on the achievable euclidean distance for signals in the above class are given upper bounds are calculated as well as minimum distance results for specific multilevel multi h signals it is concluded that quaternary and octal muiti h schemes considerably outperform the binary schemes furthermore in the important small modulation index region 2 h codes gain the maximum 3 db larger gains are not available by increasing the number of h values

an upper bound on the bit error probability of combined convolutional coding and continuous phase modulation the bit error probability properties of signals consisting of convolutional coding combined with partial response multilevel continuous phase modulation cpm are studied it is assumed that the channel is an additive white gaussian noise channel and that the receiver performs coherent maximum likelihood sequence detection by means of the viterbi algorithm an upper bound on the bit error probability is derived using the average generating function technique and evaluated numerically for a number of coded multilevel full response cpm schemes simulation results are also presented it is concluded that the free euclidean distance is the best one parameter description of the error probability for the considered class of signals for high signal to noise ratios however the upper bound results show that the free distance alone yields pessimistic bit error probability behavior for some interesting cases

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

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

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

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

multiple symbol trellis coding of cpfsk this paper describes a technique related to the design of a trellis encoder combined with the full response m ary continuous phase frequency shift keying cpfsk with modulation index 1 m a new representation of cpfsk waveforms in n signaling intervals is proposed as a function of an n 1 d vector we also decompose the generation of the proposed cpfsk waveform into two stages an n consecutive continuous phase encoder ncpe and a memoryless modulator mm this decomposition makes it possible to design binary convolutional encoders with various code rates cascaded to the ncpe specific optimal outer convolutional encoders of two and three consecutive full response four ary cpfsk with modulation index 1 4 are designed following ungerboeck s 1982 set partitioning approach these codes achieve asymptotic coding gains up to 4 77 db for the two consecutive case with code rate 3 4 and asymptotic coding gains up to 5 45 db for the three consecutive case with code rate 5 6

use of the viterbi algorithm to compute error events of trellis phase coding in order of increasing distance the use of the viterbi algorithm to evaluate the minimum distance parameters of trellis phase codes is extended to evaluate distances and paths of error events other than the free distance event distances and paths are found for error events sequentially in order of increasing distance starting with the free distance event memory requirements increase slowly with the number of error events required the time taken to find the next error event increases slowly with the number of error events already found results of sample calculations and computation times are included

power bandwidth performance of smoothed phase modulation codes constant envelope phase varying sinusoids of the form sqrt 2e t cos omega c t phi t are studied in which the phase function phi t follows some coded pattern in response to data power and bandwidth performance are studied for such patterns the patterns depend on a phase shaping function a modulation index h and a sequence of m ary underlying changes in phase which are chosen at random a cutoff rate like parameter r 0 is computed which guarantees existence of codes at all rates r bits t interval whose error performance varies as exp n r 0 r where n is the code word length in t intervals plots of r 0 are given as a function of interval energy e the shaping function h and m extensive spectral calculations give the spectra of these phased sinusoids and their performance is plotted in the power bandwidth plane the results give strong evidence that phase codes can approximate any power bandwidth combination consistent with shannon s gaussian channel capacity and that linear channels are not required for narrow band transmission

a design technique for spectral shaping in cpm systems we describe a technique of pulse shaping able to control the power spectral density of a full response cpm signal in various frequency ranges under the constraint of a prescribed minimum euclidean distance some examples illustrating the potentialities of the method and some comparisons with standard pulses are presented

m ary linear phase multi t phase codes the minimum euclidean distance properties upper bounds on the minimum distance power density spectrum and power bandwidth tradeoff for m ary phase codes where k different symbol lengths are used in a cyclical manner are considered when these lengths are all related to each other as rational numbers they give a finite state markov trellis description of the signal here k 2 is assumed it is found that from the point of view of minimum distance and spectral properties multi t phase codes are very similar to multi h codes it is also shown that quaternary codes give considerable improvement over binary codes

