UPTEC F10 001

Examensarbete 20 pFebruari 2010

The influence of the dispersion map on optical OFDM transmissions

Kamyar Forozesh

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

The influence of the dispersion map on optical OFDMtransmissions

Kamyar Forozesh

Fiber-optic networks are an integral part of todays digital communication system. In these networks, distances of typically 400 km to 6000 km are linked together, and information is transfered at extremely high data rates. As the demands for capacity increases, finding new methods for cost effective long-haul transmission systems that can be used to increase the capacity becomes of high interest. In this work Orthogonal Frequency Division Multiplexing (OFDM), which is a standard digital modulation format in many wireless communication systems, for instance the IEEE 802.11n, is adapted to the optical domain and used for data transmission. The advantage of OFDM in the optical domain is that it transforms a high data rate stream into many simultaneously low bit rate streams that are efficiently frequency multiplexed. By doing so high spectral efficiency is achieved and many of the impairments encountered in high data rate transmissions are avoided. The disadvantage is however, that OFDM has inherently a high peak-to-average power ratio. As a result, OFDM suffers from nonlinearities occurring along the transmission line. The low nonlinear tolerance of OFDM in fiber optic applications restricts the feasible transmission distance. The goal of this work is to assess the suitability of OFDM in fiber-optic communications.

ISSN: 1401-5757, UPTEC F10001Examinator: Tomas NybergÄmnesgranskare: Dr. Jan BergmanHandledare: Dr. Sander Lars Jansen

DIPLOMA THESIS

THE INFLUENCE OF THE

DISPERSION MAP ON OPTICALOFDMTRANSMISSIONS

KAMYAR FOROZESH

Uppsala School of Engineering

and

Department of Astronomy and Space Physics, Uppsala University, Sweden

APRIL 10, 2009

ABSTRACT

Fiber-optic networks are an integral part of todays digitalcommunication system. In thesenetworks, distances of typically 400 km to 6000 km are linkedtogether, and informationis transfered at extremely high data rates. As the demands for capacity increases, findingnew methods for cost effective long-haul transmission systems that can be used to in-crease the capacity becomes of high interest. In this work Orthogonal Frequency DivisionMultiplexing (OFDM), which is a standard digital modulation format in many wirelesscommunication systems, for instance the IEEE 802.11n, is adapted to the optical domainand used for data transmission. The advantage of OFDM in the optical domain is that ittransforms a high data rate stream into many simultaneouslylow bit rate streams that areefficiently frequency multiplexed. By doing so high spectral efficiency is achieved andmany of the impairments encountered in high data rate transmissions are avoided. Thedisadvantage is however, that OFDM has inherently a high peak-to-average power ratio.As a result, OFDM suffers from nonlinearities occurring along the transmission line. Thelow nonlinear tolerance of OFDM in fiber optic applications restricts the feasible trans-mission distance. The goal of this work is to assess the suitability of OFDM in fiber-opticcommunications.

iii

To my father

CONTENTS

Abstract iii

Contents vii

Acknowledgments ix

Preface xi

1 Introduction 11.1 Fiber Optic Networks 11.2 The Optical Fiber 2

2 Fiber Optic Impairments 32.1 Power Loss 32.2 Dispersion 42.3 Kerr-Effect 62.4 Self Phase Modulation SPM 72.5 Cross Phase Modulation XPM 72.6 Non Elastic Scattering Effects 82.7 Summary 8

3 The Transmission Link 113.1 Transmitter 113.2 Transmission Line 123.3 Receiver 123.4 Fiber Loss Compensation 133.5 Dispersion Compensation 133.6 Dispersion map 153.7 Summary 17

4 Digital Communication 194.1 Modulation 19

vii

CONTENTS

4.2 Baseband Signal Representation 204.3 Passband Signal Representation 214.4 Amplitude Shift Keying ASK 234.5 Orthogonal Carriers 244.6 QAM modulation 244.7 Summary 25

5 Orthogonal Frequency Division Multiplexing 275.1 Introduction to OFDM 275.2 Block Representation of OFDM 285.3 OFDM Parameters 295.4 Spectrum and Transmission 305.5 Summary 31

6 Simulations And Results 336.1 Simulation Setup 336.2 OFDM Parameters 356.3 Dispersion maps and Waveforms 356.4 Single OFDM channel transmission and SPM assessment 386.5 WDM transmissions and XPM assessment 396.6 NRZ vs OFDM neighboring channels for WDM transmissions 40

7 Conclusions And Discussion 43

A Appendix A: MatLab code for OFDM signal generation 45

B Appendix B: Published article at IEEE/LEOS summer topicals 47

Bibliography 49

Abbreviations 51

List of Figures 53

Index 57

viii

ACKNOWLEDGMENTS

I am grateful to colleagues at KDDI R&D Laboratories, in particular Dr. Sander Lars Jansenfor all the fruitful discussions and guidance. Thanks also go to Dr. Jan Bergman andSiavoush Mohammadi, colleagues at Uppsala University for their useful comments andcriticism. I am also grateful to Sweden Japan foundation as well as Knut and Alice Wal-lenberg foundation for their support of this work. Finally Iwould like to thank my fianceeOranous F.M. for being the fantastic woman she is, her encouragement made this workpossible.

ix

PREFACE

The structure of this work is as follows, Chapter 1 gives a short introduction to fiber optics.In Chapter 2 linear and nonlinear impairments associated with fiber optic transmissionsare presented and discussed. Chapter 3 presents the opticaltransmission system, andhow impairments, discussed in in Chapter 2 are compensated for. Chapter 4 introducesdigital modulation formats, in particular, the quadratureamplitude modulation (QAM).Chapter 5 presents, orthogonal frequency division multiplexing (OFDM) and associatedparameters involved in such modulation format. In Chapter 6simulations of OFDM inoptical communication systems are presented for differenttransmission setups and theresults are presented and discussed.

xi

1INTRODUCTION

In 1966, Kaoet al published a paper [1] that is considered to be the start of themodernfiber optic communications. Following quote is from Kao’s famous paper

A dielectric fibre with a refractive index higher than its surrounding regionis a form of dielectric waveguide which represents a possible medium for theguided transmission of energy at optical frequencies.

Since it’s introduction, systems based on fiber optic solutions with different propertieshave been developed for the demands in digital communication. In this chapter somebackground information will be presented. Furthermore thestandard optical fiber, mostcommonly used in todays digital communication applications will be introduced.

1.1 Fiber Optic Networks

Today, large cities around the world are interconnected with fiber optic links, In this back-bone network large amounts of data are transported over longdistances. A typical trans-mission distance in the backbone network is between 500 km and up to several thousandsof kilometers. Modern commercial transmission systems employ data rates of 10 Gbpsand 40 Gbps per channel. Wavelength division multiplexing (WDM) is used to multiplexand transmit many channels at different wavelengths over the same fiber, By doing so thecapacity of the link is significantly increased. The transmission capacity over a singlefiber in commercial networks employing 80 channels at 40 Gbpsis 3.2 Tbps; observethat this is the capacity of a single fiber. This is the main reason why fiber optic systemsare considered to have ”unlimited” bandwidth, due to the fact that an arbitrary number offibers can be encapsulated in a single cable. However, in manysituations major designalternations, such as increasing the number of fibers or amplifiers in a deployed systemis very hard to achieve, if not impossible. For instance the intercontinental transmission

1

CHAPTER 1. INTRODUCTION

Figure 1.1: Illustration of a standard single-mode fiber. a) The fiber corewith a refractive index n≈ 1.48 and a cross-section of≈ 9 µm. b) Thecladding with a slightly lower refractive index. c) The coating of the fiberfor protection and structural integrity.

links between Japan and America which is submerged in the sea. This makes the researchfor increased transmission capacity over existing networks very important.

1.2 The Optical Fiber

Fig. 1.1 shows the cross-section of a standard single-mode fiber (SSMF), which is madefrom silica glass. The SSMF allows only for one mode of propagation to exist in thefiber; hence the name single-mode fiber. There are fibers with thicker core which allowmany modes of propagation to exist at the same time, they are called multi-modal fibers.The disadvantage of the multi-mode fiber is mainly the inter-modal dispersion, whichultimately lead to decreased transmission distance. Due tothis fact, only SSMFs are usedfor long-haul transmission applications [2]. In Fig. 1.1 the main regions of an optical fiberis depicted; the fiber core, cladding, and coating. The core of the fiber has slightly higherrefractive index (n≈ 1.48) than the cladding [3] in order to achieve total internal reflection.The coating of the fiber provides structural integrity and protection from the surroundingenvironment. For wavelengths used in long-haul transmission systems usually SSMFswith a core diameter of 9µm is used. An in-depth analysis of single-mode fibers can befound in [4]. The following chapter will focus on the impairments in the SSMF.

2

2FIBER OPTIC IMPAIRMENTS

Transmission impairments in the SSMF can be divided into twocategories, linear andnonlinear. Power loss and dispersion are linear impairments and can easily be compen-sated for. The Kerr-effect and non-elastic scattering belong to the nonlinear impairmentsand are generally very hard to compensate for. In this chapter common impairments inmodern fiber-optic communication systems will be discussed.

2.1 Power Loss

The signal power in an optical fiber attenuates due to the interaction of photons with themolecules (S iO4) of the fiber. The two dominant loss mechanisms that leads to powerloss, also called fiber loss, are intrinsic absorption and Rayleigh scattering [4]. If thelaunch power into the fiber isPin [W] then the optical powerP(z) at distancez [km]exhibits an exponentially decay [2] and can be written as

P(z) = Pine−αz , (2.1)

whereα is given in Neper per kilometer [Np km−1]. Neper is a dimensionless, non SIunit of measure for natural logarithm ratios. A more common way of describing theattenuation coefficientα, is inαdB which is defined by

αdB=10

ln(10)α ≈ 4.343α . (2.2)

Fig. 2.1 shows the attenuation coefficientαdB for the SSMF as a function of the frequency.The absorption peak near 1400 nm area is caused byOH− impurities as a result of themanufacturing process of the fiber [3]. The standardizationorganization ITU-T (Interna-tional Telecommunication Union) has defined the communication bands in the SSMF [5],the bands are named O, E, S, C, L, and U-band. The most common transmission band in

3

CHAPTER 2. FIBER OPTIC IMPAIRMENTS

Figure 2.1: The attenuation coefficientαdB as a function of the fre-quency. The Standardized communication bands are marked inthe fig-ure, the C-band is the low loss window and the most common bandforlong-haul digital communications.

commercial systems is the C-band,i.e. 1530 nm to 1565 nm, as it has the lowest fiber lossin that range, with a minimum around 1550 nm / 193.1 THz. A common value for theattenuation coefficient in the C-band isαdB= 0.20 dBkm−1 [2]. This makes transmissionsover 100 km of fiber possible before the need of amplification.In this work the C-bandwas used for all fiber-optic simulations, as it is the most common communication bandfor long-haul transmission applications [2].

