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JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 31, NO. 7, APRIL 1, 2013 999

High Spectral Efficiency 400 Gb/s TransmissionUsing PDM Time-Domain Hybrid 3264 QAM

and Training-Assisted Carrier RecoveryXiang Zhou, Senior Member, IEEE, Lynn E. Nelson, Peter Magill, Rejoy Isaac, Benyuan Zhu, David W. Peckham,

Peter I. Borel, and Kenneth Carlson

AbstractWe report the successful transmission of ten494.85 Gbit/s DWDM signals on the standard 50 GHz ITU-Tgrid over 32 100 km of ultra-large-area (ULA) fiber. A net spec-

tral efficiency (SE) of 8.25 b/s/Hz was achieved, after excludingthe 20% soft-decision forward-error-correction (FEC) overhead.Such a result was accomplished by the use of a recently proposedpolarization-division-multiplexed (PDM) time-domain hybrid3264 quadrature-amplitude-modulation (QAM) format, along

with improved carrier frequency and phase recovery algorithms.It is shown that time-domain hybrid QAM provides a new degreeof design freedom to optimize the transmission performanceby fine tuning the SE of the modulation format for a specificchannel bandwidth and FEC redundancy requirement. In termsof carrier recovery, we demonstrate that 1) hardware efficient

estimation and tracking of the frequency offset between the signaland local-oscillator (LO) can be achieved by using a new feed-back-based method, and 2) a training-assisted two-stage phaseestimation algorithm effectively mitigates cyclic phase slippingproblems. This new phase recovery algorithm not only improvesthe receiver sensitivity by eliminating the need for differential

coding and decoding, but also enables an additional equalizationstage following the phase recovery. We have shown that the intro-duction of this additional equalization stage (with larger number

of taps) helps reduce the implementation penalty. This paper alsopresents the first experimental study of the impact of inphase (I)and quadrature (Q) correlation for a high-order QAM. It is shown

that an adaptive equalizer could exploit the correlation betweenI and Q signal components to artificially boost the performanceby up to 0.7 dB for a PDM time-domain hybrid 3264 QAMsignal when the equalizer length is significantly longer than I/Q

de-correlation delay.

Index TermsCoherent, equalization, fiber, frequency recovery,hybrid QAM, modulation format, optical transmission, phase re-covery, QAM, spectral efficiency.

Manuscript received July 27, 2011; revised September 14, 2012; acceptedOctober 11, 2012. Date of publication January 28, 2013; date of current versionFebruary 06, 2013. This paper should have appeared as part of the Special Issueon Optical Fiber Communications/National Fiber Optics Engineers Conference2012, Vol. 31, No. 4, February 15, 2013.

X. Zhou, L. E. Nelson, P. Magill, andR. Issac arewith AT&T Labs-Research,Middletown, NJ 07748 USA (e-mail: [email protected]).

B. Zhu is with OFS Labs, Somerset, NJ 08873 USA.D. W. Peckham is with OFS, Norcross, GA 30071 USA.P. I. Borel and K. Carlson are with OFS, Broendby 2605, Denmark.Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JLT.2013.2243643

I. INTRODUCTION

F ROM a historical point of view, lowering the cost pertransmitted bit is the main driving force for the transportinterface rate evolution, which was achieved by increasing

both the per-channel data rate and the spectral efficiency(SE). So far, the continuing advancement in transport tech-nology has enabled operation at 10 Gb/s, 40 Gb/s, and 100

Gb/s rates within the same optical networks based on the 50GHz-grid. Such a proportional increase of transport interface

rate and SE has brought significant cost saving by reducing the

transponder foot-print and power consumption and by sharingmore capacity over the common network infrastructure. For the

next-generation transport system, it would therefore be very

attractive to continue to follow this path, i.e. to transmit the 400Gb/s signals on the standard 50 GHz ITU-T grid, achieving a

SE as high as 8 b/s/Hz. Such a high-SE transport system could

be compatible with current reconfigurable optical add/dropmultiplexer (ROADM) based networks, while providing a

four-fold increase in the transport capacity.400 Gb/s transmission has been experimentally explored

by using various high-order quadrature amplitude modulation

(QAM) formats combined with different multiplexing schemes,such as orthogonal frequency division multiplexing (OFDM)

[1], [2], optical TDM [3], electrical TDM [4], and single-carrierfrequency-division-multiplexing (SC-FDM, a Nyquist-shapedsingle-carrier signal) with digital pilot tone [5]. Several of thesefirst demonstrations [1][4] reported long-haul transmissionreaches of 800 to 2000 km, yet the experiments used 50

GHz WDM channel spacing, which is sub-optimal in terms ofmaximizing the SE and/or allowing a smooth path for evolvingan existing lower-rate system based on the 50 GHz grid.

