The influence of the dispersion map on optical OFDM transmissions

7/27/2019 The influence of the dispersion map on optical OFDM transmissions

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UPTEC F10 001

Examensarbete 20 pFebruari 2010

The influence of the dispersion

map on optical OFDM transmissions

Kamyar Forozesh


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Teknisk- naturvetenskaplig fakultetUTH-enheten

Besksadress:ngstrmlaboratorietLgerhyddsvgen 1Hus 4, Plan 0

Postadress:Box 536751 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 communicationsystem. In these networks, distances of typically 400 km to 6000 km arelinked together, and information is transfered at extremely high datarates. As the demands for capacity increases, finding new methods forcost effective long-haul transmission systems that can be used toincrease the capacity becomes of high interest. In this work OrthogonalFrequency Division Multiplexing (OFDM), which is a standard digitalmodulation format in many wireless communication systems, for instancethe IEEE 802.11n, is adapted to the optical domain and used for datatransmission. The advantage of OFDM in the optical domain is that ittransforms a high data rate stream into many simultaneously low bit ratestreams that are efficiently frequency multiplexed. By doing so highspectral 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 restrictsthe feasible transmission distance. The goal of this work is to assessthe suitability of OFDM in fiber-optic communications.

ISSN: 1401-5757, UPTEC F10001Examinator: Tomas Nybergmnesgranskare: Dr. Jan Bergman

Handledare: Dr. Sander Lars Jansen


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DIPLOMA THESIS

THE INFLUENCE OF THE

DISPERSION MAP ON OPTICAL OFDM

TRANSMISSIONS

KAMYAR FOROZESH

Uppsala School of Engineering

and

Department of Astronomy and Space Physics, Uppsala University, Sweden

APRIL 10, 2009


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ABSTRACT

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 in-crease 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 trans-

mission distance. The goal of this work is to assess the suitability of OFDM in fiber-optic

communications.

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To my father


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CONTENTS

Abstract iii

Contents vii

Acknowledgments ix

Preface xi

1 Introduction 1

1.1 Fiber Optic Networks 1

1.2 The Optical Fiber 2

2 Fiber Optic Impairments 32.1 Power Loss 3

2.2 Dispersion 4

2.3 Kerr-Effect 6

2.4 Self Phase Modulation SPM 7

2.5 Cross Phase Modulation XPM 7

2.6 Non Elastic Scattering Effects 8

2.7 Summary 8

3 The Transmission Link 11

3.1 Transmitter 11

3.2 Transmission Line 12

3.3 Receiver 12

3.4 Fiber Loss Compensation 133.5 Dispersion Compensation 13

3.6 Dispersion map 15

3.7 Summary 17

4 Digital Communication 19

4.1 Modulation 19

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CONTENTS

4.2 Baseband Signal Representation 20

4.3 Passband Signal Representation 21

4.4 Amplitude Shift Keying ASK 23

4.5 Orthogonal Carriers 24

4.6 QAM modulation 24

4.7 Summary 25

5 Orthogonal Frequency Division Multiplexing 27

5.1 Introduction to OFDM 27

5.2 Block Representation of OFDM 28

5.3 OFDM Parameters 295.4 Spectrum and Transmission 30

5.5 Summary 31

6 Simulations And Results 33

6.1 Simulation Setup 33

6.2 OFDM Parameters 35

6.3 Dispersion maps and Waveforms 35

6.4 Single OFDM channel transmission and SPM assessment 38

6.5 WDM transmissions and XPM assessment 39

6.6 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

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ACKNOWLEDGMENTS

I am grateful to colleagues at KDDI R&D Laboratories, in particular Dr. Sander Lars Jansen

for all the fruitful discussions and guidance. Thanks also go to Dr. Jan Bergman and

Siavoush Mohammadi, colleagues at Uppsala University for their useful comments and

criticism. I am also grateful to Sweden Japan foundation as well as Knut and Alice Wal-lenberg foundation for their support of this work. Finally I would like to thank my fianc ee

Oranous F.M. for being the fantastic woman she is, her encouragement made this work

possible.

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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 transmissions

are presented and discussed. Chapter 3 presents the optical transmission system, and

how impairments, discussed in in Chapter 2 are compensated for. Chapter 4 introducesdigital modulation formats, in particular, the quadrature amplitude modulation (QAM).

Chapter 5 presents, orthogonal frequency division multiplexing (OFDM) and associated

parameters involved in such modulation format. In Chapter 6 simulations of OFDM in

optical communication systems are presented for different transmission setups and the

results are presented and discussed.

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1

INTRODUCTION

In 1966, Kao et al published a paper [1] that is considered to be the start of the modern

fiber optic communications. Following quote is from Kaos famous paper

A dielectric fibre with a refractive index higher than its surrounding region

is a form of dielectric waveguide which represents a possible medium for the

guided transmission of energy at optical frequencies.

Since its introduction, systems based on fiber optic solutions with different properties

have been developed for the demands in digital communication. In this chapter some

background information will be presented. Furthermore the standard 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 long distances. A typical trans-

mission distance in the backbone network is between 500 km and up to several thousands

of kilometers. Modern commercial transmission systems employ data rates of 10 Gbps

and 40 Gbps per channel. Wavelength division multiplexing (WDM) is used to multiplex

and transmit many channels at different wavelengths over the same fiber, By doing so the

capacity of the link is significantly increased. The transmission capacity over a singlefiber in commercial networks employing 80 channels at 40 Gbps is 3.2 Tbps; observe

that this is the capacity of a single fiber. This is the main reason why fiber optic systems

are considered to have unlimited bandwidth, due to the fact that an arbitrary number of

fibers can be encapsulated in a single cable. However, in many situations major design

alternations, such as increasing the number of fibers or amplifiers in a deployed system

is very hard to achieve, if not impossible. For instance the intercontinental transmission

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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 m. b) The

cladding with a slightly lower refractive index. c) The coating of the fiber

for protection and structural integrity.

links between Japan and America which is submerged in the sea. This makes the research

for 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 the

fiber; hence the name single-mode fiber. There are fibers with thicker core which allow

many 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, which

ultimately lead to decreased transmission distance. Due to this fact, only SSMFs are used

for long-haul transmission applications [2]. In Fig. 1.1 the main regions of an optical fiber

is depicted; the fiber core, cladding, and coating. The core of the fiber has slightly higher

refractive 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 surrounding

environment. For wavelengths used in long-haul transmission systems usually SSMFs

with a core diameter of 9m is used. An in-depth analysis of single-mode fibers can be

found in [4]. The following chapter will focus on the impairments in the SSMF.

