This chapter discusses the fundamentally different mental images of large-dimensional machine learning (versus its small-dimensional counterpart), through the examples of sample covariance matrices and kernel matrices, on both synthetic and real data. Random matrix theory is presented as a flexible and powerful tool to assess, understand, and improve classical machine learning methods in this modern large-dimensional setting.

This chapter exploits concentration-of-measure approach for real data modeling, via the recent advance of deep generative adversarial networks (GANs). This assessment theoretically supports the surprisingly good match between theory and practice observed on real-world data in previous chapters. Conclusion on the universality of large-dimensional machine learning is drawn at the end of the chapter.

Chapter 10, in contrast to all the previous chapters that focused on the performance of the downlink, analyzes the performance of the uplink of an ultra-dense network. Importantly, this chapter shows that the phenomena presented in – and the conclusions derived from – all the previous chapters also apply to the uplink, despite its different features, e.g. uplink transmit power control, inter-cell interference source distribution. System-level simulations are used in this chapter to conduct the study.

Chapter 9, using the new capacity scaling law presented in the previous chapter, explores three relevant network optimization problems: i) the small cell base station deployment/activation problem, ii) the network-wide user equipment admission/scheduling problem, and iii) the spatial spectrum reuse problem. These problems are formally presented, and exemplary solutions are provided, with the corresponding discussion on the intuition behind the proposed solutions.

Chapter 11 shows the benefits of dynamic time division duplexing with respect to a more static time division duplexing assignment of time resources in an ultra-dense network. As studied in previous chapters, the amount of user equipment per small cell reduces significantly in a denser network. As a result, a dynamic assignment of time resources to the downlink and the uplink according to the load in each small cell can avoid resource waste, and significantly enhance its capacity. The dynamic time division duplexing protocol is modelled and analyzed through system-level simulations in this chapter too, and its performance carefully examined.

We prove several results about the asymptotics of the distributions of nonnormalized CRPs Z(t) and Y(t). These results, known as integro-local theorems, are sharper than the central limit theorem and are concerned with the probabilities of Z(t) and Y(t) hitting intervals of small length in the normal deviation zone.

Chapter 3 summarizes the modelling, derivations and main findings of probably one of the most important works on small cell theoretical performance analysis, which concluded that the fears of an inter-cell interference overload in small cell networks were not well-grounded, and that the network capacity – or in more technical words, the area spectral efficiency – linearly grows with the number of deployed small cells. This research was the cornerstone of much of the research that followed on small cells performance analysis.

We continue the study of integro-local probabilities that was initiated in Chapter 2 in the normal deviation zone. Now, assuming that the vector (?, ?) satisfies the Cramér moment condition, we study the integro-local probability in a wider zone, which in analogy with random walks can be called the Cramér deviation zone. This zone includes the zones of normal, moderately large, and "usual" large deviations.

Chapter 1 introduces the capacity challenge faced by modern wireless communication systems and presents ultra-dense wireless networks as an appealing solution to address it. Moreover, it provides background on the small cell concept – the fundamental building block of an ultra-dense wireless network – describing its main characteristics, benefits and drawbacks. This chapter also presents the structure of the book and the fundamental concepts required for its systematic understanding.