2.2 Dispersion

The refractive index of a dielectric material, in our case, the optical fiber is not constant[6] but rather a function of the optical frequencyi.e., n= n(ω). The phase velocity,vph,of a transmitted signal in the fiber is related ton(ω) as

vph=c

n(ω), (2.3)

wherec is the speed of light. The frequency dependence of the refractive index resultsin variations in the phase velocity, thus, spectral components of a transmitted signal willhave different phase velocities according to Eq. (2.3). These variations in phase velocitiesleads to dispersion of the signal. Dispersion, also called material or fiber dispersion,distorts the signal if not compensated for.

4

2.2. DISPERSION

By Taylor expanding the mode propagation constantβ [2, 3] which is related to therefractive indexn according to

β(ω) =ω

vp= n(ω)

ω

c, (2.4)

material specific dispersion parameters can be derived. Taylor expansion of Eq. (2.4) atthe working frequencyω0 gives a linearized relationship between the mode propagationconstantβ and the angular frequencyω

β(ω) ≈ β0+β1(ω−ω0)+12β2(ω−ω0)2

+

16β3(ω−ω0)3

+O(ω4) , (2.5a)

βn =dnβ

dωnω=ω0

, (2.5b)

whereβ0 andβ1 = 1/vg correspond to a constant phase shift and the group velocity,re-spectively. β2 represents group velocity dispersion andβ3 dispersion slope. The morecommon way to expressβ2 andβ3 in fiber-optics is through fiber specific parametersDandS [2] according to

D = −2πcλ2 β2 , (2.6a)

S =4πcλ3 β2+

(

2πcλ2

)2

β3 . (2.6b)

D is expressed in [ps nm−1 km−1] and describes the amount of dispersion per kilometersandS is expressed in [ps nm−2 km−1], which describes the change of dispersion as func-tion of the working frequency. For the SSMF in the C-band the dispersion parameterD isin the range of 15-18 ps nm−1 km−1 and the dispersion slopeS around 0.06 ps nm−2 km−1.As the dispersion slope is very low in the C-band, it is usually neglected, thus the disper-sion profile of the SSMF is mainly determined byD.

It is possible to create fibers with negative dispersion parametersD, these fibers arecalled dispersion correcting fiber (DCF) [2] and are mainly used for compensating forthe accumulated dispersion. In fiber-optic transmission links the accumulated dispersionultimately leads to pulse spreading which in turn causes inter-symbol interference (ISI).Fig. 2.2 illustrates a pulse-train propagating along an SSMF sampled at different trans-mission lengths with no dispersion compensation along the fiber. Initially the pulses areintact and no dispersion is present, as the transmission length increases, the impact ofthe dispersion becomes more obvious. At high dispersion values the pulses disperse intoneighboring pulse slots causing inter symbol interference(ISI). At 30 km there is noeasy way to distinguish the pulses apart, see Fig. 2.2, in fact at this point, if dispersioncompensation is not applied to the signal, no information can be retrieved.

5

CHAPTER 2. FIBER OPTIC IMPAIRMENTS

0 1024 2048 3072 40960

1

2

3

4

5Dispersion = 0 ps nm−1 (0 km)

Sig

nal P

ower

[mW

]

0 1024 2048 3072 40960

1

2

3

4

5Dispersion = 80 ps nm−1 (5 km)

Time [ps]

Sig

nal P

ower

[mW

]

0 1024 2048 3072 40960

1

2

3

4

5Dispersion = 160 ps nm−1 (10 km)

0 1024 2048 3072 40960

1

2

3

4

5Dispersion = 480 ps nm−1 (30 km)

Time [ps]

Figure 2.2: The effect of dispersion at different transmission lengthsalong an SSMF, with no dispersion compensation employed in the trans-mission link. Initially (0 km), no dispersion is present andall the pulsesare intact, as the transmission distance increases, dispersion accumu-lates over the fiber, causing inter-symbol-interference. At 30 km if nodispersion compensation is employed, no information can beretrieved.

2.3 Kerr-Effect

The Kerr effect induces variations in the refractive index in response to an electrical field,thus, high launch powers in to the SSMF leads to changes in therefractive index of thefiber. The change in the refractive index caused by the Kerr effect is a function of theoptical power|A|2 [3] and the relationship is described by

n(ω, |A|2) = n0(ω)+n2|A|2

Ae f f, (2.7)

wheren0 is the linear refractive index as discussed in the previous section, n2 is thenonlinear refractive index andAe f f is defined as the effective mode area of the fiber.The propagation of a signal along an optical fiber is generally described by the nonlinear

6

2.4. SELF PHASE MODULATION SPM

Schrodinger equation (NLSE) [6]

∂A∂z= −α

2A−

j2β2∂2A∂T2 +

16β3∂3A∂T3 + jγ |A|2 A , (2.8a)

γ =n2ω0

cAe f f, (2.8b)

T = t−β1z= t−zvg, (2.8c)

were A is the complex amplitude of the optical-field,z is the propagation distance in[km], α is the attenuation coefficient in [Neper].γ is the nonlinear coefficient expressedin [W−1 km−1] and T is the time measured in the retarded frame. As the impact of thenonlinear Kerr effect is proportional to the signal power according to Eq. (2.7) almost allnonlinearities will be introduced at the high-power regionof the fiber, which is the firstpart of the fiber and is defined by an effective lengthLe f f according to

Le f f =1−e−αL

α. (2.9)

Fig. 2.3 shows the signal power as a function of transmissiondistance of SSMF. In thefigure, the effective lengthLe f f and the high-power region is illustrated. For an SSMF oflength 100 km, with an attenuation coefficientα = 0.2 dB km−1, the effective lengthLe f f

is calculated to be 21.5 km according to Eq. (2.9).

2.4 Self Phase Modulation SPM

Intensity variations of a signal, induces phase shifts to the signal itself. This is caused bythe intensity dependence of the refractive index (The Kerr-effect). This is referred to asself phase modulation (SPM). The SPM affects the phase of thesignal but the influence ofchromatic dispersion in conjunction with SPM lead to amplitude variations of the signal.Fig. 2.4 illustrates a Gaussian pulse and the frequency shift it will undergo due to SMP.

2.5 Cross Phase Modulation XPM

Cross phase modulation XPM is much like SPM, with the difference that XPM occurs inwavelength division multiplexed (WDM) transmission systems. The intensity variationsof a signal in a WDM channel are converted into phase variations in other WDM channelsand through the interplay with chromatic dispersion to amplitude variations. XPM alsoscales inversely with the data rate [7], the higher data ratethe lower influence of the XPMwill be.

7

CHAPTER 2. FIBER OPTIC IMPAIRMENTS

Transmission Distance [km]

Sig

nal P

ower

[mW

]Power loss

Leff

= 21.5 km

Hig

h−P

ower

Reg

ion

0 20 40 60 80 1000

2

4

6

8

10

Figure 2.3: The optical signal power as a function of transmission dis-tance. The high-power region of the fiber is illustrated in the figure as theshaded area. The effective length is marked in the figure at 21.5 km, thisvalue was calculated for 100 km of SSMF with an attenuation coefficientof α = 0.2 dB km−1.

2.6 Non Elastic Scattering Effects

Introducing two new nonlinear impairments, namely the stimulated Raman scatteringand the stimulated Brillouin scattering shortened to SRS and SBS, respectively. Theinteraction of light, or more correctly, photons with the molecules of the optical fiberis the cause of these nonlinearities. The SRS is an interaction of photons and opticalphonons [8] of the fiber. This interaction is very important as it is responsible for therealization of optical amplifiers. The SBS originates from the interaction of photons withmolecules acoustical phonons.

2.7 Summary

In this chapter, critical impairments that can occur in an SSMF based fiber-optic transmis-sion system were discussed, Such as fiber loss, chromatic dispersion, and the Kerr effect.Fiber loss and chromatic dispersion are linear impairmentsand can easily be compensated

8

2.7. SUMMARY

Time in multiples of τ

Self Phase Modulation (SPM)

a) gaussian pulse

b) Frequency shift

Inte

nsiy

∆ f

−

ω0 +

−3 −2 −1 0 1 2 3

Figure 2.4: Intensity variations of the signal is translated through theKerr-effect to phase modulation of the signal itself. a) A Gaussian pulse,b) The frequency shift of the signal in response to the intensity variationsof the signal.

for with the use of passive and active components. The Kerr effect however is a nonlinearimpairment and is relatively hard to compensate for. The Kerr effect originates from theintensity dependence of the refractive index of the fiber andis responsible for self phasemodulation (SPM) and cross phase modulation (XPM).

9

3THE TRANSMISSIONL INK

In this chapter, wave length division multiplexed (WDM) communication systems willbe discussed, together with essential components to realize these systems. Generally,all communication systems are constructed from three basicbuilding blocks, transmitter,transmission line, and receiver. The configuration of the transmission line is the most im-portant step in designing a fiber-optic communication system, as when deployed, designalternations to the line are practically not feasible.

3.1 Transmitter

At the transmitter, the electrical to optical conversion ofthe signal is done by the use ofa distributed feedback laser (DFB) and a Mach-Zehnder modulator (MZM) . The DFBin conjunction MZM is mainly used for long-haul transmissions as they together producean almost chirp free (frequency variation free) optical signal. For other applications, lesscomplex solutions are available, for instance, direct modulated lasers (DML) where theelectrical to optical transformation and light generationis done in the same component.

The SSMF has several transmission bands, as discussed previously in Section 2.1,this makes it possible to transmit many channels at the same time. For each transmissionchannel a pair of DFL and MZM is employed for the electrical tooptical conversion,these channels are subsequently merged together (multiplexed) to one optical signal com-prised of all channels. Multiplexing of the signals is realized by using thin film filtersand an arrayed waveguide grating (AWG) , At the receiver same components are used fordemultiplexing.

Directly after the AWG a pre-dispersion compensation fiber isused for dispersionmap optimization, followed by an Erbium doped fiber amplifier(EDFA) for power regu-lation. At this step the optical signal is coupled to the SSMFin the transmission line fortransmission.

