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ACCEPTED FOR PUBLICATION IN IEEE PHOTONICS TECHNOLOGY LETTERS (FINAL 1) 1

Analysis of RF-Pilot-based Phase NoiseCompensation for Coherent Optical OFDM Systems

Sebastian Randel, Member, IEEE, Susmita Adhikari, Student Member, IEEE, Sander L. Jansen, Member, IEEE

Abstract—In coherent optical long-haul transmission systemsorthogonal frequency-division multiplexing represents a promis-ing modulation format. However, due to long symbol length, laserphase noise can be a major impairment. In this manuscript, theRF-pilot-based phase noise compensation scheme is analyzed andcompared to conventional common-phase error compensation.It has been shown, that the RF-pilot-based phase noise com-pensation scheme allows for a considerable increase in tolerablelaser linewidth as compared to conventional common-phase errorcompensation at the cost of an increase in system complexity.For a 112 Gbit/s transmission scheme, the tolerable linewidth isincreased by a factor of ten as compared to common-phase errorcompensation.

Index Terms—Optical fiber communication, Digital modula-tion, Orthogonal frequency-division multiplexing, Phase noise

I. INTRODUCTION

Orthogonal frequency-division multiplexing (OFDM) is apromising modulation scheme for next generation optical long-haul transmission systems. These systems need to transmit112 Gb/s Ethernet traffic within a 50 GHz wavelength gridover distances of up to 2000 km. In recent years, a variety ofcoherent optical transmission schemes combined with digitalsignal processing (DSP) have been proposed and demon-strated, that provide a large tolerance towards impairmentslike chromatic dispersion (CD), polarization-mode dispersion,and cascaded filtering [1]–[3]. It is known, that in coherentoptical transmission systems, laser phase noise represents amajor performance impairment that must be compensated for[4], [5]. In particular because of its long symbol size, OFDMrequires an effective compensation mechanism.

In the field of wireless communications the phase noisetolerance of OFDM has already been studied in detail [6]–[9]. It has been found, that its influence is twofold, i.e., itgenerates a common phase error (CPE) of all the subcarriersin one symbol and a cross-leakage between the sub-carriersreferred to as inter-carrier interference (ICI). The former effectis commonly solved by estimating the mean phase rotation ofeach symbol from dedicated pilot subcarriers and rotating thereceived symbols back. This method has also been used inseveral fiber-optic transmission experiments and simulations,

S. Randel is with Siemens AG, Corporate Technology, CommunicationTechnologies, Otto-Hahn-Ring 6, D-81739 Munich, Germany, e-mail: sebas-tian.randel@siemens.com.

S. Adhikari is with Chair for Communications, Christian-Albrechts-Universitat zu Kiel, Kaiserstraße 2, D-24143 Kiel, Germany, e-mail:asu@tf.uni-kiel.de

S. L. Jansen is with Nokia Siemens Networks GmbH & Co. KG, St.Martinstraße 76, D-81541 Munich, Germany, e-mail: sander.jansen@nsn.com

Copyright (c) 2009 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to pubs-permissions@ieee.org.

see e.g. [2], [10]. The main drawback of CPE, however, isthat it does not correct for the ICI, since it inherently assumesthe phase of the transmit and the receive laser to be constantduring one OFDM symbol. Consequently, the OFDM symbolmust be short and the laser linewidths must be small tolimit the impact of ICI. However, shorter OFDM symbolsrequire larger cyclic-prefix overheads in order to compensatefor CD and small linewidths require costly lasers. In [3] anew phase noise compensation scheme has been introducedand referred to as RF-pilot-based phase-noise compensation,which effectively compensates for both the CPE and the ICI.With this technique, phase-noise compensation is realized byplacing a RF-pilot (RFP) tone in the center of the OFDMtransmit spectrum, which is subsequently used at the receiverin order to undo phase noise impairments.

In this manuscript a detailed comparison between CPE-based and RFP-based phase noise compensation is presented.After introducing the underlying system model, it is shown bymeans of numerical simulation that the RFP-based phase noisecompensation scheme allows for a considerable improvementin phase-noise tolerance and that it can be regarded as anenabling technique for 112 Gb/s PDM-OFDM transmissionsystems.

