trellis coded differentially coherent tcdc mpsk with carrier phase noise the authors consider trellis coded m ary phase shift keying mpsk when used with differentially coherent demodulation over a carrier phase noise dominated channel a tight upper bound to the probability of error is introduced this bound shows the presence of an irreducible probability of error when compared to coherently demodulated trellis coded mpsk the irreducible probability of error of the differentially coherent scheme is much lower this improved robustness to carrier phase noise is obtained at the expense of signal to noise ratio snr coding gain numerical results for two ungerboeck codes with differentially coherent mpsk demodulation show poor snr coding gain a modification of ungerboeck codes which makes them more suitable for use with differentially coherent demodulation is shown to increase the snr gain while maintaining good robustness to carrier phase noise

the design of trellis coded mpsk for fading channels set partitioning for optimum code design a previous work on criteria for designing trellis coded mpsk modulation to achieve minimum error probability performance on the rician fading channel see ibid vol 36 no 9 p 1004 1012 sep 1988 is extended it is demonstrated that allowing for multiple symbols per trellis branch i e multiple trellis coded modulation mtcm provides an additional degree of freedom for designing a code to meet the optimization on the fading channel diversities larger than those achievable with conventional trellis codes having the same number of trellis states are now attainable it is under these conditions that mtcm achieves its full potential

performance analysis of coded modulation with generalized selection combining in rayleigh fading we consider coded modulation with generalized selection combining gsc for bandwidth efficient coded modulation over rayleigh fading channels our results show that reception diversity with generalized selection combining can conveniently trade off system complexity versus performance we provide a number of new results by calculating the cutoff rate and by deriving analytical upper bounds on symbol interleaved trellis coded modulation tcm and bit interleaved coded modulation bicm with gsc all are verified by simulation we show that our new bounds on tcm with gsc which includes maximum ratio combining and selection combining as special cases are tighter than the previously derived bounds a new asymptotic analysis on the pairwise error probability which can be used as a guideline for designing coded modulation over gsc channels is also given finally we show that bicm with iterative decoding bicm id can achieve significant coding gain over conventional coded modulation in a multiple receiving antenna channel

differential detection of quadrature frequency phase modulated signals this paper proposes a pilot symbol assisted psa signaling format that enables the differential detection of the differentially phase encoded quadrature frequency phase modulated ndqfpm signal using n orthogonal frequencies the psa ndqfpm signal is transmitted on a frame by frame structure the channel considered is an additive white gaussian noise channel where the channel phase varies so slowly that it is assumed constant over one frame duration each frame consists of j nqfpm pilot symbols and i data blocks each containing l ndqfpm symbols with the first symbol differentially phase encoded with respect to pilot symbols based on the maximum likelihood sequence estimation principle the maximum likelihood differential detection ml dd algorithm is developed to detect the psa ndqfpm signal on a block by block basis tight upper and asymptotic bounds are derived and verified by simulation to evaluate the bit error performance of the ml dd algorithm both bandwidth and power efficiencies of psa ndqfpm with ml dd are compared to nqfpm with coherent detection constant envelope nqfpm with coherent detection constant envelope ndqfpm also known as nfsk 4dpsk with ml dd and conventional 2dqfpm also known as dq sup 2 psk with ml dd it is analytically shown that psa ndqfpm with ml dd has lower power efficiency than nqfpm with coherent detection and nfsk 4dpsk with ml dd but still can provide noticeably higher power efficiency than dq sup 2 psk with ml dd when a medium frame length is used due to the use of pilot symbols psa ndqfpm with a medium frame length has marginally lower bandwidth efficiency than its coherent counterpart nqfpm but still yields significantly higher bandwidth efficiency than constant envelope nqfpm and nfsk 4dpsk

the coc algorithm part ii topological geometrical and generalized shape optimization abstract after outlining analytical methods for layout optimization and illustrating them with examples the coc algorithm is applied to the simultaneous optimization of the topology and geometry of trusses with many thousand potential members the numerical results obtained are shown to be in close agreement up to twelve significant digits with analytical results finally the problem of generalized shape optimization finding the best boundary topology and shape is discussed

minimal transmitter complexity design of analytically described trellis codes g ungerboeck s 1982 design rules for a class of bandlimited codes called trellis codes are reviewed his design of the trellis is based on a set partitioning of the signal constellation and he realized these trellis codes by a convolutional encoder followed by a mapping rule from the coder output to modulation symbols r calderbank and j e mazo 1984 showed how to realize trellis codes for one dimensional signal sets in a single step easily derived nonlinear transformation with memory on a sliding block of source symbols the design rules that give a signal state specification in a trellis that yields the calderbank mazo transformation with the smallest number of terms are presented this gives a minimal transmitter complexity design it is shown how to realize the ungerboeck from the calderbank mazo form and as a result a step by step search free design procedure for trellis codes is presented two additional design rules are presented and applied to two examples by analytically designing two trellis codes a simple procedure for converting an analytic code expression to a convolutional encoder realization is discussed the analytic designs of a 4 d code and a 2 d code are presented

multilevel trellis coded modulations for the rayleigh fading channel the authors present coded 8 phase shift keyed 8 psk modulations for the rayleigh fading channel the schemes are based on multilevel trellis coded modulation constructions and utilize maximum free hamming distance binary convolutional codes as building blocks a suboptimal multistage decoder that utilizes interstage interleaving and iterative decoding is proposed and evaluated examples are constructed to show that the proposed schemes outperform the best modified codes of the ungerboeck type due to significantly higher implicit time diversity yielding seven branches of built in time diversity whereas the ungerboeck code yields four branches of time diversity for a 64 state system the transmission delay is higher however the new schemes can provide three levels of unequal error protection when 8 psk or 8 differential phase shift keying 8 dpsk modulations are used they provide 10 14 db channel signal to noise ratio gain over uncoded 4 dpsk at a bit error rate of 10 sup 3 for a modest decoding complexity

