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
Spectrum Estimation for Large Dimensional Covariance Matrices using Random Matrix Theory
Statistical Ensembles of Complex, Quaternion, and Real Matrices
Fluctuations of Eigenvalues and Second Order Poincare Inequalities
Spectral Measure of Large Random Hankel, Markov and Toeplitz Matrices
On Slow Fading Non-separable Correlation MIMO Systems
Untangling the SVD’s of Random Matrix Sample Paths
Capacity of the Gaussian Erasure Channel
Almost Sure Limit of the Smallest Eigenvalue of the Sample Correlation Matrix
Lecture Notes: Random Matrices and Communication Systems
Lecture 1: overview and history
Lecture 2: finite-size analysis: GOE
Lecture 3: finite-size analysis: Real Wishart Ensemble
Lecture 4: finite-size analysis: computation of marginals
Lecture 5: finite-size analysis: COE, CUE and “physical” interpretation
Lecture 6: capacity of multi-antenna channels
Lecture 7: capacity of multi-antenna channels (cont’d)
Lecture 8: rate-diversity tradeoff in multi-antenna channels
Lecture 9: asymptotic analysis: first approach
Lecture 10: asymptotic analysis of (Toeplitz) deterministic matrices
Lecture 11: probablity “review”
Lecture 12: probablity “review” (cont’d)
Lecture 13: asymptotic analysis: moments
Lecture 14: asymptotic analysis: moments (cont’d)
Lecture 15: asymptotic analysis: Stieltjes transform
Lecture 16: asymptotic analysis: Stieltjes transform (cont’d)
Lecture 17: largest eigenvalue of Wigner’s matrices
Lecture 18: capacity scaling of multi-antenna channels and ad hoc networks
Lecture 19: positive definite matrices and matrix inequalities
Lecture 20: matrix inequalities and information theory
Lecture 21: Gaussian random matrices and free probability
Lecture 22: free probability: sums of random matrices and R-transform
Lecture 23: free probability: additivity of the R-transform
Lecture 24: free probability: products of random matrices and S-transform
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