parametrically excited vibrations of an oscillator with strong cubic negative nonlinearity in this paper the parametrically excited vibrations of an oscillator with strong cubic negative nonlinearity are analyzed the two dimensional lindstedt poincare perturbation technique applied for finding an approximate solution of linear parametrically excited systems is extended for analyzing a strong nonlinear oscillator based on the solution of a nonlinear differential equation with constant coefficients an approximative solution is introduced the transition curves and transient surfaces along which periodic solutions exist are obtained their strong dependence on the initial conditions is evident to prove the analytical solution the numerical experiment is done for certain values initial conditions and parameter values the time history diagrams for the oscillator are plotted

the poisson multiple access channel the poisson multiple access channel mac models many to one optical communication through an optical fiber or in free space for this model we compute the capacity region for the two user case as a function of the allowed peak power focusing on the maximum throughput we generalize our results to the case where the users are subjected to an additional average power constraint and to the many users case we show that contrary to the gaussian mac in the poisson mac the maximum throughput is bounded in the number of users we quantify the loss that is incurred when time division multiple access tdma is employed and show that while in the two user case and in the absence of dark current the penalty is rather mild the penalty can be quite severe in the many users case in the presence of large dark current we introduce a generalized tdma technique that mitigates this loss to a large extent

response of an sdof system to periodic external and parametric excitations with random phase modulations a single degree of freedom system is considered which is excited simultaneously by external and parametric time variant loadings both these dynamic loads are assumed to be periodic in time with some random disorder or phase modulations response analysis is made for this system by using stochastic averaging with subsequent application of the method of moments to the resulting set of the shortened ito sdes the results of steady state mean square response analysis are presented in terms of the corresponding amplification factor illustrating its dependence on excitation system bandwidth ratios and detuning between expected excitation frequencies and the system s natural frequency

minimum probability of error for asynchronous gaussian multiple access channels consider a gaussian multiple access channel shared by k users who transmit asynchronously independent data streams by modulating a set of assigned signal waveforms the uncoded probability of error achievable by optimum multiuser detectors is investigated it is shown that the k user maximum likelihood sequence detector consists of a bank of single user matched filters followed by a viterbi algorithm whose complexity per binary decision is o 2 k the upper bound analysis of this detector follows an approach based on the decomposition of error sequences the issues of convergence and tightness of the bounds are examined and it is shown that the minimum multiuser error probability is equivalent in the iow noise region to that of a single user system with reduced power these results show that the proposed multiuser detectors afford important performance gains over conventional single user systems in which the signal constellation carries the entire burden of complexity required to achieve a given performance level

moment lyapunov exponent and stability index for linear conservative system with small random perturbation asymptotic expansion series for the moment lyapunov exponent and stability index are constructed and justified for the two dimensional linear stochastic system close to a harmonic oscillator as an example a one degree of freedom mechanical system parametrically excited in stiffness and damping is considered and several terms of the expansion are obtained

error probability bounds for nuclear detection a collection of static and mobile radiation sensors is tasked with deciding within a fixed time interval whether a moving target carries radioactive material formally this is a problem of detecting weak time inhomogeneous poisson signals target radiation concealed in another poisson signal naturally occurring background radiation each sensor locally processes its observations to form a likelihood ratio which is transmitted once at the end of the decision interval to a fusion center the latter combines the transmitted information to optimally in the neyman pearson sense decide whether the measurements contain a radiation signal or just noise we provide a set of analytically derived upper bounds for the probabilities of false alarm and missed detection which are used to design threshold tests without the need for computationally intensive monte carlo simulations these analytical bounds couple the physical quantities of interest to facilitate planning the motion of the mobile sensors for minimizing the probability of missed detection the network reconfigures itself in response to the target motion to allow more accurate collective decisions within the given time interval the approach is illustrated in numerical simulations and its effectiveness demonstrated in experiments that emulate the statistics of nuclear emissions using a pulsed laser

accurate evaluation of bit error rates of optical communication systems using the gram charlier series the probability densities and cumulative distribution functions of decision statistics of optical communications systems are expanded as a gram charlier g c series leading to arbitrarily accurate systematic evaluation of bit error rates bers and optimal decision thresholds of optical communication systems the method displays negligible computational complexity and is applicable whenever the moment or cumulant generating functions of the decision statistics are analytically available we applied the technique to a birth and death markovian model of a direct detection receiver with optical preamplifier in a two level amplitude shift keying system the modal expansion series rapidly converged whereas the alternative saddlepoint approximation method predicted a ber which deviated by 7 from the g c result

relationship between the saddlepoint approximation and the modified chernoff bound optical communication a comparison is made of two methods for the computation of the probability that the sum of a gaussian and a nongaussian random variable exceeds a certain threshold value the two methods the saddlepoint approximation sap and the modified chernoff bound are closely related to one another for the computation of error probabilities in digital optical communications where both methods can be applied the modified chernoff bound is found to lie close above the saddlepoint approximation for all cases of practical interest the ratio of signal dependent to additive noise has been established as the parameter dominating the bound tightness since the sap has been reported to be extremely precise this result indicates that the more versatile upper bound can be used with confidence both for performance evaluation and for optimization of optical communication systems

