Efficient Frequency-Domain Fractionally-Spaced Equalizer forFlexible Digital Coherent Optical Receivers

Fabio Pittala(1,2) and Josef A. Nossek(2)

(1) European Research Center, Huawei Technologies Dusseldorf GmbH, Riesstrasse 25, D-80992 Mu-nich, Germany, fabio.pittala@huawei.com;(2) Institute for Circuit Theory and Signal Processing, Technische Universitat Munchen, Arcisstrasse 21,D-80290 Munich, Germany.

Abstract Training-aided frequency-domain equalization for coherent receivers based on digital-signal-processing with oversampling factor below 2 samples-per-symbol (sps) is reported. The proposed ar-chitecture shows no performance degradation by reducing the oversampling factor from 2 to 1.25 sps.

Introduction

Coherent detection in combination with digital-signal-processing (DSP) has become a maturetechnology for optical transport networks. Afterthe commercialization of the coherent 100 Gbpstransponders the focus of the industry has movedto higher-capacity (i.e. 400 Gbps and beyond)and flexible-transponders which allow to trade ca-pacity with reach1. Such features, unfortunately,come at the cost of higher power consumption.

Indeed, high-capacity systems require high-speed and high-bandwidth power-hungry hard-ware and, in addition, flexible-transponders re-quire complex DSP coping with different modula-tion formats. Focusing on the DSP of the coherentreceiver, it has been shown in2 that a high por-tion of the processing power on the application-specific integrated circuit (ASIC) chip is con-sumed by the equalizer required to compensatefor chromatic dispersion (CD) and polarization-mode dispersion (PMD). Power-efficient DSPwhich allows flexible-transponders has been re-cently reported3,4. However, a further stepis needed in DSP research to relax the re-quirements on the hardware. In fact, the low-power variant of next generation digital-to-analogconverter (DAC) and analog-to-digital converter(ADC) using 14 nm processes offer the possibil-ity to have high electrical bandwidth at the cost ofreduced sampling speed. So that DSP working atlower than 2 samples-per-symbol (sps) might bea must for future transponders.

In this paper, we present a training-aidedfrequency-domain equalizer which allows ADCworking at sampling rate lower than the Nyquistrate. Performance evaluation is based on Nyquistcoherent optical transmission systems employingpolarization-division multiplexed (PDM) quadra-

ture phase-shift keying (QPSK) and 16-aryquadrature-amplitude modulation (16QAM) for-mats, as well as two popular 4D modulationformats based on set-partitioning (SP)1, 32SP-16QAM and 128SP-16QAM.

Frequency-Domain Fractionally-SpacedEqualizer ArchitectureThe proposed DSP architecture is shown in Fig.1. The equalizer presented in this paper extendsthe work recently reported in3 where the single-stage (SS) frequency-domain equalizer (FDE)with blind CD estimation and training-aided 2 ×2 multi-input multi-output (MIMO) channel esti-mation has been experimentally demonstrated.Respect to the architecture in3, the novel equal-izer allows a variable length of the fast-Fouriertransform (FFT) and a flexible FD decimation inthe data path, thanks to a different 2 × 2 MIMOchannel estimation.

Equalization in FD is performed by transferring50% overlapping blocks of the serial data into theFD by discrete FFT of size χM points, where χ isthe oversampling factor of the digitized receiveddata and M is the length of the FFT assumingsymbol spaced sampling. After applying the com-pensating function to each block, the signal is χ-fold decimated and then transferred back into thetime-domain (TD) by discrete inverse-FFT (IFFT)

CD

-FD

E

50%

-OS

/ χM-F

FT

Decisio

n

NTA-CD

Estimation

CD Filter

Update

Buffer (o

ptio

nal)

2×2 MIMO

TA-Channel

Estimation

χ-Fold

Decim

ation

50%

-OS

/ M-IF

FT

2×2

MIM

O

FDE

rx[n]

ry[n]

2×

2 M

IMO

FD

E

2×2 MIMO

TA-Channel

Estimation

and

Equalizer-tap

CalculationBlind CD

Estimation

Rx[n]

Ry[n]

Fig. 1: Single-stage FDE.