Experimental demonstration of 400 Gb/s transmission on the

50 GHz WDM grid was first achieved in [6] by using coherentOFDM-32 QAM with 80 km transmission reach. The first 400

Gb/s transmission over a 50 GHz-based system with a ROADMwas reported in [7]. In that experiment, 8 450 Gb/s polar-

ization-division-multiplexed (PDM) Nyquist-shaped 32 QAM

signals were transmitted over 4 100 km of ultra-large area(ULA) fiber and also passed through one standard 50 GHz-grid

ROADM. In [8], the transmission distance was improved to 800

km by using a broadband optical spectral shaping techniqueto counteract the ROADM filtering effects. Most recently, the

transmission distance has been extended to 1200 km by using a

hybrid 3264 QAM technique [9].In this paper, we report that a 400 Gb/s-class signal on the

standard 50 GHz ITU-T grid can be transmitted over more than

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1000 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 31, NO. 7, APRIL 1, 2013

Fig. 1. Effective channel bandwidthversus modulation SE at several FECcoderates for a 400 GigE system.

3000 km of ULA fiber by using time-domain hybrid 3264QAM combined with cascaded two-stage equalization and im-

proved carrier frequency and phase recovery algorithms. Thispaper also intends to correct a mistake made in our previouspaper [10], where the transmission distance was over-estimated

by about 1 dB due to the use of an adaptive equalizer with athird-stage length greater than both the de-correlation delaysbetween the inphase (I) and quadrature (Q) components and be-

tween the X and Y-polarizations. By using independent I/Q datasequences and increasing the X- and Y-polarization de-correla-tion delay, we verifiedthat the artificial performance gain in [10]

mainly arose from the I/Q correlation. Such an I/Q correlationproblem may also plague some earlier few-mode fiber trans-

mission experiments, where the multiple-input-multiple-output(MIMO) equalizer length was greater than I/Q de-correlationlength.

The remainder of this paper is organized as follows. In Sec-tion II we describe the concept of time-domain hybrid QAM.

Section III is devoted to the experimental setup and the dig-ital signal processing (DSP) algorithms. The measured resultsare presented in Section IV. Experimental investigation of I/Q

correlation on the coherent receiver performance is reported inSection V. Finally we summarize this paper in Section VI.

II. CONCEPT OF TIME-DOMAIN HYBRID QAM

Higher-order QAM formats such as 16 QAM, 32 QAMand 64 QAM (combined with polarization multiplexing) haverecently been experimentally explored to achieve WDM SEsgreater than 2 b/s/Hz for WDM systems at 100 G and higherrates [1][8]. However, these regular -ary QAM systemsmay not be optimal for a 400 Gb/s system on a 50 GHz grid.

In Fig. 1 we show the effective required channel bandwidthfor regular -ary QAM formats at several different FEC coderates for a 400 GigE system (net data bytaking into consideration the 66 b/64 b Ethernet line code).Here the effective channel bandwidth assumes ideal Nyquistsignaling with no filtering penalty or inter-symbol interference(ISI). One can see that regular PDM-16 QAM, PDM-32 QAM,and PDM-64 QAM (with 8, 10, and 12 bits/symbol, respec-tively) allow only certain effective channel bandwidths for aspecific FEC code rate.

Arbitrary SE can be realized by using a recently proposedtime-domain hybrid QAM technique [9][11]. For this tech-nique, two regular -ary QAMs with different SE (in termsof bit/symbol) are assigned to different time slots within eachTDM frame. Using this method, any SE that falls between the

Fig. 2. A time-domain hybrid 3264 QAM with .

SE of the two regular QAMs can be realized easily by appro-priately designing the TDM frame length and the time slot oc-cupancy ratio of the two QAMs. Fig. 2 shows a time-domainhybrid 3264 QAM with , where eachTDM frame consists of 128 symbols, where 28 symbols are 64

QAM and 97 are 32 QAM. The extra 3 symbols are used astraining symbols for carrier phase recovery. The 64 QAM sym-bols are uniformly distributed within each TDM frame: every(approximately) three 32 QAM symbols are followed by one64 QAM symbol. We used such a modulation format in the 400Gb/s transmission experiment to be reported in the followingsections. For ease of processing, the Euclidean distances for the64 QAM and 32 QAM are designed to be identical, resulting ina 64 QAM-like constellation with un-equal constellation occu-pation probability, as can be seen in Fig. 2.

