We now consider the performance of the digital modulation techniques discussed in the previous chapter when used over AWGN channels and channels with flat fading. There are two performance criteria of interest: the probability of error, defined relative to either symbol or bit errors; and the outage probability, defined as the probability that the instantaneous signal-to-noise ratio falls below a given threshold. Flat fading can cause a dramatic increase in either the average bit error probability or the signal outage probability. Wireless channels may also exhibit frequency-selective fading and Doppler shift. Frequency-selective fading gives rise to intersymbol interference (ISI), which causes an irreducible error floor in the received signal. Doppler causes spectral broadening, which leads to adjacent channel interference (small at typical user velocities) and also to an irreducible error floor in signals with differential phase encoding (e.g. DPSK), since the phase reference of the previous symbol partially decorrelates over a symbol time. This chapter describes the impact on digital modulation performance of noise, flat fading, frequency-selective fading, and Doppler.

AWGN Channels

In this section we define the signal-to-noise power ratio (SNR) and its relation to energy per bit (Eb) and energy per symbol (Es). We then examine the error probability on AWGN channels for different modulation techniques as parameterized by these energy metrics. Our analysis uses the signal space concepts of Section 5.1.

Coding allows bit errors introduced by transmission of a modulated signal through a wireless channel to be either detected or corrected by a decoder in the receiver. Coding can be considered as the embedding of signal constellation points in a higher-dimensional signaling space than is needed for communications. By going to a higher-dimensional space, the distance between points can be increased, which provides for better error correction and detection.

In this chapter we describe codes designed for additive white Gaussian noise channels and for fading channels. Codes designed for AWGN channels typically do not work well on fading channels because they cannot correct for long error bursts that occur in deep fading. Codes for fading channels are mainly based on using an AWGN channel code combined with interleaving, but the criterion for the code design changes to provide fading diversity. Other coding techniques to combat performance degradation due to fading include unequal error protection codes and joint source and channel coding.

We first provide an overview of code design in both fading and AWGN, along with basic design parameters such as minimum distance, coding gain, bandwidth expansion, and diversity order. Sections 8.2 and 8.3 provide a basic overview of block and convolutional code designs for AWGN channels. Although these designs are not directly applicable to fading channels, codes for fading channels and other codes used in wireless systems (e.g., spreading codes in CDMA) require background in these fundamental techniques.

In Chapter 6 we saw that both Rayleigh fading and log-normal shadowing exact a large power penalty on the performance of modulation over wireless channels. One of the best techniques to mitigate the effects of fading is diversity combining of independently fading signal paths. Diversity combining exploits the fact that independent signal paths have a low probability of experiencing deep fades simultaneously. Thus, the idea behind diversity is to send the same data over independent fading paths. These independent paths are combined in such a way that the fading of the resultant signal is reduced. For example, consider a system with two antennas at either the transmitter or receiver that experience independent fading. If the antennas are spaced sufficiently far apart, it is unlikely that they both experience deep fades at the same time. By selecting the antenna with the strongest signal, a technique known as selection combining, we obtain a much better signal than if we had just one antenna. This chapter focuses on common methods used at the transmitter and receiver to achieve diversity. Other diversity techniques that have potential benefits beyond these schemes in terms of performance or complexity are discussed in [1, Chap. 9.10].

Diversity techniques that mitigate the effect of multipath fading are called microdiversity, and that is the focus of this chapter. Diversity to mitigate the effects of shadowing from buildings and objects is called macrodiversity.

Wireless communications is, by any measure, the fastest growing segment of the communications industry. As such, it has captured the attention of the media and the imagination of the public. Cellular systems have experienced exponential growth over the last decade and there are currently about two billion users worldwide. Indeed, cellular phones have become a critical business tool and part of everyday life in most developed countries, and they are rapidly supplanting antiquated wireline systems in many developing countries. In addition, wireless local area networks currently supplement or replace wired networks in many homes, businesses, and campuses. Many new applications – including wireless sensor networks, automated highways and factories, smart homes and appliances, and remote telemedicine – are emerging from research ideas to concrete systems. The explosive growth of wireless systems coupled with the proliferation of laptop and palmtop computers suggests a bright future for wireless networks, both as stand-alone systems and as part of the larger networking infrastructure. However, many technical challenges remain in designing robust wireless networks that deliver the performance necessary to support emerging applications. In this introductory chapter we will briefly review the history of wireless networks from the smoke signals of the pre-industrial age to the cellular, satellite, and other wireless networks of today. We then discuss the wireless vision in more detail, including the technical challenges that must still be overcome.

