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 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

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

nd convolutional codes i performance analysis a noncoherent coded system which incorporates convolutional codes in conjunction of multiple symbol noncoherent detection is presented in this two part paper where part i focuses on the performance analysis of the system and part ii deals with the structural properties of the underlying convolutional codes these convolutional codes are referred to as nd convolutional codes it is shown that nd convolutional codes provide a general framework for various noncoherent coding systems including differential systems two models of the carrier phase are examined and the relationships between them is established for the first one the carrier phase remains constant for l channels signals whereas for the second one it unvaries throughout the transmission period the regular structure of nd codes facilitates the evaluation of a simple upper bound on the pairwise and bit error probabilities as well as a simple expression for the generalized cutoff rate the exponential rate of the error probability which is the single parameter governing the error performance at large signal to noise ratios is identified via large deviations techniques this parameter leads to the interesting conclusion that increasing l does not necessarily monotonically improve the error performance of the noncoherent system the same conclusion is reached by examining upper bounds and computer simulation results of several interesting examples these examples also reveal that optimal codes for coherent detection are not necessarily optimal for noncoherent detection and a search for good codes some of which are tabulated in part ii of the paper is required

local inequalities for plurisubharmonic functions the main objective of this paper is to prove a new inequality for plurisubharmonic functions estimating their supremum over a ball by their supremum over a measurable subset of the ball we apply this result to study local properties of polynomial algebraic and analytic functions the paper has much in common with an earlier paper br of the author

algebraic families of analytic functions i the aim of this paper is to consider analytic functions arising in connection with algebraic differential equations from the following point of view taylor coefficients of such functions usually turn out to be polynomials or rational functions in the parameters of the problem following pioneering work of bautin 1 we relate analytic properties of the functions considered with algebraic properties of various ideals generated by their taylor coefficients bautin s approach has been successfully applied to the study of the poincare mapping of the planar polynomial systems in 4 9 27 and to the study of the period function of polynomial hamiltonian systems in 5 6 12 13 however the study of the poincare mapping of the polynomial differential equations closely related to the second part of hilbert 16th problem is probably the most difficult among a wide variety of problems to which bautin s approach can be applied in particular counting zeroes of solutions of algebraic differential equations is an important and mostly open problem to our best knowledge the first application of bautin s method to this problem was given in 26 in the present paper we systematically apply this method in the following two situations to algebraic functions and to solutions of the first order polynomial differential equations higher order linear equations are also considered in section 5 article no de963250

phase noise effects on m ary psk trellis codes the performance of m ary phase shift keying psk coded systems in the presence of added white gaussian noise awgn with a noisy carrier reference in the receiver is examined the results are obtained by combining the chernoff bound technique with the generating function approach the bit error probability analysis is carried out for 8 and 16 psk with code rates of 2 3 and 3 4 respectively the numerical results obtained demonstrate the error performance degradation due to a tikhonov phase noise process with parameter alpha

counting real zeros of analytic functions satisfying linear ordinary differential equations abstract we suggest an explicit procedure to establish upper bounds for the number of real zeros of analytic functions satisfying linear ordinary differential equations with meromorphic coefficients if the equation formula has no singular points in a small neighborhooduof a real segmentk all the coefficientsaj t have absolute value aonuanda0 t 1 then any solution of this equation may have no more than a zeros onk where u k is a geometric constant depending only onkandu if the principal coefficienta0 t is nonconstant but its modulus is at leasta 0 somewhere onk then the number of real zeros onkof any solution analytic inu does not exceed a a with some u k

small amplitude limit cycles and the distribution of zeros of families of analytic functions we estimate the expected number of limit cycles of a planar polynomial vector field situated in a neighbourhood of the origin provided that the field in a larger neighbourhood is close enough to a linear center our main tool is a distributional inequality for the number of zeros of some families of univariate holomorphic functions depending analytically on a parameter we obtain this inequality by methods of pluripotential theory this inequality also implies versions of a strong law of large numbers and the central limit theorem for a probabilistic scheme associated with the distribution of zeros