Note that arbitrary SE also can be achieved by using fre-quency-domain based hybrid QAM. For example, one can as-sign two regular QAMs with different SE to different subcar-

riers, for an OFDM-modulated system [12]. Compared to sucha frequency-domain-based method, time-domain hybrid QAMexhibits several potential advantages such as lower peak-to-av-erage power ratio [13] and better tolerance toward laser phasenoise due to the fundamentally shorter symbol period. Thesetwo advantages could be important for high-SE optical commu-nication systems where, in addition to additive Gaussian noise,fiber nonlinear effects and laser phase noise are also major per-formance limiting factors.

III. EXPERIMENTAL SETUP AND DSP ALGORITHMS

Fig. 3 shows the PDM time-domain hybrid 3264 QAMtransmitter. To overcome the limitation of available dig-

ital-to-analog (D/A) converter bandwidth, five subcarriers wereutilized to create the 494.85 Gb/s per-channel signal. The fivefrequency-locked subcarriers were generated from a singlelaser source by using two Mach-Zehnder modulators (MZMs),each driven with a 9.9 GHz clock, and followed by either a12.5/25 GHz interleaverfilter (ILF) or two cascaded 25/50 GHzILFs. The spectra of the three odd and two even subcarriers aredisplayed in Fig. 3 as insets a and b, respectively. All unwantedharmonics were suppressed to be at least 40 dB below thesubcarrier signals. The odd and even subcarriers were mod-ulated by two independent I/Q data modulators, each drivenwith a Nyquist-shaped 9.7 Gbaud pre-equalized time-domainhybrid 3264 QAM signal, having2 pseudorandom pattern length. Note that independent I andQ data sequences were used in the experiments reported in


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ZHOU et al.: HIGH SPECTRAL EFFICIENCY 400 GB/S TRANSMISSION 1001

Fig. 3. 494.85 Gbits/s PDM 32/64 QAM transmitter. Insets (a) to (e) are mea-sured optical spectra in 0.01 nm bandwidth at different locations indicated in the

figure. VOA: variable attenuator, PC: polarization controller, PBS: polarizationbeam splitter.

Sections III and IV of this paper: the I data was generatedbased on generator polynomial of , while Qdata was based on . The Nyquist pulse shapinghad roll-off factor of 0.01, realized by using a T/2-spaced finiteimpulse response (FIR) filter having 128 taps. Frequency-do-main based pre-equalization [14] was used to compensate forthe band-limiting effects of the D/A converters, which have3-dB bandwidths 5 GHz at 10 bit resolution and a 24 GSa/ssampling rate. 24 GSa/s oversampling (combined with the useof four 4.9 GHz low-pass electrical filters) was employed in this

experiment to suppress the D/A converter aliasing components(to reduce inter-subcarrier crosstalk). Then the sets of two andthree 49.485 Gb/s sub-carriers (see insets c and d in Fig. 3)were passively combined and polarization multiplexed withrelative delay of 500 symbols, resulting in a 494.85 Gb/s signalthat occupied a spectral width of 49.3 GHz with a well confinedspectral shape allowing it to fit into the 50 GHz grid, as isdisplayed in inset e.

The experimental setup for 10 494.85 Gb/s PDM-32/64QAM WDM transmission is shown in Fig. 4. The ten 494.85Gb/s, 50 GHz-spaced, C-band channels are derived from odd(192.25 to 192.65 THz) and even (192.20 to 192.60 THz) setsof multiplexed, 100 GHz-spaced external cavity lasers (ECL)

with 100 kHz linewidth. They are combined using a 3 dBoptical coupler (OC) and modulated in the 494.85 Gb/s PDMhybrid 3264-QAM transmitter (see Fig. 3). The ten DWDMchannels are effectively de-correlated because they are from dif-ferent sources and their optical phases are de-correlated. Thenthe ten 494.85-Gb/s channels are sent into a re-circulating trans-mission loop, which consists of four 100-km spans of ULA fiberhaving, at 1550 nm, 135 average Aeff and 0.179 dB/kmaverage attenuation. As shown in Fig. 4, the spans are config-ured for all-Raman amplification, resulting in total span losses(fiber components) of between 19.7 and 20.1 dB. For eachspan, counter-pumps at 1435 nm and 1455 nm with 310 mWand 650 mW, respectively, provide an average of 17 dB on-offRaman gain, while co-pumps at 1455 nm with 180 mW powerprovide an average of 3 dB on-off gain. After the last span, a

Fig. 4. Experimental setup for transmission experiments.

loop-synchronous polarization controller is followed by a wave-

length-blocker-based channel power equalizer. The power vari-ation among the ten channels after 3200 km (8 loops) transmis-sion is controlled to be within 0.6 dB.