II. SYSTEM MODEL

In a DSP unit, the lth symbol of the discrete-time OFDMsignal xl,k with variance σ2

x is generated using the N -pointinverse discrete Fourier transform (DFT) according to

xl,k =1√N

N/2∑n=−N/2+1

cl,n exp[j

2πn(k − ν)N

], (1)

for k = 1, 2, . . . , N + ν. The cl,n are complex coefficientsrepresenting either information or control symbols modulatedonto the nth subcarrier. The dc component cl,0, the Nyquistcomponent cl,N/2 and Nz subcarriers with indices |n| ≥ (N−Nz)/2 are padded with zeros, in order to relax requirementsfor RF components. Furthermore, a cyclic prefix (CP) of νsamples is inserted in order to avoid ISI, e.g., due to CD.

In the transmitter, two uncorrelated OFDM signals arefirst converted to optical signals by digital-to-analog con-verters with sampling rate fs and electro-optical in-phase/quadrature-modulators. Then these signals are combinedusing polarization-division multiplexing (PDM) and transmit-ted over the optical link. Finally, the signal is detected witha digital coherent receiver and fed to the receiver DSP unit,where the two polarizations are separated with the help ofmultiple-input multiple-output processing [11]. In the pres-ence of laser phase-noise and amplified spontaneous emission

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(ASE) noise, the received discrete-time OFDM signal for eachpolarization becomes

xl,k = xl,k exp(jφl,k) + nl,k. (2)

The random phase shifts, φl,k, due to laser phase noise canbe modeled as a Wiener process according to

φl,k = φl−1,N+ν +k∑

m=1

ϕl,m, (3)

where ϕl,m is the mth element of the lth realization of aset of N + ν independent real-valued Gaussian distributedrandom variables with zero mean and variance σ2

ϕ = 2π∆f/fs[4]. In the linear channel, the parameter ∆f represents thesum of the laser linewidths of the transmit and the receivelaser. ASE noise is included by the additive zero meancomplex Gaussian random variable nl,k with variance σ2

n =σ2x×fref/fs/OSNR/2, where the optical signal-to-noise ratio

(OSNR) is referred to a bandwidth fref corresponding to0.1 nm around a center frequency of 193.1 THz.

In case of CPE-based phase noise estimation, a set of Np

equally spaced pilot symbols with indices {np} is transmittedwithin the N subcarriers. At the receiver side, the constella-tions cl,n with phase noise impairment are first received withhelp of the DFT according to

cl,n =1√N

N∑k=1

xl,k exp(−j 2πkn

N

). (4)

Afterwards, the CPE φc,l is estimated as the mean phaserotation of the l-th received OFDM symbol by

exp(jφc,l

)=

1Np

∑n∈{np}

cl,n|cl,n|cl,n|cl,n|

. (5)

Finally, the received constellations are obtained from cl,n =cl,n exp(−jφc,l).

In case of RFP-based phase noise estimation, a gap of Np

zeros is inserted around dc such that cl,n = 0 for all |n| ≤Np/2 and a single pilot is inserted at dc1 such that |cl,0|2 =Np/(Nm − Np). The received signal is filtered with a low-pass filter defined by its M -point discrete impulse responsehm resulting in

xl,k =1M

M−1∑m=0

xl,k+mhm. (6)

Then the phase noise is estimated as

exp(jφl,k

)=

xl,k|xl,k|

(7)

and finally the received constellations are obtained from

cl,n =1√N

N∑k=1

xl,k exp(−jφl,k

)exp

(−j 2πkn

N

). (8)

Clearly, The RFP based phase noise compensation schemedoes not only compensate for the CPE but also for the fast

1In practical systems this pilot is often shifted to RF frequencies, explainingthe name given to this scheme.