In this chapter we consider systems with multiple antennas at the transmitter and receiver, which are commonly referred to as multiple-input multiple-output (MIMO) systems. The multiple antennas can be used to increase data rates through multiplexing or to improve performance through diversity. We have already seen diversity in Chapter 7. In MIMO systems, the transmit and receive antennas can both be used for diversity gain. Multiplexing exploits the structure of the channel gain matrix to obtain independent signaling paths that can be used to send independent data. Indeed, the initial excitement about MIMO was sparked by the pioneering work of Winters, Foschini, Foschini and Gans, and Telatar predicting remarkable spectral efficiencies for wireless systems with multiple transmit and receive antennas. These spectral efficiency gains often require accurate knowledge of the channel at the receiver – and sometimes at the transmitter as well. In addition to spectral efficiency gains, ISI and interference from other users can be reduced using smart antenna techniques. The cost of the performance enhancements obtained through MIMO techniques is the added cost of deploying multiple antennas, the space and circuit power requirements of these extra antennas (especially on small handheld units), and the added complexity required for multidimensional signal processing. In this chapter we examine the different uses for multiple antennas and find their performance advantages. This chapter uses several key results from matrix theory: Appendix C provides a brief overview of these results.

An ad hoc wireless network is a collection of wireless mobile nodes that self-configure to form a network without the aid of any established infrastructure, as shown in Figure 16.1. Without an inherent infrastructure, the mobiles handle the necessary control and networking tasks by themselves, generally through the use of distributed control algorithms. Multihop routing, whereby intermediate nodes relay packets toward their final destination, can improve the throughput and power efficiency of the network. The Merriam-Webster dictionary lists two relevant definitions for ad hoc: “formed or used for specific or immediate problems”, and “fashioned from whatever is immediately available”. These definitions capture two of the main benefits of ad hoc wireless networks: they can be tailored to specific applications, and they can be formed from whatever network nodes are available. Ad hoc wireless networks have other appealing features as well. They avoid the cost, installation, and maintenance of network infrastructure. They can be rapidly deployed and reconfigured. They also exhibit great robustness owing to their distributed nature, node redundancy, and the lack of single points of failure. These characteristics are especially important for military applications, and much of the groundbreaking research in ad hoc wireless networking was supported by the (Defense) Advanced Research Projects Agency (DARPA) and the U.S. Navy. Many of the fundamental design principles for ad hoc wireless networks were identified and investigated in that early research.

Adaptive modulation and coding enable robust and spectrally efficient transmission over time-varying channels. The basic premise is to estimate the channel at the receiver and feed this estimate back to the transmitter, so that the transmission scheme can be adapted relative to the channel characteristics. Modulation and coding techniques that do not adapt to fading conditions require a fixed link margin to maintain acceptable performance when the channel quality is poor. Thus, these systems are effectively designed for worst-case channel conditions. Since Rayleigh fading can cause a signal power loss of up to 30 dB, designing for the worst-case channel conditions can result in very inefficient utilization of the channel. Adapting to the channel fading can increase average throughput, reduce required transmit power, or reduce average probability of bit error by taking advantage of favorable channel conditions to send at higher data rates or lower power – and by reducing the data rate or increasing power as the channel degrades. In Section 4.2.4 we derived the optimal adaptive transmission scheme that achieves the Shannon capacity of a flat fading channel. In this chapter we describe more practical adaptive modulation and coding techniques to maximize average spectral efficiency while maintaining a given average or instantaneous bit error probability. The same basic premise can be applied to MIMO channels, frequency-selective fading channels with equalization, OFDM or CDMA, and cellular systems.

In the previous chapter, we analyzed the performance benefits of MIMO communication and discussed architectures that are designed to reap those benefits. The focus was on the fast fading scenario. The story on slow fading MIMO channels is more complex. While the communication capability of a fast fading channel can be described by a single number, its capacity, that of a slow fading channel has to be described by the outage probability curve pout(·), as a function of the target rate. This curve is in essence a tradeoff between the data rate and error probability. Moreover, in addition to the power and degree-of-freedom gains in the fast fading scenario, multiple antennas provide a diversity gain in the slow fading scenario as well. A clear characterization of the performance benefits of multiple antennas in slow fading channels and the design of good space-time coding schemes that reap those benefits are the subjects of this chapter.

