linear and nonlinear chip rate minimum mean squared error multiuser cdma detection a linear kalman filter detector for code division multiple access proposed earlier in the literature is extended to a structure that can handle arbitrary detection delays through the mechanism of state augmentation because pre detection rake combining is used in the detector it is optimal for multipath channels unlike the previous structure that performed post detection combining we also derive nonlinear kalman detectors which approximate the highly complex nonlinear minimum mean squared error detector using the concept of additional observations both linear and nonlinear detectors require processing at one or more times the chip rate and knowledge of the spreading codes of interfering users they have the advantage over many other multiuser detection algorithms of not requiring the spreading codes to be periodic at the symbol rate or matrix inversion in addition two of the detectors are able to generate and update a posteriori probabilities of the transmitted symbols making them interesting for iterative multiuser detection

bandpass correlator analysis for general input assumptions corresp for general assumptions concerning bandpass signal and noise inputs previous analyses of analog cross correlators have yielded very complicated expressions for the probability density function pdf of the correlator output the inherent computational difficulties therefore limited the application of these pdf s almost exclusively to special cases of equal noise powers and noise spectrums symmetric about the signal s frequency in this correspondence it is shown that for general bandpass inputs the correlator output can always be expressed as the difference of two scaled independent noncentral chi squared variables if a certain matrix transformation of variables is employed the characteristic function method is then used to derive the pdf which is as readily computed as for the case of special assumptions

ll filters a new class of order statistic filters the ll filters are introduced to generate the order statistic filters l filters and the nonrecursive linear or finite duration impulse response fir filters such estimators are particularly effective filtering signals that do not necessarily follow gaussian distributions they can be designed to restore one dimensional or multidimensional signals corrupted by noise of impulsive type such filters are appealing since they are suitable for being made robust against the presence of spurious outliers in the data

performance of optimum and suboptimum combining diversity reception for binary and quadrature dpsk over independent nonidentical rayleigh fading channels this paper is concerned with the error performance analysis of binary and quadrature differential phase shift keying with differential detection over the nonselective rayleigh fading channel with combining diversity reception the diversity channels are independent but have nonidentical statistics the fading process in each channel is assumed to have an arbitrary doppler spectrum with arbitrary doppler bandwidth both optimum diversity reception and suboptimum diversity reception are considered results available previously apply only to the case of second order diversity and require numerical integration for their actual evaluation our results are more general in that the order of diversity is arbitrary moreover the bit error probability bep result is obtained in an exact closed form expression which shows the behavior of the bep as an explicit function of the one symbol interval fading correlation coefficient at the matched filter output the mean received signal to noise ratio per symbol per channel and the order of diversity

averaged controllability of parameter dependent conservative semigroups abstract we consider the problem of averaged controllability for parameter depending either in a discrete or continuous fashion control systems the aim being to find a control independent of the unknown parameters so that the average of the states is controlled we do it in the context of conservative models both in an abstract setting and also analysing the specific examples of the wave and schrodinger equations our first result is of perturbative nature assuming the averaging probability measure to be a small parameter dependent perturbation in a sense that we make precise of an atomic measure given by a dirac mass corresponding to a specific realisation of the system we show that the averaged controllability property is achieved whenever the system corresponding to the support of the dirac is controllable similar tools can be employed to obtain averaged versions of the so called ingham inequalities particular attention is devoted to the 1d wave equation in which the time periodicity of solutions can be exploited to obtain more precise results provided the parameters involved satisfy diophantine conditions ensuring the lack of resonances

optimal detection of digital data over the nonselective rayleigh fading channel with diversity reception based on the criterion of minimum symbol error probability an analysis is made of symbol by symbol detection of a sequence of digital data transmitted using linear suppressed carrier modulation over l independent diversity channels with awgn additive white gaussian noise and slow nonselective rayleigh fading the optimal receiver is derived but is found to be difficult to implement in practice because of its exponential growth in complexity as a function of sequence length suboptimal decision feedback approximations are then suggested which are linear and readily implementable and can be integrated as generalized differentially coherent receivers the exact bit error probabilities of these suboptimal receivers are obtained tight upper bounds on these error probabilities are also obtained which show simply how they behave as a function of signal to noise ratio and order of diversity a main conclusion of this work is that optimal data detection on a fading channel should be performed using mmse minimum mean squared error estimates of the quadrature amplitudes of the channel fading processes as a coherent reference

bit error probabilities of 2 and 4dpsk with nonselective rayleigh fading diversity reception and correlated gaussian interference a new analytical approach is presented for deriving the bit error probability results for 2 and 4dpsk with differential detection over the nonselective rayleigh fading channel with diversity reception and with an additional additive correlated gaussian interference process in each diversity channel the approach differs from that in a previous paper and is based on a well known result in the literature the results are new and reduce to known results when the correlated interference is absent they show that the correlated interference behaves like an additional component of the information bearing signal and affects the error probabilities of the various transmitted symbols differently irrespective of its statistical distribution its gaussian statistical distribution is essential only for the analysis of the bit error probability

optimum gaussian filter for differential detection of msk an optimum predetection gaussian bandpass filter for differential detection of msk is derived theoretically with numerical techniques the optimum product of bandwidth b and bit duration t compromising the noise reduction effect with the intersymbol interference effect is calculated at a given bit error rate ber it is shown that the optimum bt product is 1 21 with 4 02 db degradation at 10 6ber where the degradation is defined as the increase in e b n 0 relative to ideal coherent detection of msk

how to get a conservative well posed linear system out of thin air part ii controllability and stability let a0 be a possibly unbounded positive operator on the hilbert space h which is boundedly invertible let c0 be a bounded operator from cal d a 0 1 2 with the norm z 1 2 2 langle

a closed form expression for the symbol error rate of m ary dpsk in fast rayleigh fading the error performance of m ary differential phase shift keying on rayleigh fading channels is widely analyzed in the framework originated by pawula and the results usually take the form of an integral in this letter we formulate the same problem in a different framework and solve it by using a linear prediction based technique resulting in a simple solution in closed form

