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

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

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

exact formula for the minimum squared euclidean distance of cpfsk the exact expression for the minimum squared euclidean distance of continuous phase frequency shift keying cpfsk with modulation index h

design of serial concatenated msk schemes based on density evolution we consider the design of convolutional codes and low density parity check ldpc codes with minimum shift keying msk when the receiver employs iterative decoding and demodulation the main idea proposed is the design of coded schemes that are well matched to the iterative decoding algorithm being used rather than to hypothetical maximum likelihood decoding we first show that the design is crucially dependent on whether the continuous phase encoder cpe is realized in recursive form or in nonrecursive form we then consider the design of convolutionally coded systems and low density parity check codes with msk to obtain near capacity performance with convolutional codes we show that it is possible to improve the performance significantly by using a mixture of recursive and nonrecursive realizations for the cpe for low density parity check codes we show that codes designed for binary phase shift keying are optimal for msk only if the nonrecursive realization is used for the recursive realization we design new ldpc codes based on the concept of density evolution we show that these codes outperform the best known codes for msk and have lower decoding complexity

fock representations of the affine lie algebra a 1 1 the aim of this note is to show that the affine lie algebraa1 1 has a natural family v of fock representations on the spacec xi yj i andj parametrized by v c2 by corresponding the highest weight of to each the parameter spacec2 forms a double cover of the weight spacec 0 c 1 with singularities at linear forms of level 2 this number is 1 times the dual coxeter number our results contain explicit realizations of irreducible non integrable highest wieghta1 1 modules for generic v

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

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

a quadratic finite element method for solving biharmonic problems in ir n a family of simplicial finite element methods having the simplest possible structure is introduced to solve biharmonic problems in n n 3 using the primal variable the family is inspired in the morley triangle for the two dimensional case and in some sense this element can be viewed as its member corresponding to the valuen 2

a c1 virtual element method on polyhedral meshes abstract the purpose of the present paper is to develop c 1 virtual elements in three dimensions for linear elliptic fourth order problems motivated by the difficulties that standard conforming finite elements encounter in this framework we focus the presentation on the lowest order case the generalization to higher orders being briefly provided in the appendix the degrees of freedom of the proposed scheme are only 4 per mesh vertex representing function values and gradient values interpolation error estimates for the proposed space are provided together with a set of numerical tests to validate the method at the practical level

higher spin fields and the gelfand dickey algebra we show that in 2 dimensional field theory higher spin algebras are contained in the algebra of formal pseudodifferential operators introduced by gelfand and dickey to describe integrable nonlinear differential equations in lax form the spin 2 and 3 algebras are discussed in detail and the generalization to all higher spins is outlined this provides a conformal field theory approach to the representation theory of gelfand dickey algebras

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

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

coded continuous phase modulation with low complexity noncoherent reception coded continuous phase modulation based on a feedback free modulator with noncoherent detection is discussed low complexity receiver processing is achieved by using only two or three linear filters for demodulation and applying noncoherent sequence estimation with reduced state viterbi decoding and simple branch metric calculation overall the proposed noncoherent receiver provides significant advantages over previously presented approaches

finite element approximation of a sixth order nonlinear degenerate parabolic equation we consider a finite element approximation of the sixth order nonlinear degenerate parabolic equation equation here where generically equation here for any given equation here in addition to showing well posedness of our approximation we prove convergence in space dimensions d leq 3 furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed finally some numerical experiments in one and two space dimensions are presented

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

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

trellis termination of multi h cpm and the diophantine frobenius problem this paper presents a method for terminating the phase trellis in multi h continuous phase modulation cpm it is shown that tilted phase trellis for multi h cpm signals is periodic and enables the representation of the multi h cpm modulator as a cascade of a periodic recursive continuous phase encoder cpe and a phase modulator pm we then pose the problem of finding the minimum number of symbols that will terminate the phase trellis in a known state of the modulator and establish a connection of its solution to the diophantine frobenius problem fp analytical results are established for the existence of a terminating sequence and upper and lower bounds are derived on its length for arbitrary modulation parameters we show that the trellis terminating symbols and their quantity depends upon the initial state of the encoder the set of modulation indices the cpe memory order and the number of bits per modulated symbol it is shown that required overhead for trellis termination can be significant for schemes with integer modulation indices

