无线网络中的压缩感知应用详解与工程实践

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xiv Preface

existing CS results in the literature requires a good mathematical background, but this

book is written at a level for the engineers. Most parts of this book are suitable for

readers who want to broaden their views, and it is also very useful for engineers and

researchers in applied ﬁelds who deal with sampling problems in their work.

We would like to thank Drs. Richard Baraniuk, Stephen Boyd, Rick Chartrand, Ekram

Hossain, Kevin Kelly, Yingying Li, Lanchao Liu, Jia Meng, Lijun Qian, Stanley Osher,

Zaiwen Wen, Zhiqiang Wu, Ming Yan, and Yin Zhang for their support and encour-

agement. We also would like to thank Lanchao Liu, Nam Nguyen, Ming Yan, and Hui

Zhang for their assistance and Mr. Ray Hardesty for text editing. Finally, we would like to

acknowledge NSF support (ECCS-1028782), ARL and ARO grant W911NF-09-1-0383

and NSF grant DMS-0748839.

ZHU HAN

HUSHENG LI

WOTAO Y IN

1 Introduction

Sampling is not only a beautiful research topic with an interesting history, but also

a subject with high practical impact, at the heart of signal processing and communi-

cations and their applications. Conventional approaches to sample signals or images

follow Shannon’s celebrated theorem: the sampling rate must be at least twice the

maximum frequency present in the signal (the so-called Nyquist rate) has been to

some extent accepted and widely used ever since the sampling theorem was implied

by the work of Harry Nyquist in 1928 (“Certain topics in telegraph transmission

theory”) and was proved by Claude E. Shannon in 1949 (“Communication in the

presence of noise”). However, with the increasing demand for higher resolutions

and an increasing number of modalities, the traditional signal-processing hardware

and software are facing signiﬁcant challenges. This i s especially true for wireless

communications.

The compressive sensing (CS) theory is a new technology emerging in the interdis-

ciplinary area of signal processing, statistics, optimization, as well as many application

areas including wireless communications. By utilizing the fact that a signal is sparse

or compressible in some transform domain, CS can acquire a signal from a small set

of incoherent measurements with a sampling rate much lower than the Nyquist rate.

As more and more experimental evidence suggests that many kinds of signals in wire-

less applications are sparse, CS has become an important component in the design of

next-generation wireless networks.

This book aims at developing a uniﬁed view on how to efﬁciently incorporate the idea

of CS over assorted wireless network scenarios. This book is interdisciplinary in that it

covers materials in signal processing, optimization, information theory, communications,

and networking to address the issues in question. The primary goal of this book is to

enable engineers and researchers to understand the fundamentals of CS theory and tools

and to apply them in wireless networking and other areas. Additional important goals are

to review some up-to-date and state-of-the-art techniques for CS, as well as for industrial

engineers to obtain new perspectives on wireless communications.

1.1 Motivation and objectives

CS is a new signal-processing paradigm and aims to encode sparse signals by using far

fewer measurements than those in the Nyquist setup. It has attracted a great amount of

2 Introduction

attention from researchers and engineers because of its potential to revolutionize many

sensing modalities. For example, in a cognitive radio system, to increase the efﬁciency

of the utility of spectrum, it is necessary to separate occupied spectrum and unoccupied

spectrum ﬁrst, which becomes a spectrum s ensing problem and can leverage CS tech-

niques. However, as with many great techniques, there is a gap between the theoretical

breakthrough of CS and its practical applications, in particular the applications in wire-

less networking. This motivates us to write a book to narrow this gap by presenting the

theory, models, algorithms, and applications in one place. The book was written with

two main objectives. The ﬁrst one is to introduce the basic concepts and typical steps

of CS. The second one is to demonstrate its effective applications, which will hopefully

inspire future applications.

1.2 Outline

In order to achieve the objectives, the book ﬁrst presents an introduction to the basics of

wireless networks. The book is written in two parts as follows: the ﬁrst part studies the

CS framework, and the second part discusses its applications in wireless networks by

presenting several existing implementations. Let us summarize the remaining chapters

of this book as follows:

Chapter 2 Overview of wireless networks

Different wireless network technologies such as, cellular wireless, WLAN,

WMAN, WPAN, WRAN technologies, and the related standards are reviewed.

The review includes the basic components, features, and potential applications.

Furthermore, advanced wireless technologies such as cooperative communica-

tions, network coding, and cognitive radio are discussed. Some typical wireless

networks such as ad hoc/sensor networks, mesh networks, and vehicular networks

are also studied. The research challenges related to the practical implementations

at the different layers of the protocol stack are discussed.

Part I: Compressive sensing framework

Before we discuss how to employ CS in different wireless network problems, the

choice of a design technique is crucial and must be studied. In this context, this part

presents different CS techniques, which are applied to the design, analysis, and optimiza-

tion of wireless networks. We introduce the basic concepts, theorems, and applications

of CS schemes. Both theoretical analysis and numerical algorithms are discussed and

CS examples are given. Finally, we discuss the current state-of-the-art for CS-based

analog-to-digital converters.