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

delay constrained capacity with causal feedback a block fading channel model is considered and a k block delay constraint is imposed on data transmission the key consideration is that the channel state information is fed back to the transmitter in a causal manner a general cost function spl mu x is considered in solving the delay constrained transmission problem under the short term and the long term power constraints a causal power adaptation strategy is needed to maximize the cost function hence dynamic programming is found to give the optimum solution the general cost function is then specialized to the cases of expected and outage capacities in the case of expected capacity it is observed that optimizing the transmitted power does not give much benefit at high signal to noise ratio snr but provides a substantial gain at low snr at low snr it is proved that the capacity increases by a factor of approximately log k m due to power adaptation when the channel fades according to the spl chi sub 2m sup 2 statistics in the case of outage capacity it is shown that the optimum power adaptation solution to the long term constraint problem provides a substantial snr gain at both low and high values of snr random coding bounds are derived for the outage capacity algorithms

a characteristic equation associated to an eigenvalue problem on c2 networks abstract a characteristic equation for the spectrum of an eigenvalue problem on c 2 networks is deduced and those special cases are investigated in which the spectrum depends mainly on the structure of the abstract graph belonging to the c 2 network

multidimensional trellis coded phase modulation using a multilevel concatenation approach ii codes for the awgn and fading channels for pt i see ibid vol 45 no 1 p 64 72 1997 we use the construction technique proposed in part i to construct multidimensional trellis coded modulation tcm codes for both the additive white gaussian noise awgn and the fading channels analytical performance bounds and simulation results show that these codes perform very well and achieve significant coding gains over uncoded reference modulation systems in addition the proposed technique can be used to construct codes which have a performance decoding complexity advantage over the codes listed in literature

good lattice constellations for both rayleigh fading and gaussian channels recent work on lattices matched to the rayleigh fading channel has shown how to construct good signal constellations with high spectral efficiency we present a new family of lattice constellations based on complex algebraic number fields which have good performance on rayleigh fading channels some of these lattices also present a reasonable packing density and thus may be used at the same time over a gaussian channel conversely we show that particular versions of the best lattice packings d sub 4 e sub 6 e sub 8 k sub 12 spl lambda sub 16 spl lambda sub 24 constructed from totally complex algebraic cyclotomic fields present better performance over the rayleigh fading channel the practical interest in such signal constellations rises from the need to transmit information at high rates over both terrestrial and satellite links some further results in algebraic number theory related to ideals and their factorization are presented and the decoding algorithm used with these lattice constellations are illustrated together with practical results

performance of joint equalization and trellis coded modulation on multipath fading channels in the literature the performance of joint maximum likelihood sequence estimation for trellis coded modulation systems was analyzed under the assumption that fading is so slow that the channel does not change during all error events in this paper we extend the performance analysis to general fading processes by considering the correlation function of the time variant channel impulse response instead of assuming constant fading an easily evaluated closed form upper bound is derived for the pairwise error probability the bit error rate is then estimated by using a truncated union bound computer simulations show that our analytical results are good for all cases considered especially when diversity reception is used

regularized formulation for optimal design of axisymmetric plates abstract this paper presents a regularized mathematical formulation necessary conditions of optimality and solutions of problems of optimal design of solid elastic axisymmetric plates of prescribed total material volume single purpose design criteria of minimum static compliance maximum stiffness and maximum frequency of free transverse vibrations are considered the regularization which alleviates some anomalies and difficulties encountered earlier in plate optimization problems is based on a new compound plate model with two simultaneous design variables namely variable thickness of a solid part of the plate and variable concentration of a dense system of thin integral stiffeners attached to the solid plate part a numerical optimality criterion based method of solution is developed for the problem and several optimal designs are presented the results are compared with results obtained from optimal design formulations applied heretofore and substantiate the superiority of the new regularized formulation

multiple trellis coded modulation mtcm the authors demonstrate a trellis coded modulation technique referred to as multiple trellis coded modulation mtcm wherein more than one channel symbol per trellis branch is transmitted they have found simple two state trellis codes for symmetric mpsk multiple phase shift keying and am modulations that can achieve 3 db gain over uncoded modulation at very high signal to noise ratios without bandwidth expansion or reduction in information bit rate the gain of these codes with respect to previously reported two state trellis codes is between 1 and 2 db at very high signal to noise ratios depending on the number of bits per hertz transmitted these gains are achieved for those of the equivalent conventional trellis codes with the same number of states in the trellis diagram the authors note that additional computations per branch are needed for the multiple trellis coding scheme the concept can be extended to a higher number of states and other types of modulations

laplacians on periodic graphs with guides abstract we consider laplace operators on periodic discrete graphs perturbed by guides i e graphs which are periodic in some directions and finite in other ones the spectrum of the laplacian on the unperturbed graph is a union of a finite number of non degenerate bands and eigenvalues of infinite multiplicity we show that the spectrum of the perturbed laplacian consists of the unperturbed one plus the additional so called guided spectrum which is a union of a finite number of bands we estimate the position of the guided bands and their length in terms of geometric parameters of the graph we also determine the asymptotics of the guided bands for guides with large multiplicity of edges moreover we show that the possible number of guided bands their length and position can be rather arbitrary for some specific periodic graphs with guides

high rate diversity across time and frequency using linear dispersion to improve performance of orthogonal frequency division multiplexing ofdm for fading channels this paper proposes increasing frequency and time diversity using linear dispersion codes ldc ofdm methods of ldc ofdm processing are proposed for both zero padding zp and cyclic prefix cp type guard intervals a two step estimation tse decoding strategy is proposed that decouples symbol estimation from ldc decoding this paper analyzes the upper bound diversity order of ldc cp ofdm which is equal to the full diversity order available in the channels a criterion for full frequency time diversity design is derived a rate one code is provided and performance is examined through simulations this paper also investigates ldc cp ofdm and ldc zp ofdm performance under imperfect channel estimation and low complexity receiver structures respectively in addition tse is shown to have performance close to that of full complexity one step estimation ose

error performance analysis of quadrature partial response trellis coded modulation qpr tcm in fading mobile satellite channels in order to improve the bandwidth efficiency and error performance partial response signaling prs and trellis coded modulation tcm are combined together this method is named qpr tcm whereas previous contributions have considered the performance of tcm transmitted over an additive white gaussian noise awgn channel the emphasis in this paper is on the performance of trellis coded m ary qam combined with prs in the fading environment we only consider the case where interleaving deinterleaving is employed to further combat the fading and assume that the ideal channel state information csi is available analytical upper bounds are derived using the well known transfer function bounding technique the bandwidth efficiencies are computed and the numerical results for several practical schemes are compared to each other one interesting result is that when the combined system is used on a rician fading channel the bit error probability upper bounds of the proposed 6qpr tcm and 9qpr tcm systems are better than their counterparts the 4qam tcm systems with 2 and 4 states respectively for snr values greater than a threshold which have the best error performances in the literature