generalized drinfeld sokolov reductions and kdv type hierarchies generalized drinfeld sokolov ds hierarchies are constructed through local reductions of hamiltonian flows generated by monodromy invariants on the dual of a loop algebra following earlier work of de groot et al reductions based upon graded regular elements of arbitrary heisenberg subalgebras are considered we show that in the case of the nontwisted loop algebra l gl n graded regular elements exist only in those heisenberg subalgebras which correspond either to the partitions ofn into the sum of equal numbersn pr or to equal numbers plus onen pr 1 we prove that the reduction belonging to the grade 1 regular elements in the casen pr yields thep p matrix version of the gelfand dickeyr kdv hierarchy generalizing the scalar casep 1 considered by ds the methods of ds are utilized throughout the analysis but formulating the reduction entirely within the hamiltonian framework provided by the classical r matrix approach leads to some simplifications even forp 1

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

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

a new class of zienkiewicz type non conforming element in any dimensions in this paper a new class of zienkiewicz type non conforming finite element in n spatial dimensions with n 2 is proposed the new finite element is proved to be convergent for the biharmonic equation

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

a quasi optimum receiver for continuous phase modulation a simple receiver structure for any continuous phase modulation cpm scheme is introduced its front end is just the ordinary linear receiver followed by a subinterval sampler eliminating the need for the standard analog matched filters its design is based on the decomposition of the cpm signal in the walsh signal space this brings the hardware requirement to a minimum and near optimum performance can be easily obtained

nonconforming tetrahedral finite elements for fourth order elliptic equations this paper is devoted to the construction of nonconforming finite elements for the discretization of fourth order elliptic partial differential operators in three spatial dimensions the newly constructed elements include two nonconforming tetrahedral finite elements and one quasi conforming tetrahedral element these elements are proved to be convergent for a model bi harmonic equation in three dimensions in particular the quasi conforming tetrahedron element is a modified zienkiewicz element while the nonmodified zienkiewicz element a tetrahedral element of hermite type is proved to be divergent on a special grid

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

on the necessity and sufficiency of the patch test for convergence of nonconforming finite elements this paper proposes a weak patch test that improves both the patch test and the generalized patch test under a weak superapproximation assumption which can be obtained from certain approximation and weak continuity property it is shown that the weak patch test is equivalent to the generalized patch test thus if a nonconforming finite element passes the patch test and satisfies some approximation and weak continuity property its convergence is then guaranteed furthermore the consistency term of such a nonconforming element can be proved to be of order o h it is shown that if a nonconforming element does not pass the patch test and a condition relative to subdividing a domain by the element is true then one can find a family of triangulations for which the element is divergent

classical a n w geometry by analyzing theextrinsic geometry of two dimensional surfaces chirally embedded incp n thecp n w surface 1 we give exact treatments in various aspects of the classical w geometry in the conformal gauge first the basis of tangent and normal vectors are defined at regular points of the surface such that their infinitesimal displacements are given by connections which coincide with the vector potentials of the conformal a n toda lax pair since the latter is known to be intrinsically related with the w symmetries this gives the geometrical meaning of thea n w algebra second w surfaces are put in one to one correspondence with solutions of the conformally reduced wznw model which is such that the toda fields give the cartan part in the gauss decomposition of its solutions third the additional variables of the toda hierarchy are used as coordinates ofcp n this allows us to show that w transformations may be extended as particular diffeomorphisms of this target space higher dimensional generalizations of the wznw equations are derived and related with the zakharov shabat equations of the toda hierarchy fourth singular points are studied from a global viewpoint using our earlier observation 1 that w surfaces may be regarded as instantons the global indices of the w geometry which are written in terms of the toda fields are shown to be the instanton numbers for associated mappings of w surfaces into the grassmannians the relation with the singularities of w surface is derived by combining the toda equations with the gauss bonnet theorem

the lower bound property of the morley element eigenvalues in this paper we prove that the morley element eigenvalues approximate the exact ones from below on regular meshes including adaptive local refined meshes for the fourth order elliptic eigenvalue problems with the clamped boundary condition in any dimension and we implement the adaptive computation with the morley element to obtain lower bounds of eigenvalues for the vibration problem of clamped plate under tension and a fourth order elliptic eigenvalue problem with variable coefficients

