Random Matrices in Communications and Signal Processing (RM-CSP)5.0 ECTS
(englische Bezeichnung: Random Matrices in Communications and Signal Processing)
(Prüfungsordnungsmodul: Random Matrices in Communications and Signal Processing)

Lehrveranstaltungen:

• • Random Matrices in Communications and Signal Processing
    (Vorlesung, 2 SWS, Ralf Müller, Di, 10:15 - 11:45, 01.021; Mi, 08:15 - 09:45, 01.021)
  • Tutorial for Random Matrices in Communications and Signal Processing
    (Übung, 2 SWS, Zeit und Raum n.V.)

Empfohlene Voraussetzungen:

Recommended: Good skills in linear algebra, probability theory and complex analysis

Inhalt:

Dual antenna arrays, compressive sensing, Wishart distribution, factor iid model, Kronecker model, convergence of random variables, semi-circle law, quarter circle law, full circle law, Haar distribution, Marchenko-Pastur distribution, Stieltjes transform, Girko’s law, unitary invariance, freeness, free convolution, R-transform, free central limit theorem, free Poisson limit theorem, subordination, S-transform, R-diagonal random matrices, R-diagonal free convolution, Haagerup-Larsen law, operator-valued freeness, linearization of noncommutative polynomials, free Fourier transform, self-averaging properties, microscopic vs. macroscopic random variables, quenched random variable, a statistical physics point of view of digital systems, spin glasses, frozen disorder, replica method, replica continuity, replica symmetry, replica symmetry breaking, approximate message passing, classification of np-complete problems

Lernziele und Kompetenzen:

The students find the limiting eigenvalue distributions of various types of random matrices.
The students explain Stieltjes, R- and S-transforms.
The students explain the limits of various types of fading channels.
The students design coding and decoding methods for a given type of multiuser channel.
The students perform additive and multiplicative free convolution.
The students calculate the asymptotic eigenvalues distributions of given random matrix ensembles.
The students construct random matrix ensembles with a given eigenvalue distribution. The students linearize matrix polynomials.

The students derive the Boltzmann distribution.
The students utilize saddle point integration.
The students perform replica calculations.
The students explain the meaning of replica symmetry breaking.

The students collaborate on solving exercise problems.

Literatur:

• Mingo, J., Speicher, R.: Free Probability and Random Matrices, Springer, 2017

• Couillet, R., Debbah, M.: Random Matrix Methods for Wireless Communications, Cambridge Univ. Press, Cambridge, 2011.

• Mezard, M., Montanari, A.: Information, Physics, and Computation, Oxford Graduate Texts, 2009.
  

Verwendbarkeit des Moduls / Einpassung in den Musterstudienplan:

1. Informations- und Kommunikationstechnik (Master of Science)
   (Po-Vers. 2016s | TechFak | Informations- und Kommunikationstechnik (Master of Science) | Gesamtkonto | Wahlbereiche, Praktika, Seminar, Masterarbeit | Wahlmodule aus dem Angebot von EEI und Informatik | Random Matrices in Communications and Signal Processing)

Studien-/Prüfungsleistungen:

Random Matrices in Communications and Signal Processing (Prüfungsnummer: 451971)

(englischer Titel: Technical Elective (5 ECTS))

Prüfungsleistung, mündliche Prüfung, Dauer (in Minuten): 30, benotet, 5.0 ECTS

Anteil an der Berechnung der Modulnote: 100.0 %

Prüfungssprache: Englisch

Erstablegung: WS 2022/2023, 1. Wdh.: SS 2023

1. Prüfer:

Ralf Müller