Communications and signal processing

Summary

An important requirement of next-generation (5G) wireless systems is the ability to autonomously adjust to varying environmental conditions. Our focus in this chapter is to analyze information-theoretic models of interference networks that capture the effect of deep fading conditions through introducing random link erasure events in blocks of communication time slots.More specifically, in order to consider the effect of long-term fluctuations (deep fading or shadowing), we assume that communication takes place over blocks of time slots, and independent link erasures occur with probability p in each block.

We can observe through the results presented in Chapters 5–8 that conclusions related to the optimal associations of mobile terminals to basestations and the achievable DoF differ dramatically based on the network topology. For example, under the maximum transmit set size constraint for the downlink, local cooperation cannot lead to a gain in the achieved asymptotic per-user DoF for the fully connected channel. However, local cooperation is optimal for locally connected channels and can lead to achieving scalable DoF gains, and the optimal assignment of messages to transmitters depends on the connectivity parameter L. In practice, the topology may change due to deep fading conditions (see, e.g., [6]) or even intentionally to exploit spectrum opportunities (see, e.g., [94]). In this chapter, we extend our DoF results to dynamic interference networks where a fixed assignment of messages is selected to achieve average DoF optimal performance in networks with changing topology.

In [95], the authors analyzed the average capacity for a point-to-point channel model where slow changes result in varying severity of noise. We apply a similar concept to interference networks by assuming that slowly changing deep fading conditions result in link erasures.We consider the linear interference network (L=1) that was introduced in Chapter 6, and look at two fading effects: long-term fluctuations that result in link erasures over a complete block of time slots, and short-term fluctuations that allow us to assume that any specific joint realization for the non-zero channel coefficients will take place with zero probability. We study the problem of achieving the optimal average degrees of freedom under a maximum transmit set size constraint (5.16). We note that the problem studied in Chapter 6 reduces to the case of no erasures.

Summary

In the previous two chapters, we have considered cooperative transmission schemes that are constrained by the number of transmitters to which each message can be assigned. While meeting a backhaul capacity limit by a per-message constraint can have its analytical advantages, such as reducing a difficult information-theoretic problem to a simple combinatorial one, this approach suffers from a few important drawbacks.

For one, the maximum transmit set size constraint may not reflect most practical scenarios for two reasons. First, because fractional reuse across different resource (e.g., frequency or time) slots can be used to achieve an equal load on the backhaul per message, it may not make sense to impose a maximum transmit set size constraint for each channel use. Secondly, the maximum transmit set size constraint may not reflect the nature of the backhaul link, as we will discuss further below.

Also, as we have discussed in the previous chapter, the optimal solutions for the maximum transmit set size constraint may not fully utilize the constraint; i.e., for the optimal solution, some messages need not be assigned to the allowed maximum number of transmitters. We have seen in Chapter 6 that this is the case for the optimal schemes for linear interference networks, as well as for general locally connected networks where we impose the restriction of using only zero-forcing coding schemes.

The appropriate constraint to consider for the assignment of messages to transmitters should depend on the nature of the backhaul link used in practice (see, e.g., [69, 86]). For example, in the context of heterogeneous networks, the backhaul can be a wireless network, and an overall backhaul load constraint would be a more appropriate choice. On the other hand, for the case of wireline or optical fiber backhaul links, the maximum transmit set size constraint can be useful. However, even with wireline backhaul links, an average transmit set size constraint can allow for flexible solutions that interleave the use of the backhaul links over multiple communication sessions. In general, a constraint that bounds the average transmit set size is more relevant to practice than imposing a maximum constraint on each transmit set size. We show in this chapter how the solutions for the CoMP transmission problem provided under the maximum transmit set size constraint can be used to find solutions under an average transmit set size or backhaul load constraint.

Summary

Efficient interference management is the key to meeting the ever increasing demand for wireless data services in wireless networks. In this book, an information-theoretic framework for interference management is presented, along with a discussion of practically implementable schemes for interference management that approach provable bounds on performance and are applicable in large cellular networks.

