Edge Position Modulation for Wireless Infrared Communications

Edge Position Modulation

for Wireless Infrared Communications

Der Technischen Fakultät der

Universität Erlangen-Nürnberg

zur Erlangung des Grades

DOKTOR-INGENIEUR

vorgelegt von

Thomas Lüftner

Erlangen - 2005

Als Disseration genehmigt von

der Technischen Fakultät der

Universität Erlangen-Nürnberg

Tag der Einreichung: 18. April 2005

Tag der Promotion: 1. August 2005

Dekan: Prof. Dr. rer. nat. Albrecht Winnacker

Berichterstatter: Prof. Dr.-Ing. Dr.-Ing.habil. Robert Weigel

Prof. Dr.-Ing. Richard Hagelauer

Pulsflanken Positions Modulation

für drahtlose Infrarot-Kommunikation

Thomas Lüftner

Erlangen - 2005

Ich widme diese Arbeit meiner liebevollen Freundin Birgit und meiner großartigen Familie:

meinem Vater Alfred und meiner Mutter Gabriele, meinem Bruder Markus und seiner Frau

Silvia und deren Kindern Moritz und Elena, und meinem Opa Willy und meiner Oma Maria.

Thomas

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vi

Einleitung

Getrieben von der Infrared Data Association (IrDA) wurde die drahtlose Infrarot-

Kommunikation in den letzten Jahren zu einer sehr populären und weit verbreiteten Methode zur

Kurzstrecken-Datenübertragung zwischen mobilen Geräten wie Laptops, PDAs und

Mobiltelefonen. Aufgrund der "Point & Shoot"-Eigenschaft zeichnet sich IrDA im Besonderen

bei Anwendungen aus, die einen schnellen Verbindungsaufbau erfordern. Dabei übertrifft es

andere Lösungen wie die Funkübertragung entsprechend dem Standard "Bluetooth" oder die auf

dem Standard "Universal Serial Bus (USB)" basierende Datenübertragung mittels Kabel.

Qualität und Geschwindigkeit der Infrarot-Kommunikation sind im Wesentlichen durch die

Bandbreite des Infrarot-Transceivers limitiert. Daher ist es wichtig eine Modulationstechnik mit

hoher Bandbreiteneffizienz zu verwenden und dabei gleichzeitig eine niedrige Bitfehlerrate und

eine hohe Leistungseffizienz aufrecht zu erhalten. Konsequenterweise hat die IrDA die

Modulationstechniken ihrer Standards kontinuierlich verbessert. Es wurden schrittweise die

Verfahren "Return to Zero Inverted (RZI)" für die "Serial Infrared (SIR)"-Datenübertragung, "4

Pulse Position Modulation (4-PPM)" für die "Fast Infrared (FIR)"-Datenübertragung und

"HHH(1,13)" für die neueste "Very Fast Infrared (VFIR)"-Datenübertragung eingeführt. Die

vorliegende Arbeit soll mit dem Verfahren "Edge Position Modulation (EPM)" eine neuartige

Modulationstechnik präsentieren, die eine verbesserte Bandbreiteneffizienz und eine

verbesserte Leistungseffizienz gegenüber den oben genannten Verfahren besitzt. Diese neue

Modulationstechnik soll auf die Eigenschaften des drahtlosen Infrarotkanals optimierbar sein

und soll dadurch auch eine niedrige Bitfehlerrate aufrechterhalten können.

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viii

Zusammenfassung

Das einführende Kapitel 1 gibt nach einer kurzen Motivation einen Einblick in die Historie und

in den Stand der Technik der drahtlosen Infrarot-Kommunikation. In diesem Kapitel wird der

IrDA Standard vorgestellt und als Referenz für die darauf folgende Arbeit definiert. Die

Anforderungen an die Modulationstechnik für eine zuverlässige Datenübertragung werden

durch die Eigenschaften des drahtlosen Infrarotkanals bestimmt. Daher präsentiert Kapitel 2 die

Komponenten der physikalischen Schicht eines IrDA-Übertragungssystems und die

wesentlichen Eigenschaften der optischen Verbindung. Damit wird dann ein einfaches

mathematisches Modell des drahtlosen Infrarotkanals hergeleitet. Kapitel 3 bereitet dann die

theoretischen Grundlagen der Modulation und Demodulation durch eine generische

mathematische Beschreibung der involvierten Signale und Kodierungsschritte auf. Daraus

werden dann die grundsätzlichen Bewertungskriterien für die Modulationstechniken hergeleitet

und bestimmt. Die Bewertungskriterien werden die Bandbreiteneffizienz, die Leistungseffizienz

und die Fehlerübertragungsrate sein. Als Referenz für EPM präsentiert Kapitel 4 die wichtigsten

auf Puls-Positions-Modulation basierenden Techniken, die zurzeit in den diversen drahtlosen

Infrarot-Übertragungssystemen für mobile Geräte eingesetzt werden. Im Besonderen werden

die Modulationsverfahren, die von den IrDA-Standards verwendet werden, anhand der

Bewertungskriterien aus Kapitel 3 bewertet, wobei für die Evaluierung der

Fehlerübertragungsrate das Kanalmodell aus Kapitel 2 verwendet wird. Die neuartige

Modulationstechnik EPM wird dann in Kapitel 5 eingeführt. Nach der Präsentation der

grundlegenden Idee hinter EPM werden die erreichbaren Bandbreiteneffizienzen für

verschiedene Varianten von EPM hergeleitet. Es wird aufgezeigt, dass die Variante

EPM(5,12,1/3,1) eine viel versprechende Alternative zu den zurzeit verwendeten Methoden ist

und daher analysiert Kapitel 6 diese EPM-Variante näher im Detail. Zuerst werden die

prinzipiellen Modulations- und Demodulationsschritte von EPM(5,12,1/3,1) beschrieben und

dann wird ein neuartiger "1/3-Rate RLL(5,12) Code" eingeführt, der die Realisierung der

EPM(5,12,1/3,1)-Modulationstechnik ermöglicht. (Die Generierung dieses RLL(5,12)-Codes

wird im Anhang A beschrieben.) Anschließend werden die Bewertungskriterien angewandt,

wobei gezeigt wird, dass EPM(5,12,1/3,1) nicht nur eine exzellente Bandbreiteneffizienz

aufweist, sondern auch eine verbesserte Leistungseffizienz besitzt und auch die

Fehlerübertragungsrate konkurrenzfähig ist. Dann wird gezeigt, wie EPM(5,12,1/3,1) in ein

IrDA konformes Infrarot-Kommunikationssystem integriert werden kann. Schließlich wird in

ix

Kapitel 6 noch der angefertigte HW-Prototyp mit den entsprechenden Messergebnissen

präsentiert, wodurch die Funktionalität von EPM(5,12,1/3,1) nachgewiesen wird. Abschließend

wird in Kapitel 7 ein Vergleich zwischen den Leistungsfähigkeiten der einzelnen

Modulationsverfahren gebracht. Als Konklusion werden im Besonderen die Vorteile und

Nachteile des neuartigen EPM-Verfahrens zusammengefasst und hervorgehoben.

x

Inhaltsangabe

KAPITEL 1 Einleitung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Motivation and Ziele der Arbeit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

1.2 Geschichte der drahtlosen Infrarot-Kommunikation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

1.3 Stand der Technik. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4

KAPITEL 2 Drahtloser Infrarotkanal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1 Definition des drahtlosen Infrarotkanals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

2.2 Optischer Link . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

2.3 Sender Front-End . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20

2.4 Empfänger Front-End. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26

2.5 Basisband Modell des drahtlosen Infrarotkanals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32

KAPITEL 3 Elektrische Modulation und Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.1 Elektrische Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44

3.2 Electrische Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48

3.3 Bewertungskriterien der Modulations Techniken . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55

KAPITEL 4 Puls-Positions basierte Modulation Verfahren . . . . . . . . . . . . . . . . . . . . . . 67

4.1 Return to Zero Inverted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67

4.2 N - Pulse Position Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74

4.3 Run-Length-Limited Code Modulation RLL(d,k) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83

KAPITEL 5 Pulseflanken Positions Modulation (EPM). . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.1 Grundlagen von EPM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95

5.2 Theorie der RLL Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101

5.3 EPM Bandbreiten Effizienz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .112

5.4 EPM Varianten . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113

KAPITEL 6 EPM(5,12,1/3,1) - Implementierungsbeispiel . . . . . . . . . . . . . . . . . . . . . . . 117

6.1 EPM(5,12,1/3,1) Bewertung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117

6.2 System Implementierung mit EPM(5,12,1/3,1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .126

6.3 HW Prototyp und Messergebnisse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .147

KAPITEL 7 Konklusion and Ausblick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

ANHANG A RLL(5,12) Generierung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

A.1 Encoder Generierung. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .155

A.2 Decoder Generierung. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .165

Literaturverzeichnis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

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xii

Abstract

Driven by the Infrared Data Association (IrDA) wireless infrared communication has become a

very popular and widely used method for short range data transmission between mobile devices

like laptops, PDAs and mobile phones. Especially at ad-hoc connection applications IrDA excels

radio based solutions like Bluetooth or cable based solutions like Universal Serial Bus (USB),

due to the point-and-shoot characteristic of infrared communication. Quality and speed of

infrared communications are mainly limited by the bandwidth of the infrared transceivers.

Therefore it is important to use a modulation technique with high bandwidth efficiency, while

simultaneously maintaining low bit error rate and high power efficiency. Consequently, IrDA

has continuously improved the modulation techniques of its standards by introducing Return to

Zero Inverted (RZI) for the Serial Infrared (SIR) standard, 4 Pulse Position Modulation (4-PPM)

for the Fast Infrared (FIR) standard and HHH(1,13) for the latest Very Fast Infrared (VFIR)

standard.

This thesis shall present a novel modulation scheme called Edge Position Modulation (EPM),

which offers both increased bandwidth efficiency and increased power efficiency over the

previous methods. The novel modulation technique shall be capable to be optimized to the

characteristics of the wireless infrared channel, and thereby it shall also maintain low bit error

rates.

For that the introductory Chapter 1 of this thesis gives, after a short motivation for this thesis, a

brief insight in the history and in the state of the art of wireless infrared communications. In this

chapter the IrDA standard is introduced and defined as reference for the following work. The

modulation technique requirements for reliable data transmission are determined by the

characteristics of the wireless infrared channel. Therefore Chapter 2 presents the basic

components of the physical layer of an IrDA transmission system and the characteristics of the

optical link. From that a simple mathematical model of the wireless infrared channel is derived.

Chapter 3 provides the theoretical background for the modulation and demodulation processes

by a generic mathematical description of the involved signals and codecs. From that the basic

evaluation criteria for modulation techniques are then derived and defined. The evaluation

criteria will be bandwidth efficiency, power efficiency and transmission reliability measured in

bit error rate. As reference for EPM Chapter 4 presents the most important pulse position based

xiii

modulation techniques, which are currently used in the various wireless infrared transmission

systems for mobile devices. In particular the modulation techniques used by IrDA are assessed

by means of the evaluation criteria of Chapter 3, whereby for the evaluation of the transmission

reliability the channel model of Chapter 2 is applied. The novel modulation technique EPM is

then introduced in Chapter 5. After the presentation of the basic idea of EPM the achievable

bandwidth efficiencies for different variations of EPM are derived. It is revealed that the variant

EPM(5,12,1/3,1) is a promising alternative to the currently used modulation techniques.

Therefore Chapter 6 analyses this EPM variant in more detail. At first the modulation and

demodulation flows of EPM(5,12,1/3,1) are described and a novel 1/3-rate RLL(5,12) code is

introduced that enables the EPM(5,12,1/3,1) modulation scheme. (The generation of this

RLL(5,12) code is provided in the Appendix A of this work.) Then the evaluation criteria are

applied, whereby it is shown that EPM(5,12,1/3,1) provides not only an excellent bandwidth

efficiency, but also an improved power efficiency and a competitive transmission reliability.

Then it is shown how EPM(5,12,1/3,1) could be integrated in an IrDA compliant infrared

communication system. Eventually in Chapter 6 the HW prototype and the corresponding

measurement results are presented that have proven the functionality of EPM(5,12,1/3,1).

Finally, the conclusion of Chapter 7 provides a comparison of the capabilities of the different

modulation techniques presented in this work. In particular the advantages and disadvantages of

the novel EPM are summarized and highlighted.

xiv

Acknowledgment

I would like to express my acknowledgement to those people and institutions who have enabled

me with their support to write this dissertation.

I want to thank my sponsors Univ.-Prof. Dr. Robert Weigel from the Friedrich-Alexander

University Erlangen-Nuremberg, Germany, and Univ.-Prof. Dr. Richard Hagelauer from the

Johannes Kepler University Linz, Austria. I want to take this opportunity to express my

appreciation about their great attitude to promote and challenge young engineers as they have

done it with me so far. I am very lucky to have them as sponsors.

Then I want to express my acknowledgement to Infineon Technologies and to DICE, the

Infineon Design Center in Linz, where I am employed. During the last four years I have always

got the support and freedom to work on my thesis besides my full-time employment, and

therefore I am very grateful to my line managers Dr. Markus Schutti (DICE) and Dr. Matthias

Sauer (Infineon). My special thank goes to Univ.-Prof. Dr. Josef Hausner, who was during his

time at Infineon always a great mentor for me, and I wish him all the best in his new profession

as professor at the University of Bochum.

Furthermore I am very much indebted to Dipl.-Ing. Hans Margiol and Dipl.-Ing. Christian

Kröpl, whose diploma theses have been a very valuable contribution to my thesis. It was a

pleasure for me to work with them. The thesis of Christian is incorporated in this thesis in the

Chapter 2 about the wireless infrared channel. The work of Hans was very much the basis for

the HW prototype described in Section 6.3.

My thank goes also to the students of the University of Applied Sciences of Upper Austria in

Hagenberg, who implemented my novel modulation technique in VHDL during a practical

course and thereby significantly contributed to the HW prototyping. In particular I want to thank

Dipl.-Ing.(FH) Thomas Pühringer who has performed the measurements shown in Section 6.3.

Finally I am especially grateful to Univ.-Prof. Dr. Mario Huemer, who encouraged me during

his time at DICE to write this thesis. Furthermore he gave me a lot of valuable hints of how to

write papers and how to approach the dissertation at all.

Linz, April 2005 Thomas Lüftner

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xvi

Table of Content

CHAPTER 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Motivation and Goals of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

1.2 History of Wireless Infrared Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

1.3 State of the Art at Wireless Infrared Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4

1.3.1 Optical Link Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5

1.3.2 Optical Modulation / Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

1.3.3 Electrical Modulation / Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

1.3.4 Overview of IrDA's Wireless Infrared Communications System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

CHAPTER 2 Wireless Infrared Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1 Definition of Wireless Infrared Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

2.2 Optical Link . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

2.2.1 Basics of Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

2.2.1.1 What is Infrared Light?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

2.2.1.2 Energy related Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

2.2.2 Directed LOS Link according to IrDA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

2.2.3 Ambient Radiation and Optical Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

2.2.4 Optical Link Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18

2.2.4.1 Path Loss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19

2.2.4.2 Ambient Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20

2.3 Transmitter Front-End . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20

2.3.1 Transmitter Front-End Circuitry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20

2.3.2 Intensity Modulation by LEDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21

2.3.2.1 Basic Functionality of LEDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21

2.3.2.2 Radiant Intensity versus Induced Diode Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24

2.3.3 Transfer Function of Transmitter Front-End . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25

2.4 Receiver Front-End . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26

2.4.1 Receiver Front-End Circuitry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26

2.4.2 Direct Detection by Photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26

2.4.2.1 Basic Functionality of Photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27

2.4.2.2 Photocurrent versus Irradiance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28

2.4.3 Transfer Function of Receiver Front-End . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30

2.4.4 Receiver Noise Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31

2.4.4.1 Shot Noise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31

2.4.4.2 Amplifier Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31

2.5 Baseband Model of Wireless Infrared Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32

2.5.1 General Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32

2.5.2 Reference Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34

2.5.2.1 Time Constant of Transmitter Front-End . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34

2.5.2.2 Gain Factor KTXFE of Transmitter Front-End . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35

2.5.2.3 Path Loss of Optical Link . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35

2.5.2.4 Ambient Radiation of Optical Link . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36

2.5.2.5 Responsivity R of Receiver Front-End. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37

2.5.2.6 Time Constants of Receiver Front-End . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37

2.5.2.7 Receiver Front-End Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38

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2.5.3 Reference Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.5.4 Impulse Response of Reference Channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

CHAPTER 3 Electrical Modulation and Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.1 Electrical Modulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.1.1 Encoder Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.1.2 Pulse Shaper Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.2 Electrical Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.2.1 Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.2.2 Sampling and Receiver Clock Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.2.3 Decoder Function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.3 Evaluation Criteria for Modulation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.3.1 Reliability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.3.1.1 Quantization Error Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.3.1.2 Sampling Error Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.3.2 Bandwidth Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.3.3 Power Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

CHAPTER 4 Pulse Position based Modulation Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.1 Return to Zero Inverted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.1.1 1/4-RZI Modulation Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.1.2 1/4-RZI Demodulation Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.1.3 Reliability of 1/4-RZI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71



4.1.4 Bandwidth Efficiency of 1/4-RZI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.1.5 Power Efficiency of 1/4-RZI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.2 N - Pulse Position Modulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.2.1 4-PPM Modulation Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.2.2 4-PPM Demodulation Scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.2.3 Reliability of 4-PPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79



4.2.4 Bandwidth Efficiency of 4-PPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.2.5 Power Efficiency of 4-PPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.3 Run-Length-Limited Code Modulation RLL(d,k) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.3.1 HHH(1,13) Modulation Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.3.2 HHH(1,13) Demodulation Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.3.3 Reliability of HHH(1,13) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90



4.3.4 Bandwidth Efficiency of HHH(1,13). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

4.3.5 Power Efficiency of HHH(1,13) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

CHAPTER 5 Edge Position Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.1 Basics of EPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.2 RLL Codes in Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.2.1 State Transition Matrix of RLL(d,k) Codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.2.2 Capacity C(d,k) of RLL Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

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5.2.3 RLL Code Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105

5.3 EPM Bandwidth Efficiency in General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .112

5.4 EPM Variants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113

5.4.1 EPM Implementation Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113

5.4.1.1 Implementation Requirement for r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113

5.4.1.2 Implementation Requirements for Tchip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .114

5.4.1.3 Implementation Requirement for k. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .114

5.4.1.4 Implementation Requirement for RLL Code Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .115

5.4.2 Selected EPM Variants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .115

CHAPTER 6 EPM(5,12,1/3,1) - Implementation Example. . . . . . . . . . . . . . . . . . . . . . . 117

6.1 EPM(5,12,1/3,1) Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117

6.1.1 EPM(5,12,1/3,1) Modulation Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117

6.1.2 EPM(5,12,1/3,1) Demodulation Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .120

6.1.3 Reliability of EPM(5,12,1/3,1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .122

6.1.3.1 Quantization Error Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .122

6.1.3.2 Sampling Error Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .123

6.1.4 Bandwidth Efficiency of EPM(5,12,1/3,1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .126

6.1.5 Power Efficiency of EPM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .126

6.2 System Implementation with EPM(5,12,1/3,1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .126

6.2.1 System Impact of EPM Extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .126

6.2.2 Infrared Controller with EPM Extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .127

6.2.2.1 CRC Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .127

6.2.2.2 Modulation Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .128

6.2.2.3 Synchronization Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .129

6.2.2.4 Demodulation Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .129

6.2.2.5 Bus Interface Unit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .129

6.2.3 Clock Recovery and Edge Detection for EPM(5,12,1/3,1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .129

6.2.3.1 Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .131

6.2.3.2 Digital PLL for EPM(5,12,1/3,1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .131

6.2.3.3 Sampling and Edge Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .138

6.2.3.4 Manner of Operation for Clock Phase Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .138

6.2.3.5 Sampling Clock Phase Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .144

6.2.4 Framing Structure for EPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145

6.3 HW Prototype and Measurements Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .147

6.3.1 HW Prototype Implementation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .147

6.3.2 Measured Eye Diagrams after Quantization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .148

6.3.3 Measured Frame Processing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .149

CHAPTER 7 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

APPENDIX A RLL(5,12) Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

A.1 Encoder Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .155

A.2 Decoder Generation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .165

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

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xx

List of Figures

CHAPTER 1 Introduction ...................................................................................................... 1

Figure 1-1. Wireless Optical Communications System of A.G. Bell (1880) .................................................3Figure 1-2. Wireless Infrared Communications System.................................................................................5Figure 1-3. Classification of Optical Links ....................................................................................................6Figure 1-4. Physical Layer according to IrDA Standard ................................................................................8Figure 1-5. System Architecture.....................................................................................................................9Figure 1-6. Infrared Transceiver .....................................................................................................................9

CHAPTER 2 Wireless Infrared Channel ............................................................................ 11

Figure 2-1. Wireless Infrared Channel .........................................................................................................11Figure 2-2. Principle of Absorption and Emission of Photons.....................................................................12Figure 2-3. Electromagnetic Spectrum.........................................................................................................14Figure 2-4. Radiant Intensity Illustration......................................................................................................15Figure 2-5. Directed LOS Link according to IrDA ......................................................................................17Figure 2-6. Normalized Power Spectra of Ambient Infrared Radiation Sources .........................................18Figure 2-7. Optical Link Model....................................................................................................................19Figure 2-8. TX Path of an Infrared Transceiver............................................................................................20Figure 2-9. LED in Thermal-Equilibrium Condition ...................................................................................22Figure 2-10. LED in Forward Biased Condition ..........................................................................................23Figure 2-11. Emission Spectrum of LEDs....................................................................................................24Figure 2-12. Normalized Radiant Intensity vs. Angular Displacement........................................................25Figure 2-13. Receiver Front-End ..................................................................................................................26Figure 2-14. Cross-Section View of p-i-n Photodiode under Reverse Bias .................................................27Figure 2-15. Operation of a p-i-n Photodiode ..............................................................................................28Figure 2-16. Normalized Responsivity of a Si Diode and a Ge Diode.........................................................30Figure 2-17. Baseband Model of Wireless Infrared Channel .......................................................................32Figure 2-18. Settling Time of the High-Pass Filter due to Disturbance EAmbient......................................33Figure 2-19. Steady State Baseband Model of Wireless Infrared Channel ..................................................33Figure 2-20. Reference Channel Model........................................................................................................38Figure 2-21. Reference Channel Model in Steady State...............................................................................39Figure 2-22. Reference Input Pulse ..............................................................................................................40Figure 2-23. Impulse Response after the Transmitter Front-End .................................................................40Figure 2-24. Impulse Response after Transmitter Front-End and Optical Link...........................................41Figure 2-25. Impulse Response of complete Wireless Infrared Channel .....................................................41Figure 2-26. Settling Time of the High-Pass Filter of the Receiver Front-End............................................42

CHAPTER 3 Electrical Modulation and Demodulation .................................................... 43

Figure 3-1. Binary-Level Electrical Modulation and Demodulation............................................................43Figure 3-2. Electrical Modulation Process ...................................................................................................45Figure 3-3. Electrical Demodulation Process ...............................................................................................50Figure 3-4. Transfer Function of the Quantization Unit ...............................................................................50Figure 3-5. Pulse Extension due to Imprecise Threshold .............................................................................51Figure 3-6. Output of the Binary Level Quantization with Ideal Threshold ................................................52Figure 3-7. Receiver Clock Recovery and Sampling....................................................................................53Figure 3-8. Probability Density Function p0k and p1k ................................................................................58Figure 3-9. Eye Diagram after Receiver Front-End without Noise..............................................................61Figure 3-10. Sample Error: Pulse not Sampled by Corresponding Sample Beat .........................................62Figure 3-11. Sample Error: Pulse Mistakenly Sampled by Next Sample Beat ............................................63

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Figure 3-12. Horizontal Eye Opening of rb(t) ............................................................................................ 63

CHAPTER 4 Pulse Position based Modulation Schemes ................................................... 67

Figure 4-1. 1/4-RZI Modulation .................................................................................................................. 69Figure 4-2. 1/4-RZI Eye Diagram of r(t) after Receiver Front-End............................................................. 70Figure 4-3. 1/4-RZI Demodulation .............................................................................................................. 70Figure 4-4. 1/4-RZI Bit Error Probability due to Quantization Errors ........................................................ 71Figure 4-5. 1/4-RZI Eye Diagram of r(t) without Noise under Worst Case Condition................................ 72Figure 4-6. 1/4-RZI Eye Diagram of rb(t) after Quantization Unit ............................................................. 73Figure 4-7. 4-PPM Modulation .................................................................................................................... 77Figure 4-8. 4-PPM Eye Diagram of r(t) after Receiver Front-End .............................................................. 77Figure 4-9. 4-PPM Error Correction ............................................................................................................ 78Figure 4-10. 4-PPM Demodulation.............................................................................................................. 79Figure 4-11. 4-PPM Bit Error Probability due to Quantization Errors ........................................................ 80Figure 4-12. 4-PPM Eye Diagram of r(t) without Noise under Worst Case Condition ............................... 81Figure 4-13. 4-PPM Eye Diagram of rb(t) after Quantization Unit ............................................................. 82Figure 4-14. HHH(1,13) Modulation ........................................................................................................... 86Figure 4-15. HHH(1,13) Eye Diagram of r(t) after Receiver Front-End ..................................................... 87Figure 4-16. HHH(1,13) Single-Pulse Correction ....................................................................................... 87Figure 4-17. HHH(1,13) Demodulation....................................................................................................... 89Figure 4-18. HHH(1,13) Bit Error Probability due to Quantization Errors ................................................. 90Figure 4-19. HHH(1,13) Eye Diagram of r(t) without Noise under Worst Case Condition ........................ 91Figure 4-20. HHH(1,13) Eye Diagram of rb(t) after Quantization Unit ...................................................... 92

CHAPTER 5 Edge Position Modulation .............................................................................. 95

Figure 5-1. Principle of Pulse Position Modulation Techniques.................................................................. 95Figure 5-2. Principle of Edge Position Modulation Techniques .................................................................. 96Figure 5-3. EPM Modulator Components with Corresponding Signals ...................................................... 97Figure 5-4. EPM Demodulator Components with Corresponding Signals.................................................. 98Figure 5-5. Lower Limit of Time Slot Duration Tchip ................................................................................ 99Figure 5-6. EPM with r = 1, d = 5 and k = 10............................................................................................ 100Figure 5-7. State Transition Diagram of RLL(d,k) Codes ......................................................................... 101Figure 5-8. State Transition Diagram of RLL(d,) Codes ........................................................................... 103Figure 5-9. RLL Code Capacity CRLL(d,k) versus d and k ...................................................................... 106Figure 5-10. RLL(1,3) Transition Diagram ............................................................................................... 107Figure 5-11. Final State Transition Diagram 1/2-rate RLL(1,3)................................................................ 110Figure 5-12. Maximum Bandwidth Efficiency of EPM with r = 1 ........................................................... 113

CHAPTER 6 EPM(5,12,1/3,1) - Implementation Example .............................................. 117