(a)

Pow

er(d

Bm

)

Relative Frequency (GHz)(b)

Pow

er(d

Bm

)

Relative Frequency (GHz)(c)

Relative Frequency (GHz)

Pow

er(d

Bm

)

Transmit Receive Filtered Pilots

−0.5 −0.25 0 0.25 0.5

−10 −5 0 5 10

−10 −5 0 5 10

−30

0

20

−30

0

20

−30

0

20

Fig. 1. (a) Transmitted and received 112 Gbit/s PDM-OFDM spectra withdistributed pilots for CPE estimation. (b) Transmitted and received 112 Gbit/sPDM-OFDM spectra and pilot for RFP-based phase noise estimation as wellas filtered pilot. (c) zoomed version of (b).

temporal fluctuations of the phase causing the ICI. From (6) itbecomes evident that M complex multiplications per sampleare required to realize the low-pass filter, making RFP-basedphase noise compensation more complex to implement ascompared to CPE-based compensation. Notice, in a digitalimplementation this filter can be processed in a parallelstructure, while the OFDM symbol is stored in registers. Therequired number of complex multiplications is typically lessthan N and scales inversely proportional with the relative filterbandwidth.

III. PERFORMANCE COMPARISON

In this section the performance of both phase noise compen-sation schemes is compared using the example of a 112 Gb/sPDM-OFDM using 8-ary quadrature amplitude modulation(QAM). In order to be able to compensate for the accumulatedCD of a 2000km link with 17ps/nm/km fully in the electricaldomain, a DFT-size of N = 2048 and ν = 140 is chosencorresponding to a CP overhead of 6.84%. Notice, that theDFT size cannot be reduced without an accordant increase ofthe CP overhead. An additional overhead of 4% is appliedfor coefficient training and synchronization. For phase noisecompensation Np = 40 subcarriers are reserved in case of bothcompensation schemes and zero-padding is set to Nz = 236.The required sampling rate results in fs = 24 GHz andthe nominal data rate including training and cyclic prefixoverheads is 124.4 Gb/s.

Fig. 1(a) depicts the electrical transmit and receive spectrawith phase noise impairment of ∆f = 200 kHz in case of theCPE-based scheme as well the location of the equally spacedpilot sub-carriers. In Fig. 1(b) the same curves are shown forRFP-based phase noise compensation with a single strong pilotat the center frequency and the signal after low-pass filteringis illustrated alongside. Fig. 1(c) shows a zoomed version ofFig. 1(b) providing a better resolution of the region of interest.The phase noise impairment can clearly be observed as aLorentzian-shaped line-width broadening. In this example, a

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ACCEPTED FOR PUBLICATION IN IEEE PHOTONICS TECHNOLOGY LETTERS (FINAL 1) 3

Filt

erB

andw

idth

(MH

z)

Req

uire

dO

SNR

(dB

)

Linewidth (Hz)

RFP filter bandwidthCPE-based schemeRFP-based scheme

103 104 105 106 10715.5

16

16.5

17

17.5

18

18.5

19

19.5

0

15

30

45

60

Fig. 2. OSNR required for a bit-error rate of 10−3 versus the linewidth∆f for CPE-based and RFP-based phase noise compensation as well as theoptimum low-pass filter bandwidths.

Gaussian-shaped low-pass filter with a bandwidth of 32.5MHzis used. It can clearly be seen, that the filtered pilot includesdominant parts of the phase noise spectrum, which are thenapplied for its compensation according to (8).

Fig. 2 shows the required OSNR for a target bit-error rateof 10−3 obtained by Monte Carlo simulation as a functionof ∆f for the two phase noise compensation schemes. Thesimulations are based on the equations introduced in sectionII. In case of the CPE-based scheme, a penalty of 0.5 dBoccurs at about ∆f = 40 kHz while for RFP-based phasenoise compensation ∆f = 400 kHz can be tolerated with thesame penalty. The corresponding linewidth-to-bit-rate ratiosare thus ∆f/B = 3.28 × 10−7 and ∆f/B = 3.28 × 10−6,respectively. In [4] the linewidth tolerance of single-carrier8-ary QAM has been found to be ∆f/B = 5.23 × 10−5.Even though the symbol length for PDM-OFDM is more than2000 times larger, the phase noise sensitivity is only increasedby approximately a factor of ten. The optimum bandwidthrepresents a trade-off between the phase-noise dynamics, ASEnoise, and interference from the subcarriers modulated withdata and thus grows with increasing linewidths. In the abovesimulations, bandwidth was varied between 0 Hz and 50 MHzand the values corresponding to the lowest OSNR requirementare displayed in Fig. 2 as triangles.

