Coherent Optical Receiver

K. M. Mehta

Georgia institute of Technology

Abstract: Coherent detection of optical signal has once again gained the attention of researchcommunity because of its high sensitivity and ability to compensate linear transmission impairments.Researchers have demonstrated polarization multiplexed transmission system compatible with 100-Gb/s Ethernet standard with these receiver. This article discusses about basics of coherent receptionand digital signal processing involved.We also various types of receiver architectures and recentdemonstrations/experiments.

1. IntroductionA detection system in which phase coherence of the optical carrier plays an important role iscalled coherent detection system. These systems are well known in the context of radio andmicrowave communication but until recent its use in commercial systems has been hindered bythe additional complexity, due to the need to track the phase and the polarization of the incomingsignal. For optical communication, intensity modulated direct detection(IM/DD) systems remaineddominant in term of commercial deployment. The drive for higher performance and high data ratein optical fiber systems has renewed interest in coherent detection.

Coherent detection has following advantages over direct detection[1][2]:

• Receiver is sensitive to the phase as well as the amplitude of the optical wave, thereforelinear impairments,including chromatic dispersion and polarization-mode dispersion, can becompensated quasi-exactly using electronic filters.

• Higher data rate of the order of 111 Gbps can be achieved exploiting all parameters (inten-sity,angle,polarization) of modulation.

• Coherent detection offers an inherent ultra narrow optical filtering capability useful for densewavelength-division multiplexing

• We can have up to 20 dB improvement in receiver sensitivity when compared with IM/DDsystems.

• Some nonlinear impairments, such as intra-channel four-wave mixing and nonlinear phasenoise, can be compensated partially.

Importance in case of long-haul communication systems: For a long-haul optical fiber systemit is required to transmit the highest data throughput over the longest distance without signalregeneration. Given constraints on the bandwidth imposed by optical amplifiers, it is important tomaximize spectral efficiency. Also given constraints on signal power limited by fiber nonlinearity,we need a power efficient system which minimizes the required average transmitted energy perbit. Coherent detection with polarization multiplexing achieves both goals as in-phase (I) andquadrature-phase (Q) signals in the two orthogonal field polarizations allows information to beencoded in all the available degrees of freedom.

Importance of Digital signal processing: In this paper we will discuss various digital signalprocessing techniques. A DSP-based receiver is highly advantageous because adaptive algo-rithms can be used to compensate time-varying transmission impairments. Advanced forwarderror-correction coding can also be implemented. Moreover, digitized signals can be delayed,split and amplified without degradation in signal quality[3].

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Fig. 1. Schematic of coherent detection scheme

This paper is organized as follows: In Section 2, we review basics of coherent detection andvarious receiver architectures . In Section 3, we discuss about digital signal processing algorithmfor carrier phase recovery, equalization and detection. In Section 4, we discuss various demon-strations and research experiments and finally we conclude the discussion in Section 5.

2. Basics of Coherent detectionThe basic idea behind coherent detection is combining the optical signal coherently with a locallygenerated(with the help of narrow line width laser, called as Local oscillator/LO) optical field beforeit falls on the photo detector.This is shown in Fig. 1.

We use following complex notations to represent optical field associated with signal and localoscillator.As and ALO are also called as low pass equivalent or complex envelopes.

Es = Asexp [−i (ω0t+ φs)] (1)

ELO = ALOexp [−i (ωLOt+ φLO)] (2)

Since a photo detector responds to the optical intensity, the optical power incident at the photodetector is given by:

P = K |Es + ELO|2 (3)

where K is a constant of proportionality. Using (1) , (2) and (3) we get

P (t) = Ps + PLO + 2√PsPLOcos (ωIFt+ φs − φLO) (4)

where

Ps = KA2s, PLO = KA2

LO (5)

and

ωIF = ω0 − ωLO (6)

ωIF is also known as intermediate frequency.There are following two types of coherent receiverbased on value of ωIF :

• Homodyne receiver.• Heterodyne receiver.