Figure 6-1. EPM(5,12,1/3,1) Modulation .................................................................................................. 120Figure 6-2. EPM(5,12,1/3,1) Eye Diagram of r(t) after the Receiver Front-End....................................... 120Figure 6-3. Edge Detection for EPM(5,12,1/3,1)....................................................................................... 121Figure 6-4. EPM(5,12,1/3,1) Demodulation .............................................................................................. 123Figure 6-5. EPM(5,12,1/3,1) Bit Error Probability due to Quantization Errors ........................................ 124Figure 6-6. EPM(5,12,1/3,1) Eye Diagram of r(t) without Noise under Worst Case Condition ............... 124Figure 6-7. EPM(5,12,1/3,1) Eye Diagram after Quantization Unit.......................................................... 125Figure 6-8. IrDA Compliant Infrared Communication System ................................................................. 127Figure 6-9. IrDA Compliant Infrared Controller with EPM(5,12,1/3,1) Extension .................................. 128Figure 6-10. Clock Recovery and Edge Detection Circuitry for EPM(5,12,1/3,1).................................... 130Figure 6-11. Synchronization of Input Signal rb(t).................................................................................... 131Figure 6-12. DPLL Circuitry...................................................................................................................... 132Figure 6-13. Phase Detector Behavior at Phase Lock when 2nd MSB = ’1’............................................. 132

xxii

Figure 6-14. Phase Detector Behavior at Phase Lock when 2nd MSB = ’0’ .............................................133Figure 6-15. Phase Detector Behavior at a Phase Error of Tsysclk/2 when 2nd MSB = ’1’ .....................133Figure 6-16. Phase Detector Behavior at a Phase Error of Tsysclk/2 when 2nd MSB = ’0’ .....................134Figure 6-17. Phase Detector Behavior at a Phase Error of Tsysclk when 2nd MSB = ’1’.........................134Figure 6-18. Phase Detector Behavior at a Phase Error of Tsysclk when 2nd MSB = ’0’.........................135Figure 6-19. Phase Detector Behavior at a Phase Error of -Tsysclk/2 when 2nd MSB = ’1’ ....................135Figure 6-20. Phase Detector Behavior at a Phase Error of -Tsysclk/2 when 2nd MSB = ’0’ ....................136Figure 6-21. Phase Detector .......................................................................................................................136Figure 6-22. Sampling and Edge Detection................................................................................................138Figure 6-23. Clock Recovery with Average Phase Offset Tsysclk/2 and with 2nd MSB = ’1’ .................139Figure 6-24. Clock Recovery with Average Phase Offset Tsysclk and with 2nd MSB = ’1’.....................140Figure 6-25. Clock Recovery with Average Phase Offset -Tsysclk/2 and with 2nd MSB = ’1’ ................141Figure 6-26. Clock Recovery with Average Phase Offset Tsysclk/2 and with 2nd MSB = ’0’ .................142Figure 6-27. Clock Recovery with Average Phase Offset Tsysclk and with 2nd MSB = ’0’.....................143Figure 6-28. Clock Recovery with Average Phase Offset -Tsysclk/2 and with 2nd MSB = ’0’ ................144Figure 6-29. EPM modulation and packet Generation Flow ......................................................................146Figure 6-30. FPGA Board Description.......................................................................................................147Figure 6-31. Piggyback Prototype with FPGA Board and ARM7 Evaluation Board ................................148Figure 6-32. Measuring Setup for Eye Diagram Measuring ......................................................................148Figure 6-33. Eye Diagram after Quantization at d = 5cm, phi = 0° ...........................................................149Figure 6-34. Eye Diagram after Quantization at d = 10 cm, phi = 30° ......................................................149Figure 6-35. Eye Diagram after Quantization at d = 100 cm, phi = 0° ......................................................150Figure 6-36. Measuring Setup for Frame Processing Measuring ...............................................................150Figure 6-37. Measurement Results of Logic Analyzer...............................................................................151

CHAPTER 7 Conclusion and Outlook............................................................................... 153

APPENDIX A RLL(5,12) Generation ................................................................................ 155

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xxiv

List of Tables

CHAPTER 1 Introduction ...................................................................................................... 1

CHAPTER 2 Wireless Infrared Channel ............................................................................ 11

Table 2-1. Reference Parameters Overview..................................................................................................39

CHAPTER 3 Electrical Modulation and Demodulation .................................................... 43

CHAPTER 4 Pulse Position based Modulation Schemes................................................... 67

Table 4-1. Encoding Table for 4-PPM ..........................................................................................................75Table 4-2. Decoding Table for 4-PPM..........................................................................................................78

CHAPTER 5 Edge Position Modulation.............................................................................. 95

Table 5-1. RLL Code Capacity C(d,k)........................................................................................................105Table 5-2. State Transition Table D2 ..........................................................................................................108Table 5-3. Splitting Step 0 ..........................................................................................................................108Table 5-4. Splitting Step 1 ..........................................................................................................................109Table 5-5. Encoding Table ..........................................................................................................................109Table 5-6. Reduction of Encoding Table ....................................................................................................110Table 5-7. Final Reduced Encoding Table..................................................................................................110Table 5-8. Decoding Table..........................................................................................................................111Table 5-9. EPM Variants.............................................................................................................................115

CHAPTER 6 EPM(5,12,1/3,1) - Implementation Example.............................................. 117

Table 6-1. Value Table of Phase Detector Logic ........................................................................................137Table 6-2. Phase Shift of Sample Clock .....................................................................................................137Table 6-3. Description of Measured Signals...............................................................................................150

CHAPTER 7 Conclusion and Outlook............................................................................... 153

Table 7-1. Summary of Evaluation Parameters ..........................................................................................154

APPENDIX A RLL(5,12) Generation ................................................................................ 155

Table A-1. State Transition Table D3 .........................................................................................................156Table A-2. Splitting Step 0 .........................................................................................................................157Table A-3. Splitting Step 1 .........................................................................................................................157Table A-4. Splitting Step 2 .........................................................................................................................158Table A-5. Splitting Step 3 .........................................................................................................................159Table A-6. Splitting Step 4 .........................................................................................................................159Table A-7. Encoding Table .........................................................................................................................161Table A-8. First Reduction of Encoding Table ...........................................................................................162Table A-9. Second Reduction of Encoding Table.......................................................................................163Table A-10. Third Reduction of Encoding Table .......................................................................................164Table A-11. Forth Reduction of Encoding Table........................................................................................164Table A-12. Encoder Truth Table ...............................................................................................................165Table A-13. Decoding Table .......................................................................................................................166

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xxvi

1 Introduction

1.1 Motivation and Goals of the Thesis

In recent years mobile digital devices like PDAs, mobile phones, digital cameras, and Laptops

have penetrated the consumer market. All these devices require a powerful short range

communication method for data exchange between each other, for connections with printers or

for local area network (LAN) accesses [2]. Basically, the communication methods can be based

on cable connections, on radio links or on infrared links. Since all of them have their individual

strengths and weaknesses, each type has found its way into the various products [3].

The data exchange via cables is a well established method and especially USB has become a

widely used standard interface. USB excels due to its high baud rates of up to 480 Mbit/s, but

suffers from its limited mobility due to the cable connection [4]. Therefore USB is best for

applications, which require stable high performance connections for transmission of high data

volumes, where mobility is not that important. An example application would be the connection

of a video-conferencing camera with your laptop.

However, mobility is the big advantage of radio based short range communication methods like

Bluetooth, which recently have appeared in many mobile devices. Bluetooth can transmit data

through solid, non-metal objects and supports a nominal link range from 10 cm to 10 m at a

moderate baud rate of up to 721 kbit/s [5]. Because of the nature of radio Bluetooth is a point-

to-multipoint communication system, which supports connections of two devices as well as ad

hoc networking between several devices. But in order to prevent unauthorized access, Bluetooth

requires sophisticated authentication and encryption mechanisms, which hamper a fast

connection establishing. Therefore Bluetooth is best for applications, which require stable point-

to-point or point-to-multipoint connections for data exchange at moderate speed, where mobility

is the key requirement. An example application would be the transmission of audio data from

your mobile phone to your headset.

1

On the contrary to USB and Bluetooth, the infrared transmission based on the IrDA standard

[1][6] enables a fast and simple connection establishing due to its point-and-shoot characteristic.

Together with the high baud rates of up to 16 Mbit/s this makes IrDA transmission perfectly

suited for applications, which require high performance ad hoc point-to-point connections.

Example applications would be the download of pictures from your digital camera on your

laptop or paying your meal in your company’s cafeteria with your mobile phone via the IrDA

port.

In order to provide competitive baud rates, IrDA has continuously improved the modulation

techniques of its standards by introducing Return to Zero Inverted (RZI) for the Serial Infrared

(SIR) standard, 4 Pulse Position Modulation (4-PPM) for the Fast Infrared (FIR) standard and

HHH(1,13)1 for the latest Very Fast Infrared (VFIR) standard [1].

The goal of this thesis is to present in detail a new modulation scheme called Edge Position

Modulation (EPM) with Run-Length-Limited (RLL) coding, which is a consequent further

development of the previous techniques. The basic ideas behind EPM have already been

published in [7], [8], [9] and [10], and have been protected by patent [11] by the author. Basically

EPM shall offer both an increased bandwidth efficiency and an increased power efficiency over

previous methods. Since the novel modulation technique can be optimized to the characteristics

of the wireless infrared channel, it shall also maintain low bit error rates. EPM is intended as a

possible extension of IrDA's physical layer (IrPHY) [1] and shall be transparent for the upper

layers of the IrDA protocol stack [6][12][13][14]. Furthermore it shall be compliant to standard

infrared transceivers [15][16].

1.2 History of Wireless Infrared Communications

[17] Since communication by means of the human voice is insufficient for larger distances,

mankind has always been seeking for alternative ways for information exchange. One

recognized very early that optical signals can be used to overcome large distances very easily.

Therefore the first wide area communication systems were optical ones, like smoking signals,

fire, light-towers, signal-rockets and semaphorical wave-signals.

1. HHH is an abbreviation of the names Hirt, Hassner and Heise, the developers of the code

2

The 19th century was the era of the big discoveries and inventions in the field of communication

science. In 1838 Morse developed the telegraphy with his famous Morse signs. In 1865 Maxwell

developed the theory of electromagnetic radiation, which was verified and improved by Hertz in

1888. Due to further inventions in those years like the telephone of Bell and Gray in 1876, the

artificial electrical light of Edison in 1879, the development of the photo-electrical cell by Bell,

and the radio developments of Marconi and Popov, the reception of information signals was no

longer limited to the human organs of sense.

One of the first wireless communications system with an artificial receiver was an optical system

as illustrated in Figure 1-1 (source: [17]). This system had been introduced by Bell [18] years

before Hertz has verified the existence of electromagnetic waves. The intensity of a beam of

sunlight was modulated by an optical microphone that consists of a vibrating mirror. The

detection was realized by a light-sensitive bar of selenium. The resulting electrical signal was

converted into an audio signal by means of a telephone, which was invented also by Bell some

years before.

Figure 1-1. Wireless Optical Communications System of A.G. Bell (1880)

Although communication over several hundreds of meters was proved, the science community

was concentrating on radio based communication systems in the following years. As radio

systems offers several advantages, such as not being limited by the horizon, interest in optical

systems was very low. Nevertheless, with the development of new electro-optic components in

the 1960s, such as lasers, light-emitting diodes (LED) and photodiodes, the interest in wireless

optical transmission reawakened.

In 1979 Gfellner from IBM recognized that wireless infrared communication is especially suited

for in-door communication and so Gfellner was the first who proposed to build up a wireless

3

LAN by means of diffuse infrared [19]. Gfellner's paper can be considered as the basis for all

wireless infrared in-door communications systems, that have come up since then. (In fact, the

paper was even the first wireless LAN proposal using any medium.)

Also in 1979 the company Hewlett-Packard began to integrate infrared-interfaces in the pocket

calculators for interconnections with printers. From then on many infrared communication

systems penetrated the market and became the heart of almost any remote control system. It soon

became obvious that for interoperability between the devices of different companies an infrared

transmission standard was required. Therefore in 1993 the Infrared Data Association (IrDA) has

been founded by about 50 companies with the purpose of establishing a ubiquitous, low-cost,

point-to-point serial infrared standard. Just one year later in 1994 IrDA published its first

standards. The standard for the physical layer was mainly based on the initial work of Hewlett-

Packard (HP) [20][21] and also the name was taken over from HP: Serial Infrared (SIR). The

Link Access Protocol (IrLAP) standard was based on proposals of IBM [22][23][24]. In the

meantime IrDA has come up with several improvements and extensions of its standards and

almost any shortrange infrared communication system is based on the IrDA standard.

1.3 State of the Art at Wireless Infrared Communications

Wireless infrared communications systems are feasible for a wide range of applications like

remote controls, local area computer networks or inter-satellite communication. However, the

focus of this thesis are short-range, point to point, low power and low cost infrared data

interconnection applications as they are the focus of the IrDA standards [25]. The following

provides classification criteria of the different types of wireless infrared communications

systems and specifies the target configuration for this thesis.

In general, for the transmission of single bits over a physical channel, one has to convert the bits

into signals, which can be reliably transmitted over the channel. This process is performed in the

so called physical layer of a communications system [2]. At the physical layer of wireless

infrared communications systems the conversion is performed in two steps called electrical

modulation and optical modulation [17]. In the electrical modulation process the bit stream is

converted into an electrical waveform, which is adapted to the properties of the optical

modulator that finally converts the electrical signal into an infrared signal. The infrared signal is

4

transmitted via an optical link to the receiver, where the bit stream is retrieved by the consecutive

processes detection and electrical demodulation, which are the counterparts of optical

modulation and electrical modulation. Figure 1-2 provides an overview of the physical layer of

a wireless infrared communications system.

Figure 1-2. Wireless Infrared Communications System

ElectricalModulation

OpticalModulationBinary Source

Binary Sink ElectricalDemodulation Detection

Optical Link

1.3.1 Optical Link Design

The optical link between the optical modulator and the detector can be classified by two

independent criteria [26][27] as shown in Figure 1-3 (source: [17]):

• directed vs. non-directed link design

• Line-of-Sight vs. non-Line-of-Sight link design

Directed links employ directional transmitters and receivers, which must be aimed in order to

establish a link. Non-directed links employ wide-angle transmitters and receivers, alleviating the

need for such pointing. Directed link design maximizes power efficiency, since it minimizes

path loss and reception of ambient light noise. On the other hand, non-directed links may be

more convenient to use, particular for mobile devices, since they do not require aiming each of

the receiver or the transmitter. It is also possible to establish hybrid links, which combine

transmitter and receivers having different degrees of directionality.

5

Figure 1-3. Classification of Optical Links

The second classification criterion relies on the existence of an uninterrupted line-of-sight (LOS)

path between the transmitter and the receiver. LOS links rely on such a path, while non-LOS

links generally rely on reflection of the light from the ceiling or some other diffusely reflecting

surfaces. LOS link design maximizes power efficiency and minimizes multipath distortion.

Non-LOS link design increases link robustness and ease of use, allowing the link to operate even

when barriers stand between the transmitter and receiver.

The greatest robustness and ease of use are achieved by the non-directed-non-LOS link design,

which is often referred to as a diffuse link. However, directed LOS link design require less power

and allow higher baud rates since multi-path distortion is negligible [17] [26]. Both, power

efficiency and high baud rates, are important features of IrDA's target application. Therefore

IrDA uses directed LOS link design and consequently the focus of this thesis will be put on

directed LOS links in the following.

1.3.2 Optical Modulation / Detection

Considering the best type of optical modulation and detection for mobile systems Otte et al. [17]

evidently indicated that intensity (i.e. optical power) modulation and the corresponding direct

detection are preferable against wavelength and polarization modulation techniques with their

6

coherent detection methods. Thus in the following we are assuming an intensity modulation and

direct detection system, which can be simply realized with an LED and a photodiode (PD)

respectively. Barry [26] presented various types of multi-level intensity modulation schemes

like Pulse Amplitude Modulation (PAM). In this thesis only binary-level intensity modulation

(i.e. LED on and LED off) is addressed, since in mobile applications the distance between the

transmitter and the receiver may vary and consequently a sophisticated adaptation of the

received signal power would be necessary in the receiver, which is not really feasible in low cost

devices. Modulation and demodulation are usually performed by digital signal processing, while

intensity modulation and direct detection are obviously analog tasks, which have to be

performed on an extra chip called infrared transceiver [1][28]. Since low cost infrared

transceivers usually perform binary hard decision, the demodulation and equalization techniques

introduced in [27] and [29], which require multi-bit analog to digital conversion, are not useful

for our applications. For that reason we assume, that the infrared transceiver performs a binary

hard decision in the reception path.

1.3.3 Electrical Modulation / Demodulation

In the electrical modulation process the bit stream that needs to be transmitted is converted into

an electrical waveform, which is adapted to the properties of the optical modulator. As

mentioned above the focus of this thesis lies upon binary-level intensity modulation and

consequently only binary-level electrical modulation techniques (i.e. voltage on and voltage off)

are considered here. In the electrical demodulation process the electrical waveform recovered by

the receiver path of the infrared transceiver is converted back into the original bit stream. Since

the infrared transceiver performs binary hard decision we can assume that the input waveform

of the electrical demodulator is identical to the output waveform of the electrical modulator. I.e.

electrical modulation and electrical demodulation are inverse processes. Currently, the

following binary-level electrical modulation techniques are used by IrDA [1]:

• Return-to-Zero Inverted (RZI)

• Pulse-Position-Modulation (PPM)

• Run-Length-Limited Code HHH(1,13)

7

With Edge Position Modulation (EPM) this thesis will present a completely new binary-level

modulation technique.

1.3.4 Overview of IrDA's Wireless Infrared Communications System

A good general overview of the complete wireless infrared communication system based on

IrDA can be found in [25]. However, IrDA has specified the type of the optical link, the optical

modulation and detection scheme and the electrical modulation techniques in its standards

IrPHY [1] and IrLAP [6] as described above1. Figure 1-4 provides an overview of the physical

layer of wireless infrared communications systems according to IrDA's standards. The binary

source and the binary sink represent the data link layer [30] of the transmitter and the receiver,

respectively. Note that each IrDA device is always both transmitter and receiver, since the IrDA

link is bi-directional.

Figure 1-4. Physical Layer according to IrDA Standard


IntensityModulationBinary Source

Binary Sink ElectricalDemodulation

DirectDetection

Directed LOSLink

In order to illustrate how the physical layer is usually implemented, Figure 1-5 shows typical

system architectures of IrDA compliant devices. The data link layer and the upper protocol

layers of a device are basically implemented in software on a CPU. A digital hardware circuitry,

a so called infrared controller, performs the electrical modulation of the TX path as well as the

electrical demodulation of the RX path.

1. The IrLAP standard determines also the data link layer of an IrDA compliant device, i.e. the format of the data packets, the framing of data packets, error detection and error correction.

8

Figure 1-5. System Architecture

CPU CPUIRController

IRController

IR TransceiversDevice A Device B

In Laptops the IR controller is typically implemented by a dedicated chip [31], but e.g. for

mobile phones the IR controller is typically integrated with the CPU in one common chip [32].

All the optical signal processing tasks, including intensity modulation and direct detections, are

usually performed by a so called infrared transceiver (see also Figure 1-6).

Figure 1-6. Infrared Transceiver

9

10

2 Wireless Infrared Channel

2.1 Definition of Wireless Infrared Channel

The purpose of this Chapter 2 is to derive a mathematical baseband model that will be used in

later chapters for the evaluation of the various electrical modulation schemes. For that it is

assumed that the wireless infrared channel comprises the transmitter front-end of the infrared

transceiver, the optical link and the receiver front-end of the infrared transceiver as illustrated in

Figure 2-1 [33][26][17].

Figure 2-1. Wireless Infrared Channel

LED

UTX(t)


IntensityModulation

ElectricalDe-

modulation

DirectDetection

Directed LOSLink

Wireless Infrared Channel

PreamplifierPD

iRX(t)

Optical Filter

Receiver Front-EndTransmitter Front-End Optical Link

11

2.2 Optical Link

2.2.1 Basics of Optics

2.2.1.1 What is Infrared Light?

[34][35] Light in general is radiant energy that is emitted by atoms when they are fed with a

certain amount of energy: At first the induced energy causes a quantum jump of valence

electrons, i.e. they are brought into a higher energy state. This state of atomic excitation is not

stable, so that after a short period of time the excited electrons spontaneously releases the stored

energy and performs a quantum jump back to the origin energy state1. This second step of energy

readjustment can occur by conversion to thermal energy or by the emission of light quantums.

Thus light can be described as a stream of discrete energy packets called photons. The energy of

a photon is equal to the energy difference between the excited and the ground state of the valence

electron that has caused the emission of the photon. A typical energy source that can cause light

emission is induced heat that results in atomic collisions and thereby in atomic excitation. The

creation of light emission by other energies than induced heat, e.g. electrical current, is called

luminescence.

Figure 2-2. Principle of Absorption and Emission of Photons

+

AbsorbedEnergy Quant

Emitted LightQuant (Photon)

1. At semiconductor devices, which are investigated in later sections, the quantum jump from the excited state back to the ground state is equivalent to the recombination process, where electrons moves from the conduction band back to the valence band.

12

Light cannot only be emitted by atoms, but also be absorbed by them. In that process the

absorbed photon brings a valence electron in an excited state1. Figure 2-2 illustrates both the

emission and the absorption process.

Since most of the phenomena of light can be described by the characteristics of waves, light can

also be considered as an electromagnetic wave. The frequency ν of the electromagnetic wave

depends on the energy Wp of the photon:

Wp hν= Eq. 2-1.

with the Plank's constant h

h 4.1356692 15–×10 eVs 6.6260755 34–×10 Js.= = Eq. 2-2.

I.e. the energy of the photons increases with higher frequencies and consequently the photons of

e.g. blue light (Wp = 2.7 eV) has more energy than the photons of red light (Wp = 1.8 eV),

because it has a higher frequency. The relation between the frequency ν and the wave length λ

is given by

λ cν---= Eq. 2-3.

with the speed of light c. The speed of light in vacuum is given by

c0 2.99792458 8×10 m s⁄ .= Eq. 2-4.

If light propagates through materia, then its speed is reduced by the refraction index n:

cc0n-----= Eq. 2-5.

1. The quantum jump of valence electrons from the ground state in the excited state is at semiconductors equiva-lent to the electron-hole generation, where electrons are moved from the valence band to the conduction band.

13

The whole frequency range of the electromagnetic waves is called electromagnetic spectrum and

is illustrated in Figure 2-3.

Figure 2-3. Electromagnetic Spectrum

[nm] Ultraviolet (UV)

Extreme

Far

Near

10

20

30

40

60

80100

200

300

400

1 XE

1 pm

1 A

1 nm

1 m

1 mm

1 cm

1 m

1 Km

1 Mm

µ

10

10

3

4

105

106

[nm]

380

400

500

600

700

800

Wavelengthin vacuum

[nm] 10

10

10

10

10

10

10

10

10

10

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1

Frequencyrange (Hz)

Rays

Cosmicheights

X-ray

1THZ

1GHZ

1MHz

1KHz

1Hz

Waveregion

Micro

Centi

Deci

VHF

HF

M

SF

Alter-natingcurrent

Violet

(Visible radiation)(light)

Ultramarine

Ice blue

Bluish green

Green

Yellowgreen

Yellow

Orange

Brightred

Darkred

[nm] Infrared (IR)

Near

Medium

Far

ExtremeFar

10

10

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17

Gamma

The spectrum has a wide range from the long waves with low-energy, radio waves, to high-

energy roentgen radiation and gamma radiation of atom cores. Light covers 24 decades of the

whole spectrum, which is only a small range. While the visible light goes from 380 nm (violet)

to 780 nm (red), the infrared light ranges from 780 nm to 1 mm.

The infrared range has been discovered by the astronom Sir William Herschel in the year 1800.

Infrared light is separated in 4 regions:

14

• Near IR (780 nm - 3000 nm),

• Intermediate IR (3000 nm - 6000 nm),

• Far IR (6000 nm - 15000 nm), and

• Extreme Far IR (15000 nm - 1 mm)

2.2.1.2 Energy related Quantities

As described above light transports energy. The following provides an overview of some energy

related quantities that are required for the characterization of optical links.

• Radiant Energy Q [J] refers to the total amount of energy emitted, transferred, or collected

in a radiation process.

• Radiant Power or Radiant Flux Φ [W] is the time rate of change of radiant energy.

• Radiant Intensity I [W/sr] represents the flux per unit solid angle radiated by an entire

source in a given direction. The direction can be represented by a vector n and thus the radi-

ant intensity is given by

I n( ) dΦ n( )dΩ

---------------- .= Eq. 2-6.

The radiant intensity is of interest if the source is far away so that it can be considered as

point source and if the detector is small so that all rays from the source onto the detector are

essentially parallel. Figure 2-4 illustrates the radiant intensity.

Figure 2-4. Radiant Intensity Illustration

( )ndr

ΦΩd

nr

( ) ( )Ω

Φ=d

ndnIr

r

Φ

15

• Irradiance E [W/m²] is the radiant flux per unit area incident onto a surface.

E dΦdA-------= Eq. 2-7.

All these quantities refer to total radiation of all wavelengths. Hence, the radiant intensity I and

the irradiance E are the sums of all their respective spectral components:

I I λ( )dλ0

∞

∫= Eq. 2-8.

E E λ( )dλ0

∞

∫= Eq. 2-9.

2.2.2 Directed LOS Link according to IrDA

Since the focus of the IrDA is a low power and low cost communication system, they use

directed LOS links as described in Section 1.3 on page 4. An overview of the specified directed

LOS link is illustrated in Figure 2-5 and described in the following:

• The Link Distance that must be supported by IrDA devices is 0 m to at least 1 m.

• The Radiant Intensity of the Transmitter within a cone with a half-angle of 15° must be

between a minimum of 40 - 100 mW/sr (depending on the used bit rate) and a maximum of

500 mW/sr. For a half-angle between 15° and 30° the radiant intensity of the transmitter may

be lower than the minimum value. For larger half-angles the intensity must be lower than the

minimum value.

• The Receiver Field of View (FOV) must be at least 15°.

• If the transmitter is in the receiver FOV, then the receiver must be able to operate correctly at

all Minimum and Maximum Irradiances that may be caused by the transmitter consider-

ing the allowed range of radiant intensities and the allowed range of link distances.

• The Peak Wavelength (wavelength with the maximum radiant intensity) must be between

850 nm and 900 nm.

• The Bit Error Ratio shall be no greater than 10-8.

16

Along with that standard specification, IrDA provides also a low power version with reduced

link distances and reduced radiant intensities. For the complete specification of the directed LOS

link of IrDA see [1].

Figure 2-5. Directed LOS Link according to IrDA

0 … 1 m

Transmitter

Receiver15°...30°>15°

2.2.3 Ambient Radiation and Optical Filtering

[19][17][26] At the optical link of wireless infrared communications systems intense ambient

infrared radiation must be taken into account. The most important sources of ambient infrared

radiation are the sun, incandescent and fluorescent lamps. The normalized optical power spectra

of that infrared sources are shown in Figure 2-6 (source: [26]). Additionally, electromagnetic

fields or other infrared transmitter (e.g. IR remote controls) can disturb the infrared link. Here it

should be emphasized that direct sun-light, when present, is typically much stronger than other

sources.

Hence, optical filtering is required to reduce the influence of those ambient light sources. For

that purpose usually bandpass filtering is used that is adapted to the frequency range of the LED.

The frequencies above the upper corner frequency of the LED are basically suppressed due to

the low pass characteristic of the photodiode (see Section 2.4.2 on page 26). The frequencies

below the lower corner frequency of the LED, i.e. the visible light, can be suppressed by means

of an absorption filter. Cheap absorption filters can be realized by colored glass [36].

17

Figure 2-6. Normalized Power Spectra of Ambient Infrared Radiation Sources

However, only the side-band components of those spectra are suppressed by optical filters or the

detector photodiode, but the in-band components result in a photocurrent at the receiver. That

photocurrent due to ambient radiation can be much larger than the photocurrent due to the

payload signal from the transmitter. Fortunately, the ambient radiation is basically constant and

hence the ambient photocurrent can be easily suppressed by a high-pass filter in the receiver.

Since ambient radiation has obviously a major impact on the link design, the IrDA specification

defines the maximum ambient radiation due to electromagnetic fields, sun-light, incandescent

and fluorescent lighting, where the receiver still has to operate correctly (see appendix A.1 in

[1]).

2.2.4 Optical Link Model

[37] In order to build up a mathematical model for the optical link two things needs to be

considered - the path loss and the induced ambient radiation.

18

2.2.4.1 Path Loss

The transfer function of the optical link is defined as the ratio between the irradiance at the

receiver and the radiant intensity of the transmitter in the direction of the receiver.

HLOS f( ) EI---= Eq. 2-10.

For the definition of radiant intensity and irradiance refer to Section 2.2.1.2 on page 15. Due to

the relatively small FOV of the receiver only the LOS propagation path needs to be considered

and multipath distortions can therefore be neglected. This allows us to assume a non frequency

selective channel, where only the path loss is relevant [27].

If the dimensions of the transmitter and the detector are small compared to the distance between

them, then the transmitter can be modelled as a point source with a radiant intensity I in the

direction of the detector and the irradiance E at the receiver can be derived as

E Id2-----Ω0 ϕ ,cos= Eq. 2-11.

whereby d denotes the distance between the transmitter and the detector, and ϕ denotes the

angle of incidence of the transmitter signal on the detector area Adet as shown in Figure 2-7. The

factor Ω0 1sr= is necessary for a correct dimension of E.

