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

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

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

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

a class of convex fuzzy mappings based on the concept of ordering defined by goetschel and voxman fuzzy sets and systems 18 1996 31 in this paper we present the concepts of epigraph and convexity of the fuzzy mappings and describe characteristics of the convex fuzzy mappings and quasi convex fuzzy mappings then we discuss the properties of convex fuzzy optimizations

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

preinvexity and φ 1 convexity of fuzzy mappings through a linear ordering the preinvexity prequasiinvexity 1 convexity and 1 quasiconvexity of fuzzy mappings are defined based on a linear ordering on the set of fuzzy numbers characterizations for these fuzzy mappings are obtained the local global minimum properties of real valued preinvex functions and 1 convex functions are extended to preinvex fuzzy mappings and 1 convex fuzzy mappings respectively it is also proved that every strict local minimizer of a prequasiinvex fuzzy mapping is a strict global minimizer and that every strict local minimizer of a 1 quasiconvex fuzzy mapping is a strict global minimizer

control of stochastic discrete event systems modeled by probabilistic languages in garg et al 1999 and garg 1992 the formalism of probabilistic languages for modeling the stochastic qualitative behavior of discrete event systems dess was introduced in this paper we study their supervisory control where the control is exercised by dynamically disabling certain controllable events thereby nulling the occurrence probabilities of disabled events and increasing the occurrence probabilities of enabled events proportionately this is a special case of probabilistic supervision introduced in lawford and wonham 1993 the control objective is to design a supervisor such that the controlled system never executes any illegal traces their occurrence probability is zero and legal traces occur with minimum prespecified occurrence probabilities in other words the probabilistic language of the controlled system lies within a prespecified range where the upper bound is a nonprobabilistic language representing a legality constraint we provide a condition for the existence of a supervisor we also present an algorithm to test this existence condition when the probabilistic languages are regular so that they admit probabilistic automata representation with finitely many states next we give a technique to compute a maximally permissive supervisor online

invex and generalized convex fuzzy mappings in this paper we introduce the concepts of pseudo convexity invexity and pseudo invexity for fuzzy mappings of one variable based on the notion of differentiability proposed by goetschel and voxman 4 and investigate the relationship between convex fuzzy mappings preinvex fuzzy mappings and these classes of fuzzy mappings we shall prove that pseudo convex fuzzy mappings and invex fuzzy mappings are pseudo invex and that a differentiable convex resp preinvex fuzzy mapping is pseudo convex resp invex in addition sufficient optimality conditions are obtained for pseudo convex invex and pseudo invex fuzzy mappings

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

a note on generalized convexity for fuzzy mappings through a linear ordering in de campos ibanez and gonzalez munoz fuzzy sets syst 29 145 154 1989 6 goestschel and voxman fuzzy sets syst 18 31 43 1986 7 the authors considered a linear ordering on the space of fuzzy intervals for each fuzzy mapping fuzzy interval valued mapping f based on the aforementioned linear ordering they introduced a real valued function t f on the domain of the fuzzy mapping f recently chalco cano et al fuzzy sets syst 231 70 83 2013 4 have studied the relationship between the generalized hukuhara differentiability of a fuzzy mapping f g differentiability for short and the differentiability of t f and some properties of local global minima this paper studies such properties for fuzzy mappings using new concepts which generalize the existing ones

differentiability and convexity of fuzzy mappings abstract goetschel and voxman 1 have introduced the notion of a derivative for fuzzy mappings of one variable in a manner different from the usual one in this paper we define a differentiable fuzzy mapping of several variables in ways that parallel the definition proposed by goetschel and voxman 1 for a fuzzy mapping of one variable and then study some basic differentiability properties of fuzzy mappings from the standpoint of convex analysis

interpolation in digital modems ii implementation and performance for pt i see ibid vol 41 no 3 p 502 208 1993 properties of a specific class of interpolators that are based upon polynomials are discussed several implementations are described one of which is particularly convenient in practical hardware simulations demonstrate that simple interpolators give excellent performance in many cases two point linear interpolation is adequate if better performance is needed classical four point third order polynomials could be used better yet a novel four point interpolating filter with piecewise parabolic impulse response can have performance superior to that of the standard cubic interpolator and still be implemented much more simply the nco based control method presented in part i is shown to be equivalent to a conventional phase locked loop and its operation is verified by simulation