11

CHAPTER 3. THE TRANSMISSION LINK

Figure 3.1: Graphical representation of a fiber optic transmission sys-tem. The transmitter is composed of a distributed feedback laser in con-junction with a Mach-Zehender modulator for electrical to optical con-version, an arrayed waveguide grating is used to multiplex several opti-cal channels into a one optical signal. The transmitter EDFAcontrols theinput power to the fiber. The transmission line consists of repeated seg-ments of fiber, amplifier (EDFA), dispersion-correcting-fiber (DCF), andpower-regulator amplifier. The receiver consists of an arrayed waveguidegrating for demultiplexing, and post-dispersion-compensation fibers foroptimization of the residual dispersion for each optical channel, at thelast step, a photodiode is used for detecting the optical signal and downconversion to electrical domain.

Fig. 3.1 illustrates a common graphical representation of afiber optic transmissionsystem, from the transmitter through the transmission lineto the receiver.

3.2 Transmission Line

The transmission line consists of multiple spans, each consisting of SSMF, EDFA, DCF,and EDFA blocks. The SSMF length in each span is usually between 80 to 100 km, nextto the SSMF is the first EDFA which regulates the input power tothe DCF. After the DCFfollows the booster EDFA which amplifies the signal for the next span of fiber, this isrepeated until the destination is reached. The SSMF, power regulator EDFA, DCF, andthe power booster EDFA blocks are illustrated in Fig. 3.1 under the transmission line.

3.3 Receiver

At the receiver an AWG is employed for separation (demultiplexing) of the individualWDM channels. As the amount of residual dispersion is different for each WDM channel,post-compensation DCFs are applied for each channel to optimize the BER performance.

12

3.4. FIBER LOSS COMPENSATION

After dispersion optimization the optical signal is detected through a photodiode anddown converted to electrical domain.

3.4 Fiber Loss Compensation

In chapter 2 some of the impairments associated with fiber optic transmission systemswere discusses, for instance, power and scattering loss, SPM, and XPM. These impair-ments can be compensated for by repeaters and optical amplifiers (EDFAs). Repeatersfully regenerate the optical signal, but they are however complex to realize for high-levelmodulation formats, for instance, orthogonal frequency division multiplexing. For long-haul transmissions EDFAs are used to regenerate the opticalpower every 80 to 100 km.Given the input power, the output power can be written asPout =GPin, whereG denotesthe the amplifier gain, this is known as power-gain configuration.

Another way of configuring the EDFAs is, constant-power output, which makes theEDFA act as a power regulator, this configuration is used for the DCFs in the transmissionline, as the power must be held at low levels in order to avoid nonlinearities form theDCFs. The drawback of the EDFAs is, the addition of amplified spontaneous emission(ASE) to the optical signal, also known as optical amplifier noise. The amount of ASEdirectly affects the optical signal-to-noise ratio (OSNR)[2]. The OSNR is defined as

OS NR=Psignal

Pnoise, (3.1)

wherePnoise is defined for a given reference bandwidth.When it comes to the optical amplification process, there is a hidden problem. A low-

power optical signal require high amplification gain. But the high amplification gain resultin high ASE noise, thus in lower OSNR values. In order to keep the ASE noise at lowlevels, high-power signals are to prefer. However, a high launch power into the fiber resultin an increased influence of nonlinearities. The launch power into the fiber is an importantparameter that needs to be optimized in order to achieve the best performance. Fig. 3.2illustrates the relationship between launch power and the OSNR. There is an optimallaunch power where the nonlinearities are avoided and the ASE is held at low levels.When designing a transmission link, the input power to the EDFA’s must be optimized inorder to achieve the best performance for the link.

3.5 Dispersion Compensation

In section 2.2 the effects of chromatic dispersion on the optical signal were illustrated.Dispersion ultimately lead to ISI and data loss. The higher data rate, the more precise the

13

CHAPTER 3. THE TRANSMISSION LINK

Launch Power [dBm]

log 10

(BE

R)

BER vs Launch Power

−7 −5 −3 −1 1 3 5−9

−7

−5

−3

−1

Figure 3.2: The OSNR as a function of the launch power. At high launchpowers, nonlinearities are induced, resulting in OSNR penalties, and atlow launch powers, amplified spontaneous emission lead to accumulatednoise after transmission, resulting in low OSNR values.

dispersion compensation must be in order to recover the data. Almost all transmissionlinks are realized using DCF’s for dispersion compensation.

Fig. 3.1 illustrates a transmission system where DCF modules are placed ”in-line” andcontinuously compensate for the chromatic dispersion in each span. This is the commonway of dispersion compensation, and is referred to as ”conventional” dispersion compen-sation in the fiber-optic community.

A DCF is a fiber with the inverse sign for the dispersion parameter, D, some DCF’sare slope matched as well, this refers to the dispersion slope parameter, S. The DCF is apassive component and allows for dispersion compensation of several WDM channels atthe same time. Common fiber parameters for the DCF areD = −100 ps nm−1 km−1 andS = −0.34 ps nm−2 km−1. As indicated, the absolute value of the dispersion constant D ismuch higher for the DCF in comparison to the SSMF. This property makes it possible tocompensate for large amount of dispersion in a short distance. Typically, the accumulateddispersion over an SSMF line of 100 km can be compensated for,in just a few kilometersof DCF. The high nonlinear coefficientγ ≈ 3 W−1 km−1 of the DCF is a disadvantagehowever, it is approximately three times higher than the value of the SSMF, hence, asstated before, the optical launch power into the DCF must be held at low levels. Typical

14

3.6. DISPERSION MAP

Transmission Distance [km]

Dis

pers

ion

[ps

nm−

1 ]

Dispersion Map

0 270 540 810 1080 1350−2200

−1100

0

1100

2200DCFSSMF

In−line Undercompensation

Pre Dispersion Compensation

PostComp

ORD

Figure 3.3: The accumulated dispersion over the transmission distance.a) pre-dispersion compensation, b) accumulated dispersion along theSSMF, c) dispersion compensation using an in-line DCF, d) in-line dis-persion under-compensation, realized by not fully compensating for thedispersion with the in-line DCF, e) post-dispersion compensation, result-ing in an optimum residual dispersion.

launch powers for the DCF have to be chosen about 5dB lower than the launch power forthe SSMF.

3.6 Dispersion map

A dispersion map is a visual aid, describing how the dispersion evolves over the transmis-sion link. In Fig. 3.1 there are several fiber components thatcontribute to the accumulateddispersion over the transmission link, they are, pre-dispersion compensation fiber, SSMF,in-line DCF, and post-dispersion compensation fiber. The dispersion contribution of theseelements is visualized in a dispersion map as illustrated inFig. 3.3, this dispersion map isconsidered as a common dispersion map for long-haul transmission systems.

The dispersion map starts with a pre-dispersion compensation followed by the ac-cumulated dispersion over the SSMF. The dispersion from theSSMF is almost fullycompensated for by an in-line DCF leaving a fraction of the dispersion as, in-line un-

15

CHAPTER 3. THE TRANSMISSION LINK

Transmission Distance [km]

Dis

pers

ion

[ps

nm−

1 ]

Dispersion Map

λn

λ1

ORD

0 270 540 810 1080 1350−2200

−1100

0

1100

2200

Ch nPost

Comp

Ch 1Post

Comp

Figure 3.4: The dispersion map for different WDM channels. As WDMchannels are localized at different frequencies, the dispersion map willbe different for each WDM channel. The in-line dispersion compensationcan not compensate for the dispersion for all the WDM channels at thesame time. Different post-compensations must be applied for each WDMchannel.

der compensation. The dispersion from the SSMF and the partial compensation fromthe DCF is repeated until the end of the transmission line, atthe end a post-dispersioncompensation is applied. The post-dispersion compensation is applied at the same timeas the BER is assessed, when a minimal BER is reached the residual dispersion is calledoptimum residual dispersion (ORD). As WDM channels are located at different frequen-cies, the dispersion map will be different for each WDM channel, see Fig. 3.4. This ismainly caused by the dispersion slope parameter S of the SSMF, this makes it hard forthe inline DCF to compensate the dispersion for all WDM channels at the same time, assuch, different post-compensations must be applied for each WDM channel.

As illustrated in Fig. 2.2, dispersion leads to pulse spreading and increased peak-to-average power ratio (PAPR). The high PAPR through the interplay with the Kerr-effect in-troduces nonlinearities, the dispersion map is an important tool for minimizing the PAPR,thus minimizing the nonlinearities. In short: if the dispersion is compensated for in time,the PAPR is kept at low levels, thus nonlinearities are avoided, resulting in high perfor-mance.

16

3.7. SUMMARY

3.7 Summary

In this chapter all important blocks in a commercial transmission link were discussed. TheTransmitter consists of a distributed feedback lasers (DFB) together with a Mach-Zehndermodulator (MZM) for each channel. The channels are multiplexed and demultiplexedusing an arrayed waveguide grating (AWG). At the receiver a photodiode is used fordetection.

The power loss needs to be compensated for in a transmission line. This is done by anerbium doped fiber amplifier (EDFA). However, the gain of the EDFA’s can not be set athigh values, as that would result in amplified spontaneous emission (ASE) and result inreduced optical signal-to-noise ratio (OSNR). High launchpowers into the SSMF leadsto increased nonlinearities.

The chromatic dispersion is compensated for by dispersion correcting fibers (DCF).DCFs have high negative dispersion parameter, thus compensating for SSMF can be donein just a few kilometers. The drawback of DCFs are the high nonlinearity factor, this iswhy the input power to the DCFs must be controlled in order to minimize the nonlin-earities. In WDM transmissions, post-dispersion compensation must be applied for eachchannel to enable optimal residual dispersion (ORD) for each channel, leading to minimalbit-error-rate (BER).

The dispersion map is a powerful tool in designing a transmission link, a well de-signed fiber-optic transmission link minimizes the peak-to-average power ration (PAPR)of a signal, thus minimizing the nonlinearities along the fiber.

17

4DIGITAL COMMUNICATION

This chapter covers the basics in digital communication such as, On-Off-keying (OOK),amplitude shift keying (ASK), carrier modulation,etc. The purpose of this chapter is tohighlight important modulation formats for digital communication applications, in partic-ular the digital QAM modulation. In orthogonal frequency division multiplexing (OFDM)transmissions, the subcarriers of an OFDM symbol are modulated using the general QAMmodulation format, as proposed in IEEE 802.11a-n.

4.1 Modulation

In analog communication, for instance AM-radio, the amplitude of a carrier is modulatedwith a real and continuous signal, such as music. The carrieramplitude can take anyvalue between the maximum and the minimum of the modulating signal. During thetransmission, noise is added to the signal. There are several types of noise, the mostcommon and best modeled is the additive white Gaussian noise(AWGN). Separation ofthe signal from noise is not an easy task and in many cases not even possible, since thereceiver can not distinguish between the signal and noise. The amount of tolerable noisein the case of music transmission, is something the listenerdecides on.

