error probability bounds and approximations for ds spread spectrum communication systems with mutiple tone or multiple access interference upper and lower bounds on the average probability of error of direct sequence ds spread spectrum communication systems operating in the presence of either multiple tone or multiple access interference are presented the bounds are quite tight and can be used without the restriction that the peak level of the interference be less than the desired signal level a simple method for evaluating approximations to the bounds for multiple access systems in which the peak interference does indeed exceed the desired signal level is presented as well the tightness of both the bounds and the approximations are illustrated with numerical results

on the minimum euclidean distance for a class of signal space codes the minimum euclidean distance for a class of constant envelope phase modulation codes is studied bandwidth and power efficient signals with continuous phase are considered the information carrying phase varies piecewise linearly and the slopes are cyclically changed for successive symbol time intervals yielding the so called multi h signals it has previously been shown that this class of signals contains bandwidth and power efficient signals when coherent maximum likelihood sequence detection is used bounds on the achievable euclidean distance for signals in the above class are given upper bounds are calculated as well as minimum distance results for specific multilevel multi h signals it is concluded that quaternary and octal muiti h schemes considerably outperform the binary schemes furthermore in the important small modulation index region 2 h codes gain the maximum 3 db larger gains are not available by increasing the number of h values

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

spatio temporal blind adaptive multiuser detection we propose blind multiuser detection schemes with antenna arrays which is based on signal subspace estimation they are a multichannel extension of the decorrelating and minimum mean square error detectors and therefore they share their immunity to near far effects the blind scheme may be seen as an extension of the results in of wang and poor see ieee trans inform theory vol 44 p 677 90 1998 however it is seen that compared with the latter results when spatial diversity is considered the proposed spatio temporal detectors offer with little attendant increase in computational complexity a better performance a blind adaptive implementation based on a new orthogonal past projection approximation subspace tracking algorithm which is shown to be efficient for subspace tracking is proposed also we develop a blind estimation of the spatial signature based on the orthogonality between noise and signal subspaces it is seen that the blind adaptive multiuser detection and blind spatio temporal signature estimation can he integrated jointly

holomorphic kernels and commuting operators necessary and sufficient conditions in terms of operator polynomials are obtained for an m tuple t tl t l of commuting bounded linear operators on a separable hilbert space x to extend to an m tuple s s1 sm of operators on some hilbert space x where each s is realized as a representation of the adjoint of a multiplication operator on the tensor product of a special type of functional hilbert spaces a1so necessary and sufficient conditions in terms of operator polynomials are obtained for t to have a commuting normal extension o introduction in this paper some results in 1 and 2 for a single bounded linear operator t on a separable hilbert space x are generalized to m commuting operators on x in 1 agler introduces a special class of functional hilbert spaces and describes conditions under which an operator t on x extends to m where m denotes the multiplication operator on x and m denotes the countable direct sum of m with itself special cases of spaces x of which the classical hardy space is the prototype are considered in 1 2 the relevant conditions for the kind of extension of t referred to above are expressed in terms of the positivity of certain operator polynomials involving t and t these conditions are closely related to the reproducing kernel associated with the space s in 2 necessary and sufficient conditions are also given for a contraction t to be subnormal these conditions are really the requirement that a certain sequence of polynomials in t and t be positive it is natural to seek generalizations of these results to m commuting operators t1 tm on x an appropriate model for this generalization is obtained by constructi ng a finite tensor product of spaces s and exploiting the well known fact that the reproducing kernel of such a tensor product is the product of the reproducing kernels of the illdividual spaces suitable modifications of the reproducing kernels which render them holomorphic on the unit polydisc can be used to describe analogous extension results for t t1 tm the question of t having a commuting normal extension n n1 nm turns out to have a direct link with the multi dimensional hausdorff moment problem from the theory of probability received by the editors march 21 1986 1980 mathematics subject classification primary 47a20 secondary 47b20 47b38

dirichlet type spaces on the unit ball and joint 2 isometries abstract we obtain a formula that relates the spherical moments of the multiplication tuple on a dirichlet type space to a complex moment problem in several variables this can be seen as the ball analogue of a formula originally invented by richter in 23 we capitalize on this formula to study dirichlet type spaces on the unit ball and joint 2 isometries

on the resolution of ordering ambiguities associated with the path integral representation of stochastic processes simple path integral approaches to multiplicative stochastic processes are severely hampered by an inherent ambiguity in the underlying lagrangian associated with operator ordering problems the author shows how given the fokker planck equation the ambiguity can be resolved direct consequences for noise induced transitions reaction diffusion models and polymer dynamics are briefly discussed