Figure 2-7. Optical Link Model

Transmitter Receiver

Adet

Filter

I ϕ

d

d … Link Distance

I … Radiant Intensity

Adet … Detector Area

ϕ … Angle of Incidence

19

Note that the absorption filter has no influence on the path loss, since it filters only visible light

and does not reduce the intensity of the emitted infrared light of the LED. With the Equation 2-

10 and Equation 2-11 the transfer function of a directed LOS link can be derived as

HLOS1d2-----Ω0 ϕ .cos= Eq. 2-12.

It can be seen that the channel is non frequency selective and the path loss is basically

determined by the square of the distance d between the transmitter and the detector [38][39].

2.2.4.2 Ambient Radiation

The ambient radiation due to sun, incandescent or fluorescent lamps are additive to the payload

radiation of the LED. Therefore we can simply add the irradiance Eamb due to the ambient light

to the irradiance due to the emitted radiation of the LED.

2.3 Transmitter Front-End

2.3.1 Transmitter Front-End Circuitry

The transmitter path of an infrared transceiver basically comprises of an LED and the

corresponding control logic as illustrated in Figure 2-8. By means of an electrical binary-level

input signal UTX(t) the LED can be turned on and off and thereby binary-level intensity

modulation can be performed [33][26][17].

Figure 2-8. TX Path of an Infrared Transceiver

LED

UTX(t)

20

2.3.2 Intensity Modulation by LEDs

[40][41] LEDs can transform an electrical signal into optical radiation, whereby the radiant

intensity has basically the same waveform as the applied electrical signal (voltage). Therefore

LEDs are perfectly suited for the above described intensity modulation.

2.3.2.1 Basic Functionality of LEDs

An LED consists of a semiconductor material containing both p-type and n-type regions that

form a p-n-junction. At the p-n-junction the carrier concentration gradients cause carrier

diffusion. Holes from the p-side diffuse into the n-side, and electrons from the n-side diffuse into

the p-side. As holes continue to leave the p-side, some of the negative acceptor ions near the

junction are left uncompensated, since the acceptors are fixed in the semiconductor lattice,

whereas the holes are mobile. Similarly, some of the positive donor ions near the junction are

left uncompensated as the electrons leave the n-side. Consequently, the uncompensated acceptor

and donor ions forms a potential difference UD that is in the direction opposite to the diffusion

current of the mobile holes and electrons, what hampers further mobile charge carrier diffusion.

The schematic of the p-n-junction in Figure 2-9.a illustrates the resulting charge carrier

distribution in thermal-equilibrium condition, i.e. without an applied external voltage. The

region of the uncompensated donor and acceptor ions is called depletion layer, since it contains

no mobile charge carriers. Figure 2-9.b shows the corresponding energy bands of the p-n-

junction in thermal-equilibrium condition. The potential difference results in potential energy

difference eUD that avoids an electrons diffusion from the n-type to the p-type region and a hole

diffusion from the p-type to the n-type region.

If a forward-bias voltage UF is applied as shown in Figure 2-10, then the potential difference is

reduced and the mobile charge carrier can diffuse through the depletion layer. Electrons from

the n-type region can diffuse into the p-type regions, where they recombine with the mobile

holes, the majority carriers of the p-type semiconductor region. On the other hand, holes from

the p-type region can diffuse into the n-type regions, where they recombine with the mobile

electrons, the majority carriers of the n-type semiconductor region. At LEDs that recombination

is a radiative recombination, i.e. the released energy due to the quantum jump of the

recombination process results in emitting photons as described in Section 2.2.1. That means that

the injected charge carriers due to forward-bias voltage results in light. This process is called

21

luminescence as mentioned in Section 2.2.1, and therefore LEDs are also called luminescence

diodes.

Figure 2-9. LED in Thermal-Equilibrium Condition

p n

Conduction Band

Valence Band

DepletionLayer

eUD

p n

UD

a) Schematic of p-n Junction

... Fix Donator Ion

... Fix Acceptor Ion

... Mobile Hole

... Mobile Electron

Ec

Ev

b) Energy Bands

The emitted photons have an energy equal to the energy gap between the conduction band and

the valence band

Wp EC EV–= Eq. 2-13.

and with Equation 2-1 and Equation 2-3 the wavelength λ of the emitted light depends on the

energy band gap of the semiconductor material of the LED:

hcλ------ EC EV–= Eq. 2-14.

22

Figure 2-10. LED in Forward Biased Condition

p n

Conduction Band

Valence Band

Ec

e(UD - UF)

p n

UD

... Fix Donator Ion

... Fix Acceptor Ion

... Mobile Hole

... Mobile Electron

h*fh*f

UF

IF

h*f

h*f

Ev

a) Schematic of p-n Junction

b) Energy Bands

For infrared radiation GaAs semiconductors can be used: GaAs emits photons with a nominal

wavelength λ0 of 870 nm, and GaAs with Si impurities emits photons with a nominal

wavelength λ0 of about 940 nm. Although LEDs are wavelength selective, they have a spectral

broad emission, since the energy gap is not perfectly constant for all emitted photons. A

dimension for the spectral width is the full width at half maximum (FWHM) as indicated in

Figure 2-11. A GaAs LED emits with a FWHM of about 40 nm [42]. The total emitted power P

is the integral over all spectrum components:

P P λ( ) λd0

∞

∫= Eq. 2-15.

23

Figure 2-11. Emission Spectrum of LEDs

1

0.5

FWHM( )

maxPP λ

λ0λ

2.3.2.2 Radiant Intensity versus Induced Diode Current

The relation between the diode current IF and the emitted power P is given by

P ηexthceλ0--------IF= Eq. 2-16.

whereby e denotes the electron charge

e 1.60217733 19–×10 C.= Eq. 2-17.

The efficiency ηext denotes the relation between the emitted optical power and the induced

electrical power. If all induced charge carrier would perform radiative recombination, then ηext

would be 1. Unfortunately this is not the case, because not each recombination is a radiative

recombination, and not all of the generated optical power is really emitted.

If the LED was an isotropic source, then the resulting intensity radiation in any direction would

be constant and given by

IisoΦ4π------ .= Eq. 2-18.

But since the emitted power is not constant in each direction, the intensity radiation depends on

the angular displacement. This relation highly depends on the geometry of the LED and is

usually provided in LED data sheets. Figure 2-12 provides a typical distribution of the

normalized radiant intensity over the angular displacement. For compliance to IrDA's standard

the LED must fulfill the corresponding requirements summarized in Section 2.2.2.

24

Figure 2-12. Normalized Radiant Intensity vs. Angular Displacement

0° 10° 20°30°

40°

50°

60°

70°

80°

1.00.9

0.7

0.6 0.4 0.2

0.8N

orm

aliz

ed R

adia

nt In

tens

ity I no

rm

0

Ang

ular

Dis

plac

emen

t

However, Equation 2-16 shows that the relation between the induced diode current and the

emitted power and consequently the radiant intensity in a dedicated direction is basically linear.

Therefore LEDs are very well suited for Intensity Modulation.

2.3.3 Transfer Function of Transmitter Front-End

[37] For Intensity Modulation by means of an LED the electrical input signal is usually

modulated at a frequency in the MHz range (e.g. 24 MHz for IrDA's VFIR standard). This signal

causes direct modulation of the injected current in an LED. However, the pulses on the optical

link are slightly distorted due to the low pass characteristics of the LED. This is due to parasitic

elements such as the depletion-layer capacitance and series resistance that can cause a delay of

carrier injection into the junction and a delay in the light output, i.e. in the radiant intensity. The

ultimate limit on how fast one can vary the radiant intensity depends on the carrier lifetime τ .

The corresponding modulation bandwidth B is given by

B 12πτ--------- .= Eq. 2-19.

Since we use voltage U [V] as electrical input signal, the transfer function is defined as

HLEDIU---- W

srV--------- .= Eq. 2-20.

25

According to [42] an LED can be modelled as a first order low pass filter. With a time constant

τLED and gain KLED the transfer functions HLED(f) is given by

HLED f( )KLED

j2πfτLED 1+--------------------------------.= Eq. 2-21.

2.4 Receiver Front-End

2.4.1 Receiver Front-End Circuitry

The receiver front-end circuitry comprises basically a photodiode and a preamplifier. The

photodiode transforms the irradiance of infrared light (light with a wavelength between around

850 nm and 1100 nm) into electrical current and thereby performs the direct detection. The

bandpass characteristic of the preamplifier suppresses especially the introduced DC-current due

to ambient light (e.g. from the sun). The receiver front-end is illustrated in Figure 2-13

[33][26][17].

Figure 2-13. Receiver Front-End

Preamplifier

PD

iRX(t)

Receiver Front-End

2.4.2 Direct Detection by Photodiodes

[41] While LEDs use the effect of light emission during the recombination process, photodiodes

use the effect of electron-hole generation due to light absorption. Hence photodiodes are

semiconductor devices that can convert optical radiation into an electrical signal, whereby the

electrical signal has basically the same waveform as the irradiance. Therefore photodiodes are

perfectly suited for the above described direct detection.

26

2.4.2.1 Basic Functionality of Photodiodes

Basically a photodiode is a p-n junction operated under reverse bias. When an optical signal

impinges on the photodiode, the depletion region serves to separate the photo-generated

electron-hole pairs and an electrical current flows in the external circuit. For high-frequency

operation, the depletion region must be kept thin to reduce the transit time. On the other hand

the depletion layer must be sufficiently thick to allow a large fraction of the incident light to be

absorbed and finally to be transformed to electrical current. Unfortunately at ordinary p-n

junctions the width of the depletion layer highly depends on the applied voltage, and therefore

the operation conditions are not stable. But by insertion of an intrinsic layer, the width becomes

independent from the applied voltage and therefore it can be well defined. The resulting photo

detector is called p-i-n photodiode. Figure 2-14 shows a cross section of such a p-i-n photodiode.

Figure 2-14. Cross-Section View of p-i-n Photodiode under Reverse Bias

h*f

in

p

Metal Contact

SiO2

Anti-ReflectionCoating

RL

UR

Figure 2-15.a shows the energy band diagram of the p-i-n photodiode under reverse-bias

condition. If the photon energy of the impinging light is at least equal to the bandgap energy

hc0λ

-------- EC EV,–≥ Eq. 2-22.

then light absorption in the semiconductor produces electron-hole pairs. Pairs produced in the

depletion region or within a diffusion length of it will eventually be separated by the electric

field, whereby a current flows in the external circuit as carriers drift across the depletion layer.

Figure 2-15.b shows the optical absorption characteristics of a p-i-n photodiode. It can be seen

that most of the photons, which penetrate the semiconductor material, are absorbed at the

intrinsic layer.

27

Figure 2-15. Operation of a p-i-n Photodiode

p

Drift Space

a) Energy Band Diagram under Reversed Bias

Ec

Ev

h*fh*f

h*f

i n

HoleDiffusion

ElectronDiffusion

0 wp w + wp x

Pho

ton

Inte

nsity

a) Carrier Absorption Characteristics

2.4.2.2 Photocurrent versus Irradiance

As described in Section 2.2.1.2 irradiance is the radiant flux per unit area incident onto a surface.

Hence, the total received optical power of photodiode is determined by the irradiance E and its

detection area Adet

Popt EAdet.= Eq. 2-23.

Considering that with the photon rate rp and the wavelength λ of the impinged light the optical

power Popt is given by

Popt EAdet rphc0λ

-------- ,= = Eq. 2-24.

28

and that with the electron rate re the photocurrent iphoto is given by

iphoto ree,=Eq. 2-25.

then the relation between the irradiance and the photodiode current can be given by

iphotoE

-------------rerp---- eλ

hc0--------Adet.= Eq. 2-26.

The relation between re and rp is often denoted as quantum efficiency η and it represents the

ratio of absorbed photons that generate an electron-hole pair in the photodiode. Clearly, the

quantum efficiency η depends on the characteristics of the p-i-n photodiode (e.g., width of the

instrinsic layer) and furthermore it is obviously a function of the wavelength λ of the impinged

photons:

η λ( )rerp---- ,= Eq. 2-27.

While the long-wavelength cutoff λ c of the quantum efficiency is established by the bandgap

(see Equation 2-22 on page 27), the short-wavelength cutoff comes about because radiation with

a low wavelength is mostly absorbed very near the surface, where the carriers can recombine

before they can diffuse to the drift space of the intrinsic layer (compare Figure 2-15 on page 28).

In the literature the relation between the irradiance and the photocurrent is often defined as

photodiode responsivity R. With the quantum efficiency the responsivity can be given as

Riphoto

E------------- η λ( ) eλ

hc0--------Adet.= = Eq. 2-28.

Figure 2-16 shows the normalized responsivity of a silicon and of a germanium diode as a

function of the wavelength. It can be seen that a silicon diode fits very well to the requirements

of the optical link defined by IrDA (see Section 2.2.2).

29

Figure 2-16. Normalized Responsivity of a Si Diode and a Ge Diode

1.0

0.0

0.2

0.4

0.6

0.8

500 1000 1500 2000 nm

Si Diode Ge Diode

Wavelength

Nor

mal

ized

Res

pons

ivity

2.4.3 Transfer Function of Receiver Front-End

[37] As described above the receiver front-end circuitry works in that way that a photodiode

transforms impinged optical radiation into electrical current, which is then preamplified. Hence,

the transfer function of a receiver front-end circuitry is defined as

HRXFEiphoto

E------------- A

W m2⁄---------------- .= Eq. 2-29.

Basically a photodiode has low-pass characteristic. This is because the drift time of the carriers

through the depletion layer limits the frequency response. For carriers that have been generated

in the p-region or in the n-region also the diffusion time must be considered. The diffusion time

is the time that is required by the carriers to diffuse into the depletion region. The diffusion time

can result in tails in the response to optical pulses. Therefore the photocurrent is considered as

the sum of drift current, which arises from carrier generated inside the depletion region, and

diffusion current, which arises due to carrier diffusion to the depletion region

iphoto idrift idiff+= Eq. 2-30.

whereby drift and diffusion current have different time constants. However, the frequency

response of the receiver front-end is mainly determined by the bandpass characteristic of the

preamplifier, so that the low-pass characteristic of the photodiode can be neglected. For the gain

30

factor we stick to the responsivity R of the photodiode for the sake of simplicity. Hence, the

transfer function of the receiver front-end is given by

HRXFE Rj2πfτHP

j2πfτHP 1+( ) j2πfτLP 1+( )-------------------------------------------------------------------- .= Eq. 2-31.

2.4.4 Receiver Noise Current

The main noise sources within the receiver are shot noise and amplifier noise [43][26][17].

2.4.4.1 Shot Noise

Shot noise occurs due to the discrete nature of energy and charge in the photodiode. Carrier pairs

are generated randomly due to the incident photons. Furthermore, carriers traverse the potential

barrier of the p-n junction in a random fashion dependent to their energy. The generation and

transport of carriers generate shot noise in the photocurrent. Basically, the shot noise generation

is a discrete Poisson process with a white power spectral density. Since a Poisson process can be

approximated by a Gaussian process, the shot noise can be modelled as an additive white

Gaussian noise with a variance of

σshot2 ishot

2 t( )⟨ ⟩ 2eBiphoto,= = Eq. 2-32.

whereby B denotes the bandwidth of the front-end circuitry.

2.4.4.2 Amplifier Noise

Due to the impedance of the preamplifier a thermal noise current occurs that also can be

modelled as an additive white gaussian noise. Basically, the variance of the thermal noise of an

impedance R is given by

σth2 ith

2 t( )⟨ ⟩ 4kTBR

-------------- ,= = Eq. 2-33.

31

whereby T is the absolute temperature, B is the front-end bandwidth and k is the Boltzmann

constant that is given by

k 1.3806568 23–×10 J K⁄ .= Eq. 2-34.

However, the actual value of the thermal noise highly depends on the used preamplifier type.

2.5 Baseband Model of Wireless Infrared Channel

2.5.1 General Channel Model

[37] Considering the above described transfer functions and noise sources the baseband model

can be implemented as shown in Figure 2-17.

Figure 2-17. Baseband Model of Wireless Infrared Channel

HRXFE(f)

TransmitterFront-End Optical Link Receiver Front-End

EAmbient

+HLOS(f)HTXFE(f)I(t) E(t)uTX(t)

ishot(t)

++

ith(t)

iRX(t)

Due to the disturbance variable EAmbient the high-pass filter of the receiver front-end requires

some settling time as illustrated in Figure 2-18. But under steady state conditions the disturbance

variable EAmbiant has no influence, and so we are able to provide a simple channel model as

shown in Figure 2-19.

32

Figure 2-18. Settling Time of the High-Pass Filter due to Disturbance EAmbient

curr

ent

time

Figure 2-19. Steady State Baseband Model of Wireless Infrared Channel

n(t)

+HWIrC(f)iRX(t)uTX(t)

The channel transfer function HWIrC(f) and the noise n(t) are given by

HWIrC f( ) HTXFE f( )HLOS f( )HRXFE f( )= Eq. 2-35.

n t( ) ishot t( ) ith t( ).+= Eq. 2-36.

The corresponding transfer functions are given by

HTXFE f( ) Iu---

KTXFEj2πfτLED 1+--------------------------------= = Eq. 2-37.

HLOSEI---

1d2-----Ω0 ϕcos= = Eq. 2-38.

33

HRXFEiphoto

E------------- R

j2πfτHPj2πfτHP 1+( ) j2πfτLP 1+( )

-------------------------------------------------------------------- .= =

2.5.2 Reference Parameters

In this section reference parameters for the baseband channel model are derived in order to be

able to provide a reference channel. By means of that reference channel the various electrical

modulation schemes are evaluated in the following Chapters. The parameters are basically taken

from the ''FIR standard implementation example'' of the IrPHY standard [1] of IrDA.

2.5.2.1 Time Constant τLED of Transmitter Front-End

In section 4.2 of the IrPHY standard the maximum rise and fall times for FIR are defined as

t10...90% t90...10% 40ns.= = Eq. 2-40.

From that we can derive the time constant τLED as follows. The rising curve of a low pass is

given by [44]

I t( ) I0 1 et– τLED⁄

–( ),= Eq. 2-41.

and with

0.1I0 I0 1 et10%– τLED⁄

–( )= Eq. 2-42.

the time t10% when the curve has reached 10% of its final value can be derived as

t10% τLED 0.9( ).ln–= Eq. 2-43.

Similarly, one can derive with

0.9I0 I0 1 et90%– τLED⁄

–( )= Eq. 2-44.

Eq. 2-39.

34

the time t90%

t90% τLED 0.1( ).ln–= Eq. 2-45.

Consequently, the relation between the rise time t10...90% and the time constant τLED is given by

t10...90% τLED 0.9ln 0.1ln–( ) 2.2τLED.= = Eq. 2-46.

Hence, the time constant τLED for our reference model is given by

τLEDt10...90%

2.2------------------ 40ns

2.2------------ 18.18ns.= = = Eq. 2-47.

2.5.2.2 Gain Factor KTXFE of Transmitter Front-End

Section 4.2 of the IrPHY standard defines also the radiant intensity of the LED. For FIR the

minimum and maximum values are

Imax 500mWsr

----------= Eq. 2-48.

Imin 100mWsr

----------= Eq. 2-49.

If we assume that high levels and low levels of the input signal are represented by a voltage of

1 V and 0 V respectively, then the gain KTXFE of the LED's transfer function can be defined as

KTXFE 100...500mWsrV---------- .= Eq. 2-50.

2.5.2.3 Path Loss of Optical Link

For the standard option of an IrDA link the worst case link condition in terms of path loss occurs

with a distance d 1m= and angle of incidence of ϕ 15°= . The best case in terms of path loss1

occurs with a distance of d 0m= and angle of incidence of ϕ 0°= . With Equation

35

Equation 2-12 one could derive the transfer function of the optical link. But since the equation

is not valid for very short distances, we have to use IrDA's active input interface specification

(section 4.3 of the IrPHY standard) that defines the minimum and the maximum irradiance at the

receiver as

Emax 500mWcm2---------- ,= Eq. 2-51.

Emin 10 µWcm2---------- ,= Eq. 2-52.

Hence, with the values for radiant intensity of Equation 2-48 and Equation 2-49 the transfer

function for our reference model can be derived as

HLOS 0.0001...1 srcm2---------- ,= Eq. 2-53.

whereby 1sr cm2⁄ corresponds to the best case channel conditions (link distances of d 0m= ,

transmitter half angle ϕ 0°= ) and 0.0001sr cm2⁄ corresponds to the worst case channel

conditions (d 1m= , ϕ 15° ... 30°= ).

2.5.2.4 Ambient Radiation of Optical Link

Regarding the ambient radiation in the reference model we refer to the 4.0 Mbit/s Standard

Implementation Example in the Appendix B.4.7. of the IrPHY standard. This example provides

at an assumed responsivity R of

R 44 µAmW c⁄ m2------------------------ ,= Eq. 2-54.

a typical sunlight in-band photocurrent of

iamb isun 21.5nA.= = Eq. 2-55.

1. As we will see later, this ''best case'' condition might cause pulse extension at the receiver and so it is not gener-ally the best case.

36

Since the sun is the dominant source of ambient light, other sources are neglected in our

reference model. Hence, with the definition of responsivity by Equation 2-28 on page 29 the

additive ambient radiation is given by

Eamb 489 µWcm2---------- .= Eq. 2-56.

2.5.2.5 Responsivity R of Receiver Front-End

Regarding the transfer function of the receiver front-end in the reference model we again refer

to the 4.0 Mbit/s Standard Implementation Example in the Appendix B.4.7. of the IrPHY

standard. As already indicated in Equation 2-54 this example proposes a responsivity R of

R 44 µAmW c⁄ m2------------------------ .= Eq. 2-57.

2.5.2.6 Time Constants of Receiver Front-End

The 4.0 Mbit/s Standard Implementation Example proposes also a lower 3 dB limit of the

receiver front-end of

fHP 0.04MHz= Eq. 2-58.

and an upper 3 dB limit of

fLP 6.04MHz.= Eq. 2-59.

Consequently, the time constants of the reference transfer function of the front-end can be

derived as

τHP1

2πfHP--------------- 3.979µs= = Eq. 2-60.

37

τLP1

2πfLP-------------- 0.0264µs.= =

2.5.2.7 Receiver Front-End Noise

The 4.0 Mbit/s Standard Implementation Example in the Appendix B.4.7. of the IrPHY standard

provides also values for the standard deviation of the shot noise and the amplifier noise:

σshot ishot2 t( )⟨ ⟩ 8.06nA= = Eq. 2-62.

σth ith2 t( )⟨ ⟩ 4.87nA.= = Eq. 2-63.

The shot noise current is derived from the sunlight induced photodiode current and the front-end

bandwidth. The amplifier noise current is derived from the thermal noise of the preamplifier

impedance and from the front-end bandwidth.

2.5.3 Reference Channel

With the channel models of Figure 2-20 and Figure 2-21 and the summary of the reference

parameters of Table 2-1 our reference channel is fully defined.

Figure 2-20. Reference Channel Model


EAmbient

+HLOS

I(t) E(t)uTX(t)12

112

2+τπ+τπ

τπ

LPHP

HPfjfj

fjR12 +τπ LED

TXFEfjK

ishot(t)

++

ith(t)

iRX(t)

Eq. 2-61.

38

Figure 2-21. Reference Channel Model in Steady State


ishot(t)

HLOS ++

ith(t)

I(t) E(t) iRX(t)uTX(t)12

112

2+τπ+τπ

τπ

LPHP

HPfjfj

fjR12 +τπ LED

TXFEfjK

Table 2-1. Reference Parameters Overview

Parameter Reference value

Low pass time constant of LED τLED 18.18 ns

Gain of transmitter front-end KTXFE 100...500 mW/srV

Path loss of optical link HLOS 0.0001...1 sr/cm²

Ambient radiation Eamb 489 µ W/cm²

Receiver front-end responsivity R 44 µ A/(mW/cm²)

Low pass time constant of receiver front-end τLP 26.4 ns

High pass time constant of receiver front-end τHP 3979 ns

Standard deviation σshot of the shot noise nshot 8.06 nA

Standard deviation σth of the amplifier noise nth 4.87 nA

2.5.4 Impulse Response of Reference Channel

As described in Section 1.3 on page 4 basically only binary-level pulses are transmitted over the

wireless infrared channel. IrDA has specified at its FIR mode the pulse length to be

Tpulse 125ns.= Eq. 2-64.

Therefore in this section the response of a single pulse with that length, i.e. basically the impulse

response, is presented in order to get an idea about the channel characteristic.

For the input of the reference model we assume that high levels and low levels of the input signal

are represented by voltages of 1 V and 0 V, respectively. The resulting reference input pulse of

the wireless infrared channel is illustrated in Figure 2-22.

39

Figure 2-22. Reference Input Pulse

time [us]

0

0.2

0.4

0.6

0.8

1

0.995 1 1.05 1.1 1.15 1.2 1.25 1.30.99

Figure 2-23 shows the impulse response after the transmitter front-end that transforms the input

voltage into radiant intensity.

Figure 2-23. Impulse Response after the Transmitter Front-End

time [us]

0.995 1 1.05 1.1 1.15 1.2 1.25 1.3

0

10

20

30

40

50

60

70

80

90

100

radi

ant i

nten

sity

[mW

/sr]

0.99

Figure 2-24 shows the irradiance of the receiver front-end resulting from the pulse transmitted

from the transmitter front-end via the optical link. Obviously the irradiance due to the ambient

light is much larger than the irradiance due to payload signal from the LED.

40

Figure 2-24. Impulse Response after Transmitter Front-End and Optical Link

460

465

470

475

480

485

490

495

500

time [us]

0.995 1 1.05 1.1 1.15 1.2 1.25 1.30.99

irrad

ianc

e [µ

W/c

m2 ]

Figure 2-25 shows the resulting impulse response after the receiver front-end. Obviously, the

DC current due to ambient radiation is here already suppressed by the high-pass filter.

Figure 2-25. Impulse Response of complete Wireless Infrared Channel

time [us]

curr

ent [

nA]

0.995 1 1.05 1.1 1.15 1.2 1.25 1.30.99

-50

0

50

100

150

200

250

300

350

400

450

Figure 2-26 shows the required settling time of the channel, where no reasonable transmission

is possible.

41

Figure 2-26. Settling Time of the High-Pass Filter of the Receiver Front-End

curre

nt [u

A]

0 5 10 15 20 25

0

5

10

15

20

time [us]

42

3 Electrical Modulation and Demodulation

This chapter shall provide the fundamentals of the electrical modulation and demodulation, and

for that a mathematical signal description according to [45] is used throughout the chapter. In

general a wireless infrared transmission system is used to transmit arbitrary messages from a

digital information source to a digital information sink, whereby one particular message is

represented by a unique sequence an( )0 n N<≤ = a0, a1, a2,..., aN-1 | an 0 1 , .∈ In order to

transmit the corresponding message signal a(t)

a t( ) anδ t nTbit–( ),n 0=

N 1–

∑= Eq. 3-1.

that is basically a bit stream, in a reliable and efficient way, the electrical modulation and

demodulation are required as illustrated in Figure 3-1.

Figure 3-1. Binary-Level Electrical Modulation and Demodulation


DigitalInformation

Source

DigitalInformation

Sink

ElectricalDemodulation

WirelessInfraredChannel

s(t)

t

r(t)

t

a(t)

t

a’(t)

t

Tbit

Tbit

Tpulse

43

By the electrical modulation process the binary time-discrete message signal a(t) is converted

into a binary time-continuous electrical signal s(t) that can be reliably transmitted over the

wireless infrared channel as defined in Section 2.1 on page 11. The output signal r(t) of the

channel is given by the convolution of s(t) with the impulse response hWIrC(t) of the wireless

infrared channel plus the channel noise n(t) [27]:

r t( ) hWIrC t( ) s t( ) n t( )+⊗= Eq. 3-2.

The corresponding transfer function HWIrC(f) and n(t) are described in Section 2.5 on page 32ff.