the performance of fsk in frequency selective rayleigh fading this paper presents measured error rate performance of binary fsk with discriminator detection in simulated rayleigh fading with time delay spread measured relations between error rate and carrier to noise ratio are shown for a range of time delay spreads we have verified that the effect of time delay spread on error rate can be described by only one parameter the ratio of the rms delay spread to the transmitted baud time intersymbol interference from time delay spread causes an irreducible error rate for fsk even for infinite carrier to noise ratio for 64 kbit s binary fsk the 2 6 s rms delay spread typical of the urban environment produces an irreducible error rate of 3 percent the measured irreducible error rate for binary fsk with discriminator detection is proportional to the fourth power of the ratio of rms delay spread to baud time this functional dependence is identical to that predicted analytically for fsk with incoherent matched filter detection

hardy inequalities for robin laplacians abstract in this paper we establish a hardy inequality for laplace operators with robin boundary conditions for convex domains in particular we show explicitly how the corresponding hardy weight depends on the coefficient of the robin boundary conditions we also study several extensions to non convex and unbounded domains

the channel capacity of discrete time phase modulation in awgn the capacity of a bandlimited phase only modulated system in additive white gaussian noise is calculated where the phase is not restricted to a finite alphabet and the demodulator supplies only phase measurements the results match a known asymptote at high signal to noise ratios and form an upper limit on the capacities of mpsk for finite m

krein like extensions and the lower boundedness problem for elliptic operators abstract for selfadjoint extensions a of a symmetric densely defined positive operator a min the lower boundedness problem is the question of whether a is lower bounded if and only if an associated operator t in abstract boundary spaces is lower bounded it holds when the friedrichs extension a has compact inverse grubb 1974 also gorbachuk and mikhailets 1976 this applies to elliptic operators a on bounded domains for exterior domains a 1 is not compact and whereas the lower bounds satisfy m t m a the implication of lower boundedness from t to a has only been known when m t m a we now show it for general t the operator a a corresponding to t a i generalizing the krein von neumann extension a 0 appears here its possible lower boundedness for all real a is decisive we study this krein like extension showing for bounded domains that the discrete eigenvalues satisfy n t a a c a t n 2 m o t n 1 e 2 m for t

on the channel capacity for constant envelope signals with effective bandwidth constraint the problem of the optimization of the information rate with an assigned cost function is addressed in the case of a constant envelope channel with a prescribed effective bandwidth as a cost function an expression of the channel capacity is derived in the presence of gaussian noise for large values of signal to noise ratio the analysis of the optimum source statistics has also shown that the source signal is gaussian and therefore its autocorrelation function and power spectral density have been determined in terms of the required channel capacity

asymptotic error performance of modulation codes in the presence of severe intersymbol interference the minimum distance and hence the asymptotic error probability of trellis modulation codes that have been subjected to severe channel filtering are evaluated a general algorithm is proposed for this purpose and applied to one class of coded modulations using a frequency domain interpretation of the euclidean distance it is shown that under extreme channel band limitations the error event that causes the minimum distance is characterized by a spectral null at dc numerical results show that for filtered continuous phase modulation codes decreasing the modulation index or smoothing the frequency pulse does not improve the error performance for some of these modulations channel filtering can actually improve the minimum distance bandpass and low pass filtering are contrasted the numerical results are explained by power spectrum considerations

combined modulation and coding for continuous phase fsk with nonuniform alphabet the problem of combined coding and modulation is addressed for m ary continuous phase frequency shift keying cpfsk with a redundant symbol alphabet it is shown that in many cases of interest the use of a nonuniform mapping between coded bits and phase increments at the cpfsk modulator allows for a significant increase of free euclidean distance in the coder modulator state trellis as compared to the uniform alphabet case a systematic search for optimum encoder mapper modulator structures is carried out for short constraint length rate 1 2 and 2 3 codes combined with 4 ary and 8 ary cpfsk respectively and for a relevant set of rational modulation indexes the power bandwidth efficiency of the optimum schemes is discussed and compared with that exhibited by the best coder modulator structures previously proposed in the literature

sphere packing upper bounds on the free distance of trellis codes sphere packing arguments are used to develop upper bounds on the free distance of trellis codes a general bounding procedure is presented sphere packing bounds including bounds on the density of infinite regions packings for hypercubes and packings on the surface of a unit sphere are then used to produce bounds for a wide variety of trellis codes among the applications are convolutional codes ungerboeck codes for phase shift keying and quadrature amplitude modulation coset codes and continuous phase modulation codes the new bounds are significantly tighter than existing bounds in many cases of practical interest