Chapter 3 Compressive sensing framework

This chapter overviews the basic concepts, steps, and theoretical results of CS. It

is a methodology using incoherent linear measurements to recover sparse signals.

The preliminaries and notation are set up for further usage. This chapter also

1.2 Outline 3

presents the elements of a typical CS process. The conditions that guarantee

successful CS encoding and decoding are presented.

Chapter 4 Sparse optimization algorithms

There are a collection of various algorithms for recovering sparse solutions, as

well as low-rank matrices, from their linear measurements. Generally, they can be

classiﬁed into optimization models and algorithms and non-optimization ones. The

chapter gives more emphasis on the ﬁrst class and brieﬂy discusses the second one.

When presenting algorithms, the big picture is focused, and some detailed analyses

are omitted and referred to related papers. The advantages and disadvantages of

presented algorithms are discussed to help the reader pick appropriate ones to

solve their own problems.

Chapter 5 CS Analog-to-digital converter

Wideband analog signals push contemporary analog-to-digital conversion systems

to their performance limits. In many applications, however, sampling at the Nyquist

rate is inefﬁcient because the signals of interest contain only a small number of

signiﬁcant frequencies relative to the limited band, though the locations of the

frequencies may not be known a priori. In this chapter, we discuss several possible

strategies in the literature. First, we study the CS-based ADC and its applications

to 60 GHz communication. Then we describe the random demodulator, which

demodulates the signal by multiplying it with a high-rate pseudonoise sequence

and smears the tones across the entire spectrum. Next, we study the modulated

wideband converter, which ﬁrst multiplies the analog signal by a bank of periodic

waveforms. The product is then low-pass ﬁltered and sampled uniformly at a low

rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the

proposed samples is achieved under certain necessary and sufﬁcient conditions.

Finally, we study Xampling, a design methodology for analog CS in which analog

band-limited signals are sampled at rates far lower than Nyquist without loss of

information.

Part II: Compressive Sensing Applications in Wireless Networks

To exploit CS in wireless communication, many applications using CS are given in

detail. However, CS has more places to be adopted and emphasized. Because of the

authors’ limited time and effort, we have only contributed those listed related to wireless

networking in the book, but hope this can motivate the readers to discover more in the

future. The process of designing a suitable model for CS and problem formulation is

also described to help engineers who are also interested in using the new technology –

CS – in their research.

Chapter 6 Compressed channel estimation

In communications, CS is largely accepted for sparse channel estimation and its

variants. In this chapter, we highlight the fundamental concepts of CS channel

estimation with the fact that multipath channels are sparse in their equivalent

baseband representation. Popular channels such as OFDM and MIMO are investi-

gated by use of CS. Then, a belief-propagation-based channel estimation scheme

4 Introduction

is used with a standard bit-interleaved coded OFDM transmitter, which performs

joint sparse-channel estimation and data decoding. Next, blind channel estimation

is studied to show how to use the CS and matrix completion. Finally, a special

channel, the underwater acoustic channel, is investigated from the aspect of CS

channel estimation.

Chapter 7 Ultra-wideband systems

Ultra-wideband (UWB) has been heavily studied due to its wide applications like

short-range communications and localizing. However, it suffers from the extremely

narrow impulse width that makes the design of the receiver difﬁcult. Meanwhile,

the narrow impulse width and low duty cycle also provides the sparsity in the time

domain that facilitates the application of CS. In this chapter, we will provide a brief

model of UWB signals. Then, we will review different approaches of applying

CS to enhance the reception of UWB signals for general purposes. The waveform

template-based approach and Bayesian CS method will be explained as two case

studies.

Chapter 8 Positioning

Precise positioning (e.g., of the order of centimeters or millimeters) is useful in

many applications like robot surgery. Usually it is achieved by analyzing the narrow

pulses sent from the object and received at multiple base stations. The precision

requirement places a pressing demand on the timing acquisition of the received

pulses. In this chapter, we discuss the precision positioning using UWB impulses.

In contrast to the previous chapter, this chapter is focused on the CS with the

correlated signals received at the base stations. We will ﬁrst introduce the general

models and approaches of positioning. Then, we will introduce the framework of

Bayesian CS and explain the principle of using the a priori distribution to convey

the correlated i nformation. Moreover, we will introduce the general principle of

how to integrate CS with the subsequent positioning algorithm like the Time

Difference Arrival (TDOA) approach, which can further improve the precision of

positioning.

Chapter 9 Multiple access

In wireless communications, an important task is the multiple access that resolves

the collision of the signals sent from multiple users. Traditional studies assume that

all users are active and thus the technique of multiuser detection can be applied.

However, in many practical systems like wireless sensor networks, only a random

and small fraction of users send signals simultaneously. In this chapter, we study

the multiple access with sparse data trafﬁc, in which the task is to recover the data

packets and the identities of active users. We will formulate the general problem

as a CS one due to the sparsity of active users. The algorithm of reconstructing

the above information will be described. In particular, the feature of discrete

unknowns will be incorporated into the reconstruction algorithm. The CS-based

multiple access scheme will further be integrated with the channel coding. Finally,

we will describe the application in the advanced metering infrastructure (AMI) in

a smart grid using real measurement data.

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