on the capacity of the wiener phase noise channel bounds and capacity achieving distributions in this paper the capacity of the additive white gaussian noise awgn channel affected by time varying wiener phase noise is investigated tight upper and lower bounds on the capacity of this channel are developed the upper bound is obtained by using the duality approach and by considering a specific distribution over the output of the channel in order to lower bound the capacity first a family of capacity achieving input distributions is found by solving a functional optimization of the channel mutual information then lower bounds on the capacity are obtained by drawing samples from the proposed distributions through monte carlo simulations the proposed capacity achieving input distributions are circularly symmetric non gaussian and the input amplitudes are correlated over time the evaluated capacity bounds are tight for a wide range of signal to noise ratio snr values and thus they can be used to quantify the capacity specifically the bounds follow the well known awgn capacity curve at low snr while at high snr they coincide with the high snr capacity result available in the literature for the phase noise channel

tracking control for boundary controlled parabolic pdes with varying parameters combining backstepping and differential flatness the combination of backstepping based state feedback control and flatness based trajectory planning and feedforward control is considered for the design of an exponentially stabilizing tracking controller for a linear diffusion convection reaction system with spatially and temporally varying parameters and nonlinear boundary input for this in a first step the backstepping transformation is utilized to determine a state feedback controller which transforms the original distributed parameter system into an appropriately chosen exponentially stable distributed parameter target system of a significantly simpler structure in a second step the flatness property of the target system is exploited in order to determine the feedforward controller which allows us to realize the tracking of suitably prescribed trajectories for the system output this results in a systematic procedure for the design of an exponentially stabilizing tracking controller for the considered general linear diffusion convection reaction system with varying parameters whose applicability and tracking performance is evaluated in simulation studies

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

motion planning and open loop control design for linear distributed parameter systems with lumped controls motion planning and open loop boundary control schemes for linear spatially one dimensional distributed parameter systems with lumped control are discussed using mikusinski s operational calculus the models are formulated as ordinary operational boundary value problems their solutions are parameterized by introducing a so called basic variable as an appropriate free parameter particular classes of models considered lead to series representations involving derivatives of the basic variable of arbitrary order or to convolution operators which can be interpreted as distributed delays and advances examples of bending motions on a ring shaped plate and a heat exchanger illustrate the results

output feedback control of general linear heterodirectional hyperbolic pde ode systems with spatially varying coefficients this paper presents a backstepping solution for the output feedback control of general linear heterodirectional hyperbolic pde ode systems with spatially varying coefficients thereby the

control of 2 2 linear hyperbolic systems backstepping based trajectory generation and pi based tracking abstract we consider the problems of trajectory generation and tracking for general 2 2 systems of first order linear hyperbolic pdes with anti collocated boundary input and output we solve the trajectory generation problem via backstepping the reference input which generates the desired output incorporates integral operators acting on advanced and delayed versions of the reference output with kernels which were derived by vazquez krstic and coron for the backstepping stabilization of 2 2 linear hyperbolic systems we apply our approach to a wave pde with indefinite in domain and boundary damping for tracking the desired trajectory we employ a pi control law on the tracking error of the output we prove exponential stability of the closed loop system under the proposed pi control law when the parameters of the plant and the controller satisfy certain conditions by constructing a novel non diagonal lyapunov functional we demonstrate that the proposed pi control law compensates in the output the effect of in domain and boundary disturbances we illustrate our results with numerical examples

m ary phase coding for the noncoherent awgn channel this work considers coded m ary phase shift keying mpsk schemes with noncoherent detection a class of block codes called module phase codes is described the algebraic framework used for describing these codes relies on elements from module theory which are discussed along with a method for constructing such codes for noncoherent detection it is shown that differential encoding may be viewed as a specific code from a particular class of module phase codes two classes of codes that achieve significant coding gain with respect to coherent detection of uncoded mpsk are presented in the first class of module phase codes the coding gain is achieved at the expense of bandwidth expansion in the second class however the coding gain is achieved at the expense of signal constellation expansion without expanding bandwidth finally an integrated demodulation decoding technique based on a modification of information set decoding is presented it is shown that this reduced complexity suboptimal decoding strategy performs nearly as well as maximum likelihood decoding

design of turbo coded modulation for the awgn channel with tikhonov phase error we design 1 b symbol hz parallel concatenated turbo coded modulation pctcm for the additive white gaussian noise awgn channel with tikhonov phase error constituent recursive convolutional codes are optimized so that the turbo codes have low error floors and low convergence thresholds the pairwise error probability based on the maximum likelihood decoding metric is used to select codes with low error floors we also present a gaussian approximation method that accurately predicts convergence thresholds for pctcm codes on the awgn tikhonov channel simulation results show that the selected codes perform within 0 6 db of constellation constrained capacity and have no detectable error floor down to bit error rates of 10 sup 6

the phase of a vector perturbed by gaussian noise and differentially coherent receivers some results are presented regarding the asymptotic distribution of the phase of a vector perturbed by gaussian noise it is shown that for large signal to noise ratio the asymptotic distribution of the phase is of the tikhonov type this framework is then used for the synthesis of differentially coherent receiver structures one for m ary phase shift keying mpsk and the other for minimum shift keying msk the first structure bridges the performance gap between coherent and differentially coherent demodulation of mpsk the msk receiver uses matched filtering with differential demodulation