minimum euclidean distance and power spectrum for a class of smoothed phase modulation codes with constant envelope a class of smoothed phase modulation codes is analyzed in terms of power spectral density and error probability for large signal to noise ratios the signals have constant envelope and the information carrying phase function is of multi h partial response continuous phase type a cyclic variation of modulation index from symbol time interval to symbol time interval is introduced coherent transmission and an additive white gaussian channel are assumed both power and bandwidth efficient signals are to be found in the above class comparisons are made between fixed h and multi h systems both for the binary and multilevel cases tradeoff is performed between bandwidth and error probability performance for large signal to noise ratios it is concluded that quaternary and octal systems always seem preferable increasing the number of modulation indexes from one in the fixed h case to two in the simplest multi h case gives performance advantages at the expense of increased system complexity

robust trend inference with series variance estimator and testing optimal smoothing parameter abstract the paper develops a novel testing procedure for hypotheses on deterministic trends in a multivariate trend stationary model the trends are estimated by the ols estimator and the long run variance lrv matrix is estimated by a series type estimator with carefully selected basis functions regardless of whether the number of basis functions k is fixed or grows with the sample size the wald statistic converges to a standard distribution it is shown that critical values from the fixed k asymptotics are second order correct under the large k asymptotics a new practical approach is proposed to select k that addresses the central concern of hypothesis testing the selected smoothing parameter is testing optimal in that it minimizes the type ii error while controlling for the type i error simulations indicate that the new test is as accurate in size as the nonstandard test of vogelsang and franses 2005 and as powerful as the corresponding wald test based on the large k asymptotics the new test therefore combines the advantages of the nonstandard test and the standard wald test while avoiding their main disadvantages power loss and size distortion respectively

better rate 1 2 coded continuous phase modulation schemes and the m algorithm continuous phase modulation cpm signals may be precoded by a convolutional code followed by a mapping rule better codes may however be obtained by a more general code formed by a finite state machine we provide improved codes for one such finite state machine a new description of codes and design rules are presented better results are demonstrated for the partial response cpm schemes and previous optimum results are matched for the full response case tests of an m algorithm decoder achieve near maximum likelihood performance with only a fraction of the complexity of the viterbi algorithm

the cramer rao bound for training sequence design for burst mode cpm in this paper we study the cramer rao bound crb for continuous phase modulation cpm signals where frequency offset carrier phase and symbol timing are jointly estimated when transmitted over an additive white gaussian noise awgn channel we consider a data aided da estimation scenario in which the estimator takes advantage of a known training sequence at the start of each burst thus we first derive the joint crbs as functions of a known training sequence and cpm parameters by analyzing the crb expressions we propose the optimum training sequence for which the crb is minimized we show that the same training sequence is optimum for all three estimation parameters additionally we compare the performance of the optimum training sequence with a random one by providing a closed form expression for the unconditional crb ucrb for symbol timing estimation of cpm signals comparing the ucrb and the crb for the optimum training sequence reveals that a da estimator with the optimum training sequence leads to significant gains in terms of the mean square error of the estimation parameter when the underlying cpm scheme is non binary and or partial response

structure optimization and realization of ffsk trellis codes the structure of combinations of l k binary trellis encoders and fast frequency shift keying ffsk modulation is studied a novel method for the optimization of these combinations is proposed it is concluded that regardless of the particular realization the best combinations can always be obtained by using a so called matched convolutional code optimum ffsk codes of rates 1 2 and 2 3 for up to 64 and 32 states respectively are reported it is shown that the best matched encoders for ffsk modulation are also matched and best for any ffsk type scheme where the pulse shape is required to satisfy nyquist s third criterion

