An Unexpected Journey: There and back again
EDIC – Year 2011-2012 – Spring Semester
- 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
- Course information leaflet
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 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.