In the electrical demodulation process the electrical signal r(t) recovered by the receiver front-

end of the infrared transceiver is converted back into a binary time-discrete message signal a’(t)

that is delivered to the digital information sink. At an error free transmission the retrieved

message signal a’(t) is then identical to the original message signal a(t). The following provides

a rather theoretical inside in both electrical modulation and demodulation, in order to derive

evaluation criteria for the various modulation schemes.

3.1 Electrical Modulation

Basically, the electrical modulator consists of an encoder and a pulse shaper as illustrated in

Figure 3-2 on page 45. The pulse shaper converts the binary time-discrete signal b(t) from the

encoder into an analog binary level voltage signal s(t). For that it generates a voltage pulse of

length Tpulse each time it gets a trigger by a logical ’1’ from the encoder. Hence, the encoder

determines the distribution of the transmitted infrared pulses, and it is thereby responsible for a

good usage of the channel bandwidth and for reliable transmission, e.g. by avoiding

intersymbol-interferences. For that it converts the unconstrained digital bit stream a(t) from the

digital information source into a constrained digital chip stream b(t) that generates a proper

distribution of pulses.

44

Figure 3-2. Electrical Modulation Process

Encoder

Pulse Shaper

s(t)

0

1

tTchip

Digital InformationSource

a(t)

0

1

tTbit

b(t)

Vss

Vdd

tTpulse

s(t)


a(t)

b(t)

Wireless InfraredChannel

0 1 0 0 1 11(an) = ...

3.1.1 Encoder Function

In general, the encoder transforms the binary time-discrete signal a(t) into the binary time-

discrete signal b(t):

Encoder: a t( ) anδ t nTbit–( ) b t( ) bmδ t mTchip–( )m 0=

M 1–

∑=→n 0=

N 1–

∑= Eq. 3-3.

with bm 0 1, ∈ . That means, the encoder transforms the sequence an( )0 n N<≤ into the

sequence bm( )0 m M<≤ , and changes the time base from Tbit to Tchip. While a(t) is an

unconstrained signal, i.e. each possible sequence (an) is allowed, the signal b(t) needs to be

constrained in order to avoid signal characteristics, e.g. high DC value, that are disadvantageous

for the transmission over the wireless infrared channel. Therefore the encoder has to add some

45

redundancy to the chip stream b(t), so that M > N and consequently Tchip < Tbit. With the code

rate Rcode that is given by

RcodeNM-----= Eq. 3-4.

the time base Tchip of the encoded chip stream b(t) is obviously given by

Tchip RcodeTbit.= Eq. 3-5.

The transformation of (an) to (bm) is done by the encoder map

encoder map: an( ) a0 a1 ..., aN 1–, , bm( )→ b0 b1 ..., bM 1– ,, ,= = Eq. 3-6.

which could be implemented by a look up table that provides for each arbitrary sequence (an) a

unique sequence (bm). But this straightforward implementation would require look-up tables of

unacceptable large sizes, if the input sequences were comparatively long. Therefore usually

encoding algorithms are used instead. For that the sequence (an) is split up into blocks αk with

the length p:

an( ) α0 α1 ..., αN p⁄ 1–, ,= Eq. 3-7.

αk apk apk 1+ ..., apk p 1–+ ,, ,= Eq. 3-8.

and the sequence (bm) is split up into blocks βk with the length q:

bm( ) β0 β1 ..., βM q 1–⁄, ,= Eq. 3-9.

βk bqk bqk 1+ ..., bqk q 1–+ ., ,= Eq. 3-10.

46

With that any output block βk can be derived from a limited number of input blocks by means

of a finite state machine:

βk f αk i– ... αk j+ ζk, , ,( )= Eq. 3-11.

ζk 1+ g αk i– ... αk j+ ζk, , ,( ),= Eq. 3-12.

where ζk denotes the internal state of the encoder. The parameters i and j, called memory and

anticipation, define the number of required input blocks. The function f is called the output

function and g the next state function. The block lengths p and q defines obviously the code rate

of an encoder that is based on a finite state machine:

RcodeNM----- p

q---= = Eq. 3-13.

and with Equation 3-5 on page 46 the chip duration is then given by

Tchip Tbitpq--- .= Eq. 3-14.

3.1.2 Pulse Shaper Function

At the pulse shaper, the second step of the electrical modulation, the encoded sequence b(t) is

convoluted with ps(t) that defines the shape of the transmitted pulses.

s t( ) b t( ) ps t( )⊗=

bmδ t mTchip–( ) ps t( )⊗m 0=

M 1–

∑=

bmps t mTchip–( )m 0=

M 1–

∑=

Eq. 3-15.

47

In our case we have rectangular pulses that are transmitted via the wireless infrared channel and

thus ps(t) is given by

ps t( ) rect tTpulse-------------- 1

2---–

,= Eq. 3-16.

so that the resulting output s(t) of the pulse shaper can be derived as

s t( ) bmrm 0=

M 1–

∑ ectt mTchip–

Tpulse------------------------- 1

2---–

.= Eq. 3-17.

Note that the pulse duration Tpulse is determined by the bandwidth B of the wireless infrared

channel, i.e. of the infrared transceiver

Tpulse1B---- .= Eq. 3-18.

3.2 Electrical Demodulation

Basically, the electrical demodulator consists of a quantization unit, a sampling unit and a

decoder as illustrated in Figure 3-3. With Equation 3-2 and Equation 3-17 the input signal r(t)

of the demodulator is given by

r t( ) hWIrC t( ) bmrm 0=

M 1–

∑ ectt mTchip–

Tpulse------------------------- 1

2---–

n t( )+⊗= Eq. 3-19.

bm

m 0=

M 1–

∑= hWIrC t( ) rectt mTchip–

Tpulse------------------------- 1

2---–

⊗ n t( ).+ Eq. 3-20.

48

If we introduce pd(t) as the convolution of the rectangular pulse ps(t) with the channel impulse

response hWIrC(t):

pd t( ) hWIrC t( ) rect tTpulse-------------- 1

2---–

,⊗= Eq. 3-21.

then r(t) can also be written down as

r t( ) bmpd t mTchip–( )m 0=

M 1–

∑ n t( ).+= Eq. 3-22.

That means r(t) is basically a sequence of distorted pulses pd(t) that originate from the

transmitted rectangular pulses ps(t).

The binary level quantization circuitry transforms r(t) into a binary level signal rb(t), whereby

the pulses pd(t) should result in a logical level of ’1’. The sampling unit transforms the binary

level signal rb(t), which is still time-continuous, into a time-discrete signal b’(t). After that the

decoder converts b’(t) finally into the bit stream a’(t).

3.2.1 Quantization

The quantization unit is basically a comparator that compares the output signal r(t) of the front-

end circuitry with a certain threshold value. If r(t) is below the threshold value, then the output

of the quantization unit has the logical value ’0’, otherwise it has the logical value ’1’. Usually

the quantization unit has a hysteresis in order to be not sensitive to the noise current. Hence, the

quantization unit has obviously a non-linear transfer function as illustrated in Figure 3-4.

49

Figure 3-3. Electrical Demodulation Process

Decoder

Digital InformationSink

rb(t)

0

1

tTchip

Sampling Unit withClock Recovery

b’(t)

0

1

tTbit

a’(t)

0

1

tTpulse

rb(t)


a’(t)

b’(t)

Quantization Unit

0 1 0 0 1 11(an’) = ...

r(t)


0

i1

t

r(t)

Figure 3-4. Transfer Function of the Quantization Unit

i [nA]

Voltage [V]

Vdd

Vssioff ion

In order to handle the wide dynamic range of the signal r(t), the threshold value is adapted to the

actual amplitude of the input signal. I.e. the threshold is adjusted to approximately the half of the

50

signal's amplitude. Consequently, the 4.0 = Mbit/s Standard Implementation Example in the

Appendix B.4.7. of the IrPHY standard [1] defines as comparator threshold current

ithisignal

2------------- ,= Eq. 3-23.

and as minimum threshold current

ithmin 219.7 nA.= Eq. 3-24.

But if the adjustment is imprecisely as illustrated in Figure 3-5, then the length of the recovered

pulse becomes extended. This effect often occurs at low link distances, where the irradiance of

the receiver is very high and non-linear distortions are induced by signal amplitude clipping [33].

Additionally, the pulse extension at low link distances may be reinforced by the lower time

constant of the diffusion current of the photodiode as it is described in Section 2.4.3 on page 30.

That is basically the reason, why pulse width modulation (PWM) schemes are not feasible for

low cost wireless infrared transmission and why only pulses of fixed length are used.

Figure 3-5. Pulse Extension due to Imprecise Threshold

-100

0

100

200

300

400

500

600

700

time [us]

0.995 1 1.05 1.1 1.15 1.2 1.25 1.30.99

curr

ent [

nA]

Ideal Threshold

Imprecise Threshold

Pulse Extensions

51

However, if the threshold is precisely the half of the signal amplitude, then the recovered pulse

has the same length as the input pulse of the LED as one can see by comparing the Figure 2-22

on page 40 and Figure 3-6.

Figure 3-6. Output of the Binary Level Quantization with Ideal Threshold

time [us]

volta

ge [V

]

0.995 1 1.05 1.1 1.15 1.2 1.25 1.30.99

0

0.2

0.4

0.6

0.8

1

3.2.2 Sampling and Receiver Clock Recovery

Although the signal rb(t) from the quantization unit is already a binary-level signal, it is still an

analog signal with a continuous time domain. Thus for a proper synchronous digital signal

processing the received electrical signal from the infrared transceiver must be sampled so that it

becomes a real digital signal with a discrete time domain. For that the receiver logic needs to

know the frequency 1/Tchip and phase of the received electrical signal. At IrDA the frequency is

negotiated by upper layers of the protocol stack and so the receiver always knows the frequency

of the received signals. But the phase information must be retrieved from the received signal by

a clock recovery logic. This clock recovery logic must then provide a proper sample clock as

shown in Figure 3-7. Note, the sample phase offset Toffset is required in order to avoid sampling

on pulse edges, where the result is ambiguous.

For a simple phase recovery the receiver can be synchronized on the first detected edge of the

retrieved electrical signal from the infrared transceiver. Unfortunately phase recovery by means

of only one edge is insufficient for transmissions of long data packets. This is because minor but

unavoidable deviations of the sampling frequency compared to the signal frequency results in an

accumulating phase error of the sample clock. That phase error cannot be corrected by such a

simple phase recovery. Especially at long data packets the accumulated phase error can result in

an incorrect sampling and demodulation. Therefore a more sophisticated phase recovery by

52

means of a digital phase lock loop (DPLL) is required. A DPLL processes the phase information

of each received edge and thereby it can avoid a phase error accumulation.

Figure 3-7. Receiver Clock Recovery and Sampling

ClockRecovery

Sampling

SampleClock

0

1

t0

1

t

Tpulse b’(t)

01

tTchip

Tchiprb(t)

Toffset

However, mathematically the sampling process can be written down as the multiplication of rb(t)

with a Dirac sequence

b' t( ) rb t( ) δm 0=

M 1–

∑ t mTchip– Toffset–( ),= Eq. 3-25.

what results in

b' t( ) rb mTchip Toffset+( )m 0=

M 1–

∑ δ t mTchip Toffset––( ).= Eq. 3-26.

Considering that the binary time-discrete signal b’(t) can also be written down as

b' t( ) b'mδ t mTchip–( ),m 0=

M 1–

∑= Eq. 3-27.

53

then the terms of the sequence (b’m) with b'm 0 1, ∈ are obviously determined by

b'm rb mTchip Toffset+( ).= Eq. 3-28.

At some modulation schemes the sampling unit can also be used for error correction. If the

sampling unit detects a pulse at a position where it is not allowed to be due to the modulation

characteristic, then it may ignore this pulse. E.g. at some modulation schemes double pulses are

not allowed, and so the sampling unit may treat any double pulse as single pulse. This is very

helpful since pulse extension due to the wireless infrared channel lead very often to unwanted

double pulses.

3.2.3 Decoder Function

The decoder has to perform the inverse transformation of the encoder. Hence, it transforms the

binary time-discrete signal b’(t) into the binary time-discrete signal a’(t):

Decoder: b' t( ) b'mδ t mTchip–( )m 0=

M 1–

∑ a' t( )→ a'nδ t nTbit–( )n 0=

N 1–

∑= = Eq. 3-29.

That means, the decoder converts the sequence bm'( )0 m M<≤ into the sequence a'n( )0 n N<≤

and changes the time base from Tchip back to Tbit:

Tbit1

Rcode-------------Tchip.= Eq. 3-30.

The transformation of (bm) to (an) is done by the decoder map

Decoder map: b'm( ) b'0 b'1 ..., b'M 1– a'n( )→, , a'0 a'1 ..., a'N 1– ,, ,= = Eq. 3-31.

which again could be implemented by a look up table that provides for each possible sequence

(b’m) a unique sequence (a’n). But this again would require look-up tables of unacceptable large

sizes. Therefore usually decoding algorithms are used instead, which also make use of the blocks

54

as defined in the Equations 3-7 to 3-10. With that any output block α 'k of the decoder can be

derived from a limited number of input blocks by means of a finite state machine with an internal

state ζk :

α'k d β'k i–... β'k j+

ζk, , ,( )= Eq. 3-32.

ζk 1+ e β'k i–... β'k j+

ζk, , ,( ),= Eq. 3-33.

whereby the memory i and the anticipation j of the decoder define the number of required input

blocks.

The decoder may have error detection capabilities, i.e. it may be able to detect blocks or a

sequence of blocks that cannot be generated by the encoder. Such an error detection is usually

not mandatory, since transmission error detection is basically done on a higher protocol layer by

CRC codes.

3.3 Evaluation Criteria for Modulation Techniques

In order to be able to evaluate the various modulation techniques and to assess the new

modulation technique EPM, this section provides some evaluation criteria. Clearly, a low bit

error rate is desirable for any transmission system, and therefore the transmission reliability is a

strong criterion for a modulation technique. Additionally, two more things needs to be

considered. On the one hand the achievable bit rate of an infrared communication is mainly

limited by the bandwidth of the infrared transceivers. Therefore it is important to use a

modulation technique with high bandwidth efficiency. And on the other hand mobile devices are

usually battery powered and therefore power efficiency is also very important for our type of

application. Hence, the following provides evaluation criteria for

• the transmission reliability,

• the bandwidth efficiency and

• the power efficiency.

55

3.3.1 Reliability

The reliability of the transmission depends on the capability of the modulation technique to

adapt the signal to the wireless infrared channel in a way that allows demodulation at the receiver

with a low bit error rate. Basically there are two different errors that can occur at the receiver:

• Quantization error

• Sample error

In the following we provide evaluation criteria for the robustness of the various modulation

schemes against quantization and sample errors.

3.3.1.1 Quantization Error Robustness

A quantization error occurs, when the transmitter sends a pulse, but the quantization unit does

not detect anything, or when the transmitter does not send anything, but the quantization unit

detects a pulse. That can happen, when the signal to noise ratio is too low, so that the

quantization unit cannot distinguish between the noise and the signal. The reason for such a

quantization error is an insufficient optical link between the transmitter and the receiver, e.g.

when the distance or the alignment between the transmitter and the receiver is out of the

specification, or when a solid object lies between the transmitter and receiver.

Assuming an ideal sampling clock, the quantized signal rb(t) must take on the correct logical

levels at least at the sampling points in time. That means the signal level of r(t) must be beyond

or beneath the threshold value at least at the sampling points, if a pulse is transmitted or not,

respectively. With Equation 3-22 the value of signal r(t) at a sampling point kTchip + Toffset is

given by

r kTchip Toffset+( ) bmpd kTchip Toffset mTchip–+( ) +

m 0=

M 1–

∑=

n+ kTchip Toffset+( ).

Eq. 3-34.

56

If the respective bk is ’1’, then r(kTchip+Toffset) is given by

r kTchip Toffset+( ) r1k n kTchip Toffset+( ).+= Eq. 3-35.

with

r1k pd Toffset( ) bmpd kTchip Toffset mTchip–+( )m 0=

k 1–

∑ + +=

bmpd kTchip Toffset mTchip–+( ).m k 1+=

M 1–

∑+

Eq. 3-36.

The corresponding probability density function p1k of the level of r(t) at the sampling point

kTchip + Toffset is under the condition of bk = ’1’given by

p1k r kTchip Toffset+( )( ) 1

2πσ2-----------------

x r1k–( )2

2σ2------------------------–

.exp⋅= Eq. 3-37.

If the respective bk of Equation 3-34 is ’0’, then r(kTchip+Toffset) is given by

r kTchip Toffset+( ) r0k n kTchip Toffset+( ).+= Eq. 3-38.

with

r0k bmpd kTchip Toffset mTchip–+( )m 0=

k 1–

∑ +=

bmpd kTchip Toffset mTchip–+( ).m k 1+=

M 1–

∑+

Eq. 3-39.

57

The corresponding probability density function p0k of the level of r(t) at the sampling point

kTchip + Toffset is then given by

p0k r kTchip Toffset+( )( ) 1

2πσ2-----------------

x r0k–( )2

2σ2------------------------–

exp= Eq. 3-40.

Figure 3-8 shows both the probability density function p0k and p1k.

Figure 3-8. Probability Density Function p0k and p1k

r(kTchip+Toffset)r0k rth

p0k p1k

Pe1k

r1kPe0k

PropabilityDensity

The quantization error probability Pe1k for the case when a pulse has been transmitted, but

nothing is detected, is given by

Pe1k1

2πσ2-----------------

∞–

rth

∫x r1k–( )2

2σ2------------------------–

dxexp= Eq. 3-41.

12---erfc

r1k rth–

2σ2-------------------

= Eq. 3-42.

58

The quantization error probability Pe0k for the case when no pulse has been transmitted, but a

pulse is detected, is given by

Pe0k1

2πσ2-----------------

rth

∞

∫x r0k–( )2

2σ2------------------------–

dxexp= Eq. 3-43.

12---erfc

rth r0k–

2σ2-------------------

= Eq. 3-44.

The total quantization error probability Pek obviously depends on the probability of the logical

value of bk:

Pek P bk 0=( )Pe0 P bk 1=( )Pe1+= Eq. 3-45.

P bk 0=( )2

------------------------erfcrth r0k–

2σ2------------------- P bk 1=( )

2------------------------erfc

r1k rth–

2σ2-------------------

+= Eq. 3-46.

An extremum calculation evidently shows that the threshold value

rthr1k r0k+

2----------------------= Eq. 3-47.

is a very good approximation for the ideal threshold value1. With that the total quantization error

probability Pek for a single sample can be provided as

Pek12---erfc

r1k r0k–

2 2σ2--------------------- 1

2---erfc

r1k r0k–( )2

8σ2-----------------------------

.= = Eq. 3-48.

1. Actually it is the ideal threshold value in the case of P(bk = 0) = P(bk = 1) = 0.5.

59

By introducing the signal to noise ratio (SNR)

SNRk

r1k r0k–

2---------------------

2

σ2-----------------------------= Eq. 3-49.

the total quantization error probability of a single sample can be written down as

Pek12---erfc

SNRk2

-------------- .= Eq. 3-50.

Assuming that the complete transmitted sequence is erroneous as soon as a quantization error

has been occurred at one of the M samples, then the sequence error probability due to

quantization errors is given by

Pesequence 1 1 Pek–( ).k 0=

M 1–

∑–= Eq. 3-51.

Unfortunately Pek is generally different for each sample due to varying intersymbol

interferences, and therefore it is difficult to calculate the exact quantization error probabilities

analytically. However, there is a convenient way to determine the upper limit of the quantization

error probability Pemax of a single sample by means of the eye diagram without noise

disturbance [46] as shown in Figure 3-9. By using the vertical eye opening Ever one can easily

derive the minimum signal to noise ratio

SNRmin r1min r0max–( )2

4σ2---------------------------------------------

Ever2

4σ2----------= = Eq. 3-52.

60

and the corresponding upper limit of the quantization error probability Pemaxk of a single

sample is then given by

Pemaxk12---erfc SNRmin

2----------------------

.= Eq. 3-53.

Figure 3-9. Eye Diagram after Receiver Front-End without Noise

time

curre

nt

r0max

r1min

Tsample

Ever

For comparison of the quantization error robustness of the various modulation schemes one may

use the maximum bit error probability due to quantization errors, which can be calculated with

Equation 3-51 on page 60 and with the code rate Rcode of the respective encoder.

Pemaxbit 1 1 P– emaxk( )–1 Rcode⁄

= Eq. 3-54.

Note that this calculation of the quantization error probability is under the assumption of a

quantization with an ideal threshold value. Although this assumption does not hold in real

systems, it is fair to use the computed bit error rate in order to compare the various modulation

schemes.

61

3.3.1.2 Sampling Error Robustness

The sampling error robustness is basically determined by the required sampling clock phase

accuracy and the clock recovery support. Therefore, corresponding evaluation criteria are

derived in the following.

Sampling Clock Phase Accuracy Requirement

Basically, a sampling error occurs, when

• a pulse is not sampled by the corresponding sample beat Tk as illustrated in Figure 3-10

• or a pulse is mistakenly sampled by previous or by next sample beats as illustrated in

Figure 3-11.

Figure 3-10. Sample Error: Pulse not Sampled by Corresponding Sample Beat

Tk-1 Tk Tk+1Tk+2

rb(t)

tVss

Vdd

phaserange

Obviously, the sampling error occurs in both cases due to pulse form deviation, i.e. pulse

shortening or pulse extension, but could be prevented by a more accurate phase adjustment of

the sample clock. If the sample beat Tk was in the shown phase range, then there wouldn’t be a

sampling error. The optimal sampling time would be obviously in the middle of the indicated

62

phase range in order to be resistance against phase jitter. With the deviation T∆ from the optimal

sampling time we define the relative sampling clock deviation Θ as

Θ T∆Tchip------------ .±= Eq. 3-55.

Figure 3-11. Sample Error: Pulse Mistakenly Sampled by Next Sample Beat

Tk-1 Tk Tk+1 Tk+2

rb(t)

tVss

Vdd

phaserange

The maximum acceptable phase deviation of the sample clock can be determined by the

horizontal eye opening Ehor of the eye diagram of the signal rb(t) as shown in Figure 3-12.

Figure 3-12. Horizontal Eye Opening of rb(t)

Vss

Vdd

volta

ge le

vel

time

Vth

Ehor

Tchip

63

The horizontal eye opening Ehor under worst case conditions obviously determines the

maximum clock phase deviation. The maximum acceptable phase deviation Θmax is given by

Θmax Ehor

2Tchip--------------- .±= Eq. 3-56.

The maximum relative sampling clock deviation Θmax shall be used as an evaluation criterion

for the sampling error robustness.

Sampling Clock Recovery Support

The sampling error robustness depends besides on the eye opening also on the support of the

clock recovery for sampling phase synchronization. In general the clock recovery can be done

by means of ’0’ to ’1’ transitions of the received signal rb(t), and therefore long absences of ’0’

to ’1’ transitions can lead to a phase unlock of the sampling unit, what results in sampling errors

and finally in bit errors. Hirt et al. [33] stated that there should be at least one ’0’ to ’1’ transition

within 16 chips for an adequate sample clock recovery with a DPLL. Hence, the maximum

length of sequence of chips without any ’0’ to ’1’ transition is a further evaluation criterion for

the sampling error robustness.

3.3.2 Bandwidth Efficiency

Depending on the used modulation scheme more or less bits can be transmitted over the wireless

infrared channel within a certain time. The corresponding transmission speed is usually

measured by the so called bit rate Rbit that is given by

Rbit1

Tbit--------- .= Eq. 3-57.

The bandwidth efficiency factor ηB shall be used to classify the various modulation schemes in

terms of their achievable bit rate at a given infrared transceiver bandwidth. For that we define

64

the bandwidth efficiency ηB as the ratio between the achievable bit rate Rbit and the bandwidth

B of the infrared transceiver

ηBRbitB

--------- .= Eq. 3-58.

Consequently, the bandwidth efficiency ηB indicates how good a modulation scheme utilizes

the bandwidth of an infrared transceiver. Together with Equation 3-57 and Equation 3-18 on

page 48 the bandwidth efficiency ηB can be derived as the ratio between the pulse duration

Tpulse and the bit duration Tbit

ηBTpulseTbit

-------------- .= Eq. 3-59.

Note that the definition of the bandwidth efficiency of modulation schemes is very similar to the

code rate definition of channel codes (e.g. block codes, cyclic codes or RLL codes). But the code

rate indicates the added redundancy that can be used for error detection or error correction at the

receiver, while the bandwidth efficiency indicates the utilization of the bandwidth by a

modulation technique.

3.3.3 Power Efficiency

Depending on the used modulation scheme more or less energy is required to transmit a data

packet over the wireless infrared channel. The power efficiency factor ηP shall be used to

classify the various modulation schemes in terms of their power consumption. For that we define

the power efficiency ηP as the ratio between the energy per infrared pulse Epulse and the

required average energy per bit aveEbit.

ηPEpulse

aveEbit------------------= Eq. 3-60.

65

Consequently, the average required energy for the transmission of a data packet consisting of N

bits with a particular modulation technique can be calculated by

EpacketNEpulse

ηP------------------- .= Eq. 3-61.

At wireless infrared communications energy is only required, if an infrared pulse is transmitted.

If no infrared pulse is sent, then no energy is necessary. Therefore we need to know the average

high and low times of a modulated signal of a data packet in order to calculate the required

energy for the transmission of the packet. The ratio between high time and low time of a binary

signal is called duty cycle DC. At the modulation schemes introduced in the following the duty

cycles of the modulated signals are not always constant, but may vary between a minimum duty

cycle minDC and a maximum duty cycle maxDC. For calculating the average required energy

for the transmission of a data packet the average duty cycle aveDC of the modulated signal is

required. This average duty cycle can be gained by comparing the high and low times of a very

long data packet. Mathematically the average duty cycle is given by

aveDCThighTlow------------ ,

Thigh Tlow+( ) ∞→lim= Eq. 3-62.

Considering that we need on average aveDC ηB⁄ pulses for the transmission of one bit, then

the average required energy for the transmission of one bit can be derived as

aveEbit EpulseaveDC

ηB------------------ .= Eq. 3-63.

Following from this and Equation 3-60 the power efficiency ηP can be derived as the ratio

between the bandwidth efficiency ηB and the average duty cycle aveDC of the modulated

signal.

ηPηB

aveDC------------------= Eq. 3-64.

66

4 Pulse Position based Modulation Schemes

In this section we present several pulse position based modulation techniques, which are

currently used in the various wireless infrared transmission systems for mobile devices. The

descriptions are based on the detailed theoretical explanations of Chapter 3, and are therefore

rather straightforward. The various modulation techniques are assessed in terms of transmission

reliability, bandwidth efficiency and power efficiency by means of the evaluation criteria of

Section 3.3 on page 55ff. For the performed simulations a pulse length of 125 ns is used for all

modulation schemes and the reference channel derived in Section 2.5.3 on page 38 is applied.

4.1 Return to Zero Inverted

The simplest form of modulation is Return to Zero Inverted (RZI), which is determined by two

parameters n and m with n < m. Therefore n/m-RZI is a commonly used abbreviation. At n/m-

RZI a bit with the value ’0’ is represented by a pulse with a duration of

Tpulsenm----Tbit= Eq. 4-1.

and a bit with the value ’1’ is represented by the absence of a pulse. Basically, RZI with

n m⁄ 1= , which is de facto the modulation scheme Non Return to Zero Inverted (NRZI),

would have the best bandwidth efficiency, but it allows multiple consecutive pulses with no low

phase in between, so that the pulses would be suppressed by the high pass filter of the receiver.

Therefore NRZI is not feasible for our applications in terms of reliability. Consequently, IrDA

uses 3/16-RZI for bit rates up to 115.2 kbit/s and 1/4-RZI for the bit rates 576 kbit/s and

1.152 Mbit/s [1]. Therefore we will look more closely on the 1/4-RZI modulation.

67

4.1.1 1/4-RZI Modulation Scheme

In general RZI uses as encoder function the so called on-off-keying, where both the input block

αk and output block βk consist of only one term:

αk ak=Eq. 4-2.

