Optical Fiber Technology 25 (2015) 88–93

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Optical Fiber Technology

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Regular Articles

Peak-to-average power ratio reduction in all-optical orthogonalfrequency division multiplexing system using rotated constellationapproach

http://dx.doi.org/10.1016/j.yofte.2015.08.0071068-5200/� 2015 Elsevier Inc. All rights reserved.

⇑ Corresponding author at: Department of Electrical Engineering, Faculty ofEngineering, University of Malaya, 50603 Kuala Lumpur, Malaysia.

E-mail address: swharun@um.edu.my (S.W. Harun).

Jassim K. Hmood a,b, Kamarul A. Noordin a, Hamzah Arof a, Sulaiman W. Harun a,c,⇑aDepartment of Electrical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysiab Laser and Optoelectronic Department, University of Technology, 10066 Baghdad, IraqcPhotonics Research Center, University of Malaya, 50603 Kuala Lumpur, Malaysia

a r t i c l e i n f o a b s t r a c t

Article history:Received 5 May 2015Revised 4 August 2015

Keywords:All-optical OFDM systemsFiber nonlinearityQAM modulationPAPR reductionPhase noise

In this paper, a new approach for reducing peak-to-average power ratio (PAPR) based on modulated halfsubcarriers in all-optical OFDM systems with rotated QAM constellation is presented. To reduce the PAPR,the odd subcarriers are modulated with rotated QAM constellation, while the even subcarriers are mod-ulated with standard QAM constellation. The impact of the rotation angle on the PAPR is mathematicallymodeled. The effect of PAPR reduction on the system performance is investigated by simulating the all-optical OFDM system, which uses optical coupler-based inverse fast Fourier transform (IFFT)/fast Fouriertransform (FFT). The all-optical system is numerically demonstrated with 29 subcarriers. Each subcarrieris modulated by a QAM modulator at a symbol rate of 25 Gsymbol/s. The results reveal that PAPR isreduced with increasing the angle of rotation. The PAPR reduction can reach about 0.8 dB when the com-plementary cumulative distribution function (CCDF) is 1 � 10�3. Furthermore, both the nonlinear phasenoise and the optical signal-to-noise ratio (OSNR) of the system are improved in comparison with theoriginal all-optical OFDM without PAPR reduction.

� 2015 Elsevier Inc. All rights reserved.

1. Introduction

All-optical orthogonal frequency division multiplexing (OFDM)system has drawn great attention in recent years due to itspotential applications in high-bit-rate transmission systems [1].Furthermore, this system provides a better tolerance to chromaticand polarization-mode dispersions compared to the conventionalsystems [2–5]. For instance, the all-optical OFDM system elimi-nates the requirement of electronics signal processing and thus itis much more feasible for high bit rate transmission system[1,6,7]. However, all-optical OFDM system highly suffers fromphase noise which introduces phase rotation for each subcarrierand thus destroys orthogonality of subcarriers [8]. The phase noiseis mainly induced from fiber nonlinear effects such as cross-phasemodulation (XPM) and four-wave mixing (FWM) [9]. This is evi-dent when adding a number of subcarriers in the time domainfor high power transmission signals [10]. The combined signalsinduce the fiber nonlinear effects and degrades the system

performance [11,12]. Therefore, many approaches have been pro-posed and reported to mitigate fiber nonlinear impairment duringtransmission of signals in optical OFDM systems where high peak-to-average power ratio (PAPR) reduction is the popular approach.

In both wireless and conventional optical OFDM systems, PAPRreduction is realized in the electrical domain. Various techniqueshave been developed to reduce PAPR in optical OFDM systems suchas amplitude clipping and filtering [13,14]. Although the imple-mentation of clipping technique is simple and less complex, theclipping processes produce a distortion in the optical signal henceincreasing the bit error rate (BER). There are also other techniquessuch as selected mapping (SLM) and partial transmit sequence(PTS) methods which are considered as effective for reducing PAPRin conventional optical OFDM systems [12,15]. However, thesemethods involve a high computational complexity. Furthermore,the constant envelope of the electrical OFDM waveform has alsobeen adopted to improve the tolerance of MZM nonlinearitiesand to relax the requirements of digital-to-analog and analog-to-digital converter (DAC/ADC) [16,17]. Indeed, few investigationshave been reported on the PAPR reduction techniques in all-optical OFDM systems [18]. They focus on the all-optical OFDMsystems, which employ intensity modulation rather than phase

J.K. Hmood et al. / Optical Fiber Technology 25 (2015) 88–93 89

modulation. Phase pre-emphases method has been proposed toreduce PAPR in all-optical OFDM systems [19].