microstatistics in signal decomposition and the optimal filtering problem the author introduces and analyzes a large class of nonlinear filters which are based on signal decomposition and where the estimation in the decomposed space uses linear combinations of either the observation vector the sorted observation vector or in general a nonlinear transformation of the observation vector thus nonlinear filter response characteristics are achieved but with the machinery of linear systems theory available for their optimization and design it is shown that linear filters are a subclass of microstatistic filters and that the optimal linear filter solution is suboptimal in the decomposed signal space the filtering problem reduces to a set of filters operating on the decomposed signals the output is a weighted sum of the decomposed filtered signals the optimal interconnection structure between decomposed signals has complexity o m 1 where m is the cardinality of the decomposition the formulation is given for a radix 1 decomposition and generalized for a radix q decomposition computer simulations illustrate the performance

uniform controllability of semidiscrete approximations of parabolic control systems controlling an approximation model of a controllable infinite dimensional linear control system does not necessarily yield a good approximation of the control needed for the continuous model in the present paper under the main assumptions that the discretized semigroup is uniformly analytic and that the control operator is mildly unbounded we prove that the semidiscrete approximation models are uniformly controllable moreover we provide a computationally efficient way to compute the approximation controls an example of application is implemented for the one and two dimensional heat equation with neumann boundary control

computation of the bit error rate of coherent m ary psk with gray code bit mapping efficient computation of the bit error rate ber for the coherent m ary psk signals with gray code bit mapping is considered a closed form expression for the exact ber of 8 ary psk is presented tight upper and lower bounds on ber are also obtained for m ary psk with larger m

permutation filters a class of nonlinear filters based on set permutations introduces and analyzes a new class of nonlinear filters that have their roots in permutation theory the authors show that a large body of nonlinear filters proposed to date constitute a proper subset of permutation filters spl pscr filters in particular rank order filters weighted rank order filters and stack filters embody limited permutation transformations of a set indeed by using the full potential of a permutation group transformation one can design very efficient estimation algorithms permutation groups inherently utilize both rank order and temporal order information thus the estimation of nonstationary processes in gaussian nongaussian environments with frequency selection can be effectively addressed an adaptive design algorithm that minimizes the mean absolute error criterion is described as well as a more flexible adaptive algorithm that attains the optimal permutation filter under a deterministic least normed error criterion simulation results are presented to illustrate the performance of permutation filters in comparison with other widely used filters

tight bounds on rician type error probabilities and some applications consider the classic problem of evaluating the probability that one rician random variable exceeds another possibly correlated rician random variable this probability is given by stein 1964 in terms of the marcum s q function which requires numerical integration on the computer for its evaluation to facilitate application in many digital communication problems we derive here tight upper and lower bounds on this probability the bounds are motivated by a classic result in communication theory namely the error probability performance of binary orthogonal signaling over the gaussian channel with unknown carrier phase various applications of the bounds are reported including the evaluation of the bit error probabilities of mdpsk and mpsk with differential detection and generalized differential detection respectively the bounds prove to be tight in all cases further applications will be reported in the future

error rate performance of digital fm mobile radio with postdetection diversity an analysis of bit error rate ber in a binary digital fm system with postdetection diversity is presented expressions for the average ber due to additive white gaussian noise awgn random fm noise and delay spread in the multipath channel are derived for reception using differential demodulation dd and frequency demodulation fd assuming independent fading signals calculated results for msk show that the ber performance is strongly dependent on the rms delay bit duration ratio and that the delay spectrum shape is of no importance when the receiver predetection filter product is optimized for the effect of awgn the effect of fading correlation on the diversity improvement is also analyzed for a two branch case with multiplicative rayleigh fading signals expressions for the average ber due to awgn and random fm noise are derived calculated results are shown for the average ber due to random fm noise assuming a horizontally spaced antenna system at a mobile station it is shown that the use of small antenna spacings leads to a diversity improvement greater than that obtainable for the case of independent awgn

effect of channel estimation error on qam systems with antenna diversity this paper studies the effect of channel estimation error and antenna diversity on multilevel quadrature amplitude modulation m qam systems over rayleigh fading channels based on the characteristic function method a general closed form bit error rate ber for m qam systems is presented the effect of the inaccurate channel estimation on the performance for pilot symbol assisted modulation m qam systems with antenna diversity is investigated simulation results for m qam m 4 16 64 256 etc show that the analytical method can accurately estimate the system performance moreover numerical results show that with the antenna diversity technique the ber performance improves significantly especially in perfect channel estimation cases it is also found that the channel estimation error limits the benefit of antenna diversity by increasing the length of the channel estimator and the amplitude of the pilot symbol more accurate channel estimation can be achieved so that the ber performance is improved

effect of channel estimation error on m qam ber performance in rayleigh fading we determine the bit error rate ber of multilevel quadrature amplitude modulation m qam in flat rayleigh fading with imperfect channel estimates despite its high spectral efficiency m qam is not commonly used over fading channels because of the channel amplitude and phase variation since the decision regions of the demodulator depend on the channel fading estimation error of the channel variation can severely degrade the demodulator performance among the various fading estimation techniques pilot symbol assisted modulation psam proves to be an effective choice we first characterize the distribution of the amplitude and phase estimates using psam we then use this distribution to obtain the ber of m qam as a function of the psam and channel parameters by using a change of variables our exact ber expression has a particularly simple form that involves just a few finite range integrals this approach can be used to compute the ber for any value of m we compute the ber for 16 qam and 64 qam numerically and verify our analytical results by computer simulation we show that for these modulations amplitude estimation error leads to a 1 db degradation in average signal to noise ratio and combined amplitude phase estimation error leads to 2 5 db degradation for the parameters we consider

a new extrapolation algorithm for band limited signals using the regularization method the ill posedness of the extrapolation problem in the presence of noise is considered a stable algorithm is constructed by solving a fredholm equation based on a regularization method the algorithm appears relatively robust since the noise eta sub delta t is taken as a function in l sup 2 t t t 0 such that the error energy integral mod eta sub delta t mod sup 2 dt