A DSP-enabled coherent receiver is used for the detection anddemodulation of the received PDM hybrid 3264 QAM signal.As shown in Fig. 4, the coherent receiver front-end consists of apolarization-diverse 90-degree hybrid, a tunable external cavitylaser (ECL) of 100 kHz linewidth serving as the local oscil-lator (LO), and four balanced photo-detectors. For our experi-ments, each subcarrier is independently received by passing thesignal through a tunable optical filter with 37.5 GHz 3 dBbandwidth, and the LO is tuned to be within 200 MHz of thecenter frequency of each subcarrier. A four-channel real-time

sampling scope with 50 GSa/s sampling rate and 16 GHz analogbandwidth performs the sampling and digitization (ADC) func-tion, followed by post-transmission DSP of the captured data ona desktop computer. The ADC bandwidth was set to be 10 GHz,which we found to be the optimal electrical bandwidth for a9.7 Gbaud signal.

The major DSP functional blocks are shown in Fig. 5. Acascaded, two-stage equalization strategy is used for polar-ization demultiplexing and linear distortion mitigation. Thefirst-stage 2 2 equalizer (i.e. EQ1) has 21 T/2-spaced taps,whereas the second stage equalizer (EQ2) has 301 T/2-spacedtaps. EQ1 is initially optimized using a decision-independentconstant modulus algorithm (CMA), but it is switched to a

decision-dependent least-mean-square (LMS) algorithm oncepre-convergence is achieved, first in a training-based mannerusing 16000 T/2 spaced samples, and then in a decision-di-rected manner for steady-state operation. TDM synchronizationis achieved by using the starting training sequence.

The carrier frequency and phase recovery are performed afterEQ1 but before EQ2. The initial signal-LO frequency offset(FO) is estimated through a time-domain-based differentialphase method [15] by using the starting training sequence.For the steady-state operation, the FO is tracked through afeedback configuration using the recovered carrier phases, asshown in Fig. 6. Note that, unlike the fast-changing phase noisethat cannot tolerate extended feedback delay in high-speedoptical systems requiring a high-degree of parallel processing,carrier frequency typically varies more slowly and thus it can


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Fig. 5. Major post-transmission offline DSP functional blocks. CD: chromaticdispersion, EQ: equalizer, FOE:frequency offset estimate.

Fig. 6. Schematic illustration of the proposed frequency recovery algorithm.T: symbol period, : estimated carrier frequency offset.

be tracked by using the proposed feedback-based method. Theadvantages of this new method are: 1) it is applicable to arbi-trary QAM, and 2) its implementation complexity is very lowbecause it requires significantly fewer complex multiplicationsthan FFT-based algorithms [16], [17] or blind frequency searchbased algorithms [18], [19].

For phase recovery, a new training-assisted two-stage methodis used in this experiment. It is performed within the EQ1 loop.

In the first stage, the average carrier phase for each TDMframe (consisting of 128 symbols) is estimated by using thethree training symbols (located in the 32th, 64th, and 96th timeslots within each TDM frame) through a maximum likelihoodestimation (MLE) method [20]. The three training symbolsemploy a QPSK modulation format, which is equivalent to thefour outer-most 64 QAM symbols, because these four symbolsare most sensitive to phase change. In the second stage, wedivide each TDM frame into 4 groups, where each groupconsists of 32 consecutive symbols. The carrier phase for eachgroup is refined by using a blind phase search algorithm (BPS)[21] over a small phase-varying range ( was used inthis experiment). We have found that such a training-assisted

two-stage algorithm effectively mitigates cyclic phase slippingproblems, which improves the receiver sensitivity by removingthe need for differential coding and decoding, but also enablesan additional equalization stage (i.e. EQ2 in Fig. 5) followingthe phase recovery.

Because phase-recovered X- and Y-polarized signals are usedas the input of EQ2, a very long filter length can be used inEQ2 to mitigate some low-frequency/narrow-band distortionthat may occur in the transmitter and the receiver. Note thatthe allowable filter length used for EQ1 is limited by the phasenoise and therefore cannot be too long (see Section V). For anequalizer with a large number of taps, the implementation com-plexity can be greatly reduced by using a frequency-domainbased method [22], although the time-domain based method isused in this paper.

Fig. 7. Measured back-to-back performance.

