Nonlinearities and their Distortion Effects in COherent-OFDM

Systems

Gábor Fekete and Tibor Berceli

Department of Broadband Infocommunications and Electromagnetic Theory, Budapest University of Technology

and Economics, Egry József utca 18, Budapest, 1111 Hungary

Keywords: Coherent Optical System, OFDM, Mach-Zehnder Modulator, Dispersion, Fiber Nonlinearity, CO-OFDM,

Heterodyne Detection, 16-QAM.

Abstract: Nonlinear Mach-Zehnder Modulator and single mode fiber distort the transmitted signal. Their distortions

were examined with VPIphotonics and the results of the two cases were compared with each other. It is

important to know which element has higher effect to signal. Orthogonal Frequency Division Multiplexing

modulation was used because next generation optical network will use this modulation form.

1 INTRODUCTION

Orthogonal Frequency Division Multiplexing

(OFDM) is extensively used in electrical domain.

Wi-Fi routers, terrestrial TV broadcast (in Europe)

and so many other applications use OFDM

modulation because the distortion of the channel (i.e.

fading) can be easily compensated by DSP (Digital

Signal Processing). The drawbacks of OFDM are the

sensitivity for nonlinearity in the signal transmission

and the high PAPR (Peak to Average Power Ratio).

The optical systems require a higher-order

modulation format with high capacity because of the

amount of transmitted data is growing rapidly.

OFDM modulation can solve the problem as it did in

the electrical domain. However, the structure of the

optical systems, which use OFDM modulation, are

more complex, because the phase cannot be detected

directly with a photodiode.

In this paper we give a short overview of the

OFDM method in section 2. The coherent optical

OFDM (CO-OFDM) transmission system is

presented in section 3, which is simulated by the

VPI TransmissionMaker (VPI). Our study focuses

on the distortion of the nonlinear Mach-Zehnder

Modulator (MZM) and the signal degradation which

is caused by nonlinearities of Single Mode Fiber

(SMF). We investigate whether their distortion

effect is the same and which has stronger influence

on the transmitted signal.

Figure 1: Theoretical implementation of OFDM

modulation. (Shieh, 2011).

2 PRINCIPLE OF OFDM

OFDM is a special class of multi carrier modulation.

Figure 1 shows its theoretical implementation. This

structure contains a lot of oscillators and filters on

both transmitter and receiver sides. The transmitted

signal is represented as (Shieh, 2011):

  



skk

skki

Ttiftfjts

iTtscts











0)2exp(



(1)

is the number of the subcarriers, c

is the i

information symbol at the k

subcarrier, s

is the

waveform of the k

subcarrier, T

is the symbol

period, f

is the frequency of the subcarrier. The

optimum detector can be a matched filter or a

correlator. The detected information of a subcarrier

is given by (Shieh, 2011):

Fekete G. and Berceli T..

Nonlinearities and their Distortion Effects in COherent-OFDM Systems.

DOI: 10.5220/0004669900470050

In Proceedings of 2nd International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS-2014), pages 47-50

ISBN: 978-989-758-008-6

 2014 SCITEPRESS (Science and Technology Publications, Lda.)



dttfjiTtr

dtsiTtrc

kski









)2exp(



(2)

The subcarriers are orthogonal to each other. Its

result is that the spectrum of the OFDM signal is

smaller than a traditional multicarrier multiplexed

signal because the channels can be overlapped. The

channels are orthogonal to each other if:

,...3,2,1;

 m

mff

(3)

OFDM modulation/demodulation can be done by

Inverse Discrete Fourier Transform (IDFT)/ Discrete

Fourier Transform (DFT), which costs less than

using huge number of filters and oscillators (Figure

1). A typical OFDM transmitter can be seen in

Figure 2. Data stream is split up N

part by a serial-

to-parallel converter, and the next block creates the

transmitted symbols of the subcarrier from the bit

sequence. OFDM modulation is made by the IDFT

block. If the subcarriers are not orthogonal to each

other (i.e. there is synchronization failure), ISI (Inter

Symbol Interference) and ICI (Inter Carrier

Interference) will appear in the demodulated signal.

This can be avoided if Guard Interval (GI) is

applied. It is also called as Cyclic Prefix (CP). A

small time period from the end of symbol is copied

down. This is the CP and it is placed at the

beginning of the symbol. Until the time difference

between the subcarriers is smaller than the GI there

will not be ISI and ICI in the demodulated signal.

After GI is added to the signal, its digital samples

are converted into an analogue signal. The optical

carrier is modulated by it. The structure of an

OFDM demodulator is similar to Figure 2 but the

signal flow is reversed so there is a DFT block

instead of the IDFT and it is extended with a clock

restore or synchronization block.

Figure 2: Baseband OFDM transmitter. OFDM

modulation is created by IDFT. (Shieh, 2011).