a new class of nonlinear filters neural filters a class of nonlinear filters based on threshold decomposition and neural networks is defined it is shown that these neural filters include all filters defined either by continuous functions such as linear finite impulse response fir filters or by boolean functions such as generalized stack filters adaptive least mean absolute error and adaptive least mean square error algorithms are derived for determining optimal neural filters as special cases adaptive generalized stack and adaptive generalized weighted order statistic filtering algorithms under both error criteria are derived experimental results in 1d and 2d signal processing are presented to compare the performances of the adaptive neural filters and other widely used filters

ber expressions for differentially detected spl pi 4 dqpsk modulation closed form bit error rate ber expressions for differentially detected spl pi 4 shifted differentially encoded quadrature phase shift keying qpsk modulation spl pi 4 dqpsk are derived for both additive white gaussian noise awgn and rayleigh fading channels the derivations are carried out in an exact and most general manner in that in phase i and quadrature q channel bit error probabilities p sub cl and p sub cq are separately obtained in terms of the same quadrature and cross quadrature noise correlation functions including a measure of noise nonstationarity we then specialize the general expressions for uncorrelated noise and equal noise powers in successive symbol periods to obtain a useful bit error probability expression for the awgn channel in the form p sub e spl ap q spl radic 1 1716 spl middot e sub b n sub 0 where q spl middot is the gaussian distribution q function and e sub b n sub 0 is the bit energy to noise density ratio exact ber expressions for the rayleigh fading channel that involve the noise parameters are also given and are extended to the case of l fold diversity combining

an approximation method for exact controls of vibrating systems we propose a new method for the approximation of exact controls of a second order infinite dimensional system with bounded input operator the algorithm combines russell s stabilizability implies controllability principle with the galerkin method the main new feature of this work consists of giving precise error estimates in order to test the efficiency of the method we consider two illustrative examples with the finite element approximations of the wave and the beam equations and describe the corresponding simulations

adaptive symbol by symbol reception of mpsk on the gaussian channel with unknown carrier phase characteristics an adaptive version of the optimum decision aided symbol by symbol receiver obtained in our previous works for m ary phase shift keying over the gaussian channel with unknown carrier phase characteristics is considered it uses a first order adaptive filter for carrier reference tracking and the filter gain is adapted on line based on the observed signal samples using a least mean square error criterion the phase tracking performance of the filter in the steady state tracking mode is analyzed using a linearized model the phase tracking error variance is minimized due to the risk function used in designing the filter gain adaptation algorithm the bit error probability for quadrature phase shift keying is obtained both analytically and via computer simulations

micro and macrodiversity mdpsk on shadowed frequency selective channels the performance of m ary differential phase shift keying mdpsk on frequency selective slow rayleigh fading lognormal shadowed channels with diversity combining is analyzed for mobile and portable applications the use of l branch equal gain postdetection microdiversity combining to mitigate the effects of fading and p port macrodiversity to alleviate the effects of shadowing are investigated four performance criteria are considered for a frequency selective multipath fading intersymbol interference channel these are the short term bit error rate ber the irreducible ber the complementary distribution over the lognormal shadowing of the average ber and the probability that the instantaneous ber exceeds a threshold value averaged over a spatial environment closed form expressions for the four performance criteria are obtained the ber and outage performance results show that diversity combining is an effective method for improving the system performance and hence system reliability when the normalized delay spread is not large it is also seen that in most cases 4dpsk gives the best performance followed by 8dpsk and 2dpsk respectively for a given information throughput

design and performance of combination filters for signal restoration a class of nonlinear moving window filters is investigated for restoration and detection of signals embedded in additive white gaussian and non gaussian noise the filters of this class called combination filters c filters use both rank order and temporal order information from the input observation sequence within finite processing windows to produce the outputs a c filter combines the characteristics of linear fir finite impulse response filters and nonlinear filters of the order statistics type the output of a c filter in each processing window is defined to be the rank order dependent weighting of temporal order data both analytical and training procedures for designing the c filters are considered to get further improvement in overall performance the authors extend the concept of c filters and introduce a class of generalized c filters gc filters which are shown to have desirable properties performance characteristics of c and gc filters in signal restoration are considered through computer simulation

reconstructing initial data using observers error analysis of the semi discrete and fully discrete approximations a new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in ramdani et al automatica 46 10 1616 1625 2010 based on the concept of observers also called luenberger observers this algorithm covers a large class of abstract evolution pde s in this paper we are concerned with the convergence analysis of this algorithm more precisely we provide a complete numerical analysis for semi discrete in space and fully discrete approximations derived using finite elements in space and an implicit euler method in time the analysis is carried out for abstract schrodinger and wave conservative systems with bounded observation locally distributed

proper complex random processes with applications to information theory the covariance of complex random variables and processes when defined consistently with the corresponding notion for real random variables is shown to be determined by the usual complex covariance together with a quantity called the pseudo covariance a characterization of uncorrelatedness and wide sense stationarity in terms of covariance and pseudo covariance is given complex random variables and processes with a vanishing pseudo covariance are called proper it is shown that properness is preserved under affine transformations and that the complex multivariate gaussian density assumes a natural form only for proper random variables the maximum entropy theorem is generalized to the complex multivariate case the differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum if and only if the random vector is proper gaussian and zero mean the notion of circular stationarity is introduced for the class of proper complex random processes a discrete fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain an application of the theory is presented

analysis of the hum control operator and exact controllability for semilinear waves in uniform time we present a regularity result for the hum optimal control associated with the interior control of linear waves we use this analysis together with strichartz inequalities to get results on the exact controllability for subcritical nonlinear waves in a bounded domain of mathbb r 3

