Eigenvalue Distributions of Sums and Products of Large Random Matrices Via Incremental Matrix Expansions

Peacock, M.J.M.; Collings, Iain B.; Honig, Michael L.

doi:10.1109/tit.2008.920221

Cited by 42 publications

(14 citation statements)

References 27 publications

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“…Gaussian entries. In [7], Peacock et al extend the asymptotic result of [6] in the context of multi-user communications by considering a K-user MAC with channels H 1 , . .…”

Section: Introductionmentioning

confidence: 99%

A Deterministic Equivalent for the Analysis of Correlated MIMO Multiple Access Channels

Couillet

Debbah

Silverstein

2011

IEEE Trans. Inform. Theory

146

217

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In this article, novel deterministic equivalents for the Stieltjes transform and the Shannon transform of a class of large dimensional random matrices are provided. These results are used to characterise the ergodic rate region of multiple antenna multiple access channels, when each point-to-point propagation channel is modelled according to the Kronecker model. Specifically, an approximation of all rates achieved within the ergodic rate region is derived and an approximation of the linear precoders that achieve the boundary of the rate region as well as an iterative water-filling algorithm to obtain these precoders are provided. 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. Index TermsDeterministic equivalent, random matrix theory, ergodic capacity, MIMO, MAC, optimal precoder.

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“…Gaussian entries. In [7], Peacock et al extend the asymptotic result of [6] in the context of multi-user communications by considering a K-user MAC with channels H 1 , . .…”

Section: Introductionmentioning

confidence: 99%

A Deterministic Equivalent for the Analysis of Correlated MIMO Multiple Access Channels

Couillet

Debbah

Silverstein

2011

IEEE Trans. Inform. Theory

146

217

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show abstract

“…By Bai and Silverstein's Lemma [31]- [33], we have −→ 1 [33]. It follows from the Markov inequality and the Borel-Cantelli lemma [34]…”

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confidence: 99%

Large System Analysis of Linear Precoding in MISO Broadcast Channels with Confidential Messages

Geraci

Couillet

Yuan

et al. 2013

IEEE J. Select. Areas Commun.

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In this paper, we study the performance of regularized channel inversion (RCI) precoding in large MISO broadcast channels with confidential messages (BCC). We obtain a deterministic approximation for the achievable secrecy sum-rate which is almost surely exact as the number of transmit antennas M and the number of users K grow to infinity in a fixed ratio β = K/M . We derive the optimal regularization parameter ξ and the optimal network load β that maximize the per-antenna secrecy sum-rate. We then propose a linear precoder based on RCI and power reduction (RCI-PR) that significantly increases the high-SNR secrecy sumrate for 1 < β < 2. Our proposed precoder achieves a per-user secrecy rate which has the same high-SNR scaling factor as both the following upper bounds: (i) the rate of the optimum RCI precoder without secrecy requirements, and (ii) the secrecy capacity of a single-user system without interference. Furthermore, we obtain a deterministic approximation for the secrecy sum-rate achievable by RCI precoding in the presence of channel state information (CSI) error. We also analyze the performance of our proposed RCI-PR precoder with CSI error, and we determine how the error must scale with the SNR in order to maintain a given rate gap to the case with perfect CSI. Index TermsPhysical layer security, broadcast channel, random matrix theory, linear precoding, multi-user systems.

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“…The sums of pseudo-hermitian matrices were considered in [3]. The paper [12] is devoted to sums of the eigenvalues of random matrices. In the paper [6], non-selfadjoint operators in a Hilbert space are considered.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

Exponentials of Sums of Operators in a Banach Space

GİL’

2017

Mathematical Sciences and Applications E-Notes

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Eigenvalue Distributions of Sums and Products of Large Random Matrices Via Incremental Matrix Expansions

Cited by 42 publications

References 27 publications

A Deterministic Equivalent for the Analysis of Correlated MIMO Multiple Access Channels

A Deterministic Equivalent for the Analysis of Correlated MIMO Multiple Access Channels

Large System Analysis of Linear Precoding in MISO Broadcast Channels with Confidential Messages

Exponentials of Sums of Operators in a Banach Space

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