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

on properties of convex fuzzy mappings the objective of this paper is to obtain some important properties about convex fuzzy mappings based on a linear ordering of fuzzy numbers proposed by goetschel and voxman firstly a new kind of fuzzy mapping termed semistrictly convex fuzzy mapping is defined through this linear ordering note that semistrict convexity does not imply convexity and the interrelationships among convex strictly convex and semistrictly convex mappings are established under certain conditions furthermore this paper obtains several characterizations for the above three classes of fuzzy mappings under the conditions of upper or lower semicontinuity finally some further characteristic properties for semistrictly convex fuzzy mappings are derived

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

convexity of n dimensional fuzzy number valued functions and its applications the aim of this study is to generalize convexity from vector valued maps to n dimensional fuzzy number valued functions and to investigate some relations among the convexity and generalized convexity of n dimensional fuzzy number valued functions which are based on a new ordering of n dimensional fuzzy numbers proposed in this study furthermore some criteria are obtained for the convexity and generalized convexity under the conditions of lower and upper semicontinuity respectively finally we study the local global minimum properties of the convex fuzzy number valued functions

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

the modified cramer rao bound and its application to synchronization problems we introduce the modified cramer rao bound crb which like the true crb is a lower bound to the error variance of any parameter estimator the modified crb proves useful when in addition to the parameter to be estimated the observed data also depend on other unwanted parameters the relationship between the modified and true crb is established and applications are discussed regarding the estimation of carrier frequency offset carrier phase and timing epoch in linearly modulated signals modified crbs for phase and timing estimation have been already discussed in previous works where it is shown that several practical carrier phase and clock recovery circuits do attain such bounds frequency discrimination instead is not so well represented in the literature and a significant contribution of this paper is the calculation of the modified crb for frequency estimation this bound is compared with the performance of some frequency detectors and it is concluded that further work is needed in search of more efficient frequency discrimination methods

sequence estimation and synchronization from nonsynchronized samples the authors study the problem of maximum likelihood sequence estimation and synchronization from samples of the output of a matched filter taken at integer multiples of the symbol rate which is assumed perfectly known by the receiver a general analysis is presented of sampled receivers that handle arbitrary baseband pulse shapes and arbitrary sampling rates it is observed that the optimal processing of the matched filter samples consists of digital interpolation followed by symbol by symbol decoding when sampling is at or above the nyquist rate or viterbi decoding when sampling is below the nyquist rate performance is studied through the cramer rao bound on mean square estimation error and a lower bound on error probability

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

generalized convexity in fuzzy vector optimization through a linear ordering in this article we study efficiency and weakly efficiency in fuzzy vector optimization after formulating the problem we introduce two new concepts of generalized convexity for fuzzy vector mappings based on the generalized hukuhara differentiability pseudoinvexity i and pseudoinvexity ii we prove that pseudoinvexity is the necessary and sufficient condition for a stationary point to be a solution of a fuzzy vector optimization problem we give conditions to insure that a fuzzy vector mapping is invex and pseudoinvex i and ii moreover we present some examples to illustrate the results lastly we use these results to study the class of problems which have uncertainty and inaccuracies in the objective function coefficients of mathematical programming models

probabilistic supervisory control of probabilistic discrete event systems this paper considers supervisory control of probabilistic discrete event systems pdess pdess are modeled as generators of probabilistic languages the supervisory control problem considered is to find if possible a supervisor under whose control the behavior of a plant is identical to a given probabilistic specification the probabilistic supervisors we employ are a generalization of the deterministic ones previously employed in the literature at any state the supervisor enables disables events with certain probabilities necessary and sufficient conditions for the existence of such a supervisor and an algorithm for its computation are presented