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

i q tcm reliable communication over the rayleigh fading channel close to the cutoff rate this paper presents some trellis codes that provide high coding gain to channels with slow non frequency selective rayleigh fading it is shown that the use of two encoders in parallel used to specify the in phase and quadrature components of the transmitted signal results in greater minimum time diversity than the conventional design in which a single encoder is used using this approach which we label i q tcm codes with bandwidth efficiencies of 1 2 and 3 bits s hz are described for various constraint lengths the performance of these codes is bounded analytically and approximated via simulation the results show a large improvement in the bit error rate ber when compared with conventional trellis coded modulation tcm schemes when perfect channel state information csi is available to the receiver indeed when this approach is applied to channels with independent rayleigh fading the resulting coding gain is close to that implied by the cutoff rate limit even for only moderately complex systems the proposed codes are also simulated under less ideal assumptions for instance results for a 1 bit s hz iq tcm code without csi show a significant gain over conventional coding finally simulations over channels with correlated fading were undertaken it is concluded that an interleaver span of 4 spl nu yields performance close to what is achieved with ideal interleaving

orthogonally multiplexed orthogonal amplitude modulation family a family of coherent orthogonally multiplexed orthogonally amplitude modulated omoam signals is presented the omoam signal is constituted by orthogonally multiplexing ai component signals each constructed by a data chosen group of l orthogonal pulse amplitude modulated basis signals a generalized signal format is proposed to model the omoam signal in a unified way that the family contains not only classical orthogonally multiplexed modulations as special embodiments but also a multitude of new modulations a generalized optimum receiver for coherently demodulating omoam signals is developed and analyzed in terms of the bit error probability for the additive white gaussian noise channel the spectral characteristics of the omoam signals constructed from various time limited and band limited basis sets are studied in terms or the fractional out of band power containment several general trends of error and spectral performance characteristics are exploited

bounds on the pairwise error probability of coded ds ssma communication systems in rayleigh fading channels arbitrarily tight upper and lower bounds on the pairwise error probability pep of a trellis coded or convolutional coded direct sequence spread spectrum multiple access ds ssma communication system over a rayleigh fading channel are derived a new set of probability density functions pdfs and cumulative distribution functions cdfs of the multiple access interference mai statistic is derived and a modified bounding technique is proposed to obtain the bounds the upper bounds and lower bounds together specify the accuracy of the resulting estimation of the pep and give an indication of the system error performance several suboptimum decoding schemes are proposed and their performances are compared to that of the optimum decoding scheme by the average pairwise error probability apep values the approach can be used to accurately study the multiple access capability of the coded ds ssma system without numerical integrations

performance analysis of coded communication systems on nakagami fading channels with selection combining diversity in this paper we develop analytical tools for the performance analysis of coded coherent communication systems on independent and identically distributed nakagami m fading channels with selection combining sc diversity first we derive an exact expression for the moment generation function mgf of the signal to noise ratio snr of a code symbol at the output of the selection combiner next based on gauss chebyshev quadrature and gauss laguerre quadrature rules we propose a simple to compute yet accurate numerical solution for the pairwise error probability pep of coded m phase shift keying psk signals using the pep expressions we present the union bound based bit error performance of trellis coded modulation schemes and turbo codes finally we derive an exact expression for the computational cutoff rate of a coded system with m psk signaling and sc diversity and show that the cutoff rate expression is a simple function of the mgf of the snr at the output of the diversity combiner

the effects of phase noise on trellis coded modulation over gaussian and fading channels in this paper error performance bounds are derived for 8 psk trellis coded modulation tcm over gaussian and fading channels in the presence of phase noise coherent demodulation combined with both phase locked loop pll and transparent tone in band technique ttib for phase recovery is assumed the analysis is then applied to a number of ungerboeck 8 psk trellis codes and the results for the bit error rate ber performance obtained both analytically and by monte carlo simulation are presented the derived bounds can be directly extended to any m psk trellis code

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

constellation labeling for linear encoders this paper investigates optimal constellation labeling in the context of the edge profile a constellation s edge profile lists the minimum distance edge for each binary symbol error the paper introduces the symmetric ultracomposite su labeling structure and shows that this structure provides undominated edge profiles for 2 sup n psk 2 sup n pam and 2 sup 2n point square qam the su structure is a generalization of the commonly used reflected binary gray code with the proper choice of basis vectors su labeling can support either set partition or gray code labeling of 2 sup n psk 2 sup n pam and 2 sup 2n point square qam notably there are gray code and set partition labelings that do not have the su structure these labelings yield inferior edge profiles the su structure does not apply to cross constellations however for any standard cross constellation with 32 or more points a quasi su labeling structure can approximate the su structure with the correct choice of basis quasi su labelings produce quasi gray labelings however the quasi su structure cannot support set partition labeling in fact the quasi su structure provides a better edge profile than standard set partition labeling thus for cross constellations there is a choice between edge profile optimality and the group structure provided by set partitioning here the correct choice depends on whether the encoder trellis has parallel branches

invariants for laplacians on periodic graphs we consider a laplacian on periodic discrete graphs its spectrum consists of a finite number of bands in a class of periodic 1 forms i e functions defined on edges of the periodic graph we introduce a subclass of minimal forms with a minimal number mathcal i of edges in their supports on the period we obtain a specific decomposition of the laplacian into a direct integral in terms of minimal forms where fiber laplacians matrices have the minimal number 2 mathcal i of coefficients depending on the quasimomentum and show that the number mathcal i is an invariant of the periodic graph using this decomposition we estimate the position of each band the lebesgue measure of the laplacian spectrum and the effective masses at the bottom of the spectrum in terms of the invariant mathcal i and the minimal forms in addition we consider an inverse problem we determine necessary and sufficient conditions for matrices depending on the quasimomentum on a finite graph to be fiber laplacians moreover similar results for schrodinger operators with periodic potentials are obtained

near capacity turbo trellis coded modulation design based on exit charts and union bounds transactions papers bandwidth efficient parallel concatenated turbo trellis coded modulation ttcm schemes were designed for communicating over uncorrelated rayleigh fading channels a symbol based union bound was derived for analysing the error floor of the proposed ttcm schemes a pair of in phase i and quadrature phase q interleavers were employed for interleaving the i and q components of the ttcm coded symbols in order to attain an increased diversity gain the decoding convergence of the iq ttcm schemes was analysed using symbol based extrinsic information transfer exit charts the best ttcm component codes were selected with the aid of both the symbolbased union bound and non binary exit charts for designing capacity approaching iq ttcm schemes in the context of 8 psk 16 qam 32 qam and 64 qam modulation schemes

multiple trellis coded frequency and phase modulation multiple trellis coded modulation of constant envelope frequency and phase modulated signal sets mtcm fpm is investigated for performance on the additive white gaussian noise awgn channel and on the one sided normal rayleigh and rician fading channels the nakagami m fading model is used as an alternative to the rician fading model to calculate the error probability upper bound for trellis coded schemes on the fading channel the likeliness and the disparity between the upper bounds to the error probability for the two fading models are discussed the design criteria for the one sided normal fading channel modeled by the nakagami m distribution are observed to be the same as those for the rayleigh fading channel for the mtcm fpm schemes it is demonstrated that the set partitioning designed to maximize symbol diversity optimum for fading channels is optimum for performance on the awgn channel as well the mtcm fpm schemes demonstrate improved performance over mtcm mpsk schemes and tcm fpm schemes on the awgn channel and the fading channel