computing bit error probabilities for avalanche photodiode receivers by large deviations theory a bit error probability analysis of direct detection optical receivers is presented employing avalanche photodiodes an asymptotic analysis for large signal intensities is presented this analysis provides some useful insight into the balance between the poisson statistics the avalanche gain statistics and the gaussian thermal noise the conjugate distribution is developed it is obtained by applying the large deviation exponential twisting formula it is demonstrated that this conjugate distribution can be used to obtain numerically efficient monte carlo estimates of the bit error probability via the importance sampling method

moment lyapunov exponents of the stochastic parametrical hill s equation abstract the lyapunov exponent and moment lyapunov exponents of hill s equation with frequency and damping coefficient fluctuated by white noise stochastic process are investigated a perturbation approach is used to obtain explicit expressions for these exponents in the presence of small intensity noises the results are applied to the study of the almost sure and the moment stability of the stationary solutions of the thin simply supported beam subjected to axial compressions and time varying damping which are small intensity stochastic excitations

optical orthogonal codes new bounds and an optimal construction a technique for constructing optimal oocs optical orthogonal codes is presented it provides the only known family of optimal with respect to family size oocs having lambda 2 the parameters n omega lambda are respectively p sup 2m 1 p sup m 1 2 where p is any prime and the family size is p sup m 2 three distinct upper bounds on the size of an ooc are presented that for many values of the parameter set n omega lambda improve upon the tightest previously known bound

performance of multiuser detection for optical cdma ii asymptotic analysis for pt i see ibid vol 43 no 11 p 2803 2811 1995 this paper presents characterizations of optimum multiuser detection in intensity modulation direct detection cdma channels based on asymptotic analysis of simple bounds on optimum performance technical difficulties in applying large deviation techniques to the evaluation of asymptotic multiuser efficiencies are rigorously addressed these same difficulties also lead to the derivation of conditions under which the linear multiuser detection achieves known interference hence optimum performance asymptotic analysis of the conventional correlation receiver including derivation of the optimal decision threshold for on off signaling formats is also presented

h spl infin deconvolution filtering prediction and smoothing a krein space polynomial approach this correspondence is concerned with the infinite horizon h spl infin deconvolution for discrete time invariant systems described by polynomial equations a simple frequency domain approach in krein space is developed for the deconvolution problem with the help of an arma innovation model solutions to the problems of deconvolution filtering prediction and fixed lag smoothing are obtained the estimators are calculated by performing one j spectral factorization

multiaccess quantum channels shared communication channels are subject to multiple access interference transmitter and receiver design techniques that explicitly deal with this interference have been shown to improve substantially the performance of communication systems over radio frequency and other classical channels quantum multiple access communication channels on the other hand have received comparatively little attention in this paper an input output model for multiple access quantum channels relevant to optical communications is proposed the model accounts for multiaccess interference signal attenuation and random noise and can be used in the analysis and design of communication systems using a result from optimization a perturbation method is developed to find the minimum achievable error probability in small interference channels it is shown that the quantum measurement that minimizes the error probability in a no interference channel is robust in the presence of small multiaccess interference the results are illustrated with numerical examples which show that optimal quantum detectors can significantly outperform conventional detectors even for moderate levels of crosstalk

moment lyapunov exponents of a two dimensional system under bounded noise parametric excitation the moment lyapunov exponents of a two dimensional system under bounded noise parametric excitation are studied in this paper the method of regular perturbation is applied to obtain weak noise expansions of the moment lyapunov exponent lyapunov exponent and stability index in terms of the small fluctuation parameter

performance analysis of direct detection optical cdma communication systems with avalanche photodiodes direct detection optical code division multiple access cdma communication systems with avalanche photodiode apd photodetectors are investigated a chernoff upper bound modified chernoff upper bound and gaussian approximation on the probability of bit error are presented for general apds and arbitrary

stochastic stability of coupled oscillators simple and combination resonances in coupled oscillators under a random parametric excitation are studied an efficient numerical method for obtaining the regions of mean square stability is proposed based on the method stability diagrams for different values of the excitation parameter and for four form of the coupling parameters are presented it is found that the random excitation can have a stabilizing effect under certain conditions

moment lyapunov exponents of a two dimensional system under combined harmonic and real noise excitations abstract the moment lyapunov exponents and the lyapunov exponents of a two dimensional system under combined excitations of harmonic and real noise which is modelled as an ornstein uhlenbeck process are studied the moment lyapunov exponents and the lyapunov exponents are important characteristics determining the moment and almost sure stability of a stochastic dynamical system the eigenvalue problem governing the moment lyapunov exponent is established a regular perturbation method is applied to solve the eigenvalue problem to obtain second order weak noise expansions of the moment lyapunov exponents the influence of the real noise excitation on the parametric resonance due to the harmonic excitation is investigated