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

bernstein inequalities and applications to analytic geometry and differential equations we introduce new methods of complex analysis inequalities of bernstein type to study projections of analytic sets these techniques are applied to problems of bifurcations of periodic orbits of differential equations such as the local hilbert s 16th problem

symbol insertion a low complexity joint peak power reduction and forward error correction for single carrier systems in this paper we present a new modulation code named symbol insertion si that simultaneously achieves both peak to average power ratio papr reduction and forward error correction for pulse shaped single carrier systems in a low complexity manner based on the fact that papr highly depends on the successive phase patterns of discrete complex symbols the proposed code controls phase shifts by inserting a redundant symbol between consecutive information bearing symbols at the receiver by viewing the inserted symbols as parities we exploit them for error correction we show that when the si is used as an inner code of serially concatenated codes its error rate performance is close to those of conventional capacity approaching codes the proposed system thus becomes favorable if the amount of papr reduction is taken into account furthermore the si with a rotationally invariant insertion scheme can accommodate itself to noncoherent detection

controllability of the 1d schrodinger equation using flatness we derive in a direct way the exact controllability of the 1d schrodinger equation with dirichlet boundary control we use the so called flatness approach which consists in parametrizing the solution and the control by the derivatives of a flat output this provides an explicit and very regular control achieving the exact controllability in the energy space

trellis coded mpsk with reference phase errors with trellis coded mpsk schemes reference phase errors have a major impact on the system performance this paper analyzes the interrelation among the coded modulation format the reference phase tracker and the carrier phase noise a tight upper bound to the error probability of a maximum likelihood decoder is introduced this bound reveals eight new distance type functions which along with the wellknown minimum euclidean distance characterize the coded modulation scheme relationships between the new distance type functions and the various system parameters as well as the irreducible probability of error are pointed out numerical results for uncoded qpsk and three ungerboeck encoded 8 psk schemes showy that excessive smoothing of the reference phase in presence of carder phase noise can degrade the performance of coded 8 psk modulation considerably

graphs of zeros of analytic families let f f be a family of holomorphic functions in a domain d c depending holomorphically on u c we study the distribution of zeros of f in a subdomain r d whose boundary is a closed non singular analytic curve as an application we obtain several results about distributions of zeros of families of generalized exponential polynomials and displacement maps related to certain ode s

spectrally efficient noncoherent communication this paper considers noncoherent communication over a frequency nonselective channel in which the time varying channel gain is unknown a priori but is approximately constant over a coherence interval unless the coherence interval is large coherent communication which requires explicit channel estimation and tracking prior to detection incurs training overhead which may be excessive especially for multiple antenna communication in contrast noncoherent detection may be viewed as a generalized likelihood ratio test glrt which jointly estimates the channel and the data and hence does not require separate training the main results in this paper are as follows 1 we develop a signal space criterion for signal and code design for noncoherent communication in terms of the distances of signal points from the decision boundaries 2 the noncoherent metric thus obtained is used to guide the design of signals for noncoherent communication that are based on amplitude phase constellations these are significantly more efficient than conventional differential phase shift keying psk especially at high signal to noise ratio snr also known results on the high snr performance of multiple symbol demodulation of differential psk are easily inferred from the noncoherent metric 3 the glrt interpretation is used to obtain near optimal low complexity implementations of noncoherent block demodulation in particular this gives an implementation of multiple symbol demodulation of differential psk which is of linear complexity in the block length and whose degradation from the exact exponential complexity implementation can be made as small as desired