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CHAPTER 2. FIBER OPTIC IMPAIRMENTS

Figure 2.1: The attenuation coefficient dB as a function of the fre-

quency. The Standardized communication bands are marked in the fig-

ure, the C-band is the low loss window and the most common band for

long-haul digital communications.

commercial systems is the C-band, i.e. 1530 nm to 1565 nm, as it has the lowest fiber loss

in that range, with a minimum around 1550 nm / 193.1 THz. A common value for the

attenuation coefficient in the C-band is dB= 0.20 dB km1 [2]. This makes transmissions

over 100 km of fiber possible before the need of amplification. In this work the C-band

was used for all fiber-optic simulations, as it is the most common communication band

for 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 frequency i.e., n = n(). The phase velocity, vph,

of a transmitted signal in the fiber is related to n() as

vph =c

n() , (2.3)

where c is the speed of light. The frequency dependence of the refractive index results

in variations in the phase velocity, thus, spectral components of a transmitted signal will

have different phase velocities according to Eq. (2.3). These variations in phase velocities

leads to dispersion of the signal. Dispersion, also called material or fiber dispersion,

distorts the signal if not compensated for.

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2.2. DISPERSION

By Taylor expanding the mode propagation constant [2, 3] which is related to the

refractive index n according to

() =

vp= n()

c, (2.4)

material specific dispersion parameters can be derived. Taylor expansion of Eq. (2.4) at

the working frequency 0 gives a linearized relationship between the mode propagation

constant and the angular frequency

() 0+1( 0)+1

22( 0)2+

1

63( 0)3 +O(4) , (2.5a)

n =dn

dn =0, (2.5b)

where 0 and 1 = 1/vg correspond to a constant phase shift and the group velocity, re-

spectively. 2 represents group velocity dispersion and 3 dispersion slope. The more

common way to express 2 and 3 in fiber-optics is through fiber specific parameters D

and S [2] according to

D = 2c

22 , (2.6a)

S=4c

3 2+2c

22

3 . (2.6b)

D is expressed in [ps nm1 km1] and describes the amount of dispersion per kilometers

and S is expressed in [ps nm2 km1], which describes the change of dispersion as func-

tion of the working frequency. For the SSMF in the C-band the dispersion parameter D is

in the range of 15-18 ps nm1 km1 and the dispersion slope S around 0.06 ps nm2 km1.

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 by D.

It is possible to create fibers with negative dispersion parameters D, these fibers are

called dispersion correcting fiber (DCF) [2] and are mainly used for compensating for

the accumulated dispersion. In fiber-optic transmission links the accumulated dispersion

ultimately 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 are

intact and no dispersion is present, as the transmission length increases, the impact of

the dispersion becomes more obvious. At high dispersion values the pulses disperse into

neighboring pulse slots causing inter symbol interference (ISI). At 30 km there is no

easy way to distinguish the pulses apart, see Fig. 2.2, in fact at this point, if dispersion

compensation is not applied to the signal, no information can be retrieved.

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0 1024 2048 3072 40960

1

2

3

4

5Dispersion = 0 ps nm

1(0 km)

SignalPower[mW]

0 1024 2048 3072 40960

1

2

3

4

5

Dispersion = 80 ps nm1

(5 km)

Time [ps]

SignalPower[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

5

Dispersion = 480 ps nm1

(30 km)

Time [ps]

Figure 2.2: The effect of dispersion at different transmission lengths

along an SSMF, with no dispersion compensation employed in the trans-

mission link. Initially (0 km), no dispersion is present and all the pulses

are intact, as the transmission distance increases, dispersion accumu-

lates over the fiber, causing inter-symbol-interference. At 30 km if no

dispersion compensation is employed, no information can be retrieved.

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 the refractive index of the

fiber. The change in the refractive index caused by the Kerr effect is a function of the

optical power |A|2 [3] and the relationship is described by

n(, |A|2) = n0()+n2|A|2

Ae f f, (2.7)

where n0 is the linear refractive index as discussed in the previous section, n2 is the

nonlinear refractive index and Ae 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

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2.4. SELF PHASE MODULATION SPM

Schrodinger equation (NLSE) [6]

A

z=

2A

j

22

2A

T2+

1

63

3A

T3+ j|A|2A , (2.8a)

=n20

cAe f f, (2.8b)

T= t1z = tz

vg, (2.8c)

were A is the complex amplitude of the optical-field, z is the propagation distance in

[km], is the attenuation coefficient in [Neper]. is the nonlinear coefficient expressedin [W1 km1] and T is the time measured in the retarded frame. As the impact of the

nonlinear Kerr effect is proportional to the signal power according to Eq. (2.7) almost all

nonlinearities will be introduced at the high-power region of the fiber, which is the first

part of the fiber and is defined by an effective length Le f f according to

Le f f =1 eL

. (2.9)

Fig. 2.3 shows the signal power as a function of transmission distance of SSMF. In the

figure, the effective length Le f f and the high-power region is illustrated. For an SSMF of

length 100 km, with an attenuation coefficient = 0.2 dB km1, the effective length Le f fis 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 by

the intensity dependence of the refractive index (The Kerr-effect). This is referred to as

self phase modulation (SPM). The SPM affects the phase of the signal but the influence of

chromatic 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 in

wavelength division multiplexed (WDM) transmission systems. The intensity variations

of a signal in a WDM channel are converted into phase variations in other WDM channels

and through the interplay with chromatic dispersion to amplitude variations. XPM also

scales inversely with the data rate [7], the higher data rate the lower influence of the XPM

will be.

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Transmission Distance [km]

SignalPower[mW]

Power loss

Leff = 21.5 km

HighPowerRegion

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 the

shaded area. The effective length is marked in the figure at 21.5 km, this

value was calculated for 100 km of SSMF with an attenuation coefficient

of=

0.2 dB km

1

.

2.6 Non Elastic Scattering Effects

Introducing two new nonlinear impairments, namely the stimulated Raman scattering

and the stimulated Brillouin scattering shortened to SRS and SBS, respectively. The

interaction of light, or more correctly, photons with the molecules of the optical fiber

is the cause of these nonlinearities. The SRS is an interaction of photons and optical

phonons [8] of the fiber. This interaction is very important as it is responsible for the

realization of optical amplifiers. The SBS originates from the interaction of photons with

molecules 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 impairments and can easily be compensated

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2.7. SUMMARY

Time in multiples of

Self Phase Modulation (SPM)

a) gaussian pulse

b) Frequency shift

Intensiy

f

0

+

3 2 1 0 1 2 3

Figure 2.4: Intensity variations of the signal is translated through the

Kerr-effect to phase modulation of the signal itself. a) A Gaussian pulse,

b) The frequency shift of the signal in response to the intensity variations

of the signal.

for with the use of passive and active components. The Kerr effect however is a nonlinear

impairment and is relatively hard to compensate for. The Kerr effect originates from the

intensity dependence of the refractive index of the fiber and is responsible for self phase

modulation (SPM) and cross phase modulation (XPM).

