Holger Boche Libri

Future wireless networks will be integrated into every aspect of daily life. Therefore, the main objective of this book is to provide tools for better understanding the fundamental tradeoffs and interdependencies in wireless networks. The purpose of this book is to provide tools for a better understanding of the fundamental tradeo?s and interdependencies in wireless networks, with the goal of designing resource allocation strategies that exploit these int- dependencies to achieve signi?cant performance gains. Two facts prompted us to write it: First, future wireless applications will require a fundamental understanding of the design principles and control mechanisms in wireless networks. Second, the complexity of the network problems simply precludes the use of engineering common sense alone to identify good solutions, and so mathematics becomes the key avenue to cope with central technical problems in the design of wireless networks. In this book, two ?elds of mathematics play a central role: Perron-Frobenius theory for non-negative matrices and optimization theory. This book is a revised and expanded version of the research monograph "Resource Allocation in Wireless Networks" that was published as Lecture Notes in Computer Sciences (LNCS 4000) in 2006. Although the general structure has remained unchanged to a large extent, the book contains - merous additional results and more detailed discussion. For instance, there is a more extensive treatment of general nonnegative matrices and interf- ence functions that are described by an axiomatic model. Additional material on max-min fairness, proportional fairness, utility-based power control with QoS (quality of service) support and stochastic power control has been added. Inhaltsverzeichnis I Mathematical Framework.- On the Perron Root of Irreducible Matrices.- On the Positive Solution to a Linear System with Nonnegative Coefficients.- II Principles of Resource Allocation in Wireless Networks.- Network Model.- Resource Allocation Problem in Communications Networks.- III Algorithms.- Power Control Algorithms.- IV Appendices.- Some Concepts and Results from Matrix Analysis.- Some Concepts and Results from Convex Analysis.

Causality in system theory necessitates specific mathematical operations, such as the Riesz projection and spectral factorization mapping. The text illustrates this through the Wiener filter, which optimally estimates stationary stochastic sequences. While a non-causal filter's transfer function is straightforward, a causal filter requires additional operations to determine its optimal transfer function. This highlights the complexity involved in creating a causal estimation filter compared to its non-causal counterpart, emphasizing the importance of these mathematical tools in system analysis.

The book presents a mathematical framework for modeling and optimizing multiuser systems affected by interference. Central to this framework is the concept of general interference functions, which effectively characterize the interdependencies among users. This innovative approach aims to enhance understanding and performance in systems where multiple users interact and influence each other.

Focusing on the evolution of communication networks, this book explores the integration of computing and storage into traditional transport systems. It highlights innovative 'softwarized' solutions aimed at minimizing latency and enhancing resilience, while addressing the challenges of computing latency and energy consumption. The authors propose hybrid classical-quantum communication networks as a viable solution to these issues. By intertwining concepts from quantum networking, information theory, computing, and simulation, the book offers a comprehensive perspective on the future of quantum communication.

Das Buch bietet eine umfassende Anleitung zu Quantenkommunikationsnetzen und beleuchtet wichtige Paradigmenwechsel in der Kommunikationsnetztechnologie. Die Autoren analysieren, wie die Integration von Rechen- und Speicherfunktionen in bestehende Netzwerke die Effizienz steigern kann, indem Latenzzeiten verringert und die Ausfallsicherheit verbessert werden. Sie thematisieren die Herausforderungen, die mit der Rechenlatenz und dem Energieverbrauch verbunden sind, und präsentieren hybride klassisch-quantische Ansätze als Lösungsansatz. Zudem wird die Verbindung zwischen Quantennetzwerken, Quanteninformationstheorie und -simulationen untersucht.

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