Transmitters and receivers need to have huge

dynamic range if the PAPR is high. It is not possible

to create a device which has large and linear

Figure 3: Block scheme of the simulated CO-OFDM

system in VPI.

dynamic range. Therefore the value of PAPR must

be decreased by coding technique or clipping. The

clipping method is usually used, which cuts off the

level of the signal above a given value. However,

this increases the noise level outside of the signal

spectrum.

3 SIMULATION

Simulations were made in VPIphotonics (VPI).

Block diagram of our transmission is shown in

Figure 3. Pseudo random bit sequence with 80Gbps

data rate was used in the simulations. OFDM coder

used 16-QAM modulation and created separately the

real (I) and imaginary (Q) parts of the OFDM signal.

There is no 90° phase shift between I and Q. The

laser signal is modulated separately by I and Q

signals. Mach-Zehnder Modulators (MZM) are

applied which have sinusoidal transfer characteristic.

They are biased at the quadrature point, where the

transfer characteristic is linear. I and Q arms are

summarized by an optical coupler. Its behaviour is

similar to an electrical one. The input signal

intensity from both input ports is halved at the

output and it creates 90° phase shift between the

input ports signals. It means that the necessary 90°

phase shift is done by the coupler. So the optical I-Q

modulator is built up by two MZMs and an optical

coupler. After the coupler a standard Single Mode

Fiber (SMF) is placed, when its distortion is

examined. In the other cases it is left out from the

network. Signal detection is based on the heterodyne

detection method. There is a small frequency

difference (Δf) between the laser on the transmitter

side and the laser on the receiver side. It causes that

the detected signal (at the output of photo diodes) is

converted down at Δf frequency. This signal is

demodulated by the OFDM decoder. The analyzer

shows the constellation diagram of the detected

signal. In this article we focus on the nonlinearity of

MZM and SMF. The linewidth of the applied lasers

PHOTOPTICS2014-InternationalConferenceonPhotonics,OpticsandLaserTechnology

were 10 kHz. It means that the simulation contains

the effect of the phase noise.

Figure 4: (a) Constellation turns right, if the bias error is

positive and it turns left (b) when the bias changes

negatively.

Figure 5: Asymmetrically biased MZMs. (a) Both MZMs

are biased at the same arm. (b) MZMs are biased at

different arms and the phase change has opposite sign.

Figure 6: (a) Larger drive amplitude increases the distance

between symbols but (b) outside of the OFDM spectrum

the noise level also increases.

3.1 Distortion of Mach-Zehnder

Modulator

Two arms of the MZMs can be driven independently

from each other in VPI. The relation between arms

can be positive or negative. If it is positive then the

sign of phase change is the same in both arms. In the

other case the sign of the phase change is opposite.

Figure 4 shows those cases when MZMs upper arm

are driven. MZMs are biased with 0.5V, which

causes 90° phase shift (optimum point) in the

controlled arm. Both MZM bias points are similarly

changed. If the phase delay is less than 90°, the

constellation is turned clockwise (Figure 4b). It is

rotated the opposite way (Figure 4a), when the phase

shift is more than 90°. This rotation can be

compensated by DSP after detection. Another way

to eliminate this rotation is the differential driving of

MZMs. In this case only the distance between

constellation points will decrease when the bias

changes (Figure 5a). However, the standard

deviation of constellation points is growing linearly

(Table 1).

There is another MZM driving method when one

MZM is driven in the upper arm and the other is

driven in the lower arm with negative sign of phase

changes. It does not cause any difference in the

output light intensity but the electrical field is

different. Between the electrical fields there is a 90°

phase difference. The optical coupler which

summarizes the I and Q signals (Figure 3) also

makes 90° phase shift between them. Its result is that

if MZMs are biased at the optimum point, there will

be no carrier in the transmitted spectrum. In this case

we need an outside clock signal to demodulate the

received signal which highly complicates the

receiver. It can be avoided, if MZMs are not driven

in the optimum point. Slightly shifted from the

optimum the carrier will appear in the spectrum but

the symbols will be closer to each other as Figure 4

shows it. Figure 5b shows the received constellation

when MZMs are driven asymmetrically (same bias

point but the sign of the bias change is the opposite).

This driving method minimizes the rotation of the

constellation. The standard deviation of symbols

does not increase outside from the optimum point of

operation.

Larger drive amplitude increases the distance

between the symbols of the constellation (Figure 6a)

but it does not grow linearly. It has saturation

because of the MZM sinusoidal characteristic. Large

drive amplitude causes bigger standard deviation of

the symbols, too. 0.05V and 0.1V drive amplitude

are near to the saturation point because the distance

between the symbols changed minimally but the

standard deviation of the symbols is twice as big.

Between the two constellations there is a 3.8° angle.

The noise level also increases outside of the signal

spectrum (Figure 6b). It comes from the clipping and

nonlinearities. This growing noise is harmful in

WDM systems, because the channels have to be

placed far from each other.