game theory approach to h sub spl infin optimal discrete time fixed point and fixed lag smoothing optimal h sub spl infin fixed point and fixed lag discrete time smoothing estimators are developed by applying a game theory approach a deterministic discrete time game is defined where the estimator plays against nature nature determines the system initial condition the driving input and the measurement noise whereas the estimator tries to find an estimate that brings a prescribed cost function that is based on the error of the estimation at a fixed time instant to a saddle point equilibrium the latter estimate yields the h sub spl infin optimal fixed point smoothing differently from the usual case in h sub spl infin optimal estimation and control the critical value of the scalar design parameter of the smoothing game is obtained in closed form explicitly in the terms of the corresponding h sub 2 solution unlike the h sub 2 case the recursive application of the h sub spl infin fixed point smoothing algorithm does not lead to fixed lag smoothing in the h sub spl infin norm sense the h sub spl infin fixed lag smoothing filter is derived by augmenting the state vector of the system with additional delayed states

h optimal multichannel linear deconvolution filters predictors and smoothers a solution is presented to the h optimal deconvolution filtering smoothing and prediction problems for multivariable discrete linear signal processing problems a weighted h cost function is minimized where the dynamic weighting function can be chosen for robustness improvement the signal and noise sources can be correlated and signal channel dynamics can be included in the system model a brief example is presented to demonstrate the approach

finite horizon h_ infty filtering with missing measurements and quantization effects in this paper a new h filtering approach is developed for a class of discrete time varying systems subject to missing measurements and quantization effects the missing measurements are modeled via a diagonal matrix consisting of a series of mutually independent random variables satisfying certain probabilistic distributions on the interval 0 1 the measured output is quantized by a logarithmic quantizer attention is focused on the design of a stochastic h filter such that the h estimation performance is guaranteed over a given finite horizon in the simultaneous presence of probabilistic missing measurements quantization effects as well as external non gaussian disturbances a necessary and sufficient condition is first established for the existence of the desired time varying filters in virtue of the solvability of certain coupled recursive riccati difference equations rdes owing to its recursive nature the proposed rde approach is shown to be suitable for online application without the need of increasing the problem size the simulation experiment is carried out for the mobile robot localization problem with non gaussian disturbances missing measurements and quantization effects the effectiveness of the proposed method is demonstrated in the numerical example

robust inversion based fault estimation for discrete time lpv systems the article presents a state space based fault diagnosis fd method for discrete time affine linear parameter varying lpv systems the goal of the technical note is to develop a robust and dynamic inversion based technique for systems with parameter varying representations when an additive exogenous disturbance signal perturbs the system after applying geometric concepts for explicit fault inversion a robust strategy is proposed to attenuate the effect of the unknown disturbance input signal on the fault estimation error the proposed robust observer is derived as a solution of off line linear matrix inequality lmi conditions the technical note demonstrates the viability of the novel methodology through a numerical example

moment stability for linear systems with a random parametric excitation moment stability for linear systems with a nonwhite parametric noise is considered a method of reduction of the study of this stability to the study of stability for large scale matrices is proposed mean square stability diagrams for random harmonic oscillator are presented

chaotic motion of van der pol mathieu duffing system under bounded noise parametric excitation abstract the chaotic behavior of van der pol mathieu duffing oscillator under bounded noise is investigated by using random melnikov technique a mean square criterion is used to detect the necessary conditions for chaotic motion of this stochastic system the results show that the threshold of bounded noise amplitude for the onset of chaos in this system increases as the intensity of the noise in frequency increases which is further verified by the maximal lyapunov exponents of the system the effect of bounded noise on poincare map is also investigated in addition the numerical simulation of the maximal lyapunov exponents

large deviations and stochastic flows of diffeomorphisms previous results in the theory of large deviations for additive functionals of a diffusion process on a compact manifold m are extended and then applied to the analysis of the lyapunov exponents of a stochastic flow of diffeomorphisms of m an approximation argument relates these results to the behavior near the diagonal in m2 of the associated two point motion finally it is shown under appropriate non degeneracy conditions that the two point motion is ergodic on m2 if the top lyapunov exponent is positive

the design and performance analysis for several new classes of codes for optical synchronous cdma and for arbitrary medium time hopping synchronous cdma communication systems new families of spread spectrum codes are constructed that are applicable to optical synchronous code division multiple access cdma communications as well as to arbitrary medium time hopping synchronous cdma communications proposed constructions are based on the mappings from integer sequences into binary sequences the authors use the concept of number theoretic quadratic congruences and a subset of reed solomon codes similar to the one utilized in the welch costas frequency hop fh patterns the properties of the codes are as good as or better than the properties of existing codes for synchronous cdma communications both the number of code sequences within a single code family and the number of code families with good properties are significantly increased when compared to the known code designs possible applications are presented to evaluate the performance of the proposed codes a new class of hit arrays called cyclical hit arrays is recalled which give insight into the previously unknown properties of the few classes of number theoretic fh patterns cyclical hit arrays and the proposed mappings are used to determine the exact probability distribution functions of random variables that represent interference between users of a time hopping or optical cdma system expressions for the bit error probability in multi user cdma systems are derived as a function of the number of simultaneous cdma system users the length of signature sequences and the threshold of a matched filter detector the performance results are compared with the results for some previously known codes