nonconvex fuzzy mappings and the fuzzy pre variational inequality in this paper we introduce the concepts of fuzzy pseudoconvex fuzzy invex fuzzy pseudoinvex and fuzzy preinvex mapping from r n to the set of fuzzy numbers and put forward the concepts of fuzzy extended directional differential subgradient and subdifferential some properties are obtained for fuzzy pseudoconvex fuzzy invex fuzzy pseudoinvex and fuzzy preinvex mapping relations are discussed between the fuzzy pre variational inequality and the fuzzy vector optimization problem

derivation of gardner s timing error detector from the maximum likelihood principle in a recent paper 1 gardner described a new timing error detector for sampled receivers the detector derives timing information without decision direction from a bpsk or qpsk signal sampled at rate 2 t symbol interval t we will show how this detector can be derived from the maximum likelihood principle and thus give insight into the nature of the algorithm

continuity and semicontinuity of fuzzy mappings we study two different concepts of semicontinuity of fuzzy mappings by establishing characterizations of these fuzzy mappings relationships between semicontinuity and continuity of fuzzy mappings are explored some basic properties of these semicontinuous and continuous fuzzy mappings are presented and proved

brief paper formulae relating controllability observability and co observability we present formulae relating controllability observability and co observability arising in the context of supervisory control of discrete event systems given a discrete event plant g with event set e uncontrollable event set e u i and observation mask m i of the ith supervisor we first show that the infimal prefix closed l g i e u i controllable and l g e u i m i co observable superlanguage equals the intersection taken over all i s of the infimal prefix closed l g e u i controllable and l g m i observable superlanguage next we show that the infimal prefix closed and e m observable superlanguage computation preserves e e u controllability these results can be used to compute individual supervisors in the decentralized control setting

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

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

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

convexity and local lipschitz continuity of fuzzy valued mappings abstract two concepts of a convexity and a local lipschitz continuity are introduced into the class of fuzzy valued mappings the convexity is defined through the fuzzy max order on the class of fuzzy numbers the local lipschitz continuity of the fuzzy valued mapping cannot be defined in the same manner as in the case of the real valued function since the space of values of the fuzzy valued mapping is not a linear space owing to this reason the local lipschitz continuity is defined in a new formula through the fuzzy max order a fundamental theorem concerning the local lipschitz continuity of the fuzzy valued convex mapping is given

efficient maximum likelihood based clock and phase estimators for oqpsk signals in this paper we propose an algorithm for joint carrier phase and timing estimation with oqpsk modulations the derivation is based on the maximum likelihood criterion and exploits a very efficient algorithm for the detection of differentially encoded m psk symbols already described in literature though we are mainly interested in measuring the phase and clock parameters estimates of the transmitted symbols are also obtained as by products the resulting scheme has a feedforward structure and provides phase and timing information in a fixed time differently from closed loop architectures it can be implemented in digital form and is particularly suitable for burst mode transmissions its performance is investigated by simulation and the results are compared with cramer rao bounds it turns out that the estimation accuracy is very close to the theoretical limits even with short observation intervals and small values of the excess bandwidth in such conditions the proposed estimators largely outperform other schemes already known in literature their superiority becomes less significant as the signal bandwidth increases

inequality relation between fuzzy numbers and its use in fuzzy optimization the inequality relation between two fuzzy numbers is investigated a certain type of such a relation motivated by practical interpretation is proposed and its correspondence with the usual lattice type relation generated by the extended maximum and minimum operators and its possible interpretation are discussed the concept of r l fuzzy number is introduced the class of all r l fuzzy numbers covering practically the whole set of normal convex fuzzy numbers comparing two r l fuzzy numbers of the same type the relation introduced in the paper may be replaced by four ordinary inequalities this fact may be taken advantage of in optimization problems with linear fuzzy constraints

on invex fuzzy mappings and fuzzy variational like inequalities in this paper we first show the need for introducing invex fuzzy mappings after that we show that the concept of invex fuzzy mapping previously given by wu and xu are very restrictive and the examples presented there are not correct then we present more general concepts of invex and incave fuzzy mappings involving strongly generalized differentiable fuzzy mapping finally we show that the results obtained by wu and xu on the relationship between fuzzy variational like inequalities and fuzzy optimization problems are still valid using these new concepts