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

an error probability analysis of the optimum noncoherent multiuser detector for multipath and multiantenna diversity communications over rayleigh fading channels the optimum noncoherent multiuser detector is obtained for generalized diversity symbol synchronous communication systems that employ nonorthogonal multipulse modulation a unified approach is adopted to simultaneously address various forms of diversity such as time frequency multipath and or receiver amenna diversity upper and lower bounds on the average bit error probability of the optimum noncoherent detector are derived while these bounds are numerically computable they are too complicated to give insights about the relative influence of system parameters on the essential behavior of the bit error rate to address this issue an asymptotic low noise analysis of the bit error probability is undertaken it is shown that the upper and lower bounds are indeed asymptotically convergent a formula for the asymptotic efficiency of the optimum noncoherent detector is thereby derived interestingly the asymptotic efficiency is found to be positive and independent of the signal strengths of the interfering users

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

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

signal separation using fractional sampling in multiuser communications described is a decorrelating filter that separates signals in a multiuser environment by relying on the relative delays to be sufficiently distinct the input signal is fractionally sampled to allow for the differentiation of the user delays both zero forcing and minimum mean square error versions of this filter are derived and probability of error expressions are given the algorithm successfully separates unknown digital signals by using the known received pulse shapes and the symbol rate a delay division multiple access ddma scheme based on this signal decorrelator is proposed that will allow signals to be transmitted without spreading the signal spectrum it is shown that in a noisy environment the signal to noise ratio penalty for ddma can be severe yet the bandwidth advantage is very pronounced compared to spread spectrum systems and is similar to other bandwidth efficient schemes the performance of a code division multiple access cdma system using this signal decorrelator is also given the decorrelator can be used as a blind multiuser detector or as a preprocessor to enhance the performance of a cdma system

a recursive linear detection algorithm for asynchronous cdma communication system a recursive linear detection algorithm is proposed for the detection of signals from an asynchronous direct sequence code division multiple access ds cdma communication system this algorithm works for short as well as long codes under some reasonable conditions this algorithm is proved to be stable and converges to the ideal decorrelating detector idd with a sufficiently large memory length the performance of the algorithm is analyzed in some detail upper and lower bounds for the bit error probabilities are developed it is demonstrated that the two bounds converge to the bit error probabilities of the idd as the large memory length increases simulation results show that the recursive detector proposed outperforms the truncated decorrelating detector with less memory and less computational complexity

linear multiuser receivers in random environments we study the signal to interference sir performance of linear multiuser receivers in random environments where signals from the users arrive in random directions such a random environment may arise in a ds cdma system with random signature sequences or in a system with antenna diversity where the randomness is due to channel fading assuming that such random directions can be tracked by the receiver the resulting sir performance is a function of the directions and therefore also random we study the asymptotic distribution of this random performance in the regime where both the number of users k and the number of degrees of freedom n in the system are large but keeping their ratio fixed our results show that for both the decorrelator and the minimum mean square error mmse receiver the variance of the sir distribution decreases like 1 n and the sir distribution is asymptotically gaussian we compute closed form expressions for the asymptotic means and variances for both receivers simulation results are presented to verify the accuracy of the asymptotic results for finite sized systems

performance of multiuser detection for optical cdma ii asymptotic analysis for pt i see ibid vol 43 no 11 p 2803 2811 1995 this paper presents characterizations of optimum multiuser detection in intensity modulation direct detection cdma channels based on asymptotic analysis of simple bounds on optimum performance technical difficulties in applying large deviation techniques to the evaluation of asymptotic multiuser efficiencies are rigorously addressed these same difficulties also lead to the derivation of conditions under which the linear multiuser detection achieves known interference hence optimum performance asymptotic analysis of the conventional correlation receiver including derivation of the optimal decision threshold for on off signaling formats is also presented

