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

optimum asymptotic multiuser efficiency of randomly spread cdma this correspondence analyzes the high signal to noise ratio snr performance of optimum multiuser detectors for synchronous direct sequence spread spectrum with random spreading in an additive white gaussian noise channel under very general conditions on the received powers we show that the optimum asymptotic efficiency of a k user system with spreading gain n converges to 1 almost surely as k spl rarr spl infin and k n is kept equal to an arbitrary nonzero constant therefore the asymptotic behavior of the minimum bit error rate is equivalent to that of a single user system

a chip based multiuser detector for the downlink of a ds cdma system using a folded state transition trellis the maximum likelihood sequence estimation mlse multiuser detector has very good performance but at the expense of high computational complexity the viterbi algorithm is employed to implement the mlse in the asynchronous uplink in this scheme the various bit combinations are taken to be the different states in the decoding trellis however the number of states increases exponentially with the number of active users we propose a scheme that exploits the feature of power equality in the downlink to reduce the number of states involved each transmitted chip value can only take a certain number of possible discrete values using these discrete values as the states in the transition trellis diagram and operating the viterbi algorithm at the chip level the number of states is reduced from 4 sup k to k 1 sup l where k is the number of users and l is the number of paths in the multipath channel

blind multiuser detection from moe to subspace methods the minimum output energy moe multiuser receiver has been shown to approach the minimum mean square error mmse receiver at high signal to noise ratio snr however performance degradation is incurred by noise induced channel estimation error in this paper we propose a power of r por technique to significantly improve the performance of the moe receiver it is shown that the new receiver asymptotically converges to the mmse receiver without performance penalty the convergence is established either under high snr with large exponent raised in the power of the covariance matrix or with sufficiently large number of data samples connection between our por method and a widely studied subspace method is investigated from the respective optimization criteria asymptotic equivalence between these two methods is also established extensive simulations based on finite data samples show that the proposed method significantly outperforms the subspace method in systems with medium to heavy loading severe multipath distortion or smaller processing gain moreover adaptive implementation of the proposed method exhibits very robust performance in a dynamic loading environment

performance of constrained and unconstrained adaptive multiuser detectors for quasi synchronous cdma it has previously been shown that multiuser interference in a quasi synchronous code division multiple access qs cdma system can be effectively rejected using a nonadaptive decorrelator however the qs decorrelator is orthogonal to the inflated subspace spanned by the undesired users with arbitrary delays in the qs uncertainty interval and hence does not perform as well as a decorrelator with a priori knowledge of the delays here we consider a constrained adaptive linear suppression filter which implicitly estimates the delays of the qs undesired signals and thus approaches the ideal decorrelator of lupas and verdu 1990 for qs cdma it is shown through analysis and simulations that the constrained recursive least squares c rls algorithm converges faster than an unconstrained rls adaptive filter and generally outperforms the nonadaptive qs decorrelator a cellular quasi synchronous system is discussed in the present paper

blind parameter estimation in multiple access systems a blind algorithm for the estimation of amplitude phase and relative time delay of each user in multiple access communication systems is proposed this algorithm is based on the cyclostationarity features of the received signals and provides estimates of the unknown parameters that are intrinsically immune to the effects of noise and interference provided that a cycle frequency of the user signals exists which is not shared with the disturbance terms the proposed estimators are under mild assumptions asymptotically unbiased and consistent moreover the proposed algorithm is asymptotically near far resistant and is not based on the usual assumption of white and or gaussian noise

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

superlinearly convergent cg methods via equivalent preconditioning for nonsymmetric elliptic operators the convergence of the conjugate gradient method is studied for preconditioned linear operator equations with nonsymmetric normal operators with focus on elliptic convection diffusion operators in sobolev space superlinear convergence is proved first for equations whose preconditioned form is a compact perturbation of the identity in a hilbert space then the same convergence result is verified for elliptic convection diffusion equations using different preconditioning operators the convergence factor involves the eigenvalues of the corresponding operators for which an estimate is also given the above results enable us to verify the mesh independence of the superlinear convergence estimates for suitable finite element discretizations of the convection diffusion problems

delayed decision feedback sequence estimation the authors delayed decision feedback sequence estimation ddfse for uncoded pam signals is considered estimates on the performance of the algorithm are given and simulation results are provided for several examples a more general form of ddfse applicable to coded modulation systems is also presented as an example detection of trellis coded qpsk quadrature phase shift keyed signals over intersymbol interference channels is discussed

indecomposable error sequences in multiuser detection in this paper we provide a graph based characterization of the set of indecomposable sequences that are useful in the computation of an upper bound to error probability of maximum likelihood ml detection in code division multiple access cdma multiuser systems we apply this characterization to a k user symmetric system and to a two user two rate system it leads to a precise calculation of the bound which is then compared to the performance of a decorrelator