βk bk,= Eq. 4-3.

so that the code rate is given by

pq--- 1

1--- 1,= = Eq. 4-4.

and the chip duration is equal to the bit duration

Tchip Tbit.= Eq. 4-5.

The encoder function is state independent:

βk f αk( )= Eq. 4-6.

and is given by

bk ak.= Eq. 4-7.

Basically, the pulse shaper at RZI generates pulses with a duration n/m times of the chip

duration, ergo at 1/4-RZI the pulse duration is given by

Tpulse14---Tchip.= Eq. 4-8.

Figure 4-1 provides an example for the 1/4-RZI modulation.

68

Figure 4-1. 1/4-RZI Modulation

0

1

tTchip

Tbit

Vss

Vdd

tTpulse

s(t)

a(t)

b(t)

0

1

t

4.1.2 1/4-RZI Demodulation Scheme

The quantization unit has to process the signal r(t), which has an eye diagram as shown in

Figure 4-6. The sampling unit has to sample the received signal r(t) with a sampling offset of

ToffsetTpulse

2-------------- .= Eq. 4-9.

The decoder function is also state independent:

α'k d β'k( )= Eq. 4-10.

and is given by

a'k b'k.= Eq. 4-11.

At RZI pulses may occur at any position and so there are no error detection or error correction

mechanism possible at the RZI demodulation process. Figure 4-3 provides an example for the

RZI demodulation.

69

Figure 4-2. 1/4-RZI Eye Diagram of r(t) after Receiver Front-End

-250 -200 -150 -100 -50 0 50 100 150 200 250

-200

-100

0

100

200

300

400

500

time [ns]

curr

ent [

nA]

Figure 4-3. 1/4-RZI Demodulation

0

1

tTchip

Tbit

Vss

Vdd

t

Tpulserb(t)

a’(t)

b’(t)

0

1

t

½ Tpulse

t

r(t)

rth

70

4.1.3 Reliability of 1/4-RZI

In the following the reliability of 1/4-RZI is analyzed according to the criteria derived in

Section 3.3.1 on page 56ff.


The quantization error robustness of a modulation scheme can be determined by the maximum

bit error probability as derived in Section 3.3.1.1 on page 56ff with Equation 3-53 and

Equation 3-54. Figure 4-4 shows the maximum bit error probability due to a quantization error

for the 1/4-RZI modulation scheme at the receiver irradiance range from 0.0001 to 0.1 mW/cm².

Figure 4-4. 1/4-RZI Bit Error Probability due to Quantization Errors

1E-60

1E-50

1E-40

1E-30

1E-20

1E-10

1

0.0001 0.001 0.01 0.1

IrDA range

Receiver Irradiance E

Erro

r pro

babi

lity

Pe bi

t

d = 1m,=15°

2cm

mW

ϕ

Considering that IrDA specifies the operating range for the receiver irradiance from 0.01 to

500 mW/cm² one can evidently see that 1/4-RZI has a very good quantization error robustness.

For a quantitative comparison with the other modulation schemes the maximum bit error

probability due to a quantization error is derived in the following for IrDA’s worst case condition

of a receiver irradiance E of 0.01 mW/cm². Figure 4-5 shows the eye diagram of the received

71

signal after the receiver front-end r(t) under worst case condition and the corresponding eye

opening is given by

E 356nA.≅ Eq. 4-12.

The resulting maximum bit error probability due to quantization errors is then given by

Pemaxbit 5.499 10× 80– .≅ Eq. 4-13.

Figure 4-5. 1/4-RZI Eye Diagram of r(t) without Noise under Worst Case Condition

-250 -200 -150 -100 -50 0 50 100 150 200 250

-200

-100

0

100

200

300

400

500

time [ns]

curr

ent [

nA]


Sampling Clock Phase Accuracy Requirements

The horizontal eye opening after the quantization of RZI under worst case conditions is shown

in Figure 4-6 and is given by

Ehor 106.67 ns= Eq. 4-14.

72

and with the RZI sampling clock frequency of 2 MHz the maximum relative sample clock phase

deviation is given by

Θmax 10.7%.±= Eq. 4-15.

Figure 4-6. 1/4-RZI Eye Diagram of rb(t) after Quantization Unit

-250 -200 -150 -100 -50 0 50 100 150 200 250

time [ns]

Vss

Vdd

volta

ge le

vel

Vth


Basically RZI has no real clock recovery support, because it allows theoretically an infinitive

sequence of chips without ’0’ to ’1’ transitions. Therefore bit insertion (e.g. start and stop bits)

is required at RZI what actually reduces the effective bandwidth efficiency, since the inserted

bits do not carry information.

4.1.4 Bandwidth Efficiency of 1/4-RZI

With Equation 4-1 the bandwidth efficiency of n/m-RZI is in general given by

ηBnm---- ,= Eq. 4-16.

73

and consequently the bandwidth efficiency of 1/4-RZI is then

ηB14--- .= Eq. 4-17.

The bandwidth efficiency of 1/4-RZI is obviously not very good, and as mentioned above RZI

do not support sample clock recovery at the receiver, because it allows a long low signal without

any ’0’ to ’1’ transition. The required bit stuffing further decreases the bandwidth efficiency,

since the enforced pulses carry no information.

4.1.5 Power Efficiency of 1/4-RZI

Assuming that the probability of the occurrence of bit with the logical value ’1’ is equal to the

probability of a ’0’, then the average duty cycle aveDC of n/m-RZI is generally given by

aveDC n2m--------= Eq. 4-18.

and thus the power efficiency ηP can be derived as

ηPηB

aveDC------------------

nm----

n2m---------------- 2.= = = Eq. 4-19.

4.2 N - Pulse Position Modulation

In order to overcome the shortcomings of RZI the N - Pulse Position Modulation (N-PPM)

technique has been introduced in many wireless optical applications [47]. With the N-PPM

technique information is transmitted by varying the position of a pulse within a symbol. It allows

one pulse to be set in one of the N possible positions, thus it is called N-PPM. Since data

processing is usually byte oriented, only 2-, 4-, 16- and 256-PPM are useful methods, because

they encode 1, 2, 4 and 8 bits, respectively. While in the physical layer IR PHY of the IEEE

802.11 standard [48] 4-PPM is foreseen for 2 Mbit/s operation and 16-PPM for 1 Mbit/s, IrDA

74

uses 4-PPM for its 4 Mbit/s FIR mode. Therefore 4-PPM is investigated in more detailed in the

following. Nevertheless the bandwidth and power efficiency for any N-PPM scheme are also

provided.

4.2.1 4-PPM Modulation Scheme

At 4-PPM two bits are encoded per encoding step and thereby one pulse is set in one of 4

possible positions. Therefore the dimensions of the input block αk and output block βk are

p 2= and q 4= , respectively:

αk a2k a2k 1+,=Eq. 4-20.

βk b4k b4k 1+ b4k 2+ b4k 3+ ., , ,= Eq. 4-21.

The resulting code rate is consequently given by

pq--- 2

4--- 1

2---= = Eq. 4-22.

and the chip duration is then

Tchip12---Tbit.= Eq. 4-23.

The N-PPM encoder are in general state independent:

βk f αk( )= Eq. 4-24.

and the 4-PPM encoder is in particular given by the encoding table provided by Table 4-1.

Table 4-1. Encoding Table for 4-PPM

a2k a2k+1 b4k b4k+1 b4k+2 b4k+3

0 0 1 0 0 0

0 1 0 1 0 0

75

The resulting logical 4-PPM encoder function is given by

b4k a2k a2k 1+⋅= Eq. 4-25.

b4k 1+ a2k a2k 1+⋅= Eq. 4-26.

b4k 2+ a2k a2k 1+⋅= Eq. 4-27.

b4k 3+ a2k a2k 1+⋅= .Eq. 4-28.

The pulse shaper generates pulses with a duration equal to the chip duration

Tpulse Tchip.= Eq. 4-29.

Figure 4-7 provides an example for the 4-PPM modulation.

4.2.2 4-PPM Demodulation Scheme


Figure 4-8. The sampling unit has to sample the received signal rb(t) with a sampling offset of

ToffsetTpulse

2-------------- .= Eq. 4-30.

1 0 0 0 1 0

1 1 0 0 0 1

a2k a2k+1 b4k b4k+1 b4k+2 b4k+3

76

Figure 4-7. 4-PPM Modulation

0

1

t

Tchip

0

1

tTbit

Vss

Vdd

tTpulse

s(t)

a(t)

b(t)

Figure 4-8. 4-PPM Eye Diagram of r(t) after Receiver Front-End

-250 -200 -150 -100 -50 0 50 100 150 200 250

-200

-100

0

100

200

300

400

500

time [ns]

curr

ent [

nA]

One of the major reasons of errors at wireless infrared transmission are unwanted pulse

extension, where a single pulse appears to be a double pulse. 4-PPM has the characteristic that

77

double pulses may occur only at block borders. By knowing this fact the sampling unit can

perform error correction as proposed in [49] and illustrated in Figure 4-9.

Figure 4-9. 4-PPM Error Correction

Vss

Vdd

r(t)

0

1

b’(t)

a) b) c) d) e)

Note, that at case a) of Figure 4-9 the first pulse could occur due to a pulse extension of a pulse

in the previous block. Since there is no easy way to determine the pulse that has lead to the

unallowed double pulse, it is fair to use always the proposed error correction. (The mechanism

proposed in [49] would require a higher sampling clock.)

The N-PPM decoder are in general state independent:

α 'k d β'k( )= Eq. 4-31.

and the 4-PPM decoder is in particular given by the decoding table provided by Table 4-2.

Table 4-2. Decoding Table for 4-PPM

b’4k b’4k+1 b’4k+2 b’4k+3 a’2k a’2k+1

1 0 0 0 0 0

0 1 0 0 0 1

0 0 1 0 1 0

0 0 0 1 1 1

others error

78

The resulting logical 4-PPM decoder function is given by

a'2k b'4k b'4k 1+⋅ b'4k 2+ b'4k 3+⋅ ⋅ b'4k b'4k 1+⋅ b'4k 2+ b'4k 3+⋅ ⋅+= Eq. 4-32.

a'2k 1+ b'4k b'4k 1+⋅ b'4k 2+ b'4k 3+⋅ ⋅ b'4k b'4k 1+⋅ b'4k 2+ b'4k 3+ .⋅ ⋅+= Eq. 4-33.

Figure 4-10 provides an example for the 4-PPM demodulation.

Figure 4-10. 4-PPM Demodulation

0

1

tTchip

0

1

tTbit

Vss

Vdd

t

Tpulserb(t)

a’(t)

b’(t)

½ Tpulse

t

r(t)

rth

4.2.3 Reliability of 4-PPM

In the following the reliability of 4-PPM is analyzed also according to the criteria derived in

Section 3.3.1 on page 56ff.

79


Due to its constant duty cycle 4-PPM has an even better robustness against quantization errors

than RZI as shown in Figure 4-11.

Figure 4-11. 4-PPM Bit Error Probability due to Quantization Errors

1E-60

1E-50

1E-40

1E-30

1E-20

1E-10

1

0.0001 0.001 0.01 0.1

IrDA range


Erro

r pro

babi

lity

Pe bi

t

d = 1m,=15°

2cm

mW

ϕ

Figure 4-12 shows the eye diagram of the received signal after the receiver front-end r(t) under

worst case condition and the corresponding eye opening is given by

E 419nA.≅ Eq. 4-34.


Pemaxbit 6.04 10 110–× .≅ Eq. 4-35.

80

Figure 4-12.

0 50 100 150 200 250 300 350 400 450 500

-200

-100

0

100

200

300

400

500

time [ns]

curr

ent [

nA]

4-PPM Eye Diagram of r(t) without Noise under Worst Case Condition



The horizontal eye opening of 4-PPM under worst case conditions is shown in Figure 4-13 and

is given by

Ehor 112.14 ns.= Eq. 4-36.

and with the 4-PPM sampling clock frequency of 8 MHz the maximum relative sample clock

phase deviation is given by

Θmax 45%.±= Eq. 4-37.


At 4-PPM the maximum length of a sequence of chips without ’0’ to ’1’ transitions is limited to

6. Therefore 4-PPM offers an excellent support for the clock recovery at the receiver.

81

Figure 4-13. 4-PPM Eye Diagram of rb(t) after Quantization Unit

-250 -200 -150 -100 -50 0 50 100 150 200 250

time [ns]

Vss

Vdd

volta

ge le

vel

Vth

4.2.4 Bandwidth Efficiency of 4-PPM

With N-PPM one pulse can be set in one of N possible positions, and so N different messages

can be sent within one block. For encoding of N messages log2(N) bits are required and

consequently the relation between Tbit and Tpulse is given by

N( )Tbit2log NTpulse.= Eq. 4-38.

The resulting bandwidth efficiency of N-PPM is then

ηBN( )2log

N------------------- ,= Eq. 4-39.

so that the bandwidth efficiency of 4-PPM can be derived as

ηB24---

12---.= = Eq. 4-40.

82

I.e. 4-PPM has twice the bandwidth efficiency as 1/4-RZI and furthermore it guarantees enough

’0’ to ’1’ transitions, so that bit stuffing is also not required. Therefore 4-PPM is a considerable

improvement against 1/4-RZI.

4.2.5 Power Efficiency of 4-PPM

Since the average duty cycle of N-PPM is obviously

aveDC 1N---- ,= Eq. 4-41.

the power efficiency of N-PPM is given by

ηPηB

aveDC------------------ N( ).2log= = Eq. 4-42.

Consequently, the power efficiency of 4-PPM can be derived as

ηP 2.= Eq. 4-43.

I.e. 4-PPM has the same power efficiency as n/m-RZI.

4.3 Run-Length-Limited Code Modulation RLL(d,k)

Run-Length-Limited Code modulation is basically a superset of the previous modulation

schemes. With RLL(d,k) codes the various modulation techniques are classified by means of

two parameters d and k, whereby d is the minimum number of ’0’s between ’1’s and k is the

maximum number of ’0’s between ’1’s after the encoder [50]. For example a 4-PPM can be

considered as a 1/2-RLL(0,6), or 1/4-RZI can be considered as a 1/4-RLL(3,∞ ) code. As derived

by Shannon [51] and presented in Section 5.2 on page 101 there exists a maximum achievable

code rate for a code with certain parameters d and k. This maximum code rate is usually called

code capacity. E.g. an RLL(0,6) code has a code capacity of 0.9942. Noting that 4-PPM has with

83

0.5 a relatively poor code rate although it allows error causing double pulses, Hirt, Hassner and

Heise were seeking for an RLL code with the capability to deal with the shortcomings of the

wireless infrared channel in a better way, and with an improved bandwidth efficiency [33]. The

result was a 2/3-RLL(1,13) code, which they called HHH(1,13) code by using their own initials.

With the parameter d = 1 this code guarantees that there are no legal double pulses as they can

occur with the PPM codes. The parameter k = 13 guarantees that there are enough ’0’ to ’1’

transitions for reliable clock recovery at the receiver. At IrDA this code is now used for the latest

physical layer standard called Very Fast Infrared (VFIR)[1]. Therefore we will look more

closely into the HHH(1,13) in the following.

4.3.1 HHH(1,13) Modulation Scheme

At HHH(1,13) two new bits are encoded per encoding step and thereby three chips are generated.

Consequently, the input block αk and the output block βk are given by

αk a2k a2k 1+,= Eq. 4-44.

βk b3k b3k 1+ b3k 2+ ., ,= Eq. 4-45.

The resulting code rate is derived as

pq---

23--- ,= Eq. 4-46.


Tchip23---Tbit.= Eq. 4-47.

The HHH(1,13) encoder is a finite state machine:

βk f αk αk 1+ αk 2+ ζk, , ,( )= Eq. 4-48.

84

ζk 1+ g αk αk 1+ αk 2+ ζk, , ,( ),=

with the internal state

ζk z1k z2k z3k ,= Eq. 4-50.

and the corresponding initial state

ζ0 1 0 0( ).= Eq. 4-51.

The output function of the HHH(1,13) encoder state machine is given by

b3k z1k z2k⋅= Eq. 4-52.

b3k 1+ z1k z2k z1k z3k a2k a2k 1++( )⋅ ⋅ ⋅ ⋅=

z1k z2k z1k z3k⋅ a2k a2k 1+ a2 k 1+( ) a2 k 1+( ) 1+⋅ ⋅ ⋅ ⋅( )⋅ ⋅+

Eq. 4-53.

b3k 2+ z1k z3k a2k a2k 1++( )⋅ ⋅=

z1k z3k⋅ a2k a2k 1+ a2 k 1+( ) a2 k 1+( ) 1+⋅ ⋅ ⋅ ⋅( )+

Eq. 4-54.

and the next state function is

z1k 1+ z1k z3k⋅( ) z3k a2k⋅( ) z1k a2k a2k 1+ a2 k 1+( )⋅ ⋅ ⋅( )+ +=

z1k a2k a2k 1+ a2 k 1+( ) 1+⋅ a2 k 2+( ) a2 k 2+( ) 1+⋅ ⋅ ⋅ ⋅( )+

Eq. 4-49.

Eq. 4-55.

z2k 1+ z3k a2k⋅( ) z1k z2k a2k a2k 1+⋅ ⋅ ⋅( )+= Eq. 4-56.

85

z3k 1+ z3k a2k 1+⋅( ) z1k a2k a2k 1+⋅ ⋅( ) z1k z2k a2k a2k 1+⋅ ⋅ ⋅( )+ += .

The pulse shaper generates pulses with a duration equal to the chip duration

Tpulse Tchip.=Eq. 4-58.

Figure 4-14 provides an example for the HHH(1,13) modulation, whereby b(t) should only

illustrate the timing relation to a(t) and does not reflect a correct encoder result, since this

depends on the current internal encoder state, which is not taken into account here.

Figure 4-14. HHH(1,13) Modulation

0

1

t

Tchip

0

1

tTbit

Vss

Vdd

tTpulse

a(t)

b(t)

4.3.2 HHH(1,13) Demodulation Scheme


Figure 4-15.

Eq. 4-57.

86

The sampling unit has to sample the received signal r(t) with a sampling offset of

ToffsetTpulse

2-------------- .= Eq. 4-59.

Figure 4-15. HHH(1,13) Eye Diagram of r(t) after Receiver Front-End

-100 -50 0 50 100

-200

-100

0

100

200

300

400

500

time [ns]

curr

ent [

nA]

As HHH(1,13) has the characteristic that double pulses are not allowed, the sampling unit can

perform a single-pulse correction as proposed in [33] and illustrated in Figure 4-16 in the case

of a double pulse occurrence.

Figure 4-16. HHH(1,13) Single-Pulse Correction

Vss

Vdd

r(t)

0

1

b’(t)

t

t

87

The HHH(1,13) decoder is a finite state machine

α'k d β'k β'k 1+ β'k 2+ β, 'k 3+ ζk, , ,( )= Eq. 4-60.

ζk 1+ e β'k β'k 1+ β'k 2+ β, 'k 3+ ζk, , ,( ),= Eq. 4-61.


ζk z1k z2k z3k z4k z5k = Eq. 4-62.


ζ 3– 0 0 0 0 0( ).= Eq. 4-63.

With the auxiliary variable

xk b3 k 3+( ) b3 k 3+( ) 1+ b3 k 3+( ) 2++ += Eq. 4-64.

the output function of the HHH(1,13) decoder is given by

a'2k z3k= Eq. 4-65.

a'2k 1+ b3 k 1+( ) 2+ z1k⋅ z2k z1k xk⋅ ⋅ z4k+ +=Eq. 4-66.

and the next state function is given by

z1k 1+ xk= Eq. 4-67.

z2k 1+ z1k= Eq. 4-68.

88

z3k 1+ z2k z1k xk⋅ ⋅ z2k z1k⋅ b3 k 1+( ) z5k+ + +=

Note that there are three decoding steps (i.e. k = -3, k = -2, k = -1) necessary that generates

invalid output before with the decoding step k = 0 the first valid output is generated. That is also

the reason why as initial state ζ 3– is given. Furthermore the decoder cannot decode the last three

blocks, and therefore dummy blocks that carries no information needs to be transmitted. IrDA

uses a so called flush byte with all bits equal zero for that purpose. Note one byte with eight bit

results in twelve chips and so the decoder can fully be flushed.

Figure 4-17. HHH(1,13) Demodulation

0

1

t

Tchip

0

1

tTbit

Vss

Vdd

t

Tpulserb(t)

a’(t)

b’(t)

rth

t

r(t)

Eq. 4-69.

z4k 1+ z2k z1k xk b3k 2+⋅ ⋅ ⋅ z2k z1k xk b3 k 2+( ) 2++( )⋅ ⋅ z5k+ += Eq. 4-70.

z5k 1+ z2k z1k xk⋅ ⋅= Eq. 4-71.

89

Figure 4-17 provides an example for the HHH(1,13) demodulation, whereby a’(t) should only

illustrate the timing relation to b’(t) and does not reflect a correct decoder result, since this

depends on the current internal decoder state, which is not taken into account here.

4.3.3 Reliability of HHH(1,13)

In the following the reliability of HHH(1,13) is analyzed also according to the criteria derived

in Section 3.3.1 on page 56ff.


HHH(1,13) has a sufficient robustness against quantization errors as indicated in Figure 4-18,

but due to the high duty cycle variations the robustness is not as good as at RZI and 4-PPM.

Figure 4-18. HHH(1,13) Bit Error Probability due to Quantization Errors

1E-60

1E-50

1E-40

1E-30

1E-20

1E-10

1

0.0001 0.001 0.01 0.1

IrDA range


Err

or p

roba

bilit

y P

e bit

d = 1m,=15°ϕ

2cm

mW

Figure 4-19 shows the eye diagram of the received signal after the receiver front-end r(t) under

worst case condition and the corresponding eye opening is given by

E 335nA.≅ Eq. 4-72.

90


Pemaxbit 4.46 10 71–× .≅ Eq. 4-73.

Figure 4-19. HHH(1,13) Eye Diagram of r(t) without Noise under Worst Case Condition

-200

-100

0

100

200

300

400

500

time [ns]

curr

ent [

nA]

-100 -50 0 50 100

In order to minimize the duty cycle variations for an improved bit error probability of

HHH(1,13) Hirt et al. introduced a scrambling mechanism for VFIR (see [1]).



The horizontal eye opening of HHH(1,13) under worst case conditions is shown in Figure 4-20

and is given by

Ehor 107.17 ns.= Eq. 4-74.

91

and with the HHH(1,13) sampling clock frequency of 8 MHz the maximum relative sample

clock phase deviation is given by

Θmax 43%.±= Eq. 4-75.

Figure 4-20. HHH(1,13) Eye Diagram of rb(t) after Quantization Unit

Vss

Vdd

volta

ge le

vel

-100 -50 0 50 100

time [ns]

Vth


As mentioned above the HHH(1,13) modulation scheme limits the maximum length of a

sequence of chips without ’0’ to ’1’ transitions to 13. Therefore also HHH(1,13) offers an

efficient support for the clock recovery at the receiver.

4.3.4 Bandwidth Efficiency of HHH(1,13)

With Equation 4-47 and Equation 4-58 the bandwidth efficiency of HHH(1,13) can be derived

as

ηBTpulseTbit

--------------23--- .= = Eq. 4-76.

92

I.e. HHH(1,13) offers obviously a further improved bandwidth efficiency compared to 1/4-RZI

(ηB = 0.25) and 4-PPM (ηB = 0.5).

4.3.5 Power Efficiency of HHH(1,13)

According to Hirt et al. [33] HHH(1,13) has an average duty cycle of only 0.258 and with that

the power efficiency ηP of HHH(1,13) can be derived as

ηPηB

aveDC------------------

23---

0.258------------- 2.584 .= = = Eq. 4-77.

I.e. HHH(1,13) has not only a good bandwidth efficiency ηB , but also an attractive power

efficiency ηP .

93

94

5 Edge Position Modulation

In this chapter the novel modulation technique EPM is now introduced. After presenting the

basic idea of EPM we derive the achievable bandwidth efficiencies for different variations of

EPM. It is revealed that the variant EPM(5,12,1/3,1) is a promising alternative to the currently

used modulation techniques.

5.1 Basics of EPM

In general the modulation schemes described above are all pulse position based, i.e. time is

divided into discrete time slots Tchip with a duration equal to or longer than the pulse duration

Tpulse and depending on the information to be transmitted there is a pulse within such a time slot

or not (see Figure 5-1).

Figure 5-1. Principle of Pulse Position Modulation Techniques

ChannelCoded Data

ModulatedSignal

Tpulse

0

1

t

Vss

Vdd

t

Tchip Tpulse

An alternative way is the edge position based modulation scheme, i.e. time is divided into

discrete time slots Tchip with a duration shorter than the pulse duration Tpulse, and depending on

the information to be transmitted there is a rising edge of a pulse within such a time slot or not

(see Figure 5-2).

95

Figure 5-2. Principle of Edge Position Modulation Techniques

ChannelCoded Data

ModulatedSignal

Tpulse

0

1

t

Vss

Vdd

t

Tchip Tpulse

In order to avoid inter-symbol interferences a coding scheme is necessary, which guarantees,

that there is a long enough pause TOFFmin between two pulses, so that the rising edge of the

current pulse is not disturbed by the previous pulse. Furthermore the coding scheme should

guarantee that there is a maximum pause between two pulses TOFFmax, so that the receiver can

recover the clock from the received signal by means of a DPLL. Feasible coding schemes for

that purpose are RLL(d,k) codes, where d and k are the minimum and maximum number of ’0’s

between ’1’s after the encoder as already described in Section 4.3 on page 83. I.e. the bit stream

to be transmitted becomes RLL encoded and then the ’1’s of the encoded data stream indicate

the positions where the pulses should start as shown in Figure 5-2.

Figure 5-3 and Figure 5-4 show the required signal processing steps for data transmission by

means of EPM and the corresponding modulator and demodulator components. While the

modulator consists of an RLL(d,k) Encoder and a Pulse Shaper, the demodulator is built up by

an Edge Detector, a DPLL and an RLL(d,k) Decoder.

Figure 5-3 illustrates the corresponding data streams and waveforms of the EPM modulation

process at the transmitter. Data sequence (an) represents the data from an unconstrained digital

information source that should be transmitted over the wireless infrared channel. The

corresponding discrete signal a(t) is transformed by the RLL encoder into the discrete signal b(t).

Note that the ratio between the baud rates of a(t) and b(t) depends on the code rate RRLL of the

used RLL code. (In Figure 5-4 the code rate RRLL is 1/3.) Finally, the waveform s(t) represents

the EPM modulated binary output signal that is generated by the pulse shaper and is transmitted

over the channel. It can be seen that with each ’1’ of b(t) a new pulse starts.

96

Figure 5-3. EPM Modulator Components with Corresponding Signals

RLL Encoder

Pulse Shaper

s(t)

0

1

t

Digital InformationSource

a(t)

0

1

tTbit

b(t)

Vss

Vdd

tTpulse

s(t)


a(t)

b(t)


0 1 0 0 1 11(an) = ...

Tchip

Figure 5-4 illustrates the data streams and waveforms of the EPM demodulation process at the

receiver. Waveform r(t) and rb(t) represent the EPM modulated signal from the transmission

channel before and after the quantization unit, respectively. The waveform rb(t) should be

basically identical to waveform s(t) of Figure 5-3, but due to the wireless infrared channel there

might be some phase jitter. The discrete signal b’(t) represents the recovered RLL encoded

binary data, which should be identical to discrete signal b(t). For that an edge detection process

is used, where each detected rising edge of rb(t) results in a ’1’, otherwise a ’0’ is generated. The

required phase information is retrieved by the DPLL. Data stream b’(t) is used as input for the

RLL decoder logic that finally recovers the original data represented by data stream a’(t). I.e. at

a transmission without bit errors data streams a(t) and a’(t) are identical.