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3

THE TRANSMISSION LINK

In this chapter, wave length division multiplexed (WDM) communication systems will

be discussed, together with essential components to realize these systems. Generally,

all communication systems are constructed from three basic building 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, design

alternations to the line are practically not feasible.

3.1 Transmitter

At the transmitter, the electrical to optical conversion of the signal is done by the use of

a distributed feedback laser (DFB) and a Mach-Zehnder modulator (MZM) . The DFB

in conjunction MZM is mainly used for long-haul transmissions as they together produce

an almost chirp free (frequency variation free) optical signal. For other applications, less

complex solutions are available, for instance, direct modulated lasers (DML) where the

electrical to optical transformation and light generation is 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 transmission

channel a pair of DFL and MZM is employed for the electrical to optical 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 for

demultiplexing.

Directly after the AWG a pre-dispersion compensation fiber is used for dispersion

map optimization, followed by an Erbium doped fiber amplifier (EDFA) for power regu-

lation. At this step the optical signal is coupled to the SSMF in the transmission line for

transmission.

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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 EDFA controls the

input power to the fiber. The transmission line consists of repeated seg-

ments of fiber, amplifier (EDFA), dispersion-correcting-fiber (DCF), and

power-regulator amplifier. The receiver consists of an arrayed waveguide

grating for demultiplexing, and post-dispersion-compensation fibers for

optimization of the residual dispersion for each optical channel, at the

last step, a photodiode is used for detecting the optical signal and down

conversion to electrical domain.

Fig. 3.1 illustrates a common graphical representation of a fiber optic transmissionsystem, from the transmitter through the transmission line to 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, next

to the SSMF is the first EDFA which regulates the input power to the DCF. After the DCF

follows the booster EDFA which amplifies the signal for the next span of fiber, this is

repeated until the destination is reached. The SSMF, power regulator EDFA, DCF, and

the 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 individual

WDM 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.

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3.4. FIBER LOSS COMPENSATION

After dispersion optimization the optical signal is detected through a photodiode and

down converted to electrical domain.

3.4 Fiber Loss Compensation

In chapter 2 some of the impairments associated with fiber optic transmission systems

were discusses, for instance, power and scattering loss, SPM, and XPM. These impair-

ments can be compensated for by repeaters and optical amplifiers (EDFAs). Repeaters

fully 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 optical power every 80 to 100 km.

Given the input power, the output power can be written as Pout=GPin, where G denotes

the the amplifier gain, this is known as power-gain configuration.

Another way of configuring the EDFAs is, constant-power output, which makes the

EDFA act as a power regulator, this configuration is used for the DCFs in the transmission

line, as the power must be held at low levels in order to avoid nonlinearities form the

DCFs. 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 ASE

directly affects the optical signal-to-noise ratio (OSNR) [2]. The OSNR is defined as

OSNR =Psignal

Pnoise, (3.1)

where Pnoise 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 result

in high ASE noise, thus in lower OSNR values. In order to keep the ASE noise at low

levels, high-power signals are to prefer. However, a high launch power into the fiber result

in an increased influence of nonlinearities. The launch power into the fiber is an important

parameter that needs to be optimized in order to achieve the best performance. Fig. 3.2

illustrates the relationship between launch power and the OSNR. There is an optimal

launch power where the nonlinearities are avoided and the ASE is held at low levels.

When designing a transmission link, the input power to the EDFAs must be optimized in

order 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

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Launch Power [dBm]

log10

(BER)

BER vs Launch Power

7 5 3 1 1 3 59

7

5

3

1

Figure 3.2: The OSNR as a function of the launch power. At high launch

powers, nonlinearities 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.

dispersion compensation must be in order to recover the data. Almost all transmission

links are realized using DCFs for dispersion compensation.

Fig. 3.1 illustrates a transmission system where DCF modules are placed in-line and

continuously compensate for the chromatic dispersion in each span. This is the common

way 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 DCFs

are slope matched as well, this refers to the dispersion slope parameter, S. The DCF is a

passive component and allows for dispersion compensation of several WDM channels at

the same time. Common fiber parameters for the DCF are D = 100 ps nm1 km1 and

S= 0.34 ps nm2 km1. 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 to

compensate for large amount of dispersion in a short distance. Typically, the accumulated

dispersion over an SSMF line of 100 km can be compensated for, in just a few kilometers

of DCF. The high nonlinear coefficient 3 W1 km1 of the DCF is a disadvantage

however, it is approximately three times higher than the value of the SSMF, hence, as

stated before, the optical launch power into the DCF must be held at low levels. Typical

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3.6. DISPERSION MAP


Dis

persion[psnm

1]

Dispersion Map

0 270 540 810 1080 13502200

1100

0

1100

2200

DCFSSMF

Inline Undercompensation

Pre Dispersion Compensation

PostComp

ORD

Figure 3.3: The accumulated dispersion over the transmission distance.

a) pre-dispersion compensation, b) accumulated dispersion along the

SSMF, c) dispersion compensation using an in-line DCF, d) in-line dis-

persion under-compensation, realized by not fully compensating for the

dispersion 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 for

the 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 that contribute to the accumulated

dispersion over the transmission link, they are, pre-dispersion compensation fiber, SSMF,in-line DCF, and post-dispersion compensation fiber. The dispersion contribution of these

elements is visualized in a dispersion map as illustrated in Fig. 3.3, this dispersion map is

considered 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 the SSMF is almost fully

compensated for by an in-line DCF leaving a fraction of the dispersion as, in-line un-

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Dis

persion[psnm

1]

Dispersion Map

n

1

ORD

0 270 540 810 1080 13502200

1100

0

1100

2200

Ch nPost

Comp

Ch 1PostComp

Figure 3.4: The dispersion map for different WDM channels. As WDM

channels are localized at different frequencies, the dispersion map will

be different for each WDM channel. The in-line dispersion compensation

can not compensate for the dispersion for all the WDM channels at the

same time. Different post-compensations must be applied for each WDMchannel.

der compensation. The dispersion from the SSMF and the partial compensation from

the DCF is repeated until the end of the transmission line, at the end a post-dispersion

compensation is applied. The post-dispersion compensation is applied at the same time

as the BER is assessed, when a minimal BER is reached the residual dispersion is called

optimum 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 is

mainly caused by the dispersion slope parameter S of the SSMF, this makes it hard for

the inline DCF to compensate the dispersion for all WDM channels at the same time, as

such, 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.