error probability for direct sequence spread spectrum multiple access communications part i upper and lower bounds upper and lower bounds on the average probability of error are obtained for direct sequence spread spectrum multipleaccess communications systems with additive white gaussian noise channels the bounds which are developed from convexity properties of the error probability function are valid for systems in which the maximum multiple access interference does not exceed the desired signal and the signature sequence period is equal to the duration of the data pulse the tightness of the bounds is examined for systems with a small number of simultaneously active transmitters this is accomplished by comparisons of the upper and lower bounds for several values of the system parameters the bounds are also compared with an approximation based on the signal to noise ratio and with the chernoff upper bound

limited linear cancellation of multiuser interference in ds cdma asynchronous systems this paper presents a linear cancellation detector for the gaussian channel operating over limited time intervals of the received signal in a similar way to a multiinput multioutput finite impulse response fir filter the parameters defining the detector become time invariant and the conditions to be met by the signatures are stated a bound for the multiuser interference due to the limited time correlation and upper and lower bounds for the error probability are obtained the theoretical bounds and numerical results show that the detector is adequate for systems intended for many users whose amplitudes can be restricted to a given range

suboptimum multiuser receivers for convolutionally coded asynchronous ds cdma systems motivated by the high complexity of the optimal sequence estimator for convolutionally coded asynchronous code division multiple access cdma systems developed by giallorenzi and wilson see ibid vol 44 no 8 p 997 1996 and the potentially poor performance of the conventional receiver due to multiuser interference and the near far problem we examine relatively simple multiuser receivers which perform nearly as well as the optimal receiver the multiuser receivers discussed are of two types the first set of approaches are partitioned approaches that treat the multiuser interference equalization problem and the decoding problem separately the second set of approaches are integrated approaches that perform both the equalization and decoding operations together we study linear decision feedback and trellis tree based approaches in each category the asymptotic efficiency of this receiver relative to an uncoded coherent binary phase shift keying bpsk receiver termed asymptotic multiuser coding gain or amcg is used as a performance criterion throughout also computer simulations are used whenever the computation of the amcg is not feasible it is shown that a number of the approaches which are introduced achieve a high performance level with a moderate complexity

a matrix algebraic approach to successive interference cancellation in cdma in this paper we describe linear successive interference cancellation sic based on matrix algebra we show that linear sic schemes single stage and multistage correspond to linear matrix filtering that can be performed directly on the received chip matched filtered signal vector without explicitly performing the interference cancellation this leads to an analytical expression for calculating the resulting bit error rate which is of particular use for short code systems convergence issues are discussed and the concept of spl epsiv convergence is introduced to determine the number of stages required for practical convergence for both short and long codes

subspace based channel estimation for code division multiple access communication systems we consider the estimation of channel parameters for code division multiple access cdma communication systems operating over channels with either single or multiple propagation paths the multiuser channel estimation problem is decomposed into a series of single user problems through a subspace based approach by exploiting the eigenstructure of the received signal s sample correlation matrix the observation space can be partitioned into a signal subspace and a noise subspace without prior knowledge of the unknown parameters the channel estimate is formed by projecting a given user s spreading waveform into the estimated noise subspace and then either minimizing the likelihood or minimizing the euclidean norm of this projection both of these approaches yield algorithms which are near far resistant and do not require a preamble

average cost of duval s algorithm for generating lyndon words the average cost of duval s algorithm for generating all lyndon words up to a given length in lexicographic order is proved to be asymptotically equal to q 1 q 1 where q is the size of the underlying alphabet in particular the average cost is independent of the length of the words generated a precise evaluation of the constants is also given

indirectly estimated adaptive detectors for code division multiple access signals this paper presents the development of indirectly estimated adaptive idea detectors for code division multiple access cdma signals in wireless communication systems multiuser cdma detection is formulated as an inverse problem in the presence of noise and the estimation of the detector parameters is accomplished using elements of regularization theory the development of autonomous cdma detectors that are capable of adjusting to the channel characteristics with the support of training sequences relies on data dependent procedures designed to reduce the effect of noise and interfering users on the performance of the detector the detector parameters can be computed by adaptive algorithms that require no matrix inversion the proposed idea detector is evaluated and compared with existing multiuser cdma detectors in terms of their robustness to noise resistance to the near far problem and ability to handle multipath signals

robust blind multiuser detection based on the worst case performance optimization of the mmse receiver the conventional minimum mean square error mmse multiuser receiver requires that each particular user transmits a sequence of training symbols known to the receiver and the receiver estimates the user signatures using this knowledge however in the presence of multiaccess interference mai during the training period and or in scenarios with short training sequence length the signature estimates can be erroneous and the performance of the mmse multiuser receiver can degrade substantially in this paper we propose a new blind multiuser receiver that is robust against the effects of erroneously presumed desired user signature and short data length our approach is based on the explicit modeling of possible mismatches in the mean square error cost function and worst case performance optimization we show that this approach leads to a multiuser receiver which uses the data covariance matrix with an adaptive diagonal loading the proposed method has simple implementation with a computational complexity comparable with that of the fixed diagonal loading based multiuser receiver simulation results show performance improvements achieved by our approach relative to existing techniques

