Systems dedicated to the communication or storage of information are commonplace in everyday life. Generally speaking, a communication system is a system which sends information from one place to another. Examples include telephone networks, computer networks, audio/video broadcasting, etc. Storage systems, e.g. magnetic and optical disk drives, are systems for storage and later retrieval of information. In a sense, such systems may be regarded as communication systems which transmit information from now (the present) to then (the future). Whenever or wherever problems of information processing arise, there is a need to know how to compress the textual material and how to protect it against possible corruption. This book is to cover the fundamentals of information theory and coding theory, to solve the above main problems, and to give related examples in practice. The amount of background mathematics and electrical engineering is kept to a minimum. At most, simple results of calculus and probability theory are used here, and anything beyond that is developed as needed.

Information theory versus coding theory

Information theory is a branch of probability theory with extensive applications to communication systems. Like several other branches of mathematics, information theory has a physical origin. It was initiated by communication scientists who were studying the statistical structure of electrical communication equipment and was principally founded by Claude E. Shannon through the landmark contribution [Sha48] on the mathematical theory of communications. In this paper, Shannon developed the fundamental limits on data compression and reliable transmission over noisy channels.

For thousands of years, location information has been used for navigation. This has changed in the last century as advances in wireless communication and microelectronics have given birth to mobile computing devices. These devices enable their users to access sensing and computing capabilities from anywhere and at any time. An important consequence of such mobility is that the resource and information needs of wireless users are no longer fixed but vary with their changing location and, more generally, with their changing context. This has sparked a new generation of applications that employ location information to cater to the changing needs of mobile users. These applications, known as location-based services (LBS), are offered on top of wireless communication infrastructures to add value to existing services.

To enable and support the delivery of LBS, accurate, reliable, and realtime user location information is needed. This need has incited a new interest in positioning and tracking systems whose aim is to determine the physical coordinates of a wireless mobile device carried by a human user. The focus of this book is one class of positioning systems that employ radio signals from wireless local area networks (WLAN) for positioning. These systems are of special interest as they are able to provide high positioning accuracies in indoor and outdoor environments with minimal deployment and maintenance costs.

This book is divided into two parts. The first part focuses on topics related to the history and applications of positioning systems.

Chapter 3 detailed the fundamental techniques used in positioning. In this chapter, we review several examples of existing positioning systems that use these techniques. In particular, we focus on wireless positioning systems to motivate wireless local area network positioning. We discuss the Global Positioning System (Section 4.1) and cellular positioning (Section 4.2) as examples of positioning systems used in outdoor environments, and positioning based on ultrasound and infrared (Section 4.3) as examples of indoor positioning systems. We then proceed to motivate and describe positioning systems employing wireless local area networks (Section 4.4). Finally, we conclude the chapter by comparing the advantages offered by each system.

The Global Positioning System

Historical perspective

In 1957, the first artificial satellite known as Sputnik I was launched into the earth's orbit by the Soviet Union. Within days of the launch, scientists at Johns Hopkins University noted that they could determine the position of the satellite based on the Doppler shift associated with its radio transmissions. What was even more interesting was that if the position of the satellite were known, this Doppler shift could be used to determine the position of a satellite receiver on earth. This observation ushered in the development of global navigation satellite systems (GNSS).

The first operational satellite-based positioning system was Transit, also known as the Navy Navigation Satellite System (NAVSAT). This system was primarily used for military operations by the United States Navy.

In the previous chapters, we addressed the problem of position estimation given values of received signal strength (RSS). In this chapter, we focus on the architectural and system design aspects of a positioning solution.

We begin by outlining the five design issues that must be considered in WLAN positioning systems (Section 9.1). We then proceed to discuss architectural details of three functional modules of positioning systems, namely sensing, computation, and storage (Sections 9.2, 9.3, 9.4, and 9.5).

Design issues

Before proceeding to a discussion of the design of an RSS-based positioning system in detail, let us provide an overview of five key design challenges in these systems.