exact controllability stabilization and perturbations for distributed systems exact controllability is studied for distributed systems of hyperbolic type or for petrowsky systems like plate equations the control is a boundary control or a local distributed control exact controllability consists in trying to drive the system to rest in a given finite time the solution of the problems depends on the function spaces where the initial data are taken and also depends on the function space where the control can be chosen a systematic method named hum for hilbert uniqueness method is introduced as the terminology indicates it is based on uniqueness results classical or new and on hilbert spaces constructed in infinitely many ways by using uniqueness a number of applications are indicated having a general method for exact controllability implies having a general method for stabilization this leads to new and complicated nonlinear riccati s type pdes to be compared with direct methods when available in the last part of the paper we consider how all this behaves fo

pilot symbol assisted coded transmission over the block noncoherent awgn channel in this paper pilot symbol assisted transmission in conjunction with high performance coding over the block independent noncoherent additive white gaussian noise channel is investigated several approximate iterative receivers are proposed which either perform carrier phase estimation separately from detection or joint carrier phase estimation decoding in an iterative fashion the performance of the proposed receivers is analyzed using density evolution the power allocation to the pilot symbol is quantified and it is shown that an optimal allocation scheme exists that minimizes the overall information bit signal to noise ratio required for error free communication this optimal power allocation which could be utilized in code design is found to be sensitive to the channel coherence interval as well as to the particular receiver used in addition a simple upper bound on the performance of any receiver that performs joint iterative carrier phase estimation and detection is derived the obtained results are compared with the simulated performance of the proposed receivers

controllability of networks of spatially one dimensional second order pdes an algebraic approach we discuss controllability of systems that are initially given by boundary coupled pdes of second order these systems may be described by modules over particular rings of distributions and ultradistributions with compact support arising from the solution of the cauchy problem of the pde under consideration with data on the time axis we show that those rings are bezout domains this property is utilized in order to derive algebraic and trajectory related controllability results

on local behavior of holomorphic functions along complex submanifolds of ℂ n in this paper we establish some general results on local behavior of holomorphic functions along complex submanifolds of n as a corollary we present multi dimensional generalizations of an important result of coman and poletsky on bernstein type inequalities on transcendental curves in 2

constellation optimization in the presence of strong phase noise in this paper we address the problem of optimizing signal constellations for strong phase noise the problem is investigated by considering three optimization formulations which provide an analytical framework for constellation design in the first formulation we seek to design constellations that minimize the symbol error probability sep for an approximate ml detector in the presence of phase noise in the second formulation we optimize constellations in terms of mutual information mi for the effective discrete channel consisting of phase noise additive white gaussian noise and the approximate ml detector to this end we derive the mi of this discrete channel finally we optimize constellations in terms of the mi for the phase noise channel we give two analytical characterizations of the mi of this channel which are shown to be accurate for a wide range of signal to noise ratios and phase noise variances for each formulation we present a detailed analysis of the optimal constellations and their performance in the presence of strong phase noise we show that the optimal constellations significantly outperform conventional constellations and those proposed in the literature in terms of sep error floors and mi

flatness based boundary control of a class of quasilinear parabolic distributed parameter systems motion planning and control of a boundary controlled quasilinear parabolic partial differential equation in one spatial variable is considered the approach relies on a flatness property of the system namely that the system solution can be differentially parameterized in terms of a flat output which in the case considered is a boundary value such a parameterization allows straightforward motion planning and computation of a control law the approach is based on power series in the spatial variable and the convergence of these series is ensured by choosing the flat output to be a nonanalytic smooth function of appropriate gevrey class

flatness based trajectory planning for diffusion reaction systems in a parallelepipedon a spectral approach spectral analysis is considered for the flatness based solution of the trajectory planning problem for a boundary controlled diffusion reaction system defined on a 1 r dimensional parallelepipedon by exploiting the riesz spectral properties of the system operator it is shown that a suitable reformulation of the resolvent operator allows a systematic introduction of a basic output which yields a parametrization of both the system state and the boundary input in terms of differential operators of infinite order their convergence is verified for both infinite dimensional and finite dimensional actuator configurations by restricting the basic output to certain gevrey classes involving non analytic functions with this a systematic approach is introduced for basic output trajectory assignment and feedforward tracking control towards the realization of finite time transitions between stationary profiles