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

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

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

narrow band interference suppression in multiuser cdma systems this paper handles the simultaneous suppression of narrow band and multiaccess interference in code division multiple access cdma direct sequence spread spectrum dsss systems the basic structure we refer to is reminiscent of the decorrelating detector but here the design strategy relies on the concept of combating jointly the two interference sources precisely a decision as to the bit transmitted by each user is made based on the projection of the observables onto the orthogonal complement to the subspace spanned by the other users signatures and the narrow band interference we focus on several different implementations of such a strategy assuming a different degree of prior knowledge as to the narrow band interference an important side result of the proposed approach is that in general complete suppression of data like interference may be achieved through periodically time varying processing an adaptive version of such a receiver is also presented wherein the projection direction is estimated based on suitable estimates of the covariance properties of the observables the value of this method is also assessed by studying the rate of convergence of the estimated direction to the true projection direction

interference modeling in a direct sequence spread spectrum packet radio network a technique for characterizing multiuser interference and background noise in a direct sequence spread spectrum network is introduced and packet error probabilities are calculated the multiuser interference over a packet in the network is modeled as a compound gaussian multivariate random variable for moderate to large values of the processing gain the conditional variance is dependent on the number of users and their interference powers the method works for any interference with statistics of the block interference having a spherically symmetric distribution the best performance results in terms of the expected total interference power are obtained for the case of a large number of interferers with comparable interference powers as the number of interferers approaches infinity the performance is the same as that for gaussian noise for a small number of interferers the block error probability curve is broader than that for gaussian noise for small values of snr the probability of error is smaller than that corresponding to gaussian noise and for large values of snr it is larger modifications to the basic direct sequence scheme that improve performance in the case of one strong interferer are suggested

analysis of quasi ml multiuser detection of ds cdma systems in asynchronous channels we consider the quasi maximum likelihood quasi ml detectors of the reverse link system that uses antenna arrays in asynchronous channels when the channel vector is time invariant and time varying a channel vector estimation method based on eigendecomposition for time invariant channels and its adaptive version suitable for the time varying channels are also proposed it is shown that the proposed quasi ml detector can be regarded as a beamformer followed by a decorrelating filter and that the proposed system performs better than the conventional decorrelator scheme it is also observed that the performance gain of the proposed scheme over the conventional decorrelator system increases as the numbers of active users and antenna arrays increase

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

on optimum asymptotic multiuser efficiency of randomly spread cdma we extend the result by tse and verdu on the optimum asymptotic multiuser efficiency of randomly spread code division multiple access cdma with binary phase shift keying input random gaussian and random binary antipodal spreading are considered we obtain the optimum asymptotic multiuser efficiency of a k user system with spreading gain n when k and n rightarrow infty and the loading factor k n grows logarithmically with k under some conditions it is shown that the optimum detector in a gaussian randomly spread cdma system has a performance close to the single user system at high signal to noise ratio when k and n rightarrow infty and the loading factor k n is kept less than log 3 k 2 random binary antipodal matrices are also studied and a lower bound for the optimum asymptotic multiuser efficiency is obtained furthermore we investigate the connection between detecting matrices in the coin weighing problem and optimum asymptotic multiuser efficiency we obtain a condition such that for any binary input an n times k random matrix whose entries are chosen randomly from a finite set is a detecting matrix as k and n rightarrow infty

non equilibrium scaling in the schlogl model from the reaction diffusion master equation formulation of the schlogl model the authors develop a comprehensive description of the non equilibrium dynamics using the poisson transformation and the dynamical renormalisation group they firstly show how the equilibrium limit is recovered and secondly describe the low frequency low momenta scaling behaviour of the concentration fluctuations the approach extends simplifies or corrects previous studies and is easily generalised to treat more complicated systems

capacity of a band limited cdma mmse receiver based system when combined with trellis or convolutional coding this paper examines the achievable capacity of a direct sequence spread spectrum multiple access system based on an adaptive minimum mean square error mmse single user receiver over a gaussian channel the effect of using both trellis and convolutional codes of varying rates and complexity is investigated in relation to the effect on the maximum number of users and the achievable bit error rate for a given number of users a system based on a matched filter receiver is presented for the purposes of comparison it has been found that over the band limited channel considered the use of convolutional coding reduces the total system capacity for the high efficiency mmse receiver while still providing a coding gain for a small numbers of users the use of trellis codes however leads to increased system capacity

