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Randomly Spread CDMA: Asymptotics via Statistical Physics
, 2005
"... This paper studies randomly spread codedivision multiple access (CDMA) and multiuser detection in the largesystem 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 posterio ..."
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Cited by 98 (10 self)
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This paper studies randomly spread codedivision multiple access (CDMA) and multiuser detection in the largesystem 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 singleuser decoding. The generic detector can be particularized to the matched filter, decorrelator, linear 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 nonGaussian 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 singleuser Gaussian channel, whose signaltonoise ratio suffers a degradation due to the multipleaccess interference. The uncoded error performance (e.g., symbolerrorrate) 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 fixedpoint equations identified in this paper. Based on a general linear vector channel model, the results are also applicable to MIMO channels such as in multiantenna systems.
Game theory in communications: Motivation, explanation, and application to power control
 Proceedings to the IEEE Global Telecommunications Conference
, 2001
"... Abstract — Game theory is a set of tools developed to model interactions between agents with conflicting interests, and is thus wellsuited to address some problems in communications systems. In this paper we present some of the basic concepts of game theory and show why it is an appropriate tool fo ..."
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Cited by 74 (1 self)
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Abstract — Game theory is a set of tools developed to model interactions between agents with conflicting interests, and is thus wellsuited to address some problems in communications systems. In this paper we present some of the basic concepts of game theory and show why it is an appropriate tool for analyzing some communication problems and providing insights into how communication systems should be designed. We then provided a detailed example in which game theory is applied to the power control problem in a CDMAlike system. I.
Hopfield Neural Network Implementation of the Optimal CDMA Multiuser Detector
 IEEE Trans. Neural Networks
, 1996
"... We investigate the application of Hopfield Neural Networks (HNN) to the problem of multiuser detection in Spread Spectrum/CDMA communication systems. It is shown that the NPcomplete problem of minimizing the objective function of the Optimal Multiuser Detector (OMD) can be translated into minimizin ..."
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Cited by 31 (0 self)
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We investigate the application of Hopfield Neural Networks (HNN) to the problem of multiuser detection in Spread Spectrum/CDMA communication systems. It is shown that the NPcomplete problem of minimizing the objective function of the Optimal Multiuser Detector (OMD) can be translated into minimizing an HNN "energy" function, thus allowing to take advantage of the ability of HNNs to perform very fast gradient descent algorithms in analog hardware and produce in realtime suboptimal solutions to hard combinatorial optimization problems. The performance of the proposed HNN receiver is evaluated via computer simulations and compared to that of other suboptimal schemes as well as to that of the OMD for both the synchronous and the asynchronous CDMA transmission cases. It is shown that the HNN detector exhibits a number of attractive properties and that it provides in fact a powerful generalization of a wellknown and extensively studied suboptimal scheme, namely the Multistage Detector (MS...
Optimum Asymptotic Multiuser Efficiency of Randomly Spread CDMA
, 2000
"... This paper analyzes the high SNR performance of optimum multiuser detectors for synchronous directsequence spread spectrum with random spreading in an additive white Gaussian noise channel. Under very general conditions on the received powers, we show that the asymptotic efficiency of a Kuser syst ..."
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Cited by 19 (2 self)
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This paper analyzes the high SNR performance of optimum multiuser detectors for synchronous directsequence spread spectrum with random spreading in an additive white Gaussian noise channel. Under very general conditions on the received powers, we show that the asymptotic efficiency of a Kuser system with spreading gain N converges to 1 almost surely as K ! 1, and K=N is kept equal to an arbitrary nonzero constant. Therefore, the asymptotic behavior of the minimum biterrorrate is equivalent to that of a singleuser system. Keywords: Multiuser Detection, Asymptotic Efficiency, CDMA, Spread Spectrum, Optimum Multiuser Detection. David Tse is with the Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, dtse@eecs.berkeley.edu. Sergio Verd'u is with the Department of Electrical Engineering, Princeton University, verdu@princeton.edu 2 I Introduction This paper is concerned with the analysis of the capabilities of optimum multiuser detection...