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2.1. Homodyne receiverFor Homodyne receiver the local oscillator frequency ωLO is selected to coincide with the signalcarrier frequency ω0 so that ωIF = 0. In this case passband to baseband conversion happens in asingle stage.Photo current of diode, I(I = RP , where R is the detector responsivity) in this caseis given by:

I(t) = R (Ps + PLO) + 2R√PsPLOcos (φs − φLO) (7)

Typically, Ps � PLO and consider the case in which the local-oscillator phase is locked to thesignal phase so thatφs − φLO. The homodyne signal is then given by

I(t) = 2R√PsPLO (8)

The main advantage of homodyne detection can be seen from Eq.(8) If we note that the signalcurrent in the direct-detection case is given by Idd(t) = RPs(t). Denoting the average opticalpower by P̄s, the average electrical power is increased by a factor of 4PLO/Ps with the use ofhomodyne detection. Since PLO can be made much larger than Ps, the power enhancement canexceed 20 dB. Although in this case shot noise is also enhanced, homodyne detection improvesthe signal-to-noise ratio (SNR) by a large factor.

A disadvantage of homodyne detection is its phase sensitivity.In practice, both φs and φLOfluctuate with time in a random manner. However, their difference φs − φLO can be forced toremain nearly constant through an optical phase-locked loop. In addition,exact matching of thetransmitter and local-oscillator frequencies is required.

2.2. Heterodyne receiverIn the case of heterodyne detection the local-oscillator frequency ωLO is chosen to differ form thesignal-carrier frequencyω0 such that the intermediate frequency ωIF is in the microwave region(FIF ∼ 1 GHz).

Photo current in this case is given by:

I(t) = R (Ps + PLO) + 2R√PsPLOcos (ωIFt+ φs − φLO) (9)

Since PLO � Ps in practice, the direct-current (DC) term is nearly constant and can be removedeasily using bandpass filters. The heterodyne signal is then given by the following alternating-current (ac) term:

Iac(t) = 2R√PsPLOcos (ωIFt+ φs − φLO) (10)

Similar to the case of homodyne detection, the local oscillator amplifies the received signal by alarge factor, thereby improving the SNR. However, the SNR improvement is lower by a factor of 2(or by 3 dB) compared with the homodyne case. This reduction is called as “heterodyne detectionpenalty”. Because of the ac nature of Iac, the average signal power is reduced by a factor of 2when I2ac is averaged over a full cycle at the intermediate frequency.

The advantage gained at the expense of the 3-dB penalty is that the receiver design is consid-erably simplified and the line width requirements are quite moderate. These features makes theheterodyne detection scheme quite suitable for practical implementation.

2.3. SNR performanceNow we will calculate SNR of the receiver current which will quantify advantage of coherentreception.The receiver current fluctuates because of shot noise and thermal noise. Total varianceσ2 of current fluctuations is obtained by adding the two contributions. Thus,

σ2 = σ2s + σ2

T (11)

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where,

σ2s = 2q (I + Id) ∆f, σ2

s = (4KBT/RL)FN∆f (12)

Here, I = resultant photo current,Id = Dark current,∆f= electrical bandwidth of receiver, KB

= Boltzman’s constant,T = temperature in Kelvin,RL input resistance of the receiver and FN isnoise figure of the receiver. Thus SNR in case of heterodyne receiver is given by:

SNR =

⟨I2ac⟩

σ2=

2R2P̄sPLO

2q (RPLO + Id) ∆f + σ2T

(13)

where R is responsivity of the photo detector.The above equation assumes PLO � Ps, moreoverPLO can be made large enough such that the receiver noise is dominated by shot noise.In thiscondition dark current contribution can be assumed to be negligible.Thus final equation for SNRis given by:

SNR ≈ RP̄s

q∆f(14)

The use of coherent detection allows one to achieve the ‘‘shot-noise limit” even for PIN receiverswhose performance is generally limited by thermal noise. Moreover, in the case of avalanche photodiode (APD) receivers, this limit is realized without adding any excess shot noise.

2.4. Modulation formatsIn single-mode optical fibers, the optical field has three physical attributes that can be used tocarry information: Intensity,Phase (including frequency),Polarization.

