fast calculation of laurent expansions for matrix inverses previously described algorithms for calculating the laurent expansion of the inverse of a matrix valued analytic function become impractical already for singularity orders as low as around p 6 since they require over o 28p matrix multiplications and correspondingly large amounts of memory in place of using mathematically exact recursions we show that for floating point calculations a rational approximation approach can avoid this cost barrier without any significant loss in accuracy

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

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

analytic perturbation of generalized inverses abstract we investigate the analytic perturbation of generalized inverses firstly we analyze the analytic perturbation of the drazin generalized inverse also known as reduced resolvent in operator theory our approach is based on spectral theory of linear operators as well as on a new notion of group reduced resolvent it allows us to treat regular and singular perturbations in a unified framework we provide an algorithm for computing the coefficients of the laurent series of the perturbed drazin generalized inverse in particular the regular part coefficients can be efficiently calculated by recursive formulae finally we apply the obtained results to the perturbation analysis of the moore penrose generalized inverse in the real domain

on the local theory of regular analytic matrix functions abstract a concise exposition is given of the local spectral theory of regular analytic matrix functions without any reference to elements from the global theory

bayesian model selection for nonlinear aeroelastic systems using wind tunnel data abstract in this paper we present a bayesian framework for parameter estimation and model selection for nonlinear aeroelastic oscillatory systems using their measured response the framework is motivated by the fact that 1 the oscillations involve the complex nonlinear fluid structure interaction whose numerical modeling poses both conceptual and computational challenges 2 several plausible models fit the experimental data with reasonable accuracy and 3 the model calibration involves estimating the joint probability density function pdf of high dimensional between 10 and 22 parameter vectors including the variance of model prediction error modeling error a four stage process is followed first a candidate model set consisting of parameterized stochastic models is proposed based on the prior understanding of the physics second the joint posterior pdf of the model parameters of each model is estimated using bayesian inference which involves markov chain monte carlo mcmc sampling complemented by a nonlinear filter for state estimation owing to the dense observational data the state estimation is performed by the extended kalman filter ekf the unnormalized high dimensional joint posterior pdf is sampled through an mcmc method whereby a parallel version of single block adaptive proposal based metropolis hastings mh algorithm is employed to tune the proposal pdf third using bayes theorem each model is weighted according to the evidence provided by the data in its favor for single block mcmc sampling an estimate of the evidence is readily available through the chib jeliazkov method using the posterior samples generated after the burn in fourth the evidence is used to compute model plausibilities of each model which are later incorporated in the bayesian model averaging to make robust predictions the resulting prediction incorporates uncertainties in the measurements model parameters model structure and model selection a correction term handling the use of improper priors is shown to mimic the effect that diffuse but proper priors have on bayesian model selection the methodology is applied to wind tunnel data of a nonlinear aeroelastic oscillator consisting of a rigid wing performing self sustained small amplitude 6 limit cycle oscillation lco in pitch involving complex fluid structure interactions

perturbation of spectral inverses applied to a boundary layer phenomenon arising in chemical networks abstract a linear model showing behavior of the boundary layer type is developed the governing equations have the form t b t x t 0 t 0 where the coefficient matrix b depends continuously on two nonnegative parameters and has a discontinuity in rank at the origin of the parameter space the analysis depends on a regularization technique for linear systems and on a perturbation result for spectral group generalized inverses

separation control by alternating tangential blowing suction at multiple slots a method of separation control using alternating tangential blowing suction at small speeds on multiple slots was proposed and the properties of this method were studied by applying it to the flow control of a thick airfoil the method of numerically solving the reynolds averaged navier stokes equations was employed for the study using alternating tangential blowing suction with small speeds in the blowing phase the boundary layer velocity profiles downstream of the slot are made fuller and more separation resistant and in the suction phase the boundary layer velocity profiles both up and downstream of the slot are made fuller and more separation resistant for the airfoil considered in the paper which is of 40 percent thickness and has ten slots with a peak velocity of about 1 5

on the drazin inverse of the sum of two operators and its application to operator matrices abstract given two bounded linear operators f g on a banach space x such that g 2 f g f 2 0 we derive an explicit expression for the drazin inverse of f g for this purpose firstly we obtain a formula for the resolvent of an auxiliary operator matrix in the form m f i g f g from the provided representation of f g d several special cases are considered in particular we recover the case g f 0 studied by hartwig et al r e hartwig g wang y wei some additive results on drazin inverse linear algebra appl 322 2001 207 217 for matrices and by djordjevic and wei d s djordjevic y wei additive results for the generalized drazin inverse j aust math soc 73 1 2002 115 126 for operators finally we apply our results to obtain representations for the drazin inverse of operator matrices in the form m a b c d which are extensions of some cases given in the literature

