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

monte carlo generation of self avoiding walks with fixed endpoints and fixed length we propose a new class of dynamic monte carlo algorithms for generating self avoiding walks uniformly from the ensemble with fixed endpoints and fixed length in any dimension and prove that these algorithms are ergodic in all cases we also prove the ergodicity of a variant of the pivot algorithm

asymptotic multiuser efficiencies for decision directed multiuser detectors the asymptotic multiuser efficiencies ames are derived for various classes of decision directed multiuser detectors including multistage detectors and decision feedback detectors novel classes of soft decision multistage detectors are proposed and analyzed each class is specified in part by a soft decision nonlinearity such as a symmetric quantizer or a linear clipper closed form expressions for two user ames are derived for soft decision two stage detectors and can be used as a design criterion to optimize the soft decision nonlinearities for a special case of two synchronous users the soft decision two stage detector using an optimized linear clipper with either conventional or decorrelated tentative decisions is shown to achieve optimum ame upper and lower bounds on the ame are obtained for decision feedback detectors using either conventional or decorrelated tentative decisions it is demonstrated that decision directed multiuser detectors with conventional tentative decisions have low near far resistance compared to those with decorrelated tentative decisions

fuzzy nets and their application fuzzy net theory is enriched by the introduction of the fuzzy net of fuzzy sets the limsup liminf and limit of a fuzzy net of fuzzy sets are defined and their various properties are discussed alternative characterizations based on the notion of a fuzzy net are provided for several fuzzy topological concepts including open and closed fuzzy sets fuzzy continuity maps with closed fuzzy graph open fuzzy mapping etc thus the net theoretic approach is shown to be a promising tool in fuzzy topology

multicanonical monte carlo ensemble growth algorithm we present an ensemble monte carlo growth method to sample the equilibrium thermodynamic properties of random chains the method is based on the multicanonical technique of computing the density of states in the energy space such a quantity is temperature independent and therefore microcanonical and canonical thermodynamic quantities including the free energy entropy and thermal averages can be obtained by reweighting with a boltzmann factor the algorithm we present combines two approaches the first is the monte carlo ensemble growth method where a population of samples in the state space is considered as opposed to traditional sampling by long random walks or iterative single chain growth the second is the flat histogram monte carlo similar to the popular wang landau sampling or to multicanonical chain growth sampling we discuss the performance and relative simplicity of the proposed algorithm and we apply it to known test cases

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

absence of mass gap for a class of stochastic contour models we study a class of markovian stochastic processes in which the state space is a space of lattice contours and the elementary motions are local deformations we show under suitable hypotheses on the jump rates that the infinitesimal generator has zero mass gap this result covers among others the bfacf dynamics for fixed endpoint self avoiding walks and the sterling greensite dynamics for fixed boundary self avoiding surfaces our models also mimic the glauber dynamics for the low temperature ising model the proofs are based on two new general principles the minimum hitting time argument and the mean or mean exponential hitting time argument

finite memory length linear multiuser detection for asynchronous cdma communications decorrelating linear minimum mean squared error lmmse and noise whitening multiuser detectors for code division multiple access systems cdma are ideally infinite memory length referred to as iir detectors to obtain practical detectors which have low implementation complexity and are suitable for cdma systems with time variant system parameters e g the number of users the delays of users and the signature waveforms linear finite memory length referred to as fir multiuser detectors are studied in this paper they are obtained by truncating the iir detectors or by finding optimal fir detectors the signature waveforms are not restricted to be time invariant periodic over symbol interval thus linear multiuser detection is generalized to systems with spreading sequences longer than the symbol interval conditions for the stability of the truncated detectors are discussed stable truncated detectors are shown to be near far resistant if the received powers are upper bounded and if the memory length is large enough but finite numerical examples demonstrate that moderate memory lengths are sufficient to obtain the performance of the iir detectors even with a severe near far problem

multiuser detection of quasisynchronous cdma signals using linear decorrelators a linear decorrelator detector is proposed for a quasisynchronous code division multiple access qs cdma cellular system it is assumed that each of n users has a global positioning system gps generated local clock and attempts to transmit synchronously with the other users in its cell the base station thus receives n signature waveforms which are approximately synchronized but with a small timing error due to local oscillator drift doppler shifts and variable distances from the mobiles to the base the residual timing offset is discretized and a decorrelator is constructed which attempts to reject the multiuser interference vectors corresponding to the set of possible offsets a noncoherent version of the decorrelator detector is presented along with a maximum likelihood scheme for synchronizing to the desired signal bounds and analytical results for the bit error rate ber are obtained for various interferer conditions

a new approach to fuzzy topological spaces and various fuzzy topological notions defined by nets n fuzzy spaces introduced by the authors are further investigated various fuzzy topological motions such as fuzzy local compactness functions with closed fuzzy graph fuzzy subcontinuity inverse fuzzy subcontinuity etc are studied in the light of n i these notions are found to be more coherent in n i than in the chang s category