chernoff bounds on pairwise error probabilities of space time codes we derive chernoff bounds on pairwise error probabilities of coherent and noncoherent space time signaling schemes first general chernoff bound expressions are derived for a correlated ricean fading channel and correlated additive gaussian noise then we specialize the obtained results to the cases of space time separable noise white noise and uncorrelated fading we derive approximate chernoff bounds for high and low signal to noise ratios snrs and propose optimal signaling schemes we also compute the optimal number of transmitter antennas for noncoherent signaling with unitary mutually orthogonal space time codes

multifrequency trellis coding with low delay for fading channels an l frequency trellis coding scheme designed for fading channels that provides diversity up to order l is described l frequency coding is advantageous over channel coding schemes that achieve implicit time diversity through trellis coding in conjunction with time interleaving because it requires negligible end to end delay the authors derive an upper bound for the probability of symbol error of the l frequency code based on this upper bound they then deduce the design criteria for optimum l frequency codes a numerical approximation to this upper bound and the design of a two state and two four state two frequency codes are presented through simulations it was found that relative to the traditional dual frequency diversity approach the two state and four state codes achieve 3 and 4 db coding gains respectively this energy efficiency gain can be translated into a spectral efficiency gain a brief discussion on the difference in code design techniques for the gaussian channel and the fading channel is also presented

coded diversity on block fading channels this paper considers coded diversity schemes over block fading rician channels using random coding techniques two random coding upper bounds on the error probability of block codes are derived a new bound and a simpler but looser bound assuming binary input distribution also a new lower bound for any block code is derived using the strong converse to channel coding theorem the lower bound shows that the new random coding upper bound is quite tight furthermore it is shown that the maximum achievable diversity order in a block fading channel with finite interleaving depends not only on the number of subchannels l but also on the code rate r and that the performance can only marginally be improved by increasing the block length of the code the random coding upper bound and the lower bound are shown to converge to the capacity outage for large channel block lengths n demonstrating that the capacity outage can be used for estimating the error probability of coded diversity schemes

approximately universal codes over slow fading channels performance of reliable communication over a coherent slow fading multiple input multiple output mimo channel at high signal to noise ratio snr is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains this paper studies the problem of designing codes that optimally tradeoff the diversity and multiplexing gains the main contribution is a precise characterization of codes that are universally tradeoff optimal i e they optimally tradeoff the diversity and multiplexing gains for every statistical characterization of the fading channel this characterization is referred to as approximate universality the approximation is in the connection between error probability and outage capacity with diversity and multiplexing gains respectively the characterization of approximate universality is then used to construct new coding schemes as well as to show optimality of several schemes proposed in the space time coding literature

an investigation concerning optimal design of solid elastic plates abstract we consider the problem of maximizing the integral stiffness of solid elastic plates described by thin plate theory assuming the material volume and plate domain to be given we use the plate thickness function as the design variable and take both maximum and minimum allowable thickness values into account on the basis of a convenient tensorial formulation of the problem where the governing equations are derived by variational analysis and constitute necessary conditions for stationarity we develop an efficient and quite general numerical algorithm by means of which a number of stationary solutions for rectangular and axisymmetric annular plates with various boundary conditions are obtained these numerical results enable us to investigate the optimization problem itself in terms of its major parameters particularly the maximum and minimum values specified for the plate thickness for problems associated with large ratios between these constraint values plate designs with significant integral stiffeners are obtained we find however that these designs are only local optima and that a global optimal plate thickness function does generally neither exist within the class of smooth functions nor within the class of smooth functions with a finite number of discontinuities in order to determine a global optimal solution associated with given thickness constraint values it is therefore necessary to change the optimal design formulation with implications for a number of similar two dimensional optimization problems our results offer valuable indications of the lines along which such changes should be performed

coherent and differentially coherent detections of orthogonally multiplexed orthogonal phase modulated signals the family of orthogonally multiplexed orthogonal phase modulations omopms is investigated in this paper both coherent and differentially coherent signaling formats are considered and compared with the recently reported orthogonally multiplexed orthogonal amplitude modulated omoam signals when constructed from the same basis set both omopm and omoam signals exhibit the identical power spectral density and thus the similar spectral performance characteristics based on the maximum likelihood principle coherent and differentially coherent detection algorithms are developed tight approximate upper bounds are derived and verified by simulation to evaluate the bit error probability characteristics of the maximum likelihood algorithms it is shown that both coherent and differentially coherent omopm can provide a great choice of power and spectral efficiencies ranging among the efficiencies achieved by the classical modulations based on the orthogonal multiplexing technique

space time codes for high data rate wireless communication performance criteria in the presence of channel estimation errors mobility and multiple paths space time coding is a bandwidth and power efficient method of communication over fading channels that realizes the benefits of multiple transmit antennas specific codes have been constructed using design criteria derived for quasi static flat rayleigh or rician fading where channel state information is available at the receiver it is evident that the practicality of space time codes will be greatly enhanced if the derived design criteria remain valid in the absence of perfect channel state information it is even more desirable that the design criteria not be unduly sensitive to frequency selectivity and to the doppler spread this paper presents a theoretical study of these issues beginning with the effect of channel estimation error here it is assumed that a channel estimator extracts fade coefficients at the receiver and for constellations with constant energy it is proved that in the absence of ideal channel state information the design criteria for space time codes is still valid the analysis also demonstrates that standard channel estimation techniques can be used in conjunction with space time codes provided that the number of transmit antennas is small we also derive the maximum likelihood detection metric in the presence of channel estimation errors next the effect of multiple paths on the performance of space time codes is studied for a slowly changing rayleigh channel it is proved that the presence of multiple paths does not decrease the diversity order guaranteed by the design criteria used to construct the space time codes similar results hold for rapid fading channels with or without multiple paths the conclusion is that the diversity order promised by space time coding is achieved under a variety of mobility conditions and environmental effects

a unified snr dependent analysis of space time codes in fading channels the pairwise error probability pep for multiple input multiple output mimo radio interfaces is investigated by means of a novel formulation based on compound matrices the proposed approach is suitable for any mimo system having average upper bounded pep written as det i gamma a zeta where a is a hermitian matrix zeta an integer number and gamma the signal to noise ratio snr that bound frequently results in mimo single and multicarrier transmissions it is shown that the minimization of the bounded pep should consider the whole set of nonzero compound matrices of a in particular the snr of interest marks the compound matrix that mainly drives the system performance both diversity advantage and coding gain are given as continuous functions of the variable gamma hence their asymptotic behaviors are taken as important case of studies the interaction effects between channel code and propagation environment are also discussed it is shown how the eigenvectors and eigenvalues of the autocorrelation channel matrix may be considered for code design it is also proved the maximization of the code rank is not always a necessary requirement for performance improvement being its optimal value fixed by the channel structure and snr of interest finally the analysis is applied to space time trellis coded transmissions over spatially correlated slow rayleigh fading channels

