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48
Large System Performance of Linear Multiuser Receivers in Multipath Fading Channels
 IEEE Trans. Inform. Theory
, 2000
"... A linear multiuser receiver for a particular user in a codedivision multipleaccess (CDMA) network gains potential benefits from knowledge of the channels of all users in the system. In fast multipath fading environments we cannot assume that the channel estimates are perfect and the inevitable cha ..."
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Cited by 99 (6 self)
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A linear multiuser receiver for a particular user in a codedivision multipleaccess (CDMA) network gains potential benefits from knowledge of the channels of all users in the system. In fast multipath fading environments we cannot assume that the channel estimates are perfect and the inevitable channel estimation errors will limit this potential gain. In this paper, we study the impact of channel estimation errors on the performance of linear multiuser receivers, as well as the channel estimation problem itself. Of particular interest are the scalability properties of the channel and data estimation algorithms: what happens to the performance as the system bandwidth and the number of users (and hence channels to estimate) grows? Our main results involve asymptotic expressions for the signaltointerference ratio of linear multiuser receivers in the limit of large processing gain, with the number of users divided by the processing gain held constant. We employ a random model for the spreading sequences and the limiting signaltointerference ratio expressions are independent of the actual signature sequences, depending only on the system loading and the channel statistics: background noise power, energy profile of resolvable multipaths, and channel coherence time. The effect of channel uncertainty on the performance of multiuser receivers is succinctly captured by the notion of effective interference.
Resource Pooling and Effective Bandwidths in CDMA Networks with Multiuser Receivers and Spatial Diversity
 IEEE Trans. Inform. Theory
, 1999
"... Much of the performance analysis on multiuser receivers for directsequence codedivision multipleaccess (CDMA) systems is focused on worst case nearfar scenarios. The user capacity of powercontrolled networks with multiuser receivers are less wellunderstood. In [1], it was shown that under som ..."
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Cited by 58 (4 self)
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Much of the performance analysis on multiuser receivers for directsequence codedivision multipleaccess (CDMA) systems is focused on worst case nearfar scenarios. The user capacity of powercontrolled networks with multiuser receivers are less wellunderstood. In [1], it was shown that under some conditions, the user capacity of an uplink powercontrolled CDMA cell for several important linear receivers can be very simply characterized via a notion of effective bandwidth. In the present paper, we show that these results extend to the case of antenna arrays. We consider a CDMA system consisting of users transmitting to an antenna array with a multiuser receiver, and obtain the limiting signaltointerference (SIR) performance in a large system using random spreading sequences. Using this result, we show that the SIR requirements of all the users can be met if and only if the sum of the effective bandwidths of the users is less than the total number of degrees of freedom in the system. The effective bandwidth of a user depends only on its own requirement. Our results show that the total number of degrees of freedom of the whole system is the product of the spreading gain and the number of antennas. In the case when the fading distributions to the antennas are identical, we show that a curious phenomenon of "resource pooling" arises: the multiantenna system behaves like a system with only one antenna but with the processing gain the product of the processing gain of the original system and the number of antennas, and the received power of each user the sum of the received powers at the individual antennas.
Second order freeness and Fluctuations of Random Matrices : I. Gaussian and Wishart matrices and cyclic Fock spaces
, 2005
"... We extend the relation between random matrices and free probability theory from the level of expectations to the level of fluctuations. We introduce the concept of “second order freeness” and interpret the global fluctuations of Gaussian and Wishart random matrices by a general limit theorem for s ..."
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Cited by 53 (6 self)
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We extend the relation between random matrices and free probability theory from the level of expectations to the level of fluctuations. We introduce the concept of “second order freeness” and interpret the global fluctuations of Gaussian and Wishart random matrices by a general limit theorem for second order freeness. By introducing cyclic Fock space, we also give an operator algebraic model for the fluctuations of our random matrices in terms of the usual creation, annihilation, and preservation operators. We show that orthogonal families of Gaussian and Wishart random matrices are asymptotically free of second order.
THE HYPEROCTAHEDRAL QUANTUM GROUP
, 2007
"... Abstract. We consider the hypercube in R n, and show that its quantum symmetry group is a qdeformation of On at q = −1. Then we consider the graph formed by n segments, and show that its quantum symmetry group is free in some natural sense. ..."
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Cited by 38 (23 self)
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Abstract. We consider the hypercube in R n, and show that its quantum symmetry group is a qdeformation of On at q = −1. Then we consider the graph formed by n segments, and show that its quantum symmetry group is free in some natural sense.