design of spherical lattice space time codes in this paper we propose a systematic procedure for designing spherical lattice space time codes by employing stochastic optimization techniques we design lattice codes which are well matched to the fading statistics as well as to the decoder used at the receiver the decoders we consider here include the optimal albeit of highest decoding complexity maximum likelihood ml decoder the suboptimal lattice decoders as well as the suboptimal lattice reduction aided lra decoders having the lowest decoding complexity for each decoder our design methodology can be tailored to obtain low error rate lattice codes for arbitrary fading statistics and signal to noise ratios snrs of interest further we obtain fundamental lower bounds on the error probabilities yielded by lattice and lra decoders and characterize their asymptotic behavior

polymer conformations through wiggling a new monte carlo method is proposed which allows for the efficient generation of equilibrium conformations of polymer chains in two and three dimensions the method treats each site monomer as a potential pivot around which a new conformation may be generated by rotating a portion of the chain the method does not suffer from the severe attrition associated with the simple sampling of self avoiding walks and may be extended to treat the interacting polymer chain the authors find in two dimensions that nu 0 748 or 0 005 exact 0 750 and in three dimensions nu 0 595 or 0 005 series expansion and renormalisation group predict nu approximately 0 588 the end end distances calculated for shorter chains are in good agreement with the exact values from enumeration techniques

stochastic gradient algorithms for design of minimum error rate linear dispersion codes in mimo wireless systems linear dispersion ld codes are a good candidate for high data rate multiple input multiple ouput mimo signaling traditionally ld codes were designed by maximizing the average mutual information which cannot guarantee good error performance this paper presents a new design scheme for ld codes that directly minimizes the block error rate bler in mimo channels with arbitrary fading statistics and various detection algorithms for mimo systems employing ld codes the error rate does not admit an explicit form therefore we cannot use deterministic optimization methods to design the minimum error rate ld codes in this paper we propose a simulation based optimization methodology for the design of ld codes through stochastic approximation and simulation based gradient estimation the gradient estimation is done using the score function method originally developed in the discrete event system community the proposed method can be applied to design the minimum error rate ld codes for a variety of detector structures including the maximum likelihood ml detector and several suboptimal detectors it can also design optimal codes under arbitrary fading channel statistics in particular it can take into account the knowledge of spatial fading correlation at the transmitter and receiver ends simulation results show that codes generated by the proposed new design paradigm generally outperform the codes designed based on algebraic number theory

guided replication of random chain a new monte carlo method the authors introduce a new monte carlo method to study random chains the method uses i a link by link growth procedure of the chain ii a chain replication procedure based on boltzmann weights they apply it to various cases in two and three dimensions pure self avoiding walk repulsion between nearest neighbour links and attraction between the chain extremities etc when the competition or frustration between the different interaction terms increases the chain may get trapped in local minima to overcome this problem they introduce a guiding field or potential phi i r step ii is now performed in the presence of this guiding field which makes the chain population temporarily non boltzmannian however when the chain is completed the final population obeys again the boltzmann law they study simple cases where phi i r may be chosen on physical grounds

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

self avoiding random loops a random loop or polygon is a simple random walk whose trajectory is a simple jordan curve the study of random loops is extended in two ways first the probability p sub n x y that a random n step loop contains a point x y in the interior of the loop is studied and 1 2 1 2 is shown to be 1 2 1 n it is plausible that p sub n x y tends toward 1 2 for all x y but this is not proved even for x y 3 2 1 2 a way is offered to simulate random n step self avoiding loops numerical evidence obtained with this simulation procedure suggests that the probability p sub n 3 2 1 2 approximately 1 2 c n for some fixed c

analysis and optimization of diagonally layered lattice schemes for mimo fading channels embodiments of the diagonal bell laboratories layered space time d blast architecture for multiple input multiple output mimo communication are developed wherein information symbol vectors are encoded using codewords from a lattice code called a diagonally layered lattice dll code which are formatted onto the diagonals of a space time frame decoding is done using a sphere decoder for each diagonal based on soft statistics obtained after zero forcing zf or minimum mean square error mmse filtering and decision feedback these operations give rise to an effective parallel channel model with channel gains with nonidentical statistics and additive noise which is gaussian in the zf filtering case and non gaussian in the mmse filtering case the so called full modulation diversity fmd property is nevertheless shown to yield the maximum achievable diversity orders over the mimo channel for both the zf and the mmse filtering based decoders respectively for any arbitrary fading distribution in the case of the independent identically distributed i i d rayleigh fading mimo channel with k transmit and n receive antennas with ngesk these diversity orders are nk k k 1 2 and nk for zf and mmse filtering based decoding respectively the error probability analysis also yields a design criterion for optimizing transmit power allocations several lattice design methods are proposed for the effective parallel channel models two methods are proposed to achieve high coding gain in the rayleigh fading mimo channel a third method is proposed that minimizes the exact symbol error probability sep and can be tailored for any given fading distribution a novel soft decision feedback decoder is also proposed based on the list sphere decoder to mitigate error propagation due to hard decision feedback the salient feature of the proposed dll schemes is that they have nearly full rate and full or high diversity order and yet a much lower decoding complexity than other existing full rate full diversity space time block codes stbcs the frame error probability fep performance of the optimized dll schemes for moderate to high spectral efficiencies and a wide range of signal to noise ratios snrs can be quite close to the performance of the best performing but more complex to decode stbcs moreover the proposed dll schemes significantly outperform other existing mimo systems of comparable decoding complexity