differential space time modulation space time coding and modulation exploit the presence of multiple transmit antennas to improve the performance on multipath radio channels thus far most work on space time coding has assumed that perfect channel estimates are available at the receiver in certain situations however it may be difficult or costly to estimate the channel accurately in which case it is natural to consider the design of modulation techniques that do not require channel estimates at the transmitter or receiver we propose a general approach to differential modulation for multiple transmit antennas based on group codes this approach ran be applied to any number of transmit and receive antennas and any signal constellation we also derive low complexity differential receivers error bounds and modulator design criteria which we use to construct optimal differential modulation schemes for two transmit antennas these schemes can be demodulated with or without channel estimates this permits the receiver to exploit channel estimates when they are available the performance degrades by approximately 3 db when estimates are not available

least weight design of perforated elastic plates ii abstract the paper investigates implications of some recent mathematical developments in the fields of shape optimization and relaxation of variational problems considering the least weight design of perforated elastic plates in either flexure or plane stress for a prescribed compliance it is shown that at low rib densities microstructures consisting of a combination of first and second order infinitesimal ribs is superior to those consisting of purely first order infinitesimal ribs moreover it is indicated that thin ribs of infinite length thickness ratio do not contribute significantly to the stiffness in a direction normal to their plane on the basis of this conclusion a simple specific cost function is derived and then it is used in the design of circular uniformly loaded perforated plates with zero value of poisson s ratio as a basis for comparison several intuitively selected topographies are optimized for the case of simply supported plates and in part ii of this study a variational analysis is used to obtain the optimal solutions for plates with simply supported clamped or loaded edges

effective masses for laplacians on periodic graphs abstract we consider laplacians on both periodic discrete and periodic metric equilateral graphs their spectrum consists of an absolutely continuous part which is a union of non degenerate spectral bands and flat bands i e eigenvalues of infinite multiplicity we estimate effective masses associated with the ends of each spectral band in terms of geometric parameters of the graphs moreover in the case of the bottom of the spectrum we determine two sided estimates on the effective mass in terms of geometric parameters of the graphs the proof is based on floquet theory factorization of fiber operators perturbation theory and the relation between effective masses for laplacians on discrete and metric graphs obtained in our paper

a new formulation of the problem of optimum reinforcement of reissner mindlin plates abstract a new formulation of the problem of computing the layout of reinforcement of reissner mindlin plates for minimum compliance is presented bending and transverse shear stiffness properties of plates with an arbitrary but finite number of local rib directions and widths are computed using standard homogenization techniques these properties are then expressed in terms of only four variables that fully describe the anisotropy of the plate the optimization problem is solved in two stages consisting of a local four dimensional maximization problem where a given amount of material is optimally allocated into an arbitrary number of fine scale stiffeners of different widths and orientations and a global one dimensional optimization problem where the optimum spatial layout of material is determined a discussion of implementation issues is included and an example is solved to illustrate the approach

spectral gaps and discrete magnetic laplacians abstract the aim of this article is to give a simple geometric condition that guarantees the existence of spectral gaps of the discrete laplacian on periodic graphs for proving this we analyse the discrete magnetic laplacian dml on the finite quotient and interpret the vector potential as a floquet parameter we develop a procedure of virtualising edges and vertices that produces matrices whose eigenvalues written in ascending order and counting multiplicities specify the bracketing intervals where the spectrum of the laplacian is localised we prove higuchi shirai s conjecture for z periodic trees and apply our technique in several examples like the polypropylene or the polyacetylene to show the existence of spectral gaps

rate 5 6 trellis coded 8 psk some new short constraint length codes are described for satellite channels which are constant envelope and which have spectral and energy efficiencies intermediate to other recent coded techniques namely r 2 3 coded 8 psk and r 3 4 coded 16 psk we use two intervals of 8 psk transmission to form a modulation base for r 5 6 trellis codes a particularly attractive design is an eight state code producing 6 2 db gain on the gaussian channel over uncoded 8 psk yet sacrificing only 16 percent in spectral efficiency

bandwidth efficient concatenated coding schemes for fading channels concatenated codes consisting of trellis inner codes and reed solomon outer codes are considered to achieve large coding gains with small bandwidth expansion in the presence of frequency nonselective slow rician fading both errors only and errors erasures decoding algorithms for outer codes are applied new upper bounds on bit error probability performance in the presence of fading are obtained and compared with simulation results for zero channel memory the effect of interleaving in eliminating channel memory is investigated the performance gains that are achieved by the coding scheme relative to the reference uncoded systems are illustrated via some examples

homogenizing stiffnesses of plates with periodic structure abstract the paper develops the method of homogenization of elastic properties of reissner hencky plates with periodic structure the method is based on the new scaling which for each e preserves the shape of the three dimensional periodicity cell of the original plate structure the homogenization formulae obtained in this manner turn out to coincide with those found previously by the hencky reissner approximation of the three dimensional caillerie kohn vogelius local problems the proposed method has made it possible to derive a new closed form formula for evaluating the effective torsional stiffness of plates with one family of stiffeners the formulae for remaining stiffnesses have been known contrary to the hitherto used formula of duvaut and to the one followed from a direct homogenization of the reissner hencky equations the derived new formula is sensitive to the thickness to period ratio and hence much more realistic the formulae used previously turn out to be the upper and lower bounds for the derived expression

diversity codes for differential phase modulation in a correlated rayleigh fading channel this paper proposes a simple diversity scheme that makes use of nonlinear block coding symbol interleaving and differential phase modulation the resultant signaling mechanism merits intrinsic time diversity within each codeword which is resistant to correlated fading the maximum likelihood noncoherent receiver which operates over correlated rayleigh fading is developed exact and approximate upper bounds are derived to assess the codeword error probability characteristics of the proposed system

trellis coded modulation with multidimensional constellations trellis coded modulation schemes using four eight or 16 dimensional constellations have a number of potential advantages over the usual two dimensional schemes a smaller constituent two dimensional constellation easier tolerance to phase ambiguities and a better trade off between complexity and coding gain a number of such schemes are presented and evaluated starting with a variety of multidimensional lattices we show how to select multidimensional constellations how to partition them into subsets how to construct trellis codes using those subsets and how to map hits to constellation points simplifications of the viterbi decoding algorithm are presented we conclude that there are multidimensional trellis coded modulation schemes that perform better for the same complexity than do two dimensional schemes

the use of interleaving for reducing noisy reference loss in trellis coded modulation systems the use of interleaving deinterleaving in trellis coded modulation systems to reduce the snr loss due to imperfect carrier demodulation references is demonstrated both the discrete carrier phase locked loop and the suppressed carrier costas loop cases are considered and the differences between the two are clearly demonstrated by numerical results the special case of convolutional codes is also treated and illustrated with an example of practical interest

on the asymptotic performance of bit wise decoders for coded modulation two decoder structures for coded modulation over the gaussian channel are studied 1 the maximum likelihood symbol wise decoder and 2 the suboptimal bit wise decoder based on the bit interleaved coded modulation paradigm we consider a 16 ary quadrature amplitude constellation labeled with a gray labeling it is shown that the asymptotic loss in terms of pairwise error probability for any two codewords caused by the bit wise decoder is bounded by 1 25 db the analysis also shows that the asymptotic loss is zero for a wide range of linear codes including all rate 1 2 convolutional codes

