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

noncoherent decorrelative detection for nonorthogonal multipulse modulation over the multiuser gaussian channel this paper introduces the problem of noncoherent detection for nonorthogonal multipulse modulation in the context of the synchronous multiuser gaussian channel each user sends an m ary information symbol by transmitting one of m possibly nonorthogonal waveforms furthermore the m signals of one user are allowed to be correlated with the signals of all other users a key idea proposed here is that of a noncoherent decorrelative receiver front end like its counterpart in single pulse modulation this front end eliminates multiuser interference it therefore reduces the multiuser detection problem into decoupled single user problems over equivalent noise enhanced single user channels each equivalent single user channel is rather general and can be described as one where the waveforms employed are not only correlated but are also of unequal energies several new results pertaining to the design and analysis of optimum and suboptimum noncoherent detectors for this single user channel are obtained in the multiuser channel these detectors constitute the post decorrelative processing units for each user

bit error rate of binary and quaternary dpsk signals with multiple differential feedback detection a differentially coherent detection scheme with improved bit error rate ber performance is presented for differentially encoded binary and quaternary phase shift keying psk modulation the improvement is based on using l symbol detectors with delays of 1 2 l symbol periods and on feeding back detected psk symbols exact formulas for the bit error probability are derived for the case that correct symbols are fed back the effect of symbol errors in the feedback path on the ber is determined by computer simulations

toward a tight upper bound for the error probability of the binary gaussian classification problem it is well known that the error probability of the binary gaussian classification problem with different class covariance matrices cannot be generally evaluated exactly because of the lack of closed form expression this fact pointed out the need to find a tight upper bound for the error probability this issue has been for more than 50 years ago and is still of interest all derived upper bounds are not free of flaws they might be loose computationally inefficient particularly in highly dimensional situations or excessively time consuming if high degree of accuracy is desired in this paper a new technique is developed to estimate a tight upper bound for the error probability of the well known binary gaussian classification problem with different covariance matrices the basic idea of the proposed technique is to replace the optimal bayes decision boundary with suboptimal boundaries which provide an easy to calculate upper bound for the error probability in particular three types of decision boundaries are investigated planes elliptic cylinders and cones the new decision boundaries are selected in such a way as to provide the tightest possible upper bound the proposed technique is found to provide an upper bound tighter than many of the often used bounds such as the chernoff bound and the bayesian distance bound in addition the computation time of the proposed bound is much less than that required by the monte carlo simulation technique when applied to real world classification problems obtained from the uci repository h chernoff a measure for asymptotic efficiency of a hypothesis based on a sum of observations ann math statist 23 1952 493 507 the proposed bound was found to provide a tight bound for the analytical error probability of the quadratic discriminant analysis qda classifier and a good approximation to its empirical error probability

noncoherent detection of coherent lightwave signals corrupted by phase noise waves are treated that modulate by either on off keying ook or binary frequency shift keying fsk and are further impaired by additive gaussian noise heterodyne detection of such a waveform produces an electronic bandpass signal which to ease demodulation in the presence of phase noise is noncoherently demodulated to extract the baseband pulse stream the treatment goes beyond previous bit error rate ber analyses of optical heterodyne receivers for ook and fsk first there is full adherence to the standard brownian motion model of phase noise also the receiver structure is formulated in such a way that the probability density function of the receiver output samples can be accurately determined this permits calculations of the additive noise and phase noise tolerable when achieving bit error rates as small as 10 sup 9 finally the study is comprehensive regarding the range of parameters explored filtering at an intermediate frequency if alone as well as if filtering plus postdetection low pass filtering is considered when the receiver parameters decision threshold for ook and if filter bandwidth are optimized large amounts of phase noise can be accommodated with only minor increases in required signal to noise ratio this is especially important when the bit rate is moderate compared to the laser linewidth

portfolio optimization problem under concave transaction costs and minimal transaction unit constraints we will propose a branch and bound algorithm for calculating a globally optimal solution of a portfolio construction rebalancing problem under concave transaction costs and minimal transaction unit constraints we will employ the absolute deviation of the rate of return of the portfolio as the measure of risk and solve linear programming subproblems by introducing piecewise linear underestimating function for concave transaction cost functions it will be shown by a series of numerical experiments that the algorithm can solve the problem of practical size in an efficient manner

noncoherent coded modulation trellis coded modulation with two or multidimensional signal constellations together with coherent maximum likelihood detection is considered an attractive solution for communications over the additive white gaussian noise awgn channel in this paper a new noncoherent communication system is introduced called noncoherent coded modulation ncm as an alternative to coherent coded modulation ncm achieves almost the same power efficiency without bandwidth expansion or an extensive increase in complexity as a noncoherent system the method does not need carrier phase estimation nonetheless differential encoding is not required high performance noncoherent detection is achieved by using multiple symbol observations unlike previous approaches a sliding window for the observations is used with each observation covering several branches of the trellis such that the observations are time overlapped we define a new type of noncoherent maximum likelihood sequence estimator mlse and analyze its performance over the awgn channel by numerical calculation of the union bound we perform a computerized search and present new codes for noncoherent detection with their performance the new codes cover many useful rates and complexities and achieve higher performance than existing codes for noncoherent detection the method can also be used for multiple symbol demodulation of mdpsk with better results than existing methods

equivalence problems for first order lagrangians on the line abstract complete solutions to and applications of the equivalence problems for first order particle lagrangians under the pseudo groups of contact point and fiber preserving transformations both with and without the addition of divergence terms are presented

