Random determinants

Girko, V. L.

doi:10.1007/bf01095507

Cited by 4 publications

(5 citation statements)

References 28 publications

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“…This theorem is generalized by Girko [10] who derived a fixed-point equation for the Stieltjes transform of large Hermitian matrices H = WW H when W has independent entries wij with variance σ 2 ij /N such that the set˘σ 2 ij¯i ,j is uniformly upper-bounded. In the following, we will extensively use this result to derive the asymptotic MIMO capacity.…”

Section: XXmentioning

confidence: 99%

The Space Frontier: Physical Limits of Multiple Antenna Information Transfer

Couillet¹,

Wagner²,

Debbah³

et al. 2008

Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools

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In this paper, we study the capacity limits of dense multiantenna systems. We derive asymptotic capacity expressions for point-to-point and broadcast channels by applying recent tools from random matrix theory. In the case of broadcast channels, we focus on linear precoding techniques. We found that the asymptotic capacity depends only on the ratio between the size of the antenna array and the wavelength. This provides useful guidelines on the achievable limits of information transfer. In particular, it is shown that the total capacity grows unbounded if the transmitter has perfect knowledge on the channel, while the capacity saturates in the absence of channel knowledge at the transmitter. We provide numerical results supporting the theoretical derivations.

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Section: XXmentioning

confidence: 99%

The Space Frontier: Physical Limits of Multiple Antenna Information Transfer

Couillet¹,

Wagner²,

Debbah³

et al. 2008

Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools

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“…alors la mesure de comptage N n converge en probabilité vers la loi du demi-cercle [P1,Gi]. La réciproque est aussi vraie [Gi].…”

Section: Ensemble De Wignerunclassified

“…Certaines intégrales matricielles donnent des représentations assez utiles et efficaces des fonctions génératrices des caractéristiques numériques des graphes et des sous-variétés, ainsi que des quantités importantes de systèmes intégrables, etc. (voir par exemple les revues [Gi,GMW,KS,Me,GMW,P2,P4,TW,Vo] et les références qu'elles contiennent).…”

Section: Introductionunclassified

Matrices aléatoires: Statistique asymptotique des valeurs propres

Pastur

Lejay

2003

Lecture Notes in Mathematics

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Ce cours † est une brève introductionà la théorie de la distribution asymptotique des valeurs propres des matrices aléatoires symétriques réelles ou hermitiennes de grande taille. Cette théorie a connu récemment beaucoup d'évolutions motivées par diverses branches des mathématiques et de la physique. L'étude de quelques régimes asymptotiques mèneà des résultats età des techniques intéressants.Keywords: Matrice aléatoire, valeur propre, ensemble orthogonal gaussien, loi du demi-cercle Abstract: Ce cours † est une brève introductionà la théorie de la distribution asymptotique des valeurs propres des matrices aléatoires symétriques réelles ou hermitiennes de grande taille. Cette théorie a connu récemment beaucoup d'évolutions motivées par diverses branches des mathématiques et de la physique. L'étude de quelques régimes asymptotiques mèneà des résultats età des techniques intéressants.

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“…According to the random matrix theory [21,22,40], the ergodic Shannon transform of XX can be asymptotically approximated by a deterministic function that only depends on the secondorder statistics of X. Therefore, we only need the secondorder statistics of A ( , ), and…”

Section: Asymptotic Approximation Of the Ratementioning

confidence: 99%

“…To maximize the ergodic rate, inspired by [20,23,29], we find a deterministic approximation to the Shannon rate of the MIMO-OFDM system using the random matrix theory [21,40]. The methodology will be applied to the MIMO-OFDM system with tap correlations and intercarrier interference.…”

Section: Introductionmentioning

confidence: 99%

Downlink Linear Precoders Based on Statistical CSI for Multicell MIMO-OFDM

Baktash

Lin

Wang

et al. 2017

Wireless Communications and Mobile Computing

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With 5G communication systems on the horizon, efficient interference management in heterogeneous multicell networks is more vital than ever. This paper investigates the linear precoder design for downlink multicell multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems, where base stations (BSs) coordinate to reduce the interference across space and frequency. In order to minimize the overall feedback overhead in next-generation systems, we consider precoding schemes that require statistical channel state information (CSI) only. We apply the random matrix theory to approximate the ergodic weighted sum rate of the system with a closed form expression. After formulating the approximation for general channels, we reduce the results to a more compact form using the Kronecker channel model for which several multicarrier concepts such as frequency selectivity, channel tap correlations, and intercarrier interference (ICI) are rigorously represented. We find the local optimal solution for the maximization of the approximate rate using a gradient method that requires only the covariance structure of the MIMO-OFDM channels. Within this covariance structure are the channel tap correlations and ICI information, both of which are taken into consideration in the precoder design. Simulation results show that the rate approximation is very accurate even for very small MIMO-OFDM systems and the proposed method converges rapidly to a near-optimal solution that competes with networked MIMO and precoders based on instantaneous full CSI.

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Random determinants

Cited by 4 publications

References 28 publications

The Space Frontier: Physical Limits of Multiple Antenna Information Transfer

The Space Frontier: Physical Limits of Multiple Antenna Information Transfer

Matrices aléatoires: Statistique asymptotique des valeurs propres

Downlink Linear Precoders Based on Statistical CSI for Multicell MIMO-OFDM

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