Random matrix methods for wireless communications. (English) Zbl 1252.94001

Couillet, Romain; Debbah, Mérouane

Cambridge: Cambridge University Press (ISBN 978-1-107-01163-2/hbk; 978-1-139-14295-3/ebook). xxi, 539 p. (2011).

Publisher’s description: “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 real-world 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.”
The book contains 20 chapters, divided into Introduction (Chapter 1), Part I (Theoretical aspects, Chapters 2–10) and Part II (Applications to wireless communications, Chapters 11–20). The references contain more than 300 items. Finally, the book has a detailed index.
Features: This is the first book to explain random matrix theory from an engineering perspective, clearly divided into sections covering theory and applications, allowing the reader to develop a solid grounding in the mathematics before learning how to apply their knowledge to practical problems. It covers recently developed mathematical techniques, including deterministic equivalents and inference methods.

Reviewer: Ludwig Paditz (Dresden)

MSC:

94-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory
15B52	Random matrices (algebraic aspects)
46L54	Free probability and free operator algebras
60B20	Random matrices (probabilistic aspects)
94A05	Communication theory
94A12	Signal theory (characterization, reconstruction, filtering, etc.)
94A13	Detection theory in information and communication theory

Keywords:

random matrices; Stieltjes transform method; free probability theory; free moments and cumulants; spectrum analysis; deterministic equivalents; eigenvectors; eigenvalues; multiple antenna systems; multiple access; broadcast channels; channel modeling; CDMA; MIMO; wireless networks; signal detection