iterative decoding of binary block and convolutional codes iterative decoding of two dimensional systematic convolutional codes has been termed turbo de coding using log likelihood algebra we show that any decoder can be used which accepts soft inputs including a priori values and delivers soft outputs that can be split into three terms the soft channel and a priori inputs and the extrinsic value the extrinsic value is used as an a priori value for the next iteration decoding algorithms in the log likelihood domain are given not only for convolutional codes but also for any linear binary systematic block code the iteration is controlled by a stop criterion derived from cross entropy which results in a minimal number of iterations optimal and suboptimal decoders with reduced complexity are presented simulation results show that very simple component codes are sufficient block codes are appropriate for high rates and convolutional codes for lower rates less than 2 3 any combination of block and convolutional component codes is possible several interleaving techniques are described at a bit error rate ber of 10 sup 4 the performance is slightly above or around the bounds given by the cutoff rate for reasonably simple block convolutional component codes interleaver sizes less than 1000 and for three to six iterations

multiple symbol differential detection of mpsk a differential detection technique for mpsk multiple phase shift keying which uses a multiple symbol observation interval is presented and its performance is analyzed and simulated the technique makes use of maximum likelihood sequence estimation of the transmitted phases rather than symbol by symbol detection as in the conventional differential detection thus the performance of this multiple symbol detection scheme fills the gap between conventional two symbol observation differentially coherent detection of mpsk and ideal coherent of mpsk with differential encoding the amount of improvement gained over conventional differential detection depends on the number of phases m and the number of additional symbol intervals added to the observation what is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation the analysis and simulation results presented are for uncoded mpsk

flatness and defect of non linear systems introductory theory and examples we introduce flat systems which are equivalent to linear ones via a special type of feedback called endogenous their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of kalman s controllability the distance to flatness is measured by a non negative integer the defect we utilize differential algebra where flatness and defect are best defined without distinguishing between input state output and other variables many realistic classes of examples are flat we treat two popular ones the crane and the car with n trailers the motion planning of which is obtained via elementary properties of plane curves the three non flat examples the simple double and variable length pendulums are borrowed from non linear physics a high frequency control strategy is proposed such that the averaged systems become flat

spectral dispersion of modulated signals due to oscillator phase instability white and random walk phase model this paper considers the modeling of oscillator phase instability and the resulting spectral dispersion a phase covariance matrix method is developed for determining the autocorrelation function and the power spectral density of the oscillator sinusoidal rf signal when corrupted by a superposition of a white phase random process and a random walk phase random process by limiting the discussion to phase covariance matrices it is shown that the direct use of a certain class of nonstationary phase random processes leads to stationary rf signal autocorrelation functions and associated power spectral densities this is so despite the nonstationary phase driving force the procedures provided here are also applied towards the determination of the average autocorrelation function and the average spectrum when the cisoidal oscillator signal undergoes modulation modulating waveforms used as examples include the cw the infinite pulse train and the finite pulse train

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

turbo decoding of concatenated channel coding and trellis shaping for peak power controlled single carrier systems trellis shaping ts has found its application in the peak power control of band limited single carrier signals our recent work has demonstrated that a well designed ts can control the symbol transitions such that the output signal has almost constant envelope which significantly alleviates the linearity requirement of power amplifiers compared to transmission without constellation shaping however the ts involves signal constellation expansion exclusively for peak power control therefore unlike trellis coded modulation tcm that increases the minimum euclidean distances med the ts decreases the med thus incurring the increase in signal to noise power ratio snr required for achieving a certain error rate in this letter in order to overcome this drawback we propose a serial concatenation of coding and shaping together with an effective decoding algorithm that utilizes the memory effect i e error correcting capability of the shaped symbols the achievable performance of the proposed system is analyzed in terms of the average mutual information the simulation results demonstrate that the iterative decoding of the proposed concatenated system with outer convolutional codes and inner trellis shaping offers a significant performance gain

capacity and coding for the block independent noncoherent awgn channel communication over the noncoherent additive white gaussian noise awgn channel is considered where the transmitted signal undergoes a phase rotation unknown to the transmitter and the receiver the effects of phase dynamics are explicitly taken into account by considering a block independent model for the phase process the unknown phase is constant for a block of n complex symbols and independent from block to block in the first part of the paper the capacity achieving input distribution is characterized in particular it is shown that the maximizing density has circular symmetry is discrete in amplitude with infinite number of mass points and always has a mass point at zero furthermore asymptotic expressions and bounds for the capacity are derived based on these results the capacity is evaluated through numerical optimizations for unconstrained and modulation constrained input distributions in the second part of this paper inspired by the capacity results two classes of coding and modulation schemes are proposed for fast and moderate phase dynamics in the case of fast phase dynamics i e small n optimized modulation alphabets are designed having exponential complexity with n at the demodulator in the case of moderate phase dynamics i e moderate values of n specially designed modulation alphabets are utilized that have linear complexity with n these alphabets are used together with optimized irregular low density parity check ldpc codes simulation results show that these codes can achieve close to capacity performance with moderate complexity and outperform the best known codes so far