In this paper, we propose a simple technique to reduce PAPRbased on rotated constellation in coherent all-optical OFDM sys-tem. In this approach, the subcarriers are divided into odd andeven subsets. Then the constellation of odd subcarriers is rotatedcounter clockwise while the constellation of even subcarriers isremained without rotation. The impact of the rotation angle onthe PAPR is mathematically modeled. Then, the resulting PAPRreduction on the total phase noise in all-optical OFDM systems ismathematically modeled and numerically investigated. The simu-lation results show that the proposed technique provides 0.8 dBPAPR reduction with a better nonlinear impairment tolerance inall-optical OFDM system that employs 29 subcarriers and symbolrate of 25 Gsymbol/s.

The rest of the paper is organized as follows. Section 2 describesthe PAPR reduction principle. The effect of rotated constellationmethod on fiber nonlinearity is discussed in Section 3. The pro-posed all-optical OFDM system setup is presented in Section 4.The analytical and simulation results are presented in Section 5,where the impacts of rotation angle of constellation on the PAPRand variance of the total phase noise are studied. The validationof our analytical model using simulation results of our systems isgiven in the same section as well. Finally, a conclusion is drawnin Section 6.

2. PAPR reduction principle

In this section, a new approach to mitigate fiber nonlinearimpairment by reducing PAPR is mathematically explained. First,the subcarriers are divided into odd and even subsets. Then, atQAM modulators, the original constellation of odd subcarriers isrotated with an angle of h (clockwise) while the constellation ofeven subcarriers is determined by the standard 4QAM constella-tion as shown in Fig. 1. This approach is suitable for both conven-tional optical OFDM and all-optical OFDM systems where theconstellation is realized in electrical domain. The output of theOFDM transmitter (u(t))) is given by

uðtÞ ¼XðN�1Þ=2

k¼�ðN�1Þ=2k2O

ukðtÞ expðjhÞ expðjxktÞ þXðN�1Þ=2

k¼�ðN�1Þ=2k2e

ukðtÞ expðjxktÞ; ð1Þ

where N represents the total number of subcarriers (assumed oddwithout loss of generality), O 2 f�ðN � 1Þ=2þ 1;�ðN � 1Þ=2þ3; . . . ; ðN � 1Þ=2� 1g and e 2 f�ðN � 1Þ=2;�ðN � 1Þ=2þ 2; . . . ;ðN � 1Þ=2g represent odd and even numbers, respectively,h; 0 6 h 6 p=4 is the angle of rotation,xk ¼ 2pk=Ts is the frequency

Fig. 1. Rotated 4QAM constellation.

offset from the reference optical carrier and Ts is defined as OFDMsymbol time. Here ukðz; tÞ represents the normalized slowly varyingfield envelope of kth subcarrier and it is defined as

ukðtÞ ¼ffiffiffiP2

rAkrect

t � kTS

TS

� �; ð2Þ

where; P is the optical power of single subcarrier, Ak ¼ ak þ jbk is acomplex number and is determined by the standard 4QAM constel-lation and

rectðtÞ ¼ 1 if 0 6 t 6 1;0 otherwise:

�

By substituting (2) in (1), the optical field the OFDM signal canexpressed as

uðtÞ ¼ffiffiffiP2

rexpðjhÞ

XðN�1Þ=2

k¼�ðN�1Þ=2k2O

Akrectt � kTS

TS

� �expðjxktÞ

þffiffiffiP2

r XðN�1Þ=2

k¼�ðN�1Þ=2k2O

Akrectt � kTS

TS

� �expðjxktÞ:

ð3Þ

The maximum optical field can be obtained when all subcarriersare coherently combined. To achieve this, all subcarriers should bemodulated with the same QAM symbol, making the summations ofmagnitudes of odd and even subcarriers equal to half summationof magnitude of all subcarriers and the angle between them isequal to the rotating angle. Then, the magnitude of optical fieldof OFDM signal can be written as

juðtÞj ¼ffiffiffiP2

r1þ expðjhÞ

2

� ��������� XðN�1Þ=2

k¼�ðN�1Þ=2Akj j ð4Þ

By doing some algebra, the magnitude of optical field can beexpressed as

juðtÞj ¼ffiffiffiP2

rcos

h2

� �exp j

h2

� ��������� XðN�1Þ=2

k¼�ðN�1Þ=2jAkj

¼XðN�1Þ=2

k¼�ðN�1Þ=2

ffiffiffiP2

rcos

h2

� �jAkj:

ð5Þ

From (5), it can be considered that the magnitude of opticalfield of kth subcarrier equal to

jukðt; hÞj ¼ffiffiffiP2

rcos

h2

� �jAkj: ð6Þ

The PAPR of the signal, u(t), is defined as the ratio of the peak ofinstantaneous power to the average power, and is given as [13]

PAPR ¼max juðtÞj2

E ðuðtÞÞ2h i ; ð7Þ

where E½�� is the expectation operator. For 4QAM constellation, thejAkj ¼

ffiffiffi2

pbecause ak ¼ bk ¼ 1. The magnitude of optical field and

the power of kth subcarrier after rotating the constellation can beexpressed as

jukðt; hÞj ¼ffiffiffiP

pcos

h2

� �;

jukðt; hÞj2 ¼ P cos2h2

� �;

ð8Þ

respectively. The maximum power is occurred when power of Nsubcarriers are coherently added and it equal to

max juðtÞj2

¼XðN�1Þ=2

k¼�ðN�1Þ=2P cos2

h2

� �¼ PN cos2

h2

� �: ð9Þ

90 J.K. Hmood et al. / Optical Fiber Technology 25 (2015) 88–93

The average power can be expressed as

E ðuðtÞÞ2h i

¼ffiffiffiffiN

p Pffiffiffi2

p : ð10Þ

By substituting (9) and (10) in (7), the PAPR becomes

PAPRðhÞ ¼ffiffiffiffiffiffiffi2N

pcos2

h2

� �: ð11Þ

From (11), the relation between the PAPRs for the system withand without employing rotation constellation technique is factorcos2 h

2

� �. Therefore, the cumulative distribution function (CDF) of

ðPAPR < xÞ for proposed system can be written as

CDF ¼Z x

0

ycos2 h

2

� �r2

exp�y2

2r2 cos4ðh2Þ

!dy

¼ 1� exp�x2

2r2 cos4 h2

� � !

:

ð12Þ

For large N OFDM symbols, the PAPR is considered as a randomvariable where its distribution is given by

PðPAPR 6 xÞ ¼ 1� exp�x2

2r2 cos4 h2

� � ! !N

: ð13Þ

The complementary cumulative distribution function (CCDF)describes PAPR statistics. It shows the probability of an OFDM sig-nal exceeding a given PAPR, and is written as

CCDF ¼ 1� 1� exp�x2

2r2 cos4 h2

� � ! !N

: ð14Þ

3. Effect of rotated constellation method on fiber nonlinearity

In this section, the effect of rotated constellation of odd subcar-riers on the fiber nonlinearity impairments is described. The inten-sity of the optical signal is one of the main factors that affect thephase noise caused by XPM and FWM. By reducing the high peaksof the OFDM signal, the nonlinear distortion should decrease.