Fig. 8. Launched and received optical spectra. BW: bandwidth.

For our offline processing, the bit error ratios (BER) arecounted over of information for each subcarrier( for each channel). No differential coding/decodingis utilized in this paper. Standard Gray-coding based techniqueis used to map/de-map 32/64 QAM symbol into binary bits.

IV. MEASURED RESULTS

In Fig. 7 we show the measured back-to-back performance,where the BER versus OSNR curves are displayed for a singlePDM hybrid 3264 QAM subcarrier (98.97 Gb/s), for a single

494.85 Gb/s channel (average of the five subcarriers), and forthe center subcarrier (sub. 3) of a single 494.85 Gb/s channel.For comparison, the theoretical prediction for a single subcarrieris also presented in this figure. At the requiredOSNR for a single subcarrier is 16.9 dB, which is 1.8 dB awayfrom the theoretical prediction. The OSNR penalty for inter-subcarrier crosstalk is 0.2 dB. And, the required OSNR for asingle 494.85 Gb/s channel is 24.0 dB at .

The DWDM transmission results are displayed in Fig. 810,where the total launch power entering the transmission fiberfor the ten WDM channels was 8.5 dBm, corresponding to

1.5 dBm per channel and 8.5 dBm per subcarrier, which wefound to be the optimal launch power for 3200 km transmis-

sion. Fig. 8 shows measured optical spectra (in 0.1 nm resolu-tion bandwidth) of the DWDM signals launched into span 1 andafter 3200 km transmission. The launched OSNR was above 38dB for all the WDM channels. After 8 circulations (3200 km),the spectrum of the ten 494.85 Gb/s channels was flat to within1.2 dB. Due to the all-Raman amplification, the OSNRs after3200 km were still greater than 25.2 dB for all ten WDM chan-nels, despite the relatively low per-channel launch power.

In Fig. 9 we show the measured BER and OSNR of the cen-tral channel (Ch. 5) with transmission distance ranging from 400km to 4000 km. The measured BERs after 2800, 3200 and 3600km transmission were , , and ,respectively, with corresponding OSNRs of 26, 25.4 and 24.9dB, respectively. The measured BERs of all ten 494.85-Gb/sWDM channels after 32 100 km transmission are presented


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Fig. 9. BER and OSNR of Ch. 5 versus transmission distance.

Fig. 10. BER of all ten 494.85 Gb/s, 50 GHz-spaced WDM channels after 32100 km transmission.

Fig. 11. (a) Probability density function of the signal distortion and (b) thestatistics of error burst length for the center subcarrier of ch. 5 after 3200 km.

in Fig. 10. The BERs for the five individual subcarriers of Ch. 5are also plotted. The BERs of the ten DWDM channels rangedfrom to , which are below the

threshold for 20% soft-decision FEC using LDPCconvolution codes and layered decoding algorithm [23]. The re-covered constellation diagrams for the X- and Y-polarizationsof one of Ch. 5s subcarriers are shown in Fig. 10 as insets. Theprobability density function of the measured signal distortionand the statistics of burst error length for the center subcarrier of

ch. 5 after 3200 km transmission (at 8.5 dBm/ch launch power)is shown in Fig. 11(a) and (b), respectively. One can see thatthe signal distortion in both the in-phase and quadrature com-ponents can be well approximated as a Gaussian distribution.The measured burst error probability decreases exponentiallywith increasing burst length, agreeing with the prediction foruncorrelated error events. These results indicate that soft-deci-sion FEC can be effective in this system.

In Fig. 12 we show the recovered carrier phases using twodifferent carrier phase recovery algorithms in a back-to-backmeasurement (single subcarrier, ). One cansee that there was no phase jump when using the proposedtraining-assisted two-stage algorithm, whereas the phase-jumpproblem was severe when using the conventional single-stageBPS algorithm.

Fig. 12. Recovered carrier phases usingtwo different algorithms: trainingas-sisted two-stage algorithm and single-stage blind phase search algorithm.

Fig. 13. BER versus OSNR for different EQ2 lengths for (a) I/Qand (b) independent I and Q.

V. DISCUSSION

Recently it has been shown that an adaptive equalizer can ex-ploit the correlation between the I and Q components to artifi-cially boost the performance when the equalizer length is greaterthan the I/Q de-correlation delay [24]. To quantify this effect,here we present a comparison between the results obtained byusing independent I/Q sequences (as described in the Section IVof this paper) and the results using the transmitter setup de-scribed in [10], where the quadrature component was a delayedcopy of the in-phase component and the I/Q sequence de-cor-relation delay was 32 symbols. For the setup used in [10], the

X- and Y-polarization de-correlation delay was 228 symbols,whereas in Section IV the X- and Y-polarization de-correlationdelay was 500 symbols.