on minimal eigenvalues of a class of tridiagonal matrices it is known that the worst case near far resistance of optimum multiuser detectors for asynchronous gaussian multiple access channels can be expressed in terms of a class of block tridiagonal matrices and the minimal eigenvalues of such a class of block tridiagonal matrices serve as a good measure of the worst case near far resistance in this paper we focus on the two user scenario where each block tridiagonal matrix under consideration is a tridiagonal matrix we derive closed form expressions for the minimal eigenvalues of such a class of tridiagonal matrices in terms of the largest real solution of a trigonometric equation in 0 pi we also obtain lower bounds and upper bounds on the minimal eigenvalues which improve on previously known results in the literature

bifurcations in mean field theory annealing in this paper we investigate bifurcation processes for the mean field theory mft annealing applied to traveling salesman problems tsps due to the symmetries of the tsp free energy function some special bifurcations occur cyclic symmetry breaking bifurcations and reverse symmetry breaking bifurcations saddle node bifurcations also occur which type of bifurcation occurs depends on the symmetry of the eigenvector that corresponds to the zero eigenvalue mode of the free energy curvature matrix at the bifurcation point in the mft annealing process a sequence of bifurcations occurs and the bifurcation structure affects the quality of the annealing solution it is shown that the annealing solution in this process is not unique in general and it is not always the optimal solution our approach can also be applied to the potts spin model and its bifurcation structure is almost the same as that of the mft the practical implications of our results are also discussed textcopyright 1996 the american physical society

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

on the superlinear convergence of pcg algorithms numerical experiments for convection diffusion equations the cgm is studied for nonsymmetric elliptic problems with both dirichlet and mixed boundary conditions the mesh independence of the convergence is an important property when symmetric part preconditioning is applied to the fem discretizations of the boundary value problem computations in two dimensions are presented to illustrate the mesh independent superlinear convergence for convection diffusion equations with both types of boundary conditions preconditioning by the leading term plus a zeroth order term is also investigated in the aspect of superlinear convergence through numerical computations

nonlinear techniques for the joint estimation of cochannel signals cochannel interference occurs when two or more signals overlap in frequency and are present concurrently unlike in spread spectrum multiple access systems where the different users necessarily share the same channel cochannel interference is a severe hindrance to frequency and time division multiple access communications and is typically minimized by interference rejection suppression techniques rather than using interference suppression we are interested in the joint estimation of the information bearing narrow band cochannel signals novel joint estimators are proposed that employ a single input demodulator with oversampling to compensate for timing uncertainties assuming finite impulse response channel characteristics maximum likelihood ml and maximum a posteriori map criteria are used to derive cochannel detectors of varying complexities and degrees of performance in particular a suboptimal two stage joint map symbol detector jmapsd is introduced that has a lower complexity than the single stage estimators while accruing only a marginal loss in error rate performance at high signal to interference ratios assuming only reliable estimates of the primary and secondary signal powers a blind adaptive jmapsd algorithm for a priori unknown channels is also derived the performance of these nonlinear joint estimation algorithms is studied through example computer simulations for two cochannel sources

multiuser detection in single path fading channels the performance analysis of maximum likelihood sequence and decorrelating multiuser detectors is developed for the single path rayleigh fading channel the received signal in this multipoint to point channel is additively composed of white gaussian noise and independently faded waveforms from a finite number of asynchronous users the optimum sequence detector consists of a bank of single user matched filters followed by a dynamic programming algorithm has a demodulation complexity per symbol which is exponential in the number of users and requires the knowledge of the system as well of the fading parameters the decorrelating detector has a complexity which is polynomial in the number of users and does not require knowledge of the signal amplitudes which are assumed to vary slowly relative to the symbol rate the single user error rates are presented for both detectors and compared to conventional detection and isolated transmission and the notion of asymptotic multiuser efficiency is developed for this channel in contrast to conventional detection which suffers from near far effects due to rayleigh fading it is shown that the aforementioned multiuser detectors exhibit performance which rivals that of isolated transmission for sufficiently small thermal noise power the results of the analysis are illustrated with numerical examples and indicate that the near far problem may be alleviated by a more sophisticated receiver design