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

constellation design for trellis coded unitary space time modulation systems we consider the problem of creating signal constellations for trellis coded unitary space time communication links where neither the transmitter nor the receiver knows the fading gains of the channel our study includes constellation design techniques for trellis coded schemes with and without parallel paths which allows us to find a tradeoff between low complexity and high performance we present a new formulation of the constellation design problem for trellis coded unitary space time modulation tcustm schemes the two key differences in our approach against those of other authors are that we not only combine the constellation design and mapping by set partitioning into one step but we also use directly the chernoff bound of the pairwise error probability as a design metric by novelly employing a theorem for the clarke subdifferential of the sum of the k largest singular values of the unitary matrix we also present a numerical optimization procedure for finding signal constellations resulting in high performance communications systems to demonstrate the advantages of our new design method we report the best constellations found for tcustm systems simulation results show that these constellations achieve a 1 db coding gain at a bit error rate of 10 4 against usually used constellations

a new model for thin plates with rapidly varying thickness abstract we study the bending of a thin plate with rapidly varying thickness for example one with rib like stiffeners or perforated by small holes we obtain a fourth order equation for the midplanc displacement using an asymptotic analysis based on three dimensional linear elasticity the coefficients of this equation represent the constitutive law relating bending moments to midplane curvature they are explicitly determined by the plate geometry our analysis distinguishes between three different cases in which the thickness varies on a length scale longer than on the order of or shorter than the mean thickness

trellis coded multidimensional phase modulation a 2l dimensional multiple phase shift keyed l mpsk signal set is obtained by forming the cartesian product of l two dimensional mpsk signal sets a systematic approach to partitioning l mpsk signal sets that is based on block coding is used an encoder system approach is developed it incorporates the design of a differential precoder a systematic convolutional encoder and a signal set mapper trellis coded l 4psk l 8psk and l 16psk modulation schemes are found for 1

the design of trellis coded mpsk for fading channels performance criteria it has been well established that the appropriate criterion for optimum trellis coded modulation design on the additive white gaussian noise channel is maximization of the free euclidean distance it is shown that when the trellis coded modulation is used on a rician fading channel with interleaving deinterleaving the design of the code of optimum performance is guided by other factors in particular the length of the shortest error event path and the product of branch distances possibly normalized by the euclidean distance of the path along the path although maximum free distance d sub free is still an important consideration it plays a less significant role the more severe the fading is on the channel these considerations lead to the definition of a new distance measure of optimization of trellis codes transmitted over rician fading channels if no interleaving deinterleaving is used then once again the design of the trellis code is guided by maximizing d sub free

cutoff rates for coordinate interleaved qam over rayleigh fading channels cutoff rates for perfect coordinate interleaving over flat rayleigh fading channels are computed for some representative two dimensional 2 d and four dimensional 4 d quadrature amplitude modulation qam schemes and compared to the standard symbol interleaved approaches it is shown that for optimized coordinate interleaving i e using optimum rotation parameters that maximize the cutoff rate for a given signal to noise ratio snr coding gains can be achieved vis a vis symbol interleaving that increases with the dimensionality of the signal constellation perfect coherent detection as well as perfect channel state information are assumed

the cutoff rate of time correlated fading channels the cutoff rate of rician and rayleigh channels characterized by time correlated fading is derived for m ary phase shift keying mpsk modulation it is useful for situations where perfect interleaving cannot be achieved it indicates the practical achievable information rate of the channel when coding is employed it is used to determine the potential coding gains of coded modulation over the correlated fading channel

cantor and band spectra for periodic quantum graphs with magnetic fields we provide an exhaustive spectral analysis of the two dimensional periodic square graph lattice with a magnetic field we show that the spectrum consists of the dirichlet eigenvalues of the edges and of the preimage of the spectrum of a certain discrete operator under the discriminant lyapunov function of a suitable kronig penney hamiltonian in particular between any two dirichlet eigenvalues the spectrum is a cantor set for an irrational flux and is absolutely continuous and has a band structure for a rational flux the dirichlet eigenvalues can be isolated or embedded subject to the choice of parameters conditions for both possibilities are given we show that generically there are infinitely many gaps in the spectrum and the bethe sommerfeld conjecture fails in this case

construction of new mpsk trellis codes for fading channels in this paper a new methodology for design of mpsk trellis codes on fading channels is proposed the proposed design criteria based on effective code length the minimum product distance and the minimum euclidean distance are used to construct new 8 psk and 16 psk trellis codes with improved bit error rate performance on fading channels the code performance is evaluated analytically and by monte carlo simulation the results show that the proposed codes achieve significant improvements relative to the best known codes

analysis of multidimensional trellis coded mpsk in rice lognormal fading channels the paper addresses the analysis of multidimensional trellis coded m ary phase shift keying mpsk modulation over a rice lognormal fading channel model applicable to a variety of environments and to both terrestrial and satellite mobile communications bounds to the bit error probability are derived and applied to the analysis of a few selected trellis coded modulation tcm schemes the results confirmed by simulation show that on the rice channel there exists a threshold in bit energy to noise density ratio above which the effective code length is the dominant parameter while the free distance is dominating below however the influence of both parameters is mitigated when shadowing is present

on the design and selection of convolutional codes for an uninterleaved bursty rician channel this article focuses on code design and code selection rules under power and decoding delay constraints for an antipodal bpsk modulated and convolutionally encoded communication system the system operates over a slowly fading awgn channel described by the block fading model we emphasize perfect coherent detection with maximum likelihood decoding assuming ideal channel information the instantaneous fading values the dominant design criterion in this scenario is the code diversity level in terms of blocks while the standard hamming distance plays a secondary role a code design procedure based on maximum distance separable mds cyclic block codes is presented along with a code search algorithm the performance results of selected codes are assessed via simulation and compared to those achieved by reed solomon codes with erasure and error decoding