generalized convex fuzzy mappings and fuzzy variational like inequality in this paper we introduce the concepts of some generalized convex fuzzy mappings from r n to the set of fuzzy numbers under the condition of upper or lower semicontinuity a new criterion be obtained for the existence of a fuzzy preinvex mapping a fuzzy preinvex mapping can be achieved when the invex subset of r n satisfies certain conditions the relations between generalized convex fuzzy mappings are discussed and some properties are obtained that relate the concepts of fuzzy pseudoinvex and fuzzy prequasiinvex mapping fuzzy invex and fuzzy preinvex mapping fuzzy preinvex and fuzzy prequasiinvex mapping we also discuss the relationship between the fuzzy variational like inequality the fuzzy weak variational like inequality and fuzzy optimization problems and an application example of a fuzzy variational like inequality the fuzzy variational like inequality representation of a fuzzy transportation equilibrium problem

a class of data aided timing recovery schemes this paper develops a class of data aided timing recovery schemes whose structure and operating principle are reminiscent of zero forcing equalizer adaptation the schemes exhibit no pattern dependent jitter and are applicable to a variety of modulation codes and reception techniques they come in both oversampled and baud rate forms and permit maximum likelihood tracking performance whenever the oversampling factor satisfies the sampling theorem subject to this condition even simple schemes can be close to optimum it is shown that various existing schemes belong to the class under study or are closely related to it

fuzzy weirstrass theorem and convex fuzzy mappings the convexity and continuity of fuzzy mappings are defined through a linear ordering and a metric on the set of fuzzy numbers the local global minimum property of real valued convex functions is extended to convex fuzzy mappings it is proved that a strict local minimizer of a quasiconvex fuzzy mapping is also a strict global minimizer characterizations for convex fuzzy mappings and quasiconvex fuzzy mappings are given in addition the weirstrass theorem is extended from real valued functions to fuzzy mappings

elementary fuzzy calculus abstract in 2 dubois and prade introduced the notion of fuzzy numbers and defined the basic operations of addition subtraction multiplication and division a slightly modified definition of fuzzy numbers was presented in 4 and in that paper a metric was defined for this family of fuzzy sets another less restrictive definition of fuzzy numbers can be found in 1 in the present paper we consider fuzzy numbers from a somewhat different perspective basically we shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in 4 we will define differentiation and integration of fuzzy valued functions in ways that parallel closely the corresponding definitions for real differentiation and integration

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

symbol synchronization using signal samples and interpolation a method for symbol synchronization using two unsynchronized signal samples per symbol is presented signal values between the sample points are calculated by interpolation and then processed digitally to find a suitable strobe point the interpolated value at the strobe point is used for data detection or input to an equalizer simulations show that low variance timing estimates can be made for pulses with raised cosine spectra degraded by quadratic delay distortion

structural transformations of probabilistic finite state machines probabilistic finite state machines have recently emerged as a viable tool for modelling and analysis of complex non linear dynamical systems this paper rigorously establishes such models as finite encodings of probability measure spaces defined over symbol strings the well known nerode equivalence relation is generalized in the probabilistic setting and pertinent results on existence and uniqueness of minimal representations of probabilistic finite state machines are presented the binary operations of probabilistic synchronous composition and projective composition which have applications in symbolic model based supervisory control and in symbolic pattern recognition problems are introduced the results are elucidated with numerical examples and are validated on experimental data for statistical pattern classification in a laboratory environment

convexity and semicontinuity of fuzzy mappings in this paper a criterion for the convex fuzzy mapping is obtained under the condition of upper and lower semicontinuity respectively an upper lower semicontinuous fuzzy mapping is proved which convexity is equivalent to weak convexity or b vexity satisfying a special condition