gradient estimation for sensitivity analysis and adaptive multiuser interference rejection in code division multiple access systems in this paper we consider a direct sequence code division multiple access ds cdma system in the framework of a discrete event dynamic system deds in order to optimize the system performance based on this formulation we develop infinitesimal perturbation analysis ipa for estimating the sensitivity of the average probability of bit error to factors ranging from near far effects to imperfections in power control the above estimates are shown to be unbiased and this technique is then further incorporated into a stochastic gradient algorithm for achieving adaptive multiuser interference rejection for such systems which is also subject to frequency nonselective slow fading we use an ipa based stochastic training algorithm for developing an adaptive linear detector with the average probability of error being the minimization criterion we also develop a practical implementation of such an adaptive detector where we use a joint estimation detection algorithm for minimizing the average probability of bit error a sequential implementation that does not require a stochastic training sequence or a preamble is also developed

on minimum ber linear multiuser detection for ds cdma channels the minimum bit error rate mber linear multiuser detection of direct sequence code division multiple access ds cdma communications is considered it is shown that the problem of mber linear multiuser detection is equivalent to a constrained optimization problem where the constrained space is the surface and interior of a hyperellipsoid it is further shown that any solution of the constrained optimization problem must be a solution of a set of nonlinear equations based on these the mber linear multiuser detector of the two user case is obtained for general cases we propose a convex subspace of the constrained space and show that the ber cost function is convex on the subspace and therefore has a unique solution some sufficient conditions that guarantee the convex subspace always contains the global minimizer are provided which show that if the signal to noise ratio snr is sufficiently large the convex subspace always contains the global minimizer a newton method is developed for the set of nonlinear equations and computer simulation gives some illustrative examples

single user detectors for multiuser channels optimum decentralized demodulation for asynchronous gaussian multiaccess channels is considered it is assumed that the receiver is the destination of the information transmitted by only one active user and single user detectors that take into account the existence of the other active users in the channel are obtained the problem considered is one of signal detection in additive colored nongaussian noise and attention is focused on one shot structures where detection of each symbol is based only on the received process during its corresponding interval particular emphasis is placed on asymptotically optimum detectors for weak interferers for cdma code division multiple access signature waveforms with long spreading codes and for low background gaussian noise level

blind adaptive multiuser detection the decorrelating detector and the linear minimum mean square error mmse detector are known to be effective strategies to counter the presence of multiuser interference in code division multiple access channels in particular those multiuser detectors provide optimum near far resistance when training data sequences are available the mmse multiuser detector can be implemented adaptively without knowledge of signature waveforms or received amplitudes this paper introduces an adaptive multiuser detector which converges for any initialization to the mmse detector without requiring training sequences this blind multiuser detector requires no more knowledge than does the conventional single user receiver the desired user s signature waveform and its timing the proposed blind multiuser detector is made robust with respect to imprecise knowledge of the received signature waveform of the user of interest

a generalized conjugate gradient least square method a generalizeds term truncated conjugate gradient method of least square type proposed in 1a b is extended to a form more suitable for proving when the truncated version is identical to the full term version advantages with keeping a control term in the truncated version is pointed out a computationally efficient new algorithm based on a special inner product with a small demand of storage is also presented we also give simplified and slightly extended proofs of termination of the iterative sequence and of existence of ans term recursion identical to the full term version important earlier results on this latter topic are found in 15 16 8 and 11

single track circuit codes single track circuit codes sttcs are circuit codes with codewords of length n such that all the n tracks which correspond to the n distinct coordinates of the codewords are cyclic shifts of the first track these codes simultaneously generalize single track gray codes and ordinary circuit codes they are useful in angular quantization applications in which error detecting and or correcting capabilities are needed a parameter k called the spread of the code measures the strength of this error control capability we consider the existence of stccs for small lengths n spl les 17 and spreads k spl les 6 constructing some optimal and many good examples we then give a general construction method for stccs which makes use of ordinary circuit codes we use this construction to construct examples of codes with 360 and 1000 codewords which are of practical importance we also use the construction to prove a general result on the existence of stccs for general spreads

on the capacity loss due to separation of detection and decoding the performance loss due to separation of detection and decoding on the binary input additive white gaussian noise awgn channel is quantified in terms of mutual information results are reported for both the code division multiple access cdma channel in the large system limit and the intersymbol interference isi channel the results for cdma rely on the replica method developed in statistical mechanics it is shown that a previous result of shamai and verdu found for gaussian input alphabet holds also for binary input alphabets for the isi channel the performance loss is calculated via the bahl cocke jelinek raviv bcjr algorithm comparisons are made to the capacity of separate detection and decoding using suboptimum detectors such as a decision feedback equalizer

adaptive and self averaging thouless anderson palmer mean field theory for probabilistic modeling we develop a generalization of the thouless anderson palmer tap mean field approach of disorder physics which makes the method applicable to the computation of approximate averages in probabilistic models for real data in contrast to the conventional tap approach where the knowledge of the distribution of couplings between the random variables is required our method adapts to the concrete set of couplings we show the significance of the approach in two ways our approach reproduces replica symmetric results for a wide class of toy models assuming a nonglassy phase with given disorder distributions in the thermodynamic limit on the other hand simulations on a real data model demonstrate that the method achieves more accurate predictions as compared to conventional tap approaches