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

testing for common deterministic trend slopes we propose tests for hypotheses on the parameters for deterministic trends the model framework assumes a multivariate structure for trend stationary time series variables we derive the asymptotic theory and provide some relevant critical values monte carlo simulations suggest which tests are more useful in practice than others we apply our tests to examine real gdp convergence for a sample of seven european countries

nonlinear continuous phase frequency shift keying a novel signal space coded cpm continuous phase modulated signaling technique called nonlinear cpfsk continuous phase frequency shift keying signaling which guarantees the maximum constraint length allowed by the number of states is introduced nonlinear cpfsk signals use a suitably selected state transition matrix during all signaling intervals the selected state transition matrix is realized by changing the modulation index of the signals hence the modulation index used during any interval depends on the transmitted symbol as well as on the state of the system binary nonlinear cpfsk signaling schemes are constructed and analyzed numerical results indicate that nonlinear cpfsk signals can achieve attractive minimum distances compared with other existing cpm signaling formats

numerical solutions of the spectral problem for arbitrary self adjoint extensions of the one dimensional schrodinger equation a numerical algorithm to solve the spectral problem for arbitrary self adjoint extensions of one dimensional regular schrodinger operators is presented it is shown that the set of all self adjoint extensions of one dimensional regular schrodinger operators is in one to one correspondence with the group of unitary operators on the finite dimensional hilbert space of boundary data and they are characterized by a generalized class of boundary conditions that include the well known dirichlet neumann robin and quasi periodic boundary conditions the numerical algorithm is based on a nonlocal boundary extension of the finite element method and their convergence is proved an appropriate basis of boundary functions must be introduced to deal with arbitrary boundary conditions and the conditioning of its computation is analyzed some significant numerical experiments are also discussed as well as the comparison with some standard algorithms in particular it is shown that appropriate perturbations of stand

nonlinear multi h phase codes for cpfsk signaling two novel trellis coding techniques called nonlinear multi h signaling and nonlinear asymmetrical multi h signaling which achieve higher constraint length than ordinary multi h signals are introduced with cpfsk signals in contrast to ordinary multi h signaling where the modulation index is changed at the end of every symbol interval nonlinear multi h signals are constructed by changing the modulation index based on the previous symbol and the current symbol interval a class of nonlinear asymmetrical multi h signals which change the modulation index based on the current symbol too is then constructed by extending nonlinear multi h signals and combining them with asymmetrical multi h signals binary full response nonlinear multi h and nonlinear asymmetrical multi h cpfsk signals are constructed and analyzed minimum euclidean distances and spectral properties of these signals are calculated at different phase states and various selected modulation index patterns numerical results indicate that nonlinear multi h and nonlinear asymmetrical multi h signals achieve significantly higher distance than other existing multi h formats reported in the literature

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

spectral enclosures for non self adjoint extensions of symmetric operators abstract the spectral properties of non self adjoint extensions a b of a symmetric operator in a hilbert space are studied with the help of ordinary and quasi boundary triples and the corresponding weyl functions these extensions are given in terms of abstract boundary conditions involving an in general non symmetric boundary operator b in the abstract part of this paper sufficient conditions for sectoriality and m sectoriality as well as sufficient conditions for a b to have a non empty resolvent set are provided in terms of the parameter b and the weyl function special attention is paid to weyl functions that decay along the negative real line or inside some sector in the complex plane and spectral enclosures for a b are proved in this situation the abstract results are applied to elliptic differential operators with local and non local robin boundary conditions on unbounded domains to schrodinger operators with potentials of complex strengths supported on unbounded hypersurfaces or infinitely many points on the real line and to quantum graphs with non self adjoint vertex couplings

on the many dirichlet laplacians on a non convex polygon and their approximations by point interactions abstract by birman and skvortsov it is known that if is a planar curvilinear polygon with n non convex corners then the laplace operator with domain h 2 h 0 1 is a closed symmetric operator with deficiency indices n n here we provide a kre n type resolvent formula for any self adjoint extensions of such an operator i e for the set of self adjoint non friedrichs dirichlet laplacians on and show that any element in this set is the norm resolvent limit of a suitable sequence of friedrichs dirichlet laplacians with n point interactions

