inversion of the pieri formula for macdonald polynomials we give the explicit analytic development of macdonald polynomials in terms of modified complete and elementary symmetric functions these expansions are obtained by inverting the pieri formula specialization yields similar developments for monomial jack and hall littlewood symmetric functions

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

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

symbol by symbol map demodulation of cpm and psk signals on rayleigh flat fading channels demodulation using the symbol by symbol maximum a posteriori probability map algorithm is presented the algorithm is derived for the case of continuous phase modulation cpm signals transmitted over rayleigh flat fading channels and a corresponding receiver structure is specified it is shown that the map algorithm requires computing for each trellis branch the sum of the products of the weights of all paths through the trellis which pass through that branch and that this generic computational problem can be solved efficiently by an approach that uses a forward and backward recursion through the trellis simulation results are presented which show both the hard and soft decision performance of the map receiver to be robust even in the presence of fade rates of up to 30 of the symbol rate the application of the receiver concept to phase shift keying psk signals is also discussed and then evaluated via simulation the concept of joint demodulation and decoding using iterative processing techniques is introduced it is shown that the map receiver is well suited for iterative processing applications due to its use of a priori symbol probabilities and its production of optimal soft decisions simulation results for the reception of quaternary psk qpsk show that the bit error rate ber performance of the iterative map receiver can approach that of a receiver operating with perfect knowledge of the fading process

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

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

orthogonal polynomials of compact simple lie groups branching rules for polynomials polynomials in this paper are defined starting from a compact semisimple lie group a known classification of maximal semisimple subgroups of simple lie groups is used to select the cases to be considered here a general method is presented and all the cases of rank 3 are explicitly studied we derive the polynomials of simple lie groups b3 and c3 as they are not available elsewhere the results point to far reaching lie theoretical connections to the theory of multivariable orthogonal polynomials

optimum discrete pulse shaping in msk type signals we present in this correspondence a numerical approach to the problem of minimizing the fractional out of band power for a class of digital constant envelope modulated signals known as msktype signals the present optimization procedure is much more manageable than a recently suggested analytical one while achieving the same results

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

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

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

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

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

t norm based logics with an independent involutive negation in this paper we investigate the addition of arbitrary independent involutive negations to t norm based logics we deal with several extensions of mtl and establish general completeness results indeed we will show that given any t norm based logic satisfying some basic properties its extension by means of an involutive negation preserves algebraic and finite strong standard completeness we will deal with both propositional and predicate logics

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 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

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

some combinatorial properties of jack symmetric functions if 1 l n then write 2 n or 1 n if p is another partition then write p c j if pi 6 for all i i e if the diagram of 1 contains the diagram of p if ipl ii 1 then write p 2 1 reverse lexicographic order if either j i or the first nonvanishing difference e pi is positive for instance writing 2 1 i for ai i it 5 5 41 32 5 311 221 2111 11111 finally write p i if ipl lal and p1 pl2 pli a1 a2 li for all i macdonald m p 63 call the partial ordering the natural ordering but we will call it the dominance ordering let x x x2 be an infinite set of indeterminates as in mi we

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

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

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

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

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

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

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

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

data aided and non data aided maximum likelihood snr estimators for cpm data aided da and non data aided nda maximum likelihood ml estimators for the snr of cpm in the presence of phase and frequency offset are derived and analyzed cramer rao bounds for both are obtained and compared to the simulated performance of these estimators for a full response example cpsfk and a partial response example gmsk analysis and simulations show that the performance of the da ml estimator suffers from an unremovable bias caused by uncompensated frequency offset due to frequency offset estimation errors as a consequence the estimator error variance of the da ml estimator is not able to achieve its lower bound in contrast the estimator error variance of the nda ml estimator is capable of achieving its lower bound although the lower bound for nda ml estimator is higher than the lower bound for the da ml estimator this is because the nda ml estimator is not burdened with the requirement of relying on estimates of nuisance parameters the nda estimator only achieves its lower bound when the observation length or true snr are sufficiently large

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

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

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

a family of integral transformations and basic hypergeometric series we present a conjecture giving a family of commuting operators i c in terms of n fold integral transformations for the simplest case n 2 the commutativity is proved by using several summation and transformation formulas for the basic hypergeometric series

