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Ph.D. Level Courses

Random Matrix Theory with Applications

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Objective

This course provides a comprehensive introduction to random matrix theory with applications. The first part gives a theoretical background of large dimensional random matrix theory. The second part presents some applications to wireless communications and signal processing.

Instructor

Dr. <Unknown username: julvi06>, ISY/Communication Systems.

Registration

The course is open to students enrolled in a Ph.D. program at Linköping University/ISY. External participants upon request. If you have interest to participate, please register by sending an email to julia.vinogradova@liu.se, by September 8, 2015.

Prerequisites

Good knowledge of linear algebra, matrix analysis, and probability theory. General mathematical maturity.

Outline

The content is mainly based on the course material developed by Romain Couillet and based on the book Random matrix theory for wireless communications, Cambridge, 2011, by Romain Couillet (Centrale-Supélec) and Mérouane Debbah (Centrale-Supélec). I plan to cover most of chapters 2, 3, 6, 7, 9, 13, 14, 15, 16, 17.

Part I: Random matrix theory

  • Lecture 1: Introduction to random matrix theory and Stieltjes transform
    • From small to large dimensional random matrices
    • Historical overview
    • Marčenko-Pastur law
    • Stieltjes transform for advanced models
  • Lecture 2: Deterministic equivalents
    • Bai and Silverstein method
    • Marčenko-Pastur method
  • Lecture 3: Spectrum analysis
    • Absence of eigenvalues outside the support
    • Exact spectrum separation
    • Asymptotic spectrum analysis
  • Lecture 4: Extreme eigenvalues
    • Spiked models
    • Distribution of extreme eigenvalues

Part II: Applications

  • Lecture 5: Performance of point-to-point MIMO systems
    • Quasi-static MIMO fading channels
    • Time-varying Rayleigh channels
    • Correlated frequency flat fading channels
    • Rician flat fading channels
    • Frequency selective channels
  • Lecture 6: Performance of multi-user multi-cell systems
    • Multiple access and broadcast channels
    • Multi-cell networks
    • Multi-hop communications
  • Lecture 7: Detection
    • Cognitive radios and sensor networks
    • Neyman-Pearson criterion
    • Alternatives approaches
  • Lecture 8: Estimation
    • Directions of arrival
    • Blind multi-source localization

Literature

Main textbook:

Useful references:

Required reading

Students are expected to read chapters 1 and 2 of the main textbook on their own as a preparation for the course.

Schedule (tentative)

The lectures and homework sessions are scheduled on Wednesdays at 10:15 in Algoritmen (house B, entrance 29, ground floor), unless noted otherwise.

  • Wed, 2015.09.16, 10:15 - Session 1 - Lecture 1: Introduction to random matrix theory and Stieltjes transform
  • Wed, 2015.09.23, 10:15 - Session 2 - Lecture 2: Deterministic equivalents
  • Wed, 2015.09.30, 10:15 - Session 3 - Homework session 1
  • Wed, 2015.10.07, 10:15 - Session 4 - Lecture 3: Spectrum analysis
  • Wed, 2015.10.14, 10:15 - Session 5 - Lecture 4: Extreme eigenvalues
  • Wed, 2015.10.21, 10:15 - Session 6 - Homework session 2
  • Wed, 2015.10.28, 10:15 - Session 7 - Lecture 5: Performance of point-to-point MIMO systems
  • Wed, 2015.11.04, 10:15 - Session 8 - Lecture 6: Performance of multi-user multi-cell systems
  • Wed, 2015.11.11, 10:15 - Session 9 - Homework session 3
  • Wed, 2015.11.18, 10:15 - Session 10 - Lecture 7: Detection
  • Fri, 2015.12.04, 13:15 - Session 11 - Lecture 8: Estimation (Filtret, house B, entrance 29, ground floor )
  • Wed, 2015.12.09, 09:15 - Session 12 - Homework session 4 (Filtret, house B, entrance 29, ground floor)

Credits

Two versions of this course are offered. The first version gives 5 ECTS and is addressed to students who want to learn the general random matrix theory. Those students who want to also study the applications, need to choose the full version giving 10 ECTS.

Examination

5 ECTS version:

  • Active seminar participation in sessions 1 to 6.
  • Homework problems, to be solved individually and handed in at each meeting. Threshold for passing the course: no less than 75% solved correctly.
  • Present at least one problem per homework seminar on the board.
  • Oral exam, when necessary.

10 ECTS version:

  • Active seminar participation in all 12 sessions.
  • Homework problems, to be solved individually and handed in at each meeting. Threshold for passing the course: no less than 75% solved correctly.
  • Present at least one problem per homework seminar on the board.
  • Oral exam, when necessary.

Page responsible: Julia Vinogradova
Last updated: 2016 02 23   19:04