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

a family of likelihood ascent search multiuser detectors an upper bound of bit error rate and a lower bound of asymptotic multiuser efficiency in this paper the bit error performance of a family of likelihood ascent search las multiuser detectors is analyzed an upper bound on the ber of any las detector is obtained by bounding the fixed point region with the worst initial detector the concept of indecomposable errors developed by verdu is applied to tighten the upper bound in a special instance the upper bound is reduced to that for all the local maximum likelihood detectors the upper bound is comparable with that of the optimum detector obtained by verdu a lower bound on the asymptotic multiuser efficiency ame is then obtained it is shown that there are nontrivial cdma channels such that a las detector can achieve unit ame regardless of user number the ame lower bound provides a means for further seeking a good set of spreading sequences and power distribution for spectral and power efficient cdma

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

moment problems for multi sequences of operators abstract we give an explicit solution to the scalar moment problem on semi algebraic compact subsets of r n and apply this result to the study of some operator multi sequences

realizable mimo decision feedback equalizers structure and design we present and discuss the structure and design of optimum multivariable decision feedback equalizers dfes the equalizers are derived under the constraint of realizability that is causal and stable filters and finite decision delay the design is based on a known dispersive discrete time multivariable channel model with infinite impulse response the additive noise is described by a multivariate arma model equations for obtaining minimum mean square error mmse and zero forcing dfes are derived under the assumption of correct past decisions the design of a realizable mmse dfe requires the solution of a linear system of equations in the model parameters no spectral factorization is required we derive novel necessary and sufficient conditions for the existence of zero forcing dfes and point out the significance of these conditions for the design of multiuser detectors an optimal mmse dfe will contain iir filters in general simulations indicate that the performance improvement obtained with an iir dfe is reduced more than for a suboptimal fir dfe when error propagation is taken into account since the use of iir feedback filters tends to worsen the error propagation

blind adaptive multiuser detection for ds ssma communications with generalized random spreading a new spreading scheme and an accompanying blind adaptive receiver structure are proposed for direct sequence spread spectrum multiple access communications in a slowly varying frequency selective fading channel each user s spreading sequence is given by the kronecker product of a long period pseudonoise pn sequence which is accurately modeled by a random sequence and a short length deterministic signature code this spreading scheme bridges the gap between pure pn spreading and pure short code spreading schemes it is shown that with this spreading scheme the channel response to the desired signal component is easily estimated without relying on the spectral decomposition of the signal correlation matrix with the estimate of the channel response the receiver suppresses interference based on the maximum signal to interference ratio criterion the blind adaptive receiver requires only coarse timing information and a priori knowledge of the desired user s pn sequence for adaptation numerical results show that the adaptive receiver significantly suppresses interference by successfully estimating the channel response and the interference statistics with a low computational complexity an extension to spatio temporal processing using an array antenna is also discussed

performance bounds for optimum multiuser ds cdma systems in this letter we estimate the bit error probability bep of optimum multiuser detection for synchronous and asynchronous code division multiple access cdma systems on gaussian and fading channels we first compute an upper bound and a lower bound on the bit error probability for a given spreading code then average the bounds over a few thousand sets of spreading codes these bounds are obtained from a partial distance spectrum on gaussian channels the upper bound converges to the lower bound at moderate to large signal to noise ratios however on fading channels the upper bound does not converge hence we present our results for the lower bound only the numerical results show that 1 the bep of a 31 user cdma system with binary random spreading codes of length 31 is only two to four times higher than the bep of the single user system 2 the number of users that can be accommodated in an asynchronous cdma system is larger than the processing gain and 3 optimum multiuser detection outperforms linear detection e g the decorrelating detector by about 2 8 to 5 7 db

linear multiuser detectors for incompletely known symmetric signals in cdma systems in this paper we consider a synchronous code division multiple access cdma system with a multiuser receiver all users are assumed to have symmetric signature sequences but the presence of a subset of the users is unknown to the receiver we first calculate the signal to interference ratio sir in this environment for the matched filter receiver the decorrelating receiver and the linear minimum mean square error mmse detector we then identify the user capacity for a single class system and the effective bandwidth for a multiple class system the result is compared to the case of random sequences and of optimum sequences for symmetric sequences the effective bandwidth cannot be expressed by a scalar as in because two constraints have to be satisfied simultaneously to satisfy the sir requirement we introduce a two dimensional 2 d vector notion of effective bandwidth with and without unknown users for both the decorrelator and the mmse detector the user capacity is 1 when all users are known to the receivers and is reduced to 1 n l when n users are unknown with l the processing gain the performance of these three linear detectors with and without unknown users is compared