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

iterative diversity detection for correlated continuous time rayleigh fading channels an antenna array is proposed as a means of achieving a space diversity effect that partly overcomes the severity of continuous time rayleigh fading channels the investigated channel is assumed to be frequency nonselective with correlated diversity links where the correlation is related to the array geometry and the spatial and doppler dispersions further the error performance is improved by bit interleaving and channel coding where the encoders channel is viewed as a serially concatenated system a convolutional code constitutes the outer code whereas a differential encoder and the fading channel having truncated memory form a joint inner code in order to obtain a practical detector structure it is desirable to perform iterative decoding by applying some a posteriori probability app algorithms for this purpose we propose a novel generalization of the well known bahl cocke jelinek raviv 1974 algorithm that calculates the apps over channels having memory numerical results indicate that iterative decoding becomes more powerful when the exploited channel memory depth is extended also the error performance is significantly improved by introducing multiple antennas the interleaver gain is however seen to be quite moderate in contrast to additive white gaussian noise channels

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

reduced complexity approach to iterative detection of coded soqpsk we develop a reduced complexity approach for the detection of coded shaped offset quadrature phase shift keying soqpsk a highly bandwidth efficient and popular constant envelope modulation the complexity savings result from viewing the signal as a continuous phase modulation cpm we give a simple and convenient closed form expression for a recursive binary to ternary precoder for soqpsk the recursive nature of this formulation is necessary in serially concatenated systems where soqpsk serves as the inner code we show that the proposed detectors are optimal in the full response case and are near optimal in the partial response case due to some additional complexity reducing approximations in all cases the proposed detectors achieve large coding gains for serially concatenated coded soqpsk these gains are similar to those reported recently by li and simon which were obtained using a more complicated cross correlated trellis coded quadrature modulation xtcqm interpretation

on the classical algebra we consider the classical algebra from the integrable system viewpoint the integrable evolution equations associated with the algebra are constructed and the miura maps and consequent modifications are presented modifying the miura maps we supply a free field realization for the classical algebra we also construct the corresponding toda type integrable systems

design of ring convolutional trellis codes for map decoding of mpeg 4 images we propose a trellis coded modulation system using continuous phase frequency shift keying cpfsk and ring convolutional codes for transmitting the bits generated by an embedded zerotree wavelet encoder improved performance is achieved by using maximum a posteriori decoding of the zerotree symbols and ring convolutional trellis codes are determined for this decoding method the cpfsk transmitter is decomposed into a memoryless modulator and a continuous phase encoder over the ring of integers modulo 4 the latter is combined with a polynomial convolutional encoder over the same ring in the code design process a search is made of the combined trellis where the branch metrics are modified to include the source transition matrix simulation results of image transmission are provided using the optimized system including mismatched channel cases

a system theory approach to decompose cpm signals into pam waveforms in 1986 laurent showed that binary continuous phase modulated cpm signals can be decomposed into pulse amplitude modulated pam waveforms this result later extended to multilevel cpm signals by mengali and morelli has attracted much attention especially for the design of simplified receivers the paper proceeds from the premise that the decomposition into pam waveforms is not unique and follows a systemtheory approach that leads to a natural formulation first the cpm modulator is represented by a nonlinear part encoder followed by a linear part bank of pam modulators the two parts are then rearranged with the aim of obtaining real valued continuous pam waveforms and to reduce their number several classes of decompositions arise with this approach each of which admits an infinite number of different decompositions of the same cpm signal among which the laurent and mengalimorelli results appear as special cases throughout the paper a systematic use is made of the kronecker product which appears to be the natural tool for dealing with cpm decompositions and for expressing results in a very simple form

orthogonal space time block coding for continuous phase modulation with frequency domain equalization in this letter an orthogonal space time st block coding stbc technique for continuous phase modulation cpm is proposed and combined with a frequency domain equalizer fde to obtain high performance gains over frequency selective channels the new method maintains the constant envelope and phase continuity of the cpm waveforms perfectly by using appropriate tail symbols during the addition of cyclic prefix and interblock transitions and therefore has no negative impact on the spectral efficiency because the stcoded cpm blocks remain orthogonal fde is applied as in the case of single antenna transmissions without any increase in the computational load simulations corroborate the performance improvement offered by stbc while also preserving the desired bandwidth efficiency of cpm