analysis of the error performance of trellis coded modulations in rayleigh fading channels this work presents an exact expression for the pairwise error event probability of trellis coded modulation tcm transmitted over rayleigh fading channels it includes phase shift keying psk and multilevel quadrature amplitude modulation qam codes as well as coherent and partially coherent e g differential pilot tone etc detection due to the form of the exact pairwise error event probabilities this calculation technique cannot be used with the transfer function technique to obtain an upper union bound on the overall bit error probability for this reason the authors estimate the bit error probability by considering only a small number of short error events through simulations they found that the estimation is usually very accurate at high signal to noise ratios but not as accurate at lower signal to noise ratios they study several coded modulation schemes this way among the results are the fact that tcm provides significant improvement in the error floor when detected differentially and an asymmetry in the pairwise error event probability for 16 qam

reinforced mindlin plates with extremal stiffness for a prescribed area fraction of stiffeners we characterize the set of stiffener reinforced mindlin plates with extremal overall stiffness the method rests upon the derivation of optimal bounds of the hashin shtrikman type our method is distinct from the usual hashin shtrikman approach we make use of the underlying variational structure behind the hashin shtrikman method to show that the use of a comparison material is redundant we do this by proceeding directly and express the equilibrium equations in terms of positive definite integral operators the positivity of the operators is used to obtain a new hilbert space variational principle for the effective stiffness the associated bounds are shown to be realized by effective rigidities associated with hierarchical laminar arrangements of stiffeners

sliding regimes and anisotropy in optimal design of vibrating axisymmetric plates abstract this paper deals with optimal design of solid elastic axisymmetric plates performing free transverse vibrations it is the objective to determine the plate thickness distribution from the condition that the plate volume is minimized for a given value of the fundamental natural frequency or for a given higher order natural frequency that corresponds to a vibration mode with a prescribed number of nodal diameters it is found that the weierstrass necessary condition for optimality is generally not satisfied for a traditional formulation of this problem and that the optimal design is characterized by a sliding regime of control where the plate thickness exhibits an infinite number of discontinuities as a system of infinitely thin circumferential stiffeners are formed on the optimal axisymmetric plate this inherent anisotropy of the optimal design is taken into account in a regularization of the initial optimization problem by establishing the tensorial character of the plate bending rigidity and using the concentration of thin circumferential stiffeners as a new design variable control it is shown that the new formulation of the problem can be solved numerically and examples of optimal designs are presented in the paper

algebraic tools to build modulation schemes for fading channels a unified framework is presented in order to build lattice constellations matched to both the rayleigh fading channel and the gaussian channel the method encompasses the situations where the interleaving is done on the real components or on two dimensional signals in the latter case a simple construction of lattices congruent to the densest binary lattices with respect to the euclidean distance is proposed it generalizes in a sense to be clarified later the structural construction proposed by forney 1991 these constellations are next combined with coset codes the partitioning rules and the gain formula are similar to those used for the gaussian channel

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

adaptive trellis coded multiple phase shift keying for rayleigh fading channels an adaptive scheme for trellis coded modulation of mpsk signals called adaptive trellis coded multiple phaseshift keying atcmpsk is proposed for slowly rayleigh fading channels the adaptive scheme employs a slightly modified rate 1 2 convolutional encoder and the corresponding viterbi decoder to realize a family of codes of different rates which are employed according to channel conditions during poor channel conditions trellis coded qpsk tcqpsk together with repetition schemes are employed as channel conditions improve higher rate schemes such as trellis coded 16 psk are used an interleaving deinterleaving method suitable for the adaptive scheme is proposed theoretical bounds for the error performance and an exact expression for the throughput of the proposed adaptive scheme are derived and are compared against simulation results simulations have been performed to measure the performance of the scheme for different parameters and some nonideal conditions it is shown that atcmpsk results in considerable improvement in bit error rate ber performance of mpsk signals under ideal conditions gains in the range of 3 20 db are achieved over conventional fixed rate pragmatic trellis coded schemes

hybrid trellis coded 8 4 psk modulation systems by using codes of rate 2 3 followed by 8 psk modulation a gain of 3 6 db is obtained over uncoded 4 psk for an ideal coherent transmission on the white gaussian channel in the presence of carrier phase offset it has been shown that trellis coded 8 psk systems are more sensitive than uncoded 4 psk a more robust performance can be achieved by using rate 2 3 trellis coded 8 psk signals and 4 psk signals in a time varying manner only the mapper from the output of the binary convolutional code to the signal point number to be transmitted has to be periodically time varying in its simplest form trellis coded 8 psk and 4 psk signals alternate in time an examination has also been made of systems where the mixture of 8 psk and 4 psk signals varies with a short periodic sequence of time varying mapping rules the distance spectra and error probability are evaluated with and without phase offset simulation results of bit error rate ber and performance of the recovery loop s curve are presented it is concluded that systems which are more robust against jitter can be achieved by means of time varying hybrid trellis coded 8 4 psk systems

multilevel trellis mpsk modulation codes for the rayleigh fading channel the multilevel coding technique is used for constructing multilevel trellis m ary phase shift keying mpsk modulation codes for the rayleigh fading channel in the construction of a code all the factors which affect the code performance and its decoding complexity are considered the error performance of some of these codes based on both one stage optimum decoding and multistage suboptimum decoding has been simulated the simulation results show that these codes achieve good error performance with small decoding complexity

a modified design of trellis coded mpsk for the fading channel it is shown that the classical additive white gaussian noise awgn channel design can be retained for the fading channel with any degree of fading if carried out with the appropriate signal set size m m sub min the size of the signal set m sub min is shown to depend upon the number of parallel transitions between a given pair of states and the throughput rate in the proposed multiple trellis coded modulation mtcm scheme with a modified design mtcm md the output bits from a rate m m 1 trellis encoder are assigned multiple signals from an m sub min psk signal set compared to the mtcm with set partitioning proposed for the fading channel spf design the mtcm md scheme provides the same signal diversity and the same or increased values of the branch distance product and always leads to increased value of d sup 2 free as a result the performance is always improved on the rician fading channel due to the increased d sup 2 free and is improved on any fading channel when an increase in branch distance produce p takes place when compared to the mtcm with the set partitioning optimum for the awgn channel spa design the mtcm md scheme under certain conditions provides the same value of d sup 2 free as the mtcm spa design and is then asymptotically optimum for both the awgn channel and the fading channels