97

Figure 5-4. EPM Demodulator Components with Corresponding Signals

Decoder

Digital InformationSink

rb(t)

0

1

t

EdgeDetection

b’(t)

0

1

t

a’(t)

rb(t)


a’(t)

b’(t)

Quantization Unit

0 1 0 0 1 11(an’) = ...

r(t)


0

i1

t

r(t)

DPLL

Tbit

Vss

Vdd

tTpulse

Tchip

Obviously, the Edge Position Modulation technique has several degrees of freedom and so there

exist many different types of EPM. A specific type of EPM is fully defined by

• the parameter d of the used RLL code that defines the minimum number of ’0’s between ’1’s

of the RLL encoded data stream,

• the parameter k of the RLL code that defines the maximum number of ’0’s between ’1’s of

the encoded data stream,

• the code rate RRLL of the RLL code that defines the ratio between the time slot duration

Tchip and the bit duration Tbit, and

98

• the ratio r between the minimum pause TOFFmin between two pulses and the pulse duration

Tpulse.

Taking this into account the following naming convention is used in the following in order to

specify an EPM variant:

EPM d k RRLL r, , ,( ).

Considering that the previously described modulation technique HHH(1,13) has the parameters

d = 1, k = 13, RRLL = 2/3, and r = 1 one can see that EPM is obviously a superset of HHH(1,13).

In the EPM naming convention HHH(1,13) can be specified as EPM(1,13,2/3,1). The more

general approach of EPM has the advantage that one can find an optimized trade-off between

bandwidth efficiency and reliability. I.e. by setting the parameters accordingly one can adapt

EPM perfectly to the characteristics of the wireless infrared channel.

The ratio r should be chosen so that there are no inter-symbol interferences, i.e. there are

sufficient minimum pauses TOFFmin between two pulses. With a given pulse duration Tpulse the

minimum pause TOFFmin is given by

TOFFmin rTpulse.= Eq. 5-1.

The parameter d must be selected so that the time slot duration Tchip is larger than the jitter of

the rising edges of the received pulses as shown in Figure 5-5. Note that the jitter of the falling

edge does not influence the requirements on Tchip.

Figure 5-5. Lower Limit of Time Slot Duration Tchip

Tchip > Jitter

Jitter

Furthermore Tchip must be at least the double of the achievable granularity of the DPLL of the

receiver. The upper limit of the time slot duration Tchip is per definition the pulse duration Tpulse

99

as it is case at HHH(1,13). The relation between time slot duration Tchip and parameter d is given

by

TchipTpulse TOFFmin+

1 d+----------------------------------------- .= Eq. 5-2.

The parameter k must be selected such as to guarantee sufficient recurrence of signal transitions

for reliable clock recovery in the receiver. The relation between the maximum pause TOFFmax

between two pulses and the parameter k is given by

TOFFmax 1 k+( )Tchip Tpulse.–= Eq. 5-3.

Figure 5-6 illustrates the relations of Tpulse, TOFFmin, TOFFmax, Tchip and the parameters d, k and

r by means of an example.

Figure 5-6. EPM with r = 1, d = 5 and k = 10

RLL(d,k)Encoded Data

ModulatedSignal

TOFF maxTOFF minTpulse

d = 5 k = 10

0

1

t

b(t)

Tchip

tVss

Vdd

r = 1

With the code rate RRLL and the chosen time slot duration Tchip the bit duration Tbit is finally

given by

Tbit1

RRLL-------------Tchip.= Eq. 5-4.

100

Combining Equation 5-1, Equation 5-2 and Equation 5-4 results in the relation between bit

duration Tbit and pulse duration Tpulse given by

Tbit1

RRLL-------------

Tpulse 1 r+( )1 d+

------------------------------- .= Eq. 5-5.

I.e. for a high bandwidth efficiency the code rate RRLL of the RLL code should be as high as

possible. But the maximum achievable code rate, i.e. the code capacity, depends on the chosen

parameters d and k. Therefore we want to investigate the theory of RLL codes in the following

Section 5.2 in order to derive the capacity C(d,k) of the various RLL(d,k) codes.

5.2 RLL Codes in Theory

5.2.1 State Transition Matrix of RLL(d,k) Codes

In general, an RLL(d,k) code can be described as finite state machine by a state transition

diagram [50] as shown in Figure 5-7.

Figure 5-7. State Transition Diagram of RLL(d,k) Codes

1 2 d0 0 0

1

0k

0 0

11 1

d+1 d+2 k+1

The state transition diagram has k+1 states, which are denoted by σ1 ,...,σk 1+ . Transmission of

a ’0’ takes the state machine from state σi to state σi 1+ when i k≤ . A ’1’ may only be

transmitted when the state machine is in the states σd 1+ ,..., σk 1+ , while a ’1’ must be

101

transmitted, when the machine is in state σk 1+ . The corresponding map of states to output

values is given by

ϑ σ i( ) 0 , 2 i k≤ ≤1 , i 1=

= Eq. 5-6.

Any path through the state transition diagram results in a sequence with at least d and maximal

k ’0’s between ’1’s. The corresponding state transition matrix, which gives the number of paths

of going in one step from state σi to state σj , is given by the k 1+( ) k 1+( )× matrix D with

entries dij, where

di1 1= i d 1+≥ Eq. 5-7.

dij 1= j i 1+=

dij 0= otherwise.

For example, the state transition matrix for an RLL(2,7) code is given by

D

0 1 0 0 0 0 0 00 0 1 0 0 0 0 01 0 0 1 0 0 0 01 0 0 0 1 0 0 01 0 0 0 0 1 0 01 0 0 0 0 0 1 01 0 0 0 0 0 0 11 0 0 0 0 0 0 0

.= Eq. 5-8.

The state transition diagram of an RLL(d,k) code with k ∞→ is shown in Figure 5-8. The state

transition diagram has d+1 states, which are denoted by σ1 ,...,σd 1+ . Transmission of a ’0’ takes

the state machine from state σi to state σi 1+ when i d≤ , while a ’1’ may only be transmitted,

when the machine is in state σd 1+ . Any path through the state transition diagram results in a

sequence with at least d ’0’s between two ’1’s.

102

Figure 5-8. State Transition Diagram of RLL(d,∞ ) Codes

2 d d+10 0 0

1

01

The corresponding state transition matrix, which gives the number of paths of going in one step

from state σi to state σj , is given by the d 1+( ) d 1+( )× matrix D with entries dij, where

di1 1= i d 1+= Eq. 5-9.

dij 1= j i 1+=

dij 1= i j d 1+= =

dij 0= otherwise.

For example, the state transition matrix for an RLL(5,∞ ) code is given by

D

0 1 0 0 0 00 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 11 0 0 0 0 1

.= Eq. 5-10.

The finite state machine model allows us to compute the code capacity (see below in

Section 5.2.2), and it is also helpful to compute the number of sequences that start and end in

certain states. The number of distinct sequences of length m that emanate from state σi and

103

terminate in state σj is given by the ijth entry of the matrix Dm. For example the matrix D5 of

the RLL(2,7) code is of the following form:

D5

1 1 1 0 0 1 0 02 1 1 1 0 0 1 03 2 1 1 1 0 0 13 2 1 1 1 0 0 02 2 1 1 1 0 0 02 1 1 1 1 0 0 02 1 0 1 1 0 0 01 1 0 0 1 0 0 0

.=Eq. 5-11.

It can be seen, for instance, that there are exactly 3 sequences of length 5 that emanate from state

σ4 and terminate in state σ1 .

5.2.2 Capacity C(d,k) of RLL Codes

The code capacity C(d,k) is defined as the theoretical upper limit for the code rate p/q that can

be achieved by an RLL code with the parameters d and k:

C d k,( ) RRLL≥ Eq. 5-12.

Shannon [51] showed that the capacity of a code is determined by the largest real eigenvalue λ

of its state transition matrix. Therefore the capacity C(d,k) of RLL(d,k) codes is given by

C d k,( ) λ2log ,= Eq. 5-13.

where λ is the largest real root of the characteristic equation

det D zI–[ ] 0= Eq. 5-14.

with the transition matrix D and the identity matrix I. Table 5-1 lists the resulting code capacities

for various combinations of the runlength parameters d and k.

104

Table 5-1. RLL Code Capacity C(d,k)

k d = 0 d = 1 d = 2 d = 3 d = 4 d = 5 d = 6

2 0.8791 0.4057

3 0.9468 0.5515 0.2878

4 0.9752 0.6174 0.4057 0.2232

5 0.9881 0.6509 0.4650 0.3218 0.1823

6 0.9942 0.6690 0.4979 0.3746 0.2669 0.1542

7 0.9971 0.6793 0.5174 0.4057 0.3142 0.2281 0.1335

8 0.9986 0.6853 0.5293 0.4251 0.3432 0.2709 0.1993

9 0.9993 0.6888 0.5369 0.4376 0.3620 0.2979 0.2382

10 0.9996 0.6909 0.5418 0.4460 0.3746 0.3158 0.2633

11 0.9998 0.6922 0.5450 0.4516 0.3833 0.3282 0.2804

12 0.9999 0.6930 0.5471 0.4555 0.3894 0.3369 0.2924

13 0.9999 0.6935 0.5485 0.4583 0.3937 0.3432 0.3011

14 0.9999 0.6938 0.5495 0.4602 0.3968 0.3478 0.3074

15 0.9999 0.6939 0.5501 0.4615 0.3991 0.3513 0.3122

16 1.0000 0.6942 0.5515 0.4650 0.4057 0.3620 0.3282

Figure 5-9 illustrates that the capacity increases with a decreasing parameter d and an increasing

parameter k.

5.2.3 RLL Code Generation

In order to generate a decodable RLL(d,k) code with a certain code rate p/q, which fulfills the

requirement of Equation 5-12, one has to find a state machine that obeys the (d,k)-constraints

and where each input sequence of the length p can be assigned for each state to a distinctive state

transition that generates an output sequence of the length q. That means the corresponding

q 1+( ) q 1+( )× state transition matrix T with the entries tij must fulfill the following

requirement for each row i:

tij

j 1=

q 1+

∑ 2p≥ Eq. 5-15.

105

Figure 5-9. RLL Code Capacity CRLL(d,k) versus d and k

C(0, )

d=0

d=1

d=2

d=3d=4

d=5d=6

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8 10 12 14 16 18 20

k

CR

LL(d

,k)

∞

C(1, )∞

C(2, )∞

C(3, )∞C(4, )∞C(5, )∞C(6, )∞

While the sums of each row provide the actual numbers of successor states of each state, the term

2p defines the required successor states of each state.

The state transition matrix Dq as defined in Section 5.2.1 would obey the (d,k)-constraints, but

unfortunately it does in general not fulfill the requirement of Equation 5-15. However, there

exist several different methods for deriving from Dq a proper state transition matrix as

summarized by Immink in [50]. In the following the sliding block code algorithm of Adler et al.

[52][53] is introduced, since this method results in general in the lowest logic complexity for the

implementation.

The key idea of the sliding block code algorithm is to split first some states of Dq so that

Equation 5-15 is fulfilled, and then to merge some states in order to reduce the complexity of the

106

encoder and the decoder. The number of offspring states of each state is defined by the

approximate characteristic vector v , that fulfills the following requirement:

Dq v⋅ 2p v⋅≥ Eq. 5-16.

According to the Perron-Frobenius theory of nonnegative matrices the existence of such an

eigenvector is guaranteed [54][55][56]. An algorithm to calculate the approximate characteristic

vector can be found in the appendix of [53].

In order to illustrate the RLL code generation by means of the sliding block code algorithm the

generation of a 1/2-rate RLL(1,3) code is provided as example in the following. For a

fundamental mathematical description of the method please refer directly to [53]. The state

transition diagrams D and D2 of an RLL(1,3) code are shown in Figure 5-10 and the

corresponding state transition matrices are given by

D

0 1 0 01 0 1 01 0 0 11 0 0 0

.= D2

1 0 1 01 1 0 11 1 0 00 1 0 0

.= Eq. 5-17.

Figure 5-10. RLL(1,3) Transition Diagram

1 20 0

1

30

4

11 1 2

3

4

10

0010

01

0001

01

10

Transition Diagram D Transition Diagram D2

The matrix D2 can also be written down in a state transition table as shown in Table 5-2, whereby

the alphabet AD2 = 1, 2, 3, 4 represents the four states.

107

Table 5-2. State Transition Table D2

ζk ζk 1+

1 1 3

2 1 2 4

3 1 2

4 2

One can easily verify that v 1 2 1 1, , ,( )T= is an approximate characteristic vector for D2 that

fulfills Equation 5-16. That means that state σ2 shall be split up into two offspring states.

Therefore we aim to construct a state transition matrix D2

with the alphabet AD2 = 11, 21, 22,

31, 41.

As a first step we exchange in the state transition table the alphabet AD2 by the new alphabet

AD2 as shown in Table 5-3.

Table 5-3. Splitting Step 0

ζk ζk 1+

1 = 11 11 31

2 = 21, 22 11 21, 22 41

3 = 31 11 21, 22

4 = 41 21, 22

It can be seen that now each state has at least two successor states as it is required for a decodable

1/2-rate RLL code. Now one can start to assign two dedicated successor states to each state by

splitting up the offspring states sequentially, whereby the offspring states from one parent state

(here 21 and 22) must not have the same successor states. In our example this splitting process

is quite straightforward as it can be seen in the following Table 5-4. However, in general the

splitting process with the assignment of 2p successor states is somewhat tricky and requires

usually several steps. Therefore Adler et al. provided in [53] an algorithm for this splitting

process, which is applied later in this work for the generation of an RLL(5,12) code (see

Section A.1).

108

Table 5-4. Splitting Step 1

ζk ζk 1+

11 11 31

21 11 41

22 21 22

31 21 22 (11)

41 21 22

With the following mapping of states to output values

ϑ i( )01 , i 11 ∈

10 , i 21 22, ∈

00 , i 31 41, ∈

,

=

Eq. 5-18.

which is besides the superscripts identical to the mapping shown in Figure 5-10, the encoding

table can be then derived as follows:

Table 5-5. Encoding Tableαk 0= αk 1=

ζk ζk 1+ βk ζk 1+ βk11 11 01 31 00

21 11 01 41 00

41, 31, 22 21 10 22 10

Note that the assignment of the successor states to the input values αk 0= and αk 1= is done

in that way so that the decoder has minimized complexity as we will see below. However, by

merging the states of the encoding table that have the same successor states and result in the

same output values βk the complexity of the encoder can be reduced as shown in Table 5-6 and

Table 5-7.

109

Table 5-6. Reduction of Encoding Tableαk 0= αk 1=

ζk ζk 1+ βk ζk 1+ βk11, 21 11 01 22 00

22 21 10 22 10

Table 5-7. Final Reduced Encoding Tableαk 0= αk 1=

ζk ζk 1+ βk ζk 1+ βk11 11 01 22 00

22 11 10 22 10

Figure 5-11 shows the final state transition diagram of the simplified 1/2-rate RLL(1,3) code,

which obviously fulfills the requirements of Equation 5-15, i.e. each state has 2p (= 2) successor

states.

Figure 5-11. Final State Transition Diagram 1/2-rate RLL(1,3)

1 2

0 / 10

1 / 00

1 / 100 / 01

The RLL(1,3) encoder can now be written down as a finite state machine:

βk f αk ζk,( )= Eq. 5-19.

ζk 1+ g αk ζk,( ),= Eq. 5-20.


ζk zk ,= Eq. 5-21.

110


ζ0 0.= Eq. 5-22.

The output function of the RLL(1,3) encoder state machine can be derived from Table 5-7 as

b2k zk= Eq. 5-23.

b2k 1+ zk ak⋅= Eq. 5-24.


zk 1+ ak= . Eq. 5-25.

The decoding table as shown in Table 5-8 can be derived by using the unreduced encoder table

provided in Table 5-5 and the mapping of states to output values of Equation 5-18. For the

generation of the decoding table we make use of the fact that an incoming symbol ’10’

corresponds to the state 11 and a symbol ’01’ to either 21 or 22. With this knowledge one can

determine with at least two incoming symbols the state ζk and thereby the decoded value αk .

In the general case the required symbols are defined by the number of splitting steps of the

encoder table generation.

Table 5-8. Decoding Tableβk βk 1+ ζk ζk 1+ αk00 01 not in range of encoder

00 10 31

4121, 22

21, 221

01 00 11 - 0

01 01 11 - 0

10 00 21 41 0

10 01 21 11 0

10 10 22 21, 22 1

111

Note that it is obviously helpful that the states 31 and 41 have been assigned to the same output

value αk = 1 in Table 5-5, otherwise the decoder would require more input symbols. However,

our RLL(1,3) decoder is obviously a finite look-ahead but state independent machine:

αk d βk( ),= Eq. 5-26.

whereby the logical RLL(1,3) decoder function can be written down as

a'k b'2k 1+ b'2k 2+ b'2k 3+⋅ ⋅= . Eq. 5-27.

5.3 EPM Bandwidth Efficiency in General

As stated in Equation 3-59 on page 65 the bandwidth efficiency is given by

ηBTpulseTbit

-------------- .= Eq. 5-28.

Together with Equation 5-5 on page 101 the bandwidth efficiency of EPM is consequently given

by

ηB RRLL1 d+1 r+------------ .= Eq. 5-29.

Considering that the maximum achievable RLL code rate RRLL is given by the RLL code

capacity C(d,k), which we have derived above in Section 5.2.2 on page 104, the maximum

achievable bandwidth efficiency ηB is given by

ηBmax C d k,( )1 d+1 r+------------ .= Eq. 5-30.

Figure 5-12 shows the maximum achievable bandwidth efficiency ηBmax of EPM with r = 1 as

a function of d and k.

112

Figure 5-12. Maximum Bandwidth Efficiency ηBmax of EPM with r = 1

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

d

Max

imum

Ban

dwid

th E

ffici

ency

k = 9

k = 12

k = 15

k =∞

One can see that with EPM very attractive bandwidth efficiencies can be achieved. In the

following section we want to investigate some EPM variants.

5.4 EPM Variants

As shown above there exist many different variants of EPM with different parameters. This

section should highlight some EPM variants that are interesting for implementation in real

systems. Therefore some implementation requirements for the different EPM parameters are

defined in the following in order to select and classify the EPM variants.

5.4.1 EPM Implementation Requirements

5.4.1.1 Implementation Requirement for r

The required minimum pause TOFFmin between two consecutive pulses to avoid intersymbol-

interferences strongly depends on the filter characteristics of the receiver. However, the channel

simulations above and measurements of currently available infrared transceivers showed that

Tpulse is a reasonable lower limit for TOFFmin. On the other hand a minimal pause greater than

113

1.5 Tpulse does not increase the transmission reliability anymore. I.e. we want to limit

r TOFFmin Tpulse⁄= as follows:

1 r 1.5≤ ≤ . Eq. 5-31.

5.4.1.2 Implementation Requirements for Tchip

The upper limit of the time slot duration Tchip is per definition the pulse duration Tpulse. For the

lower limit we have to consider that Tchip must be larger than the jitter of the rising edges of the

received pulses. Taking the investigations of the wireless infrared channel into account we can

assume that the jitter is less than one third of Tpulse. I.e. we want to limit the relation Tchip/Tpulse

as follows:

13---

TchipTpulse-------------- 1≤ ≤ . Eq. 5-32.

Additionally the relation between Tchip and Tpulse should be chosen in a way that the respective

signals b(t) and s(t) can be both derived from the same system clock, which should be not larger

than the twelvefold of 1/Tpulse. This requirement can be written down as follows:

TchipTpulse--------------

uv--- v 6, and u, v are integer values≤= Eq. 5-33.

5.4.1.3 Implementation Requirement for k

As already mentioned in Section 3.3.1.2 on page 62 Hirt et al. [33] stated that there should be at

least one ’0’ to ’1’ transition within 16 chips for an adequate sample clock recovery with a

DPLL. Although this is certainly only a soft limitation, since the clock recovery capability

strongly depends on the DPLL itself, we will use a similar1 limitation for the parameter k.

k 16≤ . Eq. 5-34.

1. The limitation of Hirt et al. is with k 15≤ a bit lower, but this would exclude some interesting EPM variants as it can be seen in Table 5-9.

114

5.4.1.4 Implementation Requirement for RLL Code Rate

Unfortunately, using a code with the maximum channel capacity as shown in Figure 5-12 is

generally not feasible, since data processing is usually byte-orientated, and therefore we need an

RLL code that encodes 1, 2, 4 or 8 input bits and outputs an integer number of chips.

Additionally an RLL code with only 1 or 2 input bits are preferable, since the resulting RLL

logic circuitry is then less complex.

5.4.2 Selected EPM Variants

Table 5-9 lists some interesting EPM variants that fulfill the above defined requirements. While

the upper variants in the table excels with high bandwidth efficiency, the lower ones offer high

transmission reliability.

Table 5-9. EPM Variants

EPM variants Characteristics

RRLL = N/M d k r ηB Tchip/Tpulse

8/23 5 15 1 1.043 1/3

1/3 5 12 1 1 1/3

8/25 6 16 1.33 0.96 1/3

1/4 6 10 1.33 0.75 1/3

2/5 4 16 1 1 2/5

8/23 5 15 1.4 0.870 2/5

1/3 5 12 1.4 0.833 2/5

4/9 3 10 1 0.889 1/2

2/5 4 16 1.5 0.8 1/2

1/3 4 16 1.5 0.667 1/2

4/9 3 10 1.4 0.741 3/5

2/5 3 10 1.4 0.667 3/5

1/3 3 6 1.4 0.556 3/5

8/15 2 9 1 0.8 2/3

1/2 2 7 1 0.75 2/3

8/15 2 9 1.25 0.711 2/3

1/2 2 7 1.25 0.667 3/4

8/15 2 9 1.4 0.667 4/5

1/2 2 7 1.4 0.625 4/5

115

ηB

The EPM concept obviously allows to find an ideal trade-off between transmission speed and

reliability, and therefore EPM enables the implementation of communication systems that are

tailored to the targeted transmission channel.

In the following chapter we want to investigate EPM(5,12,1/3,1) in more detail, because this

variant appears to offer a high bandwidth efficiency at low hardware complexity.

8/15 2 9 1.5 0.64 5/6

1/2 2 7 1.5 0.6 5/6

2/3 1 13 1 0.667 1

EPM variants Characteristics

RRLL = N/M d k r Tchip/Tpulse

116

6 EPM(5,12,1/3,1) - Implementation Example

6.1 EPM(5,12,1/3,1) Evaluation

As derived in Section 5.4 the modulation scheme EPM(5,12,1/3,1) appears to be a promising

candidate for the electrical modulation of a wireless infrared communication system. Therefore

we analyze this EPM variant in this chapter in more detail and for that we use the a novel 1/3-

rate RLL(5,12) code that was presented by the author in [9]. The generation of this RLL(5,12)

code is provided in Appendix A of this work. Adler presented in [57] already an other 1/3-rate

RLL(5,12) code, but this one requires more states in the encoder and is therefore a bit more

complex than the new one.

6.1.1 EPM(5,12,1/3,1) Modulation Scheme

At EPM(5,12,1/3,1) one bit is encoded per encoding step and thereby three chips are generated.

Consequently, the input block αk and the output block βk are given by

αk ak= Eq. 6-1.

βk b3k b3k 1+ b3k 2+ ., ,= Eq. 6-2.

The resulting code rate is derived as

pq--- 1

3---= Eq. 6-3.

117


Tchip13---Tpulse.= Eq. 6-4.

The EPM(5,12,1/3,1) encoder is a finite state machine:

βk f αk ζk,( )= Eq. 6-5.

ζk 1+ g αk ζk,( ),= Eq. 6-6.


ζk z1k z2k z3k z4k = Eq. 6-7.


ζ0 0 0 0 0( ).= Eq. 6-8.

The output function of the EPM(5,12,1/3,1) encoder state machine is given by

b3k z1k z2k z3k ak z1k z3k z4k⋅⋅⋅+⋅⋅= Eq. 6-9.

b3k 1+ z1k z2k z3k z4k z1k z2k z3k z4k⋅⋅ ⋅+⋅⋅ ⋅= Eq. 6-10.

b3k 2+ ak z2k z3k z4k ak z1k z2k z3k z4k⋅⋅⋅⋅+⋅⋅⋅=

ak z1k z3k z4k ak z2k z3k z4k⋅⋅⋅+⋅⋅⋅+Eq. 6-11.

118


z1k 1+ ak z1k z3k z4k⋅ ⋅ ⋅( ) z1k z2k z3k z4k⋅ ⋅ ⋅( )+=

z1k z2k z3k z4k⋅ ⋅ ⋅( ) ak z1k z2k z4k⋅ ⋅ ⋅( )+ +

Eq. 6-12.

z2k 1+ ak z1k z3k z4k⋅ ⋅ ⋅( ) ak z2k z3k z4k⋅ ⋅ ⋅( )+=

ak z1k z2k z3k⋅ ⋅ ⋅( ) ak z1k z2k⋅ ⋅( ) ak z2k z3k z4k⋅ ⋅ ⋅( )+ + +

ak z2k z3k z4k⋅ ⋅ ⋅( ) z1k z2k z3k z4k⋅ ⋅ ⋅( )+ +

Eq. 6-13.


z1k z2k z4k⋅ ⋅( ) ak z1k z3k⋅ ⋅( ) z1k z2k z4k⋅ ⋅( )+ + +

ak z1k z2k z4k⋅ ⋅ ⋅( ) ak z2k z3k z4k⋅ ⋅ ⋅( )+ +

ak z1k z2k z4k⋅ ⋅ ⋅( )+

Eq. 6-14.


ak z⋅ 2k z3k z4k⋅ ⋅( ) ak z2k z3k z4k⋅ ⋅ ⋅( )+ +

ak z⋅ 1k z2k z3k z4k⋅ ⋅ ⋅( ) ak z1k z3k z4k⋅ ⋅ ⋅( )+ +



Eq. 6-15.

The pulse shaper generates pulses with a duration three times the chip duration

Tpulse 3Tchip.= Eq. 6-16.

Figure 6-1 provides an example for the EPM(5,12,1/3,1) modulation, whereby b(t) should only

illustrate the timing relation to a(t) and does not reflect a correct encoder result, since this

depends on the current internal encoder state, which is not taken into account here.

119

Figure 6-1. EPM(5,12,1/3,1) Modulation

0

1

t

Tchip

0

1

tTbit

Vss

Vdd

tTpulse

s(t)

a(t)

b(t)

6.1.2 EPM(5,12,1/3,1) Demodulation Scheme


Figure 6-2.

Figure 6-2. EPM(5,12,1/3,1) Eye Diagram of r(t) after the Receiver Front-End

-80 0 80

-200

-100

0

100

200

300

400

500

time [ns]

curr

ent [

nA]

120

The sampling unit has to sample the received signal r(t) with a sampling offset of

ToffsetTchip

2------------ .= Eq. 6-17.

As at EPM(5,12,1/3,1) the pulse duration is three times of the chip duration, each pulse results

in at least three consecutive logical ’1’s. With potential pulse extensions even more logical ’1’s

can occur. But with the knowledge that with the used (5,12)-RLL code after one logical ’1’s

there are at least five logical ’0’, the sampling unit performs always a pulse correction as

illustrated in Figure 6-3, which is basically an edge detection. I.e. the sampling unit is only

sensitive on pulse edges and does not care about pulse durations.

Figure 6-3. Edge Detection for EPM(5,12,1/3,1)

Vss

Vdd

r(t)

0

1

b’(t)

„allowed“ pulseextension

The EPM(5,12,1/3,1) decoder is a finite look-ahead but state independent machine

α'k d β'k β'k 1+ β'k 2+ β, 'k 3+ β'k 4+, , ,( )= Eq. 6-18.

121

and the decoder function is given by

a'k b'3k b'3k 1+ b'3 k 1+( ) b'3 k 1+( ) 1+ b'3 k 1+( ) 2+ b'3 k 3+( ) 2+⋅ ⋅ ⋅ ⋅ ⋅ +=

b'3k b'3k 1+ b'3 k 1+( ) b'3 k 3+( )⋅ ⋅ ⋅ b'3 k 2+( ) b'3 k 4+( ) 1+⋅+ + +

b'3 k 1+( ) 2+ b'3 k 4+( ) 2+⋅ b'3 k 1+( ) 2+ b'3 k 4+( )⋅+ + +

b'3 k 1+( ) 1+ b'3 k 4+( ) 2+⋅ b'3 k 1+( ) 1+ b'3 k 4+( )⋅+ + +

b'3 k 1+( ) b'3 k 3+( ) b'3 k 3+( ) 1+ b'3 k 3+( ) 2+⋅ ⋅ ⋅+ +

b'3k 2+ b'3 k 2+( ) 2+ b'3 k 4+( ) 2+⋅ ⋅ b'3k 2+ b'3 k 4+( )⋅+ + +

b'3k 1+ b'3 k 2+( ) 1+ b'3 k 2+( ) 2+ b'3 k 4+( ) 2+⋅ ⋅ ⋅+ +

b'3 k 3+( ) 1++ b'3k 1+ b'3 k 2+( ) 1+⋅ b'3k 1+ b'3 k 4+( )⋅+ + +

b'3k b'3 k 2+( ) b'3 k 2+( ) 1+ b'3 k 2+( ) 2+ b'3 k 3+( ) b'3 k 3+( ) 1+ b'3 k 3+( ) 2+⋅ ⋅ ⋅ ⋅ ⋅ ⋅+

Eq. 6-19.