The outage probability curve pout(·) is the natural benchmark for evaluating the performance of space-time codes. However, it is difficult to characterize analytically the outage probability curves for MIMO channels. We develop an approximation that captures the dual benefits of MIMO communication in the high SNR regime: increased data rate (via an increase in the spatial degrees of freedom or, equivalently, the multiplexing gain) and increased reliability (via an increase in the diversity gain). The dual benefits are captured as a fundamental tradeoff between these two types of gains.

In this chapter, we will look at the capacity of MIMO fading channels and discuss transceiver architectures that extract the promised multiplexing gains from the channel. We particularly focus on the scenario when the transmitter does not know the channel realization. In the fast fading MIMO channel, we show the following:

• At high SNR, the capacity of the i.i.d. Rayleigh fast fading channel scales like nmin log SNR bits/s/Hz, where nmin is the minimum of the number of transmit antennas nt and the number of receive antennas nr. This is a degree-of-freedom gain.

• At low SNR, the capacity is approximately nrSNR log2 e bits/s/Hz. This is a receive beamforming power gain.

• At all SNR, the capacity scales linearly with nmin. This is due to a combination of a power gain and a degree-of-freedom gain.

Furthermore, there is a transmit beamforming gain together with an opportunistic communication gain if the transmitter can track the channel as well.

Over a deterministic time-invariant MIMO channel, the capacity-achieving transceiver architecture is simple (cf. Section 7.1.1): independent data streams are multiplexed in an appropriate coordinate system (cf. Figure 7.2). The receiver transforms the received vector into another appropriate coordinate system to separately decode the different data streams. Without knowledge of the channel at the transmitter the choice of the coordinate system in which the independent data streams are multiplexed has to be fixed a priori.

Introduction

In Chapter 3, our focus was on point-to-point communication, i.e., the scenario of a single transmitter and a single receiver. In this chapter, we turn to a network of many mobile users interested in communicating with a common wireline network infrastructure. This form of wireless communication is different from radio or TV in two important respects: first, users are interested in messages specific to them as opposed to the common message that is broadcast in radio and TV. Second, there is two-way communication between the users and the network. In particular, this allows feedback from the receiver to the transmitter, which is missing in radio and TV. This form of communication is also different from the all-wireless walkie-talkie communication since an access to a wireline network infrastructure is demanded. Cellular systems address such a multiuser communication scenario and form the focus of this chapter.

Broadly speaking, two types of spectra are available for commercial cellular systems. The first is licensed, typically nationwide and over a period of a few years, from the spectrum regulatory agency (FCC, in the United States). The second is unlicensed spectrum made available for experimental systems and to aid development of new wireless technologies. While licensing spectrum provides immunity from any kind of interference outside of the system itself, bandwidth is very expensive. This skews the engineering design of the wireless system to be as spectrally efficient as possible.

In Chapter 4, we studied several specific multiple access techniques (TDMA/FDMA, CDMA, OFDM) designed to share the channel among several users. A natural question is: what are the “optimal” multiple access schemes? To address this question, one must now step back and take a fundamental look at the multiuser channels themselves. Information theory can be generalized from the point-to-point scenario, considered in Chapter 5, to the multiuser ones, providing limits to multiuser communications and suggesting optimal multiple access strategies. New techniques and concepts such as successive cancellation, superposition coding and multiuser diversity emerge.

The first part of the chapter focuses on the uplink (many-to-one) and downlink (one-to-many) AWGN channel without fading. For the uplink, an optimal multiple access strategy is for all users to spread their signal across the entire bandwidth, much like in the CDMA system in Chapter 4. However, rather than decoding every user treating the interference from other users as noise, a successive interference cancellation (SIC) receiver is needed to achieve capacity. That is, after one user is decoded, its signal is stripped away from the aggregate received signal before the next user is decoded. A similar strategy is optimal for the downlink, with signals for the users superimposed on top of each other and SIC done at the mobiles: each user decodes the information intended for all of the weaker users and strips them off before decoding its own.