exact controllability and stabilization of a vibrating string with an interior point mass in this article we examine the problems of boundary control and stabilization for a one dimensional wave equation with interior point masses we show that singularities in waves are smoothed one order as they cross a point mass thus in the case of one interior point mass with e g l 2 dirichlet control at the left end the most general reachable space from 0 that one can expect is l 2 times h 1 to the left of the mass and h 1 times l 2 to the right of the mass we show that this is in fact the optimal result modulo certain compatibility conditions several related results for both control and stabilization of such systems are also given

on the performance evaluation of trellis codes generating function techniques for analyzing the error event and the bit error probabilities for trellis codes are considered the conventional state diagram approach for linear codes where the number of states is equal to the number of trellis states cannot be applied directly to arbitrary trellis codes and instead a state diagram where the number of states is equal to the square of the number of trellis states must be used it is shown that for an interesting class of trellis codes a modified generating function can be defined for which the number of states em is equal to the number of trellis states the class of codes considered includes trellis codes of rate r n 1 n based upon set partitioning whenever the first partition breaks the signal constellation into two subsets which have the same configuration matrix i e the same ordered set of mutual distances the complexity of calculating this modified generating function is the same as for the ordinary generating function of a convolutional code with the same number of trellis states bounds on the performance of some interesting codes are given based upon this method

probability of error in frequency hop spread spectrum multiple access communication systems with noncoherent reception expressions are developed for the probability of error for asynchronous frequency hop spread spectrum multiple access networks using markov hopping patterns and binary frequency shift keying bfsk with one symbol transmitted per hop the expressions are exact when there is one interfering user and orthogonal bfsk is used they provide excellent approximations when there are more than one interfering user it is also shown that the error probability when markov hopping patterns are used is a good approximation to the error probability when memoryless hopping patterns are used by computing the channel capacity and the associated throughput a simple hard decision receiver is shown to perform much better than a receiver using perfect side information to erase the symbols transmitted on hops that were hit when all the users have the same power and one binary symbol is transmitted per hop

phase noise effects on turbo trellis coded over m ary coherent channels the effect of the phase noise on the performance of bandwidth efficient coded modulation is studied to this end the average mutual information ami for specific constellations such as 8 phase shift keying and 16 quadrature amplitude modulation is calculated in the presence of carrier phase error caused by imperfect carrier tracking over an additive white gaussian noise channel the ami not only quantifies the effect of the phase noise from an information theoretic viewpoint but also serves as an estimate for a permissible amount of the phase noise for a given signal to noise ratio the bit error rate ber performance of a near optimal turbo trellis coded modulation scheme is then investigated over such a channel for this purpose an optimal branch metric which best fits the channel characteristics is derived furthermore simple branch metrics referred to as suboptimal simplified and gaussian metrics are derived which may offer the tradeoff between ber performance and computational complexity numerical analysis shows that a near optimal coded modulation scheme renders a transmission system more robust against phase noise than is the case with a conventional trellis coded modulation scheme

linear precoders for bit interleaved coded modulation on awgn channels analysis and design criteria this paper investigates linear precoding for bit interleaved coded modulation bicm on additive white gaussian noise awgn channels concatenating a linear precoder as an inner encoder with an outer convolutional encoder produces a powerful code with a limited decoding complexity linear precoders are examined and optimized for two scenarios using i a noniterative decoding strategy and ii an iterative decoding strategy under a perfect feedback assumption the precoder design is based on an information theoretical approach on the one hand and a pair wise error probability pep analysis on the other hand both approaches render convenient precoder design rules for a binary phase shift keying bpsk signal set the optimal precoders that result from these rules are also derived numerical results confirm the analytical findings and simulations illustrate the effectiveness of the approach

