This book provides a broad understanding of the fundamental tools and methods from information theory and mathematical programming, as well as specific applications in 6G and beyond system designs. The contents focus on not only both theories but also their intersection in 6G. Motivations are from the multitude of new developments which will arise once 6G systems integrate new communication networks with AIoT (Artificial Intelligence plus Internet of Things). Design issues such as the intermittent connectivity, low latency, federated learning, IoT security, etc., are covered. This monograph provides a thorough picture of new results from information and optimization theories, as well as how their dialogues work to solve aforementioned 6G design issues.

The modern world of ubiquitous communication devices has fueled recent research into the need to find technical solutions to address energy consumption concerns raised by various stakeholders. These include: The exponential increase of connected devices that wireless communications have been experiencing poses serious sustainable growth concerns. The rapid expansion of wireless networks causes environmental concerns. Economic concerns drive the development of novel energy-efficient ICT. This monograph focuses on energy-efficient wireless network design, including resource allocation, scheduling, precoding, relaying, and decoding. Starting from simple point-to-point (P2P) systems and then gradually moving towards more complex interference networks, the energy efficiency is defined and its properties characterized. The authors show how the energy efficiency is naturally defined by fractional functions, thus establishing that a key role in the modeling, analysis, and optimization of energy efficiency is played by fractional programming; a branch of optimization theory specifically concerned with the properties and optimization of fractional functions. The monograph introduces fractional programming theory, and illustrates how it can be used to formulate and handle energy efficiency optimization problems. It provides a comprehensive introduction to the theoretical and practical aspects of these problems and describes the solutions offered with this technique. It will be of use to all researchers and engineers working on modern communication systems.

Majorization Theory and Matrix-Monotone Functions in Wireless Communications, reviews the basic definitions of Majorization Theory and Matrix-Monotone Functions, describing their concepts clearly with many illustrative examples. In addition to this tutorial, new results are presented with respect to Schur-convex functions and regarding the properties of matrix-monotone functions. The approach taken by the authors provides a valuable overview of the basic techniques for readers who are new to the subject. They then proceed to show in separate chapters the cutting edge applications of the two basic theories in wireless communications. Majorization Theory and Matrix-Monotone Functions in Wireless Communications is an invaluable resource for students, researchers and practitioners involved in the state-of-the-art design of wireless communication systems.