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Chapter 7 investigates the impact of ultra-dense networks on multi-user diversity. A denser network reduces the number of user equipment per small cell in a significant manner, and thus can significantly reduce – and potentially neglect – the gains of channel-dependent scheduling techniques. These performance gain degradations are theoretically analyzed in this chapter, and the performance of a proportional fair scheduler is compared to that of a round robin one.
Chapter 8, standing on the shoulders of all previous chapters, presents a new capacity scaling law for ultra-dense networks. Interestingly, the signal and the inter-cell interference powers become bounded in the ultra-dense regime. The former is due to the antenna height difference between the user equipment and the small cell base stations, and the latter is due to the finite user equipment density as well as the idle mode capability at the small cell base stations. This leads to a constant signal-to-interference-plus-noise ratio at the user equipment, and thus to an asymptotic capacity behaviour in such a regime. From this new capacity scaling law, it can be concluded that, for a given user equipment density, the network densification should not be abused indefinitely, and instead, it should be stopped at a certain level. Network densification beyond such a point is a waste of both invested money and energy consumption.
Chapter 4 analyzes in detail – from a theoretical perspective – the first practical caveat towards such linear growth of capacity in the ultra-dense regime, i.e. that of the impact of the transition of a large number of interfering links from non-line-of-sight to line-of-sight. Importantly, this chapter shows that the theoretical tools used until then to analyze traditional sparse or dense small cell networks, such as that presented in the previous chapter, do not directly apply to ultra-dense ones, and neither do their conclusions. In this chapter, we detail the path loss modelling upgrades necessary for a more realistic and accurate modelling of ultra-dense networks, present the subsequent and new theoretical derivations, and analyze the obtained results for the better understanding of the readers.
Discover the fundamental characteristics of ultra-dense networks with this comprehensive text. Featuring a consistent mathematical description of ultra-dense small cell networks while also covering real-world issues such as network deployment, operation and optimization, this book investigates performance metrics of coverage probability and area spectral efficiency (ASE) and addresses the aspects of ultra-dense networks that make them different from current networks. Insightful intuitions, which will assist decision-makers as they migrate their services, are explained and mathematically proven. The book presents the latest review of research outcomes on ultra-dense networks, based on both theoretical analyses and network simulations, includes over 200 sources from 3GPP, the Small Cell Forum, journals and conference proceedings, and covers all other related and prominent topics. This is an ideal reference text for professionals who are dealing with the development, deployment, operation and maintenance of ultra-dense small cell networks, as well as researchers and graduate students in communications.
How can machine learning help the design of future communication networks – and how can future networks meet the demands of emerging machine learning applications? Discover the interactions between two of the most transformative and impactful technologies of our age in this comprehensive book. First, learn how modern machine learning techniques, such as deep neural networks, can transform how we design and optimize future communication networks. Accessible introductions to concepts and tools are accompanied by numerous real-world examples, showing you how these techniques can be used to tackle longstanding problems. Next, explore the design of wireless networks as platforms for machine learning applications – an overview of modern machine learning techniques and communication protocols will help you to understand the challenges, while new methods and design approaches will be presented to handle wireless channel impairments such as noise and interference, to meet the demands of emerging machine learning applications at the wireless edge.
Compound renewal processes (CRPs) are among the most ubiquitous models arising in applications of probability. At the same time, they are a natural generalization of random walks, the most well-studied classical objects in probability theory. This monograph, written for researchers and graduate students, presents the general asymptotic theory and generalizes many well-known results concerning random walks. The book contains the key limit theorems for CRPs, functional limit theorems, integro-local limit theorems, large and moderately large deviation principles for CRPs in the state space and in the space of trajectories, including large deviation principles in boundary crossing problems for CRPs, with an explicit form of the rate functionals, and an extension of the invariance principle for CRPs to the domain of moderately large and small deviations. Applications establish the key limit laws for Markov additive processes, including limit theorems in the domains of normal and large deviations.
Jayakrishnan Nair, Indian Institute of Technology, Bombay,Adam Wierman, California Institute of Technology,Bert Zwart, Stichting Centrum voor Wiskunde en Informatica (CWI), Amsterdam
Jayakrishnan Nair, Indian Institute of Technology, Bombay,Adam Wierman, California Institute of Technology,Bert Zwart, Stichting Centrum voor Wiskunde en Informatica (CWI), Amsterdam
Jayakrishnan Nair, Indian Institute of Technology, Bombay,Adam Wierman, California Institute of Technology,Bert Zwart, Stichting Centrum voor Wiskunde en Informatica (CWI), Amsterdam
Jayakrishnan Nair, Indian Institute of Technology, Bombay,Adam Wierman, California Institute of Technology,Bert Zwart, Stichting Centrum voor Wiskunde en Informatica (CWI), Amsterdam
An introduction to the emergence of heavy-tailed distributions in the context of extremal processes.Max-stable distributions are introduced, and the extremal central limit theory is presented.Further, an example of the emergence of heavy tails in the extremes of random walks is presented.
Jayakrishnan Nair, Indian Institute of Technology, Bombay,Adam Wierman, California Institute of Technology,Bert Zwart, Stichting Centrum voor Wiskunde en Informatica (CWI), Amsterdam
An introduction to the class of heavy-tailed distributions, including formal definitions, basic properties, and examples of common distributions that are heavy-tailed.