3.2 Fiber Nonlinearity

Signal shape mainly degrades by the fiber

dispersion. Chromatic dispersion (CD) is the

significant effect in SMF. It rotates the constellation

and spreads the symbols (Figure 7a). Constellation

of the received signal will be a circle because of the

dispersion (Figure 7b). CD has much stronger effect

on the transmitted signal than the MZM. 6km fiber

-2 -1 0 1 2

-1.5

-1

-0.5

0.5

1.5

Real

Imaginary

optimum

+0.01V

+0.05V

-2 -1 0 1 2

-1.5

-1

-0.5

0.5

1.5

Real

Imaginary

optimum

-0.01V

-0.05V

-2 -1 0 1 2

-1.5

-1

-0.5

0.5

1.5

Real

Imaginary

optimum

0.01V

0.05V

-3 -2 -1 0 1 2 3

-3

-2

-1

Real

Imaginary

0.01V

0.02V

0.05V

-5 0 5

-5

Real

Imaginary

0.01V

0.05V

0.1V

a) b)

NonlinearitiesandtheirDistortionEffectsinCOherent-OFDMSystems

rotates the constellation with angle of 8°. It is twice

larger than the rotation caused by differential driving

of the MZM.

Table 1: Rotation of the constellation.

MZM’s driving

method

Bias [V]

Angle

[deg]

Deviation

at the same

optimum 0 0.024

+0.01 25 0.024

+0.05 -26 0.024

-0.01 -25 0.023

-0.05 26 0.024

differential

0.01 0.2 0.028

0.05 1 0.048

differential, phase

change in the

MZM’s arm is

opposite

0.01 0 0.037

0.02 0.9 0.029

0.05 3.6 0.025

Figure 7: (a) Dispersion spreads the symbols and rotates

the constellation. (b) Constellation diagram after 50km

fiber, if dispersion is not compensated.

Figure 8: (a) Symbol deviation caused by SPM and FWM.

(b). Only FWM caused symbol spread at one symbol.

Dispersion can be compensated by DSP or

Dispersion Compensation Fiber (DCF). Doing it by

DSP is much comfortable because it can be done

electronically beside doing other signal processing

steps. Using of pilot tones this rotation can be

calculated and the correction also can be done. Four

wave mixing (FWM) and self-phase modulation

(SPM) make smaller signal degradation than CD.

Their effect can be seen if the fiber dispersion is set

to zero. Laser power was 20W and fiber length was

50km. Increasing the laser power will not improve

the quality of transmission. Noise level increases

outside of the OFDM spectrum because of FWM.

Constellation symbols highly spread and it seems

they contain the full constellation diagram in small

size (Figure 8a). This kind of modulation mainly

comes from the SPM and in smaller extent from the

FWM. Decreasing the laser power the SPM effect

will be negligible and FWM will be dominant. FWM

causes ICI and it spreads the symbols along both

axes (Figure 8b). It is similar to the effect of white

noise. Standard deviation is 0.0472 which is twice as

much as that one caused by the MZM.

4 CONCLUSIONS

MZM and SMF have quite the same distortion

effects. Both rotate the constellation but the CD

influence on the degradation is much stronger and it

highly spreads the symbols. These rotations can be

compensated by the same algorithm because of the

similarity. The rotation caused by MZM can be

easily eliminated by differential driving. It

minimizes the rotation but the standard deviation of

symbols is increased slightly. If the electrical field of

MZM provides opposite rotation this effect does not

exist and the rotation stays small. Dispersion

compensation always needs additional equipment. It

can be done electronically using a DSP after

demodulation. Other nonlinearities of SMF (i.e. four

wave mixing, polarization mode dispersion) cause

smaller distortion and they are covered by the

distortion effect of MZM nonlinearity and CD. We

usually use low laser power so only FWM will

influence the transmission. Its effect has to be

compensated by a DSP.

REFERENCES

William Shieh, 2011, OFDM for Flexible High-Speed

Optical Networks, Journal of Lightwave Technology,

Vol. 29, No. 10.

W. Shieh, H. Bao, and Y. Tang, 2008, Coherent optical

OFDM: theory and design, Optics Express, Vol. 16,

No. 2,

Jean Armstrong, 2009, OFDM for Optical

Communications, Journal of Lightwave Technology,

Vol. 27, No. 3.

H. Louchet, A. Richter, 2007, Novel Scheme for High Bit-

Rate Coherent OFDM Transmission without PLL,

ECOC.

William Shieh, Ivan Djordjevic, 2010, Orthogonal

frequency division multiplexing for optical

communication, Academic Press, London.

-3 -2 -1 0 1 2 3

-3

-2

-1

Real

Imaginary

6km fiber

ideal

-4 -2 0 2 4

-3

-2

-1

Real

Imaginary

50km fiber

-2 -1 0 1 2

-2

-1

Real

Imaginary

2 2.1 2.2 2.3

-0.1

-0.05

0.05

0.1

0.15

0.2

Real

Imaginary

PHOTOPTICS2014-InternationalConferenceonPhotonics,OpticsandLaserTechnology