Optimum multiuser detection is tractable for synchronous CDMA systems using msequences
 IEEE Commun. Lett
, 1998
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Probabilistic Analysis of the Semidefinite Relaxation Detector in Digital Communications
, 2008
"... We consider the problem of detecting a vector of symbols that is being transmitted over a fading multiple–input multiple–output (MIMO) channel, where each symbol is an ..."
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Cited by 12 (4 self)
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We consider the problem of detecting a vector of symbols that is being transmitted over a fading multiple–input multiple–output (MIMO) channel, where each symbol is an
Estimating Random Variables from Random Sparse Observations
, 2007
"... Let X1,..., Xn be a collection of iid discrete random variables, and Y1,..., Ym a set of noisy observations of such variables. Assume each observation Ya to be a random function of some a random subset of the Xi’s, and consider the conditional distribution of Xi given the observations, namely µi(xi) ..."
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Cited by 10 (2 self)
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Let X1,..., Xn be a collection of iid discrete random variables, and Y1,..., Ym a set of noisy observations of such variables. Assume each observation Ya to be a random function of some a random subset of the Xi’s, and consider the conditional distribution of Xi given the observations, namely µi(xi) ≡ P{Xi = xiY} (a posteriori probability). We establish a general decoupling principle among the Xi’s, as well as a relation between the distribution of µi, and the fixed points of the associated density evolution operator. These results hold asymptotically in the large system limit, provided the average number of variables an observation depends on is bounded. We discuss the relevance of our result to a number of applications, ranging from sparse graph codes, to multiuser detection, to group testing. 1
Low complexity optimal joint detection for oversaturated multiple access communications
 IEEE Trans. Signal Processing
, 1997
"... Abstract—Optimal joint detection for interfering (nonorthogonal) users in a multiple access communication system has, in general, a computational complexity that is exponential in the number of users. For this reason, optimal joint detection has been thought to be impractical for large numbers of us ..."
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Cited by 8 (1 self)
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Abstract—Optimal joint detection for interfering (nonorthogonal) users in a multiple access communication system has, in general, a computational complexity that is exponential in the number of users. For this reason, optimal joint detection has been thought to be impractical for large numbers of users. A number of suboptimal lowcomplexity joint detectors have been proposed for direct sequence spread spectrum user waveforms that have properties suitable for mobile cellular and other systems. There are, however, other systems, such as satellite systems, for which other waveforms may be considered. This paper shows that there are user signature set selections that enable optimal joint detection that is extremely low in complexity. When a hierarchical crosscorrelation structure is imposed on the user waveforms, optimal detection can be achieved with a treestructured receiver having complexity that is, in typical cases, a loworderpolynomial in the number of users. This is a huge savings over the exponential complexity needed for the optimal detection of general signals. Work in recent literature has shown that a hierarchically structured signal set can achieve oversaturation (more users than dimensions) with no growth in required signaltonoise ratio. The proposed tree detector achieves lowcomplexity optimal joint detection even in this oversaturated case. I.
Polynomial Complexity Optimal Detection of Certain Multiple Access Systems
, 2000
"... It is demonstrated that optimal multiple user detection in a linear multiple access system with identical crosscorrelations requires only O (K log K) operations instead of the worst case O # 2 K # . A simple optimal detection algorithm is given, which when generalized has complexity that is ..."
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Cited by 5 (3 self)
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It is demonstrated that optimal multiple user detection in a linear multiple access system with identical crosscorrelations requires only O (K log K) operations instead of the worst case O # 2 K # . A simple optimal detection algorithm is given, which when generalized has complexity that is exponential not in the number of users, but in the number of unique crosscorrelation values. 1. Introduction It is well known that the problem of optimal detection of linear multiple access systems is NPcomplete [1], i.e., in general we require a number of operations that increases exponentially with the number of users in order to find the data vector which maximizes the likelihood function. In very special cases however, optimal detection may be much simpler. For example, a system employing orthogonal signals for each of K users requires only O (K), since optimal detection is achieved by detecting each user individually and independently. If the crosscorrelations between the signal...