Exploiting the Faster-Than-Nyquist Concept in Wavelength-Division Multiplexing Systems Using Duobinary Shaping

Jianqiang Li,Ekawit Tipsuwannakul,Magnus Karlsson,and Peter A.Andrekson

(Photonics Laboratory,Dept.of Microtechnology and Nanoscience,Chalmers University of Technology,SE-412 96,G?teborg,Sweden)

Abstract This paper begins with Nyquist wavelength-division multiplexing(WDM)and then introduces faster-than-Nyquist.In faster-than-Nyquist,a certain amount of inter-symbol interference(ISI)is accepted,which violates the fundamentalprinciple of Nyquist WDM.This results in much-relaxed transceiver bandwidth and simpler spectral design.However,in faster-than-Nyquist,implementation complexity is shifted from the transmitter side to the receiver side.Therefore,successful application of faster-than-Nyquist depends on innovation in the receiver structure.In this paper,we discuss the guidelines for implementing suboptimum,low-complexity receivers based on faster-than-Nyquist.We suggest that duobinary shaping is a good technique for trading off achievable spectral efficiency,detection performance,and implementation complexity and might be preferable to Nyquist WDM.Experiments are conducted to verify robustness of the proposed technique.

Keyw ordscoherent detection;digital signal processing;optical fiber communications;spectral-efficiency;wavelength division multiplexing

1 Introduction

E ver-increasing demand for bandwidth has driven optical communication systems to higher and higher capacities.There is a strong motivation to enhance spectral efficiency in order to upscale total capacity and reduce cost per bit.These goals have inspired intensive research and many laboratory experiments[1]-[19].Spectral efficiency can be enhanced with high-level modulation formats,but this comes at the cost of high complexity and lower power efficiency[2]-[4].If the modulation format is already specified,two research directions,based on spectral multiplexing,can be taken to achieve high spectral efficiency.One area of research is orthogonal frequency-division multiplexing(OFDM),which uses orthogonality to allow for spectral overlapping[5]-[10].The other area of research is innovations on conventional wavelength-division multiplexing(WDM).Compared to approcaches based on OFDM,approaches based on WDM relax the analog bandwidth and sampling-speed requirements of the digital-to-analog converters(DACs)and analog-to-digital converters(ADCs)in transceivers[11].Moreover,the absence of temporal and spectral overheads,that is,guard intervals,training sequences,or pilot tones,means the approaches based on WDM are more efficient and less complex.In this paper,we discuss several new concepts for improving spectral efficiency in WDM systems,and we propose solution in which spectral efficiency,performance,and complexity are traded off to achieve a reasonable compromise.

2 Nyquist WDM and Faster-Than-Nyquist

In WDM systems,an individual channelcan be viewed as band-limited with a cut-off bandwidth equal to the channel spacing.In this way,improving spectral efficiency means increasing the symbol rate for a given channel spacing or reducing the channel spacing for a given symbolrate.One recently-studied concept is Nyquist WDM,in which the Nyquist limit is approached by using Nyquist filtering or shaping[11]-[15].In Nyquist WDM,the spectrum of one WDM channel is optically or electrically tailored to fit into the near-symbol-rate channel spacing.Ideally,inter-symbol interference(ISI)is absent.However,filtering or spectral shaping often requires specialtreatment so that this Nyquist ISI-free criterion is met.It is also difficult to approach the Nyquist limit in practice;the channelspacing has to be slightly larger than the symbol rate because of inter-channel linear crosstalk[12]-[15].Nyquist WDM assumes that the overall channelhas no ISIor a small amount of linear ISI(excluding chromatic dispersion and polarization-mode dispersion,which are all-pass effects).Thus,optimum performance can be approached by combining a linear equalizer and a hard-decision-based detector,which is widely used in conventional WDM systems with coherent detection.In Nyquist WDM,the lower bound of the channel spacing is the symbol rate because the Nyquist ISI-free criterion dictates that the symbol rate cannot exceed the Nyquist rate of 2W over an ISI-free band-limited channel with single-sided cut-off bandwidth W[16].