The impact of EQ2 length on the BER performance is dis-played in Fig. 13(a) and (b). Fig. 13(a) shows the result wherethe I/Q de-correlation delay is 32 symbols and X/Y polariza-tion de-correlation delay is 228 symbols (i.e. the setup described[10], denoted as case I hereafter). Fig. 13(b) presents the resultswhere I and Q are independent and the X/Y-polarization de-cor-relation delay is 500 symbols (i.e. the experiment of Section IV,denoted as case II hereafter). Both results are based on thecentersubcarrier of a 494.85 Gb/s PDM hybrid 3264 QAM channel(back-to-back measurement with loading ASE noise).

For this study, EQ1 length was fixed at 21 taps. One can seethat, for both cases, the BER decreases as EQ2 length increases(up to 801 taps for case I and up to 301 taps for case II), butthe performance improvement is more significant for case Ias compared to case II. By increasing EQ2 length from 0 (i.e.single-stage case) to 801 taps, 1.3 dB OSNR improvement (at

) is observedfor case I, whereas only 0.6 dB improve-ment is observed for case II. For both cases one can observe thatmajor performance gain is obtained by increasing EQ2 lengthfrom 0 to 301 taps, whereas increasing EQ3 length from 301 to801 taps only results in minor BER reduction for case I (slightperformance degradation is observed for case II when the EQ2length is increased from 301 to 801 taps). These results indicatethat the extra 0.7 dB performance gain observed in case I ismostly due to I/Q correlation, and not polarization correlation.


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Fig. 14. The four FIRfilter impulse response functions of EQ2 for case I.

Fig. 15. The four FIRfilter impulse response functions of EQ2 for case II.

Fig. 16. Frequency spectrum of hxx for EQ2 with 301 taps (for case II withindependent I/Q data sequences).

Further evidence that the performance gain arises from theI/Q correlation is provided by the measured impulse responsefunctions of the four EQ2 finite impulse response (FIR) filters(hxx, hxy, hyx, and hyy, each with 801 T/2-spaced taps) shownin Fig. 14. One can observe multiple small peaks, and the spac-

ings between each two consecutive peaks are exactly equal tothe I/Q de-correlation delay. As a comparison, Fig. 15 showsthe measured impulse response functions of EQ2 for case II,also with 801 taps. No such peaks are observed for case II,where I and Q are independent. The corresponding frequencyspectrum of hxx for case II is shown in Fig. 16. One can ob-serve three dominant narrow-band ripples (below 2 GHz). Suchnarrow band distortions may arise from imperfect DAC, elec-trical-optical modulator or the ADC responses and may be com-pensated by using a fixed equalizer in a real system.

Polarization correlation does not contribute to significantperformance gain for case I when EQ2 length is as large as801 taps, because EQ2 is initiated with a centered impulseresponse for both hxx and hyy filters, and the input to EQ2is already an equalized signal (i.e. at a local minimum). As

Fig. 17. A comparison between one-stage and two-stage equalization. For thetwo-stage case, EQ1 length was fixed at 21 taps while we increases the numberof taps for EQ2.

a result, hxx and hyy of EQ2 will remain a centered impulseresponse when using typically small convergence parameters( is used in our experiments). Thus the output ofEQ2 will not converge into a single polarization, as we pointedout in [10]. However, if the length of EQ2 is allowed to begreater than twice the polarization de-correlation delay (i.e.

912 taps for case I), polarization correlation will result insignificant performance gain even with centered hxx and hyyresponses.

In Fig. 17 we compare the performance of one-stage equal-ization to that of two-stage equalization for the center subcarrierof a 494.85 Gb/s PDM hybrid 3264 QAM channel (back-to-back, , independent I and Q), where the BERversus total number of equalizer taps (the sum of EQ1 and EQ2)is displayed. For the two-stage case, EQ1 length was fixed at 21taps while we increases the number of taps for EQ2. One cansee that two-stage equalization performs better than one-stageequalization, and the performance difference increases as theEQ2 length increases. The main reason is due to the impact of

laser phase noise, because phase noise will degrade the perfor-mance of EQ1 when the length of EQ1 is too long. This resultindicates that, in order to mitigate some low-frequency/narrow-band distortions that require long equalizer length, an additionalequalizer followed by phase recovery may be needed.