generalized stokes parameters shift keying a new perspective on optimal detection over electrical and optical vector incoherent channels we consider block transmission over the incoherent channel whereby several symbols either launched consecutively in time or in parallel over several diversity paths are equally affected by common isotropic phase and additively corrupted by circularly gaussian additive noise our novel approach toward transmission over such a vector incoherent channel vic model is based on coherency matrix and generalized stokes parameters gsp descriptions of optimal detection inspired by classical optical polarization theory but further extended to the dual context of generic electrical as well as optical communication the four classical real valued parameters introduced into optics by stokes in 1853 to characterize the state of polarization of an optical beam extended to d sup 2 gsp underlie our new alternative novel description of maximum a posteriori maximum likelihood map ml optimal detection over the vic channel the modulation formats of polarization shift keying polsk differential phase shift keying and amplitude shift keying as well as recent and novel combinations thereof will all be seen to be equivalent to a new conceptual form of modulation called gsp shift keying several forms of the optimal map ml receiver for vector multienergy transmission are developed generalizing the classical scalar incoherent receiver and the known polsk receivers

group detection for synchronous gaussian code division multiple access channels the concept of group detection is introduced to address the design of suboptimum multiuser detectors for code division multiple access cdma channels a group detection scheme consists of a bank of p group detectors one each for detecting the information symbols of users in each group of a p group partition of the k simultaneously transmitting users in a parallel group detection scheme these group detectors operate independently whereas in a sequential scheme each group detector uses the decisions of the previous group detectors to successively cancel the interference from those users group detectors based on the generalized likelihood ratio test glrt are obtained for the synchronous gaussian cdma channel the complexity of these detectors is exponential in the group size whereas that of the optimum detector is exponential in k since the partition of users is a design parameter group sizes can be chosen to satisfy a wide range of complexity constraints a key performance result is that the glrt group detectors are optimally group near far resistant furthermore upper and lower bounds on the asymptotic efficiency of the sequential group detectors are derived these bounds reveal that the sequential group detectors can under certain conditions perform as well as glrt group detectors of much larger group sizes group detection provides a unifying approach to multiuser detection when the users are partitioned into k single user groups the glrt a modified form of glrt and the sequential group detectors reduce to previously proposed suboptimal detectors namely the decorrelator the two stage detector and the decorrelating decision feedback detector respectively for the other nontrivial partitions the group detectors are new and have a performance that is commensurate with their complexity

construction of higher level 3 d signal constellations and their accurate symbol error probabilities in awgn a simple and straightforward method of constructing higher level three dimensional 3 d signal constellations for a reliable digital communication system is proposed in this paper the new method expands basic 8 ary constellation into 3 d signal space systematically so that it produces lattice configurations we also derive accurate closed form symbol error probability sep of cross lattice constellations in additive white gaussian noise awgn it is verified that the theoretical seps are almost the same as simulation results minimum euclidean distance med of the higher level 3 d constellations is increased at least 49 in comparison with quadrature amplitude modulation qam when the number of symbols is 256 the 3 d constellation has around 105 longer med than the 2 d qam due to increase in med the 3 d constellations have much improved error performance compared to the qam configurations it is therefore considered that the higher level 3 d constellations are appropriate for high quality digital communications

codes based on a trellis cut set transformation ii codes for noncoherent detection for pt i see ibid vol 46 p 610 20 1998 we continue the study of cut set trellis section t sub cb codes begun in part i and show that such codes are well suited for use with multiple symbol noncoherent detection and conventional two symbol differential detection the information bit assignment for a cut set trellis section can be modified to make the resulting code noncatastrophic for noncoherent detection by this procedure many existing two dimensional 2 d and multidimensional mpsk and qam trellis codes designed for coherent detection can be easily converted into codes for both coherent and noncoherent detection compared to m dpsk trellis codes it is shown that 2 d mpsk cut set trellis section codes have improved performance for multiple symbol noncoherent detection and comparable performance for conventional two symbol differential detection thus cut set trellis section codes are a class of universal channel codes since a single encoder performs well for coherent detection multiple symbol noncoherent detection and conventional two symbol differential detection

twenty years of linear programming based portfolio optimization markowitz formulated the portfolio optimization problem through two criteria the expected return and the risk as a measure of the variability of the return the classical markowitz model uses the variance as the risk measure and is a quadratic programming problem many attempts have been made to linearize the portfolio optimization problem several different risk measures have been proposed which are computationally attractive as for discrete random variables they give rise to linear programming lp problems about twenty years ago the mean absolute deviation mad model drew a lot of attention resulting in much research and speeding up development of other lp models further the lp models based on the conditional value at risk cvar have a great impact on new developments in portfolio optimization during the first decade of the 21st century the lp solvability may become relevant for real life decisions when portfolios have to meet side constraints and take into account transaction costs or when large size instances have to be solved in this paper we review the variety of lp solvable portfolio optimization models presented in the literature the real features that have been modeled and the solution approaches to the resulting models in most of the cases mixed integer linear programming milp models we also discuss the impact of the inclusion of the real features

tcm with differential encoding set partitioning trellis designs and distance analysis differential encoding de is a classical technique at the transmitter that allows simple noncoherent detection at the receiver on the other hand trellis coded modulation tcm is a bandwidth efficient technique which offers reliable data transmission in this paper we aim to find the best concatenation order of tcm and de for channel phase coherence over n 2 symbols besides the well known tcm followed by de called tcm de we propose a new trellis coding extension of de which extends our earlier work called differential trellis coded modulation dtcm dtcm is tcm with de defined in states where distinct states may have distinct de functions we propose design methods of de functions for noncoherently non catastrophic dtcm for both tcm de and dtcm we propose additive distance measures and set partitioning based on the proposed set partitioning trellis codes are designed or searched for both tcm de and dtcm both minimum distances and simulation results show that tcm de outperforms dtcm and the obtained new codes are better than the original codes