3.1. XPM phase noise

It is well known that XPM refers to the nonlinear phase shift ofan optical field induced by another field with different wavelength,direction, or state of polarization. In long haul transmission system,the optical signal is commonly transmitted through multi-spanoptical fiber. Each span is constructed of a single mode optical fiber,a dispersion compensation fiber, and an optical amplifier. Normally,an optical amplifier is used to compensate power loss due to thefiber attenuation in each span. However, these amplifiers add a ran-dom noise to the transmitted signal where a field of amplified spon-taneous emission (ASE) noise is added to each of the subcarriers.ASE noise is effectively white noise with variance r2. The nonlinearphase noise due to XPM in the presence ASE noise is accumulatedspan-by-span [20], and it can be expressed as

/þnkXPM ¼ cLeff ðLÞ

XðN�1Þ=2

i ¼ �ðN � 1Þ=2i–k; k 2 O

XMm¼1

ui expðjhÞ þXml¼1

nilðtÞ�����

�����2

þXðN�1Þ=2

i ¼ �ðN �i–k; k 2

2666664

where c is the nonlinear coefficients, L is the fiber length of eachspan, M number of fiber spans and nilðtÞ, l 2 f1;2; . . . ;Mg, is thecomplex amplifier noise at the lth span and ith subcarrier. Here,Leff ¼ ð1� e�aLÞ=a and a is the attenuation coefficient. By substitut-ing (6) in (15), the phase noise variance can be written as

r2/nkXPM

ðML; hÞ ¼ 2MðM þ 1Þc2L2eff P cos2h2

� � XðN�1Þ=2

i¼�ðN�1Þ=2i–k

jAij2r2i ð16Þ

From the last equation, it is clear that the angle of rotation hgoverns the variance of phase noise due to interaction of XPM withASE noise.

3.2. FWM phase noise

The FWM process is a phase sensitive process where the inter-action depends on the relative phases of all subcarriers and itseffect can efficiently accumulate over longer distances. The FWMprocess adds a fluctuation to the optical field that causes a phasenoise. For M fiber spans, the phase noise variance due to ASE noiseand its interaction with FWM can be written as [20]

r2ukðnðtÞþFWMÞ

ðML;tÞ¼ Mr2k

jukj2þ 4c2

jukj2�XMm¼1

XðN�1Þ=2

h¼�ðN�1Þ=2h–k

XðN�1Þ=2

i¼�ðN�1Þ=2l¼hþi�k

i–l

�LFWMðmLÞ juhj2juij2r2l þjuhj2julj2r2

i þjuij2julj2r2h

n oð17Þ

where LFWMðzÞ ¼ 1�exp � a�jX2b22

� �z

�a�jX2b2

2

, b2 is the dispersion profile and

X2 ¼ x2h þx2

i �x2l �x2

k .First part of (18) represents the phase noise due to the ASE noise

only while the last part represents the phase noise due to the inter-action of FWM with ASE noise. For the proposed approach, themagnitude of the phase noise variance is governed by the anglebetween odd and even constellations. By substituting (6) in (17),the phase noise variance for the proposed system can be expressedas

r2ukðnðtÞþFWMÞ

ðML; tÞ ¼ 2Mr2k

PjAkj2þ 2c2P

jAkj2cos4

h2

� ��XMm¼1

XðN�1Þ=2

h¼�ðN�1Þ=2h–k

XðN�1Þ=2

i¼�ðN�1Þ=2l¼hþi�k

i–l

LFWM jAhj2jAij2r2l þ jAhj2jAlj2r2

i þ jAij2jAlj2r2h

n oð18Þ

From last equation, the phase noise variance due to interactionof FWM with ASE noise is controlled by adjusting the angle ofrotation.

4. All-optical OFDM system setup

The schematic of all-optical OFDM system setup [7], is shown inFig. 2. The system includes three subsystems: transmission, trans-

1Þ=2e

XMm¼1

ui þXml¼1

nilðtÞ�����

�����2

3777775 ð15Þ

J.K. Hmood et al. / Optical Fiber Technology 25 (2015) 88–93 91

mission link, and reception. The transmission subsystem consistsof an optical frequency comb generator (OFCG), wavelengthselected switch, optical QAM modulators, and an optical beamcombiner. The OFCG utilizes two intensity modulator (IM) andone time delayer to generate 29 subcarriers with constant fre-quency spacing [21]. Subsequently, the generated subcarriers aresplit into odd and even subcarriers. The odd subcarriers are modu-lated according to rotated QAM constellation, while standard QAMconstellation is used to modulate the even subcarriers. The odd andeven subcarriers are directly superimposed upon modulating byusing beam combiner to generate OFDM signal.

