Random Matrices and Communication Systems

Detailed Program: Random Matrices and Communication Systems

1. Matrix Analysis “Review” (2~3 weeks)

2. Finite-Size Analysis of Random Matrices (~3 weeks)

3. Applications to Communications (2~3 weeks)

3.a) Capacity of MIMO Systems

3.b) Diversity-Multiplexing Tradeoff

4. Asymptotic Analysis of Random Matrices (3~4 weeks)

4.a) Moments Method

4.b) Stieltjes Transform Method

5. Back to Applications in Communications (1-2 weeks)

6. Free Probability and CDMA systems (1 week)

Projects: Random Matrices and Communication Systems

List of papers

1. Joint Singular Value Distribution of Two Correlated Rectangular Gaussian Matrices and its Application
Related paper: Statistical Properties of EigenModes and Instantaneous Mutual Information in MIMO Time-Varying Rayleigh Channels
(project taken by Mine Alsan)

2. The Empirical Eigenvalue Distribution of a Gram Matrix: From Independence to Stationarity (project taken by Shirin Saeedi)

3. A New Approach for Capacity Analysis of Large Dimensional Multi-Antenna Channels (project taken by Rethnakaran Pulikkoonattu)

4. The Smallest Eigenvalue of a Large Dimensional Wishart Matrix
Related papers: Decoding by Linear Programming
Limit of the Smallest Eigenvalue of a Large Dimensional Sample Covariance Matrix
(project taken by Amin Karbasi)

5. On Certain Large Random Hermitian Jacobi Matrices with Applications to Wireless Communications (project taken by Mahdi Jafari Siavoshani)

6. Financial Applications of Random Matrix Theory: Old Laces and New Pieces
Related paper: Distribution of Eigenvalues for Some Sets of Random Matrices
(project taken by David Morton)

7. Bandlimited Field Reconstruction for Wireless Sensor Networks
Related paper: Reconstruction of Multidimensional Signals from Irregular Noisy Samples
(project taken by Patrick Denantes)

8. Random Vandermonde Matrices – Part I: Fundamental Results
Related paper: Random Vandermonde Matrices – Part II: Applications
(project taken by Ali Hormati)

9. Eigenvalues of Euclidean Random Matrices (project taken by Juraj Sarinay)

10. On the Concentration of Eigenvalues of Random Symmetric Matrices
(project taken by Mohammad Golbabaei)

Papers not chosen

Lecture Notes: Random Matrices and Communication Systems

Bibliography: Random Matrices and Communication Systems

Note that there is some overlap between the lists below
(which is normal, otherwise the present class would not exist 🙂
and also that the lists are by far incomplete!

Finite-size analysis of random matrices

Asymptotic analysis of random matrices

Free probability

Applications to wireless communications

Various Topics