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

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

a new a posteriori error estimate for the morley element in this paper we present a posteriori error analysis for the nonconforming morley element of the fourth order elliptic equation we propose a new residual based a posteriori error estimator and prove its reliability and efficiency these results refine those of beirao da veiga et al numer math 106 165 179 2007 by dropping two edge jump terms in both the energy norm of the error and the estimator and those of wang and zhang local a priori and a posteriori error estimates of finite elements for biharmonic equation research report 13 2006 by showing the efficiency in the sense of verfurth a review of a posteriori error estimation and adaptive mesh refinement techniques wiley teubner new york 1996 moreover the normal component in the estimators of beirao da veiga et al numer math 106 165 179 2007 and wang and zhang local a priori and a posteriori error estimates of finite elements for biharmonic equation research report 13 2006 is dropped and therefore only the tangential component of the stress on each edge comes into the estimator in addition we generalize these results to three dimensional case

the morley element for fourth order elliptic equations in any dimensions in this paper the well known nonconforming morley element for biharmonic equations in two spatial dimensions is extended to any higher dimensions in a canonical fashion the general n dimensional morley element consists of all quadratic polynomials defined on each n simplex with degrees of freedom given by the integral average of the normal derivative on each n 1 subsimplex and the integral average of the function value on each n 2 subsimplex explicit expressions of nodal basis functions are also obtained for this element on general n simplicial grids convergence analysis is given for this element when it is applied as a nonconforming finite element discretization for the biharmonic equation

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

noncoherent block demodulation of msk with inherent and enhanced encoding it is shown that there is a close relation between known noncoherent minimum shift keying msk demodulation structures such as envelope and differential receivers and schemes derived from the noncoherent maximum likelihood block estimation n mlbe principle when the observation interval is increased the performance of msk with n mlbe tends to that of binary coherently detected orthogonal binary frequency shift keying a new demodulation strategy reduced block noncoherent estimation rbne is introduced and shown to improve the performance of noncoherent msk beyond that of coherently detected orthogonal fsk when rbne is used with msk and the observation interval is increased the performance approaches that of antipodal signaling the key feature of all these structures is multisymbol noncoherent processing with exploitation of the msk inherent coding properties induced by its phase continuity the use of binary block codes for msk with n mlbe is considered it is shown that simple binary block codes with low bandwidth expansion that exploit the inherent msk memory can give significant gains

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

joint source and channel coding using punctured ring convolutional coded cpm in this paper a novel trellis source encoding scheme based on punctured ring convolutional codes is presented joint source and channel coding jscc using trellis coded continuous phase modulation cpm with punctured convolutional codes over rings is investigated the channels considered are the additive white gaussian noise awgn channel and the rayleigh fading channel optimal soft decoding for the proposed jscc scheme is studied the soft decoder is based on the a posteriori probability app algorithm for trellis coded cpm with punctured ring convolutional codes it is shown that these systems with soft decoding outperform the same systems with hard decoding especially when the systems operate at low to medium signal to noise ratio snr furthermore adaptive jscc approaches based on the proposed source coding scheme are investigated compared with jscc schemes with fixed source coding rates the proposed adaptive approaches can achieve much better performance in the high snr region the novelties of this work are the development of a trellis source encoding method based on punctured ring convolutional codes the use of a soft decoder the app algorithm for the combined systems and the adaptive approaches to the jscc problem

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

linear diophantine constrained intra fix for frequency domain equalization of multi h cpm this paper considers the problem of constructing a symbol block to generate a cyclic multi h continuous phase modulated cpm signal so as to permit frequency domain equalization fde at the receiver like single h cpm the memory inherent in a multi h cpm waveform requires the use of an additional segment called an intra fix in each transmitted block the intra fix forces the transmitter state machine to regress to the state it had at the start of the block the constraints on the symbols of the intra fix which ensure above condition are shown to be a set of linear diophantine equations ldes three different methods are proposed for finding the symbols of the intra fix such that the length of the intra fix is minimized the last two methods connect the problem of intra fix insertion to the problem of trellis termination of the tilted phase this connection enables us to state and justify that existing bounds established on the length of the terminating sequence are effective for the length of the intra fix we observe that multi h cpm schemes typically require a shorter intra fix as compared to single h cpm schemes having similar modulation parameters we apply the proposed procedure to a dual h cpm scheme

