Random Matrix Theory and Wireless Communications

By Antonia Maria Tulino, Sergio Verdú. Foundations and Trends in Communications and Information Theory, 2004

2,275 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2c1a96e25d567fe347574339ca2c22d920f8b9e5

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Citations in the corpus

Energy Efficiency in Wireless Networks via Fractional Programming Theory (2015, background): “However, in this case, additional mathematical tools like random matrix theory (RMT) [165, 47] and stochastic geometry (SG) [11, 175] are required to statistically characterize the network interference levels.”
Large System Analysis of Linear Precoding in Correlated MISO Broadcast Channels Under Limited Feedback (2009, methodology): “…per-user rate and the sum rate) is maximized for a regularization term α , α ⋆ ◦ , given by Proof: is the Stieltjes transform of the Mar˘cenko-Pastur law and reads [24] m p Substituting (68) into (23)-(27) and setting the derivative w.r.t. α to zero, a real positive solution is given by (67).”
A Review on Spectrum Sensing for Cognitive Radio: Challenges and Solutions (2010, background): “The joint PDF of the ordered eigenvalues of a Wishart random matrix has been known for many years [66].”
Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas (2010, background): “It can be shown that the vector φkjΦ ∗ l has exactly the same probability distribution as does any row vector of Φl [15], [16].”
Maximum-Minimum Eigenvalue Detection for Cognitive Radio (2007, background): “When there is no signal, R ( N s ) turns to R η ( N s ) , the sample covariance matrix of the noise deﬁned as, R η ( N s ) is a special Wishart random matrix [10].”
An Introduction to Matrix Concentration Inequalities (2015, positive): “See the book of Tulino and Verdú for more information [187].”
Mode Coupling and its Impact on Spatially Multiplexed Systems (2013, background): “Attempts have been made to exploit multiple modes to increase capacity in short-range direct-detection links [7–9], but have not yet become practical, in part, because they did not address the problem of MD.”
Concentration of measure and spectra of random matrices: Applications to correlation matrices, elliptical distributions and beyond (2009, background): “atrices Tp (p×p) and Ln (n×n), which can also be assumed to be random, as long as their spectral distributions converge to a limit. These matrices have been the subject of investigations already: see [47] Theorem 2.43, which refers to [9, 34] and [23] and the recent [41], which refers to [12] and to”
Multipair Full-Duplex Relaying With Massive Arrays and Linear Processing (2014, positive): “Thus, (cid:8) • Compute V ar w Tk g SR ,k : From (67) and (68), the variance of w Tk g SR ,k is given by where X is a K × K central Wishart matrix with N rx degrees of freedom and covariance matrix I K , and the last equality is obtained by using [30, Lemma 2.10].”
FAST COMMUNITY DETECTION BY SCORE (2012, background): “Note that the entries in the upper triangular of W are independently (but not identically) distributed as centered-Bernoulli; such W is known as a “Wigner”-type matrix [29].”
Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning (2018, background): “7 Several overviews of RMT are available [143, 41, 71, 142, 22, 42, 110, 24].”