In digital communication, the separation of signal from noise is a crucial step. Inorder to distinguish between the logical states in the transmitted signal, there must be anagreement in advance at the transmitter and the receiver. This ”agreement” determines thetype of the modulation format. The choice of modulation format is not a trivial task, usu-ally several factors must be taken into consideration, for instance, application area, noisetolerance, and complexity. A measure of performance in digital communication systemis the bit-error-rate (BER). The BER is calculated by takingthe ratio between the numberof errors and total transmitted data at the receiver. Another measure of performance is thespectral efficiency, measured in [Bits s−1 Hz−1]. The spectral efficiency, measures how

19

CHAPTER 4. DIGITAL COMMUNICATION

Time in units of T0

Am

plitu

de

On−Off−Keying RZ

1

0

0 1 2 3 4 5 6 7 8−2

−1

0

1

2

(a) Return to Zero (RZ)

Time in units of T0

Am

plitu

de

On−Off−Keying NRZ

1

0

0 1 2 3 4 5 6 7 8−2

−1

0

1

2

(b) Non Return to Zero (NRZ)

Figure 4.1: The envelope of On-Off-Keying (OOK) signals, a) OOK sig-nal with return-to-zero (RZ) pulses, b) OOK signal with non-return-to-zero (NRZ) pulses.

well the given bandwidth is disposed, or in other words how much data can be transferedwithin the given bandwidth. Usually, higher complexity at the transmitter/receiver leadsto higher spectral efficiency.

4.2 Baseband Signal Representation

The most common representation of a digital signal is the On-Off-Keying (OOK) schemeas seen in Fig. 4.1a. The presence or absence of the signal, regardless of amplitude in-formation, translates to the logical states ”1” and ”0”, respectively. In fiber optics, thiscorrespond to the laser light being ”on” or ”off” in the fiber.Fig. 4.1a represents OOKwith return-to-zero (RZ) coding. Another way of coding is non-return-to-zero (NRZ),here the two logical states are mapped onto positive and negative amplitudes of the car-rying pulse; see Fig. 4.1b. The OOK results in low complexityat the transmitter/receiverwith high performance in terms of BER. OOK is highly resilient towards noise, this ishowever at the cost of spectral efficiency. An OOK-RZ signal can mathematically berepresented as a sum of time delayed unit pulsesg(t) with amplitudesA and 0. The math-ematical expression for an OOK signal is,

Sb(t) =N−1

∑n=0

m(n)g(t−nT0) , (4.1)

wherem(n) is the message signal/vector with the amplitude informations (A and 0) andg(t−nT0) is the time delayed unit pulses. In Fig. 4.1a the message vector is [10110101].Here, the amplitudeA was chosen to be 1V representing the logical state ”1”, this is

20

4.3. PASSBAND SIGNAL REPRESENTATION

−10 −5 0 5 10−0.5

0

0.5

1.0

1.5

Time [ms]

Pul

se a

mpl

itude

g(t), T0 = 10 ms

(a) The unit pulse in time domain

Frequency [Hz]N

orm

aliz

ed a

mpl

itude

Pulse Spectrum

−300 −100 100 300−0.4

0

0.4

0.8

1.2

(b) The unit pulse in frequency domain

Figure 4.2: The unit pulse in time and frequency domain respectively. a)unit pulse of period 10 ms which correspond to a frequency of 100 Hz.b) the spectral components of the pulse, the spectrum of the pulse havezeros at multiples of 100 Hz.

however not a requirement,A can be given any value, another common value for theamplitudeA is 5V representing the logical state ”1”. The other logical statewas mappedto 0V, thus, the amplitude of the pulse goes to zero for one of the states, hence, the namereturn-to-zero (RZ). By defining the amplitudes for the logical states, a convention ischosen on what a logical ”1” or ”0” is. This act is called bit mapping. The unit pulseg(t) is an important component in digital signal generation, assuch investigation of itsproperties in time and frequency domain is necessary. In Fig. 4.2 a unit pulse is illustratedin both time and frequency domain. The pulse has a period of 0.01 s which correspond toa frequency of 100 Hz. An OOK signal employing this pulse can yield a data rate of 100bps, as each pulse carry one bit of data. The spectrum of the pulse show that the spectralcomponents of the pulse reach beyond 100 Hz, despite the factthat the pulse itself has afrequency of 100 Hz; see Fig. 4.2b. In fact the spectral components of the pulse continueall the way to infinity, the contribution of these frequencies are however very small as theamplitude of these go to zero. Notable is also the fact that the spectrum of the pulse hasnull points at multiples off0 = 100Hz, that isn f0.

4.3 Passband Signal Representation

When modulating a baseband signal on top of a carrier, a passband signal is generated.The passband modulation is done for several reasons, the most important being alloca-tion of transmission channel for the baseband signal. By doing so a specific channel isdedicated to the baseband signal, with a bandwidth of the same size of the baseband sig-

21

CHAPTER 4. DIGITAL COMMUNICATION

Time in units of T0

Am

plitu

de

On−Off−Keying RZ

1

0

0 1 2 3 4 5 6 7 8−2

−1

0

1

2

(a) OOK-RZ modulated

Time in units of T0

Am

plitu

de

On−Off−Keying NRZ

1

0

0 1 2 3 4 5 6 7 8−2

−1

0

1

2

(b) OOK-NRZ modulated

Figure 4.3: Passband representation of OOK RZ and NRZ. The basebandOOK signal modulated on top of a carrier.

nal. Consider an FM radio transmission for comparison, the baseband signal is an audiosource with a bandwidth of typically 20 kHz, and the passbandsignal is the same audiosource modulated on top of a carrier. The carrier frequencies for FM radio transmissionis between 88 to 108 MHz. For long-haul transmissions, the C-band is used at the centerfrequency of 193.1 THz (1530 nm). Fig. 4.3 illustrates previous OOK examples modu-lated on top of a carrier, here the carrier is at very low frequency in order to visualize thephase shifts due to negative amplitudes in the NRZ case. Mathematically, passband mod-ulation is performed by multiplying the baseband signalSb(t) with a sin or cos functionat the desired frequency,

Sp(t) = Sb(t)cos(2π fct) . (4.2)

At the receiver the envelope of the signal is detected as wellas the phase of the carrier.For the RZ transmission the phase information is excessive,only amplitude informationis required for decoding the digital states, see Fig. 4.3a. For NRZ transmissions the phaseof carrier is very important as the digital states of the baseband signal are now translatedto phase shifts ofπ degrees between the bit slots (bit slot = one pulse duration). Thedigital states are encoded in the phase of the carrier, see Fig. 4.3b. The amplitude value isthe excessive information for NRZ transmissions. NRZ signals are kind to amplifiers infiber optic transmission systems as there is no need of rapid amplitude changes, howeverhigh phase accuracy is required.

22

4.4. AMPLITUDE SHIFT KEYING ASK

Time in units of T0

Am

plitu

de

4−level Amplitude−Shift−Keying ASK

10

11

01

00

0 1 2 3 4 5 6 7 8

−1.5

−0.5

0.5

1.5

(a) Baseband ASK

Time in units of T0A

mpl

itude

4−level Amplitude−Shift−Keying ASK

10

11

01

00

0 1 2 3 4 5 6 7 8

−1.5

−0.5

0.5

1.5

(b) Passband ASK

Figure 4.4: Four level amplitude-shift-keying (ASK) in baseband andpassband representation.

4.4 Amplitude Shift Keying ASK

As seen in the previous section, both phase and amplitude of the carrier can be usedfor digital encoding and transmission. In the NRZ, case the negative amplitudes of thebaseband signal was translated to phase shifts ofπ degrees in the passband signal. Upto this point, only two levels of amplitude have been used to encode digital states. Am-plitude shift keying (ASK) is an encoding method that enables sets of digital states tobe coded in to the amplitudes of the pulses. A baseband and passband representation ofan ASK signal is illustrated in Fig. 4.4. Each pulse, have oneof four levels of ampli-tude (A : | −1.5, −0.5, 0.5, 1.5) and encode one of four digital sets (D : |00, 01, 10, 11).Generally,log2(N) bits of data can be encoded in each pulse for anN level ASK sig-nal. The passband representation of the ASK signal in Fig. 4.4b show that the amplitudes(A : | −1.5, −0.5, 0.5, 1.5) of the baseband signal has been transformed into two ampli-tude states (A : | 0.5, 1.5) and two phase states (φ : | 0, π), as the sign of the amplitudes canbe expressed in phase notation, cos(0) and cos(π), i.e. the carrier has been both amplitudeand phase modulated. The amplitude levels can be increased to any number, but the phaseis either 0 orπ, how is it possible to increase the number of phase states in the passbandrepresentation? This is done by the introduction of orthogonal carriers, also known asin-phase and quadrature carriers.

23

CHAPTER 4. DIGITAL COMMUNICATION

4.5 Orthogonal Carriers

The trigonometric functionssin(2π fct) andcos(2π fct) are orthogonal functions when in-tegrated over a whole periodT0,

∫ T0

0sin(2π fct)cos(2π fct)dt= 0 . (4.3)

This property of the trigonometric functions makes it possible to have two carriers at thesame frequency, called in-phase and quadrature carrier. The name quadrature comes fromthe fact that trigonometric functionssin andcoscan be expressed in terms of each other,for instancecos(t)= sin(t+π/2). The phase shift ofπ/2 radians correspond to a quarter ofa full revolution in the phase plane, hence the name quadrature. Let us now consider twoASK baseband signals and name themI andQ; see Fig. 4.4a. After passband modulationof the signals withcos(2π fct) andsin(2π fct) we multiply theQ channel with−1 and addthe channels together. This yields the baseband signal,

Sp = Icos(2π fct)−Qsin(2π fct) = (4.4)

= Re{(I + iQ)(cos(2π fct)+ isin(2π fct))} = (4.5)

= Re{

Zei2π fct} (4.6)

which is the complex notation of the passband signal. The complex carrier is defined asei2π fct andZ = I + iQ is the modulating symbol, as it both changes the amplitude and thephase of the carrier as,

A=√

(I2+Q2) , (4.7)

φ = tan−1 QI. (4.8)

At the receiver the passband signal is multiplied by the local oscillatorscos(2π fct) andsin(2π fct) and filtered in order to recover the baseband signalsI andQ.