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

noncoherently orthogonal digital phase modulation this work considers noncoherently orthogonal signaling with full response digital phase modulation and focuses on the phase function shaping problem a criterion for the phase function that ensures noncoherent orthogonality of the modulated signal over one symbol interval is introduced furthermore a new family of phase modulated signals is presented this new orthogonal modulation format lacks the well known spectral lines of noncoherently orthogonal fsk and hence uses the power efficiently to convey information

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

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

hyperdeterminantal expressions for jack functions of rectangular shapes abstract we derive a jacobi trudi type formula for jack functions of rectangular shapes in this formula we make use of a hyperdeterminant which is cayley s simple generalization of the determinant in addition after developing the general theory of hyperdeterminants we give summation formulas for schur functions involving hyperdeterminants and evaluate toeplitz type hyperdeterminants by using jack function theory

first order satisfiability in godel logics an np complete fragment defined over sets of truth values v which are closed subsets of 0 1 containing both 0 and 1 godel logics g v are prominent examples of many valued logics we investigate a first order fragment of g v extended with d that is powerful enough to formalize important properties of fuzzy rule based systems the satisfiability problem in this fragment is shown to be np complete for all g v also in the presence of an additional involutive negation in contrast to the one variable case in the fragment considered only two infinite valued godel logics extended with d differ w r t satisfiability only one of them enjoys the finite model property

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

optimum bandwidth distance performance in full response cpm systems the problem of minimizing the effective bandwidth of a binary full response continuous phase modulation cpm signal with respect to the shape of the frequency pulse for a prescribed value of the minimum euclidean distance which is directly related to the error probability for high signal to noise ratio is considered an analytical procedure is presented that allows the determination of the optimum pulse shape together with its bandwidth and the minimum distance characteristics the solution contains an unknown parameter that is determined by numerical of a nonlinear equation the results are compared to some standard pulses in terms of bandwidth spectral density minimum euclidean distance and error probability some gain in bandwidth is obtained for high values of minimum distance

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

p ell torsion points in finite abelian groups and combinatorial identities abstract the main aim of this article is to compute all the moments of the number of p l torsion elements in some type of finite abelian groups the averages involved in these moments are those defined for the cohen lenstra heuristics for class groups and their adaptation for tate shafarevich groups in particular we prove that the heuristic model for tate shafarevich groups is compatible with the recent conjecture of poonen and rains about the moments of the orders of p selmer groups of elliptic curves for our purpose we are led to define certain polynomials indexed by integer partitions and to study them in a combinatorial way moreover from our probabilistic model we derive combinatorial identities some of which appearing to be new the others being related to the theory of symmetric functions in some sense our method therefore gives for these identities a somehow natural algebraic context

pieri formulas for macdonald s spherical functions and polynomials we present explicit pieri formulas for macdonald s spherical functions or generalized hall littlewood polynomials associated with root systems and their q deformation the macdonald polynomials for the root systems of type a our pieri formulas recover the well known pieri formulas for the hall littlewood and macdonald symmetric functions due to morris and macdonald as special cases

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

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

receiver structures for multi h signaling formats a method of utilizing the available communication bandwidth efficiently is provided by multi h phase coding a receiver structure for joint estimation of data carrier phase and symbol timing is derived based on ml estimation techniques and subsequently assessed analytically and by means of monte carlo simulation procedures results indicate that the receiver structure although not strictly optimum yields near optimum performance on the additive white gaussian noise channel

timing carrier and frame synchronization of burst mode cpm in this paper we propose a complete synchronization algorithm for continuous phase modulation cpm signals in burst mode transmission over additive white gaussian noise awgn channels the timing and carrier recovery are performed through a data aided da maximum likelihood algorithm which jointly estimates symbol timing carrier phase and frequency offsets based on an optimized synchronization preamble our algorithm estimates the frequency offset via a one dimensional grid search after which symbol timing and carrier phase are computed via simple closed form expressions the mean square error mse of the algorithm s estimates reveals that it performs very close to the theoretical cramer rao bound crb for various cpms at signal to noise ratios snrs as low as 0 db furthermore we present a frame synchronization algorithm that detects the arrival of bursts and estimates the start of signal we simulate the performance of the frame synchronization algorithm along with the timing and carrier recovery algorithm the bit error rate results demonstrate near ideal synchronization performance for low snrs and short preambles

