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44
A new approach for mutual information analysis of large dimensional multiantenna chennels
 4004, 2008. FOR CERTAIN STATISTICS OF GRAM RANDOM MATRICES 41
"... This paper adresses the behaviour of the mutual information of correlated MIMO Rayleigh channels when the numbers of transmit and receive antennas converge to + ∞ at the same rate. Using a new and simple approach based on PoincaréNash inequality and on an integration by parts formula, it is rigorou ..."
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Cited by 29 (7 self)
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This paper adresses the behaviour of the mutual information of correlated MIMO Rayleigh channels when the numbers of transmit and receive antennas converge to + ∞ at the same rate. Using a new and simple approach based on PoincaréNash inequality and on an integration by parts formula, it is rigorously established that the mutual information when properly centered and rescaled converges to a Gaussian random variable whose mean and variance are evaluated. These results confirm previous evaluations based on the powerful but non rigorous replica method. It is believed that the tools that are used in this paper are simple, robust, and of interest for the communications engineering community.
EnergyEfficient Precoding for MultipleAntenna Terminals
, 2011
"... The problem of energyefficient precoding is investigated when the terminals in the system are equipped with multiple antennas. Considering static and fastfading multipleinput multipleoutput (MIMO) channels, the energyefficiency is defined as the transmission rate to power ratio and shown to be ..."
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Cited by 27 (10 self)
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The problem of energyefficient precoding is investigated when the terminals in the system are equipped with multiple antennas. Considering static and fastfading multipleinput multipleoutput (MIMO) channels, the energyefficiency is defined as the transmission rate to power ratio and shown to be maximized at low transmit power. The most interesting case is the one of slow fading MIMO channels. For this type of channels, the optimal precoding scheme is generally not trivial. Furthermore, using all the available transmit power is not always optimal in the sense of energyefficiency [which, in this case, corresponds to the communicationtheoretic definition of the goodputtopower (GPR) ratio]. Finding the optimal precoding matrices is shown to be a new open problem and is solved in several special cases: 1. when there is only one receive antenna; 2. in the low or high signaltonoise ratio regime; 3. when uniform power allocation and the regime of large numbers of antennas are assumed. A complete numerical analysis is provided to illustrate the derived results and stated conjectures. In particular, the impact of the number of antennas on the energyefficiency is assessed and shown to be significant.
Power Allocation Games for MIMO Multiple Access Channels with Coordination
, 2009
"... A game theoretic approach is used to derive the optimal decentralized power allocation (PA) in fast fading multiple access channels where the transmitters and receiver are equipped with multiple antennas. The players (the mobile terminals) are free to choose their PA in order to maximize their indiv ..."
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Cited by 25 (18 self)
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A game theoretic approach is used to derive the optimal decentralized power allocation (PA) in fast fading multiple access channels where the transmitters and receiver are equipped with multiple antennas. The players (the mobile terminals) are free to choose their PA in order to maximize their individual transmission rates (in particular they can ignore some specified centralized policies). A simple coordination mechanism between users is introduced. The nature and influence of this mechanism is studied in detail. The coordination signal indicates to the users the order in which the receiver applies successive interference cancellation and the frequency at which this order is used. Two different games are investigated: the users can either adapt their temporal PA to their decoding rank at the receiver or optimize their spatial PA between their transmit antennas. For both games a thorough analysis of the existence, uniqueness and sumrate efficiency of the network Nash equilibrium is conducted. Analytical and simulation results are provided to assess the gap between the decentralized network performance and its equivalent virtual multiple input multiple output system, which is shown to be zero in some cases and relatively small in general.
From Spectrum Pooling to Space Pooling: Opportunistic Interference Alignment in MIMO Cognitive Networks
"... We describe a noncooperative interference alignment (IA) technique which allows an opportunistic multiple input multiple output (MIMO) link (secondary) to harmlessly coexist with another MIMO link (primary) in the same frequency band. Assuming perfect channel knowledge at the primary receiver and ..."
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Cited by 24 (8 self)
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We describe a noncooperative interference alignment (IA) technique which allows an opportunistic multiple input multiple output (MIMO) link (secondary) to harmlessly coexist with another MIMO link (primary) in the same frequency band. Assuming perfect channel knowledge at the primary receiver and transmitter, capacity is achieved by transmiting along the spatial directions (SD) associated with the singular values of its channel matrix using a waterfilling power allocation (PA) scheme. Often, power limitations lead the primary transmitter to leave some of its SD unused. Here, it is shown that the opportunistic link can transmit its own data if it is possible to align the interference produced on the primary link with such unused SDs. We provide both a processing scheme to perform IA and a PA scheme which maximizes the transmission rate of the opportunistic link. The asymptotes of the achievable transmission rates of the opportunistic link are obtained in the regime of large numbers of antennas. Using this result, it is shown that depending on the signaltonoise ratio and the number of transmit and receive antennas of the primary and opportunistic links, both systems can achieve transmission rates of the same order.
A Deterministic Equivalent for the Analysis of Correlated MIMO Multiple Access Channels
, 2011
"... This article provides novel deterministic equivalents for the Stieltjes transform and the Shannon transform of a class of large dimensional random matrices. These results are used to characterise the ergodic rate region of multiple antenna multiple access channels, when each pointtopoint propagati ..."