simple robust testing of regression hypotheses in this paper we consider the problem of hypothesis testing in models with errors that have serial correlation or heteroskedasticity of unknown form this situation is often encountered in regression models applied to economic time series data it is a classic textbook result that while ordinary least squares ols estimates of regression parameters remain consistent and asymptotically normal when errors are heteroskedastic or autocorrelated provided usual regularity conditions hold and no lagged dependent variables are in the model standard tests are no longer valid if the true form of serial correlation heteroskedasticity were known then generalized least squares gls provides efficient estimates and standard inference can be conducted on the gls transformed model but in practice the form of serial correlation heteroskedasticity is often unknown and this has led to the development of techniques that permit valid asymptotic inference without having to specify a model of the serial correlation or heteroskedasticity the most common approach is to estimate the variance covariance matrix of the ols estimates nonparametrically using spectral methods heteroskedasticity and autocorrelation consistent hac estimators and construct standard tests using the asymptotic normality of the ols estimates hac estimators have been extensively analyzed in the econometrics literature and important contributions are given by andrews 1991 andrews and monahan 1992 gallant 1987 hansen 1992 newey and west 1987 robinson 1991 1998 and white 1984 among others the benefit of hac estimator tests is asymptotically valid inference that is robust to general forms of serial correlation heteroskedasticity in the errors we propose an alternative method of constructing robust test statistics we apply a nonsingular data dependent stochastic transformation to the ols estimates the asymptotic distribution of the transformed estimates does not depend on nuisance parameters then test statistics that are asymptotically invariant to nuisance parameters asymptotic pivotal statistics are constructed the resulting test statistics have nonstandard asymptotic distributions that only depend on the number of restrictions being tested and critical values are easy to simulate using standard techniques the main advantage of our approach compared to standard approaches is that estimates of the variance covariance matrix are not explicitly required to construct the tests this is potentially important for two reasons first with the exception of the estimator proposed by robinson 1998 2 consistent nonparametric estimates of variance covariance matrices in models with serial

boundary value problems for elliptic partial differential operators on bounded domains for a symmetric operator or relation a with infinite deficiency indices in a hilbert space we develop an abstract framework for the description of symmetric and self adjoint extensions a of a as restrictions of an operator or relation t which is a core of the adjoint a this concept is applied to second order elliptic partial differential operators on smooth bounded domains and a class of elliptic problems with eigenvalue dependent boundary conditions is investigated

optimal and suboptimal symbol by symbol demodulation of continuous phase modulated signals in applications requiring soft decision metrics e g systems with interleaved coded modulation symbol by symbol detection is preferred to sequence detection this paper develops the optimum soft output algorithm osa for the demodulation of continuous phase modulated cpm signals since this optimum detector is computationally complex a class of suboptimum symbol by symbol detectors called the reduced state soft output algorithm rs soa is developed by varying certain parameters the rs soa offers an effective tradeoff between performance and complexity as measured by arithmetic operation count and the number of integrators required additionally some simple complexity reduction schemes can be used in conjunction with the osa and the rs soa the properties of the osa and the rs soa and the various complexity reduction schemes are explored in an extensive simulation study

combined coding and modulation theory and applications the theoretical aspects of the encoding process are investigated resulting in a precise definition of linear codes together with theorems that clarify how they can be obtained a particular subset of linear codes called superlinear codes for which the performance analysis is highly simplified is identified the most relevant performance measures for the analysis of this class of codes are discussed the minimum euclidean distance and the event and bit error probabilities are found analytically using the uniform error property when applicable or variations on it this yields accurate upper and lower bounds to the error rate at the price of reasonable computational complexity the theory is then applied to the search for good codes and to their performance evaluation the cases of 16 and 32 psk codes which are good candidates for use in digital satellite transmission are considered several new results in terms of error event and bit error probabilities are presented showing considerable gains in terms of snr with respect to the uncoded case

block encoding with continuous phase modulation block encoding is considered to increase the minimum distance of cpm signals codes are constructed to prevent merging events with low euclidean distances numerical results presented with full response partial response and trellis coded cpm signals indicate that block coding can significantly increase the minimum distance of the signals nonlinear block codes are also considered