t convergence of nets of l fuzzy sets and its applications abstract in this paper the theory of convergence on nets of l fuzzy sets which is a generalization of the convergence theory of fuzzy nets introduced by sarma and ajmal is established some important and interesting results in l fuzzy topology are obtained by means of the theory

multiuser detection in mismatched multiple access channels we consider an additive white gaussian noise multiple access channel and investigate the performance degradation of several multiuser detectors due to imperfect knowledge of the channel parameters induced by either estimation errors or sampling quantization of the receiver s sufficient statistics the symbol error rates and the asymptotic multiuser efficiencies ames of these detectors are examined as functions of both true and approximated channel parameters for 2 asynchronous users the results quantify the loss of near far resistance due to parameter estimation errors and demonstrate that detectors which are optimal for ideal conditions are often more sensitive to parameter mismatch examples are given which illustrate a reverse ordering of the symbol error rates for these detectors in the high signal to noise regime and also illustrate cases when the conventional matched filter detector exhibits superior performance over multiuser detectors

multiuser detection for overloaded cdma systems multiuser detection for overloaded code division multiple access cdma systems in which the number of users is larger than the dimension of the signal space is of particular interest when bandwidth is at a premium in this paper certain fundamental questions are answered regarding the asymptotic forms and performance of suboptimum multiuser detectors for cases where the desired and or interfering signal subspaces are of reduced rank and or have a nontrivial intersection in the process two new suboptimum detectors are proposed that are especially well suited to overloaded systems namely the group pseudo decorrelator and the group minimum mean squared error mmse detector the former is seen to be the correct extension of the group decorrelator in the sense that it is the limiting form in the low noise regime of the group mmse detector pseudo decorrelation is also used as a feedforward filter in a new decision feedback scheme for the particular case of real valued modulation it is shown that the proposals of the so called improved linear also known as linear conjugate or widely linear detectors were more simply derived earlier using the idea of minimal sufficiency which we also apply to the new detectors of this paper

a new multistage detector for synchronous cdma communications in this paper we develop a new multistage detector to approach the optimal solution of the detection problem in a synchronous code division multiple access cdma system the transformation modifies the diagonal elements of the hessian matrix of the quadratic likelihood function and brings the continuous minimum of the transformed function as close to the optimal solution as possible the computational complexity is essentially linear with the number of users except that a few computations of a quadratic function are needed

new applications of l nets in l fuzzy multifunctions in this paper we will give new applications of l net in l fuzzy multifunctions using l net we will further study l fuzzy continuous almost continuous and r continuous multifunctions some interesting characterizations are obtained

equal diagonal qr decomposition and its application to precoder design for successive cancellation detection in multiple input multiple output mimo multiuser detection theory the qr decomposition of the channel matrix h can be used to form the back cancellation detector in this paper we propose an optimal qr decomposition which we call the equal diagonal qr decomposition or briefly the qrs decomposition we apply the decomposition to precoded successive cancellation detection where we assume that both the transmitter and the receiver have perfect channel knowledge we show that for any channel matrix h there exists a unitary precoder matrix s such that hs qr where the nonzero diagonal entries of the upper triangular matrix r in the qr decomposition of hs are all equal to each other the precoder and the resulting successive cancellation detector have the following properties a the minimum euclidean distance between two signal points at the channel output is equal to the minimum euclidean distance between two constellation points at the precoder input up to a multiplicative factor that equals the diagonal entry in the r factor b the superchannel hs naturally exhibits an optimally ordered column permutation i e the optimal detection order for the vertical bell labs layered space time v blast detector is the natural order c the precoder s minimizes the block error probability of the qr successive cancellation detector d a lower and an upper bound for the free distance at the channel output is expressible in terms of the diagonal entries of the r factor in the qr decomposition of a channel matrix e the precoder s maximizes the lower bound of the channel s free distance subject to a power constraint f for the optimal precoder s the performance of the qr detector is asymptotically at large signal to noise ratios snrs equivalent to that of the maximum likelihood detector mld that uses the same precoder further we consider two multiplexing schemes time division multiple access tdma and orthogonal frequency division multiplexing ofdm we d

speed and accuracy comparison of techniques for multiuser detection in synchronous cdma in this letter we compare the complexity and efficiency of several methods used for multiuser detection in a synchronous code division multiple access system various methods are discussed including decision feedback df detection group decision feedback gdf detection coordinate descent quadratic programming with constraints space alternating generalized em sage detection tabu search a boltzmann machine detector semidefinite relaxation probabilistic data association pda branch and bound bbd and the sphere decoding sd method the efficiencies of the algorithms defined as the probability of group detection error divided by the number of floating point computations are compared under various situations of particular interest is the appearance of an efficient frontier of algorithms primarily composed of df detector gdf detector pda detector the bbd optimal algorithm and the sd method the efficient frontier is the convex hull of algorithms as plotted on probability of error versus computational demands axes algorithms not on this efficient frontier can be considered dominated by those that are