near optimum tree search detection schemes for bit synchronous multiuser cdma systems over gaussian and two path rayleigh fading channels simple reduced tree search detection schemes of the breadth first type are applied to suboptimal joint multiuser detection in bit synchronous code division multiple access cdma systems over both gaussian and two path rayleigh fading channels it is pointed out that in contrast to the case of the optimal multiuser detector the choice of the receiver filter severely influences the performance of suboptimal multiuser detectors simulation results supported by analysis show that breadth first tree search algorithms using a decorrelating noise whitening receiver filter perform better than similar receivers which solely use a matched filter mf for virtually all nonsingular spreading code sets studied most of the code sets are randomly generated the m and t algorithm detectors based on decorrelating noise whitening filter wf outputs can achieve near optimum performance at a very low complexity compared to the optimal detector although the proposed detectors are more complex than some known suboptimum detectors furthermore the use of combining techniques is considered for a two path rayleigh fading channel and a semi synchronous cdma structure is proposed it is shown that if maximum ratio combining mrc is employed the decorrelating noise wf still exists the corresponding suboptimal combining detector with a decorrelating noise wf outperforms a similar noncombining detector

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

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

moment problems and subnormality abstract we investigate the connection between certain algebraic conditions on a subnormal tuple s and the support of the representing measure s for s

field theoretic treatment of an effective action for a model of catalyzed autoamplification reaction diffusion models can exhibit continuous phase transitions in behaviors and their dynamics at criticality often exhibit scalings with key parameters that can be characterized by exponents while models with only a single field that transitions between absorbing and nonabsorbing states are well characterized and typically fall in the directed percolation universality class the effects of coupling multiple fields remain poorly understood we recently introduced a model which has three fields one of which relaxes exponentially one of which displays critical behavior and one of which has purely diffusive dynamics but exerts an influence on the critical field tchernookov j chem phys 130 134906 2009 simulations suggested that this model is in a universality class distinct from other reaction diffusion systems studied previously although the three fields give rise to interesting physics they complicate analysis of the model with renormalization group methods here we show how to systematically simplify the action for this model such that analytical expressions for the exponents of this universality class can be obtained by standard means we expect the approach taken here to be of general applicability in reaction diffusion systems with coupled order parameters that display qualitatively different behaviors close to criticality

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

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

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

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

fluctuations in the limit cycle state and the problem of phase chaos abstract gaussian fluctuations and first order fluctuation corrections to the deterministic solution are investigated in the framework of the generalized ginzgurg landau type equation of motion exhibiting a hard mode transition leading to a homogeneous limit cycle state it is shown that the stationary distribution of the fluctuations around the limit cycle is not of the form of a ginzburg landau functional the nature of the further instability in the post bifurcational region resulting in the phase chaos in the deterministic problem is found to be qualitatively changed by the presence of noise

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

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 simple way to compute the minimum distance in multiuser cdma systems a simple method to compute the minimum distance d sub min in multiuser code division multiple access cdma systems based on the cholesky decomposition of the positive definite symmetric correlation matrix is proposed although finding d sub min is known to be np hard this decomposition allows the computation of the minimum distance and the asymptotic efficiency of optimum multiuser detection to be performed very efficiently in almost all cases of practical interest numerical results for synchronous cdma with binary random signature waveforms of length 31 are used to illustrate the method

achieving near optimum asymptotic efficiency and fading resistance over the time varying rayleigh faded cdma channel we study multiuser receiver design and analysis for synchronous code division multiple access cdma channels with time varying rayleigh fading starting from an error probability criterion we first derive a near optimum receiver for this channel that admits a detector estimator decomposition has certain asymptotic optimality properties and a complexity which is independent of the length of the observation interval the performance of this detector is analytically characterized and contrasted with that of the optimal multiuser detector for the time invariant or static cdma rayleigh fading channel when it is implemented over the time varying channel notable among our conclusions is the fact that unlike the static channel multiuser detector the time varying channel detector is able to withstand not only the estimated interference from the other system users but also the residual interference that cannot be estimated arising out of imperfect estimation of the interferer fading parameters using estimation error covariance information this detector shows flexibility in accommodating a wide range of interferer fading conditions