VI. CONCLUSIONS

In conclusion, we demonstrated 32 100 km ULA fibertransmission of ten 400 Gb/s DWDM signals on the standard50 GHz grid. The net SE of 8.25 b/s/Hz was achieved by usingPDM time-domain hybrid 3264 QAM, along with improvedcarrier frequency and phase recovery algorithms.

We have shown that time-domain hybrid QAM can be used

to fine tune the SE of the modulation format to optimize thetransmission performance for specific channel bandwidth andFEC redundancy requirements. We also proposed and demon-strated a new hardware-efficient carrier frequency offset esti-mation algorithm and a new training-assisted two-stage phaseestimation algorithm. The proposed phase recovery algorithmeffectively mitigates cyclic phase slipping problems, which notonly improves the receiver sensitivity by removing the need fordifferential coding, but also allows an additional equalizationstage following the phase recovery. We have shown that the in-troduction of such an additional equalization stage with longerfilter length helps to reduce the implementation penalty.

This paper also presented the first experimental study of theimpact of I/Q correlation for a high-order QAM. Results showedthat an adaptive equalizer could exploit the correlation between


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I and Q signal components, artificially boosting the performanceby up to 0.7 dB for a PDM time-domain hybrid 3264 QAMsignal when the equalizer length is significantly longer than theI/Q de-correlation delay in the transmitter.

ACKNOWLEDGMENT

The authors would like to thank Robert Lingle, Jr. of OFS,

and Mark Feuer and Ken Reichmann of AT&T Labs-Researchfor their generous support of these results. The authors alsothank Peter Winzer for helpful discussions.

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[5] T. Kobayashi, A. Sano, A. Matsuura, Y. Miyamoto, and K. Ishihara,Nonlinear tolerant long-haul WDM transmission over 1200 km using538 Gb/s/ch PDM-64 QAM SC-FDM signals with pilot tone, pre-sentedat the OFC-NFOEC 2012, Los Angeles, CA, March 2012, paperOM2A.5, unpublished.

[6] H. Takahashi, K. Takeshima, I. Morita, and H. Tanaka, 400-Gbit/soptical OFDM transmission over 80 km in 50-GHz frequency grid,presented at the ECOC 2010, Torino, Italy, September 2010, paperTu.3.C.1, unpublished.

[7] X. Zhou, L. E. Nelson, P. Magill, R. Isaac, B. Zhu, D. W. Peckham, P.Borel,and K. Carlson, 8 450-Gb/s,50-GHz-spaced, PDM-32QAMtransmissionover 400 km andone 50GHz-grid ROADM,presented atthe OFC-NFOEC 2011, Los Angeles, CA, March 2011, paper PDPB3,unpublished.

[8] X. Zhou, L. E. Nelson, P. Magill, R. Isaac, B. Zhu, D. W. Peckham, P.Borel, andK. Carlson, 800 km transmission of 5 450-Gb/s PDM-32QAM on the50 GHzgrid using electricaland optical spectral shaping,presented at the ECOC 2011, Geneva, Switzerland, September 2011,paper We.8.B.2, unpublished.

[9] X. Zhou, L. E. Nelson, P. Magill, R. Isaac, B. Zhu, D. W. Peckham,P. Borel, and K. Carlson, 1200 km transmission of 50 GHz spaced,5 504-Gb/s PDM-32-64 hybrid QAM using electrical and opticalspectral shaping, presented at the OFC-NFOEC 2012, Los Angeles,CA, March 2012, paper OM2A.2, unpublished.

[10] X. Zhou, L. E. Nelson, P. Magill, R. Isaac, B. Zhu, D. W. Peckham, P.Borel, and K. Carlson, 4000 km transmission of 50 GHz spaced, 10

494.85 Gb/s hybrid- 32-64 QAM using cascaded equalization andtraining-assisted phase recovery, presented at the OFC-NFOEC 2012,Los Angeles, CA, March 2012, paper PDP5C.6, unpublished.

[11] W. R. Peng, I. Morita, and H. Tanaka, Hybrid QAM transmissiontechniques for single-carrier ultra-dense WDM systems, presented atthe OECC 2011, Kaohsiung, Taiwan, July 2011, paper 8D2-4, unpub-lished.

[12] H. Takahashi, I. Morita, and H. Tanaka, The impact of the combined8-QAM and QPSK subcarrier modulationfor coherent optical OFDM,presented at the OFC-NFOEC 2011, Los Angeles, CA, March 2011,paper JWA30, unpublished.