noncoherent block demodulation of msk with inherent and enhanced encoding it is shown that there is a close relation between known noncoherent minimum shift keying msk demodulation structures such as envelope and differential receivers and schemes derived from the noncoherent maximum likelihood block estimation n mlbe principle when the observation interval is increased the performance of msk with n mlbe tends to that of binary coherently detected orthogonal binary frequency shift keying a new demodulation strategy reduced block noncoherent estimation rbne is introduced and shown to improve the performance of noncoherent msk beyond that of coherently detected orthogonal fsk when rbne is used with msk and the observation interval is increased the performance approaches that of antipodal signaling the key feature of all these structures is multisymbol noncoherent processing with exploitation of the msk inherent coding properties induced by its phase continuity the use of binary block codes for msk with n mlbe is considered it is shown that simple binary block codes with low bandwidth expansion that exploit the inherent msk memory can give significant gains

noncoherent sequence detection new noncoherent sequence detection algorithms for combined demodulation and decoding of coded linear modulations transmitted over additive white gaussian noise channels possibly affected by intersymbol interference are presented optimal sequence detection in the presence of a random rotation of the signal phase assumed to be constant during the entire transmission requires a receiver complexity exponentially increasing with the duration of the transmission based on proper approximations simple suboptimal detection schemes based on the viterbi algorithm are presented whose performance approaches that of coherent detection in a companion paper by colavolpe and raheli see ibid vol 47 no 9 p 1303 7 1999 noncoherent sequence detection is extended to continuous phase modulations in the proposed schemes the tradeoff between complexity and performance is simply controlled by a parameter referred to as implicit phase memory and the number of states of a trellis diagram besides being realizable these schemes have the convenient feature of allowing us to remove the constant phase assumption and encompass time varying phase models the proposed schemes compare favorably with other solutions previously proposed in the technical literature

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

maximum likelihood block detection of noncoherent continuous phase modulation the authors examine maximum likelihood block detection of uncoded full response continuous phase modulation cpm over an additive white gaussian noise awgn channel both the maximum likelihood metrics and the bit error probability performances of the associated detection algorithms are considered the special and popular case of minimum shift keying msk corresponding to h 0 5 and constant amplitude frequency pulse is treated separately the many new receiver structures that result from this investigation can be compared to the traditional ones that have been used in the past both from the standpoint of simplicity of implementation and optimality of performance

noncoherent decision feedback multiuser detection the problem of noncoherent multiuser detection for multipulse modulation over the gaussian multiuser channel is studied it is assumed that neither the energies nor the carrier phases of the signals of any of the users are available at the receiver previously a post decorrelative generalized likelihood ratio test glrt based detector was proposed as a solution to this problem in this paper we introduce the concept of noncoherent decision feedback df that forms the basis for an improved solution to the same problem the users are detected sequentially in some fixed order and the decision for a particular user takes advantage of the reduction of uncertainty associated with the signal space resulting from decisions already made for previous users in contrast to coherent df therefore the feedforward and feedback transformations in the noncoherent case are themselves functions of the matched filter outputs an efficient implementation of the noncoherent df detector for m ary modulation and spl rho dimensional signal space requires o m sub spl rho computational complexity per user upper and lower bounds on its symbol error probability are obtained it is shown that significant improvements over the post decorrelative glrt based detector are often possible sufficient conditions are obtained which guarantee without ignoring error propagation effects that the high signal to noise performance of the df strategy can be as good as its genie aided version in which perfect past users decisions are used

the performance of trellis coded mdpsk with multiple symbol detection the idea of using a multiple more than two symbol observation interval to improve error probability performance is applied to differential detection of trellis coded multiple phase shift keying mpsk over an additive white gaussian noise awgn channels an equivalent euclidean distance measure per trellis branch is determined for this detection scheme this is used to define an augmented larger multiplicity trellis code whose distance measure is the conventional squared euclidean distance typical of conventional trellis coded modulation on the awgn such an augmented multiple trellis code is a convenient mathematical tool for simplifying the analysis results are obtained by a combination of analysis and computer simulation it is shown that only a slight increase e g one symbol in the length of the observation interval will provide a significant improvement in bit error probability performance

differential invariants of a class of lagrangian systems with two degrees of freedom abstract we consider systems of euler lagrange equations with two degrees of freedom and with lagrangian being quadratic in velocities for this class of equations the generic case of the equivalence problem is solved with respect to point transformations using lie s infinitesimal method we construct a basis of differential invariants and invariant differentiation operators for such systems we describe certain types of lagrangian systems in terms of their invariants the results are illustrated by several examples

noncoherent block coded tapsk for coherent detection block coded modulation is a bandwidth efficient scheme in this paper we propose theorems about the error performance of block coded modulation using m ary phase shift keying mpsk for noncoherent detection based on these theorems we propose a novel block coded modulation scheme for noncoherent detection called noncoherent block coded mpsk the proposed scheme provides flexible designs of noncoherent block codes with different code rate block length and error performance good noncoherent block codes can be easily obtained by properly choosing binary linear block codes as the component codes moreover noncoherent block codes of this new scheme can be decoded by multistage decoding which has the advantage of low complexity and satisfactory error performance in this paper two algorithms of multistage decoding for noncoherent detection are proposed as well the error performance of some designed codes and decoding algorithms is verified by computer simulation