Limited communication bandwidth

Communication via wireless channels imposes severe limitations on the available band-width (5 and 11 Mbps for an IEEE 802.11b wirelessLAN[81]). This is due to the intensity drop as a function of the fourth power of the distance, the presence of obstructing objects (shadowing effects), and multipath fading [69]. As a result, RSS-based positioning systems must be designed in such a way as to minimize the number and frequency of wireless communications.

Distributed operation

Because communication is much more expensive than most processing operations, it is highly desirable for the processing to take place in a distributed manner to reduce traffic volume and energy costs [69]. Also, in large environments, access and anchor points are distributed over a large geographical area.

In the first part of this book, we motivated the need for accurate and cost-effective positioning systems that can enable the delivery of location-based services (LBS). Moreover, we suggested positioning based on wireless local area networks as a cost-effective and reliable solution for supporting such services in indoor environments. The second part of this book provides an in-depth treatment of the technical fundamentals of these systems. This chapter will begin by providing an overview of wireless local area networks (Section 5.1) and the radio features that can be used for positioning in these networks (Section 5.2). After motivating the use of received signal strength as the feature of choice for positioning, we proceed to describe the details of the experimental data set used for illustrating various concepts in this book (5.3). This is followed by a discussion of the spatial and temporal properties of received signal strength (Section 5.4), challenges in using this radio feature (Section 5.6), and techniques for modeling the relationship between received signal strength and position (Section 5.5).

Wireless local area networks

Wireless local area networks (WLANs) are radio-based communication network infrastructures based on the IEEE 802.11 family of standards. These networks operate in the unlicensed frequency bands [27], primarily employing the 2.4 GHz ISM band. As shown in Figure 5.1, WLANs use an architecture that relies on a set of base-stations for facilitating communication among the devices within the network, and between the network and the outside world (for example, the Internet).

The objective of a positioning system is to determine the position of a mobile device. This position, however, is not directly observable and must be determined based on some observable measurement. In the case of RSS-based positioning, this observable measurement is the received signal strength (RSS) at the mobile device. If the relationship between the RSS values and the position of mobile devices were known, the positioning problem would be trivial. However, as discussed in Chapter 5, this relationship is not deterministic in practice, but depends on the stochastic characteristics of the propagation environment. Consequently, the unknown position can only be estimated using RSS measurements. The focus of this chapter is the various estimation methods used to accomplish this task. In particular, this chapter focuses on memoryless estimators, which rely on an RSS measurement at a given time to compute the position estimate at that time. In other words, memoryless estimators do not consider the past history of user positions or RSS measurements during estimation.

We begin this chapter by developing a mathematical formulation of the memoryless positioning problem (Section 6.1) and show that this problem reduces to a density estimation problem. We next review two methods for density estimation based on the implicit training information provided in the radio map (Section 6.2). Using these density estimation techniques, we proceed to develop several position estimators (Sections 6.3 and 6.4). Finally, we conclude the chapter with the presentation of some experimental results (Section 6.5).

Positioning systems employ information from a large number of access points and anchor points distributed over large areas to locate a mobile device. In order to form a position estimate, the system must combine or fuse the information provided by these sources to make inferences regarding the location of a mobile device. Fusion of data from multiple sources is not a trivial task as redundancy and conflict among the information can significantly affect the accuracy and reliability of the final estimate. In the context of positioning, data fusion is especially challenging as the unreliable and time-varying nature of the radio-propagation channel means that erroneous and out-of-date information may be received from access and anchor points. In this Chapter, we focus on one data fusion challenge, namely sensor selection. In our context, sensor selection refers to selecting a subset of the available access and anchor points for positioning.

The rest of this chapter is organized as follows. We begin by motivating sensor selection for WLAN-based positioning (Section 8.1). We then proceed to discuss several methods for access point and anchor point selection (Sections 8.2 and 8.3). We conclude this chapter by illustrating the benefits of sensor selection using experimental data (Section 8.4).

Motivation

In WLAN-positioning, information from multiple anchor points and access points is fused to form a position estimate. Careful selection of the sensors that contribute to positioning can benefit RSS-based positioning in two ways.