iterative multisymbol noncoherent reception of coded cpfsk a system involving the multisymbol noncoherent reception of coded continuous phase frequency shift keying is developed optimized and analyzed unlike coherent systems the modulation index of the waveform does not need to be rational with a small denominator and the oscillator only needs to be stable for the duration of a small block of symbols the achievable performance over awgn and rayleigh block fading channels is determined by computing the average mutual information which is the capacity of a channel using the given modulation format and receiver architecture under the constraint of uniformly distributed input symbols the code rate and modulation index are jointly optimized with respect to average mutual information under a bandwidth constraint for binary and quaternary signaling the information theoretic results are corroborated by bit error rate curves generated using a standardized turbo code in conjunction with iterative demodulation and decoding it is shown that while more robust than a system with coherent reception the proposed system offers superior energy efficiency compared with conventional single symbol noncoherent reception

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

correlatively encoded multi h signals a correlatively encoded multi h cpfsk signaling technique which performs significantly better than partial response multi h signaling is introduced numerical results presented for binary 2 h signaling indicate that correlatively encoded 2 h signals can achieve significant gains over both constant h signals and partial response 2 h signals

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

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

a new performance bound for pam based cpm detectors it is well understood that the pulse amplitude modulation pam representation of continuous phase modulation cpm can lead to reduced complexity detectors with near optimum performance it has recently been shown that the pam representation also extends to cpm schemes with multiple modulation indexes multi h cpm in this paper we present a detector for multi h cpm which is based on the pam representation we also give an exact expression for the pairwise error probability for the entire class of pam based cpm detectors single and multi h optimal and reduced complexity over the additive white gaussian noise awgn channel and show that this bound is tighter than the previously published bound for approximate pam based detectors in arriving at this expression we show that pam based detectors for cpm are a special case of the broad class of mismatched cpm detectors we also show that the metrics for pam based detectors accumulate distance in a different manner than metrics for other cpm detectors these distance properties are especially useful in applications with greatly reduced trellis sizes we give thorough examples of the analysis for different single and multi h signaling schemes we also apply the new bound in comparing the performance of pam based detectors with other reduced complexity detectors for cpm

the f e m test for convergence of nonconforming finite elements on etablit un nouveau critere de convergence pour les elements finis non conformes qui est facilement verifiable le long de chaque interface

conformal field theories via hamiltonian reduction constraining thesl 3 wzw model we construct a reduced theory which is invariant with respect to the new chiral algebraw 3 2 this symmetry is generated by the stress energy tensor two bosonic currents with spins 3 2 and theu 1 current we conjecture a kac formula that describes the highly reducible representation for this algebra we also discuss the quantum hamiltonian reduction for the general type of constraints that leads to the new extended conformal algebras

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

reduced complexity detection and phase synchronization of cpm signals based on an extension of laurent 1986 decomposition of continuous phase modulation cpm signals into a sum of linearly modulated components we derive a class of reduced complexity maximum likelihood ml coherent detection and closed loop phase synchronization schemes the complexity of the resulting detection schemes expressed in terms of the number of matched filters and states of a viterbi algorithm is significantly reduced with respect to that of optimal coherent receivers with negligible performance loss this result extends a known one valid for the binary case to multilevel cpm the proposed synchronization schemes do not require an increased number of matched filters and are perfectly suitable to be used in conjunction with these receivers based on the phase locked loop pll equivalent linear model a method for optimizing the parameters of digital second order pll s is presented numerical examples based on theoretical analysis and computer simulation are provided for two specific formats in the cpm class tamed frequency modulation tfm and a quaternary raised cosine rc modulation