flatness of heavy chain systems in this paper the flatness m fliess j levine p martin and p rouchon internat j control 61 1995 pp 1327 1361 m fliess j levine p martin and p rouchon ieee trans automat control 44 1999 pp 922 937 of heavy chain systems i e trolleys carrying a fixed length heavy chain that may carry a load is addressed in the partial derivatives equations framework we parameterize the system trajectories by the trajectories of its free end and solve the motion planning problem namely steering from one state to another state when considered as a finite set of small pendulums these systems were shown to be flat r m murray in proceedings of the ifac world congress san francisco ca 1996 pp 395 400 our study is an extension to the infinite dimensional case under small angle approximations these heavy chain systems are described by a one dimensional 1d partial differential wave equation dealing with this infinite dimensional description we show how to get the explicit parameterization of the chain trajectory using distributed and punctual advances and delays of its free end this parameterization results from symbolic computations replacing the time derivative by the laplace variable s yields a second order differential equation in the spatial variable where s is a parameter its fundamental solution is for each point considered along the chain an entire function of s of exponential type moreover for each we show that thanks to the liouville transformation this solution satisfies modulo explicitly computable exponentials of s the assumptions of the paley wiener theorem this solution is in fact the transfer function from the flat output the position of the free end of the system to the whole state of the system using an inverse laplace transform we end up with an explicit motion planning formula involving both distributed and punctual advances and delays operators

analysis of optimum detector of trellis coded mpsk in phase noise channels this paper presents a novel analytical expression which approximates the bit error rate ber of the joint phase and symbol maximum a posteriori jmap sequence estimator for trellis code modulation tcm with m ary phase shift keying mpsk modulation any arbitrary phase noise model i e not limited to the wiener process and either a matched or mismatched decoder first we derived convenient closed form expressions for approximating the pairwise error probability of two code sequences for both matched and mismatched decoders since the expressions are formulated either in the time or in the frequency domain it is possible to indicate the contribution of every frequency in the phase noise spectrum we then applied the union bound on the code sequence pairwise errors the analytical expression was tight usually 1db for mpsk constellations with m 4 and code rates 0 5 once developed the expressions will assist designers to consider the influence on receiver performance of the code characteristics decoder implementation and rf synthesizer phase noise it further enables joint optimization of the rf synthesizer the code and the decoder for achieving the lowest error rate or other design targets

exact boundary controllability of 1 d parabolic and hyperbolic degenerate equations the boundary controllability of a class of one dimensional degenerate equations is studied in this paper the novelty of this work is that the control acts through the part of the boundary where degeneracy occurs first we consider a class of degenerate hyperbolic equations then we prove sharp observability estimates for these equations using nonharmonic fourier series the transmutation method yields a result for the corresponding class of degenerate parabolic equations

how many zeros of a random polynomial are real we provide an elementary geometric derivation of the kac integral formula for the expected number of real zeros of a random polynomial with independent standard normally distributed coefficients we show that the expected number of real zeros is simply the length of the moment curve 1 t tn projected onto the surface of the unit sphere divided by the probability density of the real zeros is proportional to how fast this curve is traced out we then relax kac s assumptions by considering a variety of random sums series and distributions and we also illustrate such ideas as integral geometry and the fubini study metric

coding for the discretely phase ambiguous additive white gaussian channel communication over the additive white gaussian channel subject to a discrete phase ambiguity at the receiver is considered when this phase ambiguity is considered as a discretely distributed random variable the channel is termed the acoherent additive white gaussian aawg channel it is shown that the optimum decoder for the aawg channel is not practically implementable and a suboptimum decoder that is asymptotically optimum at high signal to noise ratio is developed the low signal to noise ratio performance of the suboptimum decoder is also examined by considering the structural possibilities for this decoder it is shown that one implementation leads to rotationally invariant codes other implementations based on a rotationally disjoint property lead to a variety of solutions that offer a general framework for communication over this channel some of these solutions use a parallel receiver configuration various solutions are compared in terms of implementation and performance

on the capacity of the blockwise incoherent mpsk channel the capacity of m ary phase shift keying mpsk over an additive white gaussian noise awgn channel with carrier phase unknown but constant over l symbols is investigated it is shown that capacity achieving channel inputs are uniformly distributed and independent mpsk symbols capacity over a range of signal to noise ratio snr and l is presented for binary phase shift keying bpsk and quaternary phase shift keying qpsk upper and lower easy to compute bounds on capacity are derived it is proven that for large l the coherent capacity is approached an analytic asymptotic expression for low l spl middot snr is derived exhibiting the expected quadratic dependence on the snr