principal response of duffing oscillator to combined deterministic and narrow band random parametric excitation abstract the principal resonance of a duffing oscillator to combined deterministic and narrow band random parametric excitations is investigated in particular the case in which the parametric terms share close frequencies is examined the method of multiple scales is used to determine the equations of modulation of amplitude and phase the behavior stability and bifurcation of steady state response are studied by means of qualitative analyses jumps are shown to occur if the random excitation is small the effects of damping detuning and magnitudes of deterministic and narrow band parametric excitations are analyzed the theoretical analyses are verified by numerical results

moment lyapunov exponents of a two dimensional system under real noise excitation abstract the moment lyapunov exponents of a two dimensional system under real noise excitation an ornstein uhlenbeck process are studied in this paper the method of regular perturbation is applied to obtain the weak noise expansions of the moment lyapunov exponent lyapunov exponent and stability index in terms of the small fluctuation parameter

unipolar codes with ideal in phase cross correlation for spectral amplitude coding optical cdma systems unipolar codes with ideal in phase cross correlation are important in spectral amplitude coding optical code division multiple access cdma systems since these codes eliminate multiuser interference and also suppress the effect of phase induced intensity noise however very little research work has been done on such codes although codes with ideal cross correlation have been studied for many years in the paper by zhou et al see electron lett vol 36 p 728 29 2000 such a code has been introduced without a clear construction method in this paper we firstly review this old code and then construct two new codes with ideal in phase cross correlation in algebraic ways both of the proposed new codes are obtained by modifying former codes with ideal cross correlation it has been shown that the system performance can be improved significantly by using codes with ideal in phase cross correlation instead of the hadamard code these codes can also be used in synchronous optical cdma systems for multiuser interference cancellation

chaotic motion in the resonant separatrix bands of a mathieu duffing oscillator with a twin well potential the m 1 resonant bands in the left and right potential wells are skew symmetric and the 2m 1 resonant bands of the large orbit motion are symmetric the analytical conditions for the onset and destruction of a resonant band are developed through the incremental energy approach the numerical predictions of such onset and destruction are also completed by the energy increment spectrum method the sub resonance interaction occurs for strong excitations which needs to be further investigated these results are applicable to the small and large orbit motions of post buckled structure under a parametric excitation

on discrete time h sub spl infin fixed lag smoothing the h sub spl infin fixed lag smoothing problem for discrete time linear systems is considered it is well known that such a problem can be reformulated as a filtering problem for a suitable augmented system however in order to check the solvability of the smoothing problem and compute the relevant gains one must solve a riccati equation involving the augmented system matrices which is an approach that may be inefficient especially for long lags in this paper efficient algorithms are worked out that permit checking of solvability and implementation of the smoother relying only on the solution of the h sub spl infin filtering riccati equation in particular this provides a fast method to compute the minimum lag guaranteeing a desired attenuation level

probability guaranteed h finite horizon filtering for a class of nonlinear time varying systems with sensor saturations in this paper the probability guaranteed h finite horizon filtering problem is investigated for a class of nonlinear time varying systems with uncertain parameters and sensor saturations the system matrices are functions of mutually independent stochastic variables that obey uniform distributions over known finite ranges attention is focused on the construction of a time varying filter such that the prescribed h performance requirement can be guaranteed with probability constraint by using the difference linear matrix inequalities dlmis approach sufficient conditions are established to guarantee the desired performance of the designed finite horizon filter the time varying filter gains can be obtained in terms of the feasible solutions of a set of dlmis that can be recursively solved by using the semi definite programming method a computational algorithm is specifically developed for the addressed probability guaranteed h finite horizon filtering problem finally a simulation example is given to illustrate the effectiveness of the proposed filtering scheme 2012 elsevier b v all rights reserved

on linear h sup spl infin equalization of communication channels as an alternative to existing techniques and algorithms we investigate the merit of the h sup spl infin approach to the linear equalization of communication channels we first give the formulation of all causal h sup spl infin equalizers using the results of and then look at the finite delay ease we compare the risk sensitive h sup spl infin equalizer with the mmse equalizer with respect to both the average and the worst case ber performances and illustrate the improvement due to the use of the h sup spl infin equalizer

a semiclassical analysis of optical code division multiple access a model noncoherent optical asynchronous cdma system is described the error rate for a single user matched filter receiver that is valid for arbitrary photomultipliers and signature sequence sets adheres to the semiclassical model of light and does not depend on approximations for large user groups strong received optical fields or chip synchronism is analyzed the exact minimum probability of error and optimal threshold are compared to those obtained with user synchronism and multiple access interference mai distribution approximations for the special case of unity gain photodetectors and prime sequences it is shown that the approximation of chip synchronism yields a weak upper bound on the exact error rate it is demonstrated that the approximations of perfect optical to electrical conversion and gaussian distributed mai yield a poor approximation to the minimum error rate and an underestimate of the optimal threshold arbitrarily tight bounds are developed on the error rate for unequal energies per bit in the case when the signal energies coincide these bounding expressions are considerably easier to compute than the exact error rate