effects of distributed suction on an airfoil at low reynolds number a suction distribution was designed based on thwaites criterion of separation the effectiveness of the designed suction distribution in controlling the size of the laminar separation bubble on a la2573a airfoil was investigated the suction distribution was capable of maintaining an unseparated laminar boundary up to the original transition location the effects of applying different suction rates on the drag were tested drag reductions between 14 and 24 were achieved the penalty for utilizing suction was estimated by introducing an equivalent suction drag the analysis showed that the penalty for using suction to reduce the drag was relatively small

error performance of multiple symbol differential detection of psk signals transmitted over correlated rayleigh fading channels the error performance of multiple symbol differential detection of uncoded qpsk signals transmitted over correlated rayleigh fading channels is studied the optimal detector is presented along with an exact expression for the corresponding pairwise error event probability it is shown that multiple symbol differential detection is a very effective strategy for eliminating the irreducible error floor associated with a conventional differential detector in all of the cases investigated a detector with an observation interval as small as two symbols is sufficient for this purpose it is also found that the error performance of a multiple symbol differential detector is not sensitive to the mismatch between the decoding metric and the channel fading statistics

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

coded modulation for a coherent ds cdma system employing an mmse receiver in a fading channel previous results have shown that high rate codes tend to yield a lower average bit error rate than low rate codes when employing a minimum mean square error mmse receiver for a direct sequence code division multiple access cdma system in either an additive white gaussian noise channel or a flat rayleigh fading channel we consider the use of larger signal constellations with both trellis coded modulation and bit interleaved coded modulation bicm to determine if further gains can be achieved in either the rayleigh or ricean fading channel the average bit error probability is derived for both coding schemes using the general ricean fading channel model based upon the common assumptions of infinite interleaving perfect channel state information and optimal mmse receiver coefficients new bounds are presented for bicm with 8 psk and 16 qam symbols which take advantage of the symmetries inherent in the signal constellations with gray code mapping in addition simulation results are presented which show the important effect a finite interleaving delay constraint has on the comparison of various codes the results show that there are cases when coded modulation does yield a significant improvement in performance for a cdma system using an mmse receiver compared to standard convolutional coding however the best coding strategy depends upon several factors including the nature of the fading process rayleigh or ricean the operating signal to noise ratio the interleaving delay constraint the time variability of the channel the number of users in the system and the severity of the near far problem

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

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

bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations a bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation lco of a pitching airfoil in the transitional reynolds number regime at small angles of attack laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the lco the fluid structure interaction of the rigid but elastically mounted airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to lco the likelihood in the posterior parameter probability density function pdf is available semi analytically using the extended kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model the posterior parameter pdf is sampled using a parallel and adaptive markov chain monte carlo mcmc algorithm the posterior probability of each model is estimated using the chib jeliazkov method that directly uses the posterior mcmc samples for evidence marginal likelihood computation the bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind tunnel test data at various reynolds numbers

complex neural network models for time varying drazin inverse two complex zhang neural network znn models for computing the drazin inverse of arbitrary time varying complex square matrix are presented the design of these neural networks is based on corresponding matrix valued error functions arising from the limit representations of the drazin inverse two types of activation functions appropriate for handling complex matrices are exploited to develop each of these networks theoretical results of convergence analysis are presented to show the desirable properties of the proposed complex valued znn models numerical results further demonstrate the effectiveness of the proposed models

impact of diversity reception on fading channels with coded modulation ii differential block detection for pt i see ibid vol 45 no 6 p 563 572 1997 we study coded modulation with block differential detection in an arbitrarily correlated rician fading channel with space diversity coded differential q psk is included in our analysis as a special case a metric is chosen that is optimum for perfect interleaving slow fading and independent diversity branches for slow fading we compare the the cutoff rates of the channels resulting from different choices of block length n and diversity index m specifically we show that block detection with diversity may or may not generate a better coding channel than usual differential detection according to the code selected and the combination of values of m and n in particular for low diversity orders m 1 2 and for low to medium code rates differential detection is still an optimal or near optimal solution while for high diversity orders m spl ges 2 and medium to high code rates up to uncoded modulation block detection with n 2 can provide a significant gain an error floor always exists when fading is fast it decreases exponentially with the product of code diversity and space diversity so that the latter emerges as a very effective technique for lowering the error floor of a system affected by fast fading performance examples based on actual coding schemes are also shown