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

appearance of correlations and symmetry breaking in non equilibrium reaction diffusion systems using the reaction diffusion master equation of chemical kinetics the authors study fluctuations and correlation functions around non equilibrium steady states they demonstrate that the underlying lagrangian description in the poisson representation possesses in the equilibrium limit an exact symmetry which ensures that statistical mechanics is recovered and that the intrinsically non equilibrium long range correlations in these systems vanish an explicit form for the two time single particle correlation function including both the long range and short range contributions is constructed using mean field arguments

field theories for kinetic growth models field theories for kinetic growth models such as dla or the eden model are formulated using simple reaction diffusion master equations the approach based on poisson transform techniques specifies the stochastic fluctuations exactly the author studies the mean field approximations fluctuations and the renormalisation group

critical fluctuations around non equilibrium steady states scaling and renormalisation group concepts are used to derive phenomenological langevin equations for non equilibrium steady states for the schlogl model the authors unambiguously identify the critical langevin equation in 4 epsilon dimensions simply by requiring that the correct mean field limit be reproduced the approach is applicable to models for which only the mean field behaviour is well established

parallel group detection for synchronous cdma communication over frequency selective rayleigh fading channels a group detector jointly detects a group of users and a parallel group detection scheme is a bank of j independently operating group detectors one for each group of a j group partition of the k transmitting users of a code division multiple access cdma channel in this paper two group detectors are introduced for the frequency selective rayleigh fading fsrf cdma channel while the optimum multiuser detector has a time complexity per symbol tcs of o m sup k k for m ary signaling each of the two group detectors has a tcs of o m g g where g is the group size hence there are parallel group detection schemes based on each of the two group detectors that satisfy a wide range of complexity constraints that result from the choice of partition each of the two group detectors is minimax optimal in the corresponding conditional group near far resistance measure furthermore a succinct indicator of the average ber over high snr regions is defined via the asymptotic efficiency a lower bound and an exact formula for the asymptotic efficiency are derived for the first and second group detectors respectively the group detection approach for the fsrf cdma channel generalizes previous approaches to the complexity performance tradeoff problem it yields the optimum detector when the group size is k when the group size is equal to one the first group detector results in a new optimum linear detector and the second reduces to a recently proposed suboptimum linear detector all other nontrivial partitions yield new multiuser detectors whose performances are commensurate with their complexities

on the average near far resistance for mmse detection of direct sequence cdma signals with random spreading the performance of a near far resistant finite complexity minimum mean squared error mmse linear detector for demodulating direct sequence ds code division multiple access cdma signals is studied assuming that the users are assigned random signature sequences we obtain tight upper and lower bounds on the expected near far resistance of the mmse detector averaged over signature sequences and delays as a function of the processing gain and the number of users since the mmse detector is optimally near far resistant these bounds apply to any multiuser detector that uses the same observation interval and sampling rate the lower bound on near far resistance implies that even without power control linear multiuser detection provides near far resistant performance for a number of users that grows linearly with the processing gain

iterative multiuser receivers for cdma channels an em based approach maximum likelihood detection for the multiuser code division multiple access cdma channel is prohibitively complex this paper considers new iterative multiuser receivers based on the expectation maximization em algorithm and related more powerful space alternating algorithms the latter algorithms include the sage algorithm and a new missing parameter space alternating algorithm that alternately updates individual parameter components or treats them as probabilistic missing data application of these em based algorithms to the problem of discrete parameter estimation i e data detection in the gaussian multiple access channel leads to a variety of convergent receiver structures that incorporate soft decision feedback for interference cancellation and or sequential updating of iterative bit estimates convergence and performance analyses are based on well known properties of the em algorithm and on numerical simulation

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

a covariance shaping framework for linear multiuser detection a new class of linear multiuser receivers referred to as the covariance shaping multiuser csmu receiver is proposed for suppression of interference in multiuser wireless communication systems this class of receivers is based on the recently proposed covariance shaping least squares estimator and is designed to minimize the total variance of the weighted error between the receiver output and the observed signal subject to the constraint that the covariance of the noise component in the receiver output is proportional to a given covariance matrix so that we control the dynamic range and spectral shape of the output noise some of the well known linear multiuser receivers are shown to be special cases of the csmu receiver this allows us to interpret these receivers as the receivers that minimize the total error variance in the observations among all linear receivers with the same output noise covariance and to analyze their performance in a unified way we derive exact and approximate expressions for the probability of bit error as well as the asymptotic signal to interference noise ratio in the large system limit we also characterize the spectral efficiency versus energy per information bit of the csmu receiver in the wideband regime finally we consider a special case of the csmu receiver equivalent to a mismatched minimum mean squared error mmse receiver in which the channel signal to noise ratio snr is not known precisely using our general performance analysis results we characterize the performance of the mismatched mmse receiver we then treat the case in which the snr is known to lie in a given uncertainty range and develop a robust mismatched mmse receiver whose performance is very close to that of the mmse receiver over the entire uncertainty range