Depending on which of the three quantities is used for information transport, coherent re-ceiver has different architecture.Intensity and phase modulation formats have been widely usedin RF/optical communications. Encoding information onto the polarization of light (Pol-SK) is veryspecial type of modulation scheme in optical communication.It has advantage of increase spectralefficiency but it requires an active polarization management at the receiver, because of randompolarization changes in optical fiber. Two different schemes used with polarization are:

1) Polarization-multiplexing: transmitting two different signals at the same wavelength but intwo orthogonal polarizations,

2) Polarization-interleaving: transmitting adjacent WDM channels in alternating polarizations toreduce coherent WDM crosstalk or nonlinear interactions between the channels.

Using all the three attributes for modulation significantly reduces symbol rate/ baud rate.Popular modulation schemes used with coherent receiver are:

• Binary Differential Phase Shift Keying (DPSK)• Differential Quadrature Phase Shift Keying (DQPSK): RZ or NRZ, Pol-Mux or single polar-

ization.

2.5. Sensitivity degradation of coherent receiverThere are various sources which contribute to sensitivity degradation of coherent receiver. Letus discuss them one by one. An important source of sensitivity degradation is the phase noiseassociated with the transmitter laser and the local oscillator.A receiver design approach whichsolves the phase-noise problem by designing special receivers having two or more photo detectorswhose outputs are combined to produce a signal that is independent of the phase differenceφIF = φs − φLO known as “phase-diversity” receivers.

Relative intensity noise (RIN) of the local oscillator is another source of sensitivity degradation.Asolution to the intensity-noise problem is offered by the “balanced coherent” receiver made withtwo photo detectors.

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Fig. 2. Schematic of Phase diversity balanced detection

polarization-mismatch is the third major contributor.Several schemes have been developedfor solving the polarization-mismatch problem.The most commonly used approach solves thepolarization problems by using a two-branch receiver with the difference that the two branchesprocess orthogonal polarization components. Such receivers are called ‘‘polarization-diversityreceivers”.The technique of polarization diversity can be combined with phase diversity to realizea receiver that is independent of both phase and polarization fluctuations of the signal received.Let us discuss these receiver architectures in detail:

2.5.1. Phase-diversity balanced receiverFig. 2 shows the configuration of a phase-diversity coherent receiver.The optical signal is mixedwith local oscillator light in a 90◦ hybrid. The local oscillator path is longer by a quarter cycle(90◦)in the lower arm than the upper arm, which means that the balanced photo detector in the upperarm effectively sees an in-phase beat product while the one in the lower arm sees a quadraturebeat product.The photo detectors at the outputs of the 90◦ hybrid each see the signal and LOadding as electric field. The powers at the two balanced outputs of the upper arm are

P1a(t) = |As(t)|2 + |ALO(t)|2 + 2Re{As(t)A?LO(t)exp (iωIFt+ iφs − iφLO)} (15)

P1b(t) = |As(t)|2 + |ALO(t)|2 − 2Re{As(t)A?LO(t)exp (iωIFt+ iφs − iφLO)} (16)

and the balanced photo detector output is, therefore, proportional to

∆P1(t) = P1a(t)− P1b(t) ≈ 4Re{As(t)A?LO(t)exp (iωIFt+ iφs − iφLO)} (17)

The DC term is eliminated completely during the subtraction process when the two branchesare balanced (each branch receives equal signal and local-oscillator powers). More importantly,the intensity noise associated with the DC term is also eliminated during the subtraction processsince intensity fluctuations in the two branches are perfectly correlated and cancel out. The quarterwave shift in LO path of the lower arm of the 90◦ hybrid means that the balanced photo detectorin the lower arm responds to

∆P2(t) = 4Re{−iAs(t)A?LO(t)exp (iωIFt+ iφs − iφLO)} (18)

∆P2(t) = 4Im{As(t)A?LO(t)exp (iωIFt+ iφs − iφLO)} (19)

Hence, the electric field envelope of the signal can be obtained by:

As(t) =

(exp (−iωIFt− iφs + iφLO)

4A?LO

)(∆P1(t) + i∆P2(t)) (20)

The frequency difference and phase difference must be estimated from ∆P1 and ∆P2 to deduceAs

, which would be discussed in the later part of the paper.