optimal control with stochastic pde constraints and uncertain controls abstract the optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed the lagrangian that defines the problem is postulated in terms of stochastic functions with the control function possibly decomposed into an unknown deterministic component and a known zero mean stochastic component the extra freedom provided by the stochastic dimension in defining cost functionals is explored demonstrating the scope for controlling statistical aspects of the system response one shot stochastic finite element methods are used to find approximate solutions to control problems it is shown that applying the stochastic collocation finite element method to the formulated problem leads to a coupling between stochastic collocation points when a deterministic optimal control is considered or when moments are included in the cost functional thereby forgoing the primary advantage of the collocation method over the stochastic galerkin method for the considered problem the application of the presented methods is demonstrated through a number of numerical examples the presented framework is sufficiently general to also consider a class of inverse problems and numerical examples of this type are also presented

permutation weighted order statistic filter lattices we introduce and analyze a new class of nonlinear filters called permutation weighted order statistic pwos filters these filters extend the concept of weighted order statistic wos filters in which filter weights associated with the input samples are used to replicate the corresponding samples and an order statistic is chosen as the filter output pwos filters replicate each input sample according to weights determined by the temporal order and rank order of samples within a window hence pwos filters are in essence time varying wos filters by varying the amount of temporal rank order information used in selecting the output for a given observation window size we obtain a wide range of filters that are shown to comprise a complete lattice structure at the simplest level in the lattice pwos filters reduce to the well known wos filter but for higher levels in the lattice the obtained selection filters can model complex nonlinear systems and signal distortions it is shown that pwos filters are realizable by a n piecewise linear threshold logic gate where the coefficients within each partition can be easily optimized using stack filter theory simulations are included to show the advantages of pwos filters for the processing of image and video signals

bit error probabilities mdpsk over the nonselective rayleigh fading channel with diversity reception data transmission using m ary differential phase shift keying mdpsk over the nonselective rayleigh fading channel with diversity reception is considered while previous studies on error probability mostly assume no fading fluctuation the author considers exclusively the case in which the fading process fluctuates from one symbol interval to the next exact bit error probability results for 2 4 and 8 dpsk as well as tight upper bounds are derived some applications of the results are discussed

propagation observation and control of waves approximated by finite difference methods this paper surveys several topics related to the observation and control of wave propagation phenomena modeled by finite difference methods the main focus is on the property of observability corresponding to the question of whether the total energy of solutions can be estimated from partial measurements on a subregion of the domain or boundary the mathematically equivalent property of controllability corresponds to the question of whether wave propagation behavior can be controlled using forcing terms on that subregion as is often desired in engineering applications observability controllability of the continuous wave equation is well understood for the scalar linear constant coefficient case that is the focus of this paper however when the wave equation is discretized by finite difference methods the control for the discretized model does not necessarily yield a good approximation to the control for the original continuous problem in other words the classical convergence consistency stability property of a numerical scheme does not suffice to guarantee its suitability for providing good approximations to the controls that might be needed in applications observability controllability may be lost under numerical discretization as the mesh size tends to zero due to the existence of high frequency spurious solutions for which the group velocity vanishes this phenomenon is analyzed and several remedies are suggested including filtering tychonoff regularization multigrid methods and mixed finite element methods we also briefly discuss these issues for the heat beam and schrodinger equations to illustrate that diffusive and dispersive effects may help to retain the observability controllability properties at the discrete level we conclude with a list of open problems and future subjects for research

averaged control we analyze the problem of controlling parameter dependent systems we introduce the notion of averaged control according to which the quantity of interest is the average of the states with respect to the parameter first we consider the problem of controllability for linear finite dimensional systems and show that a necessary and sufficient condition for averaged controllability is an averaged rank condition in the spirit of the classical rank condition for linear control systems but involving averaged momenta of any order of the matrices generating the dynamics and representing the control action we also describe some open problems and directions of possible research in particular on the average controllability of evolution partial differential equations in this context we analyze also the averaged version of a classical optimal control problem for a parameter dependent elliptic equation and derive the corresponding optimality system

error probability for coherent and differential psk over arbitrary rician fading channels with multiple cochannel interferers this paper discusses the performance of communication systems using binary coherent and differential phase shift keyed psk modulation in correlated rician fading channels with diversity reception the presence of multiple rician faded cochannel users which may have arbitrary and nonidentical parameters is modeled exactly exact bit error probability bep expressions are derived via the moment generating functions mgfs of the relevant decision statistics which are obtained through coherent detection with maximum ratio combining for coherent psk modulation and differential detection with equal gain combining egc for differential modulation evaluating the exact expressions requires a complexity that is exponential in the number of interferers to avoid this potentially time consuming operation we derive two low complexity approximate methods each for coherent and differential modulation formats which are more accurate than the traditional gaussian approximation approach two new and interesting results of this analysis are 1 unlike in the case of rayleigh fading channels increasing correlation between diversity branches may lead to better performance in rician fading channels and 2 the phase distribution of the line of sight or static fading components of the desired user has a significant influence on the bep performance in correlated diversity channels

microstatistic lms filtering adaptive microstatistic filters are developed for applications in which the second order statistics of the thresholded signals are not known or may be nonstationary a multilevel threshold decomposition such that real valued stochastic processes can be filtered is used and the computational complexity of the algorithm can be arbitrarily specified by the designer the adaptation uses the least mean squares error approach of the least mean square lms algorithm the convergence of the adaptive algorithm is proved due to the nonhomogeneous statistical characteristic of the threshold signals a different step size adaptation parameter can be assigned to each threshold level simple design guidelines are developed for finding the set of nonhomogeneous step sizes which in practice yield better convergence characteristics

tight bounds on the bit error probabilities of 2dpsk and 4dpsk in nonselective rician fading the bit error probabilities beps of matched filtered differentially detected two differential phase shift keying 2dpsk and 4dpsk over the nonselective rician fading channel are studied using the upper bound in kam 1994 the bound coincides with the exact error probability result in the binary case and provides very accurate estimates of the bep in the quadriphase case especially for high signal to noise ratio snr and small k factor the bound provides a simple analytical handle for studying the behavior of the error probability as a function of the doppler spectrum the doppler bandwidth and the k factor a new result is obtained for the irreducible error rate floor the results are useful for the design of digital mobile radio communication systems