multiuser square law detection with applications to fiber optic communications optimal and suboptimal multiuser noncoherent detection for square law receivers is studied in this paper great potential is found for the multiuser square law detector when compared with the conventional single user square law detector we study the optimal detector and two detectors with simpler structures the asymptotically optimal detector and the pairwise linear detector the saddle point approximation method is used to study the error performance and its asymptotic behavior as noise reduces due to difficulty in optimizing the detectors at an arbitrary noise level we propose to use the asymptotic efficiency for detector optimization for a low error rate system like a fiber optic communication system the asymptotic efficiency is found to be an efficient way to design detectors numerical results show that the asymptotically optimized detectors perform as well as the optimal detector even for nonzero noise levels of practical interest despite their exponential complexity these detectors are applicable to wavelength division multiplexed systems in which only a few neighboring channels produce strong interference

a hybrid fuzzy goal programming approach to multiple objective decision making problems this paper introduces a solution method based on the theory of fuzzy sets and goal programming gp for multiple objective decision making modm problems the solution method called hybrid fuzzy goal programming hfgp combines and extends the attractive features of both fuzzy set theory and goal programming for modm problems hfgp approach has been introduced to determine weights and weights to the objectives under the same priorities using the concept of fuzzy membership functions along with the notion of degree of conflict among objectives also hfgp converts a modm problem into a lexicographic goal programming problem by fixing the priorities and aspiration levels appropriately the proposed method is illustrated by solving a real life problem

multilevel polarization shift keying optimum receiver structure and performance evaluation multilevel digital coherent optical modulation schemes based on the state of polarization of a fully polarized lightwave are proposed and analyzed based on the complete statistical characterization of the stokes parameters extracted through appropriate signal processing in the presence of shot and additive gaussian noise the optimum maximum likelihood receiver operating symbol by symbol is derived the exact performance in terms of the average symbol error probability is found optimum constellations for the case of equipower 4 8 16 and 32 signals are found on the basis of the minimization of the error probability for a given average power their performance turns out to be promising as compared to other standard modulation techniques the spectral analysis of polarization modulated signals is presented a new receiver structure which solves the problem of the excess penalties incurred in the presence of channel dichroism is proposed and analyzed

classical invariant theory and the equivalence problem for particle lagrangians i binary forms abstract the problem of equivalence of binary forms under linear changes of variables is shown to be a special case of the problem of equivalence of particle lagrangians under the pseudogroup of transformations of both the independent and dependent variables the latter problem has a complete solution based on the equivalence method of cartan there are two particular rational covariants of any binary form which are related by a universal function the main result is that two binary forms are equivalent if and only if their universal functions are identical construction of the universal function from the syzygies of the covariants and explicit reconstruction of the form from its universal function are also discussed new results on the symmetries of forms and necessary and sufficient conditions for the equivalence of a form to a monomial or to a sum of two n th powers are consequences of this result finally we employ some syzygies due to stroh to relate our result to a theorem of clebsch on the equivalence of binary forms

large scale mv efficient frontier computation via a procedure of parametric quadratic programming abstract despite the volume of research conducted on efficient frontiers in many cases it is still not the easiest thing to compute a mean variance mv efficient frontier even when all constraints are linear this is particularly true of large scale problems having dense covariance matrices and hence they are the focus in this paper because standard approaches for constructing an efficient frontier one point at a time tend to bog down on dense covariance matrix problems with many more than about 500 securities we propose as an alternative a procedure of parametric quadratic programming for more effective usage on large scale applications with the proposed procedure we demonstrate through computational results on problems in the 1000 3000 security range that the efficient frontiers of dense covariance matrix problems in this range are now not only solvable but can actually be computed in quite reasonable time

rotationally invariant and rotationally robust codes for the awgn and the noncoherent channel the paper investigates the design and robustness of rotationally invariant ri codes first ri codes are extended to the case of serially concatenated sc trellis coded modulation tcm and several high rate powerful ri sctcm codes are designed over 8 phase shift keying and 16 quadrature amplitude modulation alphabets the investigation continues by considering more realistic channels that introduce cycle slips during phase estimation and thus rotate only part of the transmitted codeword it is proven that ri codes with small state space are robust in these channels even when traditional coherent decoders are utilized furthermore it is demonstrated through simulations that the addition of a simple stopping criterion to the coherent iterative decoding algorithm is sufficient for robustness of the more powerful ri sctcm codes when partial codeword rotations are considered finally it is investigated whether ri codes are useful for transmission in the noncoherent channel it is proved that ri codes are as good as any other good codes for this channel when the phase dynamics are low and optimal decoding is performed however it is shown that for a certain class of receivers ri codes are also robust to partial phase rotations in this channel

noncoherent amplitude phase modulated transmission schemes for rayleigh block fading channels in this paper we investigate noncoherent transmission schemes using amplitude phase modulation for uncoded transmission schemes we derive the pairwise error probability pep and its high snr approximation for signal vectors with unequal power values using a noncoherent maximum likelihood detector under rayleigh block fading channels for coded transmission schemes we consider differential amplitude phase modulated signals and introduce a codeword interleaving strategy to improve the error performance the design criteria for the signal labelling and bit interleaving are also derived via the high snr approximation of the pep at the receiver we devise an iterative channel amplitude estimator to enhance the detection reliability with the help of a specially designed iterative receiving algorithm the designed noncoherent coded scheme can provide a significant improvement either in the error floor or the waterfall region

hybrid bi objective portfolio optimization with pre selection strategy abstract classical markowitz mean variance model is widely used for portfolio assets selection and allocation which aims at simultaneously maximizing the expected return of the portfolio and minimizing portfolio variance many numerical approaches and metaheuristic algorithms have been proposed to effectively solve this portfolio optimization problem under an ideal condition however introducing various realistic constraints inadvertently leads to a non convex search space which has hindered the application of many classic exact algorithms such as quadratic programming qp the increasing size of available assets and complex constraints has made the effectiveness of metaheuristic algorithms deteriorated this paper proposes a hybrid bi objective algorithm combining with the respective advantages of local search algorithm evolutionary algorithm and qp with a pre selection strategy the algorithm first down select the assets that have greater contribution to the pareto frontier by applying the pre selection strategy then local search and evolutionary algorithm combined with qp are employed to fully exploit the useful assets combination modes to lead the search process toward the frontier direction quickly the experimental study demonstrates that the proposed hybrid approach can obtain faster and better convergence compared with eight state of the art multi objective evolutionary algorithms the results also show that the proposed method with the pre selection strategy always displays a closer proximity to the pareto frontier compared with k means strategy