The decoder requires similar to the HHH(1,13) dummy chips in order to flush its content

completely. The EPM(5,12,1/3,1) decoder requires 12 flush chips, and therefore the transmitter

should add at least 4 bits to the payload data.

Figure 6-4 provides an example for the EPM(5,12,1/3,1) demodulation, whereby a’(t) should

only illustrate the timing relation to b’(t) and does not reflect a correct decoder result.

6.1.3 Reliability of EPM(5,12,1/3,1)


Figure 6-5 shows the bit error probabilities due to quantization errors of EPM(5,12,1/3,1) and of

the other modulation schemes. It can be seen that EPM has a better robustness against

quantization errors than RZI and HHH(1,13) and is only outperformed by 4-PPM.

Figure 6-6 shows the eye diagram of the received signal after the receiver front-end r(t) without

noise under worst case condition and the corresponding eye opening is given by

E 377nA.≅ Eq. 6-20.

122

Figure 6-4. EPM(5,12,1/3,1) Demodulation

0

1

t

Tchip

0

1

tTbit

Vss

Vdd

t

Tpulserb(t)

a’(t)

b’(t)

rth

t

r(t)


Pemaxbit 1.96 10 89–× .≅ Eq. 6-21.



The horizontal eye opening of EPM under worst case conditions is shown in Figure 6-7 and is

given by

Ehor 25.35 ns.= Eq. 6-22.

123

Figure 6-5. EPM(5,12,1/3,1) Bit Error Probability due to Quantization Errors

1E-60

1E-50

1E-40

1E-30

1E-20

1E-10

1

0.0001 0.001 0.01 0.1

HHH

RZI

EPM

4PPM

IrDA range

d = 1m,=15°


Err

or p

roba

bilit

y P

e bit

2cm

mW

ϕ

Figure 6-6. EPM(5,12,1/3,1) Eye Diagram of r(t) without Noise under Worst Case Condition

-200

-100

0

100

200

300

400

500

curr

ent [

nA]

-100 -50 0 50 100

time [ns]

This results in a maximum sample clock deviation of

Tmax∆ 12.675 ns±= Eq. 6-23.

124

and with the EPM sampling clock frequency of 24 MHz the maximum relative sample clock

phase deviation is given by

Θmax 30%.±= Eq. 6-24.

Figure 6-7. EPM(5,12,1/3,1) Eye Diagram after Quantization Unit

time [ns]

-80 0 80

Vss

Vdd

volta

ge le

vel

Vth

EPM(5,12,1/3,1) obvioulsy requires at the receiver a phase recovery with a fairly high

granularity compared to the previous methods. Therefore this thesis presents in Section 6.2.3 a

DPLL that can provide the required granularity without the need of a higher system clock of the

receiver logic.


As mentioned above the EPM modulation scheme limits the maximum length of a sequence of

chips without ’0 to ’1’ transitions to 12. Therefore also EPM offers an efficient support for the

clock recovery at the receiver.

125

6.1.4 Bandwidth Efficiency of EPM(5,12,1/3,1)

As already described in Section 5.4.2 the bandwidth efficiency of EPM(5,12,1/3,1) can be

derived as

ηB RRLL1 d+1 δ+------------⋅ 1

3--- 1 5+

1 1+------------⋅ 1= = = Eq. 6-25.

Therefore the bandwidth efficiency of EPM(5,12,1/3,1) significantly excels the bandwidth

efficiencies of the current IrDA modulation schemes.

6.1.5 Power Efficiency of EPM

According to simulation results EPM(5,12,1/3,1) has an average duty cycle of 0.29, what causes

an outstanding power efficiency of

ηPηB

aveDC------------------ 1

0.29---------- 3.448 .= = = Eq. 6-26.

Note that the average duty cycle is slightly worse than the HHH(1,13) duty cycle, but due to

excellent bandwidth efficiency, also EPM’s power efficiency excels.

6.2 System Implementation with EPM(5,12,1/3,1)

This section describes how EPM(5,12,1/3,1) can be implemented in a wireless infrared

communication system. In particular it is shown that existing IrDA compliant systems can easily

enhanced by EPM.

6.2.1 System Impact of EPM Extension

Figure 6-9 shows the basic system architecture of an IrDA compliant communication system as

already described in Section 1.3.4 on page 8. The novel EPM modulation technique can be very

126

easily integrated in such a system just by enhancing the infrared controller by the EPM

modulator and demodulator. The infrared transceiver is not at all affected by EPM. The impact

on the IrDA protocol stack, which is running as SW on the CPU, is limited to the Hardware

Abstraction Layer (HAL) and the Infrared Link Access Protocol (IrLAP), which need to be

slightly enhanced so that the EPM mode of the IR controller can be utilized. Actually, the

required change of IrLAP is very similar to the change that was necessary at the introduction of

HHH(1,13) [58]. But since IrLAP is already prepared for an additional modulation scheme, the

effort for this modifications can be more or less neglected.

Figure 6-8. IrDA Compliant Infrared Communication System

CPU CPUIRController

IRController

IR TransceiversDevice A Device B

HALIrLAP

IrLMP

UpperLayers

SWApplication

HALIrLAP

IrLMP

UpperLayers

SWApplication

6.2.2 Infrared Controller with EPM Extension

Figure 6-9 illustrates how a typical architecture of an IrDA compliant infrared controller can be

extended by EPM(5,12,1/3,1). Basically the IR controller architecture can be subdivided into

five main building blocks as described in the following.

6.2.2.1 CRC Unit

The CRC unit serves to append a CRC flag to the outgoing IrLAP frames and it performs an error

detection by checking the CRC of the incoming frames. The CRC unit is not affected by the

127

EPM modulation technique, since for EPM the same CRC flags can be used as for FIR and

VFIR, i.e. for 4-PPM and HHH(1,13), respectively.

Figure 6-9. IrDA Compliant Infrared Controller with EPM(5,12,1/3,1) Extension

System Bus

CRCChecking

Serial/Parallel

TX SignalRX Signal

MUX

CRC Unit

Modulation UnitSynchronizationUnit

Infrared Controller

IrLAP frame +CRC

Demodulation Unit

RZI

FIFO

Bus InterfaceUnit

4PPM HHH(1,13) EPM(5,12,1/3,1)

RZI 4PPM HHH(1,13) EPM(5,12,1/3,1)

CRCGeneration

DPLL

MUX

Synchronization

Registers

IrLAP frame +CRC

IrLAP frame

6.2.2.2 Modulation Unit

The Modulation Unit modulates the bits of the IrLAP frame with the CRC flag from the CRC

unit in order to create the TX signal, which drives the off-chip infrared transceiver. Here the

novel EPM(5,12,1/3,1) modulation state machine as described in Section 6.1.1 can be

implemented in parallel to the state machines of the other modulation schemes of the IrDA

128

standard. Besides the pure modulation this unit has to perform also some framing operations as

described for EPM in Section 6.2.4.

6.2.2.3 Synchronization Unit

The synchronization unit detects and synchronizes the RX signal from the off-chip IrDA

infrared transceiver, and furthermore it performs the sample clock phase recovery. Since

EPM(5,12,1/3,1) requires a phase recovery with a high granularity, a somewhat more

sophisticated clock recovery method with a novel DPLL is recommended as described in

Section 6.2.3. However, the introduced DPLL can also be used for 4-PPM and for HHH(1,13)

and therefore the implementation overhead is negligible.

6.2.2.4 Demodulation Unit

The Demodulation Unit demodulates the synchronized RX signal in order to retrieve the RX

frame. The EPM edge detection and the RLL decoder of the EPM demodulator can be

implemented in parallel to the other demodulators. The EPM demodulation with the RLL

decoder is described in Section 6.1.2. The edge detection should be implemented as described

in Section 6.2.3.3 so that it fits to the introduced DPLL.

6.2.2.5 Bus Interface Unit

The bus interface unit with its data and control registers builds up the interface of the infrared

controller to the bus system of the system architecture. The FIFO is used as buffer in order to

compensate the bandwidth difference between the Infrared communication system and the bus

system. However, the EPM modulation technique does not influence the bus interface unit

besides some control bits that are required to control the EPM modulation and demodulation.

6.2.3 Clock Recovery and Edge Detection for EPM(5,12,1/3,1)

As described in Section 3.2.2 on page 52 the sample clock phase needs to be retrieved at the

receiver from the received signal. Since EPM(5,12,1/3,1) requires a relatively high sample clock

frequency of 24 MHz with a maximum sampling clock phase deviation of 12.675 ns (see

Section 6.1.3.2), a sophisticated clock recovery by means of a DPLL is required. Millar et al.

presented in [47] a DPLL that is suited for IrDA's FIR standard and that could be adapted to our

129

needs. But this DPLL requires a system clock that is six times higher than the sampling clock.

That means for EPM(5,12,1/3,1) we would need a system clock of 144 MHz. Such a high system

clock is usually available in modern system architectures, but nevertheless the following will

present an edge detection method for EPM with a DPLL that requires only a system clock of

48 MHz as it is typically used for today’s 4-PPM implementations. Figure 6-10 shows the main

building blocks that are required for the clock recovery and edge detection at EPM(5,12,1/3,1)

with a system clock of 48 MHz.

Figure 6-10. Clock Recovery and Edge Detection Circuitry for EPM(5,12,1/3,1)

rneg(t)

Edge detection

b’(t)

1:2 DPLL

Synchronization

rb(t)

rpos(t)

sample clock

polarity

The edge detection block detects any rising edge of the received signal and thereby the signal

b’(t) is recovered. The correct phase of the sampling clock is retrieved and provided by the

DPLL. In order to keep the required system clock frequency to a minimum, the incoming RX

signal rb(t) is synchronized on both the rising and the falling edge of the system clock resulting

in rpos(t) or rneg(t), respectively. The DPLL indicates with the signal ’polarity’ whether rpos(t) or

rneg(t) shall be used for the edge detection. The following describes the individual building

blocks in more detail.

130

6.2.3.1 Synchronization

In general input signals to digital circuits are usually synchronized to the rising edge of the

system clock in order to achieve a fully synchronous design. This is also done in our case with

the input signal rb(t) from the infrared transceiver, which is sampled by the rising edge of the

48 MHz system clock. But in addition to that the signal rb(t) is also sampled with the falling edge

of the system clock, as shown in Figure 6-11, in order to preserve important phase information

for the sample clock recovery.

Figure 6-11. Synchronization of Input Signal rb(t)

D Q

Clk

D Q

Clk

D Q

Clk

rpos(t) D Q

Clk

rneg(t)

rb(t)

Synchronization

Note that for each path two consecutive flip-flops are used. Although one flip-flop would be

sufficient from a pure functional perspective, it is recommend to use two flip-flops in order to

avoid unambiguous states after the synchronization.

6.2.3.2 Digital PLL for EPM(5,12,1/3,1)

Figure 6-12 shows the proposed DPLL for EPM(5,12,1/3,1) that retrieves the sample clock with

additional phase information, i.e. signal ’polarity’, from the synchronized RX signals rneg(t) and

rpos(t). The DPLL consists basically of a phase detector, a filter and a variable oscillator that are

all clocked by the positive edge of the 48 MHz system clock. They are described in the

following:

Phase Detector

The phase detector is a state machine that compares the rising edges of the synchronized RX

signals rpos(t) and rneg(t) with those of the recovered sample clock. If the rising edges of the RX

131

signals do not occur within the expected phase ranges, then the phase detector produces an UP

or DOWN signal. The following Figures 6-13 to 6-20 illustrate the behavior of the phase

detector depending on the deviation of the position of the rising edges from the expected phase

range.

Figure 6-12. DPLL Circuitry

Phasedetector

Filter(4-bit timer)

Variableoscillator

Up

Down

1st MSB

2nd MSB

rneg(t) rpos(t)

sample clock

polarity

If the 2nd MSB of the DPLL filter (see Figure 6-12) is ’1’, then the rising edge of the RX input

signal rb(t) should be within the phase range as shown in Figure 6-13. If the 2nd MSB of the

DPLL filter is ’0’, then the rising edge of the RX input signal rb(t) should be within the phase

range as shown in Figure 6-14. In both cases neither an UP signal nor a DOWN signal is

generated by the phase detector.

Figure 6-13. Phase Detector Behavior at Phase Lock when 2nd MSB = ’1’

48MHz system clock

RX input signal rb(t)

Recovered sample clock

UP

DOWN

rneg(t)

expectedphase range

132

Figure 6-14. Phase Detector Behavior at Phase Lock when 2nd MSB = ’0’

48MHz system clock



UP

DOWN

rpos(t)

expectedphase range

If the rising edge of the RX input signal rb(t) is a half system clock period earlier than expected,

then the phase detector generates an UP signal. Figure 6-15 and Figure 6-16 illustrate this

behavior if the 2nd MSB is ’1’ and if the 2nd MSB is ’0’, respectively.

Figure 6-15. Phase Detector Behavior at a Phase Error of Tsysclk/2 when 2nd MSB = ’1’

48MHz system clock



UP

DOWN

rneg(t)

expectedphase range

133

Figure 6-16. Phase Detector Behavior at a Phase Error of Tsysclk/2 when 2nd MSB = ’0’

48MHz system clock



UP

DOWN

rpos(t)

expectedphase range

If the rising edge of the RX input signal rb(t) is a full system clock period earlier than expected,

then the phase detector generates an UP signal. Figure 6-17 and Figure 6-18 illustrate this


Figure 6-17. Phase Detector Behavior at a Phase Error of Tsysclk when 2nd MSB = ’1’


UP

DOWN

rneg(t)

expectedphase range

134

Figure 6-18. Phase Detector Behavior at a Phase Error of Tsysclk when 2nd MSB = ’0’

48MHz system clock



UP

DOWN

rpos(t)

expectedphase range

If the rising edge of the RX input signal rb(t) is a half system clock period later than expected,

then the phase detector generates a DOWN signal. Figure 6-19 and Figure 6-20 illustrate this


Figure 6-19. Phase Detector Behavior at a Phase Error of -Tsysclk/2 when 2nd MSB = ’1’

48MHz system clock



UP

DOWN

rneg(t)

expectedphase range

135

Figure 6-20. Phase Detector Behavior at a Phase Error of -Tsysclk/2 when 2nd MSB = ’0’

48MHz system clock



UP

DOWN

rpos(t)

expectedphase range

Figure 6-21 shows the circuitry of the phase detector and Table 6-1 shows the corresponding

value table of the phase detector logic.

Figure 6-21. Phase Detector

D Q

Clk

rpos(t)

rneg(t)

Phasedetector

logic

Up

2nd MSBrecoveredsample clock

Down

a

bc

d

D Q

Clk

D Q

Clk

D Q

Clk

Filter

The filter consists of a 4-bit counter, which is increased by 1, when it gets a DOWN and is

decreased by 1, when it gets an UP from the phase detector. The initial value of the counter is

0101.

136

The 2 most significant bits of the 4-bit counter determines the phase of the recovered clock and

whether the RX signal is sampled by the rising or the falling edge of the 48 MHz system clock.

The 2 least significant bits ensure that the counter acts as a low-pass filter, since several UP and

DOWN signals are required to change the phase of the sample clock.

Table 6-1.

Input Output

2nd MSB

recovered sample clock a b c d UP DOWN

1 0 0 0 1 0 1 0

0 0 1 0 1 0 1 0

0 0 0 0 1 0 1 0

1 1 0 0 1 0 0 1

0 1 1 0 1 0 0 1

1 1 1 0 1 0 0 1

otherwise 0 0

Value Table of Phase Detector Logic

Variable Oscillator

The variable oscillator generates the sample clock by means of a free-running 1-bit counter,

which is clocked by the 48 MHz system clock. The phase of the sample clock is shifted in

dependency of changes of the 2 MSBs from the Filter as indicated in Table 6-2.

Table 6-2. Phase Shift of Sample Clock

Change of the 2 MSBs Phase shift

’00’ ’11’→ ’10’ ’01’→

’01’ ’10’→ ’11’ ’00’→

137

6.2.3.3 Sampling and Edge Detection

Figure 6-22 shows the basic sampling and edge detection circuitry, which corresponds to the

above described DPLL. The signal rneg(t) is sampled with the rising edge and rpos(t) is sampled

with the falling edge of the 48 MHz system clock each time the recovered sampling clock is

high. The signal polarity, which is basically the 2nd MSB from the Filter of the DPLL,

determines, which recovered data stream is used for the following edge detection, which is

realized by a flip-flop and ’AND’ gate. The resulting signal b’(t) is then ready for being RLL

decoded in order to derive the origin data stream.

Figure 6-22. Sampling and Edge Detection

MUX

D

En

recoveredsample clock

rpos(t)

rneg(t)

polarity

Q

D Q

En

D Q

En

D Q

En

&

Signal b’(t) toRLL decoder

Sampled RXsignal

Edge detectorinput

6.2.3.4 Manner of Operation for Clock Phase Recovery

This section describes how the DPLL establishes phase lock, i.e. how it balances a phase offset

of the actual positions of the rising edges of the RX input signal rb(t) from the expected phase

range. As consecutively described in the following the clock phase recovery depends on the

value of the 2nd MSB and the degree of the average phase error.

Average Phase Offset of Tsysclk/2 and 2nd MSB = ’1’

Figure 6-23 illustrates the case when the 2nd MSB of the DPLL filter is ’1’ and when the

expected phase range of the rising edge of the RX input signal rb(t) is too late by a half system

clock period. The DPLL phase detector generates UP signals and thereby reduces the value of

the DPLL filter. As soon as the 2nd MSB changes from ’1’ to ’0’ the signal rpos(t), which is

138

sampled with the falling edge of the system clock, is used as edge detection input. Thereby the

expected phase range of the rising edge of the RX input signal rb(t) is earlier and matches with

the actual edge position. Consequently no UP signals are generated anymore and phase lock is

established.

Figure 6-23. Clock Recovery with Average Phase Offset Tsysclk/2 and with 2nd MSB = ’1’

48MHz system clock



rpos(t)

b’(t)

Sampled RX signal

Edge detection input

rneg(t)

UP

2 MSBs of filter ‚01' or ‚11' ‚00' or ‚10'

expectedphase range

expectedphase range



expected phase range of the rising edge of the RX input signal rb(t) is too late by a full system


the DPLL filter. As soon as the 2nd MSB changes from ’1’ to ’0’ the signal rpos(t), which is

sampled with the falling edge of the system clock, is used as edge detection input. Thereby the

expected phase range of the rising edge of the RX input signal rb(t) is earlier, but is still too late

by a half system clock period. Consequently further UP signals are generated and phase lock is

139

not yet established. The final phase lock is then achieved as described below and illustrated in

Figure 6-26.

Figure 6-24. Clock Recovery with Average Phase Offset Tsysclk and with 2nd MSB = ’1’

48MHz system clock



rpos(t)

b’(t)

Sampled RX signal


rneg(t)

UP


expectedphase range

expectedphase range

Average Phase Offset of -Tsysclk/2 and 2nd MSB = ’1’


expected phase range of the rising edge of the RX input signal rb(t) is too early by a half system

clock period. The DPLL phase detector generates DOWN signals and thereby increases the

value of the DPLL filter. As soon as the 2nd MSB changes from ’1’ to ’0’ the signal rneg(t), which

is sampled with the rising edge of the system clock, is used as edge detection input. Thereby the

expected phase range of the rising edge of the RX input signal rb(t) is later and matches with the

actual edge position. Consequently no DOWN signals are generated anymore and phase lock is

established.

140

Figure 6-25. Clock Recovery with Average Phase Offset -Tsysclk/2 and with 2nd MSB = ’1’

48MHz system clock



rpos(t)

b’(t)

Sampled RX signal


rneg(t)

DOWN


expectedphase range

expectedphase range



expected phase range of the rising edge of the RX input signal rb(t) is too late by a half system

clock period. The DPLL phase detector generates UP signals and thereby increases the value of

the DPLL filter. As soon as the 2nd MSB changes from ’0’ to ’1’ the signal rneg(t), which is

sampled with the rising edge of the system clock, is used as edge detection input. Thereby the

expected phase range of the rising edge of the RX input signal rb(t) is earlier and matches with

the actual edge position. Consequently no UP signals are generated anymore and phase lock is

established.

141

Figure 6-26. Clock Recovery with Average Phase Offset Tsysclk/2 and with 2nd MSB = ’0’

48MHz system clock



rpos(t)

b’(t)

Sampled RX signal


rneg(t)

UP


expectedphase range

expectedphase range

Average Phase Offset of Tsysclk and 2nd MSB = ’0’


expected phase range of the rising edge of the RX input signal rb(t) is too late by a full system


the DPLL filter. As soon as the 2nd MSB changes from ’0’ to ’1’ the signal rneg(t), which is

sampled with the rising edge of the system clock, is used as edge detection input. Thereby the

expected phase range of the rising edge of the RX input signal rb(t) is earlier, but is still too late

by a half system clock period. Consequently further UP signals are generated and phase lock is

not yet established. The final phase lock is then achieved as described above and illustrated in

Figure 6-23.

142

Figure 6-27. Clock Recovery with Average Phase Offset Tsysclk and with 2nd MSB = ’0’

48MHz system clock



rpos(t)

b’(t)

Sampled RX signal


rneg(t)

UP


expectedphase range

expectedphase range

Average Phase Offset of -Tsysclk/2 and 2nd MSB = ’0’


expected phase range of the rising edge of the RX input signal rb(t) is too early by a half system

clock period. The DPLL phase detector generates DOWN signals and thereby increases the

value of the DPLL filter. As soon as the 2nd MSB changes from ’0’ to ’1’ the signal rpos(t), which

is sampled with the falling edge of the system clock, is used as edge detection input. Thereby the

expected phase range of the rising edge of the RX input signal rb(t) is later and matches with the

actual edge position. Consequently no DOWN signals are generated anymore and phase lock is

established.

143

Figure 6-28. Clock Recovery with Average Phase Offset -Tsysclk/2 and with 2nd MSB = ’0’

48MHz system clock



rpos(t)

b’(t)

Sampled RX signal


rneg(t)

DOWN


expectedphase range

expectedphase range

6.2.3.5 Sampling Clock Phase Accuracy

The sampling clock phase can obviously be adjusted with a granularity of half the system clock

period. That means that the maximum phase deviation of the DPLL from the optimal sample

clock phase is given by

T∆Tsysclk 2⁄

2-----------------------± 1

4 48MHz×---------------------------- 5.208 ns±= = = Eq. 6-27.

With the EPM sampling clock frequency of 24 MHz the maximum relative sample clock phase

deviation of the DPLL is given by

Θ T∆Tchip------------

24MHz4 48× MHz---------------------------- 12.5%.±=±=±= Eq. 6-28.

144

Considering that the introduced EPM(5,12,1/3,1) scheme allows a maximum sample clock

deviation of Tmax∆ 12.675 ns±= respectively a maximum relative deviation of Θmax 30%±=

(see Section 6.1.3.2), one can see that the proposed clock recovery method fulfills obviously our

requirements for EPM.

6.2.4 Framing Structure for EPM

In order to transmit payload data (e.g. an IrLAP frame according to the IrDA standard) over the

wireless infrared channel in a secure manner, it needs to be packed into a frame that consists of

a preamble PA, a start flag STA, the payload data itself, Flush bits FB, a CRC field, a stop flag

STO and a NULL field [1][2].

The preamble is necessary for phase synchronization at the receiver. It should have enough ’0’

to ’1’ transitions, so that the DPLL at the receiver can achieve its phase-lock, and it should have

the same average duty cycle as the RLL code. We define the preamble PA for EPM as the

concatenation of ten times the 72-chip preamble period PP.

PP = [100000000 000100000 000100000 000000100 000000100 000100000 100000000]

PA = [PP PP PP PP PP PP PP PP PP PP]

The start and stop flags are necessary to indicate the beginning and the end of the frame. In order

to distinguish these flags from payload data we use a sequence that cannot be generated by the

RLL(5,12) encoder. By using such “illegal” sequences we can avoid bit or character stuffing as

it is necessary at the RZI modulation technique. The start and stop flags are given by:

STA = [000001000 000000000 100000000 000100000 010000001 000000000 000100000

000000100 000001000 000000000 100000000 000100000 010000001 000000000 000100000

000000100]

STO = [000001000 000000000 100000000 000100000 010000001 000000000 000100000

000000100 000001000 000000000 100000000 000100000 010000001 000000000 000100000

000000100]

145

The CRC (cyclic redundancy check) field is used for error detection at the receiver. Here we

propose to use the same 32-bit CRC code as it is specified for FIR and VFIR in the IrDA standard

[1].

The flush bits FB are necessary to flush the RLL(5,12) decoder at the receiver, so that the

payload data and the CRC field can be completely decoded. For that 4 flush bits are required,

which we define as

FB = [0000].

The NULL field is used to enforce a pause between two consecutive frames, so that the receiver

does not get a data overflow. It can also be used as end of frame detection, if the receiver did not

recognize the STO flag. The NULL field is defined as:

NULL = [000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000].

Figure 6-29 shows the complete frame generation process. It indicates that only the payload

data, the CRC field and the flush bits are fed through the RLL(5,12) encoder.

Figure 6-29.

Stop FlagStart FlagPreamble

TX Frame

IrLAP Frame + CRC32

IrLAP Frame + CRC32

FB appending

RLL(5,12) encoded TX Frame Null Flag

TX Signal with extended pulses

Pulse extension

RLL(5,12) encoding andflag appending

FB

EPM modulation and packet Generation Flow

146

6.3 HW Prototype and Measurements Results

In order to verify the functionality of EPM(5,12,1/3,1) a hardware prototype has been build up.

This section describes the prototype itself and the measurement results that have been achieved.

6.3.1 HW Prototype Implementation

Figure 6-30 describes the FPGA board that has been used for the prototype implementation of

the EPM(5,12,1/3,1) modulation scheme. The main components are the infrared transceiver,

which is compliant to the IrDA’s FIR standard, and the Xilinx FPGA, which comprises the

infrared controller with the EPM modulation and demodulation as described in Section 6.2.2.

Figure 6-30. FPGA Board Description

In order to control the FPGA board it has been plugged on an ARM7 evaluation board as shown

in Figure 6-31. On the ARM7 the hardware abstraction layer (HAL) and the lower layers of the

IrDA protocol stack are implemented, so that two prototype boards are able to establish a

connection and exchange data.

147

Figure 6-31. Piggyback Prototype with FPGA Board and ARM7 Evaluation Board

The prototype is describe in more detail in [59] and the implemented SW is described in [60].

6.3.2 Measured Eye Diagrams after Quantization

The first goal of the prototype was to verify the eye diagram simulation results of Section 6.1.3.

For that the measuring setup with an oscilloscope as shown in Figure 6-32 has been established.

Figure 6-32. Measuring Setup for Eye Diagram Measuring

FPGAwith IR

Controller

Prototype board B

Transmitter

Receiver

Oscilloscope

FPGA

with IR

Controller

Prototype board A

RX

TX

RX

TX

d

ϕ

Figure 6-33 to 6-35 show the measurement results for different distances d and different angles

ϕ . Obviously the simulation results are basically confirmed by the eye diagrams that has been

148

measured with an oscilloscope. In particular it is of interest that the trailing edges of the pulses

show much more jitter than the leading edges. Here the fact is of benefit that the EPM

demodulation is only sensitive on the trailing edges.