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3.7. SUMMARY

3.7 Summary

In this chapter all important blocks in a commercial transmission link were discussed. The

Transmitter consists of a distributed feedback lasers (DFB) together with a Mach-Zehnder

modulator (MZM) for each channel. The channels are multiplexed and demultiplexed

using an arrayed waveguide grating (AWG). At the receiver a photodiode is used for

detection.

The power loss needs to be compensated for in a transmission line. This is done by an

erbium doped fiber amplifier (EDFA). However, the gain of the EDFAs can not be set at

high values, as that would result in amplified spontaneous emission (ASE) and result in

reduced optical signal-to-noise ratio (OSNR). High launch powers 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 done

in just a few kilometers. The drawback of DCFs are the high nonlinearity factor, this is

why 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 each

channel to enable optimal residual dispersion (ORD) for each channel, leading to minimal

bit-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.

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4

DIGITAL 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 to

highlight 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 QAM

modulation format, as proposed in IEEE 802.11a-n.

4.1 Modulation

In analog communication, for instance AM-radio, the amplitude of a carrier is modulated

with a real and continuous signal, such as music. The carrier amplitude can take any

value between the maximum and the minimum of the modulating signal. During the

transmission, noise is added to the signal. There are several types of noise, the most

common and best modeled is the additive white Gaussian noise (AWGN). Separation of

the signal from noise is not an easy task and in many cases not even possible, since the

receiver can not distinguish between the signal and noise. The amount of tolerable noise

in the case of music transmission, is something the listener decides on.

In digital communication, the separation of signal from noise is a crucial step. In

order to distinguish between the logical states in the transmitted signal, there must be an

agreement 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, noise

tolerance, and complexity. A measure of performance in digital communication system

is the bit-error-rate (BER). The BER is calculated by taking the ratio between the number

of errors and total transmitted data at the receiver. Another measure of performance is the

spectral efficiency, measured in [Bits s1 Hz1]. The spectral efficiency, measures how

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CHAPTER 4. DIGITAL COMMUNICATION

Time in units of T0

Amplitude

OnOffKeying RZ

1

0

0 1 2 3 4 5 6 7 82

1

0

1

2

(a) Return to Zero (RZ)

Time in units of T0

Amplitude

OnOffKeying NRZ

1

0

0 1 2 3 4 5 6 7 82

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 transfered

within the given bandwidth. Usually, higher complexity at the transmitter/receiver leads

to higher spectral efficiency.

4.2 Baseband Signal Representation

The most common representation of a digital signal is the On-Off-Keying (OOK) scheme

as 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, this

correspond to the laser light being on or off in the fiber. Fig. 4.1a represents OOK

with 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 complexity at the transmitter/receiver

with high performance in terms of BER. OOK is highly resilient towards noise, this is

however at the cost of spectral efficiency. An OOK-RZ signal can mathematically be

represented as a sum of time delayed unit pulses g(t) with amplitudes A and 0. The math-

ematical expression for an OOK signal is,

Sb(t) =N1

n=0

m(n)g(t nT0) , (4.1)

where m(n) is the message signal/vector with the amplitude informations (A and 0) and

g(t nT0) is the time delayed unit pulses. In Fig. 4.1a the message vector is [10110101].

Here, the amplitude A was chosen to be 1V representing the logical state 1, this is

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4.3. PASSBAND SIGNAL REPRESENTATION

10 5 0 5 100.5

0

0.5

1.0

1.5

Time [ms]

Pulseamplitude

g(t), T0

= 10 ms

(a) The unit pulse in time domain

Frequency [Hz]

Normalizedamplitude

Pulse Spectrum

300 100 100 3000.4

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 have

zeros at multiples of 100 Hz.

however not a requirement, A can be given any value, another common value for the

amplitude A is 5V representing the logical state 1. The other logical state was mapped

to 0V, thus, the amplitude of the pulse goes to zero for one of the states, hence, the name

return-to-zero (RZ). By defining the amplitudes for the logical states, a convention is

chosen 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, as such investigation of its

properties in time and frequency domain is necessary. In Fig. 4.2 a unit pulse is illustrated

in both time and frequency domain. The pulse has a period of 0.01 s which correspond to

a frequency of 100 Hz. An OOK signal employing this pulse can yield a data rate of 100

bps, as each pulse carry one bit of data. The spectrum of the pulse show that the spectral

components of the pulse reach beyond 100 Hz, despite the fact that the pulse itself has a

frequency of 100 Hz; see Fig. 4.2b. In fact the spectral components of the pulse continue

all the way to infinity, the contribution of these frequencies are however very small as the

amplitude of these go to zero. Notable is also the fact that the spectrum of the pulse has

null points at multiples of f0 = 100 Hz, that is n 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 is

dedicated to the baseband signal, with a bandwidth of the same size of the baseband sig-

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CHAPTER 4. DIGITAL COMMUNICATION

Time in units of T0

Amplitude

OnOffKeying RZ

1

0

0 1 2 3 4 5 6 7 82

1

0

1

2

(a) OOK-RZ modulated

Time in units of T0

Amplitude

OnOffKeying NRZ

1

0

0 1 2 3 4 5 6 7 82

1

0

1

2

(b) OOK-NRZ modulated

Figure 4.3: Passband representation of OOK RZ and NRZ. The baseband

OOK signal modulated on top of a carrier.

nal. Consider an FM radio transmission for comparison, the baseband signal is an audio

source with a bandwidth of typically 20 kHz, and the passband signal is the same audio

source modulated on top of a carrier. The carrier frequencies for FM radio transmission

is between 88 to 108 MHz. For long-haul transmissions, the C-band is used at the center

frequency 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 the

phase shifts due to negative amplitudes in the NRZ case. Mathematically, passband mod-

ulation is performed by multiplying the baseband signal Sb(t) with a sin or cos function

at the desired frequency,

Sp(t) = Sb(t)cos(2fct) . (4.2)

At the receiver the envelope of the signal is detected as well as the phase of the carrier.

For the RZ transmission the phase information is excessive, only amplitude information

is 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 translated

to phase shifts of degrees between the bit slots (bit slot = one pulse duration). The

digital states are encoded in the phase of the carrier, see Fig. 4.3b. The amplitude value is

the excessive information for NRZ transmissions. NRZ signals are kind to amplifiers in

fiber optic transmission systems as there is no need of rapid amplitude changes, however

high phase accuracy is required.

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4.4. AMPLITUDE SHIFT KEYING ASK

Time in units of T0

Amplitude

4level AmplitudeShiftKeying 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 T0

Amplitude


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 and

passband representation.