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

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

composite three dimensional grids generated by elliptic systems a technique is presented for constructing a boundary conforming grid throughout a general threedimensional flow region as a composite of subregion grids each subregion grid is generated numerically by solving a nonlinear system of elliptic equations the boundary values represent nodal points in a quasi twodimensional grid that covers the curved surface bounding the subregion and are generated numerically by a modified elliptic system a primary feature of the technique is that the composite three dimensional grid remains both continuous and smooth across the surface of juncture between any two adjoining subregions sample results are given for a wing body combination

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

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

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

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

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

the laurent expansion of pencils that are singular at the origin abstract this paper gives two new proofs of a theorem of langenhop on the laurent expansion of a matrix pencil that is singular at the origin the second based on a decomposition of van dooren leads to a computational algorithm

the fundamental equations for the generalized resolvent of an elementary pencil in a unital banach algebra abstract we show that the generalized resolvent of a linear pencil in a unital banach algebra over the field of complex numbers is analytic on an open annular region of the complex plane if and only if the coefficients of the laurent series expansion satisfy a system of left and right fundamental equations and are geometrically bounded our analysis includes the case where the resolvent has an isolated essential singularity at the origin we find a closed form for the resolvent and use the fundamental equations to establish key spectral separation properties when the resolvent has only a finite number of isolated singularities we show that our results can be used to solve an infinite system of ordinary differential equations and to solve the generalized sylvester equation we also show that our results can be extended to polynomial pencils

multiple antenna signaling over fading channels with estimated channel state information performance analysis multiple antenna concepts for wireless communication systems promise high spectral efficiency and low error rates by proper exploitation of the randomness in multipath propagation in this paper we investigate the impact of channel uncertainty caused by channel estimation errors on the error rate performance we consider a training based multiple antenna system that reserves a portion of time to sound the channel training symbols are used to estimate the channel by means of an arbitrary linear filter at the receiver no channel state information csi is assumed at the transmitter we present a new framework to analyze training based multiple antenna systems by introducing an equivalent system model that specifies the channel by the estimated and hence known channel coefficients and an uncorrelated data dependent multiplicative noise we derive the maximum likelihood ml detector and highlight its behavior in the limiting cases of perfect csi and no csi and its relation to several mismatched detectors we deduce new exact expressions and chernoff bounds of the pairwise error probability pep used to assess word error and bit error rate bounds for ml and mismatched detection finally we review the code design guidelines in terms of the deleterious effect of channel uncertainty for coherent and noncoherent signaling schemes and present numerical results

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

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

bit error probability for noncoherent orthogonal signals in fading with optimum combining for correlated branch diversity due to the interest in wireless personal communications there has been a lot of research on the performance of receivers with diversity most analyses assume the diversity branches are independent this paper presents an analysis of the bit error probability for receivers in which the diversity branches are correlated noncoherent orthogonal digital modulation ncodm with rician and rayleigh slow nonselective fading models are assumed through the use of the diagonalization of quadratic forms most of the calculations of the bit error probability can be reduced to a two dimensional numerical integration for some cases for dual diversity a closed form expression for the error probability is given a number of diversity combining laws including square law and maximum likelihood are considered we find that rician fading can be worse than rayleigh fading in correlated diversity environments a situation quite different from the independent diversity case also for the rayleigh fading model with correlated branch diversity we find that an equal weight square law combiner usually has the same error performance as the more complex maximum likelihood combiner however this is not the case for a rician fading model with the same correlation environment simple diagonalization methods that compensate for the lossy effect of correlation are specified and found to be effective when the dominant noise and interference have almost the same correlation distribution as the fading signals

laurent expansion of the inverse of perturbed singular matrices in this paper we describe a numerical algorithm to compute the laurent expansion of the inverse of singularly perturbed matrices the algorithm is based on the resolvent formalism used in complex analysis to study the spectrum of matrices the input of the algorithm are the matrix coefficients of the power series expansion of the perturbed matrix the matrix coefficients of the laurent expansion of the inverse are computed using recursive analytical formulae we show that the computational complexity of the proposed algorithm grows algebraically with the size of the matrix but exponentially with the order of the singularity we apply this algorithm to several matrices that arise in applications we make special emphasis to interpolation problems with radial basis functions