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

rms bandwidth constrained signature waveforms that maximize the total capacity of pam synchronous cdma channels optimum time limited signal sets of equal and unequal energies are obtained under root mean square rms bandwidth constraints the total capacity and the total asymptotic efficiency of the pam synchronous gaussian cdma psg cdma channel are considered as the optimality criteria the latter measure is monotonic with the determinant of the correlation matrix r and the former is monotonic with det i spl sigma sup 2 r where spl sigma sup 2 represents the noise level average as well as maximum rms bandwidth constraints are considered in the equal energy case and the energy weighted rms bandwidth constraint is considered for unequal energy signals for the equal energy problem signal sets are found that simultaneously optimize the total asymptotic efficiency under both average and maximum rms bandwidth constraints for the total capacity measure such simultaneously optimal signal sets are also obtained albeit under the restriction that the number of signals n be a hadamard matrix dimension when the hadamard dimension is in particular a power of two we obtain optimum signal sets that are shown to yield equal optimum multiuser detector asymptotic efficiencies for all users of an uncoded psg cdma channel unequal energy signal sets are also found under an energy weighted rms bandwidth constraint for both optimality criteria

invariants for the lagrangian equivalence problem abstract let m be a connected smooth manifold let aut p be the group automorphisms of the bundle p r m r and let q j 1 r m r j 1 r m be the canonical projection invariant functions on j r q under the natural action of aut p are discussed in relationship with the lagrangian equivalence problem the second order invariants are determined geometrically as well as some other higher order invariants for dim m 2

noncoherent hybrid ds sfh spread spectrum multiple access communications the performance of noncoherent reception in synchronous and asynchronous hybrid direct sequence slow frequency hopped spread spectrum multiple access communication systems operating through additive white gaussian noise channels is investigated systems with binary and m ary frequency shift keying modulation and noncoherent demodulation as well as systems with differential phase shift keying modulation and differentially coherent demodulation are examined and their probability of error is evaluated for random frequencyhopping patterns and signature sequences the multiple access capability of noncoherent hybrid spread spectrum is shown to be superior to that of noncoherent purely frequency hopped spread spectrum and inferior to that of noncoherent purely directsequence spread spectrum for systems with the same bandwidth expansion comparison of hybrid systems with coherent and noncoherent demodulation shows a considerable loss in the performance of the noncoherent systems

heuristic algorithms for the portfolio selection problem with minimum transaction lots the problem of selecting a portfolio has been largely faced in terms of minimizing the risk given the return while the complexity of the quadratic programming model due to markowitz has been overcome by the recent progress in algorithmic research the introduction of linear risk functions has given rise to the interest in solving portfolio selection problems with real constraints in this paper we deal with the portfolio problem with minimum transaction lots we show that in this case the problem of finding a feasible solution is independently of the risk function np complete moreover given the mixed integer linear model new heuristics are proposed which starting from the solution of the relaxed problem allow to find a solution close to the optimal one the algorithms are based on the construction of mixed integer subproblems using only a part of the securities available formulated using the information obtained from the solution of the relaxed problem the heuristics have been tested with respect to two disjoint time periods using real data from the milan stock exchange

mean absolute deviation portfolio optimization model and its applications to tokyo stock market the purpose of this paper is to demonstrate that a portfolio optimization model using the l1 risk mean absolute deviation risk function can remove most of the difficulties associated with the classical markowitz s model while maintaining its advantages over equilibrium models in particular the l1 risk model leads to a linear program instead of a quadratic program so that a large scale optimization problem consisting of more than 1 000 stocks may be solved on a real time basis numerical experiments using the historical data of nikkei 225 stocks show that the l1 risk model generates a portfolio quite similar to that of the markowitz s model within a fraction of time required to solve the latter

noncoherent multiuser detection for nonlinear modulation over the rayleigh fading channel the jointly optimum noncoherent multiuser detector is obtained for nonlinear nonorthogonal modulation over the frequency nonselective rayleigh fading multiple access channel upper and lower bounds on the average bit error probability are derived while these bounds are numerically computable they are too complicated to give insight into the relative influence of the system parameters on the essential behavior of the bit error rate hence this paper develops an asymptotic analysis of the average bit error probability in particular it is shown that the upper and lower bounds are asymptotically convergent an exact formula for the asymptotic efficiency of the optimum noncoherent detector is derived interestingly the asymptotic efficiency is found to be positive and independent of the signal strengths of the interfering users in contrast the noncoherent detector which would be optimal in a single user channel the conventional detector when used over the multiuser channel has an asymptotic efficiency that is identically equal to zero no matter what the powers of the interferers may be while the performance analysis of the optimum detector provides the fundamental limit on achievable error rate the implementational complexity of the optimum detector is exponential in the number of users as a low complexity alternative a decorrelative energy detector is also proposed and analyzed in terms of error probability and asymptotic efficiency

priority structure in fuzzy goal programming abstract this paper introduces priority structure in fuzzy goal programming fgp this approach utilizes the lexicographic order of goal programming gp and yields an efficient computational algorithm for solving fgp fuzzy priorities are also discussed a numerical example is given to highlight the procedure concluding remarks are also made