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Fig. 3. Schematic of Pol-Mux QPSK receiver

Fig. 4. Typical Digital signal processing blocks

2.5.2. Pol-Muxed QPSK receiverFig. 3 shows a typical architecture of Pol-mux QPSK receiver.The receiver composes of a po-larization beam splitter (PBS), two 90◦ hybrids and 4 detectors. Note that this receiver doesnot use balanced detectors to reduce the associated cost. We can write similar expressionsfor outputs xi,xq,yi,yq as we had derived in the previous case, where X and Y represents twostates of polarization.The input polarization state of the received signal is not controlled, and anarbitrary mix of each transmitted polarization state is incident on the photo detectors whereaspolarization controllers are required for the LO.Main advantage of this type of receiver is thatwe are able to recover information from in-phase and quadrature phase components of bothorthogonal polarization. Thus, xi,xq,yi,yq have complete information of the incoming signal.

3. Digital signal processing and electronic equalizationThe output signals from optoelectronic converter is filtered and then simultaneously sampled.Thesampling can be synchronous or asynchronous.When the signal envelope is modulated in thereturn-to-zero (RZ) waveform, the intensity of RZ pulses can be used as the sampling clock forsynchronous sampling. For asynchronous sampling, the signal must be sampled at 1.5 to 2 timesthe symbol rate (‘‘Nyquist rate”) and then re-sampled to keep one sample per symbol. Samplingbecomes challenging when symbol rates are of the order of tens of MHz. Such a receiver requirevery high speed analog-to-digital converters (ADCs). The sampled signals xi(n),xq(n),yi(n),yq(n),where n denotes the number of the sample, are then processed with DSP circuits.Typical DSPblocks are shown in Fig. 4. As the digitized waveform retains full information of the electric field, itenables us to compensate for linear and nonlinear transmission impairments. We will now discusseach of these blocks in detail:

3.1. Clock recovery and re-timingThis is an important signal processing block in case of asynchronous sampling, which enablesus to achieve symbol period synchronization. One of the methods of clock recovery is to usepower envelope of the received signal. The power envelopeP is calculated from the square of

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the received signal components(P = x2i + x2q + y2i , y

2q

). The incoming signal is divided in blocks

of length M and the power signal for the mth block is then filtered to get sampling phase error.The sampling phase error is then used to resample the data using an interpolator.

3.2. EqualizationElectronic equalization is used to compensate for linear transmission impairments and recoverthe polarization multiplexed data. This usually involves a filtering operation[4]. Equalization canbe partitioned into two distinct stages.

• Chromatic Dispersion compensation• Polarization dependent impairment (Polarization rotation and PMD)compensation

3.2.1. Chromatic dispersion compensationNow we will discuss design of a typical dispersion compensating filter[5]. In absence of fibernonlinearity, chromatic dispersion of the envelope of a pulse may be modeled as,

∂A(z, t)

∂z= j

Dλ2

4πc

∂2A(z, t)

∂t2(21)

where z is distance of propagation, A(z, t) is complex envelope of the optical signal,λ iswavelength and D is dispersion coefficient. Taking Fourier transform and solving for A(z, ω) weget,

A(z, ω) = A(0, ω)exp

(−jDλ2

4πcω2z

)(22)

This can be viewed as LTI system with frequency response of

H(z, ω) = exp

(−jDλ2

4πcω2z

)(23)

and thus frequency response of dispersion compensating filter is given byHc(z, ω) = 1/H(z, ω).Sucha filter can be implemented using FIR or IIR system(as in case of [6]). Let us discuss design ofFIR filter. Time domain impulse response of Hc(z, ω) is given by:

hc(z, t) =

√jc

Dλ2zexp

(−jπct2

Dλ2z

)(24)

It can be seen that this impulse response is of infinite duration, non-causal and since it passes allfrequencies, for a finite sampling frequency aliasing will occur.By truncating this to finite length byusing a Kaizer window we can solve these problems. Length of the window(which is proportionalto N taps of an FIR filter) can be calculated using following criterion as specified in [5]

−Dλ2z

2cTs≤ t ≤ Dλ2z

2cTs(25)

where Ts is sampling interval.Filter coefficients of N tap FIR filter are given by

ak =

√jcT 2

s

Dλ2zexp

(−j πcT

2s

Dλ2zk2)

(26)

where

−⌊N

2

⌋≤ k ≤

⌊N

2

⌋and N = 2

⌊Dλ2z

2cT 2s

⌋+ 1 (27)

This filter can be implemented in FPGA using shift registers or with FFT algorithm.