R= Spcos(2π fct) = {Icos(2π fct)−Qsin(2π fct)}cos(2π fct) = (4.9)

=

12

I +12

Icos(4π fct)+12

Qsin(4π fct) (4.10)

After low pass filtering, the high frequency termssin(4π fct) andcos(4π fct) will vanishand theI andQ channels are recovered, depending on the local oscillator used.

4.6 QAM modulation

A common modulation format in digital communication systems is quadrature amplitudemodulation (QAM). The QAM signal is composed of two ASK modulated channels, one

24

4.7. SUMMARY

Time in units of T0

Qua

drat

ure

Q

0 1 2 3 4 5 6 7 8

−1.5

−0.5

0.5

1.5

In−

phas

e I

4−level Amplitude−Shift−Keying ASK

0 1 2 3 4 5 6 7 8

−1.5

−0.5

0.5

1.5

−1.5−0.5 0.5 1.5

−1.5

−0.5

0.5

1.5

Qua

drat

ure

Q

QAM constellation diagram

−1.5−0.5 0.5 1.5

−1.5

−0.5

0.5

1.5

In−phase I

Qua

drat

ure

Q

Transmitted QAM symbols

10001

11112

01113

00104

00005

01006

11107

10018

10

11

01

00

10

11

01

00

Figure 4.5: To the left, the in-phase and quadrature channels of a QAMsignal are shown. The QAM constellation diagram to the right, displaysthe possible QAM symbols that can be generated. The transmitted sym-bols according to the I and Q channels can be in seen in the panel, Trans-mitted QAM symbols.

for the in-phaseI and one for the quadratureQ channel. The QAM symbolZ = I + iQdescribes the complex modulation of the carrier as discussed in the previous section. InFig 4.5 the in-phase and quadrature channels are displayed,both channels have 4-levelASK pulses. The constellation diagram in Fig 4.5 shows all the possible QAM symbolsthat can be generated, here the constellation size is 16. Thesymbols generated by the Iand Q channels are displayed as well in Fig 4.5, transmitted QAM symbols.

4.7 Summary

In this chapter some of the important digital modulation formats were discussed, suchas, on-off-keying (OOK), Amplitude Shift Keying (ASK), andthe more general, thequadrature-amplitude-modulation (QAM). In this work QAM modulation was chosen formodulating the subcarriers of an orthogonal-frequency-division-multiplexing (OFDM)transmission system.

25

5ORTHOGONAL FREQUENCYDIVISION

MULTIPLEXING

Orthogonal Frequency Division Multiplexing (OFDM) belongs to the group of modula-tion formats that fall in the category of multitone or spreadspectrum. Generally thesemodulation formats brake down a high data rate stream to several low data rate chan-nels and subsequently modulate each on separate carriers. As such, instead of a highbandwidth signal, the signal is spread over the entire allowed spectrum at lower bit rates,thus the name spread spectrum. The major difference betweenOFDM and other spreadspectrum modulation formats is, as the name OFDM indicate, orthogonality between thecarriers. In this chapter an introduction to OFDM will be given, furthermore a simplifiedOFDM transmitter will be exemplified using MatLab.

5.1 Introduction to OFDM

The carriers in an OFDM based transmission are spaced in suchway that they all aremutually orthogonal with respect to the OFDM symbol time. This is done efficiently byutilizing a digital signal processor (DSP) with a fast Fourier transform (FFT) cell, and itsinverse (IFFT). The IFFT cell of the DSP generates and modulates the subcarriers at thesame time, thus saving processing time. After analog to digital conversion at the receiver,the FFT cell of the DSP decodes the signal and recovers the modulated subcarriers. Sinceall the subcarriers in an OFDM signal are orthogonal with respect to each other, highspectral efficiency can be achieved for the OFDM signal in comparison to other spreadspectrum formats such as frequency division multiplexing (FDM). Fig. 5.1 displays theoccupied frequency space for an OFDM and FDM signal, respectively. The subcarriers ofa FDM transmission must be separated in order to avoid inter carrier interference (ICI),the separation of the subcarriers is referred to as, guardband. The orthogonality of the

27

CHAPTER 5. ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING

(a) OFDM spectrum (b) FDM spectrum

Figure 5.1: The occupied frequency space of an OFDM and FDM trans-mission. The orthogonality of the subcarriers in the OFDM transmissionmakes it possible to save bandwidth, in comparison to conventional FDMtransmissions, where guardband is necessary.

Figure 5.2: Block Representation of OFDM. Serial to parallel converter,multiplexes the high data rate stream to several low bit ratestreams,these streams are converted to QAM symbols through the symbol map-per. The QAM symbols will subsequently modulate the subcarriers of theOFDM symbol. The modulation process of all subcarriers is done by theIFFT block. The time data from the IFFT block is passed to the cyclicprefix block for extension of time samples. Time samples are converted toa serial stream and subsequently converted to the analog domain throughthe digital to analog converter.

subcarriers in an OFDM based transmission solves this problem, as a result, bandwidth issaved.

5.2 Block Representation of OFDM

The steps involved for an OFDM symbol generation are illustrated in Fig. 5.2. The firstblock, the serial to parallel (S/P) converter, branches a high data rate stream into several

28

5.3. OFDM PARAMETERS

low data rate streams. The number of data-subcarriers in theOFDM signal dictates thenumber of output streams from the S/P converter. For each of the streams, the binarydata is selected block wise, and mapped to QAM symbols. This is done by the symbolmapping block in Fig. 5.2. The QAM symbols modulate each of the data-subcarriersof the OFDM symbol. The generation and modulation of all the subcarriers is donesimultaneously by the IFFT block. The output of the IFFT block are the time samples,describing the OFDM symbol. At this stage, cyclic prefix is added to the OFDM symbolin order to increase the tolerance towards multi path delays, or in fiber optics, dispersion.This is done by the CP block by copying the first segment of the time samples and addingit to the end of the time series, thus increasing the time window. The parallel output fromthe CP block, describing the OFDM symbol, in the time domain,is now converted to aserial stream via the parallel to serial (P/S) converter. The time data is still in the digitaldomain. At this stage the stream is converted to an analog signal for transmission, ormodulation of a carrier.

5.3 OFDM Parameters

Designing an OFDM transmission system implies optimization of OFDM parameters,some of these parameters are, number of subcarriers, QAM constellation diagram size,and cyclic prefix samples. There is no right way of deciding these parameters, for someapplication, such as the IEEE 802.11a-n, there are predefined values for all the parame-ters. This is however not the case in fiber optic applications, the best settings are thosewhich result in low BER values. In this work, many simulations were done to find the op-timal OFDM parameters for fiber optic applications, these are presented in later section.It is important to remember that, there is no rule of thumb forchoosing these parameters,usually the application area dictates the parameter settings of an OFDM transmission.

5.3.1 FFT size, Zero padding, and Pilot tones

The FFT size determines the number of available subcarriersfor the OFDM symbol. allof the subcarriers can be used for data transmission, but some are zero padded and someare used as pilot tones. Zero padding is done to mitigate the influence of inter symbolinterference (ISI). The pre-allocated subcarriers for pilot tones are used for synchroniza-tion purpose and phase estimation. The number of pilot tonesand zero paddings are alsoadjustable parameters for the OFDM symbol generation.

5.3.2 QAM size

The QAM size is usually determined by the noise tolerance of the transmission. For trans-missions with low noise, high QAM constellations can be selected for the OFDM symbol,

29

CHAPTER 5. ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING

−3 −2 −1 0 1 2 3−30

−20

−10

0

10

Normalized Frequency [−π, π]

Nor

mal

ized

Pow

er [d

B] OFDM Spectrum

(a) The Spectrum of an OFDM transmission

200 400 600 800 1000−1

−0.5

0

0.5

1

Time sample [n]

Nor

mal

ized

Am

plitu

de

OFDM signal

(b) The OFDM signal

Figure 5.3: The time and frequency domain representation of an OFDMtransmission with 16 out of 64 subcarriers zero padded and 8 cyclic pre-fix samples. a) The spectrum of OFDM transmission, averaged for 32OFDM symbols. b) Time domain transmission of a single OFDM sym-bol.

hence increasing the throughput. When noise becomes a problem, lower QAM constel-lation is selected, in order to reduce the BER. The IEEE 802.11 standard has an adaptiveQAM constellation selection, the QAM size is selected by analyzing the transmissionchannel by the use of OFDM training symbols. For fiber optic applications, usually lowQAM constellations are selected, for several reasons, one of them being noise tolerance.

5.3.3 Cyclic Prefix

The cyclic prefix determines the amount of tolerable multi path delay, or in fiber opticapplications, dispersion. The number of samples, usually is determined by using OFDMtraining symbols. The cyclic prefix increases the reliability of the OFDM transmission,this is however at the cost of data throughput.

5.4 Spectrum and Transmission

In Fig. 5.3 the spectrum of an OFDM transmission is illustrated as well as the time domaintransmission of a single OFDM symbol. The MatLab code for generating the signal canbe found in appendix. The OFDM parameters used for generating the illustrated signal inFig. 5.3 were as follows: Total number of subcarriers = 64, zero padded subcarriers = 16,number of cyclic prefix samples = 8, QAM size = 16, and number ofOFDM symbols = 32.The zero padded subcarriers are the ones suppresses -20 dB relative to the data carriers.

30

5.5. SUMMARY

The DC subcarrier is at the center of the spectrum. The DC carrier is used for furthermodulation on top of a high frequency carrier. The major drawback of OFDM modulationis its inherently high peak-to-average power ratio (PAPR);see Fig. 5.3b. The high PAPRincreases the demands on the amplifiers in an OFDM based transmission system. ThePAPR is a major problem in optical transmission system as thenonlinearities in an opticallink scale with the intensity of the electrical field in the fiber, thus, PAPR values must bekept at low values. There are several ways to reduce the PAPR of an OFDM symbol,for instance, pre-coding of data for avoidance of specific QAM patterns that generatehigh PAPR’s, selective subcarrier mapping for reduction ofconstructively addition ofharmonics, and clipping.

5.5 Summary

The parameters of an OFDM transmission system can be summarized as,

• FFT size determines the number of available subcarriers fordata transmission.

• Zero padding size sets the number of ”silent” subcarriers. This is done for mitiga-tion of inter-symbol-interference.

• The number of pilot tones for synchronization purpose and phase estimation.

• QAM constellation size determines the number of bits per QAMsymbol, hence thetotal number of bits per OFDM symbol.

• Cyclic prefix samples determines the amount of tolerable dispersion, or time delayin an OFDM transmission.