optimal and robust noncausal filter formulations the paper describes an optimal minimum variance noncausal filter or fixed interval smoother the optimal solution involves a cascade of a kalman predictor and an adjoint kalman predictor a robust smoother involving h sub spl infin predictors is also described filter asymptotes are developed for output estimation and input estimation problems which yield bounds on the spectrum of the estimation error these bounds lead to a priori estimates for the scalar spl gamma in the h sub spl infin filter and smoother design the results of simulation studies are presented which demonstrate that optimal robust and extended kalman smoothers can provide performance benefits

multiuser detections for optical cdma networks based on expectation maximization algorithm in this paper we introduce new unblind and blind multiuser detectors for an optical code division multiple access system the detectors have two soft and hard stages in the soft stage a soft estimation of the interference is obtained by solving an unconstrained maximum likelihood problem via the iterative expectation maximization em algorithm then the hard stage detects the user information bit by solving a one dimensional boolean constrained problem conditioned on knowing the interference our results reveal that the proposed detectors have very low complexity and are robust against changes in parameters moreover the numerical results illustrate that despite of their simplicities our detectors substantially outperform other well known suboptimum detectors such as multistage and decorrelating detectors

maximal lyapunov exponent and almost sure stability for stochastic mathieu duffing systems abstract the principal resonance of a mathieu duffing oscillator to random excitation is investigated the method of multiple scales is used to determine the equations of modulation of amplitude and phase the effects of damping detuning cubic term and magnitudes of random excitation are analyzed the explicit asymptotic formulas for the maximal lyapunov exponent is obtained the almost sure stability or instability of the stochastic mathieu duffing system depends on the sign of the maximal lyapunov exponent in the last part of the work the numerical results are obtained

optical orthogonal codes design analysis and applications an optical orthogonal code ooc is a family of 0 1 sequences with good auto and cross correlation properties i e the autocorrelation of each sequence exhibits the thumbtack shape and the cross correlation between any two sequences remains low throughout the use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably the thumbtack shaped autocorrelation facilitates the detection of the desired signal and low profile cross correlation reduces interference from unwanted signals theoretical upper and lower bounds on the maximum possible size of oocs are derived methods for the design and analysis of oocs using tools from projective geometry the greedy algorithm iterative constructions algebraic coding theory block design and various other combinational disciplines are discussed

modified chernoff bounds for pam systems with noise and interference corresp by using principles of analytic continuation upper and lower bounds on the error probability of a canonical binary system corrupted by additive interference and independent zero mean gaussian noise are derived the bounds which are simple functions require only the evaluation or bounding of the moment generating function of the interference for large signal to noise ratios snr and even for moderately large interference the bounds are shown to be tight and useful

acquisition sequences in ppm communications corresp in pulse position modulation ppm communications an acquisition sequence is needed to establish frame synchronization for subsequent data transmission this sequence must have ppm structure one pulse per frame and desirable autocorrelation properties for its detection the problem of finding aperiodic ppm acquisition sequences having the minimum possible autocorrelation for all off shifted positions is investigated sequences with the maximum possible number of frames have been found up to frame size 15 examples are given for every frame length up to 88 and powers of two up to 1024 an interesting relation between the ppm sequence problem costas and sonar arrays and golomb s ruler is explored

comparison of some approaches to stability of a sdof system under random parametric excitation we give a rigorous comparison of the asymptotic stochastic averaging method and the moment lyapunov exponent approach in assessing the mean square stability through an example of a single degree of freedom system under small periodic parametric excitation with random phase modulation the comparison is based on an efficient numerical procedure to determine the regions of mean square stability

a spectral factorization approach for h spl infin estimation problems in discrete time this note deals with the h filtering prediction and smoothing problems for discrete time linear systems the j spectral factorization approach is pursued and for each of the three problems a computationally efficient procedure to derive a j spectral factor is presented the construction of filter smoother and predictor hinges on the stabilizing solution of the same algebraic riccati equation this fact allows for the avoidance of any fictitious augmentation of the state space dimensions

linear multiuser detectors for synchronous code division multiple access channels under the assumptions of symbol synchronous transmissions and white gaussian noise the authors analyze the detection mechanism at the receiver comparing different detectors by their bit error rates in the low background noise region and by their worst case behavior in a near far environment where the received energies of the users are not necessarily similar optimum multiuser detection achieves important performance gains over conventional single user detection at the expense of computational complexity that grows exponentially with the number of users it is shown that in the synchronous case the performance achieved by linear multiuser detectors is similar to that of optimum multiuser detection attention is focused on detectors whose linear memoryless transformation is a generalized inverse of the matrix of signature waveform crosscorrelations and on the optimum linear detector it is shown that the generalized inverse detectors exhibit the same degree of near far resistance as the optimum multiuser detectors the optimum linear detector is obtained