exact asymptotic behavior of digital fm spectra the problem of calculating accurate power spectral densities for an extended class of digital fm schemes is considered this extended class includes partial response as well as multilevel schemes a method suitable for numerical calculation using a computer is developed this new method consists of two parts first the spectral main lobe is calculated then the spectral tail is calculated by a different approach the accuracy of the spectral tail is that of a correction term to an analytical asymptotic tail formula this method yields accurate power spectra down to a level considerably below 100 db numerical results obtained from calculations are given the power spectra can be calculated for an arbitrary modulation index value

mlse and soft output equalization for trellis coded continuous phase modulation this paper presents two equalizer structures for trellis coded continuous phase modulation tc cpm on multipath fading intersymbol interference isi channels an equivalent discrete time dt model is developed by combining the tapped delay line tdl model of the frequency selective channel and by oversampling at the receiver the noninterleaved fractionally spaced maximum likelihood sequence estimation mlse equalizer performs continuous phase modulation cpm demodulation trellis coded modulation tcm decoding and channel equalization by exploiting the finite state nature of the isi corrupted tc cpm signal both simulation and analytical results show diversity like improvement when performing joint mlse decoding and equalization for the interleaved soft output equalizer the soft symbol metric is delivered to the tcm decoder by using a forward and backward recursion algorithm three variants of the soft output equalizer are examined we conclude that the backward recursion is essential to partial response cpm schemes and with moderate complexity the soft output equalizer can have a substantial advantage over a noninterleaved mlse equalizer

symbol error probability bounds for coherently viterbi detected continuous phase modulated signals recently the minimum euclidean distance and bandwidth properties of continuous phase modulated cpm signals have been considered it has also been shown that for rational modulation indexes a state description of these signals is possible and that the viterbi algorithm va can be used for demodulation in this paper the performance analysis of cpm systems is extended to obtain bounds on the symbol error probability when the va is used the calculation of these bounds is based on the transfer function technique which has been generalized from numerical comparisons of the upper and lower bounds it is concluded that the minimum euclidean distance is a good performance measure for a broad class of cpm signals even when the symbol error probability is as large as 10 2

trellis coded continuous phase frequency shift keying with ring convolutional codes trellis coding techniques are applied to continuous phase frequency shift keying cpfsk a new coding scheme based on convolutional codes on the ring of integers modulo p is shown to be a natural way to apply trellis coding to cpfsk previous work has decomposed cpfsk into two parts a linear encoder with memory called the continuous phase encoder cpe and a memoryless modulator mm where the cpe often has a code structure defined over the ring of integers modulo p the combination of a modulo p convolutional channel encoder ce and the cpe is a linear modulo p encoder design examples are given for rate 1 2 coded quaternary cpfsk with modulation indexes 1 2 and 1 4 and rate 2 3 coded octal cpfsk with modulation index 1 8 combinations are optimized in the normalized minimum euclidean distance sense for a given total number of states in the overall mlse receiver numerical results show that this new coding scheme consistently obtains better performance than previous schemes

boundary dynamics driven entanglement we will show how to generate entangled states out of unentangled states on a bipartite system by means of dynamical boundary conditions the auxiliary system is defined by a symmetric but not self adjoint hamiltonian and we will also study the space of self adjoint extensions of the bipartite system we will show that only a small set of these extensions leads to separable dynamics and we will characterize these extensions various simple examples illustrating this phenomenon are discussed in particular we will analyze the hybrid system consisting of a planar quantum rotor and a spin system under a wide class of boundary conditions

symbol synchronization for digital signals with multisegment trajectory digital data transition tracking loop the symbol synchronizer presented is an all digital data transition tracking loop which permits simple implementation and voltage control of the loop bandwidth the equivalent loop integration constant is changed by changing the threshold level of a comparator at the output of the loop phase error detector phase error probability distribution function its variance and the average probability of cycle slipping are analyzed analytically for the general case the theory of finite markov chains is used to analyze statistical properties of the tracking error primarily with regard to the phase error distribution and its variance the average probability of the cycle slipping the synchronizer time response and bandwidth as an example numerical results for generalized tamed frequency modulation gtfm with b 0 62 and r 0 36 are presented and discussed