To exceed the Nyquist limit,faster-than-Nyquist has been proposed[16]-[19].The fundamental idea behind this new concept is to increase the symbol rate above Nyquist rate by accepting a certain amount of ISIleft to the detectors.The optimum detectors are those based on maximum a-posteriori probability(MAP)and maximum-likelihood(ML)criteria,not hard-decision criteria.Relaxing the ISI-free criterion greatly reduces bandwidth requirements on the transceiver and eases the difficulty of Nyquist filtering or shaping in practice.These benefits encourage the application of faster-than-Nyquist in realistic WDM systems.Our intention is to use faster-than-Nyquist without forcing the symbol rate beyond the Nyquist rate(even though it can be done).Although faster-than-Nyquist is relatively new in optical communications,it has already been leveraged in the systems described in[20]-[25].In these systems,ISIwas introduced by commercial electrical or optical analog filters(without any specific designs),and some ISIwas left to the final MAPor ML detectors.A problem with an optimal MAPor MLreceiver is that computations and storage grow exponentially with channel memory[26].The channel memory induced by ISIin constrained-bandwidth systems(such as those in[20]-[22])often spans a large number of symbols,and this results in unacceptably complex detectors.Moreover,the ISIpattern in these systems is unknown and unconditioned,and additional channel estimators are needed.Therefore,the success of faster-than-Nyquist depends on innovations that address all these problems.

3 A Practical Suboptimal Receiver

In[27],a finite impulse response(FIR)equalizer is used to shape the channel response into an intermediate truncated channel response with a short memory.The FIRequalizer then feeds the equalized output to a simplified maximum-likelihood sequence detector(MLSD)(Fig.1).This equalizer is a partial-response equalizer because its shaping goal is one channel with a specified truncated ISIpattern.By using a partial-response equalizer,the overall memory or accounted-for ISIcan be arbitrarily shared between the partial-response equalizer and the MLSD.This allows a trade-off between complexity and performance,and the solution has been the basis of numerous receiver structures[28]-[30].In these receivers,the least-mean-square(LMS)algorithm is commonly used so that the equalizer is adaptive.The adaptive equalizer can operate in a decision-directed[28],[29]or decision-feedback manner[30].Regardless of which structure is used,the performance advantage of the MLSD is retained by carefully selecting the intermediate truncated channel so that the amplitude response is similar to that of the original channel.The reason for this guideline is that the shaping process by the partial-response equalizer would alter the spectral characteristic and power of the noise,which would ultimately influence the effective signal-to-noise ratio(SNR)and MLSD performance.

▲Figure1.The typicalsystem structure suggested in[27].

Linear equalizers in fiber-optic systems are essential and have been widely applied[31].Adaptive equalizers can conveniently perform polarization demultiplexing and compensate for almost all static and time-varying linear impairments.In optical coherent receivers,adaptive equalizers using constant modulus algorithm(CMA)and decision-directed LMS(DD-LMS)algorithm are used to mitigate ISIin the channel.However,noise may be strong if ISI is strong[26].The shaping goal of an adaptive equalizer is an ISI-free channel,and an adaptive equalizer cannot be used for partial-response shaping.Moreover,it might also be inadvisable to modify the equalizer in an opticalcoherent receiver referring to[28]-[30]because this would not only complicate the equalizer itself but also significantly change the carrier recovery algorithms.For example,the equalizer structure proposed in[22]is similar to that in[29]for optical coherent receivers whereas the frequency offset was assumed to be known and had to be compensated for before the equalizer.Therefore,it is desirable to innovate on receiver structures without altering the existing mature coherent receiver algorithms.