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z

Tim

e-Dom

ain W

indow

ing

and Z

ero P

addin

g

Av

eragin

g o

ver M

/N

CA

ZA

C seq

uen

ces

Zero

Pad

din

g

(Nyquist S

pectru

m)

Spectrum of Reference

CAZAC Sequence

(2-fold oversampled)

2N

-IFF

T

xx

xx

x

xx

xx

x

2M

-FF

T

2/χ -F

old

Decim

ation

Filter-tap

Calcu

lation

Wyx[n]

Wyy[n]

Wxx[n]

Wxy[n]

Rx[n]

Ry[n]

Fig. 2: Detailed structure of the 2× 2 MIMO channel estimation and equalizer-tap calculation.

of length M points. The overlap is finally cut off torestore the serial data stream (overlap-save (OS)method). The compensation is applied with a two-tap per sub-band equalizer, where the first tapis dedicated for CD compensation and the sec-ond tap for PMD compensation. The length M ofthe equalizer is chosen accordingly with the maxi-mum CD expected at the point of estimation. Notethat a tap of the CD compensation refers to onecomplex coefficient while a tap of the PMD com-pensation consists of four complex coefficients.The buffer is an optional module which can beused to compensate for the 2 × 2 MIMO channelestimation and filter-update processing-delay. CDestimation can be performed either in TD or in FDas in5,6. The last DSP module makes bit decisionand bit-error counting.

The novel 2 × 2 MIMO channel estimation isillustrated in Fig. 2. The channel is acquiredbased on M/N consecutive constant-amplitudezero auto-correlation (CAZAC) sequences, whereN ≤ M is the length of the CAZAC code in sym-bols4. Based on the spectral properties of a re-peated sequence, averaging of the M/N CAZACcodes is performed by retaining every M/N spec-tral component and discarding the other fre-quency components containing only noise. Theobtained spectra (x- and y-polarization) are thenextended to a length of 2N spectral componentsby zero padding. At this point, it should be notedthat the reference CAZAC sequences used for2×2 MIMO channel estimation at the receiver are2-fold oversampled and consist of RZ50 pulsesindependently of the pulse shaping used at thetransmitter. This choice has been made to pre-serve the constant amplitude and zero-circularauto-correlation properties of the original CAZACcode. The channel is acquired by a multiplicationper sub-band between the received spectra andthe conjugate spectra of the reference CAZAC

sequences4. Such operation is not needed atthe frequencies where the spectra contain zeros.The obtained channel elements are then trans-ferred into the TD by discrete IFFT such to ex-tract the four channel impulse responses (CIR) ofthe 2 × 2 MIMO channel. This operation is per-formed by a rectangular time domain windowingfunction of length NTDW symbols. The four CIRare zero padded such that the length of each vec-tor is 2M points. Following, the four channel ele-ments are transferred into the FD by discrete FFTand χ-fold downsampled in order to finally matchthe length of the equalizer χM taps. The tapsof the equalizer can be calculated by using theminimum-mean-square-error, the zero-forcing ormatched filter criteria. Depending on the criterionemployed a different equalizer-tap solution mightbe obtained for every χ value.

Performance EvaluationThe performance evaluation is based on sim-ulated 28-GBaud PDM-QPSK, 32SP-16QAM,128SP-16QAM and PDM-16QAM coherent opti-cal systems transmitting Nyquist shaped pulses(roll-off factor α = 0.1). Simulations of the lin-ear channel include CD, first-order PMD referredalso as differential group delay (DGD), polariza-tion rotation angle and polarization phase. Addi-tive white-Gaussian noise (AWGN) is loaded ontothe signal before an optical Gaussian band-passfilter (2nd-order, double-sided 35-GHz) and anelectrical Bessel filter (5th-order, 19-GHz) whichdefines the opto-electronic front-end of the coher-ent receiver. An ADC digitizes the received signalat χ sps with χ ∈ {1.25, 1.5, 1.75, 2} sps. The χ-fold oversampled signal is then processed by theequalizer architecture illustrated in Fig. 1.