The transmission link comprises multi-span fiber loops. Eachspan consists of 55 km standard single mode fiber (SSMF), disper-sion compensating fiber (DCF) and an Erbium doped fiber amplifier(EDFA) as shown in Fig. 2. The SSMF is modeled with an attenua-tion coefficient a of 0.2 dB/km, chromatic dispersion (CD) coeffi-cient of 16 ps/nm/km, an effective area of 80 lm2, and fibernonlinearity c of 1.3 W�1 km�1. The DCF fully compensates theCD of SSMF with CD coefficient of �160 ps/nm/km. The EDFAs witha noise figure of 6 dB are employed to compensate the fiber lossand control the launching power into the SSMF and DCF.

The all-optical OFDM receiver comprises all-optical FFT (OFFT)circuit [22] and coherent QAM optical detectors. The main functionof the OFFT circuit is to perform serial-to-parallel conversions infrequency domain. The OFFT circuit consists of three cascadedMach–Zehnder Interferometers (MZIs), optical filters and electro-absorption modulators (EAMs). Each MZI has one optical timedelayer and one optical phase shifter as shown in Fig. 2. The timedelay and phase shift of first MZI are adjusted to Ts=2 and 0 rad,respectively. The time delay of the other two subsequent parallelMZIs is set to Ts=4, while the phase shift of the upper and lowerones are set at 0 rad and p=2 rad respectively. Four de-multiplexers are directly employed to split and filter thesubcarriers. Then, the signals are sampled by EAM sampling gates.Afterwards, the output of the EAM is filtered by a third-order band-pass filter before it is demodulated by the coherent QAM opticaldetector.

5. Results and discussion

In order to investigate the validity of our approach, model anal-ysis is carried out and the finding is compared with the result ofnumerical simulation generated by VPItransmissionMaker 9.0.The analytical and simulation results are obtained for 29 subcarri-ers. Each subcarrier is modulated with 4QAM constellation at a

Fig. 2. All-optical OFD

symbol rate of 25 Gsymbol/s and transmitted through multi-spanfiber with a total length of 1100 km.

5.1. Transmitter side

Fig. 3 depicts the impact of rotation angle on the PAPR. Theresults are achieved for N = 29, 4QAM mapping and subcarrierpower of �3 dBm. The comparison of CCDF performances for theproposed approach at h ¼ p=6 rad and h ¼ p=4 rad against the orig-inal system (without using any PAPR reduction method) is shownin Fig. 3(a). It is shown that for the original OFDM ðh ¼ 0Þ, 1 inevery 103 OFDM frames has its PAPR greater than 8.9 dB. Usingthe rotated constellation technique, at h ¼ p=4rad, 1 in every 103

OFDM frames has its PAPR exceeding 8.1 dB. The PAPR is improvedby more than 0.8 dB for CCDF = 1 � 10�3 over the conventional sys-tem. The PAPR for various rotation angles is shown in Fig. 3(b). It isclear that the PAPR is reduced with increasing the rotation anglefrom 0 to p=4 rad. However, when the rotation angle is increasedbeyond the p=4, the PAPR is also increased because the constella-tion of odd subcarriers approaches to the constellation of even sub-carriers in next quarter as shown in inset of Fig. 3(b). Therefore, thePAPR(h) is consider a periodic function and the optimum angle isp=4. The analytical result (dashed line) indicates that the PAPRdrops from 8.8 dB to 8.1 dB when the rotation angle increases fromzero to p=4rad. The simulation result (solid line) exhibits similarbehavior and there exist a good agreement between the analyticaland simulation results.