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

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

joint carrier phase estimation and turbo decoding using bit carrier phase app decoder in this paper we present an algorithm for joint carrier phase estimation and turbo decoding for the case of rapidly varying carrier phase during the transmitted block the proposed algorithm shows improved performance over previously proposed communication schemes both coherent and noncoherent for channels with additive white gaussian noise and high carrier phase noise the novel algorithm utilizes a modified two dimensional bit carrier phase a posteriori probability bcapp decoder containing additional states representing the received carrier phase the bcapp decoder calculates two extrinsic metrics one representing the bit soft value and the other representing the received carrier phase probability density function approximation a modified structure of the turbo code iterations is suggested implementing separate propagation of the two metrics between the bcapp decoders one additional attractive property of the suggested algorithm is its robustness against phase noise model mismatch

fuzzy mean variance skewness portfolio selection models by interval analysis in portfolio selection problem the expected return risk liquidity etc cannot be predicted precisely the investor generally makes his portfolio decision according to his experience and his economic wisdom so deterministic portfolio selection is not a good choice for the investor in most of the recent works on this problem fuzzy set theory is widely used to model the problem in uncertain environments this paper utilizes the concept of interval numbers in fuzzy set theory to extend the classical mean variance mv portfolio selection model into mean variance skewness mvs model with consideration of transaction cost in addition some other criteria like short and long term returns liquidity dividends number of assets in the portfolio and the maximum and minimum allowable capital invested in stocks of any selected company are considered three different models have been proposed by defining the future financial market optimistically pessimistically and in the combined form to model the fuzzy mvs portfolio selection problem in order to solve the models fuzzy simulation fs and elitist genetic algorithm ega are integrated to produce a more powerful and effective hybrid intelligence algorithm hia finally our approaches are tested on a set of stock data from bombay stock exchange bse

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

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

genetic algorithms for portfolio selection problems with minimum transaction lots abstract conventionally portfolio selection problems are solved with quadratic or linear programming models however the solutions obtained by these methods are in real numbers and difficult to implement because each asset usually has its minimum transaction lot methods considering minimum transaction lots were developed based on some linear portfolio optimization models however no study has ever investigated the minimum transaction lot problem in portfolio optimization based on markowitz model which is probably the most well known and widely used based on markowitz model this study presents three possible models for portfolio selection problems with minimum transaction lots and devises corresponding genetic algorithms to obtain the solutions the results of the empirical study show that the portfolios obtained using the proposed algorithms are very close to the efficient frontier indicating that the proposed method can obtain near optimal and also practically feasible solutions to the portfolio selection problem in an acceptable short time one model that is based on a fuzzy multi objective decision making approach is highly recommended because of its adaptability and simplicity

artificial bee colony algorithm for constrained possibilistic portfolio optimization problem abstract in this paper we discuss the portfolio optimization problem with real world constraints under the assumption that the returns of risky assets are fuzzy numbers a new possibilistic mean semiabsolute deviation model is proposed in which transaction costs cardinality and quantity constraints are considered due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently thus a modified artificial bee colony mabc algorithm is developed to solve the corresponding optimization problem finally a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm

theoretical analysis and performance limits of noncoherent sequence detection of coded psk a theoretical performance analysis of noncoherent sequence detection schemes previously proposed by the authors for combined detection and decoding of coded m ary phase shift keying m psk is presented a method for the numerical evaluation of the pairwise error probability for which no closed form expressions exist is described the classical union bound is computed and results are compared with computer simulations an upper bound on this pairwise error probability is also presented this upper bound may be effectively used for the definition of an equivalent distance which may be useful in exhaustive searches for optimal codes using this bound it is proven that in the general coded case the considered noncoherent decoding schemes perform as close as desired to an optimal coherent receiver when a phase memory parameter is sufficiently large in the case of differentially encoded m psk a simple expression of the asymptotic bit error probability is derived which is in agreement with simulations for high as well as low signal to noise ratio snr

a noncoherent coded modulation for 16qam we present a noncoherent coded 16qam nc 16qam scheme by modifying the trellis coded 16qam tc 16qam scheme our simulation results show that the performance of the nc 16qam with noncoherent detection is close to the one of the original tc 16qam with coherent detection the nc 16qam is an extension of the nc 8psk previously obtained by wei and lin see ieee commun lett vol 2 p 260 62 1998 a noncoherent initial phase estimation algorithm is also proposed

portfolio selection based on fuzzy cross entropy in this paper the kapur cross entropy minimization model for portfolio selection problem is discussed under fuzzy environment which minimizes the divergence of the fuzzy investment return from a priori one first three mathematical models are proposed by defining divergence as cross entropy average return as expected value and risk as variance semivariance and chance of bad outcome respectively in order to solve these models under fuzzy environment a hybrid intelligent algorithm is designed by integrating numerical integration fuzzy simulation and genetic algorithm finally several numerical examples are given to illustrate the modeling idea and the effectiveness of the proposed algorithm

multilevel differential polarization shift keying we analyze the performance of coherent optical communication systems which employ polarization shift keying polsk modulation introducing for the first time the requirements for multilevel differential polsk for m ary signal constellations with m 2 the three dimensional 3 d nature of the signal constellations within stokes space requires the use of double differential modulation and detection m ddpolsk coding constraints on the signals place an additional restriction on such systems we present detailed analysis and simulations for a 6 ddpolsk modulation scheme in which the signal points are located at the vertices of an octahedron in stokes space

