Blending theoretical results with practical applications, this book provides an introduction to random matrix theory and shows how it can be used to tackle a variety of problems in wireless communications. The Stieltjes transform method, free probability theory, combinatoric approaches, deterministic equivalents and spectral analysis methods for statistical inference are all covered from a unique engineering perspective. Detailed mathematical derivations are presented throughout, with thorough explanation of the key results and all fundamental lemmas required for the reader to derive similar calculus on their own. These core theoretical concepts are then applied to a wide range of real-world problems in signal processing and wireless communications, including performance analysis of CDMA, MIMO and multi-cell networks, as well as signal detection and estimation in cognitive radio networks. The rigorous yet intuitive style helps demonstrate to students and researchers alike how to choose the correct approach for obtaining mathematically accurate results.
Romain Couillet is an Assistant Professor at the Chair on System Sciences and the Energy Challenge at Supelec, France. Previously he was an Algorithm Development Engineer for ST-Ericsson and he received his Ph.D. from Supelec in 2010. Merouane Debbah is a Professor at Supelec, where he holds the Alcatel-Lucent Chair on Flexible Radio. He is the recipient of several awards, including the 2007 General Symposium IEEE Globecom best paper award and the Wi-Opt 2009 best paper award.
1. Introduction; Part I. Theoretical Aspects: 2. Random matrices; 3. The Stieltjes transform method; 4. Free probability theory; 5. Combinatoric approaches; 6. Deterministic equivalents; 7. Spectrum analysis; 8. Eigen-inference; 9. Extreme eigenvalues; 10. Summary and partial conclusions; Part II. Applications to Wireless Communications: 11. Introduction to applications in telecommunications; 12. System performance of CDMA technologies; 13. Performance of multiple antenna systems; 14. Rate performance in multiple access and broadcast channels; 15. Performance of multi-cellular and relay networks; 16. Detection; 17. Estimation; 18. System modeling; 19. Perspectives; 20. Conclusion.