prediction filtering smoothing and deconvolution in a discrete h infinity setting a game theory approach the problems of prediction filtering smoothing and deconvolution are formulated and solved for a discrete time linear system in an h infinity setting over a finite interval the measurement noise and process noise have bounded energies the case with known initial conditions is considered the approach uses a basic quadratic game theory in a discrete time domain h infinity setting

construction of one coincidence sequence quasi cyclic ldpc codes of large girth one approach for designing the one coincidence sequence ocs low density parity check ldpc codes of large girth is investigated these ocs ldpc codes are quasi cyclic and their parity check matrices are composed of circulant permutation matrices generally the cycle structures in these codes are determined by the shift values of circulant permutation matrices and the existence of cycles in the corresponding tanner graph is governed by certain cycle governing equations cges therefore finding the proper shift values is the key point to increase the girth of these codes in this paper we provide an effective method to systematically find out the cges for these codes of girth 6 8 and 10 respectively then one less computation intensive algorithm is used to generate the proper shift values for constructing the ocs ldpc codes of large girth simulation results show that significant gains in signal to noise ratio over an additive white gaussian noise channel can be achieved by increasing the girth of the ocs ldpc codes

multiple access channels with point process observations optimum demodulation the derivation and analysis of optimum multiuser detectors for additive rate and additive light poisson multiple access channels are studied the observed point process models the output of an ideal photodetector illuminated by several synchronous or asynchronous users who modulate coherent light of the same frequency dynamic programming based decision rules for the asynchronous multiple access channel exhibit the same computational complexity as their synchronous counterparts and are shown to be optimum under the criteria of minimum error probability and maximum likelihood sequence detection upper and lower bounds on the minimum uncoded bit error rate achievable with arbitrary signal constellations are obtained in terms of the error probability of binary hypothesis testing problems a particular case of these results namely the single user finite length intersymbol interference problem solves the error rate analysis of optimum direct detection systems for dispersive optical fibers

performance of multiuser detection for optical cdma i error probabilities characterization of optimum multiuser performance in intensity modulation direct detection optical cdma channels is addressed analysis is based on some simple bounds on optimum performance provided by receivers with side information or by a linear decorrelating receiver numerical comparisons of the performance bounds are obtained via application of saddlepoint approximations to the multiuser photocount statistics general analytical relations comparing these approximations to similar asymptotic approximations based on the chernoff bound are also derived the numerical results illustrate the fundamental importance of two of the performance bounds in addition the numerical error probability results verify the relevance of the asymptotically based performance analysis for optical cdma in part ii

largest lyapunov exponent for second order linear systems under combined harmonic and random parametric excitations the principal resonance of a second order linear stochastic oscillator to combined harmonic and random parametric excitations is investigated the method of multiple scales is used to determine the equations of modulation of amplitude and phase the effects of damping detuning bandwidth and magnitudes of random excitation are analyzed the method of path integration is used to obtain the steady state probability density function of the system and then the largest lyapunov exponent is calculated the almost sure stability or instability of the stochastic system depends on the sign of the largest lyapunov exponent the theoretical analyses are verified by numerical results

performance analysis of single user and multiuser detectors for optical code division multiple access communication systems code division multiple access cdma is a powerful multiplexing scheme particularly suited to the optical domain with its broad spectrum unfortunately analysis of optical cdma ocdma systems has been almost exclusively restricted to systems employing a correlation detector which suffer high degradation when received user powers are dissimilar this study examines the performance of an optimum single user detector and two multiuser detectors for ocdma in the presence of additive light intensity noise and poisson detection the optimized single user detector is the maximum likelihood detector given the interference from other users is a random process with known distribution one multiuser detector is based on a local search algorithm for maximizing the likelihood function the second multiuser detector is a generalization of the optical multistage detector to accept soft decision from the previous stage approximations to the error probabilities of the ocdma system based on either random signature sequences or deterministic codes are derived for each detector using a large deviations theory approach the asymptotic multiuser efficiency is found to be related to the large deviations rate function the analysis shows that the correlation detector performance decreases rapidly as the number of users increases while the optimized single user detector and the two multiuser detectors proposed perform considerably better and show less sensitivity to unequal received user powers

closure method and asymptotic expansions for linear stochastic systems a closure procedure for the hierarchy of moment equations related to linear systems of ordinary differential equations with a random parametric excitation is introduced a generalization of pringsheim s theorem for continued fractions is used in a proof of the procedure convergence the boundary function method for singular perturbation problems is applied to obtain asymptotic expansions for the moments of the solutions of such systems

