The influence of the dispersionmap on optical OFDM transmissions

UPTEC F10 001

Examensarbete 20 p Februari 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 OFDM transmissions

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.

DIPLOMATHESIS

THE INFLUENCE OF THE

DISPERSION MAP ON OPTICAL OFDM

TRANSMISSIONS

K

F

and

Department of Astronomy and Space Physics, Uppsala University, Sweden

APRIL10, 2009

A BSTRACT

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.

To my father

C ONTENTS

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 3

2.1 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 13

3.5 Dispersion Compensation 13

3.6 Dispersion map 15

3.7 Summary 17

4 Digital Communication 19

4.1 Modulation 19

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 29

5.4 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

A CKNOWLEDGMENTS

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.

P REFACE

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 introduces digital 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.

1

I NTRODUCTION

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 Kao’s 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 it’s 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, most commonly 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 single fiber 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

Figure 1.1: Illustration of a standard single-mode fiber. a) The fiber core with a refractive index n ≈ 1.48 and a cross-section of ≈ 9 µm. 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 made from 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 9µm 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.

2

F IBER O PTIC I MPAIRMENTS

Transmission impairments in the SSMF can be divided into two categories, linear and nonlinear. 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 impairments and are generally very hard to compensate for. In this chapter common impairments in modern 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 the molecules (S iO₄) of the fiber. The two dominant loss mechanisms that leads to power loss, also called fiber loss, are intrinsic absorption and Rayleigh scattering [4]. If the launch power into the fiber is P_in [W] then the optical power P(z) at distance z [km]

exhibits an exponentially decay [2] and can be written as

P(z) = Pine^−αz, (2.1)

where α is given in Neper per kilometer [Np km⁻¹]. Neper is a dimensionless, non SI unit of measure for natural logarithm ratios. A more common way of describing the attenuation coefficient α, is in α_dBwhich is defined by

α_dB= 10

ln(10)α ≈ 4.343α . (2.2)

Fig. 2.1 shows the attenuation coefficient αdBfor the SSMF as a function of the frequency.

The absorption peak near 1400 nm area is caused by OH⁻impurities as a result of the manufacturing process of the fiber [3]. The standardization organization 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

Figure 2.1: The attenuation coefficient α_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 α_dB= 0.20 dB km⁻¹[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(ω). The phase velocity, vph, of a transmitted signal in the fiber is related to n(ω) as

v_ph= c

n(ω), (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.

2.2. DISPERSION

By Taylor expanding the mode propagation constant β [2, 3] which is related to the refractive index n according to

β(ω) = ω

v_p= n(ω)ω

c , (2.4)

material specific dispersion parameters can be derived. Taylor expansion of Eq. (2.4) at the working frequency ω₀gives a linearized relationship between the mode propagation constant β and the angular frequency ω

β(ω) ≈ β0+ β1(ω − ω₀) +1

2β₂(ω − ω₀)²+1

6β₃(ω − ω₀)³+ O(ω⁴) , (2.5a) β_n= dⁿβ

dωⁿ_ω=ω0 , (2.5b)

where β₀and β₁= 1/vgcorrespond to a constant phase shift and the group velocity, re- spectively. β₂ represents group velocity dispersion and β₃dispersion slope. The more common way to express β₂and β₃in fiber-optics is through fiber specific parameters D and S [2] according to

D = −2πc

λ² β₂, (2.6a)

S =4πc

λ³ β₂+ 2πc λ²

2

β₃. (2.6b)

D is expressed in [ps nm⁻¹km⁻¹] and describes the amount of dispersion per kilometers and S is expressed in [ps nm⁻²km⁻¹], 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 nm⁻¹km⁻¹and the dispersion slope S around 0.06 ps nm⁻²km⁻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 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.

0 1024 2048 3072 4096 0

1 2 3 4 5

Dispersion = 0 ps nm⁻¹ (0 km)

Signal Power [mW]

0 1024 2048 3072 4096

0 1 2 3 4 5

Dispersion = 80 ps nm⁻¹ (5 km)

Time [ps]

Signal Power [mW]

0 1024 2048 3072 4096

0 1 2 3 4 5

Dispersion = 160 ps nm⁻¹ (10 km)

0 1024 2048 3072 4096

0 1 2 3 4 5

Dispersion = 480 ps nm⁻¹ (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(ω, |A|²) = n0(ω) + n2

|A|²

A_{e f f} , (2.7)

where n₀ is the linear refractive index as discussed in the previous section, n₂ is the nonlinear refractive index and A_{e 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

2.4. SELF PHASE MODULATION SPM

Schr¨odinger equation (NLSE) [6]

∂A

∂z = −α 2A − j

2β₂∂²A

∂T²+1 6β₃∂³A

∂T³+ jγ |A|²A , (2.8a) γ = n₂ω₀

cA_{e f f} , (2.8b)

T = t − β1z = t − z

v_g , (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 expressed in [W⁻¹km⁻¹] 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

L_{e f f} =1 − e^−αL

α . (2.9)

Fig. 2.3 shows the signal power as a function of transmission distance of SSMF. In the figure, the effective length L_{e f f} and the high-power region is illustrated. For an SSMF of length 100 km, with an attenuation coefficient α = 0.2 dB km⁻¹, the effective length L_{e 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 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.