The parameter M is set to 256 symbols. CDestimation is performed blindly in FD as proposedin5. The 2×2 MIMO channel is estimated by using

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CD [ps/nm]

ROSNR

(0.1nm)@

BER=10−3

14

16

18

20

22

24

26

28

0 5000 10000 15000 20000 25000 30000

1 0 25 50 75 100 125 150 175 200 225

mCD [Symbols]

PDM-QPSK

32SP-16QAM

128SP-16QAM

PDM-16QAM

2 sps

1.75 sps

1.5 sps

1.25 sps

(a) CD Tolerance

DGD [ps]

ROSNR

(0.1nm)@

BER=10−3

14

16

18

20

22

24

26

28

0 100 200 300 400 500 600

1 0 2 4 6 8 10 12 14 16

mDGD [Symbols]

PDM-QPSK

32SP-16QAM

128SP-16QAM

PDM-16QAM

2 sps

1.75 sps

1.5 sps

1.25 sps

(b) DGD ToleranceFig. 3: SS-FDE: performance evaluation.

4 consecutive CAZAC sequences of length N =

64 symbols with guard interval of length NGI = 8

symbols. The TDW is set to be NTDW = 16 sym-bols. The k = 1, 2, ..., 256χ taps dedicated forCD compensation are calculated as WCD(ωk) =

H∗CD(ωk), where HCD(ωk) is the transfer func-

tion of the CD and (·)∗ denotes the complex-conjugate operation. The k = 1, 2, ..., 256χ tapsof 2 × 2 MIMO equalizer part are calculated by amatched filter defined as W(ωk) = HH(ωk)

Θ(ωk) , whereH(ωk) is the estimated 2×2 MIMO channel, Θ(ωk)

serves as a noise-whitening filter (NWF) and (·)Hdenotes the complex-conjugate transpose opera-tion. The NWF is calculated as a Frobenius normof the 2×2 channel matrix H(ωk). These matchedfilter solutions are valid for any χ4.

Fig. 3 present the SS-FDE tolerance with re-gard to CD (Fig. 3a) and DGD (Fig. 3b), respec-tively. The required optical-to-signal-noise-ratio(ROSNR) at bit-error-rate (BER) = 10−3 is plot-ted as function of the impairment under consider-ation and as function of the channel memory mCh

defined in terms of adjacent symbols over whicha transmitted pulse spreads due to the influenceof the channel. Assuming that CD and DGDare the major players for inter-symbol interference(ISI) in an optical transmission system: mCh =

mCD +mDGD, where mCD = D ·∆ω ·Bs · λc2

c andmDGD = τ · Bs, where D is the accumulated CD,∆ω is the signal bandwidth, Bs is the signal bau-drate, λc = 1550 nm is the carrier wavelength, c isthe speed of light in vacuum and τ is the DGD.

Results show that for the PDM-QPSK system,20000 ps/nm of CD and 440 ps of DGD canbe compensated without OSNR penalty with re-spect to the back-to-back (B2B) case. Suchtolerances are progressively reduced for 32SP-16QAM, 128SP-16QAM and PDM-16QAM, re-spectively, due to the higher noise sensitivity. As

observed from the channel memory tolerance,these curves are strictly dependent on the param-eter M , N , NGI , NTDW and on the pulse shap-ing4. However, here it is important to note that forNyquist systems with α = 0.1 no OSNR penaltyis observed when the oversampling factor χ is re-duced from 2 sps to 1.25 sps. For α > 0.1, dueto aliasing, the oversampling factor χ needs to beincreased to values larger than 1.25 sps.

ConclusionsSingle-stage frequency-domain equalization fordata oversampled below 2 sps has been demon-strated in PDM-QPSK, 32SP-16QAM, 128SP-16QAM and PDM-16QAM Nyquist systems. Forroll-off factor equal to 0.1, no BER performancedegradation has been observed for oversamplingdown to 1.25 sps. The proposed equalizer ar-chitecture is suitable for next generation high-capacity and flexible-transponders.

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