4.4 Amplitude Shift Keying ASK

As seen in the previous section, both phase and amplitude of the carrier can be used

for digital encoding and transmission. In the NRZ, case the negative amplitudes of the

baseband signal was translated to phase shifts of degrees in the passband signal. Up

to 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 to

be coded in to the amplitudes of the pulses. A baseband and passband representation of

an ASK signal is illustrated in Fig. 4.4. Each pulse, have one of 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 an N 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 ( : | 0, ), as the sign of the amplitudes can

be expressed in phase notation, cos(0) and cos(), i.e. the carrier has been both amplitude

and phase modulated. The amplitude levels can be increased to any number, but the phase

is either 0 or , how is it possible to increase the number of phase states in the passband

representation? This is done by the introduction of orthogonal carriers, also known as

in-phase and quadrature carriers.

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4.7. SUMMARY

Time in units of T0

QuadratureQ

0 1 2 3 4 5 6 7 8

1.5

0.5

0.5

1.5

InphaseI


0 1 2 3 4 5 6 7 8

1.5

0.5

0.5

1.5

1.50.5 0.5 1.5

1.5

0.5

0.5

1.5

QuadratureQ

QAM constellation diagram

1.50.5 0.5 1.5

1.5

0.5

0.5

1.5

Inphase I

QuadratureQ

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 QAM

signal are shown. The QAM constellation diagram to the right, displays

the 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-phase I and one for the quadrature Q channel. The QAM symbol Z= I+ iQ

describes the complex modulation of the carrier as discussed in the previous section. In

Fig 4.5 the in-phase and quadrature channels are displayed, both channels have 4-level

ASK pulses. The constellation diagram in Fig 4.5 shows all the possible QAM symbols

that can be generated, here the constellation size is 16. The symbols generated by the I

and 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, such

as, on-off-keying (OOK), Amplitude Shift Keying (ASK), and the more general, the

quadrature-amplitude-modulation (QAM). In this work QAM modulation was chosen for

modulating the subcarriers of an orthogonal-frequency-division-multiplexing (OFDM)

transmission system.

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5

ORTHOGONAL FREQUENCY DIVISION

MULTIPLEXING

Orthogonal Frequency Division Multiplexing (OFDM) belongs to the group of modula-

tion formats that fall in the category of multitone or spread spectrum. Generally these

modulation 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 high

bandwidth signal, the signal is spread over the entire allowed spectrum at lower bit rates,

thus the name spread spectrum. The major difference between OFDM and other spread

spectrum modulation formats is, as the name OFDM indicate, orthogonality between the

carriers. In this chapter an introduction to OFDM will be given, furthermore a simplified

OFDM transmitter will be exemplified using MatLab.

5.1 Introduction to OFDM

The carriers in an OFDM based transmission are spaced in such way that they all are

mutually orthogonal with respect to the OFDM symbol time. This is done efficiently by

utilizing a digital signal processor (DSP) with a fast Fourier transform (FFT) cell, and its

inverse (IFFT). The IFFT cell of the DSP generates and modulates the subcarriers at the

same 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, high

spectral efficiency can be achieved for the OFDM signal in comparison to other spread

spectrum formats such as frequency division multiplexing (FDM). Fig. 5.1 displays the

occupied frequency space for an OFDM and FDM signal, respectively. The subcarriers of

a 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

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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 transmission

makes it possible to save bandwidth, in comparison to conventional FDM

transmissions, 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 rate streams,

these streams are converted to QAM symbols through the symbol map-

per. The QAM symbols will subsequently modulate the subcarriers of the

OFDM symbol. The modulation process of all subcarriers is done by the

IFFT block. The time data from the IFFT block is passed to the cyclic

prefix block for extension of time samples. Time samples are converted to

a serial stream and subsequently converted to the analog domain through

the digital to analog converter.

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

saved.

5.2 Block Representation of OFDM

The steps involved for an OFDM symbol generation are illustrated in Fig. 5.2. The first

block, the serial to parallel (S/P) converter, branches a high data rate stream into several

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5.3. OFDM PARAMETERS

low data rate streams. The number of data-subcarriers in the OFDM signal dictates the

number of output streams from the S/P converter. For each of the streams, the binary

data is selected block wise, and mapped to QAM symbols. This is done by the symbol

mapping block in Fig. 5.2. The QAM symbols modulate each of the data-subcarriers

of the OFDM symbol. The generation and modulation of all the subcarriers is done

simultaneously 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 symbol

in 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 adding

it to the end of the time series, thus increasing the time window. The parallel output from

the 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 digital

domain. At this stage the stream is converted to an analog signal for transmission, or

modulation 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 some

application, 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 for choosing 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 subcarriers for the OFDM symbol. all

of the subcarriers can be used for data transmission, but some are zero padded and some

are used as pilot tones. Zero padding is done to mitigate the influence of inter symbol

interference (ISI). The pre-allocated subcarriers for pilot tones are used for synchroniza-

tion purpose and phase estimation. The number of pilot tones and 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,

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CHAPTER 5. ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING

3 2 1 0 1 2 330

20

10

0

10

Normalized Frequency [, ]NormalizedPower[dB] OFDM Spectrum

(a) The Spectrum of an OFDM transmission

200 400 600 800 10001

0.5

0

0.5

1

Time sample [n]NormalizedAmplitude

OFDM signal

(b) The OFDM signal

Figure 5.3: The time and frequency domain representation of an OFDM

transmission with 16 out of 64 subcarriers zero padded and 8 cyclic pre-

fix samples. a) The spectrum of OFDM transmission, averaged for 32

OFDM 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 adaptive

QAM constellation selection, the QAM size is selected by analyzing the transmission

channel by the use of OFDM training symbols. For fiber optic applications, usually low

QAM 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 optic

applications, dispersion. The number of samples, usually is determined by using OFDM

training 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 domain

transmission of a single OFDM symbol. The MatLab code for generating the signal can

be found in appendix. The OFDM parameters used for generating the illustrated signal in

Fig. 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 of OFDM symbols = 32.

The zero padded subcarriers are the ones suppresses -20 dB relative to the data carriers.

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5.5. SUMMARY

The DC subcarrier is at the center of the spectrum. The DC carrier is used for further

modulation on top of a high frequency carrier. The major drawback of OFDM modulation

is its inherently high peak-to-average power ratio (PAPR); see Fig. 5.3b. The high PAPR

increases the demands on the amplifiers in an OFDM based transmission system. The

PAPR is a major problem in optical transmission system as the nonlinearities in an optical

link scale with the intensity of the electrical field in the fiber, thus, PAPR values must be

kept 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 generate

high PAPRs, selective subcarrier mapping for reduction of constructively addition of

harmonics, and clipping.