Another concern is how to determine the intermediate channelresponse in spectrally-efficient optical WDM systems by using the previously mentioned guideline.For general time-varying channels,an algorithm has been developed to adaptively optimize the intermediate channel response by minimizing the mean-square error[28].In realoptical networks,the memory or ISIin one channel(excluding the ISI induced by dispersion)is commonly introduced by bandwidth-limiting components such as the optical modulators,WDM components,reconfigurable optical add-drop multiplexers(ROADMs),analog electrical/microwave driving circuits,and photodetectors.The amplitude responses of these components are relatively constant.Although a cascade of multiple ROADMs causes accumulated narrowband filtering,the rough shape of the overall channel response is maintained.Therefore,daptations such as those in[28]are not imperative in optical communication systems where the channel is quasi-static.This means that the desired intermediate channel response can be determined in back-to-back(B2B)and can be kept fixed in the real optical network where the setup and hardware are specified.This reduces implementation complexity,but performance is compromised when the channel response changes slightly.

4 Duobinary Shaping

Partial-response maximum-likelihood(PRML)technology is widely applied in magnetic recording systems.Amagnetic recording channel can be shaped into a partial-response channel because the memory in the read-out signals from magnetic media is inherently similar to a certain partial-response class[32],[33].This leads us to consider whether the channel in a spectrally efficient WDM system can be shaped into a partial-response channel with a short memory.Recently,we showed that the channel amplitude response in the presence of regular electrical or optical filters has a similar shape to the well-known duobinary response[23]-[25].More importantly,a novel receiver structure has been proposed for duobinary shaping or equalization prior to the MLSD.A simple duobinary digital post-filter is introduced after the conventional adaptive linear equalizers and carrier recovery modules.In this way,the existing digital signal processing(DSP)algorithms in the conventional digital coherent receivers were allpreserved.The short one-symbol memory of the duobinary response considerably simplifies the MLSD.The proposed duobinary shaping scheme is robust to narrowband opticalfiltering,and the requirements on the transceiver hardware are greatly relaxed.An ideal duobinary response has a double-sided cut-off bandwidth that is the same as the symbol rate.According to the shaping guideline previously mentioned,the proposed duobinary shaping scheme applies to WDM systems with a channel spacing approximately equal to the symbol rate(maybe slightly higher or lower).The symbol rate can be pushed beyond the Nyquist limit through more aggressive filtering and searching other intermediate channel responses with longer memory.However,this might disable the convergence of the conventional adaptive equalizers because noise would(possibly)be infinitely augmented.Although this problem could be solved by modifying the whole DSPstructure and associated algorithms,we suggest that duobinary shaping provides a good trade-off between spectral-efficiency,detection performance,and DSPcomplexity.

5 Experiment with the Proposed Duobinary Shaping Technique in a PM-QPSK WDM System

To determine the benefits and robustness of the proposed duobinary shaping technique,we carried out experiments using 25 GHz spaced,100 Gb/s polarization-multiplexed QPSK(PM-QPSK)WDM with up to five channels.

Fig.2 shows the experiment setup and DSPflow.One external-cavity laser(ECL)and four distributed-feedback(DFB)lasers provide up to five 25 GHz-spaced continuous-wave(CW)optical carriers.An ECLwith approximately 100 kHz linewidth serves for the central channel that we are investigating.Four decorrelated 25 Gb/s or 28 Gb/s pseudo-random bit sequence(PRBS)signals all have a codeword length of 215-1.These PRBSsignals are generated from a quad-channel pulse pattern generator(PPG).The decorrelation between channel D1and D2is 214 bits,and the decorrelation between D1andis 54 bits.These paired PRBSdata streams drive two I/Q modulators with full swings to produce optical QPSK signals.The odd and even channels are further decorrelated by a differential delay of approximately 180 symbols.Prior to being combined by a 3 d B optical coupler,the odd and even channels are spectrally shaped and filtered by two commercial WaveShapers,both programmed with fourth-order super-Gaussian profiles for each WDM channel.Spectral shaping and filtering allows the PM-QPSK signals to be accommodated on a 25 GHz grid with acceptable linear crosstalk.The two WaveShapers and 3 d Bcoupler act as an optical interleaver with the ability to tune the optical-filtering bandwidth.This tunability allows us to determine the tolerance of the proposed duobinary shaping scheme to the optical-filtering bandwidth.Spectral shaping can also be done by electrical filters such as those in[23]and[24].Here,we take an opticalapproach to spectralshaping because WDM components are used in practice to combine WDM channels.Then,the entire WDM signal is polarization-multiplexed with a differential delay of approximately 180 symbols between the two polarizations.The fiber link was built up in a straight line using eight 80 km standard single-mode fiber(SSMF)spans with erbium-doped fiber amplifiers(EDFAs)only.The optical power,PL,launched into the SSMFspool in each span was the same.At the receiver,the WDM signal was pre-amplified and then filtered by a 0.8 nm optical bandpass filter(BPF)to suppress wideband noise.Intradyne detection of the central channel was implemented using a commercial integrated-coherent receiver in a conventional polarization-and phase-diverse configuration.Finally,the four detected tributaries were captured,each with 3×106samples,by a 50 GSa/s digital sampling oscilloscope with 16 GHz analog bandwidth for offline processing.