A particular focus of the book is on exploiting recent technological advancements in the wireless infrastructure that enable cooperative transmission and reception. Our theoretical framework highlights the potential of this technology to deliver the rate gains promised by interference alignment, while using simple zero-forcing schemes that are easier to implement in practice. The schemes that we present rely on local cooperation, and they are shown to be optimal in locally connected interference networks, where the path loss effect allows us to neglect connections between transmitters and receivers that are far away from each other. It is also shown that cooperative communication can be used to deliver significant rate gains using simple zero-forcing with no or minimal extra load on the backhaul, by selecting cell associations and allocation of backhaul resources based on centralized processing and knowledge of the network topology. The insights obtained are also extended to dynamic interference networks that capture the effect of deep fading conditions.

This book is organized as follows:

Summary

Over the years since Claude Shannon [12] introduced the subject, information theory has proven to be a powerful mathematical tool that is also practically relevant in terms of guiding the design of transmitters and receivers for communication systems and networks. From the analysis of the capacity of point-to-point communication links [12] to the more advanced analysis of network information theory [99], there is evidence that information-theoretic tools not only provide performance benchmarks but also inspire new designs for coding schemes and communication protocols. In this book, our focus has been on information-theoretic tools that are geared toward laying a framework for interference management in modern wireless networks. We started with a discussion of the information-theoretic capacity of the two-user interference channel in Chapter 2, which is a long-standing open problem. We do not yet understand how interfering signals should be handled by the decoders at the receivers except in special cases: (i) where the interference power is high and the interfering signal(s) can be decoded, and (ii) and where the interference power is low and the interfering signal(s) can be treated as noise. We then considered the degrees of freedom criterion in the rest of the book, due to its attractive simplicity and utility in providing insights for interference management. We considered general K-user interference channels in Chapter 3, and introduced the concept of asymptotic interference alignment. We then studied in Chapters 5–9 the potential gains of cooperative communication through the lens of DoF analysis in large interference networks. In these studies we assumed a centralized controller, one that has a global view of the network and can make decisions on cell associations and transmission schedules for the whole network, with the goal of maximizing the sum DoF. It is important to note that our study of models with centralized controllers does not imply that we are advocating a centralized approach in next-generation wireless networks over a distributed one that only requires local network knowledge for making decisions. Analyzing fundamental bounds on the performance for the centralized solution can also lead to good design choices for distributed schemes, as well as providing benchmarks for their performance, as we have seen in our study of distributed interference management algorithms in Chapter 4 and Section 5.7.

Summary

Principles of Wireless Cloud Coding

The termWireless Cloud Coding (WCC) will denote the coding concept suited for large and complex networks with a stochastic structure and connectivity. A simple low-scale WPNC network with a known deterministic structure can be designed in a “handcrafted” style.We usually also easily identify the critical points of performance or design aspects that need to be optimized. On the other hand, a complex large stochastic network adds some specific problems.

Stochastic Network Structure

The network structure and connectivity may be stochastic and unknown. A standard NCM design needs to know the participating signals forming the H-constellation in the H-MAC stage, and also the full end-to-end hierarchical encapsulation of all involved HNC maps to guarantee the end-to-end solvability. In a large randomly changing network, this creates a significant problem for (a) identifying and estimating the system/ channel state, (b) making a decision on the processing form, and (c) signaling this decision to all involved nodes. Instead of using this traditional solution, we can try to devise the NCM that is blind to the network structure that will not require a separate NCM/WPNC control protocol but will treat the unknown network structure as an additional degree of freedom fully integrated with the actual payload data (see Section 10.2).

Clustered, Nested, and Modular Cloud Framework

The number of the design degrees of freedom may be prohibiting in a large network. A nested modular encapsulation of some of its fragments/clusters can help. This has two aspects. (a) It simplifies the overall design by clustering the nodes and nesting the clusters. (b) Each cluster performs some processing as a “black-box” self-contained virtual super-node. It does not reveal its internal structure to the outside world and simply provides some functionality as a super-node. Its global level of clustering can even comprise the whole cloud. It can serve its outside terminals as if it was some super-relay performing some complex internal hidden processing (see Section 10.3).

Wireless Cloud-Coding-Based Design of NCM

Random Channel Class H-MAC and Joint HNC Map

Joint HNC map vs. Classical Signaling

A classical signaling solution (Figure 10.1a) is based on the channel sensing and then switching the NCM map at the node depending on the channel class (connection/ disconnection).