The theory of error-correcting codes comes from the need to protect information from corruption during transmission or storage. Take your CD or DVD as an example. Usually, you might convert your music into MP3 files for storage. The reason for such a conversion is that MP3 files are more compact and take less storage space, i.e. they use fewer binary digits (bits) compared with the original format on CD. Certainly, the price to pay for a smaller file size is that you will suffer some kind of distortion, or, equivalently, losses in audio quality or fidelity. However, such loss is in general indiscernible to human audio perception, and you can hardly notice the subtle differences between the uncompressed and compressed audio signals. The compression of digital data streams such as audio music streams is commonly referred to as source coding. We will consider it in more detail in Chapters 4 and 5.

What we are going to discuss in this chapter is the opposite of compression. After converting the music into MP3 files, you might want to store these files on a CD or a DVD for later use. While burning the digital data onto a CD, there is a special mechanism called error control coding behind the CD burning process. Why do we need it? Well, the reason is simple. Storing CDs and DVDs inevitably causes small scratches on the disk surface.

Up to this point we have been concerned with coding theory. We have described codes and given algorithms of how to design them. And we have evaluated the performance of some particular codes. Now we begin with information theory, which will enable us to learn more about the fundamental properties of general codes without having actually to design them.

Basically, information theory is a part of physics and tries to describe what information is and how we can work with it. Like all theories in physics it is a model of the real world that is accepted as true as long as it predicts how nature behaves accurately enough.

In the following we will start by giving some suggestive examples to motivate the definitions that follow. However, note that these examples are not a justification for the definitions; they just try to shed some light on the reason why we will define these quantities in the way we do. The real justification of all definitions in information theory (or any other physical theory) is the fact that they turn out to be useful.

Motivation

We start by asking the question: what is information?

Let us consider some examples of sentences that contain some “information.”

• The weather will be good tomorrow.

• The weather was bad last Sunday.

• The president of Taiwan will come to you tomorrow and will give you one million dollars.

Since the first WLAN-positioning system was introduced in 2000 [4], rapid advances in signal processing methods have been made in this area. A decade later, fundamental positioning techniques have matured significantly, allowing these systems to offer highly accurate positioning estimates with accuracies on the order of several meters in both indoor and outdoor environments.

The previous chapters have reviewed the fundamental techniques used in WLAN positioning. In this chapter, we look ahead to opportunities and challenges remaining to be addressed in this area.

Highlights

The focus of this book has been WLAN-based positioning. Chapters 1 to 4 discussed the history, applications, and various positioning systems to motivate these systems. In particular, the development of these systems is motivated by the need for accurate, reliable, and cost-efficient positioning solutions to enable the delivery of location-based services (LBS).

The second part of the book was dedicated to fundamental signal processing concepts in these systems. In Chapter 5, we saw that the unpredictability of radio signal features poses a significant challenge to the development of accurate and reliable WLAN systems. In Chapter 6, we discussed a number of non-parametric techniques that can be used to model these radio signals using training samples collected at a set of anchor points with known locations. In addition to their effectiveness as modeling tools, these nonparametric techniques also allowed the estimation of a measure of uncertainty associated with position estimates.

We end this introduction to coding and information theory by giving two examples of how coding theory relates to quite unexpected other fields. Firstly we give a very brief introduction to the relation between Hamming codes and projective geometry. Secondly we show a very interesting application of coding to game theory.

Hamming code and projective geometry

Though not entirely correct, the concept of projective geometry was first developed by Gerard Desargues in the sixteenth century for art paintings and for architectural drawings. The actual development of this theory dated way back to the third century to Pappus of Alexandria. They were all puzzled by the axioms of Euclidean geometry given by Euclid in 300 BC who stated the following.

1. (1) Given any distinct two points in space, there is a unique line connecting these two points.

2. (2) Given any two nonparallel lines in space, they intersect at a unique point.

3. (3) Given any two distinct parallel lines in space, they never intersect.

The confusion comes from the third statement, in particular from the concept of parallelism. How can two lines never intersect? Even to the end of universe?

In your daily life, the two sides of a road are parallel to each other, yet you do see them intersect at a distant point. So, this is somewhat confusing and makes people very uncomfortable. Revising the above statements gives rise to the theory of projective geometry.