soft metrics and their performance analysis for optimal data detection in the presence of strong oscillator phase noise in this paper we address the classical problem of maximum likelihood ml detection of data in the presence of random phase noise we consider a system where the random phase noise affecting the received signal is first compensated by a tracker estimator then the phase error and its statistics are used for deriving the ml detector specifically we derive an ml detector based on a gaussian assumption for the phase error probability density function pdf further without making any assumptions on the phase error pdf we show that the actual ml detector can be reformulated as a weighted sum of central moments of the phase error pdf we present a simple approximation of this new ml rule assuming that the phase error distribution is unknown the ml detectors derived are also the aposteriori probabilities of the transmitted symbols and are referred to as soft metrics then using the detector developed based on gaussian phase error assumption we derive the symbol error probability sep performance and error floor analytically for arbitrary constellations finally we compare sep performance of the various detectors metrics in this work and those from literature for different signal constellations phase noise scenarios and snr values

nd convolutional codes ii structural analysis for pt i see ibid vol 43 no 2 p 558 75 1997 the structural properties of a noncoherent coded system which incorporates convolutional codes in conjunction with multiple symbol noncoherent detection is presented in this second part of a two part paper where the performance analysis was provided in part i these convolutional codes are referred to as nd convolutional codes and they provide a general framework for various noncoherent coding systems including differential systems for several practical models of the carrier phase the exponential rate in which the error probability decays to zero derived in part i of the paper is used here to obtain the free equivalent distance of nd codes which is the single parameter dominating the error performance at large signal to noise ratios the free equivalent distance is upper bounded by the free nd distance which constitutes a more convenient and practical parameter to work with and it is the basis for a computer search for optimal nd codes the resultant codes of the computer search are compared to codes which are optimal for coherent detection and it is verified that the latter codes are not necessarily optimal for noncoherent detection since they exhibit in many cases a relatively small nd distance the ambiguity problem inherent to noncoherent systems is also treated in this paper in the general framework of nd catastrophic codes and necessary and sufficient conditions for catastrophic error propagation are identified

trajectory planning for boundary controlled parabolic pdes with varying parameters on higher dimensional spatial domains the flatness based design of a feedforward tracking control is considered for the solution of the trajectory planning problem for a boundary controlled diffusion convection reaction system with spatially and temporally varying parameters defined on a 1 les m dimensional parallelepipedon with the nonlinear input being restricted to a m 1 dimensional hyperplane for this an implicit state and input parametrization in terms of a basic output is determined via a volterra type integral equation with operator kernel by recursively computing successive series coefficients a series solution of the integral equation is obtained whose absolute and uniform convergence is verified by restricting the system parameters and the basic output to a certain but broad gevrey class hence prescribing an admissible desired trajectory for the basic output directly yields the feedforward control by evaluating the input parametrization this results in a systematic procedure for trajectory planning and feedforward control design for boundary controlled parabolic distributed parameter systems defined on higher dimensional domains

maximum likelihood differential detection of uncoded and trellis coded amplitude phase modulation over awgn and fading channels spl minus metrics and performance this paper derives metrics for maximum likelihood differential detection of uncoded and trellis coded mpsk and qam transmitted over rayleigh and rician fading channels receiver structures based on these metrics are proposed and their error probability performance analyzed and or simulated the results represent a generalization of the notion of multiple symbol differential detection previously introduced by the authors for mpsk over an awgn to the fading channel and other modulations for the coded cases ideal interleaving deinterleaving is assumed and furthermore the presence or absence of channel state information an interesting side result is that for a constant envelope modulation transmitted over a fading channel with unknown but rapidly varying phase error the other extreme to the slowly varying phase error case normally assumed for differential detection under certain practical assumptions it is shown that the optimum receiver is of the limiter discriminator type

a lie backlund approach to equivalence and flatness of nonlinear systems a new system equivalence relation using the framework of differential geometry of jets and prolongations of infinite order is studied in this setting two systems are said to be equivalent if any variable of one system may be expressed as a function of the variables of the other system and of a finite number of their time derivatives this is a lie backlund isomorphism the authors prove that although the state dimension is not preserved the number of input channels is kept fixed they also prove that a lie backlund isomorphism can be realized by an endogenous feedback the differentially flat nonlinear systems introduced by the authors 1992 via differential algebraic techniques are generalized and the new notion of orbitally flat systems is defined they correspond to systems which are equivalent to a trivial one with time preservation or not the endogenous linearizing feedback is explicitly computed in the case of the vtol aircraft to track given reference trajectories with stability

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