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Cited by 22 (8 self)
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This article provides novel deterministic equivalents for the Stieltjes transform and the Shannon transform of a class of large dimensional random matrices. These results are used to characterise the ergodic rate region of multiple antenna multiple access channels, when each pointtopoint propagation channel is modelled according to the Kronecker model. We specifically provide an approximation of all rates achieved within the ergodic rate region and we provide an approximation of the linear precoders that achieve the boundary of the rate region as well as an iterative waterfilling algorithm to obtain these precoders. An original feature of this work is that the proposed deterministic equivalents are proved valid even for strong correlation patterns at both communication sides. The above results are validated by Monte Carlo simulations.
On the capacity achieving covariance matrix for frequency selective MIMO channels using the asymptotic approach
 IEEE Trans. Inf. Theory
, 2011
"... Abstract—In this contribution, an algorithm for evaluating the capacityachieving input covariance matrices for frequency selective Rayleigh MIMO channels is proposed. In contrast with the flat fading Rayleigh case, no closedform expressions for the eigenvectors of the optimum input covariance matr ..."
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Cited by 11 (1 self)
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Abstract—In this contribution, an algorithm for evaluating the capacityachieving input covariance matrices for frequency selective Rayleigh MIMO channels is proposed. In contrast with the flat fading Rayleigh case, no closedform expressions for the eigenvectors of the optimum input covariance matrix are available. Classically, both the eigenvectors and eigenvalues are computed numerically and the corresponding optimization algorithms remain computationally very demanding. In this paper, it is proposed to optimize (w.r.t. the input covariance matrix) a large system approximation of the average mutual information derived by Moustakas and Simon. The validity of this asymptotic approximation is clarified thanks to Gaussian large random matrices methods. It is shown that the approximation is a strictly concave function of the input covariance matrix and that the average mutual information evaluated at the argmax of the approximation is equal to the capacity of the channel up to a O(1/t) term, where t is the number of transmit antennas. An algorithm based on an iterative waterfilling scheme is proposed to maximize the average mutual information approximation, and its convergence studied. Numerical simulation results show that, even for a moderate number of transmit and receive antennas, the new approach provides the same results as direct maximization approaches of the average mutual information. Index Terms—Ergodic capacity, frequency selective MIMO channels, large random matrices I.
A CLT for informationtheoretic statistics of noncentered Gram random matrices
, 2012
"... In this article, we study the fluctuations of the random variable: In(ρ) = 1 N logdet(ΣnΣ ∗ n +ρIN), (ρ> 0) where Σn = n−1/2D 1/2 n Xn ˜ D 1/2 n + An, as the dimensions of the matrices go to infinity at the same pace. Matrices Xn and An are respectively random and deterministic N ×n matrices; ma ..."
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Cited by 6 (2 self)
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In this article, we study the fluctuations of the random variable: In(ρ) = 1 N logdet(ΣnΣ ∗ n +ρIN), (ρ> 0) where Σn = n−1/2D 1/2 n Xn ˜ D 1/2 n + An, as the dimensions of the matrices go to infinity at the same pace. Matrices Xn and An are respectively random and deterministic N ×n matrices; matrices Dn and ˜ Dn are deterministic and diagonal, with respective dimensions N×N and n×n; matrixXn = (Xij)has centered, independent and identically distributed entries with unit variance, either real or complex. We prove that when centered and properly rescaled, the random variable In(ρ) satisfies a Central Limit Theorem and has a Gaussian limit. The variance of In(ρ) depends on the moment EX2 ij of the variables Xij and also on its fourth cumulant κ = EXij  4−2− EX2 ij 2. The main motivation comes from the field of wireless communications, where In(ρ) represents the mutual information of a multiple antenna radio channel. This article closely follows the companion article ”ACLT for Informationtheoretic statistics of Gram random matrices with a given variance profile”, Ann. Appl. Probab. (2008) by Hachem et al., however the study of the fluctuations associated to noncentered large random matrices raises specific issues, which are addressed here.
Joint beamforming and power control in coordinated multicell: Maxmin duality, effective network and large system transition
 IEEE Trans. Wireless Commun
, 2013
"... Abstract—This paper studies joint beamforming and power control in a coordinated multicell downlink system that serves multiple users per cell to maximize the minimum weighted signaltointerferenceplusnoise ratio. The optimal solution and distributed algorithm with geometrically fast convergence ..."
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Cited by 5 (1 self)
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Abstract—This paper studies joint beamforming and power control in a coordinated multicell downlink system that serves multiple users per cell to maximize the minimum weighted signaltointerferenceplusnoise ratio. The optimal solution and distributed algorithm with geometrically fast convergence rate are derived by employing the nonlinear PerronFrobenius theory and the multicell network duality. The iterative algorithm, though operating in a distributed manner, still requires instantaneous power update within the coordinated cluster through the backhaul. The backhaul information exchange and message passing may become prohibitive with increasing number of transmit antennas and increasing number of users. In order to derive asymptotically optimal solution, random matrix theory is leveraged to design a distributed algorithm that only requires statistical information. The advantage of our approach is that there is no instantaneous power update through backhaul. Moreover, by using nonlinear PerronFrobenius theory and random matrix theory, an effective primal network and an effective dual network are proposed to characterize and interpret the asymptotic solution. Index Terms—Power control, coordinated beamforming, maxmin duality, effective network, large system analysis, multicell network, nonlinear PerronFrobenius theory, random matrix theory. I.