analysis of differential orthogonal space time block codes over semi identical mimo fading channels we study the performance of differential orthogonal space time block codes ostbc over independent and semi identically distributed block rayleigh fading channels in this semiidentical fading model the channel gains from different transmit antennas to a common receive antenna are identically distributed but the gains associated with different receive antennas are nonidentically distributed arbitrary fluctuation rates of the fading processes from one transmission block to another are considered we first derive the optimal symbol by symbol differential detector and show that the conventional differential detector is suboptimal we then derive expressions of exact bit error probabilities beps for both the optimal and suboptimal detectors the results are applicable for any number of receive antennas and any number of transmit antennas for which ostbcs exist for two transmit antennas explicit and closed form bep expressions are obtained for an arbitrary number of transmit antennas a chernoff bound on the bep for the optimal detector is also derived our results show that the semi identical channel statistics degrade the error performance of differential ostbc compared with the identical case also the proposed optimal detector substantially outperforms the conventional detector when the channel fluctuates rapidly but in near static fading channels the two detectors have similar performances

risk averse shape optimization risk averse optimization has attracted much attention in finite dimensional stochastic programming in this paper we propose a risk averse approach in the infinite dimensional context of shape optimization we consider elastic materials under stochastic loading as measures of risk awareness we investigate the expected excess and the excess probability the developed numerical algorithm is based on a regularized gradient flow acting on an implicit description of the shapes based on level sets we incorporate topological derivatives to allow for topological changes in the shape optimization procedure numerical results in two dimensions demonstrate the impact of the risk averse modeling on the optimal shapes and on the cost distribution over the set of scenarios

the performance of fsk in frequency selective rayleigh fading this paper presents measured error rate performance of binary fsk with discriminator detection in simulated rayleigh fading with time delay spread measured relations between error rate and carrier to noise ratio are shown for a range of time delay spreads we have verified that the effect of time delay spread on error rate can be described by only one parameter the ratio of the rms delay spread to the transmitted baud time intersymbol interference from time delay spread causes an irreducible error rate for fsk even for infinite carrier to noise ratio for 64 kbit s binary fsk the 2 6 s rms delay spread typical of the urban environment produces an irreducible error rate of 3 percent the measured irreducible error rate for binary fsk with discriminator detection is proportional to the fourth power of the ratio of rms delay spread to baud time this functional dependence is identical to that predicted analytically for fsk with incoherent matched filter detection

weighted median image sharpeners for the world wide web a class of robust weighted median wm sharpening algorithms is developed in this paper unlike traditional linear sharpening methods weighted median sharpeners are shown to be less sensitive to background random noise or to image artifacts introduced by jpeg and other compression algorithms these concepts are extended to include data dependent weights under the framework of permutation weighted medians leading to tunable sharpeners that in essence are insensitive to noise and compression artifacts permutation wm sharpeners are subsequently generalized to smoother sharpener structures that can sharpen edges and image details while simultaneously filter out background random noise a statistical analysis of the various algorithms is presented theoretically validating the characteristics of the proposed sharpening structures a number of experiments are shown for the sharpening of jpeg compressed images and sharpening of images with background film grain noise these algorithms can prove useful in the enhancement of compressed or noisy images posted on the world wide web www as well as in other applications where the underlying images are unavoidably acquired with noise

gradient based design optimization under uncertainty via stochastic expansion methods abstract we present a computational framework for robust and reliability based design optimization which combines stochastic expansion methods namely polynomial chaos expansion with design sensitivity analysis it is well known that the statistical moments and their gradients with respect to design variables can be readily obtained from the polynomial chaos expansion however the evaluation of the failure probabilities of the cost and constraint functions and their gradients requires integrations over failure regions to simplify this we introduce an indicator function into the integrand whereby the integration region becomes the known range of random variables and to alleviate the non differentiable property of the indicator function a smooth approximation is adopted to facilitate the sensitivity analysis both intrusive and non intrusive polynomial chaos approaches for uncertainty propagation are employed in the design optimization of linear elastic structures guidelines to assess the computational costs associated with both polynomial chaos approaches are also presented

fast adaptation and performance characteristics of fir wos hybrid filters fast adaptive algorithms are developed for training weighted order statistic wos filters and fir wos hybrid fwh filters under the mean absolute error mae criterion these algorithms are based on the threshold decomposition of real valued signals introduced in this paper with this method an n length wos filter can be implemented by thresholding the input signals at most n times independent of the accuracy used beside saving in computations the proposed algorithms can be applied to process arbitrary real valued signals directly performance characteristics of fwh filters in 1 d and 2 d signal restoration are investigated through computer simulations we show that both in restoration of signals containing edges and in the case of heavy tailed nongaussian noise considerable improvement in performance can be achieved with fwh filters over wos filters ll filters and adaptive linear filters two new fwh filter design strategies are found for removal of impulsive noise and for restoration of a square wave respectively

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

differentially amplitude and phase encoded qam for the correlated rayleigh fading channel with diversity reception this paper studies the differentially amplitude and phase encoded dape quadrature amplitude modulation qam transmission over correlated rayleigh channels with diversity reception operating over two successive received symbols the optimum and an asymptotic maximum likelihood aml differentially coherent receiver are developed and compared with a conventional switched diversity combining sdc grid receiver it is shown that the aml and sdc grid receivers are much simpler in complexity than the optimum receiver in that no channel side information is required in their realization an exact expression of the bit error probability bep is obtained for the sdc grid receiver based on a union bound argument a bep upper bound for the aml receiver is also derived and verified by simulation numerical results on 16 and 64 point constellations show that the aml receiver exhibits an almost optimum performance and the sdc grid receiver with a small level of diversity is nearly optimum it is also shown by simulation that the conventional equal gain diversity receiver is almost optimal for demodulating a 16 point dape qam signal