two dimensional error pattern correcting codes two dimensional 2d cyclic codes are presented which correct any single occurrence of known 2d error patterns within a 2d array of bits applications for this type of codes include storage and display devices the code construction begins with a generation of distinct syndrome sets for all targeted 2d error patterns a method to refine the syndrome sets is then presented for making each syndrome set to contain distinct members thereby guaranteeing full correction capability for the given list of known error patterns using an example construction the effectiveness of the proposed coding approach is demonstrated versus the maximum distance separable mds random error correcting code and known 2d burst correcting codes for a 2d intersymbol interference isi channel that yields a few dominant but relatively large error patterns

nonergodicity of local length conserving monte carlo algorithms for the self avoiding walk it is proved that every dynamic monte carlo algorithm for the self avoiding walk based on a finite repertoire of local n conserving elementary moves is nonergodic heren is the number of bonds in the walk indeed for largen each ergodic class forms an exponentially small fraction of the whole space this invalidates at least in principle the use of the verdier stockmayer algorithm and its generalizations for high precision monte carlo studies of the self avoiding walk

on the tightness of two error bounds for decision feedback equalizers a new upper bound on the probability of error for decision feedback equalizers that is valid for serially independent and dependent stationary noise processes was presented by p kabaila 1987 it is shown that a bound of d l duttweiler et al 1974 is tighter than the bound of kabaila when the noise component shows no serial dependence and with equalization over the full channel response length

fuzzy almost continuity and its pointwise characterization by dual points and fuzzy nets abstract we introduce the notions of fuzzy almost continuity and fuzzy weak continuity at a fuzzy point following the pointwise approach we investigate their fuzzy topological properties we also obtain a pointwise characterization of fuzzy almost continuous functions by dual points and fuzzy nets the main idea behind this work is to establish a local theory in the study of continuity and its weaker forms in general fuzzy topological spaces

net convergence in fuzzy neighborhood spaces our aim is to introduce a concept of net convergence in the well behaved subcategory of lowen fuzzy neighborhood spaces of the category of fuzzy topological spaces in doing so we notice that our present notion of net convergence in addition to katsaras and papageorgeou net convergence is generalized sequential convergence we also apply this notion of net convergence in fuzzy neighborhood groups and fuzzy neighborhood linear spaces

optimum multiuser asymptotic efficiency the degradation in bit error rate due to the presence of multiple access interference in a white gaussian channel can be measured by the multiuser asymptotic efficiency defined as the ratio between the snr required to achieve the same uncoded bit error rate in the absence of interfering users and the actual snr in this paper the asymptotic efficiency of the optimum multiuser demodulator a bank of matched filters followed by a viterbi algorithm is investigated and compared to that of the conventional single user matched filter receiver the computation of the optimum asymptotic efficiency of any given user is equivalent to the minimization of the euclidean distance between any pair of multiuser signals which differ in at least one of the symbols of that user it is shown that the optimum multiuser efficiency of asynchronous systems is nonzero with probability 1 and therefore the optimum demodulator does not become multiple access limited in contrast to the single user receiver a class of signal constellations with moderate cross correlation requirements is shown to achieve unit optimum multiuser efficiencies and hence to be equivalent to orthogonal signal sets from the viewpoint of performance of the optimum multiuser detector

decision feedback multiuser detection a systematic approach a systematic approach to decision feedback multiuser detection is introduced for the joint detection of symbols of k simultaneously transmitting users of a synchronous correlated waveform multiple access cwma channel with gaussian noise a new performance criterion called symmetric energy is defined which is a low noise indicator of the joint error rate that at least one user is detected erroneously even the best linear detectors can perform poorly in terms of symmetric energy compared to the maximum likelihood detector a general class of decision feedback detectors dfds is defined with o k implementational complexity per user the symmetric energy of arbitrary dfd and bounds on their asymptotic effective energy aee performance are obtained along with an exact bit error rate and aee analysis for the decorrelating dfd the optimum dfd that maximizes symmetric energy is obtained each one of the k optimum decorrelating and conventional dfds that correspond to the k orders in which the users can be detected are shown to outperform the linear optimum decorrelating and conventional detectors respectively in terms of symmetric energy moreover algorithms are obtained for determining the choice of order of detection for the three dfds which guarantee that they uniformly user wise outperform their linear counterparts in addition to optimality in symmetric energy it is also shown that under certain conditions the optimum dfd achieves the aee performance of the exponentially complex maximum likelihood detector for all users simultaneously none of the results of this paper make the perfect feedback assumption the implications of our work on power control for multiuser detection are also discussed

mmse interference suppression for direct sequence spread spectrum cdma we consider interference suppression for direct sequence spread spectrum code division multiple access cdma systems using the minimum mean squared error mmse performance criterion the conventional matched filter receiver suffers from the near far problem and requires strict power control typically involving feedback from receiver to transmitter for acceptable performance multiuser detection schemes previously proposed mitigate the near far problem but are complex and require explicit knowledge or estimates of the interference parameters in this paper we present and analyze several new mmse interference suppression schemes which have the advantage of being near far resistant to varying degrees depending on their complexity and can be implemented adaptively when interference parameters are unknown and or time varying numerical results are provided that show that these schemes offer significant performance gains relative to the matched filter receiver we conclude that mmse detectors can alleviate the need for stringent power control in cdma systems and may be a practical alternative to the matched filter receiver