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

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

trellis coded modulation on time selective fading channels a general analysis of trellis coded modulation tcm on time selective fading channels with correlated signal samples is presented gaussian quadratic forms are used to evaluate the pairwise sequence error probability the effect of interleaving is studied and it is shown that moderate interleaving with respect to the doppler frequency of the channel suffices to achieve good performance the analysis is then extended to treat non ideal estimation of the complex channel gain in the coherent case using a general linear channel estimator it is shown that differential phase shift keying dpsk and differential trellis coded modulation dtcm on correlated fading channels call be treated analytically and that the error probability of dtcm like of coherent tcm depends only on the euclidean distance of the error sequences results show that dtcm suffers a degradation of up to 3 db with respect to coherent tcm on slow fading channels but performs better on fast fading channels error floor curves are presented for dtcm for different interleaving depths the event error probability p sub e and the bit error probability p sub b of tcm approximated by truncated averaged union bounds are calculated for the codes used a comparison of the approximations of p sub b with simulation results show that the union bound is relatively loose for fading channels

control of low speed airfoil aerodynamics nomenclature cd drag coefficient 2d pulc cf local skin friction coefficient 2rw pul cl lift coefficient 2l pu c cq suction coefficient i vw i uq c airfoil s chord d drag force per unit span l lift force per unit span p instantaneous hydrostatic pressure po pressure outside boundary layer p mean pressure r wall s radius of curvature 6 displacement thickness reynolds number uod v ro momentum thickness reynolds number u0de v re reynolds number based on distance from leading edge or chord and freestream velocity t instantaneous temperature t mean temperature j7 instantaneous velocity component uj mean velocity component u0 velocity outside the boundary layer t oo freestream velocity hi fluctuating velocity component u friction velocity vr p vw normal velocity of fluid injected or withdrawn through the wall x cartesian coordinates x streamwise distance from leading edge y normal distance from the wall y normal distance in wall units yu v z spanwise coordinate a angle of attack 6 boundary layer thickness 60 momentum thickness 6 displacement thickness x dynamic coefficient of viscosity v kinematic viscosity v u viscous length scale wall unit p density p uv tangential reynolds stress t w shear stress at the wall pu ajo instantaneous spanwise vorticity at the wall fijo rnean spanwise vorticity at the wall du dy q

two finite time convergent zhang neural network models for time varying complex matrix drazin inverse abstract this paper concerns the computation of the drazin inverse of a complex time varying matrix based on two zhang functions constructed from two limit representations of the drazin inverse we present two complex zhang neural network znn models with the li activation function for computing the drazin inverse of a complex time varying square matrix we prove that our znn models globally converge in finite time in addition upper bounds of the convergence time are derived analytically via the lyapunov theory our simulation results verify the theoretical analysis and demonstrate the superiority of our znn models over the gradient based gnn models

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

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

discretization of free surface flows and other moving boundary problems a system of elliptic partial differential equations and boundary conditions has been developed for generating boundary fitted element discretizations of two dimensional free and moving boundary problems terms in the differential equations are scaled for dimensional homogeneity and adjustable weighting of orthogonality smoothness and concentration of the coordinate mesh they govern grid points become finite element nodes mapped isoparametrically or subparametrically from a simple or patched computational domain concentration terms contain control functions and parameters that influence node spacing along each coordinate independently overall control is by patchwise parameters and functions successful selection of these to follow deforming flow regions is straightforward and is illustrated by analysis of steady and transient slide coating flows

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

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

perturbation of null spaces with application to the eigenvalue problem and generalized inverses we consider properties of a null space of an analytically perturbed matrix in particular we obtain taylor expansions for the eigenvectors which constitute a basis for the perturbed null space furthermore we apply these results to the calculation of puiseux expansion of the perturbed eigenvectors in the case of general eigenvalue problem as well as to the calculation of laurent series expansions for the perturbed group inverse and pseudoinverse matrices

additive perturbation results for the drazin inverse abstract in this paper some new additive results for the drazin inverse are presented we give a formula for the drazin inverse of a sum of two matrices under conditions on the matrices less restrictive than those imposed in the corresponding theorem given by hartwig et al linear algebra appl 322 2001 207 217 we consider some aplications of our results to the perturbation of the drazin inverse and analyze a number of special cases