blind adaptive noncoherent multiuser detection for nonlinear modulation noncoherent multiuser detection for nonlinear modulation was previously studied and the idea of phase independent noncoherent decorrelation was introduced and three post decorrelative detectors were obtained and analyzed however their implementation requires the knowledge of the signature waveforms of all the users which may be available only for centralized implementation in this paper we obtain a blind adaptive noncoherent decorrelative detector for nonlinear modulation that is suitable for distributed implementation with the knowledge of only the normalized signals of the desired user and the additive noise variance this detector is based on the stochastic approximation method and does not require the overhead of any kind of training two adaptive algorithms are developed one guided by every signal in the desired user s signal set individually and the other by the user s entire signal space while this paper focuses on the particular problem of blind adaptive noncoherent decorrelative detection it addresses a more general adaptation issue namely that of improving the convergence properties of an adaptive scheme by effectively using all the information that is known and adapting only to the part of the desired solution that is truly unknown convergence is shown in the mean squared error sense for both the fixed step size and time varying step size versions of the two algorithms

partially coherent detection of digital full response continuous phase modulated signals recently bandwidth efficient constant envelope digital modulation schemes have been shown also to he power efficient if detected coherently in this paper the performance of such systems is analyzed for an optimum noncoherent or partially coherent detector at large signal to noise ratios the considered schemes are m ary with arbitrary pulse shaping over one symbol interval full response the performance is analyzed by means of a parameter called equivalent minimum euclidean distance mathematically playing the same role as the minimum euclidean distance used for coherent detectors it is shown that noncoherent detectors perform as well as coherent although the observation interval must be increased

noncoherent multiuser detection for cdma systems with nonlinear modulation a non bayesian approach this paper considers the problem of multiuser detection for a system in which each user employs nonlinear modulation with an emphasis on noncoherent detection techniques which do not require knowledge of the users channel parameters at the receiver our goals are to gain fundamental insight into the capabilities of multiuser detection in such a setting and to provide practical algorithms that perform better than conventional matched filter reception we begin by providing fundamental performance benchmarks by considering coherent maximum likelihood ml detection which requires knowledge of the users channel parameters as well as noncoherent detection formulated in a non bayesian generalized likelihood ratio test glrt framework the asymptotic performance of each detector as the noise level vanishes is characterized yielding simple geometric criteria for near far resistance in general both the ml and glrt detectors have complexity which is exponential in the number of users we therefore propose the more practical sequential decision projection sdp detector which has complexity which is quadratic in the number of users it is shown that the sdp detector has nonzero asymptotic efficiency if the users powers are suitably disparate

a weighted max min model for fuzzy goal programming abstract after narasimhan s pioneering study of applying fuzzy set theory to goal programming in 1980 many achievements in the field have been recorded most of them followed the max min approach however when objectives have different levels of importance only the weighted additive model of tiwari et al seems to be applicable however the shortcoming of the additive model is that the summation of quasiconcave functions may not be quasiconcave this study proposes a novel weighted max min model for fuzzy goal programming fgp and for fuzzy multiple objective decision making the proposed model adapts well to even the most complicated membership functions numerical examples demonstrate that the proposed model can be effectively incorporated with other approaches to fgp and is superior to the weighted additive approach

robust ranking and portfolio optimization the portfolio optimization problem has attracted researchers from many disciplines to resolve the issue of poor out of sample performance due to estimation errors in the expected returns a practical method for portfolio construction is to use assets ordering information expressed in the form of preferences over the stocks instead of the exact expected returns due to the fact that the ranking itself is often described with uncertainty we introduce a generic robust ranking model and apply it to portfolio optimization in this problem there are n objects whose ranking is in a discrete uncertainty set we want to find a weight vector that maximizes some generic objective function for the worst realization of the ranking this robust ranking problem is a mixed integer minimax problem and is very difficult to solve in general to solve this robust ranking problem we apply the constraint generation method where constraints are efficiently generated by solving a network flow problem for empirical tests we use post earnings announcement drifts to obtain ranking uncertainty sets for the stocks in the djia index we demonstrate that our robust portfolios produce smaller risk compared to their non robust counterparts

soft decision metrics for coded orthogonal signaling in symmetric alpha stable noise this paper derives new soft decision metrics for coded orthogonal signaling in impulsive noise more specifically symmetric alpha stable noise for the case of a known channel amplitude and known noise dispersion exact metrics are derived both for cauchy and gaussian noise for the case that the channel amplitude or the dispersion is unknown approximate metrics are obtained in closed form based on a generalized likelihood ratio approach the performance of the new metrics is compared numerically for a turbo coded system and the sensitivity to side information of the optimum receiver for cauchy noise is considered the gain that can be achieved by using a properly chosen decoding metric is quantified and it is shown that this gain is significant the application of the results to frequency hopping ad hoc networks is also discussed

trellis coded polarization shift keying modulation for digital optical communications the application of the well known technique of trellis coded modulation to coherent optical communications using polarization shift keying polsk is described and analyzed the resulting receiver is formed by a front end which performs the heterodyne detection and the stokes parameter extraction cascaded with an electronic viterbi processor operating the maximum likelihood estimate of the transmitted sequence results in terms of the error event probability using optimum as well as a simpler suboptimum branch metric show power gains of the order of 3 4 db at the expense of a reasonable increase in complexity only concerning the processing in the electronic domain these coding gains are not lost even in the presence of high levels of phase noise to which polsk in general is highly insensitive