hermitian boundary conditions at a dirichlet singularity the marletta rozenblum model in domains b with smoothly varying boundary conditions points where wavefunctions are required to vanish were recently identified as dirichlet singularities d points where the hamiltonian h does not define discrete eigenvalues and a scattering phase is undetermined berry and dennis 2008 j phys a math theor 41 135203 this is explained marletta and rozenblum 2009 j phys a math theor 42 125204 by the observation illustrated with an exactly solvable separable model that a d point requires the specification of an additional parameter defining a family of self adjoint extensions of h here the underlying theory is presented in an elementary way and a d point is identified as a leak through which current can flow into or out of b hermiticity seals the leak ensuring that no current flows though the d point as well as across the boundary of b the solvable model is examined in detail for bound states where b is a semidisk and for wave reflections where b is a half plane the quantization condition for a nonseparable billiard is obtained explicitly

a laplace operator with boundary conditions singular at one point we discuss a recent paper of berry and dennis j phys a math theor 2008 41 135203 concerning a laplace operator on a smooth domain with singular boundary condition we explain a paradox in the article j phys a math theor 2008 41 135203 and show that if a certain additional condition is imposed the result is a spectral problem for a self adjoint operator having only eigenvalues and no continuous spectrum the eigenvalues accumulate at only and we obtain the asymptotic behaviours of the counting functions n and n for positive and negative eigenvalues the physical meaning of the additional boundary condition is not yet clear

an improved algorithm for evaluating trellis phase codes corresp a method is described for evaluating the minimum distance parameters of trellis phase codes including continuous phase frequency shift keying cpfsk partial response fm and more importantly coded continuous phase modulation cpm schemes the algorithm provides dramatically faster execution times and smaller memory requirements than previous algorithms results of sample calculations and timing comparisons are included

random modulation a review a unified treatment of various aspects of random modulation is presented with emphasis on the spectral properties of fm signals the study includes reexamination of rice s representation woodward s theorem fsk and processes with normal markov and cyclostationary frequencies

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

signal codes convolutional lattice codes the coded modulation scheme proposed in this paper has a simple construction an integer sequence representing the information is convolved with a fixed continuous valued finite impulse response fir filter to generate the codeword a lattice point due to power constraints the code construction includes a shaping mechanism inspired by precoding techniques such as the tomlinson harashima filter we naturally term these codes convolutional lattice codes or alternatively signal codes due to the signal processing interpretation of the code construction surprisingly properly chosen short fir filters can generate good codes with large minimal distance decoding can be done efficiently by sequential decoding or for better performance by bidirectional sequential decoding error analysis and simulation results indicate that for the additive white gaussian noise awgn channel convolutional lattice codes with computationally reasonable decoders can achieve low error rate close to the channel capacity

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

euclidean distance for combinations of some hamming codes and binary cpfsk modulation corresp the integration of channel coding and modulation in a communication system to increase the euclidean distance between modulated signals is analyzed systems using binary continuous phase frequency shift keying modulation and some block codes such as hamming codes and shortened hamming codes are considered it is shown that the minimum euclidean distance depends on the configuration of the parity check matrix h of the code for the examined codes the optimum configurations of h which give the maximum values of the minimum euclidean distance are determined

phase smoothing functions for continuous phase modulation in this paper the problem of signal design for continuous phase modulation is examined using the performance measures of effective bandwidth and minimum distance optimal signal shapes are calculated for various receiver observation intervals for full and partial response signalling for the partial response case the optimization could only be done for receiver observation interval of one symbol due to the difficulty of the optimization therefore a family of signals based on previously calculated optimal signals is introduced the tradeoffs that result between bandwidth and bit error rate are then compared as a function of the receiver observation interval and as a function of the memory length of the signalling scheme then the signals introduced in this paper are compared to well known signals in terms of their effective bandwidth minimum distance tradeoffs power spectra and percent in band power the signals obtained by the optimization process are found to have good spectral properties in relation to well known signals

finite element method to solve the spectral problem for arbitrary self adjoint extensions of the laplace beltrami operator on manifolds with a boundary abstract a numerical scheme to compute the spectrum of a large class of self adjoint extensions of the laplace beltrami operator on manifolds with boundary in any dimension is presented the algorithm is based on the characterisation of a large class of self adjoint extensions of laplace beltrami operators in terms of their associated quadratic forms the convergence of the scheme is proved a two dimensional version of the algorithm is implemented effectively and several numerical examples are computed showing that the algorithm treats in a unified way a wide variety of boundary conditions