φ1 φ2 convex fuzzy mappings abstract the concepts of 1 2 convexity 1 b vexity and 1 convexity for fuzzy mappings are introduced through the so called fuzzy max order among fuzzy numbers we show that the class of 1 2 convex fuzzy mappings 1 b vex fuzzy mappings and 1 convex fuzzy mappings includes many well known classes of fuzzy mappings such as convex fuzzy mappings and preinvex fuzzy mappings as its subclasses we also give a characterization for 1 b vex fuzzy mappings by proposing the concept of 1 b vex sets in addition some basic properties of fuzzy mappings from the standpoint of convex analysis are discussed

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

design of optimal interpolation filter for symbol timing recovery we propose an optimal interpolation filter for symbol timing recovery in a digital receiver where the input analog to digital a d conversion sampling clock is not synchronized to the transmitter symbol clock the optimal filter is designed by minimizing the mean square error mse at the output of the receiver assuming that the correct timing difference between the nonsynchronized input samples and the correct strobe synchronized to the symbol is given the mse minimization procedure results in a system of linear equations which can easily be solved to yield the optimal filter coefficients we also analyze the symbol tracking performance of a symbol synchronizer that employs the proposed optimal interpolation filter although the proposed optimal filter is designed assuming the availability of the correct timing difference we show that it minimizes the timing estimation error variance even when the computed timing difference values deviate from the ideal we also show that the timing estimation is virtually unbiased if the length of the interpolation filter is greater than or equal to 4 simulation results are included to show the performance improvement realizable by employing the optimal interpolation filter

reliable decentralized supervisory control of fuzzy discrete event systems decentralized supervisory control has been introduced to deal with a class of fuzzy discrete event systems des in which state transitions are uncertain in this paper we develop the work on fuzzy des to consider the reliable decentralized supervisor problem with possible failures of some local supervisors by presenting a new definition of co observable language the reliable decentralized supervisory control problem is solved since the co observable languages are not closed under union a new normal language that is co observable is defined to solve the synthesis problem finally a numerical example is given

performance study of a near maximum likelihood code aided timing recovery technique in this paper we propose a new code aided ca timing recovery algorithm for various linear constant modulus constellations based on the maximum likelihood ml estimator the first contribution is the derivation of a soft estimator expression of the transmitted symbol instead of its true or hard estimated value which is fed into the timing error detector ted equation the proposed expression includes the log likelihood ratios llrs obtained from a turbo decoder our results show that the proposed ca approach achieves almost as good results as the data aided da approach over a large interval of snr values while achieving a higher spectral efficiency we also derive the corresponding ca cramer rao bounds crb for various modulation orders contrarily to former work we develop here the crb analytical expression for different m psk modulation orders and validate them through comparison to empirical crb obtained by monte carlo iterations the proposed ca estimator realizes an important gain over the nondata aided approach nda and achieves a smaller gap when compared to its relative ca crb especially at moderate snr values where modern systems are constrained to work

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

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

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

on fuzzy generalized convex mappings and optimality conditions for fuzzy weakly univex mappings in this paper we first introduce the weakly invex fuzzy mappings based on weakly differentiable functions and discuss the relationships between several kinds of fuzzy generalized convex mappings then a kind of fuzzy weakly univex functions are introduced and some properties of them are investigated furthermore optimality and duality results are derived for a class of generalized convex optimization problems with fuzzy weakly univex functions

a bpsk qpsk timing error detector for sampled receivers a simple algorithm for detection of timing error of a synchronous band limited bpsk or qpsk data stream is proposed the algorithm requires only two samples per symbol for its operation one of the two samples is also used for the symbol decision derivation of the s curve reveals a sinusoidal shape

the crystallizing substochastic sequential machine extractor cryssmex this letter presents an algorithm cryssmex for extracting minimal finite state machine descriptions of dynamic systems such as recurrent neural networks unlike previous algorithms cryssmex is parameter free and deterministic and it efficiently generates a series of increasingly refined models a novel finite stochastic model of dynamic systems and a novel vector quantization function have been developed to take into account the state space dynamics of the system the experiments show that 1 extraction from systems that can be described as regular grammars is trivial 2 extraction from high dimensional systems is feasible and 3 extraction of approximative models from chaotic systems is possible the results are promising and an analysis of shortcomings suggests some possible further improvements some largely overlooked connections of the field of rule extraction from recurrent neural networks to other fields are also identified