[13] R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, A. Ludwig, B.Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J.Becker, C. Koos, W. Freude, andJ. Leuthold,Real-timeNyquistpulse

generation beyond 100 Gbit/s and its relation to OFDM, Optics Ex-press, vol. 20, no. 1, pp. 317337, Dec. 2012.

[14] X. Zhou, J. Yu, M.-F. Huang, Y. Shao, T. Wang, L. E. Nelson, P. D.Magill, M. Birk, P. I. Borel, D. W. Peckham, and R. Lingle, 64-Tb/s,8 b/s/Hz, PDM-36 QAM transmission over 320 km using both pre- andpost-transmission digital signal processing, J. Lightwave Technol.,vol. 29, no. 4, pp. 571577, February 15, 2011.

[15] A. Leven, Frequency estimation in intradyne reception, IEEEPhoton. Technol. Lett., vol. 19, no. 6, Mar. 15, 2007.

[16] Y. Cao, S. Yu, J. Shen, W. Gu, and Y. Ji, Frequency estimation for op-tical coherent MPSK without removing modulated data phase, IEEE

Photonics Technol. Lett., vol. 22, no. 10, pp. 691693, May 2010.[17] M. Selmi, Y. Jaouen, and P. Ciblat, Accurate, digital frequency offset

estimator for coherent PolMux QAM transmission systems, presentedat the ECOC 2009, Vienna, Austria, September 2024, 2009, paper P3.08, unpublished.

[18] X. Zhou, Hardware efficient carrier recovery algorithms forsingle-carrier QAM systems, presented at the OSA 2012 topicalmeeting, signal processing in photonic communication (SPPCom),Colorado Springs, USA, June 1821, 2012, paper SpTu3A.1, unpub-lished.

[19] S. Dris, I. Lazarou, P. Bakopoulos, and H. Avramopoulos, Phase en-tropy-based frequency offset estimation for coherent optical QAM sys-tems, presented at the OFC-NFOEC 2012, Los Angeles, CA, March2012, paper PDP5C.6, unpublished.

[20] X. Zhou, An improved feed-forward carrier recovery algorithm forcoherent receiver with M-QAM modulation format, IEEE Photonics

Technol. Lett., vol. 22, no. 14, pp. 10511053, July 15, 2010.[21] T. Pfau, S. Hoffmann, andR. No, Hardware-efficient coherent digital

receiver concept with feed-forward carrier recovery for M-QAM con-stellations, J. Lightwave. Technol., vol. 27, no. 8, pp. 989999, April15, 2009.

[22] M. Dentino, J. M. McCool, and B. Widrow, Adaptive filtering in thefrequency domain, Proc. IEEE, vol. 66, no. 12, pp. 16581659, Dec.1978.

[23] D.Chang1, F. Yu,Z. Xiao, N. Stojanovic, F. N. Hauske, Y.Cai,C. Xie,L. Li, X. Xu, and Q. Xiong, LDPC convolutional codes using layereddecoding algorithm for high speed coherent optical transmission, pre-sented at the OFC-NFOEC 2012, Los Angeles, CA, March 2012, paperOW1H.4, unpublished.

[24] A. Sierra, S. Randel, P. J. Winzer, R. Ryf, A. H. Gnauck, and R. Essi-ambre, On the Use of Delay-Decorrelated I/Q Test Sequences for QPSKand QAM Signals, vol. 24, no. 12, pp. 10001002, June 2012.

Xiang Zhou received his Ph.D. degree in electrical engineering from BeijingUniversity of Posts & Telecommunications in 1999. From 1999 to 2001, he waswith Nangang Technological University, Singapore,as a Research Fellow,doingresearch on optical CDMA and wide-band Raman amplification. He has beenwith AT&T Labs-Research since October 2001, working on various aspects oflong-haul optical transmissionand photonic networkingtechnologies, includingRaman amplification, polarization-related impairments, optical power transientcontrol, advanced modulation formats and digital signal processing at bit rate100 Gb/s and beyond. He has authorized/co-authorized more than 100 peer-reviewed journals and conferences publication, and holds 32 USA patents. Hecurrently serves as an associate editor of Optics Express. He is member of OSA,and a senior member of IEEE.

Lynn E. Nelson, biography not available at the time of publication.

Peter Magill, biography not available at the time of publication.

Rejoy Isaac, biography not available at the time of publication.

Benyuan Zhu, biography not available at the time of publication.

David W. Peckham, biography not available at the time of publication.

Peter I. Borel, biography not available at the time of publication.

Kenneth Carlson biography not available at the time of publication.

high spectral efﬁciency 400 gbps transmission

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