5.5 Summary

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

FFT size determines the number of available subcarriers for data 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 QAM symbol, hence the

total number of bits per OFDM symbol.

Cyclic prefix samples determines the amount of tolerable dispersion, or time delay

in an OFDM transmission.

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6

SIMULATIONS 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 presented followed by XPM induced

penalties for WDM transmissions, the performance difference between NRZ and OFDM

neighboring channels are presented in the last section. The results in this chapter were

presented 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, all

OFDM transmission experiments so far are realized without an inline optical dispersion

compensation. 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 usually

employ periodic inline dispersion compensation. By upgrading such link with a 40 Gbps

OFDM channel, the periodic dispersion map is inevitable for the OFDM signal. Further-

more, it has been recognized that co-propagating NRZ channels can result in significant

XPM penalties [11]. As such, the influence of the dispersion map on optical OFDM

transmissions were simulated in order to assess the nonlinear tolerance of OFDM as a

modulation format in optical transmission systems. By choosing appropriate parametersfor the DCFs in the transmission link, see Fig. 6.1, the dispersion maps of interest were

selected for the simulations. For non-dispersion managed transmission link simulation,

the DCFs and the pre-EDFAs were removed. Three dispersion maps were considered

for 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

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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 link

is mainly build up from spans of SSMFs and DCFs. The DCFs are used

for dispersion management. The input-power to the fibers are controlled

by the EDFAs. At the receiver the center channel is selected using an

ideal bandpass filter with a 50 GHz bandwidth. OSNR is controlled by

adding noise at the receiver.

effects of SPM and XPM were assessed, respectively. The influence of co-propagating

NRZ and OFDM channels were evaluated by WDM transmissions with OFDM at the

center frequency and co-propagating NRZ and OFDM neighboring channels. Fig. 6.2

shows all the simulated waveforms, b) The single OFDM channel waveform, d) WDM

transmission with co-propagating OFDM neighboring channels, and f) WDM transmis-

sion with co-propagating NRZ neighboring channels. At the receiver, the center channel

is selected using an ideal rectangular filter with 50 GHz bandwidth. The OSNR is con-

trolled by adding ASE at the receiver, in the simulations the OSNR was set to 8.6 dB

resulting in a BER of 104 with respect to back-to-back configuration. The transmitter

and receiver in Fig. 6.1 were simulated using MatLab and a fiber-optic network simulator.In real transmission systems, the input power to the DCFs are controlled and kept at

low levels relative to the SSMF in order to avoid nonlinearities from the DCFs. By man-

aging the input power to the DCFs, all the nonlinearities can be considered to originate

from the SSMF. In this work, the DCFs are modeled as linear, thus resulting in the same

conditions as in real transmission systems. The fiber parameters used in the simulations

are given in Table 6.1.

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6.2. OFDM PARAMETERS

Table 6.1: Fiber parameters used in the simulations.

Parameter Value Unit

Working frequency f = 193.1 [THz]

Working wavelength = 1550 [nm]

Attenuation = 0.2 [dB km1]

Dispersion D = 17 [ps nm1 km1]

Dispersion slope S = 0.057 [ps nm2 km1]

Nonlinearity = 1.365 [W1 km1]

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 reported

in [12]. The number of subcarriers for the OFDM transmissions were 256 with 88 zero

padded subcarriers, resulting in 168 data carrying subcarriers. For each simulation, 320

individual 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 of OFDM transmissions. The

dispersion maps and waveforms are listed below and can be viewed in Fig. 6.2. For each

dispersion map all the waveforms were simulated, resulting in 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 optical

OFDM experiments reported so far. No inline or pre dispersion compensation is

used, 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 dispersion compensating 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 in

commercial 10 Gbps transmission systems today [13]. This dispersion map consists

of -510 ps nm1 pre-dispersion-compensation and an inline under-compensation of

60 ps nm1.

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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 effect

of SPM is assessed for this waveform.

WDM transmission with co propagating OFDM neighboring channels A total

number of eleven OFDM channels are present in this waveform. As co propagating

OFDM channels are present in the waveform, the effects of XPM can be studied

with 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 channels

are NRZ except, the center OFDM channel. With this waveform the effects of XPM

can be studied with respect to NRZ neighboring channels.

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6.3. DISPERSION MAPS AND WAVEFORMS


Dispersion[psnm] No Inline DCF

0 243 486 729 972 12156800

0

6800

13600

20400

(a)

200 100 0 100 20040

20

0

20

40

Frequency [GHz]

Power[dBm]

Single OFDM Channel

(b)


Dispersion[psnm] Fully Periodic Compensation

0 270 540 810 1080 13501100

0

1100

2200

(c)

200 100 0 100 20040

20

0

20

40

Frequency [GHz]

Power[dBm]

WDM with OFDM Channels

(d)


Dispersion[psnm] 10G Optimum

0 270 540 810 1080 13501100

0

1100

2200

(e)

200 100 0 100 20040

20

0

20

40

Frequency [GHz]

Power[dBm]

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 accumulated dispersionalong 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 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.

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Launch Power [dBm]

log

10

(BER)

Single OFDM Channel Transmission

14 12 10 8 6 4 2 0

1

2

3

4

5

No inline DCF

10G OPT

Fully Periodic

Figure 6.3: The influence of SPM for all dispersion maps. At low input

powers the transmission system is in its linear regime, thus no penaliesare observed. At high input powers, > -10 dBm, the nonlinearities be-

come more apparent. The highest nonlinear tolerance is observed for the

dispersion map with no inline DCF, at BER limit of103 both the fully pe-

riodic and the 10G optimum dispersion map suffers from a launch power

penalty 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 of

SPM 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 and thus after the

transmission, for all the dispersion maps, no performance degradation can be observed.

At high input powers ( > -10 dBm), the highest nonlinear tolerance is observed for the

dispersion map without inline dispersion compensation. At the BER limit of 1x103 both

the fully periodic and the 10G optimum dispersion map exhibit a launch power penalty

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6.5. WDM TRANSMISSIONS AND XPM ASSESSMENT

Launch Power [dBm]

log

10

(BER)

Single OFDM channel and WDM OFDM

14 12 10 8 6 4 2 0

1

2

3

4

5

Single No inline DCF

Single 10G OPTSingle Fully Periodic

WDM No inline DCF

WDM 10G OPT

WDM Fully Periodic

Figure 6.4: The influence of XPM for all the dispersion maps. The XPM

penalty, for the dispersion map with no inline DCF was 1 dB with respectto the single channel transmission. The 10G optimum and fully periodic

dispersion 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 inline DCF.