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

fuzzy sets and functions on fuzzy spaces abstract we generally follow the terminology of azad j math anal appl 82 1981 14 32 and ming j math anal appl 76 1980 571 599 in addition to the fundamental concepts for fuzzy sets we emphasize the usefulness of the concepts of fuzzy point fuzzy elementhood for fuzzy sets a and b a new characterization is given for relations a b and a b this knowledge permits us to combine the two definitions of fuzzy point fuzzy elementhood in the third section some results are given concerning various special types of fuzzy sets in fuzzy topological spaces and the fuzzy semi regular fuzzy regular spaces defined by azad in the last section the definitions of h almost continuous w almost open functions urysohn space which are defined by hussain wilansky and noiri respectively are extended to fuzzy sets furthermore some results are obtained in the functions of the fuzzy topological spaces defined by azad and those are defined here

an analysis of the mimo sdma channel with space time orthogonal and quasi orthogonal user transmissions and efficient successive cancellation decoders we consider space time transceiver architectures for space division multiple access sdma fading channels with simultaneous transmissions from multiple users each user has up to four transmit antennas and employs a space time orthogonal or a quasi orthogonal design as an inner code at the multiple antenna receiver efficient successive group interference cancellation strategies based on zero forcing or minimum mean square error mmse filtering are employed in some fixed or channel dependent order these strategies are efficient in the sense that they exploit the special structure of the inner codes to yield much higher diversity orders than would be otherwise possible while at the same time preserving what we call the decoupling property of the constituent inner codes which enables the use of low complexity outer encoders decoders for each user motivated by the special structure of the effective channel matrix induced by the inner codes we obtain several new distribution results on the qr and eigenvalue decompositions of certain structured random matrices these results are the key to a comprehensive performance analysis of the proposed multiuser transceiver architectures including the characterization of diversity multiplexing tradeoff dmt curves and exact per user bit error rates bers without making simplifying assumptions about error propagation

reduced dimension multiuser detection we present a reduced dimension multiuser detector rd mud structure for synchronous systems that significantly decreases the number of required correlation branches at the receiver front end while still achieving performance similar to that of the conventional matched filter mf bank rd mud exploits the fact that in some wireless systems the number of active users may be small relative to the total number of users in the system hence the ideas of analog compressed sensing may be used to reduce the number of correlators the correlating signals used by each correlator are chosen as an appropriate linear combination of the users spreading waveforms we derive the probability of symbol error when using two methods for recovery of active users and their transmitted symbols the reduced dimension decorrelating rdd detector which combines subspace projection and thresholding to determine active users and sign detection for data recovery and the reduced dimension decision feedback rddf detector which combines decision feedback matching pursuit for active user detection and sign detection for data recovery we derive probability of error bounds for both detectors and show that the number of correlators needed to achieve a small probability of symbol error is on the order of the logarithm of the number of users in the system the theoretical performance results are validated via numerical simulations

trellis coding for partial response channels we consider trellis coding techniques for improving the reliability of digital transmission over noisy partial response channels such channels are commonly encountered in digital communication systems and also play a role in devices for data recording concentrating on the channels with characteristics 1 mp d we study methods to obtain codes which increase free euclidean distance between permitted sequences of channel outputs and avoid the occurrence of unlimited runs of identical outputs at the expense of some loss in data rate one technique employs the concept of set partitioning the other is based on using convolutional codes designed for maximum free hamming distance in conjunction with a precoder both methods lead to essentially equivalent codes

blind multiuser detection via interference identification previous results on blind multiuser detection apply in situations where the signal parameters of the users of interest are known and those of the interferers are unknown in this paper we consider the new paradigm of an n user system in which k users are active and the problem is to detect g users of interest out of those k active users when the signal parameters codes amplitudes of the g users of interest are known as are the codes of all n users what is not known at the receiver however is k g the number of active interferers and the identity of these interferers a solution to such a problem could be to ignore the knowledge of the remaining n g codes and apply known blind multiuser detectors based on stochastic approximation or subspace tracking techniques however it is shown here that the additional knowledge of those codes can be used to obtain an interference identification based blind multiuser receiver that has much faster convergence properties we illustrate the underlying principle in the context of blind group detection in synchronous direct sequence code division multiple access ds cdma systems operating in channels that exhibit frequency selective fading

on fuzzy topological spaces abstract in this paper a few separation properties and some aspects of subspace fuzzy topology have been studied where both the crisp and the fuzzy elements have been taken into consideration since the conventional definition of compactness is not quite meaningful in hausdorff fuzzy spaces as introduced by us a new more natural definition of proper compactness is given and a few properties resulting from this are established

matched subspace detectors we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise we derive the generalized likelihood ratio glr for each problem in the class we then establish the invariances for the glr and argue that these are the natural invariances for the problem in each case the glr is a maximal invariant statistic and the distribution of the maximal invariant statistic is monotone this means that the glr test glrt is the uniformly most powerful invariant detector we illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise in each case we give the distribution for the detector and compute performance curves