31

6SIMULATIONS AND RESULTS

All simulations and results are presented in this chapter. Different configuration param-eters were chosen for the transmitter, transmission link, and the receiver to cover sev-eral representative cases. The influence of SPM is presentedfollowed by XPM inducedpenalties for WDM transmissions, the performance difference between NRZ and OFDMneighboring channels are presented in the last section. Theresults in this chapter werepresented at IEEE/LEOS Summer Topical Meetings 2008, Acapulco [9].

6.1 Simulation Setup

By choosing an appropriate cyclic prefix for the OFDM symbols, virtually unlimited dis-persion tolerance can be realized for the OFDM transmission[10]. For this reason, allOFDM transmission experiments so far are realized without an inline optical dispersioncompensation. For green field deployments where one can choose the optimum disper-sion map this is not a problem. However, the existing 10 Gbps WDM networks usuallyemploy periodic inline dispersion compensation. By upgrading such link with a 40 GbpsOFDM channel, the periodic dispersion map is inevitable forthe OFDM signal. Further-more, it has been recognized that co-propagating NRZ channels can result in significantXPM penalties [11]. As such, the influence of the dispersion map on optical OFDMtransmissions were simulated in order to assess the nonlinear tolerance of OFDM as amodulation format in optical transmission systems. By choosing appropriate parametersfor the DCF’s in the transmission link, see Fig. 6.1, the dispersion maps of interest wereselected for the simulations. For non-dispersion managed transmission link simulation,the DCF’s and the pre-EDFA’s were removed. Three dispersionmaps were consideredfor investigation in this work.

The configuration of the transmitter, see Fig. 6.1, determines the waveform for simu-lation over the fiber. With a single channel OFDM and WDM waveform transmission, the

33

CHAPTER 6. SIMULATIONS AND RESULTS

Figure 6.1: The simulated transmission system. The transmitter gener-ates an OFDM signal at the center channel for SPM assessment.ForWDM transmissions and XPM assessment the OFDM channel is com-pleted with NRZ or OFDM neighboring channels. The transmission linkis mainly build up from spans of SSMF’s and DCF’s. The DCF’s are usedfor dispersion management. The input-power to the fibers arecontrolledby the EDFA’s. At the receiver the center channel is selectedusing anideal bandpass filter with a 50 GHz bandwidth. OSNR is controlled byadding noise at the receiver.

effects of SPM and XPM were assessed, respectively. The influence of co-propagatingNRZ and OFDM channels were evaluated by WDM transmissions with OFDM at thecenter frequency and co-propagating NRZ and OFDM neighboring channels. Fig. 6.2shows all the simulated waveforms, b) The single OFDM channel waveform, d) WDMtransmission with co-propagating OFDM neighboring channels, and f) WDM transmis-sion with co-propagating NRZ neighboring channels. At the receiver, the center channelis selected using an ideal rectangular filter with 50 GHz bandwidth. The OSNR is con-trolled by adding ASE at the receiver, in the simulations theOSNR was set to 8.6 dBresulting in a BER of 10−4 with respect to back-to-back configuration. The transmitterand receiver in Fig. 6.1 were simulated using MatLab and a fiber-optic network simulator.

In real transmission systems, the input power to the DCF’s are controlled and kept atlow levels relative to the SSMF in order to avoid nonlinearities from the DCF’s. By man-aging the input power to the DCF’s, all the nonlinearities can be considered to originatefrom the SSMF. In this work, the DCF’s are modeled as linear, thus resulting in the sameconditions as in real transmission systems. The fiber parameters used in the simulationsare given in Table 6.1.

34

6.2. OFDM PARAMETERS

Table 6.1: Fiber parameters used in the simulations.

Parameter Value Unit

Working frequency f = 193.1 [THz]Working wavelength λ = 1550 [nm]Attenuation α = 0.2 [dB km−1]Dispersion D = 17 [ps nm−1 km−1]Dispersion slope S = 0.057 [ps nm−2 km−1]Nonlinearity γ = 1.365 [W−1 km−1]Fiber length l = 80 [km]Number of spans N = 15 []

6.2 OFDM Parameters

For all the waveforms, a data rate of 26.3 Gbps was chosen for the center OFDM channel,which correspond to one polarization of the 52.6 Gbps transmission experiment reportedin [12]. The number of subcarriers for the OFDM transmissions were 256 with 88 zeropadded subcarriers, resulting in 168 data carrying subcarriers. For each simulation, 320individual OFDM symbols were used for BER evaluation.

6.3 Dispersion maps and Waveforms

Three dispersion maps with three different waveforms were simulated, to assess the in-fluence of the dispersion maps, on the nonlinear tolerance ofOFDM transmissions. Thedispersion maps and waveforms are listed below and can be viewed in Fig. 6.2. For eachdispersion map all the waveforms were simulated, resultingin nine possible configura-tions covering all possible impairments over the fiber.

• No inline DCF: This dispersion map represents the map as it is used in all opticalOFDM experiments reported so far. No inline or pre dispersion compensation isused, thus the chromatic dispersion accumulates over the transmission distance.

• Fully periodic: In this dispersion map, the chromatic dispersion is fully com-pensated for after each span of SSMF, by an inline dispersioncompensating fiber(DCF), leading to no residual dispersion at the end of the fiber.

• 10G OPT: The 10 Gbps optimal dispersion map is the commonly used map incommercial 10 Gbps transmission systems today [13]. This dispersion map consistsof -510 ps nm−1 pre-dispersion-compensation and an inline under-compensation of60 ps nm−1.

35

CHAPTER 6. SIMULATIONS AND RESULTS

• Single OFDM channel: Only one single OFDM channel is present in this wave-form, thus SPM is the only possible impairment for this transmission. The effectof SPM is assessed for this waveform.

• WDM transmission with co propagating OFDM neighboring channels A totalnumber of eleven OFDM channels are present in this waveform.As co propagatingOFDM channels are present in the waveform, the effects of XPMcan be studiedwith respect to OFDM neighboring channels.

• WDM transmission with co propagating NRZ neighboring channels As previ-ous, a total number of 11 channels are present in this waveform. All the channelsare NRZ except, the center OFDM channel. With this waveform the effects of XPMcan be studied with respect to NRZ neighboring channels.

36

6.3. DISPERSION MAPS AND WAVEFORMS

Transmission Distance [km]

Dis

pers

ion

[ps

nm−

1 ] No Inline DCF

0 243 486 729 972 1215−6800

0

6800

13600

20400

(a)

−200 −100 0 100 200−40

−20

0

20

40

Frequency [GHz]P

ower

[dB

m]

Single OFDM Channel

(b)

Transmission Distance [km]

Dis

pers

ion

[ps

nm−

1 ] Fully Periodic Compensation

0 270 540 810 1080 1350−1100

0

1100

2200

(c)

−200 −100 0 100 200−40

−20

0

20

40

Frequency [GHz]

Pow

er [d

Bm

]

WDM with OFDM Channels

(d)

Transmission Distance [km]

Dis

pers

ion

[ps

nm−

1 ] 10G Optimum

0 270 540 810 1080 1350−1100

0

1100

2200

(e)

−200 −100 0 100 200−40

−20

0

20

40

Frequency [GHz]

Pow

er [d

Bm

]

WDM with NRZ Channels

(f)

Figure 6.2: The dispersion maps and waveforms assessed in this work.a) No inline DCF: This dispersion map results in accumulateddispersionalong the fiber. c) Fully periodic: The dispersion is fully compensated forin each span of fiber. e) 10G OPT: This is the dispersion map commonlyused in 10 Gbps transmission systems. b) Single OFDM channel. d)WDM transmission with co propagating OFDM neighboring channels.f) WDM transmission with co propagating NRZ neighboring channels.

37

CHAPTER 6. SIMULATIONS AND RESULTS

Launch Power [dBm]

log 10

(BE

R)

Single OFDM Channel Transmission

−14 −12 −10 −8 −6 −4 −2 0−1

−2

−3

−4

−5

No inline DCF10G OPTFully Periodic

Figure 6.3: The influence of SPM for all dispersion maps. At low inputpowers the transmission system is in its linear regime, thusno penaliesare observed. At high input powers,> -10 dBm, the nonlinearities be-come more apparent. The highest nonlinear tolerance is observed for thedispersion map with no inline DCF, at BER limit of10−3 both the fully pe-riodic and the 10G optimum dispersion map suffers from a launch powerpenalty of 2.5 dB.

6.4 Single OFDM channel transmission and SPM assessment

By selecting the ”single OFDM channel” waveform at the transmitter, the influence ofSPM were analyzed with respect to the dispersion maps. To assess the induced nonlinear-ities for all the dispersion maps, launch power variations were performed at the transmitterand the BER was evaluated at the receiver. The results are displayed in Fig. 6.3, at low in-put powers (< -10 dBm), the transmission system is in its linear regime andthus after thetransmission, for all the dispersion maps, no performance degradation can be observed.At high input powers (> -10 dBm), the highest nonlinear tolerance is observed for thedispersion map without inline dispersion compensation. Atthe BER limit of 1x10−3 boththe fully periodic and the 10G optimum dispersion map exhibit a launch power penalty

38

6.5. WDM TRANSMISSIONS AND XPM ASSESSMENT

Launch Power [dBm]

log 10

(BE

R)

Single OFDM channel and WDM OFDM

−14 −12 −10 −8 −6 −4 −2 0−1

−2

−3

−4

−5

Single − No inline DCFSingle − 10G OPTSingle − Fully PeriodicWDM − No inline DCFWDM − 10G OPTWDM − Fully Periodic

Figure 6.4: The influence of XPM for all the dispersion maps. The XPMpenalty, for the dispersion map with no inline DCF was 1 dB with respectto the single channel transmission. The 10G optimum and fully periodicdispersion map exhibited a launch power penalty of 2 dB and 3 dB, re-spectively.

of 2.5 dB with respect to the dispersion map without an inlineDCF.

6.5 WDM transmissions and XPM assessment

The influence of XPM were assessed by selecting WDM waveform with co-propagatingOFDM channels at the transmitter. As similar to the SPM assessment, launch power vari-ations were performed, and the BER was evaluated at the receiver for all the dispersionmaps. The results are presented in Fig. 6.4, for the WDM and thesingle OFDM channeltransmission, respectively. As the only difference between the waveforms are the excessWDM channels, it can be concluded that any changes in the BER evaluation is caused byXPM. At the BER limit of 10−3, for the dispersion map with no inline DCF, the WDM

39

CHAPTER 6. SIMULATIONS AND RESULTS

Launch Power [dBm]

log 10

(BE

R)

WDM with NRZ and OFDM neighboring channels

−14 −12 −10 −8 −6 −4 −2 0−1

−2

−3

−4

−5

NRZ − No inline DCFNRZ − 10G OPTNRZ − Fully PeriodicOFDM − No inline DCFOFDM − 10G OPTOFDM − Fully Periodic

Figure 6.5: The influence of XPM for OFDM and NRZ neighboringchannels. The choice of co-propagating neighboring channels does notaffect the nonlinear tolerance of the WDM transmission. In other words,the XPM caused by OFDM neighboring channels is as strong as that of10 Gbps NRZ channels.

transmission suffers from a launch power penalty of 1dB caused by XPM, relative to thesingle OFDM channel. As for the 10G optimum and the fully periodic dispersion mapthe launch power penalties are 2 dB and 3 dB, respectively.