on non smoothness in optimal design of solid elastic plates abstract in the present paper minimum compliance design problems of thin solid elastic plates are discussed we follow up indications provided by numerical results obtained in a recent paper 1 and propose a new plate model where a uniform plate is equipped with an infinite number of infinitely thin integral stiffeners on the basis of this new plate model numerical and analytical investigations of a new formulation of the minimum compliance design problem are carried out it is demonstrated that the new formulation is under certain conditions superior to the corresponding traditional formulation for determining a possible global optimal solution for solid plates since both the new formulation and the traditional formulation are based on classical thin plate theory the superiority of the new plate model over the corresponding smooth one directly implies that optimal thickness distributions for thin solid elastic plates are generally not smooth functions but functions with an infinite number of discontinuities

error performance of interleaved trellis coded psk modulations in correlated rayleigh fading channels the authors derive an exact and easily computed expression for the pairwise error event probability of interleaved coded psk modulations transmitted over channels with correlated rayleigh flat fading and additive white gaussian noise both coherent and differential detection are considered in the case of coded dpsk it is found that full interleaving does not necessarily provide the best error performance especially when the fading is relatively fast and when the autocorrelation function of the channel fading process exhibits an oscillating behavior for coherent detection or for differential detection in channels with relatively slow fading increasing the interleaving depth always improves the error performance in these cases an interleaving depth equivalent to one fifth to one quarter the duration of a fade cycle is almost as good as full interleaving

multilevel coded cpfsk systems for awgn and fading channels in this paper we introduce multilevel coded continuous phase frequency shift keying cpfsk systems for both additive white gaussian noise and fading channels based on multilevel coding and multistage decoding techniques these schemes are designed under the constraint m spl ges 2p for m ary cpfsk with modulation index j p in order to maintain the phase continuity property after multilevel coding we use some specific set partitioning rules we construct examples to show that the proposed systems outperform the corresponding conventional one level schemes for the fading case we consider an ideal fading channel where adjacent fading symbols are assumed to be independent and a correlated fading channel where bit interleavers are needed at each coding level the computer simulation results show that the proposed systems have bit error performance and decoder complexity advantages over the corresponding reference codes taken from the literature it is also shown that there is only a slight degradation on the bit error performance for correlated fading compared to the ideal fading case

coded phase frequency modulation channel coding combined with expanded signal sets has been shown 1 to improve error performance over uncoded modulation without expanding the bandwidth of the transmitted signals in this paper new coded modulation formats defined over an expanded set of signals varying both in phase and frequency are presented the new schemes combine fsk and psk modulation and make use of trellis coding and viterbi decoding to improve error performance over uncoded modulation the free euclidean distance is calculated for several classes of codes and upper bounds and simulation results are also presented for some simple codes the spectral characteristics of the proposed coded modulation formats are evaluated and compared to conventional two dimensional modulation formats differential encoding and various extensions of the basic scheme are also discussed

universal space time trellis codes this article gives practical examples of space time trellis codes performing as predicted by root and varaiya s 1968 compound channel theorem specifically 32 state and 64 state 2 spl times 2 space time trellis codes are presented that provide a bit error rate ber of 10 sup 5 on all 2 spl times 2 matrix channels with an excess mutual information mi within 8 of the excess mi required by standard trellis codes of the same complexity operating only in additive white gaussian noise awgn not surprisingly the universal space time trellis coded modulations st tcms provide average bit and frame error rates in quasi static rayleigh fading qrf that are comparable to those achieved by st tcms designed specifically for qrf as well as standard tcms followed by the alamouti 1998 space time block code however all of these other schemes require more excess mi in the worst case and some have a significantly wider variation in the required excess mi the article also compares the universal and quasi static rayleigh fading design approaches analytically and bounds the worst case distance of a trellis code on a 2 spl times 2 channel using the distances of the code on singular and unitary channels this bound is extended to the more general n sub t spl times n sub r scenario

exact calculation of the union bound on performance of trellis coded modulation in fading channels this paper presents a method for the exact calculation of the union bound on the error performance of trellis coded modulation tcm in fading channels previous analyses have approximated the error expression to allow the use of the transfer function or restricted their attention to the most common error events or both in contrast we combine the transfer function which counts all error events with exact calculation of event probabilities and produce an exact expression for the union bound although computationally intensive the technique produces the tightest bound yet published in addition it is very general and is applicable to coherent differential and pilot based detection and to phase shift keying psk and quadrature amplitude modulation qam types of constellations

noncoherent sequential acquisition of pn sequences for ds ss communications with without channel fading studies sequential acquisition schemes of m sequences based on the sequential probability ratio test sprt and a truncated sprt tsprt with noncoherent demodulation most reported results on sequential acquisition schemes assume that independent samples are available for the decision process the assumption of independent and identically distributed i i d samples requires the integrator in the receiver to be reset periodically this introduces loss in the effective signal to noise ratio degrading the performance in the present paper on the contrary the authors two sequential schemes use continuous integration it can be shown that the likelihood ratio is monotonic consequently the tests can be easily implemented in realtime methods are proposed for designing the decision thresholds to achieve the desired false alarm and miss probabilities performances of the proposed schemes are obtained and they suggest that the tsprt is more desirable the effect of slowly varying channel fading is also investigated results show that fading does not affect the false alarm probabilities but it can drastically reduce the probability of detecting the alignment of the two pn sequences especially when the fading is severe

error bounds for trellis coded mpsk on a fading mobile satellite channel analytical performance bounds are presented for trellis coded mpsk transmitted over a satellite based land mobile channel upper bounds are evaluated using the well known transfer function bounding technique and lower bounds are achieved through knowledge of exact pairwise error probabilities in order to analyze practical trellis codes four or more states the uniform properties displayed by a certain class of trellis codes are exploited enabling the encoder transfer function to be obtained from a modified state transition diagram having no more states than the encoder itself monte carlo simulation results are presented in confirmation of all performance bounds and indicate a general weakness in the transfer function upper bounds a new asymptotically tight upper bound is derived based on a simple modification to the standard transfer function bound and results are presented for the four and eight state trellis codes in rician and rayleigh fading

on occurrence of spectral edges for periodic operators inside the brillouin zone the paper discusses the following frequently arising question on the spectral structure of periodic operators of mathematical physics e g schrodinger maxwell waveguide operators etc is it true that one can obtain the correct spectrum by using the values of the quasimomentum running over the boundary of the reduced brillouin zone only rather than the whole zone or do the edges of the spectrum occur necessarily at the set of corner high symmetry points this is known to be true in 1d while no apparent reasons exist for this to be happening in higher dimensions in many practical cases though this appears to be correct which sometimes leads to the claims that this is always true there seems to be no definite answer in the literature and one encounters different opinions about this problem in the community in this paper starting with simple discrete graph operators we construct a variety of convincing multiply periodic examples showing that the spectral edges might occur deeply inside the brillouin zone on the other hand it is also shown that in a generic case the situation of spectral edges appearing at high symmetry points is stable under small perturbations this explains to some degree why in many maybe even most practical cases the statement still holds