fuzzy subcontinuity inverse fuzzy subcontinuity and a new category of fuzzy topological spaces the notions of subcontinuity and inverse subcontinuity are extended to the fuzzy setting adopting fuzzy net theoretic approach various properties of fuzzy subcontinuous and inversely fuzzy subcontinuous mappings are studied a category of fuzzy topological spaces is constructed canonical example is constructed by using fuzzy translation of fuzzy numbers introduced by rodabaugh to show that fuzzy subcontinuity does not imply kfuzzy continuity in the process n compactness is characterized and fuzzy unit interval is shown to be n compact also a direct proof is provided showing that fuzzy addition of fuzzy numbers is fuzzy continuous

various fuzzy topological notions and fuzzy almost continuity abstract we extend the notion of almost continuity in the sense of husain 1966 to the fuzzy setting we obtain a pointwise characterization of the notion by dual point and fuzzy net also we formulate conditions under which the two notions of fuzzy almost continuity the one defined in this paper and the one defined by ajmal and azad 1990 turn out to be equivalent the main idea behind this work is to show that using the localized approach developed in earlier papers the study of fuzzy almost continuity can be carried out as successfully as that of its counterpart in general topology in the process we exhibit the compatibility of various existing fuzzy topological notions such as fuzzy regularity c i connectedness i 3 4 c i local connectedness i 3 4 fuzzy t 1 axiom fuzzy t 2 axiom etc

new monte carlo method for the self avoiding walk we introduce a new monte carlo algorithm for the self avoiding walk saw and show that it is particularly efficient in the critical region long chains we also introduce new and more efficient statistical techniques we employ these methods to extract numerical estimates for the critical parameters of the saw on the square lattice we find 2 63820 0 00004 0 00030 1 352 0 006 0 025 v 0 7590 0 0062 0 0042 where the first error bar represents systematic error due to corrections to scaling subjective 95 confidence limits and the second bar represents statistical error classical 95 confidence limits these results are based on saws of average length 166 using 340 hours cpu time on a cdc cyber 170 730 we compare our results to previous work and indicate some directions for future research

some important applications of nets of l fuzzy sets in this paper some compactness adherence point and accumulation point in l fuzzy topological space are characterized by means of the nets of l fuzzy subsets

a new approach to fuzzy topological spaces and fuzzy perfect mappings abstract a net theoretic approach is provided for defining a fuzzy topological space fuzzy topological spaces so defined form a category the main features and advantages of this category which is denoted by n here are discussed the notion of a perfect mapping is introduced and studied in the fuzzy setting it is found that in n a fts is n compact iff any mapping x x where x is any singleton is fuzzy perfect a fuzzy continuous mapping x y from an n compact fts x to a hausdorff fts y is fuzzy perfect in n however these results do not hold in c the chang s category in general it is found that the divergences in the study of fuzzy perfect mappings disappear if the study is carried out in n instead of c

on the limitation of linear mmse detection this correspondence highlights the performance limitation of linear minimum mean squared error mmse detection in underdetermined vector gaussian channels as in overloaded code division multiple access cdma systems where the number of symbols users exceeds the signal space dimension spread factor it is shown that for such a simple receiver it is not possible to construct signal sets or spreading codes to even satisfy the basic requirement that every user s symbol error probability decays exponentially as noise power vanishes this result holds for arbitrary received energies modulation schemes and any strictly underdetermined system with a finite signal space dimension and a finite number of users

on the limitation of generalized welch bound equality signals this correspondence characterizes the performance limitation of the well acclaimed generalized welch bound equality wbe signals under linear minimum mean squared error mmse detection it is analytically proven and experimentally verified that when users in an overloaded but finite size code division multiple access cdma system are allocated such signals the error rate of at least one user floors i e it cannot be driven to zero even in the absence of additive noise independently of the symbol energies if in addition all users are received with equal energy then the error rate of every user floors

blind multiuser detection a subspace approach a new multiuser detection scheme based on signal subspace estimation is proposed it is shown that under this scheme both the decorrelating detector and the linear minimum mean square error mmse detector can be obtained blindly i e they can be estimated from the received signal with the prior knowledge of only the signature waveform and timing of the user of interest the consistency and asymptotic variance of the estimates of the two linear detectors are examined a blind adaptive implementation based on a signal subspace tracking algorithm is also developed it is seen that compared with the previous minimum output energy blind adaptive multiuser detector the proposed subspace based blind adaptive detector offers lower computational complexity better performance and robustness against signature waveform mismatch two extensions are made within the framework of signal subspace estimation first a blind adaptive method is developed for estimating the effective user signature waveform in the multipath channel secondly a multiuser detection scheme using spatial diversity in the form of an antenna array is considered a blind adaptive technique for estimating the array response for diversity combining is proposed it is seen that under the proposed subspace approach blind adaptive channel estimation and blind adaptive array response estimation can be integrated with blind adaptive multiuser detection with little attendant increase in complexity