6.6 NRZ vs OFDM neighboring channels for WDM transmissions

To assess the difference in the nonlinear tolerance of WDM transmissions with respect toco propagating NRZ or OFDM channels, launch power variations were performed as inprevious transmissions. WDM waveforms with NRZ and OFDM neighboring channelswere selected at the transmitter and the BER was assessed at the receiver. Fig. 6.5 dis-plays the BER evaluations at the receiver, for all the dispersion maps, and the two WDM

40

6.6. NRZ VS OFDM NEIGHBORING CHANNELS FOR WDM TRANSMISSIONS

transmissions with NRZ and OFDM neighboring channels, respectively. For the WDMtransmissions, with OFDM and 10 Gbps NRZ neighboring channel and for all the dis-persion maps, no significant launch power penalties could beobserved at the BER limit1x10−3. It can thus be concluded that the influence of XPM resulting from 10 Gbps NRZneighboring channels does not reduce the nonlinear tolerance compared to the configura-tion where the neighboring channels are OFDM modulated. Or in other words, the XPMcaused by OFDM neighboring channels is as strong as that of 10Gbps NRZ channels.

41

7CONCLUSIONSAND DISCUSSION

In this work, the influence of SPM and XPM were analyzed on optical OFDM trans-mission for different dispersion maps. It was observed thatthe nonlinear tolerance withrespect to both SPM and XPM is severely degraded when inline dispersion compensa-tion is employed. For WDM transmissions, it was observed thatthe influence of XPMresulting from 10 Gbps NRZ neighboring channels does not reduce the nonlinear toler-ance compared to OFDM neighboring channels. The XPM caused by OFDM and NRZneighboring channels in a WDM transmission system are as strong.

A possible explanation for the reduction of the nonlinear tolerance in a periodicallycompensated dispersion map is that the symbol rate of OFDM issignificantly lower thanthat of conventional modulation formats such as NRZ. As a result, the dispersion mapwithout inline dispersion compensation provides a better distribution of the nonlinearphase shifts resulting from SPM and XPM over the waveform, which reduces the impactof these nonlinear impairments.

These results indicate that the suitability for overlay of high data rate OFDM channelson the existing 10 Gbps infrastructure is questionable.

43

AAPPENDIX A: M ATLAB CODE FOROFDM

SIGNAL GENERATION

45

%########################################################################## %# This program illustrates a simple OFDM transmitter according to the %# IEEE 802.11a implementation. The IEEE 802.11a implements 4 pilot %# tones for synchronization. In this version of the transmitter no pilot %# tones were used. %# %# Author: Kamyar Forozesh %# Date: 2009-12-10 %# Email: kamyar.forozesh@gmail.com %# %########################################################################## clear all; close all; clc; % OFDM parameters OFDM_Symbols = 32; QAM_Constellation = 16; FFT_Window = 64; Zero_Padding = 16; Cyclic_Prefix = 8; % Defining subcarriers with zero padding Zero_Subcarriers = [-FFT_Window/2:1:((-FFT_Window+Zero_Padding)/2-1) 0 ((FFT_Window-Zero_Padding)/2+1):1:FFT_Window/2-1] + FFT_Window/2+1 ; % Defining data carrying subcarriers Data_Subcarriers = [-(FFT_Window-Zero_Padding)/2:1:-1 1:1:(FFT_Window-Zero_Padding)/2] + FFT_Window/2+1; % Defining pilot subcarriers Pilot_Subcarriers = []; % Vector Initialization OFDM_Symbol_Freq = zeros(1,FFT_Window); OFDM_Symbol_Time = []; OFDM_Sequence = []; for i=1:OFDM_Symbols % Data generation, QAM modulation, QAM normalization Tx_Data_Bin = randint(log2(QAM_Constellation),FFT_Window-Zero_Padding); Tx_Data_QAM = modulate(modem.qammod('M',QAM_Constellation,'InputType','bit'),Tx_Data_Bin); Tx_Data_QAM = Tx_Data_QAM./abs(max(Tx_Data_QAM)); % Subcarrier assignment, Zero padding OFDM_Symbol_Freq(Data_Subcarriers) = Tx_Data_QAM; OFDM_Symbol_Freq(Zero_Subcarriers) = 0; % IFFT operation, Cyclic prefix insertion OFDM_Symbol_Time = ifft(OFDM_Symbol_Freq,FFT_Window); OFDM_Symbol_Time_CP = [OFDM_Symbol_Time((end-Cyclic_Prefix):end) OFDM_Symbol_Time]; % Stacking OFDM symbols to a time sequence OFDM_Sequence = [OFDM_Sequence OFDM_Symbol_Time_CP]; end % Displaying OFDM spectrum C1 = [142 026 026]/256; C2 = [026 026 142]/256;

fig1 = figure('Name','None',... 'NumberTitle','off',... 'InvertHardcopy','off',... 'Color',[1 1 1],... 'Position',[1250 400 640 400],... 'PaperPositionMode','auto'); fig2 = figure('Name','None',... 'NumberTitle','off',... 'InvertHardcopy','off',... 'Color',[1 1 1],... 'Position',[610 400 640 400],... 'PaperPositionMode','auto'); ax1 = axes('Position',[0.15 0.2 0.75 0.7], ... 'PlotBoxAspectRatio',[2 1 1],... 'Box','on',... 'Xgrid','on',... 'Ygrid','on',... 'Visible','on', ... 'GridLineStyle',':',... 'XLim',[-3 3], ... 'YLim',[-30 10], ... 'YTick',[-30 -20 -10 0 10], ... 'YTickLabel',[{'-30','-20','-10','0','10'}],... 'fontsize',22, ... 'linewidth',3, ... 'layer','bottom',... 'parent',fig1); ax2 = axes('Position',[0.15 0.2 0.75 0.7], ... 'PlotBoxAspectRatio',[2 1 1],... 'Box','on',... 'Xgrid','on',... 'Ygrid','on',... 'Visible','on', ... 'GridLineStyle',':',... 'XLim',[1 1000], ... 'YLim',[-1 1], ... 'YTick',[-1 -.5 0 .5 1], ... 'YTickLabel',[{'-1','-0.5','0','0.5','1'}],... 'fontsize',22, ... 'linewidth',3, ... 'layer','bottom',... 'parent',fig2); hold (ax1,'on'); hold (ax2,'on'); xlabel(ax1,'Normalized Frequency [-\pi, \pi]' ); ylabel(ax1,'Normalized Power [dB]'); title (ax1,'OFDM Spectrum'); xlabel(ax2,'Time sample [n]' ); ylabel(ax2,'Normalized Amplitude'); title (ax2,'OFDM signal'); [Pxx,f] = pwelch(OFDM_Sequence,[],[],2^10); Mag_Spec = 10*log10(Pxx)- max(10*log10(Pxx));

plot((f-pi),Mag_Spec,'Color',C1,'linewidth',2,'parent',ax1); % Resampling time domain data and plotting OFDM_Symbol_Time_plot = real(ifft(OFDM_Symbol_Freq,2^10))/max(abs(ifft(OFDM_Symbol_Freq,2^10))); Time_samples = 1:1:2^10; plot(Time_samples,OFDM_Symbol_Time_plot,'Color',C2,'linewidth',2,'parent',ax2); % Information display disp(['Number of OFDM symbols ',num2str(OFDM_Symbols)]); disp(['Number of subcarriers ',num2str(FFT_Window)]); disp(['Number of data subcarriers ',num2str(FFT_Window-Zero_Padding)]); disp(['Number of zero padded subcarriers ',num2str(Zero_Padding)]); disp(['Number of cyclic prefix samples ',num2str(Cyclic_Prefix)]); disp(['---------------------------------------------']); disp(['QAM constellation size ',num2str(QAM_Constellation)]) disp(['OFDM symbol duration ',num2str((4*10^-6))]) disp(['Bits per OFDM symbol ',num2str(log2(QAM_Constellation)*(FFT_Window-Zero_Padding))]); disp(['Transmission rate (bps) ',num2str(log2(QAM_Constellation)*(FFT_Window-Zero_Padding)*(1/(4*10^-6)))]); %print -f1 -depsc2 -tiff -r300 OFDM_Spectrum %print -f2 -depsc2 -tiff -r300 OFDM_Symbol

BAPPENDIX B: PUBLISHED ARTICLE AT

IEEE/LEOSSUMMER TOPICALS

47

BIBLIOGRAPHY

[1] K. C. Kao and G. A. Hockham, “Dielectric-fibre surface waveguides for opticalfrequencies,”in proc. I.E.E., vol. 113, no. 7, pp. 1151–1158, 1966.

[2] G. P. Agrawal,Fiber-optic communication systems, second edition ed. JohnWiley and Sons, 1997.

[3] G. Keiser,Optical Fiber Communications, second edition ed. McGraw-Hill,1991.

[4] E. G. Neumann,Single-Mode Fibers. Springer Verlag, 1988.

[5] ITU, “Optical system design and engineering considerations,” InternationalTelecommunication Union (ITU), vol. G., Oct. 2003.

[6] J. K. Shaw,Mathematical Principles of Optical Fiber Communications. SIAM,2004.

[7] V. Mamyshev and N. A. Mamysheva, “Pulse-overlapped dispersion-managed datatransmission and intrachannel four-wave mixing,”Optics Letters, vol. 24, no. 21,pp. 1454–1456, 1999.

[8] M. N. Islam,Raman amplifiers for telecommunications 1. Springer Verlag, 2004.

[9] F. Kamyaret al., “The influence of the dispersion map in coherent optical ofdmtransmission systems,”IEEE/LEOS Summer Topical Meetings, pp. 135–136, 2008.

[10] S. L. Jansenet al., “Coherent optical 25.8-gb/s ofdm transmission over 4,160-kmssmf,”Journal of Lightwave Technology letters, vol. 26, pp. 6–15, 2008.