The conventional DSPblocks for a PM-QPSK coherent receiver are preserved without modification,which is a tenet of the proposed DSPstructure.The proposed structure allows DSPreconfiguration because all the DSPblocks work in a feed-forward fashion,and the additional post-filter and MLSD can be easily switched to hard decision.After I/Q imbalance is compensated for using the Gram-Schmidt algorithm[31],electronic dispersion compensation(EDC)based on static time-domain equalization is performed to compensate for all the accumulated dispersion.The sample streams are then resampled to two samples per symbol.A blind adaptive equalizer with four 15-tap T/2-spaced butterfly FIRfilters adapted using the classic CMAfollows.Carrier recovery is then performed,which includes frequency offset estimation based on fast Fourier transform(FFT)[34]and carrier phase estimation based on the fourth-power Viterbi-Viterbialgorithm[31].After these conventional DSP blocks,the digital post-filter performs duobinary shaping and the MLSD performs suboptimum detection on each signal quadrature of each polarization,that is,each electrical lane in a practical PM-QPSK transponder.(Fig.2,highlighted boxes).On each signal quadrature in each polarization,the signal can be considered to have a 2-ary pulse-amplitude modulation(PAM)format.Therefore,the MLSD based on Viterbialgorithm only has two states for each quadrature of each polarization.Differential coding is used for all cases to overcome cycle slipping and phase ambiguity.

We first investigated performance at different symbol rates.Fig.3 shows B2B performance at a 25 Gbaud symbol rate,which is equal to the channel spacing.First,the performance of a single-channel PM-QPSKsignal was measured by configuring the WaveShaper in all-pass mode.The post-filter and MLSD were turned off in the DSPbecause there was no strong ISI.Compared with the theoretical limit and taking into account the differential coding,there is approximately 1 d B typical optical SNR(OSNR)penalty at a bit error rate(BER)of 10-3.Second,aggressive spectral shaping was performed on the single-channel PM-QPSK signal by configuring the WaveShaper with a 22 GHz 3 d B bandwidth.The post-filter and MLSD were activated to perform duobinary shaping and suboptimum detection.By virtue of the post-filter and MLSD,a single-channel PM-QPSK signal only suffers approximately 0.5 d B required OSNRpenalty.Third,we turned on the two channels that were closest to each other in order to determine the effect of inter-channel linear crosstalk.Another 0.4 d B required OSNRpenalty appears(Fig.3).There is less than 1 d B OSNRpenalty in WDM systems with a channel spacing equal to symbol rate.Next,we pushed the symbol rate to 28 Gbaud while maintaining the 25 GHz channel spacing.The symbol rate was faster than Nyquist,and the raw spectral efficiency was above 4 b/s/Hz.Fig.4 shows B2B BERas a function of OSNRat 28 Gbaud.There is only 0.6 d B implementation penalty for single channel,similar to the penalty at 25 Gbaud.However,the penalty is larger when there is linear crosstalk due to the boosted symbol rate.This implies that the proposed duobinary shaping technique works well,and performance loss is mainly due to interchannel linear crosstalk not the technique itself.The BERof 10-3cannot be reached in the three-channelsetup if the proposed technique is disabled at 25 Gbaud or 28 Gbaud.In sum,we have shown that there is an implementation penalty of approximately 0.9 d Bat 25 Gbaud and an implementation penalty of approximately 1.7 d B at 28 Gbaud on a 25 GHz WDM grid.By comparison,the systems in[13],[15],and[20]had greater than 2 d BOSNRpenalty at B2B.To the best of our knowledge,the implementation penalties described in this paper are the smallest for PM-QPSK WDM systems with such high spectral efficiency.This small implementation penalty is achieved by only using one-symbol memory in the MLSD.