Fig. 4 shows the optical waveforms of all-optical OFDM signalsfor various rotation angles. The results are obtained for 4QAMmapping with different rotation angles but at the same power ofsubcarriers (P = �3 dBm). It can be observed from Fig. 4(a) thatthe original system (h = 0) generates an optical OFDM signal witha maximum peak of 20.4 mW. By increasing the rotation angle hto p=4, the maximum peaks of the transmitted optical OFDM signalare obtained at 17.2 mW as shown in Fig. 4(b). This indicates thatthe increment of the rotation angle decreases the signal peaks sig-nificantly. This phenomenon results from combining the odd andeven subcarriers with different rotated angles. In agreement with(9), a higher rotation angle leads to reduction in peak power ofthe generated OFDM signal.

5.2. Receiver side

To show the mitigation results of the fiber nonlinear impair-ments, Fig. 5 depicts the nonlinear phase noise variance against

M system setup.

92 J.K. Hmood et al. / Optical Fiber Technology 25 (2015) 88–93

the power of subcarrier for the proposed system at rotation anglesof h ¼ p=4 rad and the original OFDM system. The results are quan-tified using both simulation and the analytical model for 29 sub-carriers and transmission distance of 1100 km. It is found thatthe phase noise variance is successfully reduced when the angle

Fig. 3. The impact of rotation angle on the PAPR.

Fig. 4. Effect of rotation angle on the optical waveforms of all-optical OFDM signals.

Fig. 5. Influence of rotated constellation on the fiber nonlinearities impairments.

Fig. 6. Influence of the angle of rotation on the BER performance of the all-opticalOFDM system.

of rotation is set to h = p/4. At low signal power, the phase noisevariances of both systems are slightly different. This is becausethe performance of the system is governed by the optical amplifiernoises at low signal power. However, with higher signal power, thedifference between the phase noise variances is become clearer.This is because the proposed system reduces the PAPR and miti-gates the fiber nonlinear impairments without any additional dis-tortion. In addition, it can be noted that the presented analyticalresults show good agreement with the simulation results.

Fig. 6(a) shows the influence of the angle of rotation on bothOSNR and BER performance in the all-optical OFDM system thatemploy 4QAM. Referring to (16) and (18), both XPM and FWMare reduced with increasing the rotation angle because the powerof the OFDM symbol is reduced with employing proposedapproach. Clearly, the BER reduces as the angle of the rotationincreases. The highest BER occurs at h ¼ 0, whereas the minimum

J.K. Hmood et al. / Optical Fiber Technology 25 (2015) 88–93 93

BER occurs at h ¼ p=4. Furthermore, the OSNR is raised withincreasing the angle of rotation. This indicates that the perfor-mance of the system improves with the increment of the rotationangle due to mitigation of fiber nonlinearity impairments. Insets ofFig. 6(a) depict the received constellations for h ¼ 0; p=6 and p=4.Fig. 6(b) illustrates BER versus OSNR for the both proposed andoriginal OFDM system. The rotation angle is set to h ¼ p=4rad.The receiver sensitivity is obtained at a symbol rate of 25 Gsym-bol/s and transmission distance of 1100 km. At h ¼ p=4, the all-optical OFDM system acquires the best BER performance wherethe required OSNR to obtain a BER = 1 � 10�7 is reduced by 0.5 dB.

Finally yet importantly, we can confirm that the rotated con-stellation approach is a simple and viable method for reducingPAPR value, mitigating phase noise, and improving performanceof OFDM systems. Furthermore, to implement this approach, onlysimple computations or components are required.

6. Conclusion

In this paper, an efficient new approach for mitigating the phasenoise in all-optical OFDM system is proposed. This approach usesrotated constellation to reduce PAPR and mitigates the phase noise.The performance of the system is dependent on the angle differ-ence between the odd and even subcarriers constellations. In thiswork, the modulation constellation of odd subcarriers is rotatedclockwise with an angle of p=4, while the modulation constellationof even subcarriers is remain without rotating. By using thisscheme, the PAPR is improved by 0.8 dB at CCDF = 1 � 10�3. More-over, the proposed method reduces the phase noise variance due tofiber nonlinearity. In addition, at transmission distance of 1100 kmand rotation angle of p=4, the required OSNR decreases by 0.5 dBfor BER of 10�7.

Acknowledgment

This work was financially supported by the University ofMalaya, Malaysia under various grant schemes (Grant No:D000009-16001, PG100-2014B and PG105-2014B).

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