An Unexpected Journey: There and back again

EDIC – Year 2011-2012 – Spring Semester

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The course starts Monday, February 20, 2012, at 1:15 PM in room INR 113.

Oral exam schedule (room INR 113):

Monday, June 25
10:00 AM : Ivan

Wednesday, June 27
9:00 AM : Chien-Yi
9:30 AM : Jingge
10:00 AM : Mitra
10:30 AM : Nicholas
11:00 AM : Sreenivas –>

Handwritten lecture notes from a former year
Typewritten lecture notes from this year
Week 2: Single antenna systems
Week 3: Multiple antenna systems: capacity
Week 4: Multiple antenna systems: outage probability
Week 5: Wishart random matrices: joint distribution of the entries
Week 6: Wishart random matrices: joint eigenvalue distribution
Week 7: Wishart random matrices: marginal eigenvalue distribution
Week 8: Toeplitz matrices and the Grenander-Szegö theorem
Week 9: Distributions without random variables
Week 10: Wigner’s theorem: moments method
Week 11: End of Wigner’s theorem – Largest eigenvalue
Week 12: Marchenko-Pastur’s theorem: Stieltjes transform method
Week 13: Capacity and diversity-multiplexing tradeoff
Week 14: End of diversity-multiplexing tradeoff

General
Course information leaflet
Overview:
My intention in this course is to first motivate the study of random matrices from applications in wireless communications, then go through the main results of the field, and come back to applications at the end.

There will be four graded homeworks (5% each), as well as an oral exam (80%).

Teacher	E-mail	Voice	Office	Office Hours
Olivier Lévêque, IC-LTHI	olivier.leveque#epfl.ch	021 693 81 12	INR 132	Friday 2-4 PM

Type	Day	Hour	Room
Lectures	Monday	1:15 PM – 3:00 PM	INR 113
Exercise Sessions	Monday	3:15 PM – 5:00 PM	INR 113

Date	Subject
Monday, February 20	1. Overview – Basics of information theory
Monday, February 27	2. Single antenna systems: various fading models
Monday, March 5	3. Multiple antenna systems: capacity
Monday, March 12	4. Multiple antenna systems: outage probability
Monday, March 19	5. Wishart random matrices: joint distribution of entries
Monday, March 26	6. Wishart random matrices: joint eigenvalue distribution
Monday, April 2	7. Wishart random matrices: marginal eigenvalue distribution
Monday, April 16	8. Toeplitz matrices: Grenander-Szego’s theorem
Monday, April 23	9. Distributions without random variables
Monday, April 30	10. Wigner’s theorem: moments method
Monday, May 7	11. End of Wigner’s theorem – Largest eigenvalue
Monday, May 14	12. Marchenko-Pastur’s theorem: Stieltjes transform method
Monday, May 21	13. Capacity and diversity-multiplexing tradeoff
Wednesday, May 30, 1:15-3:00 PM, INR 113	14. End of diversity-multiplexing tradeoff

Problem sets	Date	Due	Solutions
Homework 1	March 5	March 19	Solutions 1
Homework 2	March 26	April 5	Solutions 2
Homework 3	April 16	April 30	Solutions 3
Homework 4	May 14	May 28	Solutions 4
Oral Exam	June 25 and 27

E. Telatar, Capacity of Multi-antenna Gaussian Channels, European Transactions on Telecommunications, 1999.
L. Zheng, D. Tse, Diversity and Multiplexing: A Fundamental Tradeoff in Multiple Antenna Channels, IEEE Transactions on Information Theory, 2003.
E. Abbe, E. Telatar, L. Zheng, The Algebra of MIMO Channels, Allerton Conference, 2005.
J. Wishart, The Generalised Product Moment Distribution in Samples from a Normal Multivariate Popuplation, Biometrika, 1928.
A. Edelman, Eigenvalues and Condition Numbers of Random Matrices, PhD Thesis, MIT, 1989.
R. M. Gray, Toeplitz and Circulant Matrices: A Review, Now Publishers, 2006.
E. Wigner, Characteristic Vectors of Bordered Matrices with Infinite Dimensions, The Annals of Mathematics, 1955.
E. Wigner, Random Matrices in Physics, SIAM Review, 1967.
V. Marchenko, L. Pastur, Distribution of Eigenvalues for some Sets of Random Matrices, Math USSR – Sbornik, 1967.
Z.-D. Bai, Methodologies in Spectral Analysis of Large Dimenional Random Matrices, a Review, Statistica Sinica, 1999.
A. Tulino, S. Verdu, Random Matrix Theory and Wireless Communications, Now Publishers, 2004.
G. Anderson, A. Guionnet, O. Zeitouni, An Introduction to Random Matrices, Cambridge University Press, 2010.
T. Tao, Topics in Random Matrix Theory, Graduate Studies in Mathemtacis Nr. 123, AMS, 2012.
Z.-D. Bai, J. W. Silverstein, Spectral Analysis of Large Dimensional Random Matrices, 2nd ed., Springer Series in Statistics, 2009.