a systematic approach to the design and analysis of optimum dpsk receivers for generalized diversity communications over rayleigh fading channels a generalized diversity channel is introduced that models a variety of wireless communication systems that use time frequency multipath and or antenna diversity with various interbranch correlations between signaling waveforms and the fading and additive noise processes in the context of this general model a systematic approach to the design and analysis of optimum noncoherent differential phase shift keying dpsk receivers is introduced in particular it is shown how the minimum error probability mep and the generalized likelihood ratio tests glrt can be applied to obtain optimal noncoherent combining rules a comparative error rate analysis of the glrt and mep detectors and an ad hoc equal gain combiner is provided for binary signaling and the suitability of the three schemes is determined as a function of fading characteristics the asymptotic bit error rate analysis is undertaken for the mep detector for slow and fast fading channels an estimator detector decomposition of the noncoherent mep rule is obtained which allows an insightful comparative study of the fundamental limits of binary phase shift keying and dpsk modulation detection methods for both slow and fast fading the results of this paper are also applicable to postdecorrelative receivers in multiuser channels

a simple bit error probability analysis for square qam in rayleigh fading with channel estimation a new approach is presented for analyzing the bit error probability bep of square multilevel quadrature amplitude modulation over a nonselective rayleigh fading channel with imperfect channel estimation employing pilot symbol assisted modulation it is much simpler and more powerful than those in the literature and the average bep is obtained by calculating the bep for each individual bit the results are given in simple exact closed form expressions that do not require any numerical integration these expressions show explicitly the behavior of the bep as a function of various system parameters three channel estimation schemes are investigated it is shown that existing channel estimation schemes using sinc interpolation and gaussian interpolation can be improved

the fuzzy transformation and its applications in image processing the spatial and rank sr orderings of samples play a critical role in most signal processing algorithms the recently introduced fuzzy ordering theory generalizes traditional or crisp sr ordering concepts and defines the fuzzy spatial samples fuzzy order statistics fuzzy spatial indexes and fuzzy ranks here we introduce a more general concept the fuzzy transformation fzt which refers to the mapping of the crisp samples order statistics and sr ordering indexes to their fuzzy counterparts we establish the element invariant and order invariant properties of the fzt these properties indicate that fuzzy spatial samples and fuzzy order statistics constitute the same set and under commonly satisfied membership function conditions the sample rank order is preserved by the fzt the fzt also possesses clustering and symmetry properties which are established through analysis of the distributions and expectations of fuzzy samples and fuzzy order statistics these properties indicate that the fzt incorporates sample diversity into the ordering operation which can be utilized in the generalization of conventional filters here we establish the fuzzy weighted median fwm fuzzy lower upper middle flum and fuzzy identity filters as generalizations of their crisp counterparts the advantage of the fuzzy generalizations is illustrated in the applications of dct coded image deblocking impulse removal and noisy image sharpening

permutation filter lattices a general order statistic filtering framework a general nonlinear filtering framework permutation order statistic filter lattices is introduced which defines a highly modular and robust class of filters which effectively addresses both the nonlinear characteristics of a system as well as the possible noise contamination permutation filters much like polynomial filters are flexible and modular where instead of having polynomial expansions we have permutation lattice expansions at the simplest level in the filter lattice permutation filters reduce to either a simple linear fir or to an order statistic os filter but at higher levels in the lattice the obtained filters can model complicated nonlinear systems more accurately while still preserving their robust properties in order to enhance the robustness of permutation fitters we develop spl alpha trimmed permutation indicators and their associated filter lattices we conclude by presenting simulation examples where permutation filters are used in nonlinear system identification and in the rejection of narrowband interference in a direct sequence multiple access system this paper thus extends the potential of order statistic filters which have been shown to be somewhat limited in general nonlinear estimation problems

equal gain performance of mdpsk in nakagami fading and correlated gaussian noise the general formula for evaluating the bit error probability of m ary differential phase shift keying with l diversity equal gain combining over frequency nonselective m distributed uncorrelated nakagami fading channels and correlated gaussian noise is presented the evaluation usually takes a one dimensional integration and this integration can be reduced to a closed form for integer m by applying the residue theorem

uniform exponential long time decay for the space semi discretization of a locally damped wave equation via an artificial numerical viscosity we consider the finite difference space semi discretization of a locally damped wave equation the damping being supported in a suitable subset of the domain under consideration so that the energy of solutions of the damped wave equation decays exponentially to zero as time goes to infinity the decay rate of the semi discrete systems turns out to depend on the mesh size h of the discretization and tends to zero as h goes to zero we prove that adding a suitable vanishing numerical viscosity term leads to a uniform with respect to the mesh size exponential decay of the energy of solutions this numerical viscosity term damps out the high frequency numerical spurious oscillations while the convergence of the scheme towards the original damped wave equation is kept we discuss this problem in 1d and 2d in the interval and the square respectively our method of proof relies on discrete multiplier techniques

accurate evaluation for mdpsk with noncoherent diversity the error probability analysis of m ary differential phase shift keying signals with noncoherent diversity combining over general fading channels is not available in the literature except for some simple cases the difficulty lies in the philosophy which attempts to explicitly determine the phase distribution expressions of the received signal and this often leads to a mathematically intractable issue in this paper we take a novel approach by formulating the phase distribution in terms of joint moment generating functions of the real and imaginary parts of the decision variable at the receiver output we further derive fast convergent techniques for two dimensional 2 d inverse laplace transform enabling us to accurately evaluate the phase distribution the error probability formulas thus obtained involve a twofold integral which can be efficiently evaluated by using our algorithms developed on the basis of the 2 d trapezoidal summation and gauss chebyshev quadrature the new technique is very general taking into account the effects of arbitrary diversity order symbol alphabet size m and arbitrary diversity branches correlation numerical results are also presented for illustration

further results on the bit error probabilities of mdpsk over the nonselective rayleigh fading channel with diversity reception this paper presents a fundamental approach for deriving the bit error probability of bdpsk and qdpsk over the nonselective rayleigh fading channel for a receiver with an arbitrary if filter and for a fading process with an arbitrary doppler spectrum with arbitrary doppler bandwidth the results generalize those published earlier which were restricted to matched filter reception and to a fading process with a small doppler bandwidth compared to the symbol rate this allows the error probability to be studied in the presence of varying degrees of isi due to the bandlimitation of the received signal by the if filter and in the presence of fading fluctuations of various rates the analytical approach presented is simple and yet powerful in that it can handle the case of diversity reception this is a great advantage over the alternative approach of using the distribution of the differential phase of the received signal over a symbol interval the bit error probability results apply to both conventional bdpsk and qdpsk as well as spl pi 2 2dpsk and spl pi 4 4dpsk and allow the irreducible bit error probability as well as the snr at which this irreducible value sets in to be studied as a function of the doppler bandwidth and if filter bandwidth the computed results are applicable to the design of digital cellular mobile communication systems