equivalent operator preconditioning for elliptic problems with nonhomogeneous mixed boundary conditions the numerical solution of linear elliptic partial differential equations often involves finite element discretization where the discretized system is usually solved by some conjugate gradient method the crucial point in the solution of the obtained discretized system is a reliable preconditioning that is to keep the condition number of the systems under control no matter how the mesh parameter is chosen the pcg method is applied to solving convection diffusion equations with nonhomogeneous mixed boundary conditions using the approach of equivalent and compact equivalent operators in hilbert space it is shown that for a wide class of elliptic problems the superlinear convergence of the obtained preconditioned cgm is mesh independent under fem discretization

error probability for direct sequence spread spectrum multiple access communications part ii approximations approximations are obtained for the average probability of error in an asynchronous direct sequence spread spectrum multiple access communications system both binary and quaternary systems are considered and the chip waveforms are allowed to be arbitrary time limited waveforms with time duration equal to the inverse of the chip rate the approximation is based on the integration of the characteristic function of the multiple access interference the amount of computation required to evaluate this approximation grows only linearly with the product of the number of simultaneous transmitters and the number of chips per bit the accuracy of the approximation is extremely good in most cases but it can be improved if necessary by an application of a series expansion numerical results are presented for specific chip waveforms and signature sequences

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

limited magnitude error correcting gray codes for rank modulation we construct error correcting codes over permutations under the infinity metric which are also gray codes in the context of rank modulation i e are generated as simple circuits in the rotator graph these errors model limited magnitude or spike errors for which only single error detecting gray codes are currently known surprisingly the error correcting codes we construct achieve a better asymptotic rate than that of presently known constructions not having the gray property and exceed the gilbert varshamov bound additionally we present efficient ranking and unranking procedures as well as a decoding procedure that runs in linear time finally we also apply our methods to solve an outstanding issue with error detecting rank modulation gray codes also known in this context as snake in the box codes under a different metric the kendall tau metric in the group of permutations over an even number of elements s 2n where we provide asymptotically optimal codes

a generalized minimum mean output energy strategy for cdma systems with improper mai it has been shown that in a direct sequence code division multiple access ds cdma system employing binary phase shift keying bpsk modulation the baseband equivalent of the cdma multiplex is under very mild assumptions an improper complex random process i e it has a nonzero pseudoautocorrelation function the problem of linear multiuser detection for asynchronous ds cdma systems with improper multiaccess interference mai is considered a new mean output energy moe cost function is introduced whose constrained minimization leads to two new linear multiuser detectors exploiting the information contained in the pseudoautocorrelation of the observables and which generalize the classical decorrelating and minimum mean square error mmse receivers the problem of blind adaptive receiver implementation based on subspace tracking is also tackled finally the superiority of the new detectors with respect to the classical linear detection structures present in the literature is demonstrated through both theoretical considerations and computer simulations

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

mean field approaches to independent component analysis we develop mean field approaches for probabilistic independent component analysis ica the sources are estimated from the mean of their posterior distribution and the mixing matrix and noise level is estimated by maximum a posteriori map the latter requires the computation of a good approximation to the correlations between sources for this purpose we investigate three increasingly advanced mean field methods the variational also known as naive mean field approach linear response corrections and an adaptive version of the thouless anderson and palmer 1977 tap mean field approach which is due to opper and winther 2001 the resulting algorithms are tested on a number of problems on synthetic data the advanced mean field approaches are able to recover the correct mixing matrix in cases where the variational mean field theory fails for handwritten digits sparse encoding is achieved using nonnegative source and mixing priors for speech the mean field method is able to separate in the underdetermined overcomplete case of two sensors and three sources one major advantage of the proposed method is its generality and algorithmic simplicity finally we point out several possible extensions of the approaches developed here

randomly spread cdma asymptotics via statistical physics this paper studies randomly spread code division multiple access cdma and multiuser detection in the large system limit using the replica method developed in statistical physics arbitrary input distributions and flat fading are considered a generic multiuser detector in the form of the posterior mean estimator is applied before single user decoding the generic detector can be particularized to the matched filter decorrelator linear minimum mean square error mmse detector the jointly or the individually optimal detector and others it is found that the detection output for each user although in general asymptotically non gaussian conditioned on the transmitted symbol converges as the number of users go to infinity to a deterministic function of a hidden gaussian statistic independent of the interferers thus the multiuser channel can be decoupled each user experiences an equivalent single user gaussian channel whose signal to noise ratio snr suffers a degradation due to the multiple access interference mai the uncoded error performance e g symbol error rate and the mutual information can then be fully characterized using the degradation factor also known as the multiuser efficiency which can be obtained by solving a pair of coupled fixed point equations identified in this paper based on a general linear vector channel model the results are also applicable to multiple input multiple output mimo channels such as in multiantenna systems