Figure 6-33. Eye Diagram after Quantization at d = 5cm, phi = 0°

Figure 6-34. Eye Diagram after Quantization at d = 10 cm, phi = 30°

6.3.3 Measured Frame Processing

The second goal of the prototype was to verify whether the infrared controller with the novel

DPLL is able to demodulate the received signals that have been measured above. For that the

measuring setup with a logic analyzer as shown in Figure 6-36 has been established. Table 6-3

describes the corresponding signals that have been measured by the logic analyzer.

149

Figure 6-35. Eye Diagram after Quantization at d = 100 cm, phi = 0°

Figure 6-36. Measuring Setup for Frame Processing Measuring

FPGAwith IR

Controller

Prototype board B

Transmitter Receiver

RX

TXFPGAwith IR

Controller

Prototype board A

TX

RX

Logic Analyzer

Con

nect

or fr

ame

Table 6-3. Description of Measured SignalsTX The frame sent by the board A, measured at the transceiver

RX The received signal measured at the transceiver of board B

RX_DELAYED The received signal from the transceiver looped through the FPGA

REC_EN_PULSE The recovered enable pulse signal from the DPLL

RX_SAMPLED The received signal sampled with rec_en_pulse

RX_EDGE The sampled signal after the edge detection

STARTFLAG Indicates the reception of a valid startflag

STOPFLAG Indicates the reception of a valid stopflag

DATAVALID Strobes for each decoded data bit

150

Figure 6-37 shows the measurement results for the transmission and demodulation of the byte

0x5952. It can be seen that the byte has been correctly demodulated and therefore the full

functionality of the EPM modulation technique has been verified on hardware.

Figure 6-37. Measurement Results of Logic Analyzer

LASTDATA Indicates the last decoded data bit

RX_DECODED The decoded user-data+crc

151

152

7 Conclusion and Outlook

This thesis investigated various modulation techniques that are appropriate for mobile, short-

range, point to point and low cost infrared data interconnection applications. In particular the

novel Edge Position Modulation with Run-Length-Limited coding has been introduced, which

is a consequent further development of the existing methods. The evaluation criteria of the

modulation techniques were the bandwidth efficiency, the power efficiency, and the

transmission reliability.

The achievable bit rate of infrared communications systems is mainly limited by the bandwidth

of the infrared transceivers, thus the bandwidth efficiency is a major criterion of the modulation

techniques. We showed that certain EPM variants offer a significantly increased bandwidth

efficiency over existing methods. For example by using EPM(5,12,1/3,1) in combination with a

FIR infrared transceiver, which has a specified bandwidth of 8 MHz, one could achieve a bit rate

of 8 Mbit/s in contrary to HHH(1,13) that would enable only a bit rate of 5.33 Mbit/s with a FIR

transceiver.

But EPM excels not only with superior bandwidth efficiency, but also with an excellent power

efficiency as proven in this thesis. This is in particular of importance, since mobile devices are

usually battery powered and therefore power efficiency is a key requirement for our type of

applications.

The transmission reliability mainly depends on the capability of the modulation technique to

adapt the signal to the wireless infrared channel in a way that allows demodulation at the receiver

with a low bit error rate. Therefore a linear baseband model of the wireless infrared channel had

been derived in this thesis and then the various modulation schemes were applied to this model.

The thesis revealed the strengths and weaknesses of the different methods and showed that EPM

can guarantee a reliable transmission, since it can easily be optimized for the wireless infrared

channel. However, EPM requires at the receiver a phase recovery with a fairly high granularity,

what is the only major drawback of this novel modulation technique. But this thesis presented

153

also a DPLL that can provide the required granularity without the need of a higher system clock

of the receiver logic.

Table 7-1 provides a comparison of the currently used modulation techniques with the

introduced EPM(5,12,1/3,1) variant, and thereby gives a summary of the key findings of this

thesis.

Table 7-1. Summary of Evaluation Parameters

Modulation scheme 1/4-RZI 4-PPM HHH(1,13) EPM(5,12,1/3,1)

Bandwidth efficiency 0.25 0.5 0.667 1

Bit rate with Tpulse = 125 ns 2 Mbit/s 4 Mbit/s 5.33 Mbit/s 8 Mbit/s

Power efficiency 2 2 2.584 3.448

Quantization error probabil-ity under worst case condi-tions

5.50E-80 6.04E-110 4.46E-71 1.96E-89

Sample clock frequency 2 MHz 8 MHz 8 MHz 24 MHz

Maximum absolute sample clock phase deviation

53.33 ns± 56.07 ns± 53.59 ns± 12.67 ns±

Maximum relative sample clock phase deviation

10.7%± 45%± 43%± 30%±

Maximum sequence length without ’0’ to ’1’ transitions

∞ 6 13 12

Finally this thesis has shown that EPM(5,12,1/3,1) could be very easily integrated into IrDA

compliant communication systems, since it is basically transparent for the infrared transceiver

and the IrDA SW protocol stack.

In order to give an outlook we want to refer to the latest development at IrDA. In [61] and [62]

the IrDA community has proposed a new standard called Ultra Fast Infrared (UFIR). This new

standard is supposed to support a data rate of 100 Mbit/s and shall therefore be a significant

improvement compared to VFIR (16 Mbit/s). This improvement shall be mainly achieved by an

enhanced infrared transceiver, but UFIR shall also use the faster 8B10B modulation code [63].

This modulation technique has a bandwidth efficiency of 8/10, which is better than the efficiency

of HHH(1,13), but is still worse than the bandwidth efficiency of EPM(5,12,1/3,1). However,

one would have to analyze how good EPM fits to the new infrared transceivers. This could be

subject of further investigations on EPM.

154

A RLL(5,12) Generation

This appendix describes the generation of the novel 1/3-rate RLL(5,12) code that has been

presented in Section 6.1 on page 117ff. The generation is done according to the sliding block

code algorithm, which has been provided by Adler et al. in [53] and briefly introduced in

Section 5.2.3 on page 105 of this work.

A.1 Encoder Generation

The state transition matrix D of an RLL(5,12) code is according to Equation 5-7 given by

D

0 1 0 0 0 0 0 0 0 0 0 0 00 0 1 0 0 0 0 0 0 0 0 0 00 0 0 1 0 0 0 0 0 0 0 0 00 0 0 0 1 0 0 0 0 0 0 0 00 0 0 0 0 1 0 0 0 0 0 0 01 0 0 0 0 0 1 0 0 0 0 0 01 0 0 0 0 0 0 1 0 0 0 0 01 0 0 0 0 0 0 0 1 0 0 0 01 0 0 0 0 0 0 0 0 1 0 0 01 0 0 0 0 0 0 0 0 0 1 0 01 0 0 0 0 0 0 0 0 0 0 1 00 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0

,= Eq. A-1.

155

and the corresponding matrix D3, which we need for the 1/3-rate code, can be derived as

D3

0 0 0 1 0 0 0 0 0 0 0 0 00 0 0 0 1 0 0 0 0 0 0 0 00 0 0 0 0 1 0 0 0 0 0 0 01 0 0 0 0 0 1 0 0 0 0 0 01 1 0 0 0 0 0 1 0 0 0 0 01 1 1 0 0 0 0 0 1 0 0 0 01 1 1 0 0 0 0 0 0 1 0 0 01 1 1 0 0 0 0 0 0 0 1 0 01 1 1 0 0 0 0 0 0 0 0 1 01 1 1 0 0 0 0 0 0 0 0 0 11 1 1 0 0 0 0 0 0 0 0 0 00 1 1 0 0 0 0 0 0 0 0 0 00 0 1 0 0 0 0 0 0 0 0 0 0

.= Eq. A-2.

The matrix D3 can also be written down in a state transition table as shown in Table A-1,

whereby the alphabet AD2 = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 represents the thirteen states.

Table A-1. State Transition Table D3

ζk ζk 1+

1 4

2 5

3 6

4 1 7

5 1 2 8

6 1 2 3 9

7 1 2 3 10

8 1 2 3 11

9 1 2 3 12

10 1 2 3 13

11 1 2 3

12 2 3

13 3

156

An approximate characteristic vector for D3 can be derived as

v 3 4 5 6 8 10 9 9 8 6 6 4 1, , , , , , , , , , , ,( )T= Eq. A-3.

and therefore we modify the state transition table as shown in Table A-2, whereby the offspring

states of a parent state i are written down as i1 vi,

. E.g. the term 21,4 represents the offspring states

21, 22, 23 and 24.

Table A-2. Splitting Step 0

ζk ζk 1+

1 = 11,3 41,6

2 = 21,4 51,8

3 = 31,5 61,10

4 = 41,6 11,3 71,9

5 = 51,8 11,3 21,4 81,9

6 = 61,10 11,3 21,4 31,5 91,8

7 = 71,9 11,3 21,4 31,5 101,6

8 = 81,9 11,3 21,4 31,5 111,6

9 = 91,8 11,3 21,4 31,5 121,4

10 = 101,6 11,3 21,4 31,5 131

11 = 111,6 11,3 21,4 31,5

12 = 121,4 21,4 31,5

13 = 131 31,5

In order to assign two dedicated successor states to each state we apply now the splitting

algorithm provided by Adler et al. in [53] as shown in Table A-3 to A-6. At each step the parent

states are of the form ij,k having weight vij k, k j– 1+= . Their offspring become symbols of the

form ij' k, ' , where j j'≤ , k' k≤ , having weight k' j'– 1+ . In addition ij j, is abbreviated by ij .


ζk ζk 1+

11,3 41,6

21,4 51,6 57,8

31,5 61,4 65,6 67,10

41,6 11,3 71,4 75,6 77,9

51,6 11,3 81,4 85,6 87,9

157

ζk ζk 1+


ζk ζk 1+

11,3 41,3 44,5 46

21,3 51,3 54,5 56

24 57,8

31,2 61,4

33 65,6

34,5 67,8 69 610

41,3 11,3 77,8 79

44,5 71,4

46 75,6

51,3 11,3 87,8 89

54,5 81,4

56 85,6

123,4, 115,6, 105,6, 95,6, 85,6, 75,6, 65,6, 57,8 21,3 24

111,4, 101,4, 91,4, 81,4, 71,4, 61,4 11,3 31,2 33 34,5

67,8 91,4

69 95,6

610 97 98

77,8 101,4

79 105,6

87,8 111,4

89 115,6

97 121,2

98 123,4

121,2 31,2 (33) 34,5

123,4, 115,6, 105,6, 95,6, 85,6, 75,6, 65,6, 57,8 21,4

111,4, 101,4, 91,4, 81,4, 71,4, 61,4 11,3 31,5

67,10 91,4 95,6 97,8

77,9 101,4 105,6

87,9 111,4 115,6

97,8 121,2 123,4

121,2 31,5

158


ζk ζk 1+

11,2 41,2 43 46

13 44,5

21,2 51,2 53 56

23 54,5

24 57,8

31,2 61,2 63 64

33 65,6

34 67,8

35 69 610

41,2 11,2 13 79

43 77,8

44,5 71,2 73 74

46 75,6

51,2 11,2 13 89

53 87,8

54,5 81,2 83 84

56 85,6

123,4, 115,6, 105,6, 95,6, 85,6, 75,6, 65,6, 57,8 21,2 23 24

111,2, 101,2, 91,2, 81,2, 71,2, 61,2 11,2 13 33

121, 113, 103, 93, 83, 73, 63 31,2

122, 114, 104, 94, 84, 74, 64 34 35

67,8 91,2 93 94

69 95,6

610 97 98

77,8 101,2 103 104

79 105,6

87,8 111,2 113 114

89 115,6

97 121 122

98 123,4


ζk ζk 1+

11 41 42

12 43 46

13 44 45

159

ζk ζk 1+

21 51 52

22 53 56

23 54 55

24 57 58

31 61 62

32 63 64

33 65 66

34 67 68

35 69 610

111, 101, 91, 81, 71, 61, 51, 41 11 12

42 13 79

43 77 78

44 71 72

45 73 74

46 75 76

52 13 89

53 87 88

54 81 82

55 83 84

56 85 86

123, 115, 105, 95, 85, 75, 65, 57 21 22

124, 116, 106, 96, 86, 76, 66, 58 23 24

112, 102, 92, 82, 72, 62 13 33

121, 113, 103, 93, 83, 73, 63 31 32

122, 114, 104, 94, 84, 74, 64 34 35

67 91 92

68 93 94

69 95 96

610 97 98

77 101 102

78 103 104

79 105 106

87 111 112

88 113 114

89 115 116

97 121 122

98 123 124

160

With the following mapping of states to output values

ϑ i( )

001 , i 11 12 13, , ∈

010 , i 21 22 23 24, , , ∈

100 , i 31 32 33 34 35, , , , ∈000 , else

,

= Eq. A-4.

the encoding table can be then derived as

Table A-7. Encoding Table

αk 0= αk 1=

ζk ζk 1+ βk ζk 1+ βk11 41 000 42 000

12 46 000 43 000

13 44 000 45 000

21 51 000 52 000

22 56 000 53 000

23 54 000 55 000

24 57 000 58 000

31 61 000 62 000

32 63 000 64 000

33 65 000 66 000

34 67 000 68 000

35 69 000 610 000

111, 101, 91, 81, 71, 61, 51, 41 11 001 12 001

42 79 000 13 001

43 77 000 78 000

44 71 000 72 000

45 73 000 74 000

46 75 000 76 000

52 89 000 13 001

53 87 000 88 000

54 81 000 82 000

55 83 000 84 000

56 85 000 86 000

123, 115, 105, 95, 85, 75, 65, 57 21 010 22 010

161

αk 0= αk 1=

ζk ζk 1+ βk ζk 1+ βk

Note that the assignment of the successor states to the input values αk 0= and αk 1= is done

in that way so that the decoder has minimized complexity as we will see below in Section A.2.

By merging the states of the encoding table, which have the same successor states and result in

the same output values βk , the complexity of the encoder can be reduced as shown in Table A-

8 to A-11.

Table A-8. First Reduction of Encoding Table

αk 0= αk 1=


124, 116, 106, 96, 86, 76, 66, 58 23 010 24 010

112, 102, 92, 82, 72, 62 33 100 13 001

121, 113, 103, 93, 83, 73, 63 31 100 32 100

122, 114, 104, 94, 84, 74, 64 34 100 35 100

67 91 000 92 000

68 93 000 94 000

69 95 000 96 000

610 98 000 97 000

77 101 000 102 000

78 103 000 104 000

79 105 000 106 000

87 111 000 112 000

88 113 000 114 000

89 115 000 116 000

97 121 000 122 000

98 123 000 124 000

11 41 000 42 000

12 46 000 43 000

13 44 000 45 000

21 41 000 52 000

22 56 000 53 000

23 54 000 55 000

98, 89, 79, 69, 56, 46, 33, 24 57 000 58 000

87, 77, 67, 54, 44, 31 41 000 62 000

162

αk 0= αk 1=


Table A-9. Second Reduction of Encoding Table

αk 0= αk 1=

ζk ζk 1+ βk ζk 1+ βk11 41 000 42 000

12 24 000 43 000

53, 43, 34, 23, 13 31 000 32 000

21 41 000 52 000

22 24 000 53 000

24 57 000 58 000

31 41 000 62 000

32 63 000 64 000

35 24 000 610 000

41 11 001 12 001

52, 42 24 000 13 001

57 21 010 22 010

58 23 010 24 010

62 24 100 13 001

63 31 100 32 100

64 34 100 35 100

610 24 000 32 000

97, 88, 78, 68, 55, 45, 32 63 000 64 000

34 67 000 68 000

35 69 000 610 000

41 11 001 12 001

42 79 000 13 001

43 77 000 78 000

52 89 000 13 001

53 87 000 88 000

57 21 010 22 010

58 23 010 24 010

62 33 100 13 001

63 31 100 32 100

64 34 100 35 100

610 98 000 97 000

163

Table A-10. Third Reduction of Encoding Table

αk 0= αk 1=

ζk ζk 1+ βk ζk 1+ βk21, 11 41 000 42 000

22, 12 24 000 13 000

13 31 000 32 000

24 57 000 58 000

31 41 000 62 000

32 63 000 64 000

35 24 000 610 000

41 11 001 12 001

42 24 000 13 001

57 21 010 22 010

58 13 010 24 010

62 24 100 13 001

63 31 100 32 100

64 13 100 35 100

610 24 000 32 000

Table A-11. Forth Reduction of Encoding Table

αk 0= αk 1=

ζk ζk 1+ βk ζk 1+ βk11 41 000 42 000

12 24 000 13 000

13 31 000 32 000

24 57 000 58 000

31 41 000 62 000

32 63 000 64 000

35 24 000 610 000

41 11 001 12 001

42 24 000 13 001

57 11 010 12 010

58 13 010 24 010

62 24 100 13 001

63 31 100 32 100

64 13 100 35 100

610 24 000 32 000

164

By introducing binary values one can derive from Table A-11 the encoder truth table for the

encoder logic as shown in Table A-12.

Table A-12. Encoder Truth Table

αk 0= αk 1=

ζk ζk 1+ βk ζk 1+ βk11 = 0000 0111 000 1000 000

12 = 0001 0011 000 0010 000

13 = 0010 0100 000 0101 000

24 = 0011 1001 000 1010 000

31 = 0100 0111 000 1011 000

32 = 0101 1100 000 1101 000

35 = 0110 0011 000 1110 000

41 = 0111 0000 001 0001 001

42 = 1000 0011 000 0010 001

57 = 1001 0000 010 0001 010

58 = 1010 0010 010 0011 010

62 = 1011 0011 100 0010 001

63 = 1100 0100 100 0101 100

64 = 1101 0010 100 0110 100

610 = 1110 0011 000 0101 000

From the encoder truth table one can easily derive the encoder state machine as described in

Section 6.1.1.

A.2 Decoder Generation

The decoding table as shown in Table A-13 can be derived by using the unreduced encoder table

provided in Table A-7 and the mapping of states to output values of Equation A-4. For the

generation of the decoding table we make use of the fact that an incoming symbol ’100’

corresponds to the states 11, 12 or 13, a symbol ’010’ to 21, 22, 23 or 24, and a symbol ’001’ to

31, 32, 33, 34 or 35. With this knowledge one can determine with at least five incoming symbols

the state ζk and thereby the decoded value αk .

165

Table A-13. Decoding Table

βk βk 1+ βk 2+ βk 3+ βk 4+ ζk ζk 1+ ζk 2+ ζk 3+ ζk 4+ αk000 000 000 001 000 43

5377

87101,2

111,211,3

11,31

000 000 000 010 000 42

52

610

79

89

98

105,6

115,6

123,4

21,4

21,4

21,4

1

000 000 000 100 000 43

53

610

77,8

87,8

97

102,4

112,4

121,2

31,5

31,5

31,5

1

000 000 001 44

54

67

77

87

71,2

81,2

91,2

101,2

111,2

11,3

11,3

11,3

11,3

11,3

0

000 000 010 46

56

69

79

89

98

75,6

85,6

95,6

105,6

115,6

123,4

21,4

21,4

21,4

21,4

21,4

21,4

0

000 000 100 000 000 45

55

68

78

88

97

74

84

94

104

114

122

34,5

34,5

34,5

34,5

34,5

34,5

67,10

67,10

67,10

67,10

67,10

67,10

91,8

91,8

91,8

91,8

91,8

91,8

1

000 000 100 000 001 45

55

68

78

88

97

73

83

93

103

113

121

31

31

31

31

31

31

61,2

61,2

61,2

61,2

61,2

61,2

11,3

11,3

11,3

11,3

11,3

11,3

1

000 000 100 000 010 44

54

67

77

87

72

82

92

102

112

33

33

33

33

33

65,6

65,6

65,6

65,6

65,6

21,4

21,4

21,4

21,4

21,4

0

000 000 100 000 100 45

55

68

78

88

97

73

83

93

103

113

121

31,2

31,2

31,2

31,2

31,2

31,2

62,4

62,4

62,4

62,4

62,4

62,4

31,5

31,5

31,5

31,5

31,5

31,5

1

000 001 000 000 000 41

51

61

71

81

91

101

111

11,2

11,2

11,2

11,2

11,2

11,2

11,2

11,2

42,3

42,3

42,3

42,3

42,3

42,3

42,3

42,3

77,9

77,9

77,9

77,9

77,9

77,9

77,9

77,9

101,6

101,6

101,6

101,6

101,6

101,6

101,6

101,6

0

166


52

62

72

82

92

102

112

13

13

13

13

13

13

13

13

44

44

44

44

44

44

44

44

71,2

71,2

71,2

71,2

71,2

71,2

71,2

71,2

11,3

11,3

11,3

11,3

11,3

11,3

11,3

11,3

1

000 001 000 000 010 41

51

61

71

81

91

101

111

12

12

12

12

12

12

12

12

46

46

46

46

46

46

46

46

75,6

75,6

75,6

75,6

75,6

75,6

75,6

75,6

21,4

21,4

21,4

21,4

21,4

21,4

21,4

21,4

0

000 001 000 000 100 42

52

62

72

82

92

102

112

13

13

13

13

13

13

13

13

44,5

44,5

44,5

44,5

44,5

44,5

44,5

44,5

72,4

72,4

72,4

72,4

72,4

72,4

72,4

72,4

31,5

31,5

31,5

31,5

31,5

31,5

31,5

31,5

1

000 001 000 001 41

51

61

71

81

91

101

111

11

11

11

11

11

11

11

11

41,2

41,2

41,2

41,2

41,2

41,2

41,2

41,2

11,3

11,3

11,3

11,3

11,3

11,3

11,3

11,3

0

000 010 000 000 000 57

65

75

85

95

105

115

123

21,2

21,2

21,2

21,2

21,2

21,2

21,2

21,2

52,3

52,3

52,3

52,3

52,3

52,3

52,3

52,3

87,9

87,9

87,9

87,9

87,9

87,9

87,9

87,9

111,6

111,6

111,6

111,6

111,6

111,6

111,6

111,6

0

000 010 000 000 001 58

66

76

86

96

106

116

124

23

23

23

23

23

23

23

23

54

54

54

54

54

54

54

54

81,2

81,2

81,2

81,2

81,2

81,2

81,2

81,2

11,3

11,3

11,3

11,3

11,3

11,3

11,3

11,3

1

167


65

75

85

95

105

115

123

22

22

22

22

22

22

22

22

56

56

56

56

56

56

56

56

85,6

85,6

85,6

85,6

85,6

85,6

85,6

85,6

21,4

21,4

21,4

21,4

21,4

21,4

21,4

21,4

0

000 010 000 000 100 58

66

76

86

96

106

116

124

23

23

23

23

23

23

23

23

54,5

54,5

54,5

54,5

54,5

54,5

54,5

54,5

82,4

82,4

82,4

82,4

82,4

82,4

82,4

82,4

31,5

31,5

31,5

31,5

31,5

31,5

31,5

31,5

1

000 010 000 001 57

65

75

85

95

105

115

123

21

21

21

21

21

21

21

21

51,2

51,2

51,2

51,2

51,2

51,2

51,2

51,2

11,3

11,3

11,3

11,3

11,3

11,3

11,3

11,3

0

000 010 000 010 58

66

76

86

96

106

116

124

24

24

24

24

24

24

24

24

57,8

57,8

57,8

57,8

57,8

57,8

57,8

57,8

21,4

21,4

21,4

21,4

21,4

21,4

21,4

21,4

1

000 100 000 000 64

74

84

94

104

114

122

34,5

34,5

34,5

34,5

34,5

34,5

34,5

67,10

67,10

67,10

67,10

67,10

67,10

67,10

91,8

91,8

91,8

91,8

91,8

91,8

91,8

1

000 100 000 001 63

73

83

93

103

113

121

31

31

31

31

31

31

31

61,2

61,2

61,2

61,2

61,2

61,2

61,2

11,3

11,3

11,3

11,3

11,3

11,3

11,3

0

000 100 000 010 62

72

82

92

102

112

33

33

33

33

33

33

65,6

65,6

65,6

65,6

65,6

65,6

21,4

21,4

21,4

21,4

21,4

21,4

1

168

βk βk 1+ βk 2+ βk 3+ βk 4+ ζk ζk 1+ ζk 2+ ζk 3+ ζk 4+ αk

From the decoding table one can easily derive the finite look-ahead but state independent

decoder as described in Section 6.1.2.

000 100 000 100 63

73

83

93

103

113

121

31,2

31,2

31,2

31,2

31,2

31,2

31,2

62,4

62,4

62,4

62,4

62,4

62,4

62,4

31,5

31,5

31,5

31,5

31,5

31,5

31,5

0

001 000 000 000 001 12 43 77 101,2 11,3 1

001 000 000 000 010 11 42 79 105,6 21,4 0

001 000 000 000 100 12 43 77,8 102,4 31,5 1

001 000 000 001 13 44 71,2 11,3 1

001 000 000 010 12 46 75,6 21,4 1

001 000 000 100 13 44,5 72,4 31,5 1

001 000 001 11 41,2 11,3 0

010 000 000 000 001 22 53 87 111,2 11,3 1

010 000 000 000 010 21 52 89 115,6 21,4 0

010 000 000 000 100 22 53 87,8 112,4 31,5 1

010 000 000 001 23 54 81,2 11,3 0

010 000 000 010 22 56 85,6 21,4 1

010 000 000 100 23 54,5 82,4 31,5 0

010 000 001 21 51,2 11,3 0

010 000 010 24 57,8 21,4 1

100 000 000 000 35 610 97,8 121,4 1

100 000 000 001 34 67 91,2 11,3 0

100 000 000 010 35 69 95,6 21,4 1

100 000 000 100 34 67,8 92,4 31,5 0

100 000 001 31 61,2 11,3 0

100 000 010 33 65,6 21,4 0

100 000 100 000 000 32 64 34,5 67,10 91,8 1

100 000 100 000 001 32 63 31 61,2 11,3 1

100 000 100 000 010 31 62 33 65,6 21,4 0

100 000 100 000 100 32 63 31,2 62,4 31,5 1

169

170

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175

176

Lebenslauf

Thomas Lüftner

A-4040 Linz, Leopold-Figl-Str. 46

[email protected]

Persönliche Daten

Geburtsdatum / -ort: 16.04.1975 / Linz, Oberösterreich

Staatsbürgerschaft: Österreich

Familienstand: Ledig

Werdegang

1981 bis 1989 Grundschule in Oftering und Linz

1989 bis 1994 Höhere Technische Bundeslehranstalt für Maschinenbau Linz

Reifeprüfung mit ausgezeichnetem Erfolg bestanden

10/1994 bis 06/2000 Diplom-Studium der Mechatronik

Johannes Kepler Universität Linz

Abschluss mit Auszeichnung

07/1999 bis 10/1999 Forschungsaufenthalt an der University of California, Berkeley

01/2000 bis 09/2000 Präsenzdienst beim Österreichischen Bundesheer

10/2000 bis 06/2005 Mitarbeiter bei Danube Integrated Circuits Engineering

Design Center von Infineon Technologies in Linz

10/2002 Abschluss 1. Studienabschnitt Wirtschaftswissenschaften

Johannes Kepler Universität Linz

03/2002 bis 06/2003 Lehrbeauftragter für Project Engineering

Fachhochschule Hagenberg, Oberösterreich

seit 07/2005 Mitarbeiter bei Infineon Technologies in München

177

Curriculum Vitae

Thomas Lüftner

A-4040 Linz, Leopold-Figl-Str. 46

[email protected]

Personal Information

Day / Place of Birth: 16.04.1975 / Linz, Austria

Nationality: Austria

Maritial Status: Single

Educational and Professional Career

1981 to 1989 Elementary school in Oftering und Linz

1989 to 1994 Higher Technical School for Mechanical Engineering in Linz

Graduation with honors

10/1994 to 06/2000 Study of Mechatronics

Johannes Kepler University, Linz

Graduation with honors

07/1999 to 10/1999 Research internship at University of California, Berkeley

01/2000 to 09/2000 Military service

10/2000 to 06/2005 Employee at Danube Integrated Circuits Engineering

Design Center of Infineon Technologies in Linz

10/2002 Degree in Economics (1. Studienabschnitt)

Johannes Kepler University Linz

03/2002 to 06/2003 Visiting lecturer for Project Engineering

Fachhochschule Hagenberg, Upperaustria

since 07/2005 Employee at Infineon Technologies in Munich, Germany

178

Documents

Edge Position Modulation for Wireless Infrared Communications