While Chapter 13 has shown that various CoMP concepts discussed in this book do indeed work in practice and yield gains that match fairly well to theoretical predictions, any field trial result is of course always limited to a particular, not necessarily representative, scenario, and, more importantly, to a very limited number of terminals. Before an operator invests into the technology and infrastructure required for certain CoMP schemes, however, he will want to assess their performance in large-scale systems with a large number of mobile terminals and potentially complex traffic models.

In this chapter, we hence want to discuss how system level simulations can be conducted in order to assess CoMP performance in large system contexts at reasonable complexity. First, Section 14.1 introduces the standard assumptions and simulation methodology used by 3GPP for the simulation of LTE and LTE-A schemes. Section 14.2 then shows how channel sounding measurements or ray-tracing in a 3D city model can be used to parameterize channel models, especially as the simulation of CoMP systems shifts the focus to different largescale parameters than that of non-cooperative systems. The chapter is concluded with system level results on a subset of the uplink and downlink CoMP concepts covered in this book in Sections 14.3 and 14.4, respectively.

Simulation and Link-2-System Mapping Methodology

Before any mobile communication system is deployed in the real world, a lot of design decisions have to be taken, and the cost of features have to be balanced with the gain that they promise.

In this chapter, the reader is made familiar with a set of theoretical concepts to analytically capture the variety of CoMP schemes considered in this book. The reader will obtain a first understanding of the general capacity gains expectable from multi-cell joint signal processing, and the many degrees of freedom involved. The chapter introduces notation that will be reused in most parts of the book.

Observed Cellular Scenarios

Throughout the book, we generally consider (subsets of) a large cellular system as depicted in Fig. 3.1. Here, a large number of mobile terminals, or user equipments (UEs), is distributed over a set of cells, where we assume that each cell is served by exactly one BS. As this is the case for most currently deployed cellular systems, we further assume that multiple BSs are grouped into so-called sites. Note that, differing from some other publications, we consider a sector to be equivalent to a cell. The term cluster is used to indicate a set of cells between which some form of CoMP may take place. Note that we assume that each UE in the system aims at transmitting or receiving dedicated information, i.e. multi-cast concepts are not covered in the book. As the number of UEs is typically significantly larger than the number of cells, UEs have to be scheduled to resources, i.e. to certain transmission windows.

In this chapter, we address the issue how channel knowledge - referring to both desired channels and the channels towards interferers - needed for various CoMP schemes can be made available where it is needed. We first investigate channel estimation techniques at the receiver side in Section 9.1, and then discuss how the obtained channel knowledge can be efficiently fed back to the transmitter side in Section 9.2, which is for example a crucial requirement for the downlink CoMP schemes investigated in Sections 6.3 and 6.4. The chapter shows that standard channel estimation and feedback concepts can principally be extended to enable CoMP in general. However, it also becomes apparent that large CoMP cooperation sizes may be considered questionable in practice, due to the fact that weak links cannot be estimated accurately, and the involved pilot and channel state information (CSI) feedback overhead may become prohibitive.

Channel Estimation for CoMP

One of the main challenges for CoMP schemes like joint transmission (JT) is to obtain accurate channel information in a multi-cell mobile radio environment with acceptable overhead for pilot signals.

The section is structured as follows. In Subsection 9.1.1, main characteristics of the mobile radio channel and state-of-the-art estimation and interpolation techniques like Wiener filtering will be introduced, with a special focus on channel prediction. For CoMP, the analysis then has to be extended to multiple channel components and multi-cell scenarios, which will be done in Subsections 9.1.2 and 9.1.3, respectively.

Information theory was created by Claude E. Shannon for the study of certain quantitative aspects of information, primarily as an analysis of the impact of coding on information transmission. Research in this field has resulted in several mathematical theories. Our subject is the stochastic theory, often referred to as the Shannon theory, which directly descends from Shannon's pioneering work.

This book is intended for graduate students and research workers in mathematics (probability and statistics), electrical engineering and computer science. It aims to present a well-integrated mathematical discipline, including substantial new developments of the 1970s. Although applications in engineering and science are not covered, we hope to have presented the subject so that a sound basis for applications has also been provided. A heuristic discussion of mathematical models of communication systems is given in the Introduction, which also offers a general outline of the intuitive background for the mathematical problems treated in the book.

As the title indicates, this book deals with discrete memoryless systems. In other words, our mathematical models involve independent random variables with finite range. Idealized as these models are from the point of view of most applications, their study reveals the characteristic phenomena of information theory without burdening the reader with the technicalities needed in the more complex cases. In fact, the reader needs no other prerequisites than elementary probability and a reasonable mathematical maturity. By limiting our scope to the discrete memoryless case, it was possible to use a unified, basically combinatorial approach.

The results of Chapter 15 enable us to solve a number of coding problems for various source and channel networks. Most of the resulting coding theorems are presented as problems which can be solved more or less in the same way. As an illustration of the methods, we shall discuss in detail a channel network and a (normal) source network. In addition, we shall consider a source network with a more general fidelity criterion than probability of error.

Channel networks with a single intermediate vertex are called broadcast channels. The simplest case of a network with two outputs has been studied intensively. Without loss of generality, one can suppose that this network has three inputs. This two-output broadcast channel (BC) is illustrated in Fig. 16.1.

At present, a computable characterization of the capacity region of the two-output broadcast channel is available only in special cases. A model of independent interest is obtained if “either of inputs 1 and 2 of the network is idle.” This corresponds to the new channel network in Fig. 16.2, the asymmetric two-output broadcast channel (ABC), which is treated as our next problem.

In the following, the DMCs corresponding to the outputs addressed by 10 and 0 will be denoted by {V : X → Y} resp. {W : X → Z}.

Contemporary techniques of data security are primarily based on computational complexity, typically on the infeasibility of inverting certain functions using currently available mathematical techniques and computing power. Among the various protocols based on such ideas, those approved by the cryptography community appear secure enough, but mathematical and technological progress may render them insecure in the future. Indeed, past experience suggests that this is likely to happen.

Information-theoretic secrecy offers provable security even against an adversary with unlimited computing power. This chapter provides a glimpse into the substantial progress that has been made towards clarifying the theoretical possibilities in this direction. Practical applications are reasonably expected within a much shorter time than capacity-achieving coding techniques have followed Shannon's discovery of the noisy channel coding theorem.

Two kinds of problems will be addressed: secure transmission over insecure channels and secret key generation taking advantage of public communication. After introducing necessary concepts and tools in Section 17.1, these problems will be treated in Sections 17.2 and 17.3. Let us emphasize that the mathematical models and techniques will be similar to those in previous chapters. These models, however, are now studied from a non-cooperative aspect: a major goal is to keep (at least) one party ignorant of (at least part of) the information exchanged.