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

minimum mean absolute error estimation over the class of generalized stack filters a class of sliding window operators called generalized stack filters is developed this class of filters which includes all rank order filters stack filters and digital morphological filters is the set of all filters possessing the threshold decomposition architecture and a consistency property called the stacking property conditions under which these filters possess the weak superposition property known as threshold decomposition are determined an algorithm is provided for determining a generalized stack filter which minimizes the mean absolute error mae between the output of the filter and a desired input signal given noisy observations of that signal the algorithm is a linear program whose complexity depends on the window width of the filter and the number of threshold levels observed by each of the filters in the superposition architecture the results show that choosing the generalized stack filter which minimizes the mae is equivalent to massively parallel threshold crossing decisions making when the decision are consistent with each other

a stochastic collocation method for elliptic partial differential equations with random input data this work proposes and analyzes a stochastic collocation method for solving elliptic partial differential equations with random coefficients and forcing terms these input data are assumed to depend on a finite number of random variables the method consists of a galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials gauss points in the probability space and naturally leads to the solution of uncoupled deterministic problems as in the monte carlo approach it treats easily a wide range of situations such as input data that depend nonlinearly on the random variables diffusivity coefficients with unbounded second moments and random variables that are correlated or even unbounded we provide a rigorous convergence analysis and demonstrate exponential convergence of the probability error with respect to the number of gauss points in each direction of the probability space under some regularity assumptions on the random input data numerical examples show the effectiveness of the method finally we include a section with developments posterior to the original publication of this work there we review sparse grid stochastic collocation methods which are effective collocation strategies for problems that depend on a moderately large number of random variables

new expressions for the pdf and cdf of the filtered output of an analog cross correlator corresp a general expression is derived for the probability density function pdf associated with the filtered output of an analog cross correlator the inputs of which consist of deterministic signals having the same frequency plus correlated stationary gaussian noise processes the correlator is composed of input bandpass filters a multiplier and a zonal iowpass filter the noise components in each channel have distinct variances and obey no spectral symmetry condition using the derived expression for the pdf the cumulative distribution function cdf under the same general conditions is calculated all previous known special cases are subsequently deduced from the general expressions given here the general results derived here are more suitable for numerical computations than comparable previous results found in the literature due to the fact that expressions here do not involve multiple infinite series lastly asymptotic formulas are developed for both the pdf and cdf which may be helpful in certain calculations

comparison of diversity with simple block coding on correlated frequency selective fading channels we investigate the effects of correlation on the performance of diversity systems in wideband wireless radio environments specifically the average bit error rate ber performance of m ary differential phase shift keying mdpsk on correlated frequency selective slow rayleigh fading channels is analyzed a two branch diversity receiver with postdetection equal gain combining is considered nyquist pulse shaping is used and differential detection is employed at the receiver the effects of cochannel interference on the system performance are assessed using a gaussian interference model to further enhance the system performance the effects of combined diversity and forward error correction fec coding on the average ber are investigated results using short cyclic block codes with perfect bit interleaving are obtained the effects of the root mean square rms delay spread the amount of correlation and the level of modulation m on the average ber are investigated in detail for both coded and uncoded systems the results show that dual branch diversity combining with a correlation coefficient of 0 5 outperforms in terms of ber short block codes with perfect bit interleaving and that combined diversity and coding strategies are effective in combatting the effects of frequency selective fading

locally distributed control and damping for the conservative systems in this paper we note the equivalence between exact controllability and exponential stabilizability for an abstract conservative system with bounded control this enables us to establish a frequency domain characterization for the exact controllability uniform exponential decay property of second order elastic systems such as the wave equation and the petrovsky equation with locally distributed control damping a piecewise multiplier method for frequency domain is introduced for several classes of pdes on regions which are not necessarily smooth we obtain a sufficient condition for the subregion on which the application of control damping will yield the exact controllability uniform exponential decay property this result provides useful information for designing the location of controllers dampers for distributed systems with a law of conservation

exact error rate analysis of diversity 16 qam with channel estimation error the bit error rate ber performance of multilevel quadrature amplitude modulation with pilot symbol assisted modulation channel estimation in static and rayleigh fading channels is derived both for single branch reception and maximal ratio combining diversity receiver systems the effects of noise and estimator decorrelation on the received ber are examined the high sensitivity of diversity systems to channel estimation error is investigated and quantified the influence of the pilot symbol interpolation filter windowing is also considered

robust optimal robin boundary control for the transient heat equation with random input data the problem of robust optimal robin boundary control for a parabolic partial dierential equation with uncertain input data is considered as a measure of robustness the variance of the random system response is included in two dierent cost functionals uncertainties in both the underlying state equation and the control variable are quantied through random elds the paper is mainly concerned with the numerical resolution of the problem to this end a gradient method is proposed a stochastic collocation nite element method is used for the numerical resolution of the associated state and adjoint state equations two numerical experiments illustrate the performance of the algorithm

analysis of the properties of median and weighted median filters using threshold logic and stack filter representation the deterministic properties of weighted median wm filters are analyzed threshold decomposition and the stacking property together establish a unique relationship between integer and binary domain filtering the authors present a method to find the weighted median filter which is equivalent to a stack filter defined by a positive boolean function because the cascade of wm filters can always be expressed as a single stack filter this allows expression of the cascade of wm filters as a single wm filter a direct application is the computation of the output distribution of a cascade of wm filters the same method is used to find a nonrecursive expansion of a recursive wm filter as applications of theoretical results several interesting deterministic and statistical properties of wm filters are derived