a near optimal multiuser detector for ds cdma systems using semidefinite programming relaxation a multiuser detector for direct sequence code division multiple access systems based on semidefinite programming sdp is proposed it is shown that maximum likelihood ml detection can be carried out by relaxing the associated integer programming problem to a dual sdp problem which leads to a detector of polynomial complexity computer simulations that demonstrate that the proposed detector offers near optimal performance with considerably reduced computational complexity compared with that of existing primal sdp relaxation based detectors are presented

lattice decoding for joint detection in direct sequence cdma systems a new joint detection method based on sphere packing lattice decoding is presented in this paper the algorithm is suitable for both synchronous and asynchronous multiple access direct sequence code division multiple access ds cdma systems and it may jointly detect up to 64 users with a reasonable complexity the detection complexity is independent of the modulation size and large m pam or m qam constellations can be used furthermore a theoretical gain analysis is performed in which the multiple access system performance is derived from the lattice parameters

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

a heuristic approach for constructing symmetric gray codes interest in the symmetric gray sg code is high because of its importance in the design and testing of many types of electrical circuits and information systems the conventional methods for constructing such a code are complicated a heuristic approach is described in this paper examples of constructing the sg code of order 5 6 and 7 are included

constant weight gray codes for local rank modulation we consider the local rank modulation lrm scheme in which a sliding window going over a sequence of real valued variables induces a sequence of permutations lrm is a generalization of the rank modulation scheme which has been recently suggested as a way of storing information in flash memory we study constant weight gray codes for the lrm scheme in order to simulate conventional multilevel flash cells while retaining the benefits of rank modulation we present a practical construction of codes with asymptotically optimal rate and weight asymptotically half the length thus having an asymptotically optimal charge difference between adjacent cells next we turn to examine the existence of optimal codes by specifically studying codes of weight 2 and 3 in the former case we upper bound the code efficiency proving that there are no such asymptotically optimal cyclic codes in contrast for the latter case we construct codes which are asymptotically optimal we conclude by providing necessary conditions for the existence of cyclic and cyclic optimal gray codes

a survey of combinatorial gray codes the term combinatorial gray code was introduced in 1980 to refer to any method for generating combinatorial objects so that successive objects differ in some prespecified small way this notion generalizes the classical binary reflected gray code scheme for listing n bit binary numbers so that successive numbers differ in exactly one bit position as well as work in the 1960s and 1970s on minimal change listings for other combinatorial families including permutations and combinations the area of combinatorial gray codes was popularized by herbert wilf in his invited address at the siam conference on discrete mathematics in 1988 and his subsequent siam monograph combinatorial algorithms an update 1989 in which he posed some open problems and variations on the theme this resulted in much recent activity in the area and most of the problems posed by wilf are now solved in this paper we survey the area of combinatorial gray codes describe recent results variations and trends and highlight some open problems

low complexity blind detection of ds cdma signals auxiliary vector receivers a fresh look on the design of practical low complexity direct sequence code division multiple access ds cdma receivers is proposed from the wiener reconstruction filter point of view the natural outcome is the emergence of a new class of linear scalar parameterized auxiliary vector receivers filters then the blind optimization of these receivers in the maximum signal to interference plus noise ratio sinr sense becomes a straightforward procedure the conceptual and computational simplicity of this general approach promises immediate practical utility this new generation of receivers exhibits minimal optimization requirements and near matched filter mf operational complexity yet theoretical arguments supported by numerical and simulation results included in this work suggest that the blind auxiliary vector receiver compares favorably both complexity wise and performance wise to multiuser mu detectors such as the minimum output energy moe and the decorrelating receiver although the latter utilizes the assumed known spreading codes of all interfering users

differentially coherent decorrelating detector for cdma single path time varying rayleigh fading channels this paper describes a differentially coherent decorrelating detector for a k user reverse link code division multiple access environment that exhibits time varying rayleigh fading the channel is modeled as providing only a single fading path for each user and with no additional means to achieve diversity the design of the detector is based on using fractionally sampled matched filter outputs to simultaneously achieve two goals 1 the novel realization of a one shot decorrelator with lower computational complexity and 2 the forming of the maximum likelihood decision rule on the decorrelated outputs which results in an effective increase of the correlation in the fading process analytical evaluation and simulation of the error probability of the detector demonstrates significant lowering of the error floor in comparison to the decorrelating detector that employs conventional differentially coherent detection