on the convergence properties of the quadrilateral elements of sander and beckers a class of nonconforming quadrilateral membrane elements introduced by sander and beckers is discussed in all details it is proved that two elements that do not pass the patch test may still yield convergence under a suitable condition on mesh subdivisions whereas one such element is found to be divergent for all mesh subdivisions all other finite elements in this class that pass the patch test are convergent the mathematical analysis provides a clear explanation of the convergence behavior appearing in the numerical examples of sander and beckers 1 introduction quadrilateral finite elements are attractive for discretizations of domains of arbitrary shapes but these approximations are hardly conforming therefore such elements have to be tested for convergence in connection with a variational interpretation of the patch test 2 sander and beckers 3 have recently introduced a class of nonconforming quadrilateral membrane elements having 8 to 16 degrees of freedom and have shown by numerical computations for a trapezoidal membrane problem that two elements that do not pass the patch test still exhibit convergence and yield good approximations whereas one such element diverges this result is of great interest and leads to the question whether the patch test is necessary for convergence of these nonconforming elements as stated in 3 additional investigations are certainly required to understand their behavior the present paper establishes a detailed mathematical analysis of these elements we formulate a condition on mesh subdivisions under which two elements that do not pass the patch test indeed yield convergence whereas another element is proved to be divergent whatever the mesh subdivision may be all other quadrilateral elements in this class that pass the patch test are convergent the theoretical analysis clearly explains the convergence behavior discussed in the numerical computations of sander and beckers in their examples a bisection scheme of mesh subdivisions is used for the discretization of the trapezoidal membrane in such cases the proposed condition on the mesh subdivisions is automatically fulfilled and thus convergence occurs for two elements it is seen therefore that the range of applicability of the patch test as a necessary condition for convergence is limited at this point it is worth noting that stummel 5 has presented basic examples which show that spaces of nonconforming trial functions

convergence properties of two nonconforming finite elements abstract two nonconforming triangular elements for second order problems are analyzed one element is found to be convergent the other does not yield approximate solutions converging to the solution of the given boundary value problem but to a wrong limit which is the solution of another variational equation this strange convergence behaviour may be typical for a wider class of nonconforming elements violating the basic precondition for convergence the problem of patch subdivisions is also considered

an explicit analysis of stummel s patch test examples a constructive approach for the treatment of stummel s examples to the patch test is presented together with generalizations of these examples the strange convergence phenomenon of nonconforming approximations is discussed in detail and a kind of modified variational equation for remedying these defects is introduced our variational equation uses a combination of hybrid and penalty methods that define a convergent procedure with optimal order of convergence to the exact solution with respect to a mesh dependent norm

sur la convergence des methodes d elements finis nonconformes pour des problemes lineaires de coques minces in this paper we study the convergence of nonconforming finite element method for the approximation of general thin shell problems we give sufficient conditions of convergence for a large class of finite elements then we estimate the error on the displacements and on the stresses dans cet article nous etudions la convergence des methodes d elements finis nonconformes pour l approximation des problemes de coques minces generales nous etablissons des conditions suffisantes de convergence pour une large classe d elements finis puis nous donnons des estimations de l erreur sur les deplacements et les contraintes

generalized concatenation of encoded tamed frequency modulation a novel construction for encoded tamed frequency modulation tfm is introduced which is based on the principles of generalized concatenation the inner tfm is partitioned into nested subsystems which increases the free euclidean distances in order to obtain a large distance among the nested tfm subsystems the scrambler matrices have to be computed which transfer the original tfm into the equivalent tfm with better partitioning properties then outer convolutional codes with different error correcting capabilities are used to protect the partitioning the new concatenated and generalized concatenated constructions were simulated in an additive white gaussian noise channel a multistep decoding algorithm based on soft output demodulation was used we present various simulation results which show a significant coding gain in comparison with the best known trellis codes having the same trellis state complexity

convergence analysis of a family of 14 node brick elements in this paper we will give convergence analysis for a family of 14 node elements which was proposed by smith and kidger 1992 the 14 dofs are taken as the values at the eight vertices and the six face centroids for second order elliptic problems we will show that among all the smith kidger 14 node elements type 1 type 2 and type 5 elements provide optimal order convergent solutions while type 6 element gives one order lower convergent solutions motivated by our proof we also find that the order of convergence of the type 6 14 node nonconforming element improves to be optimal if we change the dofs into the values at the eight vertices and the integration values on the six faces we also show that type 1 type 2 and type 5 keep the optimal order convergence if the integral dofs on the six faces are adopted

a convergence condition for the quadrilateral wilson element the paper deals with the convergence properties of the nonconforming quadrilateral wilson element which violates the patch test the convergence of the element is proved under a certain condition on mesh subdivisions without any modifications of the variational formulation this result extends the range of applicability of wilson s element the necessity of the proposed condition is also discussed

iterative decoding of serially concatenated cpm in fading channels with noisy channel state information we use the sum product algorithm spa to propose a reduced complexity detector for serially concatenated continuous phase modulated sccpm signals with noisy channel state information csi at the receiver two channel effects phase noise pn and flat fading are tackled using the statistical model and associated factor graph fg of the problem although optimal performance is not assured due to the loopy nature of the fg as well as simplifying assumptions made in the algorithm development simulations show that very significant performance gains are possible and the gap between systems with noiseless and noisy csi can be reduced to about 1 db using the proposed methods the increase in complexity compared to the conventional decoder which treats csi estimates as if they were equal to their true values is small