fuzzy rank lum filters the rank information of samples is widely utilized in nonlinear signal processing algorithms recently developed fuzzy transformation theory introduces the concept of fuzzy ranks which incorporates sample spread or sample diversity information into the sample ranking framework thus the fuzzy rank reflects a sample s rank as well as its similarity to the other sample namely joint rank order and spread and can be utilized to improve the performance of the conventional rank order based filters in this paper the well known lower upper middle lum filters are generalized utilizing the fuzzy ranks yielding the class of fuzzy rank lum f lum filters statistical and deterministic properties of the f lum filters are derived showing that the f lum smoothers have similar impulsive noise removal capability to the lum smoothers while preserving the image details better the f lum sharpeners are capable of enhancing strong edges while simultaneously preserving small variations the performance of the f lum filters are evaluated for the problems of image impulsive noise removal sharpening and edge detection preprocessing the experimental results show that the f lum smoothers can achieve a better tradeoff between noise removal and detail preservation than the lum smoothers the f lum sharpeners are capable of sharpening the image edges without amplifying the noise or distorting the fine details the joint smoothing and sharpening operation of the general f lum filters also showed superiority in edge detection preprocessing application in conclusion the simplicity and versatility of the f lum filters and their advantages over the conventional lum filters are desirable in many practical applications this also shows that utilizing fuzzy ranks in filter generalization is a promising methodology

bit error probability for orthogonal space time block codes with differential detection explicit closed form expressions of the bit error probabilities are obtained for space time block codes based on generalized orthogonal designs with differential encoding and differential detection using 2 sup b ary phase shift keying mapping the frequency nonselective block wise constant rayleigh fading channel is considered here the results are applicable to any number of transmit and receive antennas where the number of transmit antennas is dictated by the available coding schemes

frequency analysis and synthesis of a class of nonlinear filters nonlinear filters are analyzed from a spectral point of view the equivalent frequency behavior of a filter is described by its linear part which represents the linear nonrecursive filter that best matches in the mean square sense the behavior of the filter the class considered includes all the order statistic filters l filters such as median midrange alpha trim and some new order statistic filters ll filters defined by the authors to generalize l filters and fir filters the formulation leads to a technique for imposing on the nonlinear filters a given spectral behavior a simulation of the design for a low pass ll filter is given

differential versus limiter discriminator detection of narrow band fm the error probability performance of differential detection of narrow band fm is determined and compared with the analogous results for limiter discriminator detection of the same modulation it is shown that over a large class of benign and hostile environments e g gaussian if filter 1 leq bt leq 3 h leq 1 awgn partial band noise jamming the differential detector offers no theoretical performance advantage over the limiter discriminator receiver with integrate and dump postdetection filtering

differential modulation for decode and forward multiple relay systems in this paper differential modulation and demodulation in a multiple relay system using either the decode and forward df protocol or the selection relaying sr protocol are investigated for the df protocol the detectors at the destination take the average bit error probabilities beps of all the source relay transmissions into account for a df single relay system the exact bep and its approximation at high signal to noise ratio snr are obtained the approximation of the bep at high snr shows explicitly the diversity order and the different effects of the source relay link and the relay destination link on the end to end error performance for a df multiple relay system a chernoff upper bound on the bep and a high snr approximation for the bep are obtained for the sr protocol some computational complexity is shifted from the destination to all the relays each relay computes the instantaneous beps of the source relay transmissions and uses the instantaneous beps to decide whether to transmit or remain silent the destination performs simple maximal ratio combining mrc reception whose error performance is analyzed at high snr it shows from an error probability perspective that the sr protocol offers a space diversity order equal to the number of all the potential cooperating nodes

effect of channel estimation error on bit error probability in ofdm systems over rayleigh and ricean fading channels a characteristic function based method is used to derive closed form bit error probability bep expressions for orthogonal frequency division multiplexing ofdm systems in the presence of channel estimation error over frequency selective rayleigh fading channels and frequency selective ricean fading channels both single channel reception and diversity reception with maximal ratio combining mrc are examined the bep expressions are shown to be sums of several conditional probability functions which can be calculated by using proper complex gaussian random variable theory and a characteristic function method the closed form bep expressions can be used to accurately investigate the bit error rate performance degradation caused by channel estimation error under different wireless channel environment models the performances of two interpolation methods a sine interpolator with hamming windowing and a wiener interpolator are compared

regularity and exact controllability for a beam with piezoelectric actuator we consider an initial and boundary value problem modelling the vibrations of a bernoulli euler beam with an attached piezoelectric actuator we show that the sobolev regularity of the solution is by frac 1 2 epsilon higher than that one obtains by simply using the sobolev regularity of the control term the main results concern the dependence of the space of exactly controllable initial data on the location of the actuator our approach is based on the hilbert uniqueness method introduced by lions em contr olabilit e exacte des syst emes distribu es masson paris 1988 combined with some results from the theory of diophantine approximation

fast adaptive equalization diversity combining for time varying dispersive channels we examine adaptive equalization and diversity combining methods for fast rayleigh fading frequency selective channels we assume a block adaptive receiver in which the receiver coefficients are obtained from feedforward channel estimation for the feedforward channel estimation we propose a novel reduced dimension channel estimation procedure where the number of unknown parameters are reduced using a priori information of the transmit shaping filter s impulse response fewer unknown parameters require a shorter training sequence we obtain least squares maximum likelihood and maximum a posteriori map estimators for the reduced dimension channel estimation problem for symbol detection we propose the use of a matched filtered diversity combining decision feedback equalizer dfe instead of a straightforward diversity combining dfe the matched filter form has lower computational complexity and provides a well conditioned matrix inversion to cope with fast time varying channels we introduce a new dfe coefficient computation algorithm which is obtained by incorporating the channel variation during the decision delay into the minimum mean square error mmse criterion we refer to this as the non toeplitz dfe nt dfe we also show the feasibility of a suboptimal receiver which has a lower complexity than a recursive least squares adaptation with performance close to the optimal nt dfe