constrained maximum likelihood detection in cdma the detection strategy usually denoted optimal multiuser detection is equivalent to the solution of a 0 1 constrained maximum likelihood ml problem a problem which is known to be np hard in contrast the unconstrained ml problem can be solved quite easily and is known as the decorrelating detector in this paper we consider the constrained ml problem where the solution vector is restricted to lie within a closed convex set ccs such a design criterion leads to detector structures which are ml under the constraint assumption a close relationship between a sphere constrained ml detector and the well known minimum mean square error detector is found and verified an iterative algorithm for solving a ccs constraint problem is derived based on results in linear variational inequality theory special cases of this algorithm subject to a box constraint are found to correspond to known nonlinear successive and parallel interference cancellation structures using a clipped soft decision for making tentative decisions while a weighted linear parallel interference canceler with signal dependent weights arises from the sphere constraint convergence issues are investigated and an efficient implementation is suggested the bit error rate performance is studied via computer simulations and the expected performance improvements over unconstrained ml are verified

counting sequences a gray sequence is a counter sequence where the hamming distance between successive states is one a construction for any fixed odd distance between successive states is given based on error correcting codes such sequences could be used in testing and fault diagnosis when sequencing through all possible input combinations sequences with the maximum possible difference between successive states alternately n and n 1 are given a characterization of such maximal change sequences is given the most nearly uniform even difference sequences are described the distribution of bit changes or transition counts for individual variables for a counting sequence is considered

time varying narrow band interference rejection in asynchronous multiuser ds cdma systems over frequency selective fading channels in this paper we handle the problem of joint suppression of multiple access interference mai and narrowband interference nbi in fading dispersive channels the detectors we consider are linear one shot structures which allow for possible window enlargement and signal space oversampling to improve performance we focus on both zero forcing and minimum mean square error design strategies showing that the presence of nbi generally requires a time varying processing of the observables no matter what the optimization criterion a thorough performance assessment of the proposed detectors is also presented either through analytical formulas or through computer simulations we finally deal with the problem of blind suppression of both mai and nbi introducing batch estimation procedures to be implemented offline which require very little and sometimes no prior knowledge as to the interference structure

direct sequence spread spectrum multiple access communications with random signature sequences a large deviations analysis a direct sequence spread spectrum multiple access bit error probability analysis is developed using large deviations theory let m denote the number of interfering spread spectrum signals and let n denote the signature sequence length then the large deviations limit is as n to infinity with m fixed a tight asymptotic expression for the bit error probability is proven and in addition recent large deviations results with the importance sampling monte carlo estimation technique are applied to obtain accurate and computationally efficient estimates of the bit error probability for finite values of m and n the large deviations point of view is compared also to the conventional asymptotics of central limit theory and the associated gaussian approximation the gaussian approximation is accurate and the ratio m n is moderately large and all signals have roughly equal power in the near far situation however the gaussian approximation is quite poor in contrast large deviations techniques are more accurate in the near far situation and it is here that these methods provide some important practical insight

on adaptive minimum probability of error linear filter receivers for ds cdma channels receiver architectures in the form of a linear filter front end followed by a hard limiting decision maker are considered for ds cdma communication systems based on stochastic approximation concepts a recursive algorithm is developed for the adaptive optimization of the linear filter front end in the minimum ber sense the recursive form is decision driven and distribution free for additive white gaussian noise awgn channels theoretical analysis of the ber surface of linear filter receivers identifies the subset of the linear filter space where the optimal receiver lies and offers a formal proof of guaranteed global optimization with probability one for the two user case to the extent that the output of a linear ds cdma filter can be approximated by a gaussian random variable a minimum mean square error optimized linear filter approximates the minimum ber solution numerical and simulation results indicate that for realistic awgn ds cdma systems with reasonably low signature cross correlations the linear minimum ber filter and the mmse filter exhibit approximately the same performance the linear minimum ber receiver is superior however when either the signature cross correlation is high or the background noise is non gaussian

trellis coded direct sequence spread spectrum communications this paper considers the application of trellis coding techniques to direct sequence spread spectrum multiple access ds ssma communication the unique feature of the trellis codes considered is that they are constructed over the set of possible signature sequences rather than over some standard 2 d signal constellation the resulting codes have a small number of signals per dimension we present several examples of these trellis codes and suggest possible methods of implementation we also present a detailed error analysis for this system which employs techniques developed by lehnert and pursley 1987 1989 to accurately model the multiple access interference we generate numerical results for several examples and conclude that the proposed trellis coded systems yield significant performance improvements over binary antipodal ds ssma systems in addition the new trellis codes perform better than standard error control techniques with the same complexity and code rate analytic results are verified with simulations

em based joint data detection and channel estimation of ds cdma signals we present two efficient iterative receiver structures of tractable complexity for joint multiuser detection and multichannel estimation jde of direct sequence code division multiple access signals the schemes result from an application of the expectation maximization em and the space alternating generalized expectation maximization sage algorithms respectively the em jde receiver updates the data bit sequences in parallel while the sage jde receiver reestimates them successively the channel parameters are updated in parallel in both schemes the em algorithm provides a set of free parameters called weight coefficients which can be selected to optimize its performance two optimality criteria are defined and analytical expressions for the corresponding optimized weight coefficients are given monte carlo simulations of a synchronous scenario show that the proposed jde receivers have excellent multiuser efficiency and are robust against errors in the estimation of the channel parameters moreover very short training sequences are required for the jde schemes to converge simulation results further demonstrate that the sage jde receiver exhibits a better performance when the users bit sequences are updated in the order of increasing signal strength i e the bit sequence of the user with the weakest signal strength is updated first at each stage