Transmission Distance [km]

Signal Power [mW]

Power loss

Leff = 21.5 km

High−Power Region

0 20 40 60 80 100

0 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 α = 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

2.7. SUMMARY

Time in multiples of τ Self Phase Modulation (SPM)

a) gaussian pulse

b) Frequency shift Intensiy∆ f − ω 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).

3

T HE T RANSMISSION L INK

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 filters and 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.

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 transmission system, 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.

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-level modulation 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 P_out= 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

OS NR =P_signal

P_noise , (3.1)

where P_noiseis 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 EDFA’s 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

Launch Power [dBm]

log 10(BER)

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 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 DCF’s 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 DCF’s 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 nm⁻¹km⁻¹and S = −0.34 ps nm⁻²km⁻¹. As indicated, the absolute value of the dispersion constant D is much 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 γ ≈ 3 W⁻¹km⁻¹of 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

3.6. DISPERSION MAP

Transmission Distance [km]

Dispersion [ps nm−1 ]

Dispersion Map

0 270 540 810 1080 1350

−2200

−1100 0 1100 2200

DCF SSMF

In−line Undercompensation Pre Dispersion Compensation

Post Comp

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-

Transmission Distance [km]

Dispersion [ps nm−1 ]

Dispersion Map

λ

λ

ORD

0 270 540 810 1080 1350

−2200

−1100 0 1100 2200

Ch n Post Comp

Ch 1 Post Comp

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 WDM channel.

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.

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 EDFA’s 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 leads to 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.

4

D IGITAL C OMMUNICATION

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 the type 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 s⁻¹Hz⁻¹]. The spectral efficiency, measures how

Time in units of T0

Amplitude

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

Amplitude

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 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,

S_b(t) =

N−1

∑

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

4.3. PASSBAND SIGNAL REPRESENTATION

−10 −5 0 5 10

−0.5 0 0.5 1.0 1.5

Time [ms]

Pulse amplitude

g(t), T

0 = 10 ms

(a) The unit pulse in time domain

Frequency [Hz]

Normalized amplitude

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 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 pulse g(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-

Time in units of T0

Amplitude

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

Amplitude

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 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 S_b(t) with a sin or cos function at the desired frequency,

S_p(t) = Sb(t)cos(2π f_ct) . (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 phase of carrier is very important as the digital states of the baseband signal are now translated to phase shifts of π 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.

4.4. AMPLITUDE SHIFT KEYING ASK

Time in units of T0

Amplitude

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 T0

Amplitude

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 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 π 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 (φ : | 0, π), as the sign of the amplitudes can be expressed in phase notation, cos(0) and cos(π), 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 π, 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.

4.5 Orthogonal Carriers

The trigonometric functions sin(2π f_ct) and cos(2π f_ct) are orthogonal functions when in- tegrated over a whole period T₀,

Z _T0 0

sin(2π fct)cos(2π fct)dt = 0 . (4.3)

This property of the trigonometric functions makes it possible to have two carriers at the same frequency, called in-phase and quadrature carrier. The name quadrature comes from the fact that trigonometric functions sin and cos can be expressed in terms of each other, for instance cos(t) = sin(t + π/2). The phase shift of π/2 radians correspond to a quarter of a full revolution in the phase plane, hence the name quadrature. Let us now consider two ASK baseband signals and name them I and Q; see Fig. 4.4a. After passband modulation of the signals with cos(2π f_ct) and sin(2π f_ct) we multiply the Q channel with −1 and add the channels together. This yields the baseband signal,

S_p= Icos(2π fct) − Qsin(2π f_ct) = (4.4)

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

= ReZe^{i2π fct}

(4.6) which is the complex notation of the passband signal. The complex carrier is defined as e^{i2π fct}and Z = I + iQ is the modulating symbol, as it both changes the amplitude and the phase of the carrier as,

A =p

(I²+ Q²) , (4.7)

φ = tan⁻¹Q

I . (4.8)

At the receiver the passband signal is multiplied by the local oscillators cos(2π f_ct) and sin(2π f_ct) and filtered in order to recover the baseband signals I and Q.

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

=1 2I +1

2Icos(4π f_ct) +1

2Qsin(4π f_ct) (4.10)

After low pass filtering, the high frequency terms sin(4π f_ct) and cos(4π f_ct) will vanish and the I and Q channels are recovered, depending on the local oscillator used.

4.6 QAM modulation

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

4.7. SUMMARY

Time in units of T0

Quadrature Q

0 1 2 3 4 5 6 7 8

−1.5

−0.5 0.5 1.5

In−phase 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

Quadrature Q

QAM constellation diagram

−1.5−0.5 0.5 1.5

−1.5

−0.5 0.5 1.5

In−phase I

Quadrature Q

Transmitted QAM symbols

1000 1 1111

2 0111

3 0010

4

0000 5

0100 6

1110 7

1001 8

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.

5

O RTHOGONAL F REQUENCY D IVISION

M ULTIPLEXING

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. Since all 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

(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

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 a serial 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 those which 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 also adjustable 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,

−3 −2 −1 0 1 2 3

−30

−20

−10 0 10

Normalized Frequency [−π, π]

Normalized Power [dB]

OFDM Spectrum

(a) The Spectrum of an OFDM transmission

200 400 600 800 1000

−1

−0.5 0 0.5 1

Time sample [n]

Normalized Amplitude

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.

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 PAPR’s, 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.

6

S IMULATIONS A ND R ESULTS

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 parameters for the DCF’s 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 DCF’s and the pre-EDFA’s 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