On the empirical distribution of eigenvalues of a class of large dimensional random matrices
Jack W. Silverstein,Zhidong Bai +1 more
TLDR
In this article, a stronger result on the limiting distribution of the eigenvalues of random Hermitian matrices of the form A + XTX *, originally studied in Marcenko and Pastur, is presented.About:
This article is published in Journal of Multivariate Analysis.The article was published on 1995-08-01 and is currently open access. It has received 775 citations till now. The article focuses on the topics: Circular law & Hermitian matrix.read more
Citations
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Massive MIMO in the UL/DL of Cellular Networks: How Many Antennas Do We Need?
TL;DR: How many antennas per UT are needed to achieve η% of the ultimate performance limit with infinitely many antennas and how many more antennas are needed with MF and BF to achieve the performance of minimum mean-square error (MMSE) detection and regularized zero-forcing (RZF), respectively are derived.
Book
Random Matrix Theory and Wireless Communications
Antonio M. Tulino,Sergio Verdu +1 more
TL;DR: A tutorial on random matrices is provided which provides an overview of the theory and brings together in one source the most significant results recently obtained.
Journal ArticleDOI
Guaranteeing Secrecy using Artificial Noise
Satashu Goel,Rohit Negi +1 more
TL;DR: This paper considers the problem of secret communication between two nodes, over a fading wireless medium, in the presence of a passive eavesdropper, and assumes that the transmitter and its helpers (amplifying relays) have more antennas than the eavesdroppers.
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Spectral efficiency in the wideband regime
TL;DR: The fundamental bandwidth-power tradeoff of a general class of channels in the wideband regime characterized by low, but nonzero, spectral efficiency and energy per bit close to the minimum value required for reliable communication is found.
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Capacity scaling in MIMO wireless systems under correlated fading
TL;DR: Results show that empirical capacities converge to the limit capacity predicted from the asymptotic theory even at moderate n = 16, and the assumption of separable transmit/receive correlations via simulations based on a ray-tracing propagation model is analyzed.
References
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Distribution of eigenvalues for some sets of random matrices
V A Marčenko,Leonid Pastur +1 more
TL;DR: In this article, the authors studied the distribution of eigenvalues for two sets of random Hermitian matrices and one set of random unitary matrices in the energy spectra of disordered systems.
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Maximum Properties and Inequalities for the Eigenvalues of Completely Continuous Operators.
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Some limit theorems for the eigenvalues of a sample covariance matrix
TL;DR: The limit of the cumulative distribution function of the eigenvalues is determined by use of a method of moments as discussed by the authors, which is mainly combinatorial, and it is shown that the sum of eigen values, raised to k -th power, k = 1, 2, 3, 4, 5, 6, m is asymptotically normal.
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The Strong Limits of Random Matrix Spectra for Sample Matrices of Independent Elements
TL;DR: In this paper, the authors prove almost-sure convergence of the empirical measure of the normalized singular values of increasing rectangular submatrices of an infinite random matrix of independent elements, where the matrix elements are required to have uniformly bounded central $2 + εth moments, and the same means and variances within a row.
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Limiting spectral distribution for a class of random matrices
TL;DR: In this paper, the spectral distribution of A p = (1 n ) X p X p p T p ⊆ T p, where Xp = [Xij:i, j = 1, 2,…,n] tends to a non-random limit distribution as p → ∞, n → ǫ, but p n → y > 0, under the mild conditions that Xy's are i.i.d.s.