fast optimal and suboptimal any time algorithms for cdma multiuser detection based on branch and bound a fast optimal algorithm based on the branch and bound bbd method is proposed for the joint detection of binary symbols of k users in a synchronous code division multiple access channel with gaussian noise relationships between the proposed algorithms depth first bbd and fast bbd and both the decorrelating decision feedback df detector and sphere decoding algorithm are clearly drawn it turns out that decorrelating df detector corresponds to a one pass depth first bbd sphere decoding is in fact a type of depth first bbd but one that can be improved considerably via tight upper bounds and user ordering as in the fast bbd a fast any time suboptimal algorithm is also available by simply picking the current best solution in the bbd method theoretical results are given on the computational complexity and the performance of the current best suboptimal solution

computation of a chemical potential using a residence weight algorithm the test particle insertion method and its generalization to biased insertion schemes allows the computation of chemical potentials in fluids even though these techniques can be implemented in dense systems the convergence of the estimated value for the chemical potential must be carefully checked and additional simulations are actually required we propose to compute the chemical potential using a residence weight algorithm with this algorithm it is shown that for a given amount of computer time the degree of convergence towards the exact chemical potential correlates with the mean rate for accepting the trial particle insertions or deletions the residence weight algorithm thus offers a reliable built in tool for diagnosing the numerical convergence

open maps closed maps and local compactness in fuzzy topological spaces on donne des caracterisations des applications floues ouvertes et fermees et on montre que la normalite definie par hutton est invariante sous des applications f fermees f continues

on fuzzy convergence classes abstract the concept of fuzzy point and its quasi coincidence neighborhood have been introduced in 1 using these notions we give the theory of fuzzy convergence classes especially a characterization of fuzzy topology via the fuzzy convergence classes and relative analysis are given

binary convolutional codes with application to magnetic recording calderbank heegard and ozarow 1 have suggested a method of designing codes for channels with intersymbol interference such as the magnetic recording channel these codes are designed to exploit intersymbol interference the standard method is to minimize intersymbol interference by constraining the input to the channel using run length limited sequences calderbank heegard and ozarow considered an idealized model of an intersymbol interference channel that leads to the problem of designing codes for a partial response channel with transfer function 1 d n 2 where the channel inputs are constrained to be pm 1 this problem is considered here channel inputs are generated using a nontrivial coset of a binary convolutional code the coset is chosen to limit the zero run length of the output of the channel and so maintain clock synchronization the minimum squared euclidean distance between outputs corresponding to distinct inputs is bounded below by the free distance of a second convolutional code which we call the magnitude code an interesting feature of the analysis is that magnitude codes that are catastrophic may perform better than those that are noncatastrophic

adaptive reduced rank receive processing based on minimum symbol error rate criterion for large scale multiple antenna systems in this work we propose a novel adaptive reduced rank receive processing strategy based on joint preprocessing decimation and filtering jpdf for large scale multiple antenna systems in this scheme a reduced rank framework is employed for linear receive processing and multiuser interference suppression based on the minimization of the symbol error rate ser cost function we present a structure with multiple processing branches that performs a dimensionality reduction where each branch contains a group of jointly optimized preprocessing and decimation units followed by a linear receive filter we then develop stochastic gradient sg algorithms to compute the parameters of the preprocessing and receive filters along with a low complexity decimation technique for both binary phase shift keying bpsk and m ary quadrature amplitude modulation qam symbols in addition an automatic parameter selection scheme is proposed to further improve the convergence performance of the proposed reduced rank algorithms simulation results are presented for time varying wireless environments and show that the proposed jpdf minimum ser receive processing strategy and algorithms achieve a superior performance than existing methods with a reduced computational complexity

an iterative extension of blast decoding algorithm for layered space time signals we propose an iterative extension of the bell laboratory layered space time blast algorithm and its variant vertical blast vblast a characteristic feature of the blast type algorithm is that symbol decisions with low reliability are fed back to decode other symbols both performance analysis based on gaussian approximation of residual interference and simulation results demonstrate that error propagation due to unreliable decision feedback can severely limit system performance the extended algorithm exploits inherent signal diversity in blast to mitigate residual interference thus overcoming the performance bottleneck due to error propagation it yields an impressive performance gain over blast in particular the extension of blast with zero forcing interference nulling admits a simple qr implementation and exhibits excellent performance with low complexity

category n and functions with closed fuzzy graph abstract a net theoretic approach for defining a fuzzy topological space is provided the fuzzy topological spaces so obtained form a category which we denote by n in this paper it is found that the limitations exhibited by the chang category particularly with respect to projections closure of a fuzzy set compactness etc no longer exist in n the notion of closed fuzzy graph is investigated the divergences shown by this notion are immediately put to rest if the study is carried out in n instead of c the chang category

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

error pattern correcting cyclic codes tailored to a prescribed set of error cluster patterns a new class of cyclic codes is discussed which is highly tailored to a prescribed set of dominant error cluster patterns the cyclic code construction is based on a generator polynomial that produces a distinct syndrome set for each error pattern in the target set by tailoring the generator polynomial specifically to the set of dominant error patterns the code becomes highly effective in handling single and multiple occurrences of dominant error patterns at a very high code rate a list decoding strategy based on a set of test word error events is developed for the proposed codes which efficiently utilizes both the algebraic information from the captured syndrome and the reliability measures provided by the local correlators matched to the dominant error patterns by forcing a decoder to correct a single pattern event for each test input word multiple decoders running in parallel on the list of test words can effectively correct multiple error pattern occurrences within the channel detector output word

error exponents for maximum likelihood and successive decoders for the gaussian cdma channel random coding error exponents are derived for the gaussian code division multiple access cdma channel for the maximum likelihood and optimum successive decoders error exponents not only specify the capacity region of the channel which is known but also give lower bounds on the rate of exponential decay of the average probability of error as a function of the block length of random codes a comparison of the two decoders in terms of their error exponents is included