analysis of mean field annealing in substactive interference cancellation in this contribution we derive the cost function corresponding to the linear complexity subtractive interference cancellation with tangent hyperbolic tentative decisions we use the cost function to analyse the fix points of solving the subtractive interference cancellation equations the analysis show that we can control the slope of the tangent hyperbolic functions so that the corresponding cost function is convex we also show that increasing the slope can make the cost non convex going from the convex regime into the non convex regime we prove that the bifurcation of the fix points for non singular signal correlation matrices consist of the fix point of interest together with a saddle node bifurcation this proves that tracking the solution from low slopes with a convex cost gradually increasing to higher slopes with non convex cost can bring us to the best solution being very close to the optimal determined by enumeration this tracking is the idea behind annealing we show monte carlo studies with a substantial signal to noise ratio gain compared to not using annealing we also show how annealing can be used to increase capacity at a given target bit error rate in fact this capacity gain is the same obtained by improved parallel interference cancellation making us believe that the latter includes a mechanism to avoid local minima similar to annealing

computing binary combinatorial gray codes via exhaustive search with sat solvers the term binary combinatorial gray code refers to a list of binary words such that the hamming distance between two neighboring words is one and the list satisfies some additional properties that are of interest to a particular application e g circuit testing data compression and computational biology new distance preserving and circuit codes are presented along with a complete list of equivalence classes of the coil in the box codes for codeword length with respect to symmetry transformations of hypercubes a gray ordered code composed of all necklaces of the length is presented improving the known result with length

multiple access interference reduction for qs cdma systems with a novel class of polyphase sequences in this paper a new class of polyphase sequences for cdma systems and its generation method are suggested and the correlation properties of the sequence are investigated the performance of the sequence in quasi synchronous cdma qs cdma systems is investigated under a frequency selective time nonselective slow nakagami fading channel with additive white gaussian noise awgn it is shown that the performance of the qs cdma systems using the suggested sequence is independent of the number of users and is much better than that using the pn sequence

optimal equivalent preconditioners preconditioning strategies for elliptic partial differential operators and corresponding difference operators are compared by way of a model problem the technique considered here makes use of a selfadjoint positive definite operator b as the preconditioner for the nonselfadjoint convection diffusion operator a preconditioning by a s leading term plus a positive zeroth order term sigma i and optimizing over sigma is proposed the analysis of a model problem indicates that when a has large first order terms both the spectral and norm condition of b 1 a are minimized by sigma gg 0

a maximum likelihood approach to blind multiuser interference cancellation this paper addresses the problem of blind multiple access interference mai and intersymbol interference isi suppression in direct sequence code division multiple access ds cdma systems a novel approach to obtain the coefficients of a linear receiver using the maximum likelihood ml principle is proposed the method is blind because it only exploits the statistical features of the transmitted symbols and gaussian noise in the channel we demonstrate that an adequate linear constraint on these coefficients ensures that the desired user is extracted and the resulting linearly constrained maximum likelihood linear lcmll receiver can be efficiently implemented using the iterative space alternating generalized expectation maximization sage algorithm in order to take advantage of the diversity inherent to multipath channels we also introduce a blind rake multiuser receiver that proceeds in two steps first soft estimates of the desired user transmitted symbols are obtained from each propagation path using a bank of appropriate lcmll receivers afterwards these estimates are adequately combined to enhance the signal to interference and noise ratio sinr computer simulations show that the proposed blind algorithms for multiuser detection are near far resistant and attain convergence using small blocks of data thus outperforming existing linearly constrained minimum variance lcmv blind receivers

the structure of single track gray codes single track gray codes are cyclic gray codes with codewords of length n such that all the n tracks which correspond to the n distinct coordinates of the codewords are cyclic shifts of the first track we investigate the structure of such binary codes and show that there is no such code with 2 sup n codewords when n is a power of 2 this implies that the known codes with 2 sup n 2n codewords when n is a power of 2 are optimal this result is then generalized to codes over gf p where p is a prime a subclass of single track gray codes called single track gray codes with k spaced heads is also defined all known systematic constructions for single track gray codes result in codes from this subclass we investigate this class and show it has a strong connection with two classes of sequences the full order words and the full order self dual words we present an iterative construction for binary single track gray codes which are asymptotically optimal if an infinite family of asymptotically optimal seed codes exists this construction is based on an effective way to generate a large set of distinct necklaces and a merging method for cyclic gray codes based on necklaces representatives