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

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

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

operator methods and lagrange inversion a unified approach to lagrange formulas on presente une methode generale de demonstration des formules d inversion de lagrange et de leurs variantes on considere le cas de plusieurs variables

effective bandwidth optimization for noncoherent full response cpm systems the optimization of the baseband pulse shape for full response cpm signals when a noncoherent lowest complexity receiver is used is carried out the effective bandwidth is chosen as the objective of the optimization in order to obtain the minimum error probability for high signal to noise ratio orthogonal signaling is taken into consideration a closed form for the optimum pulse shape the value of the optimum modulation index and of the optimum effective bandwidth is determined the power spectral density and the fractional out of band power have been compared with some phase functions considered in the literature

digitally phase modulated dpm signals some properties of digitally phase modulated dpm signals are presented phase modulation with overlapping pulses generated by a digital fir filter belong to this class which may be considered to be a practical approximation to continuous phase modulated cpm signals the power spectra of dpm signals are derived analytically the ability of these signals to operate through an additive white gaussian noise channel is assessed by calculating their minimum euclidean distance their noise and spectral properties are found to be similar to those of cpm signals assuming that a viterbi decoder is used to resolve symbol interference the out of band power tends to decrease as the pulse duration increases and the noise immunity is enhanced at the same time the receiver complexity grows exponentially hence noise immunity and spectrum compactness are achieved at the cost of higher received complexity modems for dpm signals are believed to be easier to implement than those for cpm signals this is because filter design is simple and a residual carrier component can be retained to facilitate carrier regeneration furthermore the accumulated carrier phase does not need to be continuously evaluated in order to perform matched filtering the analytic results derived are supported by measurements and simulations

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

optimum bandwidth distance performance in partial response cpm systems the problem of optimizing the baseband pulse shape in order to obtain the minimum effective bandwidth for a prescribed value of minimum euclidean distance is treated for partial response cpm some comparisons with standard pulses are performed and the results are presented in the form of bandwidth distance and spectral density plots

reasoning in fuzzy description logics using automata automata based methods have been successfully employed to prove tight complexity bounds for reasoning in many classical logics and in particular in description logics dls very recently the ideas behind these automata based approaches were adapted for reasoning also in fuzzy extensions of dls with semantics based either on finitely many truth degrees or the godel t norm over the interval 0 1 clearly due to the different semantics in these logics the construction of the automata for fuzzy dls is more involved than for the classical case in this paper we provide an overview of the existing automata based methods for reasoning in fuzzy dls with a special emphasis on explaining the ideas and the requirements behind them the methods vary from deciding emptiness of automata on infinite trees to inclusions between automata on finite words overall we provide a comprehensive perspective on the automata based methods currently in use and the many complexity results obtained through them

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

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

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

nonlinear continuous phase modulation a class of nonlinear cpm signals is introduced by extending nonlinear cpfsk signals to other forms of frequency pulses the distance results and spectral properties of nonlinear cpm signals are reported bit error probabilities of nonlinear cpm signals are simulated in presence of adjacent channel interference

breadth first maximum likelihood sequence detection basics the problem of performing breadth first maximum likelihood sequence detection mlsd under given structural and complexity constraints is solved and results in a family of optimal detectors given a trellis with s states these are partitioned into c classes where b paths into each class are selected recursively in each symbol interval the derived result is to retain only those paths which are closest to the received signal in the euclidean hamming distance sense each member in the sa b c family of sequence detectors sa denotes search algorithm performs complexity constrained mlsd for the additive white gaussian noise awgn bsc channel the unconstrained solution is the viterbi algorithm va analysis tools are developed for each member of the sa b c class and the asymptotic snr probability of losing the correct path is associated with a new euclidean distance measure for the awgn case the vector euclidean distance ved the traditional euclidean distance is a scalar special case of this termed the scalar euclidean distance sed the generality of this ved is pointed out some general complexity reductions exemplify those associated with the va approach

nyquist 3 pulse shaping in continuous phase modulation continuous phase modulation cpm schemes using nyquist 3 pulse shaping and correlative codes are popular candidates for mobile radio applications this paper presents a detailed study of the effects of nyquist 3 pulse shaping on the spectral characteristics of cpm schemes with a modulation index of 1 2 the influence of pulse parameters such as its shape bandwidth coding polynomial and truncation length on spectral characteristics such as main lobe fractional power bandwidths and out of band power levels is thoroughly investigated error performance is also briefly analyzed among uncoded schemes a new scheme using a pulse satisfying both nyquist 3 and nyquist 2 criteria is pointed out as a promising candidate and as a good compromise between spectral and power efficiencies

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