h sub infinity fixed lag smoothing filter for scalar systems the solution of the h sub infinity optimal linear fixed lag smoothing problem is considered using a polynomial matrix description for the discrete system the smoother is obtained from the solution of a linear equation and a spectral factorization calculation the pole zero properties of the optimal smoother are obvious in the polynomial representation and insights into the measurement noise rejection properties of the smoother are obtained allowance is made for both dynamic cost weighting and colored measurement noise the polynomial form of the smoothing filter may be incorporated into a self tuning algorithm and a simple adaptive smoother is discussed

on designing h_ infty fault detection filter for linear discrete time varying systems this technical note deals with the problem of finite horizon h fault detection for linear discrete time varying systems using an observer based fault detection filter fdf with residual feedback as a residual generator a new problem formulation of fault detection is first presented then the design of finite horizon h fdf is converted into a minimum problem of certain quadratic form through building a relationship with krein space projection and applying innovation analysis a sufficient and necessary condition for the minimum is derived and a solution to the h fdf is obtained by recursively computing riccai recursions numerical examples are given to show the effectiveness of the proposed method

asymptotic error probability of binary hypothesis testing for poisson point process observations corresp it is shown that the asymptotic probability of error of a binary equiprobable hypothesis test for observed poisson point processes with rates lambda i t b i t rho i t z 2 i 0 1 z rightarrow infty is equal to the error probability of optimum deterministic signal detection in additive white gaussian noise when the signals coincide with the square roots of the point process rates the implication of this result in the error rate analysis of optical digital communication systems is discussed

ber analysis of bpsk signals in ricean faded cochannel interference the bit error rate of a binary phase shift keying bpsk signal in ricean faded cochannel interference is studied a precise bit error rate expression is derived for a bandlimited bpsk signal corrupted by an arbitrary number of asynchronous ricean faded interfering signals an error rate estimation based on a saddlepoint approximation is also provided it is shown that this approximation is highly accurate for the special case when there is one synchronous ricean faded interfering signal in an interference limited environment an asymptotic error rate analysis based on the saddle point approximation reveals that fading in the cochannel interfering signal can have different impacts on the desired user s error rate performance our study shows that when the signal to interference ratio sir is sufficiently large the error floor of the desired user signal decreases with an increase of the rice factor in the interfering user s fading channel however the opposite phenomenon can happen when the sir is small

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

on the existence of square dot matrix patterns having a specific three valued periodic correlation function the author examines square matrices of size n containing dot patterns satisfying the following two restrictions 1 each column contain precisely one dot and 2 if the pattern is moved around over a plane tied by the same pattern when in all positions except the home position there is at most one overlap in dots from differing viewpoints there matrices are the characteristic functions of either a certain class of relative difference sets or else a select subset of bent functions also the existence of such an n n matrix implies the existence of a finite projective plane of order n a family of constructions for such matrices is available when n is prime a polynomial equation characterizing such matrices and resembling the hall polynomial equation of cyclic difference sets is presented analogs of known existence tests for cyclic difference sets are then applied to rule out existence for most nonprime values of n it is shown how such patterns can be used to provide hopping patterns for a frequency hopped multiple access system

performance analysis of an asymptotically quantum limited optical dpsk receiver an optical direct detection differential phase shift keying dpsk receiver whose error probability is quantum limited as the transmitting laser linewidth vanishes is analyzed the receiver design is based on a binary equiprobable hypothesis test with doubly stochastic point process observations the conditional random rates of which depend on the transmitting laser phase noise which is modeled as a brownian motion the receiver structure consists of a simple delay and sum optical preprocessor followed by a photoelectric converter and an integrate and dump circuit upper and lower bounds on the receiver bit error rate are derived by developing bounds on the conditional rates of the point process and it is shown that the error probability bounds converge to the true value as the transmitting laser linewidth decreases bounds on the power penalty are computed for parameters corresponding to existing semiconductor injection lasers and are seen to be less than the limiting power penalty for the balanced dpsk receiver

a transfer function approach to the problems of discrete time systems h sub infinity optimal linear control and filtering a solution is derived to the problems of h sub infinity optimal linear state regulation and filtering the solution method for both problems is based on a transfer function approach which applies standard spectral factorization return difference relations are given which are extensions of the relations associated with the linear quadratic problem

performance bounds for mismatched decision schemes with poisson process observations abstract this paper develops a framework for analyzing the performance loss in fixed time interval decision algorithms that are based on observations of time inhomogeneous poisson processes when some parameters characterizing the observation process are not known exactly key to the development is the formulation of an analytically computable performance metric which can be used in lieu of the true but intractable error probabilities the proposed metric is obtained by identifying analytical upper bounds on the error probabilities in terms of the uncertain parameters using these tools it is shown that performance degrades gracefully as long as the true values of the parameters remain within a neighborhood of the nominal values used in decision making the results find direct application to problems of detecting illicit nuclear materials in transit