To determine the robustness of the proposed scheme,the optical filtering bandwidth was swept from 19 GHz to 26 GHz by reconfiguring the WaveShapers.The symbolrate was set to 28 Gbaud.This bandwidth sweep altered the original channel response and changed the deviation of the channel response to the ideal duobinary response.Fig.5 shows the optical spectra of a single-channel 28 Gbaud PM-QPSK signal after spectral shaping with different 3 d B bandwidths.Fig.6 shows the experiment results for single-channel and triple-channel setups,given a fixed per-channel OSNRof 15.2 d B.There are several important observations from Fig.6.The function marked with solid dots shows that stronger spectral shaping is possible despite a slightly larger penalty.Furthermore,a system in which the proposed technique is used is tolerant to the spectral-shaping bandwidth.The function marked with solid squares shows there is an optimal bandwidth(22 GHz)for the triple-channel setup.This means a tradeoff has been made between inter-channelcrosstalk and intra-channel shaping or filtering.If the post-filter and MLSD were turned off,the triple-channel setup would have a much larger penalty compared with the single-channel setup.Therefore,increasing linear crosstalk plays a dominant role in increasing in-band noise enhancement.

Finally,25 GHz-spaced 5×112 Gb/s PM-QPSK signals were transmitted over 640 km SSMFusing the setup shown in Fig.2.The WaveShapers were programmed with a 22 GHz fourth-order super-Gaussian profile for each WDM channel.Fig.7 shows the transmitted WDM optical spectra.Channel isolation greater than 30 d B is achieved on a 25 GHz grid,and the interchannel linear crosstalk occurs on the spectral edge of each channel.Limited equipment availability meant that 640 km SSMFtransmissions with EDFAs could only be implemented in a straight line,leaving an OSNRmargin.Therefore,we adjusted the attenuator before the Rx pre-amplifier(Fig.2)to obtain a reasonable OSNRrange in which we would have a sufficient error count.Fig.8 shows the Q-factor of the central channel as a function of the launched power after 640 km SSMFtransmission.The insets in Fig.8 show that the enhanced in-band noise and linear crosstalk are suppressed,and the constellation evolves to a nine-point constellation after duobinary shaping.With the post-filter and MLSD,the optimal launch power is-1 d Bm.The case without post-filter and MLSD has a higher optimal optical launch power and less sensitivity to the launch power because performance is mainly penalized by increased in-band noise and interchannel linear crosstalk.In this case,more nonlinearity is required to further penalize the signal.

▲Figure 6.Tolerance to spectralshaping bandwidth of the WaveShapers.

▲Figure 7.Transmitted opticalspectra in experiments on 25 GHz-spaced five-channel112 Gb/s PM-QPSKWDM.

▲Figure 8.640 km SSMFtransmission performance versus launch power per channel.

6 Conclusion

Applying the faster-than-Nyquist concept in spectrally-efficient WDM systems has been discussed.The fundamental idea behind faster-than-Nyquist is to increase spectral efficiency by accepting ISI.In light of this idea,we have proposed a novel receiver structure based on duobinary shaping in order to achieve a balanced trade-off between spectral efficiency,detection performance,and implementation complexity in optical WDM systems.Experiments were carried out in 25 GHz-spaced 100 Gb/s PM-QPSKWDM system with smallimplementation penalty and promising robustness.The proposed scheme can be expanded to higher-level modulation formats,for example,16-ary quadrature amplitude modulation(QAM)for higher spectral efficiency[25].