The principle of RFP-based phase noise compensation isfurther illustrated in Fig. 3. An example of the temporalevolution of random phase noise with ∆f = 200kHz is shownfor three consecutive OFDM symbols. Furthermore, the phasenoise estimates obatined with the CPE-based as well as theRFP-based scheme are shown. Clearly, the CPE compensationaccounts for the mean phase noise per OFDM symbol but doesnot correct for the fast fluctuations. However, these residualphase dynamics can result in considerable ICI as illustrated bythe constellation diagram shown in Fig. 3. In contrast, the RFP-based scheme provides an exact estimate also of the fast phasedynamics and ICI can almost completely be compensated.

IV. CONCLUSIONS

It has been shown, that the RFP-based phase noise compen-sation scheme allows for a considerable increase in tolerable

Time (OFDM Symbols)

Pha

se(r

ad)

Random phase noiseCPE-based schemeRFP-based scheme

CPE RFP

0 1 2 3−π/2

−π/4

0

π/4

π/2

Fig. 3. Example of random phase noise evolution over three OFDM symbolstogether with results of CPE estimation and RFP phase noise estimation. Thesubplots show the corresponding 8-QAM constellations (without ASE).

laser linewidth as compared to conventional CPE compensa-tion at the cost of an increase in system complexity. Appliedto a 112 Gb/s PDM-OFDM transmission system, simulationresults reveal that the tolerable laser linewidth can be increasedfrom 40 kHz to 400 kHz at penalty of only 0.5 dB. The RFP-based scheme thus considerably relaxes the laser phase noiserequirement and can be an enabling technique for future PDM-OFDM long-haul transmission systems.

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[1] K. Roberts, M. OSullivan, K.-T. Wu, H. Sun, A. Awadalla, D. J. Krause,and C. Laperle, “Performance of Dual-Polarization QPSK for OpticalTransport Systems,” J. Lightwave Technol., vol. 27, no. 16 pp. 3546–3559, Aug. 2009.

[2] W. Shieh, X. Yi and Y. Tang, “Transmission experiment of multi-gigabitcoherent optical OFDM systems over 1000km SSMF fibre,” Electron.Lett., vol. 43, no. 3, pp. 183–184, Feb. 2007.

[3] S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, “Co-herent Optical 25.8-Gb/s OFDM Transmission Over 4160-km SSMF,”J. Lightwave Technol., vol. 26, no. 1 pp. 6–15, Jan. 2008.

[4] E. Ip and J. M. Kahn, “Feedforward Carrier Recovery for Coherent Op-tical Communications,” J. Lightwave Technol., vol. 25, no. 9 pp. 2675–2692, Sep. 2007.

[5] Y. Atzmon and M. Nazarathy, “Laser Phase Noise in Coherent andDifferential Optical Transmission Revisited in the Polar Domain,” J.Lightwave Technol., vol. 27, no. 1 pp. 19–29, Jan. 2009.

[6] A. G. Armada, “Understanding the Effects of Phase Noise in OrthogonalFrequency Division Multiplexing (OFDM),” IEEE Trans. Broadcast.,vol. 47, no. 2, pp. 153–159, Jun. 2001.

[7] T. Schenk, RF Imperfections In High-Rate Wireless Systems, New York:Springer-Verlag, 2008.

[8] Z. Jianhua, H. Rohling, and Z. Ping, “Analysis of ICI CancellationScheme in OFDM Systems With Phase Noise,” IEEE Trans. Broadcast.,vol. 50, no. 2, pp. 97–106, Jun. 2004.

[9] D. Petrovic, W. Rave, and G. Fettweis, “Effects of Phase Noise onOFDM Systems With and Without PLL: Characterization and Com-pensation,” in Proc. 60th IEEE Vehicular Technology Conference, LosAngeles, CA, vol. 3, pp. 2191–2195, Sept. 2004.

[10] X. Yi, W. Shieh, and Y. Tang, “Phase Estimation for Coherent OpticalOFDM,” IEEE Photon. Technol. Lett., vol. 19, no. 12, pp. 919–921, Jun.2007.

[11] S.L. Jansen, I. Morita, T.C.W. Schenk and H. Tanaka, “Long-haultransmission of 16x52.5-Gb/s polarization division multiplexed OFDMenabled by MIMO processing,” OSA J. of Optical Networking, vol. 7,no. 2, pp. 173-182, 2008.

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