a near ideal noise whitening filter for an asynchronous time varying cdma system a near ideal noise whitening filter for a time varying code division multiple access cdma system is examined first the structure of the ideal noise whitening filter is determined the ideal noise whitening filter for a time varying cdma system is dependent on unknown future system parameters and is therefore impractical a near ideal realizable whitening filter is introduced as a solution the convergence of the factorization method for a time varying cdma system is considered the truncation of the number of taps of the ideal noise whitening filter is studied and a metric function based on the near ideal noise whitening filter for a tree search detection algorithm is formulated simulation results are obtained for five and ten user time varying cdma systems with binary random signature sequences of length 10 and a rectangular chip waveform the results show that the near ideal noise whitening filter can accurately approximate the ideal noise whitening filter at a low complexity level the performance degradation of a suboptimal tree search detector for a time varying asynchronous cdma system using a typical near ideal noise whitening filter is minimal compared to an identical system using the ideal noise whitening filter

smoluchowski and beyond a field theoretical study of coagulation fragmentation processes adopting simple field theoretical techniques the author demonstrates how the smoluchowski approach to reaction diffusion models can be systematically corrected focusing on coagulation fragmentation processes he identifies the upper critical dimension dc 2 below which finite mobility corrections are important and full universality lattice independence etc can be achieved trends seem by direct simulation of simple lattice models for d 2 are confirmed whilst problems of interpretation exist for d 2

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

scaling in reaction diffusion systems the authors study irreversible reaction diffusion models of the form px from k1 from mx to k2 to qx sx from k3 from nx m dc 2 n m 1 n 1 which they study for d dc using the renormalisation group in conjunction with then epsilon expansion and exact techniques for m 1 and any n the transition remains continuous they present epsilon expansions for the case n 3 by contrast for m 2 and any n the system shows a fluctuation induced first order transition

pole expansion determination of the pair correlation function of a simple fluid abstract an explicit expression for the pair correlation function is given in terms of an expansion in the poles of the structure factor s q in the complex q plane this is derived when the direct correlation function or structure factor is of known analytical form an illustrative example is given for a hard sphere yukawa fluid in the mean spherical approximation

performance analysis of an improved mmse multiuser receiver for mismatched delay channels motivated by the fact that time delays in a practical direct sequence code division multiple access ds cdma system can never be perfectly estimated an improved minimum mean squared error mmse based receiver is proposed and analyzed via the simple assumption of a probability distribution for the delay estimation errors the proposed receiver can achieve a performance superior to that of the conventional mmse cmmse receiver the performances of this improved receiver and the cmmse receiver are compared in terms of the mean squared error mse probability of error and asymptotic multiuser efficiency ame as the original definition of ame does not consider mismatched channels the behavior of three single user receivers bearing imperfect delay estimation is also investigated these single user receivers are employed to define a more appropriate ame finally an efficient update mechanism to accommodate dynamic channel statistics and thus practical implementation is proposed

multiuser ml sequence estimator for convolutionally coded asynchronous ds cdma systems the optimal multiuser sequence estimator is formulated for an asynchronous direct sequence code division multiple access ds cdma system where each user employs convolutional coding to improve its performance on a nondispersive additive white gaussian noise awgn channel it is shown that the decoder may be implemented efficiently using a viterbi algorithm which operates on a time varying trellis with a number of states which is exponential in the product of the number of users in the system and the constraint length of the codes used for the rate 1 2 code case 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 then upper and lower bounded the amcg parameter unifies the asymptotic coding gain parameter and the asymptotic multiuser efficiency parameter which are traditional figure of merit parameters for single user coded systems and multiuser uncoded systems respectively finally some simulations are presented to illustrate the performance of the maximum likelihood sequence estimator mlse at moderate and low bit error rates