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 dispersion

maps. The results are presented in Fig. 6.4, for the WDM and the single OFDM channel

transmission, respectively. As the only difference between the waveforms are the excess

WDM channels, it can be concluded that any changes in the BER evaluation is caused by

XPM. At the BER limit of 103, for the dispersion map with no inline DCF, the WDM

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Launch Power [dBm]

log

10

(BER)

WDM with NRZ and OFDM neighboring channels

14 12 10 8 6 4 2 0

1

2

3

4

5

NRZ No inline DCF

NRZ 10G OPTNRZ Fully Periodic

OFDM No inline DCF

OFDM 10G OPT

OFDM Fully Periodic

Figure 6.5: The influence of XPM for OFDM and NRZ neighboring

channels. 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 of

10 Gbps NRZ channels.

transmission suffers from a launch power penalty of 1dB caused by XPM, relative to the

single OFDM channel. As for the 10G optimum and the fully periodic dispersion map

the 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 to

co propagating NRZ or OFDM channels, launch power variations were performed as in

previous transmissions. WDM waveforms with NRZ and OFDM neighboring channels

were 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

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6.6. NRZ VS OFDM NEIGHBORING CHANNELS FOR WDM TRANSMISSIONS

transmissions with NRZ and OFDM neighboring channels, respectively. For the WDM

transmissions, with OFDM and 10 Gbps NRZ neighboring channel and for all the dis-

persion maps, no significant launch power penalties could be observed at the BER limit

1x103. It can thus be concluded that the influence of XPM resulting from 10 Gbps NRZ

neighboring channels does not reduce the nonlinear tolerance compared to the configura-

tion where the neighboring channels are OFDM modulated. Or in other words, the XPM

caused by OFDM neighboring channels is as strong as that of 10 Gbps NRZ channels.

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7

CONCLUSIONS AND DISCUSSION

In this work, the influence of SPM and XPM were analyzed on optical OFDM trans-

mission for different dispersion maps. It was observed that the nonlinear tolerance with

respect to both SPM and XPM is severely degraded when inline dispersion compensa-

tion is employed. For WDM transmissions, it was observed that the influence of XPM

resulting from 10 Gbps NRZ neighboring channels does not reduce the nonlinear toler-

ance compared to OFDM neighboring channels. The XPM caused by OFDM and NRZ

neighboring channels in a WDM transmission system are as strong.

A possible explanation for the reduction of the nonlinear tolerance in a periodically

compensated dispersion map is that the symbol rate of OFDM is significantly lower than

that of conventional modulation formats such as NRZ. As a result, the dispersion map

without inline dispersion compensation provides a better distribution of the nonlinear

phase shifts resulting from SPM and XPM over the waveform, which reduces the impact

of these nonlinear impairments.

These results indicate that the suitability for overlay of high data rate OFDM channels

on the existing 10 Gbps infrastructure is questionable.

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A

APPENDIX A: MATLAB CODE FOR OFDM

SIGNAL GENERATION

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%##########################################################################%# Thi s progr am i l l ust r at es a si mpl e OFDM t r ansmi t t er accor di ng t o the%# I EEE 802. 11a i mpl ement at i on. The I EEE 802. 11a i mpl ement s 4 pi l ot%# t ones f or synchr oni zat i on. I n t hi s ver si on of t he t r ansmi t t er no pi l ot%# t ones wer e used.%#

%# Aut hor : Kamyar For ozesh%# Dat e: 2009- 12- 10%# Emai l : kamyar . f orozesh@gmai l . com%#%##########################################################################

cl ear al l ; cl ose al l ; cl c;

% OFDM par ametersOFDM_Symbol s = 32; QAM_Const el l at i on = 16; FFT_Wi ndow = 64; Zer o_Paddi ng = 16;

Cycl i c_Pr ef i x = 8;

% Def i ni ng subcar r i er s wi t h zer o paddi ngZero_Subcar r i ers = [ - FFT_Wi ndow/ 2: 1: ( ( - FFT_Wi ndow+Zero_Paddi ng) / 2- 1) 0( ( FFT_Wi ndow- Zero_Paddi ng) / 2+1) : 1: FFT_Wi ndow/ 2- 1] + FFT_Wi ndow/ 2+1 ; % Def i ni ng dat a car r yi ng subcar r i er sData_Subcar r i ers = [ - ( FFT_Wi ndow- Zer o_Paddi ng) / 2: 1: - 1 1: 1: ( FFT_Wi ndow-Zero_Paddi ng) / 2] + FFT_Wi ndow/ 2+1; % Def i ni ng pi l ot subcar r i er sPi l ot _Subcar r i er s = [ ] ;

% Vector I ni t i al i zat i onOFDM_Symbol _Fr eq = zer os( 1, FFT_Wi ndow) ; OFDM_Symbol _Ti me = [ ] ; OFDM_Sequence = [ ] ;

f or i =1: OFDM_Symbol s% Dat a gener at i on, QAM modul at i on, QAM nor mal i zat i onTx_Dat a_Bi n = r andi nt ( l og2( QAM_Const el l at i on) , FFT_Wi ndow- Zer o_Paddi ng) ; Tx_Dat a_QAM =

modul at e( modem. qammod( ' M' , QAM_Const el l at i on, ' I nput Type' , ' bi t ' ) , Tx_Dat a_Bi n);

Tx_Dat a_QAM = Tx_Dat a_QAM. / abs( max( Tx_Dat a_QAM) ) ;

% Subcar r i er assi gnment , Zer o paddi ng

OFDM_Symbol _Fr eq(Dat a_Subcar r i er s) = Tx_Dat a_QAM; OFDM_Symbol _Fr eq( Zero_Subcar r i ers) = 0;

% I FFT oper at i on, Cycl i c pr ef i x i nser t i onOFDM_Symbol _Ti me = i f f t ( OFDM_Symbol _Fr eq, FFT_Wi ndow) ; OFDM_Symbol _Ti me_CP = [ OFDM_Symbol _Ti me( ( end- Cycl i c_Pr ef i x) : end)

OFDM_Symbol _Ti me] ;

% Stacki ng OFDM symbol s t o a t i me sequenceOFDM_Sequence = [ OFDM_Sequence OFDM_Symbol _Ti me_CP] ;

end

% Di spl ayi ng OFDM spect r um

C1 = [ 142 026 026] / 256; C2 = [ 026 026 142] / 256;


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f i g1 = f i gur e( ' Name' , ' None' , . . .

' Number Ti t l e' , ' of f ' , . . . ' I nver t Har dcopy' , ' of f ' , . . . ' Col or ' , [ 1 1 1] , . . . ' Pos i t i on' , [ 1250 400 640 400] , . . .