In this book, we have seen several different uses of multiple antennas in wireless communication. In Chapter 3, multiple antennas were used to provide diversity gain and increase the reliability of wireless links. Both receive and transmit diversity were considered. Moreover, receive antennas can also provide a power gain. In Chapter 5, we saw that with channel knowledge at the transmitter, multiple transmit antennas can also provide a power gain via transmit beamforming. In Chapter 6, multiple transmit antennas were used to induce channel variations, which can then be exploited by opportunistic communication techniques. The scheme can be interpreted as opportunistic beamforming and provides a power gain as well.

In this and the next few chapters, we will study a new way to use multiple antennas. We will see that under suitable channel fading conditions, having both multiple transmit and multiple receive antennas (i.e., a MIMO channel) provides an additional spatial dimension for communication and yields a degree-of-freedom gain. These additional degrees of freedom can be exploited by spatially multiplexing several data streams onto the MIMO channel, and lead to an increase in the capacity: the capacity of such a MIMO channel with n transmit and receive antennas is proportional to n.

Historically, it has been known for a while that a multiple access system with multiple antennas at the base-station allows several users to simultaneously communicate with the base-station.

In the previous two chapters, we studied specific techniques for communication over wireless channels. In particular, Chapter 3 is centered on the point-to-point communication scenario and there the focus is on diversity as a way to mitigate the adverse effect of fading. Chapter 4 looks at cellular wireless networks as a whole and introduces several multiple access and interference management techniques.

The present chapter takes a more fundamental look at the problem of communication over wireless fading channels. We ask: what is the optimal performance achievable on a given channel and what are the techniques to achieve such optimal performance? We focus on the point-to-point scenario in this chapter and defer the multiuser case until Chapter 6. The material covered in this chapter lays down the theoretical basis of the modern development in wireless communication to be covered in the rest of the book.

The framework for studying performance limits in communication is information theory. The basic measure of performance is the capacity of a channel: the maximum rate of communication for which arbitrarily small error probability can be achieved. Section 5.1 starts with the important example of the AWGN (additive white Gaussian noise) channel and introduces the notion of capacity through a heuristic argument. The AWGN channel is then used as a building block to study the capacity of wireless fading channels. Unlike the AWGN channel, there is no single definition of capacity for fading channels that is applicable in all scenarios.

Book objective

Wireless communication is one of the most vibrant areas in the communication field today. While it has been a topic of study since the 1960s, the past decade has seen a surge of research activities in the area. This is due to a confluence of several factors. First, there has been an explosive increase in demand for tetherless connectivity, driven so far mainly by cellular telephony but expected to be soon eclipsed by wireless data applications. Second, the dramatic progress in VLSI technology has enabled small-area and low-power implementation of sophisticated signal processing algorithms and coding techniques. Third, the success of second-generation (2G) digital wireless standards, in particular, the IS-95 Code Division Multiple Access (CDMA) standard, provides a concrete demonstration that good ideas from communication theory can have a significant impact in practice. The research thrust in the past decade has led to a much richer set of perspectives and tools on how to communicate over wireless channels, and the picture is still very much evolving.

There are two fundamental aspects of wireless communication that make the problem challenging and interesting. These aspects are by and large not as significant in wireline communication. First is the phenomenon of fading: the time variation of the channel strengths due to the small-scale effect of multipath fading, as well as larger-scale effects such as path loss via distance attenuation and shadowing by obstacles.

Why we wrote this book

The writing of this book was prompted by two main developments in wireless communication in the past decade. First is the huge surge of research activities in physical-layer wireless communication theory. While this has been a subject of study since the sixties, recent developments such as opportunistic and multiple input multiple output (MIMO) communication techniques have brought completely new perspectives on how to communicate over wireless channels. Second is the rapid evolution of wireless systems, particularly cellular networks, which embody communication concepts of increasing sophistication. This evolution started with second-generation digital standards, particularly the IS-95 Code Division Multiple Access standard, continuing to more recent third-generation systems focusing on data applications. This book aims to present modern wireless communication concepts in a coherent and unified manner and to illustrate the concepts in the broader context of the wireless systems on which they have been applied.

Structure of the book

This book is a web of interlocking concepts. The concepts can be structured roughly into three levels:

1. channel characteristics and modeling;

2. communication concepts and techniques;

3. application of these concepts in a system context.

A wireless communication engineer should have an understanding of the concepts at all three levels as well as the tight interplay between the levels. We emphasize this interplay in the book by interlacing the chapters across these levels rather than presenting the topics sequentially from one level to the next.