Summary

Introduction

As shown in Chapter 5 in general, and in Chapter 6 in more concrete forms, the design of NCM is relatively straightforward and its performance provides an advantage only under specific conditions. It particularly applies to the form of HNC maps and some requirements on the SNR balance of component channels in H-MAC. For example, the isomorphic layered NCM for HDF strategy gives an H-rate advantage if the HNC map is a GF-based linear minimal cardinality map and the component channels have roughly the same SNRs. When applied for example to a butterfly network, it implies symmetric distances on the source-to-relay channels and a perfect HSI with the same rate as the H-rate at the relay. All relays that use a minimal cardinality linear GF HNC map must be on the same GF vector space as the source messages. The resulting equations and therefore also the HI processed by the relay have the same codebook size as the component messages. Similarly, CF strategy requires a common nested lattice code on sources and the HNC map also implies that all flows of hierarchical information from relays to the destination will have the same codebook size.

Clearly, many practical WPNC networks will need to operate with asymmetric SNR conditions or asymmetric parametrization on the H-MAC, and also the destination might have available only a limited HI or HSI (w.r.t. source codebook sizes) to compute the desired data. The “brute force” solution is to use minimal common source rates, which are bottlenecked by the weakest channel, either on the H-MAC or on the HSI side. This chapter, however, offers a solution allowing us to design NCM for partial HSI and asymmetric H-MAC. It is based on splitting the source data streams into several lower-rate independent components. The split sources can be viewed as virtual component nodes. The split allows us to use different strategies for selected virtual components. We can also group a selected subset of virtual nodes and apply a given strategy that matches to the selected group. For example, we can use layered NCM for the group of virtual nodes having the same rate and having a similar SNR. We can form multiple groups in this way and combine them by another coding strategy. For example, if the groups have very asymmetric rates or SNRs, we can use a classical multi-user strategy.

Summary

Introduction

Wireless networks are becoming more and more ubiquitous in the modern world, and more and more essential to today's society. In 30 years they have progressed from the province of a tiny minority of the world's population in only the most developed nations, to the point where there are very nearly as many wireless subscriptions as people in the world [24]. The services offered have extended from very limited speech services at the introduction of first-generation mobile systems in 1985, to broadband Internet access and full motion video today. Moreover, we are at the point where wireless networks will extend beyond connecting people (of whom there are a limited number), to connecting their devices – an effectively unlimited number. Some believe that there are already more devices than people connected to the Internet, and predictions that 50 billion or more devices will be connected by 2020 are circulating widely [60]. Of course, that is only the start.

All this implies that the density of wireless networks will inevitably increase. To provide telecommunication services to the human populations of our cities, at continually increasing data rates, will require increasing numbers of access points, for which backhaul will become an increasing problem, and require more widespread use of wireless backhaul. The devices will also form a network many times as dense as any current wireless networks, also likely to require connection to the core network. In both cases it is likely that the current point-to-multipoint architecture of wireless networks, exemplified by both cellular and WiFi systems, will be replaced by a multi-hop mesh network architecture.

The concept of the mobile ad-hoc network (MANET), one of the best-established concepts in wireless mesh networking, has been in existence for many years [9], yet has not really fulfilled its predicted potential. There are very few wireless networks in use today that implement a truly multi-hop networking approach. There seems to be a barrier to the practical implementation of multi-hop wireless networking that will surely have to be overcome in order to implement the ultra-dense wireless networks that are likely to be required in the near future.

Communications and signal processing

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Acknowledgments

6 - Locally Connected Channels with CoMP

9 - Dynamic Interference Management

Summary

4 - Iterative Algorithms for Interference Management

Contents

2 - System Model and Sum Capacity Characterization

References

Appendix B - Algebraic Geometry

3 - Degrees of Freedom and Interference Alignment

7 - Backhaul Load Constraint

Summary

Frontmatter

Index

Preface

Summary

10 - Recent Advances and Open Problems

Summary

Appendix A - Information Theory

10 - WPNC in Complex Stochastic Networks

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Part I - Motivation and Gentle Introduction

8 - NCM Design for Partial HSI and Asymmetric H-MAC

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Frontmatter

1 - Introduction

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