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

nonconforming finite element methods for the equations of linear elasticity in the adaptation of nonconforming finite element methods to the equations of elasticity with traction boundary conditions the main difficulty in the analysis is to prove that an appropriate discrete version of korn s second inequality is valid such a result is shown to hold for nonconforming piecewise quadratic and cubic finite elements and to be false for nonconforming piecewise linears optimal order error estimates uniform for poisson ratio v e 0 1 2 are then derived for the corresponding p2 and p3 methods this contrasts with the use of c finite elements where there is a deterioration in the convergence rate as v 1 2 for piecewise polynomials of degree 3 modifications of the continuous methods and the nonconforming linear method which also give uniform optimal order error estimates are discussed

multiple bit differential detection of shaped offset qpsk we consider multiple bit differential detection mbdd of differentially encoded shaped offset quadrature phase shift keying soqpsk a highly bandwidth efficient and popular constant envelope modulation we propose two mbdd schemes that are based on a recent continuous phase modulation interpretation of soqpsk we show that the performance of these mbdd schemes approaches that of coherent detection cd as the multiple bit observation n window increases the first scheme uses a detection window that spans the full bit observation window f mbdd and is shown to require very large values of n to approach the performance of cd this presents a practical problem since the complexity of mbdd grows exponentially with n the second scheme is an improved version i mbdd with a detection window that is shortened to n 2 bit intervals although the complexity of i mbdd also increases exponentially with n it represents a significant improvement since only modest values of n are needed for high performance these performance characteristics are identified via a detailed performance analysis which provides asymptotic formulas for the bit error probability that are confirmed with computer simulations the analysis is also used to find the symmetric frequency pulse shapes with the best and worst error performance finally we develop a simplified and practical decision feedback differential detection algorithm that achieves near optimal performance with complexity that grows only linearly with n

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

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

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

woven coded cpfsk with hierarchical code structure we introduce hierarchical woven coded continuous phase frequency shift keying hierarchical wccpfsk as the serial concatenation of different outer convolutional codes and inner cpfsk we compare it to wccpfsk with identical outer convolutional codes with the proposed code combinations hierarchical wccpfsk achieves superior decoding capability simulations show that it performs better at medium snrs

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

hexahedral volume coordinate method hvcm and improvements on 3d wilson hexahedral element abstract a new volume coordinate method for developing 3d hexahedral elements called hexahedral volume coordinate method hvcm is systematically established in this paper i several characteristic parameters of a hexahedron are defined and the degeneration conditions under which a hexahedron degenerates into other special polyhedrons are given ii the volume coordinates l 1 l 2 l 3 l 4 l 5 l 6 of any point within a convex hexahedron are defined iii transformation relations between the volume coordinates and the cartesian or isoparametric coordinates are presented iv the differential formulas for volume coordinates in hexahedral elements are given this new coordinate system can keep not only the advantages of local natural coordinate system but also a linear relation with the cartesian coordinate system then for checking the validity of the new hvcm it is used to formulate three new incompatible eight node hexahedral elements hvcc8 hvcc8 es and hvcc8 em by a similar procedure of famous wilson s incompatible mode numerical results show that the present elements exhibit much better performance than that of conventional isoparametric elements in most distorted mesh cases especially for macneal s thin beam problem it demonstrates that the new hvcm is a powerful tool for constructing high performance hexahedral finite element models

serially concatenated continuous phase modulation with iterative decoding serially concatenated and interleaved continuous phase modulation cpm with iterative decoding is investigated an a posteriori probability app algorithm for cpm is developed based on the classic app algorithm for channel codes the system is analyzed through upper bounds on the average bit error probability for coded and interleaved minimum shift keying the weight spectrum is computed resulting in a transfer function bound this is cumbersome for a general cpm system instead only the most significant error events contributing to the weight spectrum are identified simulations show that firstly these events give a satisfactory view of system performance when equal outer codes are used and secondly that remarkably good performance can be obtained for some simple systems finally power spectral densities and bandwidths are computed allowing for a bandwidth performanee comparison of different combinations

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