estimating deterministic trends with an integrated or stationary noise component abstract we propose a test for the slope of a trend function when it is a priori unknown whether the series is trend stationary or contains an autoregressive unit root the procedure is based on a feasible quasi generalized least squares method from an ar 1 specification with parameter the sum of the autoregressive coefficients the estimate of is the ols estimate obtained from an autoregression applied to detrended data and is truncated to take a value 1 whenever the estimate is in a t neighborhood of 1 this makes the estimate super efficient when 1 and implies that inference on the slope parameter can be performed using the standard normal distribution whether 1 or 1 theoretical arguments and simulation evidence show that 1 2 is the appropriate choice simulations show that our procedure has better size and power properties than the tests proposed by bunzel h vogelsang t j 2005 powerful trend function tests that are robust to strong serial correlation with an application to the prebish singer hypothesis journal of business and economic statistics 23 381 394 and harvey d i leybourne s j taylor a m r 2007 a simple robust and powerful test of the trend hypothesis journal of econometrics 141 1302 1330

spectrum distance and receiver complexity of encoded continuous phase modulation a comparison of different classes of encoded continuous phase modulation cpm schemes is presented in terms of joint power bandwidth performance it is found that coded eight level systems are better than coded four level systems and that partial response signalling is better than full response signalling in general the price paid for better performance is increased receiver complexity heuristic design rules have been used to find good codes for cpm in most cases the coding gains found are identical to published results that were generated by exhaustive search indicating that the choice of design rules is quite appropriate in the present study bandwidth efficiency is considered from both the 99 and 99 9 power bandwidth points of view it is found that partial response signalling is even more jointly power and bandwidth efficient for the latter than for the former bandwidth criterion

nonlinear psk and combined nonlinear psk fsk modulation two classes of constant envelope signals called nonlinear psk and combined nonlinear psk fsk are introduced nonlinear psk signals select a constant phase angle during each interval depending on the state of the signal and the transmitted symbol combined nonlinear psk fsk signals select a linear phase variation during each interval and a discrete phase variation at the end of each interval depending on the current state and the transmitted symbol both classes of signals achieve the highest constraint length allowed by the number of states the numerical results presented at preselected numbers of states show that these signals produce significantly high minimum distances distances higher than those found in the literature at the same number of states are reported the spectra of nonlinear psk signals are almost identical to the spectrum of bpsk signals while those of combined nonlinear psk fsk signals are continuous but similar to that of bpsk signals

multiple symbol trellis coded modulation applied to noncoherent continuous phase frequency shift keying this paper considers a maximum likelihood ml noncoherent detection scheme for multiple full response continuous phase frequency shift keying cpfsk waveforms and introduces a trellis coded modulation tcm scheme for this noncoherent modulation by utilizing a gaussian approximation for rician random variables we express the pairwise error probability as a function of the equivalent normalized squared distance ensd ensd plays the same role as normalized squared euclidean distance when evaluating error probability performance for coherent detection we derive an analytical approximation on the bit error probability by employing ensd for both the coded system and the uncoded system for the uncoded system we show that the bit error probability of noncoherent detection approaches that of coherent symbol by symbol detection in the limit as the multiplicity of the symbol goes to infinity for large signal to noise ratio snr we determine specific optimal trellis encoders for binary and 4 ary cpfsk with modulation index 1 2 and 1 4 respectively by application of ungerboeck s 1982 set partitioning approach

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

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

robustifying multivariate trend tests to nonstationary volatility abstract this article studies inference of multivariate trend model when the volatility process is nonstationary within a quite general framework we analyze four classes of tests based on least squares estimation one of which is robust to both weak serial correlation and nonstationary volatility the existing multivariate trend tests which either use non robust standard errors or rely on non standard distribution theory are generally non pivotal involving the unknown time varying volatility function in the limit two step residual based i i d bootstrap and wild bootstrap procedures are proposed for the robust tests and are shown to be asymptotically valid simulations demonstrate the effects of nonstationary volatility on the trend tests and the good behavior of the robust tests in finite samples

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