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3.2.2. Polarization dependent impairment compensationThese impairments are usually modeled as ‘‘Jones matrix”.The Jones matrices are the operatorsthat act on the Jones Vectors,which describes the polarization of light.[7] In general, this matrixis not unitary and will be frequency dependent.Unlike chromatic dispersion this impairment is notconstant and may vary rapidly with time, thus requiring adaptive computations.This equalizationcan be achieved by implementing a Butterfly structure filter for MIMO system. Assume xp and ypare two input streams in two orthogonal polarization and x′ and y′ are output of the module.Theyare related by following system of equations:

x′(k) = HTxxXp +HT

xyYp =

M−1∑m=0

hxx(m)xp(k −m) + hxy(m)yp(k −m) (28)

and

y′(k) = HTyxXp +HT

yyYp =

M−1∑m=0

hyx(m)xp(k −m) + hyy(m)yp(k −m) (29)

where hxx,hxy,hyx,hyy are all adaptive filters of length M .Various methods have been suggestedfor calculating coefficients of these filters but we will look into ‘‘Constant Modulus Algorithm”(CMA)suggested by Dominique[8].This algorithm exploits the constant modulus property of QPSK mod-ulated signal. Let us assume unit amplitude of the modulated signal.The equalizer will try tominimize mean square error εx and εy given by:

εx = 1− |x′|2 and εy = 1− |y′|2 (30)

giving following four criterion:

d⟨ε2x⟩

dHxx= 0 ,

d⟨ε2x⟩

dHxy= 0 ,

d⟨ε2y⟩

dHyx= 0 ,

d⟨ε2y⟩

dHyy= 0 (31)

To determine optimum tap weights stochastic gradient algorithm is used.In the initialization stageall tap weights are set to zero with the exception of central tap of hxx and hyy. Once the equalizerhas converged it moves to decision directed mode using DD-LMS algorithm. The filter coefficientsare now adapted as:

Hxx → Hxx −µ

2

d |εx|2

dHxx= Hxx + µεxx̄p (32)

where x̄p is complex conjugate of xp and µ is a convergence parameter. and εx = dx − x′ withdx being the symbol closest to x′. Similarly filter coefficients of Hxy,Hyx,Hyy are calculated onthe fly.

3.3. Carrier recovery/Phase estimationThere are various phase estimation algorithm studied and experimented[9]. Here is a list of fewof them:

• MAP(Maximum a posteriori) phase estimator.• Decision directed phase estimator.• Power law- average phase estimator

We will discuss power law -average phase estimator(’’Viterbi-and-Viterbi”) in detail[10]. Sincethe line-width of lasers used as the transmitter and LO typically ranges from 100 kHz to 10 MHz,assuming a homodyne receiver, the optical carrier phase φn(t) = φs(t)− φLO varies much moreslowly than the phase modulation, whose symbol rate is in order of tens of Gsymbol/s.Therefore, byaveraging the carrier phase over many symbol intervals, it is possible to obtain an accurate phase

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Fig. 5. Phase estimator

Fig. 6. Architecture of a processing unit of phase estimator

estimate, as shown in the following. Coherent detection using such a method for carrier phaseestimation will offer significant improvement in BER performance over differential detection[11].

The equalized signal samples(x′(n) = Equalized (xi + jxq)) and (y′(n) = Equalized (yi + jyq))in both the polarization are processed with the DSP circuit shown in Fig. 5.Let us call x′(n) ory′(n) by E(n) for explaining the algorithm. The processing module consists of a demultiplexingunit, several processing units (PUs) that estimate the phase offset, and a remultiplexing unit. Thestream of E(n) are demultiplexed into M blocks of N complex samples (as shown in Fig. 5)before being sent to the PUs.When ASE noise is the dominant noise N should be as large aspossible. The core processing functions residing in the PUs can demodulate the data in paralleland independently from each other, which allows this architecture to support high symbol rates.