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

a reduction process for perturbed markov chains given a perturbed markov chain with generator a varepsilon a 0 varepsilon a 1 varepsilon 2 a 2 cdots it is shown that to each time scale t t varepsilon t varepsilon 2 cdots is associated a reduced markov chain this process of reduction has only finitely many steps it is given in a recursive way and each reduced chain admits as state space the recurrent classes of the reduced chain defined at the previous stage it is shown that if lambda is an eigenvalue different from zero of the generator of the kth reduced chain with multiplicity p then a varepsilon admits p eigenvalues lambda varepsilon such that lambda varepsilon varepsilon k lambda o varepsilon k a basis of ker a 0 resp ker a 0 which is robust to the perturbation is constructed

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

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

a laplacian equation method for numerical generation of boundary fitted 3d orthogonal grids abstract a sethod for generating boundary fitted orthogonal curvilinear grids in 3 dimensional space is described the mapping between the curvilinear coordinates and the cartesian coordinates is provided by a set of laplace equations which expressed in curvilinear coordinates involve the components of the metric tensor and are therefore non linear and coupled an iterative algorithm is described which achieves a numerical solution grids appropriate for the calculation of flow fields over complex topography or in complex flow passages as those found in turbomachinery and for other engineering applications can be constructed using the proposed method various examples are presented and plotted in perspective and data for the assessment of the properties of the resulting meshes is provided

probabilistic parameter estimation of a fluttering aeroelastic system in the transitional reynolds number regime abstract we present a bayesian parameter estimation results of a self sustaining aeroelastic oscillator the system consists of an elastically mounted rigid wing on a rig fixed in a wind tunnel for certain flow conditions in the transitional reynolds number regime i e 10 000 re 1 000 000 the wing absorbs energy from the flow and settles in a stable limit cycle oscillation lco the lco originates from laminar boundary layer separation which leads to negative aerodynamic damping at small angles of attack we propose an empirical model of the aeroelastic system in the form of a generalized duffing van der pol oscillator a statistical technique is developed to estimate the linear and nonlinear parameters of the aeroelastic oscillator in addition the model noise term in part accounting for the amplitude modulation of the lco is also estimated in particular we apply a bayesian inference technique for parameter estimation that involves a state estimation problem using the measurement data we exploit the extended kalman filter for the state estimation to generate samples from the posterior joint probability density functions of the aeroelastic parameters we use the markov chain monte carlo mcmc simulation finally the confidence interval of the static aerodynamic moment coefficient is presented

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

on one dimensional stretching functions for finite difference calculations abstract the class of one dimensional stretching functions used in finite difference calculations is studied for solutions containing a highly localized region of rapid variation simple criteria for a stretching function are derived using a truncation error analysis these criteria are used to investigate two types of stretching functions one is an interior stretching function for which the location and slope of an interior clustering region are specified the simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine it was first employed by thomas et al aiaa j 10 1972 887 the other type of function is a two sided stretching function for which the arbitrary slopes at the two ends of the one dimensional interval are specified the simplest such general function is found to be one based on the inverse tangent the special case where the slopes were both equal and greater than one was first employed by roberts the general two sided function has many applications in the construction of finite difference grids examples of such applications are found in the listed references

impact of diversity reception on fading channels with coded modulation i coherent detection we address the problem of designing and analyzing the performance of a coded modulation scheme for the fading channel when space diversity is used under fairly general conditions a channel affected by fading can be turned into an additive white gaussian noise awgn channel by increasing the number of diversity branches consequently it can be expected and is indeed verified by our analyses and simulations that a coded modulation scheme designed to be optimal for the awgn channel also will perform asymptotically well on a fading channel with diversity this paper presents bounds on the bit error probability of a system with coded modulation and diversity for space and time correlated rician flat fading specifically we derive a new method which allows evaluation of the pairwise error probability extremely easily as well as accurately and computationally fast the accuracy achieved improves considerably on the widely used but rather loose chernoff bound starting from this analysis we study the asymptotic behavior of the fading channel with diversity as the number of diversity branches increases and we address the effects of diversity on coded modulation performance and design criteria including the effect on interleaver depth which affects the total delay of the system

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

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

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

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