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

extended gardner detector for improved symbol timing recovery of m psk signals in a recent paper the modified gardner detector has been proposed for advanced symbol timing recovery of m ary phase shift keying signals compared with the original algorithm the self noise jitter can be considerably reduced for highly bandlimited systems and smaller values of m in this letter a completely different approach is investigated which improves the self noise performance for larger values of m as well

a probabilistic language formalism for stochastic discrete event systems the formalism of probabilistic languages has been introduced for modeling the qualitative behavior of stochastic discrete event systems a probabilistic language is a unit interval valued map over the set of traces of the system satisfying certain consistency constraints regular language operators such as choice concatenation and kleene closure have been defined in the setting of probabilistic languages to allow modeling of complex systems in terms of simpler ones the set of probabilistic languages is closed under such operators thus forming an algebra it also is a complete partial order under a natural ordering in which the operators are continuous hence recursive equations can be solved in this algebra this is alternatively derived by using the contraction mapping theorem on the set of probabilistic languages which is shown to be a complete metric space the notion of regularity i e finiteness of automata representation of probabilistic languages has been defined and it is shown that regularity is preserved under choice concatenation and kleene closure we show that this formalism is also useful in describing system performance measures such as completion time reliability etc and present properties to aide their computation

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

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

controlled markov chains with safety upper bound in this note we introduce and study the notion of safety control of stochastic discrete event systems dess modeled as controlled markov chains for nonstochastic dess modeled by state machines or automata safety is specified as a set of forbidden states or equivalently by a binary valued vector that imposes an upper bound on the set of states permitted to be visited we generalize this notion of safety to the setting of stochastic dess by specifying it as an unit interval valued vector that imposes an upper bound on the state probability distribution vector under the assumption of complete state observation we identify 1 the set of all state feedback controllers that satisfy the safety requirement for any given safe initial state probability distribution and 2 the set of all safe initial state probability distributions for a given state feedback controller

optimal supervisory control of probabilistic discrete event systems probabilistic discrete event systems pdes are modeled as generators of probabilistic languages and the supervisors employed are a probabilistic generalization of deterministic supervisors used in standard supervisory control theory in the case when there exists no probabilistic supervisor such that the behavior of a plant under control exactly matches the probabilistic language given as the requirements specification we want to find a probabilistic control such that the behavior of the plant under control is as close as possible to the desired behavior first as a measure of this proximity a pseudometric on states of generators is defined two algorithms for the calculation of the distance between states in this pseudometric are described then an algorithm to synthesize a probabilistic supervisor that minimizes the distance between generators representing the achievable and required behavior of the plant is presented

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

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

observability and decentralized control of fuzzy discrete event systems fuzzy discrete event systems as a generalization of crisp discrete event systems have been introduced in order that it is possible to effectively represent uncertainty imprecision and vagueness arising from the dynamic of systems a fuzzy discrete event system has been modeled by a fuzzy automaton its behavior is described in terms of the fuzzy language generated by the automaton in this paper we are concerned with the supervisory control problem for fuzzy discrete event systems with partial observation observability normality and co observability of crisp languages are extended to fuzzy languages it is shown that the observability together with controllability of the desired fuzzy language is a necessary and sufficient condition for the existence of a partially observable fuzzy supervisor when a decentralized solution is desired it is proved that there exist local fuzzy supervisors if and only if the fuzzy language to be synthesized is controllable and co observable moreover the infimal controllable and observable fuzzy superlanguage and the supremal controllable and normal fuzzy sublanguage are also discussed simple examples are provided to illustrate the theoretical development

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

necessary and sufficient conditions for fuzzy optimality problems in this paper we define a new minimum concept for fuzzy optimization problems more general than those that exist in the literature we find necessary optimality conditions based on a new fuzzy stationary point definition and we prove that these conditions are also sufficient under new fuzzy generalized convexity notions