[11] B. Spinnleret al., “Nonlinear tolerance of differential phase shift keying modulatedsignals reduced by xpm,” inproc. OFC, 2008, p. TuF3.

[12] S. L. Jansenet al., “Long-haul transmission of 1652.5 gbit/spolarization-division-multiplexed ofdm enabled by mimo processing,”OSAJournal of Optical Networking, vol. 7, pp. 173–182, 2008.

[13] Furstet al., “Influence of the dispersion map on limitations due to cross-phasemodulation in wdm multispan transmission systems,” inproc. OFC, 2001, pp.MF4–3.

49

ABBREVIATIONS

ASE Amplified Spontaneous EmissionASK Amplitude Shift KeyingAWG Arrayed Waveguide GratingAWGN Additive White Gaussian NoiseBER Bit-Error RateDCF Dispersion Correcting FiberDFB Distributed Feedback LaserDML Direct Modulated LaserDSP Digital Signal ProcessorEDFA Erbium Doped Fiber AmplifierFFT Fast Fourier TransformISI Inter-Symbol InterferenceITU-T International Telecommunication UnionMZM Mach Zehender ModulatorNLSE Nonlinear Schrdinger EquationOFDM Orthogonal Frequency Division MultiplexingOOK On-Off-KeyingORD Optimal Residual DispersionOSNR Optical Signal-to-Noise RatioPAPR Peak-to-Average Power RatioQAM Quadrature Amplitude ModulationRZ Return-to-ZeroSBS Stimulated Brillouin ScatteringSPM Self Phase ModulationSRS Stimulated Raman ScatteringSSMF Standard Single-Mode FiberWDM Wavelength Division MultiplexingXPM Cross Phase Modulation

51

L IST OF FIGURES

1.1 Illustration of a standard single-mode fiber. a) The fibercore with a refractiveindex n≈ 1.48 and a cross-section of≈ 9 µm. b) The cladding with a slightlylower refractive index. c) The coating of the fiber for protection and structuralintegrity. 2

2.1 The attenuation coefficientαdB as a function of the frequency. The Standard-ized communication bands are marked in the figure, the C-bandis the lowloss window and the most common band for long-haul digital communications. 4

2.2 The effect of dispersion at different transmission lengths along an SSMF,with no dispersion compensation employed in the transmission link. Initially(0 km), no dispersion is present and all the pulses are intact, as the transmis-sion distance increases, dispersion accumulates over the fiber, causing inter-symbol-interference. At 30 km if no dispersion compensation is employed,no information can be retrieved. 6

2.3 The optical signal power as a function of transmission distance. The high-power region of the fiber is illustrated in the figure as the shaded area. Theeffective length is marked in the figure at 21.5 km, this valuewas calculatedfor 100 km of SSMF with an attenuation coefficient ofα = 0.2 dB km−1. 8

2.4 Intensity variations of the signal is translated through the Kerr-effect to phasemodulation of the signal itself. a) A Gaussian pulse, b) The frequency shiftof the signal in response to the intensity variations of the signal. 9

53

L IST OF FIGURES

3.1 Graphical representation of a fiber optic transmission system. The transmit-ter is composed of a distributed feedback laser in conjunction with a Mach-Zehender modulator for electrical to optical conversion, an arrayed waveg-uide grating is used to multiplex several optical channels into a one opticalsignal. The transmitter EDFA controls the input power to thefiber. Thetransmission line consists of repeated segments of fiber, amplifier (EDFA),dispersion-correcting-fiber (DCF), and power-regulator amplifier. The re-ceiver consists of an arrayed waveguide grating for demultiplexing, and post-dispersion-compensation fibers for optimization of the residual dispersion foreach optical channel, at the last step, a photodiode is used for detecting theoptical signal and down conversion to electrical domain. 12

3.2 The OSNR as a function of the launch power. At high launch powers, nonlin-earities are induced, resulting in OSNR penalties, and at low launch powers,amplified spontaneous emission lead to accumulated noise after transmission,resulting in low OSNR values. 14

3.3 The accumulated dispersion over the transmission distance. a) pre-dispersioncompensation, b) accumulated dispersion along the SSMF, c)dispersion com-pensation using an in-line DCF, d) in-line dispersion under-compensation, re-alized by not fully compensating for the dispersion with thein-line DCF, e)post-dispersion compensation, resulting in an optimum residual dispersion. 15

3.4 The dispersion map for different WDM channels. As WDM channels are lo-calized at different frequencies, the dispersion map will be different for eachWDM channel. The in-line dispersion compensation can not compensate forthe dispersion for all the WDM channels at the same time. Different post-compensations must be applied for each WDM channel. 16

4.1 The envelope of On-Off-Keying (OOK) signals, a) OOK signal with return-to-zero (RZ) pulses, b) OOK signal with non-return-to-zero(NRZ) pulses. 20

4.2 The unit pulse in time and frequency domain respectively. a) unit pulse ofperiod 10 ms which correspond to a frequency of 100 Hz. b) the spectralcomponents of the pulse, the spectrum of the pulse have zerosat multiples of100 Hz. 21

4.3 Passband representation of OOK RZ and NRZ. The baseband OOK signalmodulated on top of a carrier. 22

4.4 Four level amplitude-shift-keying (ASK) in baseband and passband represen-tation. 23

4.5 To the left, the in-phase and quadrature channels of a QAMsignal are shown.The QAM constellation diagram to the right, displays the possible QAM sym-bols that can be generated. The transmitted symbols according to the I and Qchannels can be in seen in the panel, Transmitted QAM symbols. 25

54

L IST OF FIGURES

5.1 The occupied frequency space of an OFDM and FDM transmission. Theorthogonality of the subcarriers in the OFDM transmission makes it possibleto save bandwidth, in comparison to conventional FDM transmissions, whereguardband is necessary. 28

5.2 Block Representation of OFDM. Serial to parallel converter, multiplexes thehigh data rate stream to several low bit rate streams, these streams are con-verted to QAM symbols through the symbol mapper. The QAM symbols willsubsequently modulate the subcarriers of the OFDM symbol. The modulationprocess of all subcarriers is done by the IFFT block. The timedata from theIFFT block is passed to the cyclic prefix block for extension of time samples.Time samples are converted to a serial stream and subsequently converted tothe analog domain through the digital to analog converter. 28

5.3 The time and frequency domain representation of an OFDM transmissionwith 16 out of 64 subcarriers zero padded and 8 cyclic prefix samples. a) Thespectrum of OFDM transmission, averaged for 32 OFDM symbols. b) Timedomain transmission of a single OFDM symbol. 30

6.1 The simulated transmission system. The transmitter generates an OFDMsignal at the center channel for SPM assessment. For WDM transmissionsand XPM assessment the OFDM channel is completed with NRZ or OFDMneighboring channels. The transmission link is mainly build up from spansof SSMF’s and DCF’s. The DCF’s are used for dispersion management. Theinput-power to the fibers are controlled by the EDFA’s. At thereceiver thecenter channel is selected using an ideal bandpass filter with a 50 GHz band-width. OSNR is controlled by adding noise at the receiver. 34

6.2 The dispersion maps and waveforms assessed in this work.a) No inline DCF:This dispersion map results in accumulated dispersion along the fiber. c)Fully periodic: The dispersion is fully compensated for in each span of fiber.e) 10G OPT: This is the dispersion map commonly used in 10 Gbpstrans-mission systems. b) Single OFDM channel. d) WDM transmissionwith copropagating OFDM neighboring channels. f) WDM transmissionwith copropagating NRZ neighboring channels. 37

6.3 The influence of SPM for all dispersion maps. At low input powers the trans-mission system is in its linear regime, thus no penalies are observed. At highinput powers,> -10 dBm, the nonlinearities become more apparent. Thehighest nonlinear tolerance is observed for the dispersionmap with no in-line DCF, at BER limit of 10−3 both the fully periodic and the 10G optimumdispersion map suffers from a launch power penalty of 2.5 dB. 38

6.4 The influence of XPM for all the dispersion maps. The XPM penalty, forthe dispersion map with no inline DCF was 1 dB with respect to the singlechannel transmission. The 10G optimum and fully periodic dispersion mapexhibited a launch power penalty of 2 dB and 3 dB, respectively. 39

55

L IST OF FIGURES

6.5 The influence of XPM for OFDM and NRZ neighboring channels. Thechoice of co-propagating neighboring channels does not affect the nonlin-ear tolerance of the WDM transmission. In other words, the XPMcaused byOFDM neighboring channels is as strong as that of 10 Gbps NRZ channels. 40

56

INDEX

OH− impurities, 3

absorption peak, 3additive white Gaussian noise

(AWGN), 19amplified spontaneous emission (ASE),

13arrayed waveguide grating (AWG), 11attenuation coefficient, 3

chromatic dispersion, 13communication bands in SSMF, 3conclusions, 43cross phase modulation, 7

D parameter, 5DCF, 14direct modulated laser (DML), 11dispersion, 4dispersion correcting fiber (DCF), 5dispersion map, 15dispersion slope, 5distributed feedback laser (DFB), 11

effective lengthLe f f, 7effective mode area, 6Erbium doped fiber amplifier (EDFA),

11

fiber cladding, 2fiber coating, 2fiber core, 2fiber optic transmission system, 12

high-power region, 7

in-line DCF, 15

inter symbol interference (ISI), 5intrinsic absorption, 3

Kerr-effect, 6

launch power, 3linear impairments, 8

Mach-Zehnder modulator (MZM), 11mode propagation constantβ, 5

neper, 3Non-Return-to-Zero (NRZ), 20nonlinear coefficientγ, 7nonlinear coefficient of DCF, 15nonlinear impairments, 8nonlinear refractive index, 6nonlinear Schrodinger equation

(NLSE), 7

On-Off-Keying (OOK), 20optical amplifier noise, 13optical power, 3optical signal-to-noise ratio (OSNR), 13optimal launch power, 13optimum residual dispersion (ORD), 16Orthogonal Frequency Division

Multiplexing, 27

peak-to-average power ratio (PAPR), 16post-compensation DCF, 12post-dispersion compensation, 15pre-dispersion compensation, 11, 15

Rayleigh scattering, 3receiver, 12refractive index, 2

57

INDEX

residual dispersion, 12return-to-zero (RZ), 20

S parameter, 5self phase modulation (SPM), 7simulated dispersion maps, 35simulated OFDM parameters, 35simulated waveforms, 34simulations, 33slope matched, 14spectral efficiency, 19SPM results, 39SSMF, 2standard single-mode fiber (SSMF), 2stimulated Brillouin scattering (SBS), 8stimulated Raman scattering (SRS), 8

WDM, 1

XPM results, 40

58