Capacity of MIMO Channels: Asymptotic Evaluation Under Correlated Fading
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2003
"... This paper investigates the asymptotic uniform power allocation capacity of frequency nonselective multipleinput multipleoutput channels with fading correlation at either the transmitter or the receiver. We consider the asymptotic situation, where the number of inputs and outputs increase without ..."
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Cited by 35 (1 self)
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This paper investigates the asymptotic uniform power allocation capacity of frequency nonselective multipleinput multipleoutput channels with fading correlation at either the transmitter or the receiver. We consider the asymptotic situation, where the number of inputs and outputs increase without bound at the same rate. A simple uniparametric model for the fading correlation function is proposed and the asymptotic capacity per antenna is derived in closed form. Although the proposed correlation model is introduced only for mathematical convenience, it is shown that its shape is very close to an exponentially decaying correlation function. The asymptotic expression obtained provides a simple and yet useful way of relating the actual fading correlation to the asymptotic capacity per antenna from a purely analytical point of view. For example, the asymptotic expressions indicate that fading correlation is more harmful when arising at the side with less antennas. Moreover, fading correlation does not influence the rate of growth of the asymptotic capacity per receive antenna with high 0 .
Free Diffusions, Free Entropy And Free Fisher Information
"... . Motivated by the stochastic quantization approach to large N matrix models, we study solutions to free stochastic differential equations dX t = dS t \Gamma 1 2 f(X t )dt where S t is a free brownian motion. We show existence, uniqueness and Markov property of solutions. We define a relative free ..."
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Cited by 32 (1 self)
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. Motivated by the stochastic quantization approach to large N matrix models, we study solutions to free stochastic differential equations dX t = dS t \Gamma 1 2 f(X t )dt where S t is a free brownian motion. We show existence, uniqueness and Markov property of solutions. We define a relative free entropy as well as a relative free Fisher information, and show that these quantities behave as in the classical case. Finally we show that, in contrast with classical diffusions, in general the asymptotic distribution of the free diffusion does not converge, as t ! 1, towards the master field (i.e. the Gibbs state). 1. Introduction The purpose of this paper is to start the study of diffusion equations where the driving noise is a free brownian motion. Reasons for considering such equations will be explained in the next sections of this introduction. 1.1 Gibbs states and diffusion theory. Let V be a C 2 function on R d , with Z = Z R d e \GammaV (x) dx ! 1: The probability measur...
Integration over quantum permutation groups
 J. Funct. Anal
"... Abstract. We find a combinatorial formula for the Haar measure of quantum permutation groups. This leads to a dynamic formula for laws of diagonal coefficients, explaining the Poisson/free Poisson convergence result for characters. ..."
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Cited by 32 (15 self)
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Abstract. We find a combinatorial formula for the Haar measure of quantum permutation groups. This leads to a dynamic formula for laws of diagonal coefficients, explaining the Poisson/free Poisson convergence result for characters.
First order asymptotics of matrix integrals; a rigorous approach towards the understanding of matrix models
, 2002
"... ..."
A ContextTheoretic Framework for Compositionality in Distributional Semantics
"... Formalizing “meaning as context ” mathematically leads to a new, algebraic theory of meaning, in which composition is bilinear and associative. These properties are shared by other methods that have been proposed in the literature, including the tensor product, vector addition, pointwise multiplicat ..."
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Cited by 26 (2 self)
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Formalizing “meaning as context ” mathematically leads to a new, algebraic theory of meaning, in which composition is bilinear and associative. These properties are shared by other methods that have been proposed in the literature, including the tensor product, vector addition, pointwise multiplication, and matrix multiplication. Entailment can be represented by a vector lattice ordering, inspired by a strengthened form of the distributional hypothesis, and a degree of entailment is defined in the form of a conditional probability. Approaches to the task of recognizing textual entailment, including the use of subsequence matching, lexical entailment probability, and latent Dirichlet allocation, can be described within our framework. 1.
Large deviations and stochastic calculus for large random matrices
, 2004
"... Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they attracted lots of interests, in particular due to a serie of math ..."
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Cited by 22 (1 self)
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Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they attracted lots of interests, in particular due to a serie of mathematical breakthroughs allowing for instance a better understanding of local properties of their spectrum, answering universality questions, connecting these issues with growth processes etc. In this survey, we shall discuss the problem of the large deviations of the empirical measure of Gaussian random matrices, and more generally of the trace of words of independent Gaussian random matrices. We shall describe how such issues are motivated either in physics/combinatorics by the study of the socalled matrix models or in free probability by the definition of a noncommutative entropy. We shall show how classical large deviations techniques can be used in this context. These lecture notes are supposed to be accessible to non probabilists and non freeprobabilists.