a hybrid intelligent algorithm for portfolio selection problem with fuzzy returns portfolio selection theory with fuzzy returns has been well developed and widely applied within the framework of credibility theory several fuzzy portfolio selection models have been proposed such as mean variance model entropy optimization model chance constrained programming model and so on in order to solve these nonlinear optimization models a hybrid intelligent algorithm is designed by integrating simulated annealing algorithm neural network and fuzzy simulation techniques where the neural network is used to approximate the expected value and variance for fuzzy returns and the fuzzy simulation is used to generate the training data for neural network since these models are used to be solved by genetic algorithm some comparisons between the hybrid intelligent algorithm and genetic algorithm are given in terms of numerical examples which imply that the hybrid intelligent algorithm is robust and more effective in particular it reduces the running time significantly for large size problems

optimum noncoherent multiuser decision feedback detection a theory of noncoherent decision feedback multiuser detection for nonorthogonal binary modulation is developed that parallels that of coherent decision feedback multiuser detection for single pulse modulation in particular an optimum noncoherent decision feedback detector is obtained that maximizes symmetric energy over a newly defined class of decision feedback detectors unlike the usual per user performance metrics such as asymptotic efficiency or near far resistance the symmetric energy measure captures with a single number the asymptotic high signal to noise ratio snr bit error performance of all users at once several properties of the optimum decision feedback detector are established one of which is that it outperforms the decision feedback generalized likelihood ratio glr detector in symmetric energy it is also shown that regardless of the order in which users are detected the optimum noncoherent decision feedback detector outperforms its non decision feedback counterpart in symmetric energy furthermore two simple rules are obtained for determining the order in which users must be detected to guarantee that the optimum decision feedback detector outperforms its non decision feedback counterpart which in turn is superior to the decorrelative glr detector presented earlier in terms of asymptotic effective energy for every user in fact one of the two greedy ordering rules also maximizes symmetric energy among all possible orderings such ordering rules are not available for the noncoherent decision feedback glr detector in earlier work of the authors feasible sets of received energies are characterized in which it is possible with power control to achieve quality of service objectives for each user none of the results in this paper make simplifying assumptions about the effects of error propagation the term noncoherent in this work is used to denote that the receiver has no knowledge of the carrier phases and received signal energies of any of the users

multiuser detection for square law receiver under gaussian channel noise with applications to fiber optic communications in fiber optic wavelength division multiplexing wdm communications systems the nonlinearity of the channel and the limitations of optical filters result in received channel signals that are correlated furthermore the square law nature of the detector converts the additive fiber amplifier noise to a data dependent asymmetric and non gaussian noise the optimal multiuser detector for a gaussian approximation is compared to the actual statistics and found to give a close performance estimate through bounds on the error probability and the asymptotic multiuser efficiency the optimal multiuser detector based on a gaussian approximation is found to improve significantly performance in highly correlated data cases this result is applied to a practical optical wdm system

a differential coding method for the symmetrically differential polarization shift keying system this paper presents a novel differential coding method for the symmetrically differential polarization shift keying system the proposed differential coding method which can overcome the slow polarization variation in the fiber constructs the reference frame by setting the sum the difference and the cross product of previous two symbols as the first second and the last axes of the signal space obviously each axis is determined by the previous two symbols together thus at the receiver the new scheme constructs a noisy reference frame more accurately than other schemes and yields better performance the optimal constellation for the system is symmetric and easy to find the analytical integral form for the bit error rate ber of the proposed system is derived and the saddle point method is applied to obtain the analytical results it is found that the performance in terms of ber is much better than that of other differential polarization shift keying systems the analytical results agree with the simulation very well

noncoherent mmse multiuser receivers and their blind adaptive implementations three noncoherent minimum mean squared error nmse based multiuser receivers are proposed for multipulse modulation these receivers have a common mmse prefilter and are followed by one of three phase independent decision rules the simplest decision rule selects the maximum magnitude of the mmse filter outputs and the other two account for the second order statistics of the residual multiple access interference that remains after mmse filtering blind adaptive algorithms are then proposed for the three noncoherent mmse receivers the common adaptive algorithm for the mmse prefilter which is based on the stochastic approximation method is shown to converge in the mean squared error sense to the nonblind nmse prefilter our convergence analysis yields new insight into the tradeoff between the rate of convergence and the residual mean squared error the noncoherent blind receivers obtained here do not require the knowledge of the received signals of any of the interfering users and are hence well suited for distributed implementation in cellular wireless networks or in communication systems that must operate in noncooperative environments

optimally near far resistant multiuser detection in differentially coherent synchronous channels the noncoherent demodulation of differentially phase shift keyed signals transmitted simultaneously via a synchronous code division multiple access cdma channel is studied under the assumption of white gaussian background noise a class of noncoherent linear detectors is defined with the objective of obtaining the optimal one the performance criterion considered is near far resistance that denotes worst case multiuser asymptotic efficiency over near far environments it is shown that the optimal linear detector is a noncoherent decorrelating detector the commonality between the properties of the decorrelating detectors for coherent and noncoherent channels is established in particular it is shown that no other differential phase shift keying dpsk multiuser detector achieves a higher near far resistance than does the noncoherent decorrelator

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

linear programming with multiple fuzzy goals abstract this paper describes the use of fuzzy set theory in goal programming gp problems in particular it is demonstrated how fuzzy or imprecise aspirations of the decision maker dm can be quantified through the use of piecewise linear and continuous functions models are then presented for the use of fuzzy goal programming with preemptive priorities with archimedean weights and with the maximization of the membership function corresponding to the minimum goal examples are also provided

the number of functionally independent invariants of a pseudo riemannian metric the number of functionally independent scalar invariants of arbitrary order of a generic pseudo riemannian metric on an n dimensional manifold is determined