' PaperPosi t i onMode' , ' aut o' ) ;

f i g2 = f i gur e( ' Name' , ' None' , . . . ' Number Ti t l e' , ' of f ' , . . . ' I nver t Har dcopy' , ' of f ' , . . . ' Col or ' , [ 1 1 1] , . . . ' Pos i t i on' , [ 610 400 640 400] , . . . ' PaperPosi t i onMode' , ' aut o' ) ;

ax1 = axes( ' Pos i t i on' , [ 0. 15 0. 2 0. 75 0. 7] , . . . ' Pl ot BoxAspect Rat i o' , [ 2 1 1] , . . . ' Box' , ' on' , . . . ' Xgri d' , ' on' , . . . ' Ygr i d' , ' on' , . . . ' Vi si bl e' , ' on' , . . . ' Gr i dLi neSt yl e' , ' : ' , . . . ' XLi m' , [ - 3 3] , . . . ' YLi m' , [ - 30 10] , . . . ' YTi ck' , [ - 30 - 20 - 10 0 10] , . . . ' YTi ckLabel ' , [ {' - 30' , ' - 20' , ' - 10' , ' 0' , ' 10' }] , . . . ' f ont s i ze' , 22, . . . ' l i newi dt h' , 3, . . . ' l ayer ' , ' bot t om' , . . . ' par ent ' , f i g1) ;

ax2 = axes( ' Pos i t i on' , [ 0. 15 0. 2 0. 75 0. 7] , . . . ' Pl ot BoxAspect Rat i o' , [ 2 1 1] , . . . ' Box' , ' on' , . . . ' Xgri d' , ' on' , . . . ' Ygr i d' , ' on' , . . . ' Vi si bl e' , ' on' , . . . ' Gr i dLi neSt yl e' , ' : ' , . . . ' XLi m' , [ 1 1000] , . . . ' YLi m' , [ - 1 1] , . . . ' YTi ck' , [ - 1 - . 5 0 . 5 1] , . . . ' YTi ckLabel ' , [ {' - 1' , ' - 0. 5' , ' 0' , ' 0. 5' , ' 1' }] , . . . ' f ont s i ze' , 22, . . . ' l i newi dt h' , 3, . . . ' l ayer ' , ' bot t om' , . . . ' par ent ' , f i g2) ;

hol d ( ax1, ' on' ) ; hol d ( ax2, ' on' ) ;

xl abel ( ax1, ' Nor mal i zed Fr equency [ - \ pi , \ pi ] ' ) ; yl abel ( ax1, ' Normal i zed Power [ dB] ' ) ;t i t l e ( ax1, ' OFDM Spect r um' ) ;

xl abel ( ax2, ' Ti me sampl e [ n] ' ) ; yl abel ( ax2, ' Normal i zed Ampl i t ude' ) ;t i t l e ( ax2, ' OFDM si gnal ' ) ;

[ Pxx, f ] = pwel ch(OFDM_Sequence, [ ] , [ ] , 2 10) ; Mag_Spec = 10*l og10( Pxx) - max(10*l og10(Pxx) ) ;


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pl ot ( ( f - pi ) , Mag_Spec, ' Col or ' , C1, ' l i newi dt h' , 2, ' par ent ' , ax1) ;

% Resampl i ng t i me domai n data and pl ot t i ngOFDM_Symbol _Ti me_pl ot =r eal ( i f f t ( OFDM_Symbol _Fr eq, 2 10) ) / max( abs( i f f t ( OFDM_Symbol _Fr eq, 2 10) ) ) ; Ti me_sampl es = 1: 1: 2 10;

pl ot ( Ti me_sampl es, OFDM_Symbol _Ti me_pl ot , ' Col or ' , C2, ' l i newi dt h' , 2, ' par ent ' , ax2) ;

% I nf or mat i on di spl aydi sp( [ ' Number of OFDM symbol s ' , num2st r ( OFDM_Symbol s) ] ) ; di sp( [ ' Number of subcar r i er s ' , num2st r ( FFT_Wi ndow) ] ) ; di sp( [ ' Number of dat a subcar r i er s ' , num2st r ( FFT_Wi ndow-Zer o_Paddi ng) ] ) ; di sp( [ ' Number of zero padded subcarr i ers ' , num2st r ( Zero_Paddi ng) ] ) ; di sp( [ ' Number of cycl i c pr ef i x sampl es ' , num2str ( Cycl i c_Pr ef i x) ] ) ; di sp( [ ' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ' ] ) ; di sp( [ ' QAM constel l at i on si ze ' , num2st r ( QAM_Const el l at i on) ] ) di sp( [ ' OFDM symbol durat i on ' , num2st r ( ( 4*10 - 6) ) ] )

di sp( [ ' Bi t s per OFDM symbol' , num2st r ( l og2( QAM_Const el l at i on) *( FFT_Wi ndow- Zero_Paddi ng) ) ] ) ; di sp( [ ' Tr ansmi ssi on r at e ( bps)' , num2st r ( l og2( QAM_Const el l at i on) *( FFT_Wi ndow- Zero_Paddi ng)*( 1/ ( 4*10 -6) ) ) ] ) ;

%pr i nt - f 1 - depsc2 - t i f f - r 300 OFDM_Spect r um%pri nt - f 2 - depsc2 - t i f f - r 300 OFDM_Symbol


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B

APPENDIX B: PUBLISHED ARTICLE AT

IEEE/LEOS SUMMER TOPICALS

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ABBREVIATIONS

ASE Amplified Spontaneous Emission

ASK Amplitude Shift Keying

AWG Arrayed Waveguide Grating

AWGN Additive White Gaussian NoiseBER Bit-Error Rate

DCF Dispersion Correcting Fiber

DFB Distributed Feedback Laser

DML Direct Modulated Laser

DSP Digital Signal Processor

EDFA Erbium Doped Fiber Amplifier

FFT Fast Fourier Transform

ISI Inter-Symbol Interference

ITU-T International Telecommunication Union

MZM Mach Zehender Modulator

NLSE Nonlinear Schrdinger Equation

OFDM Orthogonal Frequency Division Multiplexing

OOK On-Off-Keying

ORD Optimal Residual Dispersion

OSNR Optical Signal-to-Noise Ratio

PAPR Peak-to-Average Power Ratio

QAM Quadrature Amplitude Modulation

RZ Return-to-Zero

SBS Stimulated Brillouin Scattering

SPM Self Phase Modulation

SRS Stimulated Raman Scattering

SSMF Standard Single-Mode Fiber

WDM Wavelength Division Multiplexing

XPM Cross Phase Modulation

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LIST O

Documents

The influence of the dispersion map on optical OFDM transmissions