saddle point bit error rate computations for optical communication systems incorporating equalizers bit error rate computations for optical communication systems incorporating equalizers and under both noise and intersymbol interference isi are discussed an accurate method based on saddle point approximation is used previous work using saddle point approximation considered only basic integration and dump detection the use of equalizers other than integration and dump complicates the computation because of the complexity of the moment generating function involved when isi is strong use of an equalizer such as raised cosine filtering is important for isi reduction to help optical receiver design this paper explains the use of saddle point approximation when an equalizer is used in addition to integration and dump cosine and raised cosine equalizers are considered for isi reduction to study the interdependence between the received waveform and equalizer used two different input pulses are also considered to verify the computation accuracy exact contour integration based on the numerical quadrature method is performed results show that saddle point approximation can provide a fast and accurate computation from the bit error rate ber performance computed it is found that the traditional use of matched filtering has a poor performance when either isi is strong or the apd gain is large and the use of a proper equalizer can significantly improve the performance in other words the best choice of an equalizer design depends on the input waveform amount of isi and the apd gain

explanation on the importance of narrow band random excitation characters in the response of a cantilever beam a detailed theoretical investigation into the first and second mode response of a parametrically excited slender cantilever beam where the narrow band random excitation characters are taken into consideration is presented the method of multiple scales is used to determine a uniform first order expansion of the solution of the nonlinear integro differential equations the first order moment frequency and force response data curves of a specimen beam tested by other investigators are obtained further comparisons have been made and results show that whether the first order moment frequency response data curves or the first order moment force response data curves of the first two modes are all in agreement with other investigators experimental results furthermore the stochastic jump and bifurcation have been investigated for the first modal parametric principal resonance by using the stationary joint probability of amplitude and phase results show that stochastic jump occurs mainly in the region of triple valued solution for the frequency response domain if the bandwidth is a variable and others keep constant the basic phenomena indicate that the most probable motion is around the higher branch when the bandwidth is smaller whereas the most probable motion gradually approaches the lower one when the bandwidth becomes higher if the excitation central frequency f is a variable and others keep constant the basic phenomena imply that the higher is f the more probable is the jump from the higher branch to the lower one once f exceeds an certain value for the force response domain there is a region of excitation acceleration a within which the joint probability density has two peaks an upper peak and a lower peak results show that the upper peak decreases while the lower peak increases as the value of a decreases

monotonicity of likelihood ratio of map correlation detection for ocdma communication in this paper the monotonicity of the likelihood ratio used in the optimal correlation detection is established for optical code division multiple access ocdma the monotonicity property not only guarantees the optimality of the detection it also enables us to calculate the bit error rate bounds for ocdma in the presence of uncertain a priori probabilities

mean square stability of a second order parametric linear system excited by a colored gaussian noise abstract the stochastic stability of a second order linear parametric oscillator whose stiffness is perturbed by a stationary zero mean colored gaussian process is investigated in this paper referring to the stability in the second response moments mean square stability the stochastic perturbation is the output of a linear filter excited by a stationary gaussian white noise stochastic process and the hypothesis of weak excitation is not formulated the first assumption allows using ito s stochastic differential calculus the moment equations of the response are written till the second order by means of ito s differential rule they form an infinite hierarchy that is the equations for the moments of order r contain moments of order larger than r in order to close the hierarchy the cumulant neglect closure method is applied herein the moment equation set is closed by neglecting the cumulants of third order nonlinear moment equations result they are linearized and the limit of stability is searched by studying the eigenvalues of the matrix of the coefficients of the linearized moment equations several numerical analyses are performed to evaluate the critical mean square value of the excitation when a system parameter is varied for the cases of both first and second order parametric excitation a first order excitation an ornstein uhlenbeck process does not cause stochastic resonance while a second order excitation does the first result was not known previously

mutual information and conditional mean estimation in poisson channels following the discovery of a fundamental connection between information measures and estimation measures in gaussian channels this paper explores the counterpart of those results in poisson channels in the continuous time setting the received signal is a doubly stochastic poisson point process whose rate is equal to the input signal plus a dark current it is found that regardless of the statistics of the input the derivative of the input output mutual information with respect to the intensity of the additive dark current can be expressed as the expected difference between the logarithm of the input and the logarithm of its noncausal conditional mean estimate the same holds for the derivative with respect to input scaling but with the logarithmic function replaced by x log x similar relationships hold for discrete time versions of the channel where the outputs are poisson random variables conditioned on the input symbols

further results on differential detection of gmsk signals we evaluate the performance in terms of bit error rate of 1 and 2 bit differential detectors for gaussian minimum shift keying gmsk signals by using a very fast numerical technique which makes use of the saddle point approximation moreover the performance of each detector is optimized by using a closed form expression of the optimum threshold in the slicer

analysis of avalanche diode receivers by saddlepoint integration the error probability in a binary fiber optical communication system whose receiver utilizes an avalanche diode detector is calculated by applying the method of numerical saddlepoint integration to laplace inversion integrals for the probabilities of errors of the first and second kinds it is shown how to choose the contours of integration for efficient numerical quadrature the effects of shot noise intersymbol interference and additive gaussian noise are taken into account and the decision level on the receiver output is set to minimize the average probability of error examples show how the method can be used in receiver design to select system parameters such as the output pulsewidth and the sampling time in order to minimize the probability of error