A schematic of a PU is shown in Fig. 6.E(i)(i = 1, ..., N) to the fourth power cancels theQPSK phase modulation θs(= 0, π/2, π, π/2), sinceE4 ∝ exp[j(4θs)]. The complex amplitudes E4

are summed, so that the phase is averaged over the entire block. The phase of the resultingcomplex amplitude is divided by 4, leading to a phase correction for the kth block θ′(k) that liesbetween π/4 and π/4. The phase correction θ′(k) is, thus, given as

θ′(k) =1

4arg

[N∑i=1

E4(kN + i)

](33)

This phase error can be subtracted form each symbol of the block to get modulated symbolback.It may be noted that differential phase encoding solves the problem of phase ambiguity asin this case absolute phase is not relevant and the information is encoded in phase difference oftwo consecutive symbols.

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3.4. Slicer and Decoder UnitIt consists a of a slicer (threshold decoder) and digital decision logic which maps the receivedsymbols onto binary 1 and 0. This block will perform differential decoding if transmitted signal isdifferentially encoded.

4. Demonstrations and conclusionRecently, many researchers have shown long-haul (upto 2375km) transmission using a coherentreceiver with data rates of the order of 111 Gbit/s.[12] It is also possibility of use existing in-frastructure designed for 10 Gbps system for 100 Gbps transmission. 2 Tbits/s DWDM transmis-sion has also been demonstrated. Penalty free compensation of chromatic dispersion and otherimpairments have open up the possibility of employing such systems cost effectively[3].Nortelhas introduced commercially available 100G solution, already deployed and carrying in-servicecustomer traffic in Verizons European network.Alcatel Lucent and Kazakh telecom have alsodemonstrated 100Gbps transmission trial over the existing fiber optic network. Various vendorshave started investing in design and manufacturing of 100 G components.Thus a coherent receiveralong with digital signal processing can be seen as the system for future long-haul communication.

References[1] G. P. Agrawal, Fiber-Optic Communications Systems, Third Edition. John Wiley and Sons, 2002.[2] D. J. F. B. J. M. K. Ezra Ip, Alan Pak Tao Lau, “Coherent detection in optical fiber systems,” Optical express, vol. 16,

no. 2, 2008.[3] M. G. Taylor, “Coherent detection method using dsp for demodulation of signal and subsequent equalization of

propagation impairments,” IEEE Photonics Technology Letters., vol. 16, no. 2, pp. 674–676, 2004.[4] R. I. K. P. B. Seb J. Savory, Giancarlo Gavioli, “Electronic compensation of chromatic dispersion using a digital

coherent receiver,” Optical express, vol. 15, no. 5, 2007.[5] S. J. Savoryl, “Digital filters for coherent optical receivers,” Optical express, vol. 16, no. 2, 2008.[6] G. Goldfarb and G. Li, “Chromatic dispersion compensation using digital iir filtering with coherent detection,” IEEE

Photonics Technology letters, vol. 19, no. 13, pp. 969–971, 2007.[7] Jones calculus. http://en.wikipedia.org/wiki/Jones calculus.[8] D. N. Gorald, “Self-recovering equalization and carrier tracking in two-dimensional data communication system,” IEEE

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Lightwave Technology, vol. 27, no. 7, pp. 901–914, 2009.[10] S. T. Kazuro Kikuchi, Dany-Sebastien Ly-Gagnon and K. Katoh, “Coherent detection of optical quadrature phase-shift

keying signals with carrier phase estimation,” Journal of Lightwave Technology, vol. 24, no. 1, pp. 12–21, 2006.[11] K. K. Dany-Sebastien Ly-Gagnon and K. Kikuchi, “Unrepeated optical transmission of 2o=gbit/s quadrature phase-

shift keying signal over 210-km transmission using homodyne phase-diversity receiver and digital signal processing,”Electronic letters, vol. 41, no. 4, 2005.

[12] C. R. S. F. et al., “Coherent equalization and plomux-rz-dqpsk for robust 100-ge transmission,” Journal of LightwaveTechnology, vol. 26, no. 1, pp. 64–71, 2008.

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