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

the pivot algorithm a highly efficient monte carlo method for the self avoiding walk the pivot algorithm is a dynamic monte carlo algorithm first invented by lal which generates self avoiding walks saws in a canonical fixed n ensemble with free endpoints heren is the number of steps in the walk we find that the pivot algorithm is extraordinarily efficient one effectively independent sample can be produced in a computer time of ordern this paper is a comprehensive study of the pivot algorithm including a heuristic and numerical analysis of the acceptance fraction and autocorrelation time an exact analysis of the pivot algorithm for ordinary random walk a discussion of data structures and computational complexity a rigorous proof of ergodicity and numerical results on self avoiding walks in two and three dimensions our estimates for critical exponents are 0 7496 0 0007 ind 2 and 0 592 0 003 ind 3 95 confidence limits based on saws of lengths 200 n 10000 and 200 n 3000 respectively

analysis of decision feedback detection for mimo rayleigh fading channels and the optimization of power and rate allocations for an uncoded k transmit n receive antenna coherent narrow band communication system employing a decorrelating decision feedback detector d dfd the exact average over channel realizations joint error probability jep as well as the average per symbol error probabilities seps are derived without making any simplifying assumptions on error propagation it is proved that the diversity orders of the jep and the sep of every symbol is limited by error propagation to n k 1 based on our exact error probability analysis however we suggest an optimization of jep over nonnegative quadrature amplitude modulation qam constellation sizes rates and average powers across transmitters which yield significant improvements over the usual equal power and equal rate assignment in fact the jep of such an optimized design has the much improved diversity order of n which is also the diversity order obtained through the optimum maximum likelihood ml detector moreover it is seen that these simple optimized designs can achieve a significant fraction of the spl epsi outage capacity even without outer codes it is also known but only through simulations that when the symbols are detected in certain channel realization dependent orders it is possible to improve substantially over fixed order detection in the case of the equal rate and equal power assignment we provide an analysis for a recently proposed channel dependent ordering rule and show that it does not provide an improvement of the diversity order of the jep beyond n k 1 another ordering rule that was proposed earlier to maximize the worst case post detection signal to noise ratio snr under the perfect feedback assumption is shown to be optimal under a more compelling criterion that does not involve that simplifying assumption while efficiently computable this ordering rule is seen to perform almost as well as the optimal channel dependent ordering rule that minimizes the conditional jep and hence the jep nevertheless a multiple input multiple output mimo system with an optimized rate and power allocation and a fixed order of detection is not only less complex but also has a significantly lower jep than that of the equal power equal rate system where transmitters are detected in a channel dependent order optimal or otherwise

iterative space time processing for multiuser detection in multipath cdma channels space time processing and multiuser detection are two promising techniques for combating multipath distortion and multiple access interference in code division multiple access cdma systems to overcome the computational burden that rises very quickly with increasing numbers of users and receive antennas in applying such techniques iterative implementations of several space time multiuser detection algorithms are considered here these algorithms include iterative linear space time multiuser detection cholesky iterative decorrelating decision feedback space time multiuser detection multistage interference canceling space time multiuser detection and expectation maximization em based iterative space time multiuser detection a new space time multiuser receiver structure that allows for efficient implementation of iterative processing is also introduced fully exploiting various types of diversity through joint space time processing and multiuser detection brings substantial gain over single receiver antenna or single user based methods it is shown that iterative implementation of linear and nonlinear space time multiuser detection schemes discussed in this paper realizes this substantial gain and approaches the optimum performance with reasonable complexity among the iterative space time multiuser receivers considered in this paper the em based sage iterative space time multiuser receiver introduced here achieves the best performance with excellent convergence properties

design of block transceivers with decision feedback detection this paper presents a method for jointly designing the transmitter receiver pair in a block by block communication system that employs intrablock decision feedback detection we provide closed form expressions for transmitter receiver pairs that simultaneously minimize the arithmetic mean squared error mse at the decision point assuming perfect feedback the geometric mse and the bit error rate of a uniformly bit loaded system at moderate to high signal to noise ratios separate expressions apply for the zero forcing and minimum mse mmse decision feedback structures in the mmse case the proposed design also maximizes the gaussian mutual information and suggests that one can approach the capacity of the block transmission system using independent instances of the same gaussian code for each element of the block our simulation studies indicate that the proposed transceivers perform significantly better than standard transceivers and that they retain their performance advantages in the presence of error propagation

joint transmitter receiver optimization for multi input multi output systems with decision feedback the joint transmit receive optimization problem for multiuser communication systems with decision feedback is investigated it is shown that minimization of the geometric mean squared error defined as the determinant of the error covariance matrix leads to a tractable transmitter optimization problem for general multi input multi output decision feedback systems several computational results are included that highlight system performance for a variety of useful transmission scenarios