We investigate in this letter the use of electronic equalization on dispersion limited systems for different modulation formats. Besides analyzing equalization on standard NRZ intensity modulation as a reference, we focus on two advanced modulation formats, Duobinary and Differential Phase Shift Keying (DPSK) which are recently gaining large attention. We demonstrate that the introduction of an electronic equalizer strongly improves standard NRZ performance, whereas it has a limited effect on Duobinary and DPSK formats. Moreover, we give rules for the optimal choice of the equalizer transversal filter parameters, i.e., the number of taps and the delay between taps

Curri, Vittorio

Gaudino, Roberto

Napoli, A.

Poggiolini, Pierluigi

English

We investigate in this letter the use of electronic equalization
on dispersion limited systems for different modulation formats.
Besides analyzing equalization on standard NRZ intensity modulation
as a reference, we focus on two advanced modulation
formats, Duobinary and Differential Phase Shift Keying (DPSK)
which are recently gaining large attention. We demonstrate that
the introduction of an electronic equalizer strongly improves
standard NRZ performance, whereas it has a limited effect on
Duobinary and DPSK formats. Moreover, we give rules for the
optimal choice of the equalizer transversal filter parameters, i.e.,
the number of taps and the delay between taps

CURRI, Vittorio

GAUDINO, ROBERTO

POGGIOLINI, PIERLUIGI

A. NAPOLI

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

05 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEElectronic equalization for advanced modulation formats in dispersion-limited systems / V. CURRI; R. GAUDINO; A.NAPOLI; POGGIOLINI P.. - In: IEEE PHOTONICS TECHNOLOGY LETTERS. - ISSN 1041-1135. - 16(2004), pp. 2556-2558.OriginalElectronic equalization for advanced modulation formats in dispersion-limited systemsPublisher:PublishedDOI:10.1109/LPT.2004.835192Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/1403866 since:IEEE2556 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 16, NO. 11, NOVEMBER 2004Electronic Equalization for Advanced ModulationFormats in Dispersion-Limited SystemsV. Curri, Member, IEEE, R. Gaudino, Member, IEEE, A. Napoli, and P. Poggiolini, Member, IEEEAbstract—We investigate in this letter the use of electronicequalization on dispersion-limited systems for different mod-ulation formats. Besides analyzing equalization on standardnonreturn-to-zero (NRZ) intensity modulation as a reference,we focus on two advanced modulation formats, duobinary (DB)and differential phase-shift keying (DPSK) which are recentlygaining a lot of attention. We demonstrate that the introduction ofan electronic equalizer strongly improves standard NRZ perfor-mance, whereas, it has a limited effect on DB and DPSK formats.Moreover, we give rules for the optimal choice of the equalizertransversal filter parameters, i.e., the number of taps and thedelay between taps.Index Terms—Adaptive equalization, dispersion equalization,intersymbol interference (ISI), modulation, optical fiber commu-nications, factor.I. INTRODUCTIONTHE USE of electronic equalization as a way to mitigatethe effects of intersymbol interference (ISI) in traditionalcommunications systems (i.e., wireless and copper wireline sys-tems) has been deeply studied, and an extremely large amountof literature is available [1], [2]. In general, all these techniquesare based on the use of a transversal digital filter (which actsas a finite impulse response (FIR) filter) at the receiver witha proper choice of taps parameter. In early 1990s, Winters etal. [3] proposed for the first time the use of electronic equal-ization in optical communication system. This approach has re-cently gained momentum, as it is today seen as a cheaper (eventhough less performing) alternative to all-optical equalization.Several solutions have been proposed, mainly in order to reducethe system impact of chromatic dispersion (CD) [4], [6] and po-larization-mode dispersion (PMD) [5].Electronic compensation in optical systems still lacks a com-plete theoretical understanding. This is mainly due to the factthat the analysis carried out for equalization of linear channelsin traditional communication systems [1], [2] cannot be directlyapplied to the optical environment, where CD and PMD arelinear at the “optical” level, but (particularly for CD) becomenonlinear at the receiver side after the photodiode “square-law”conversion [4]–[6].In this letter, we focus on CD electrical compensation for sys-tems limited by amplified spontaneous emission (ASE) noise,Manuscript received March 29, 2004; revised June 30, 2004.V. Curri is with the Dipartimento di Elettronica, OCG-PhotonLab, Politec-nico di Torino, Torino 10129, Italy, and also with ATS Srl, Torino 10129, Italy(e-mail: vittorio.curri@polito.it).R. Gaudino, A. Napoli, and P. Poggiolini are with the Dipartimento di Elet-tronica, OCG-PhotonLab, Politecnico di Torino, Torino 10129, Italy.Digital Object Identifier 10.1109/LPT.2004.835192Fig. 1. Block diagram of the analyzed system setup.focusing on advanced modulation formats. Recently, alterna-tive modulation formats have been proposed in order to over-come linear and nonlinear propagation limits of standard NRZ.Among these formats, the most promising for an advantageousimplementation seem to be the differential phase-shift keying(DPSK) [7] and the optical duobinary (DB) [8]. Anyway, thecombination of advanced modulation formats with electronicequalization has not been deeply studied yet, at least to the bestof our knowledge.The purpose of this work is, thus, twofold. On one side, weanalyze the impact of electronic equalization on DB and DPSKmodulation formats, comparing the results to standard NRZ,which is taken as a reference. On the other side, we present aset of results on the optimization of equalizer transversal filternumber of taps and delay between taps (for each modulationformat).This letter is organized as follows. In Section II, we describethe reference scenario and the equalizer scheme together withthe algorithm used for the evaluation of the FIR filter coeffi-cients. In Section III, we present the simulation results, demon-strating that the electronic equalization may strongly improveNRZ performance, but has a limited effect on systems based onDB and DPSK modulation formats. Finally, in Section IV, wedraw the conclusions and envision possible evolutions of thiswork.II. SYSTEM SETUPWe analyzed and simulated [9] the system scenario shownin Fig. 1, corresponding to an externally modulated systemlimited by the accumulation of ASE noise and by CD-inducedISI, while we neglect other effects, such as fiber nonlinearities.These assumptions are reasonable for high-capacity metro andextended metro links using single-mode fibers, a scenario that1041-1135/04$20.00 © 2004 IEEECURRI et al.: ELECTRONIC EQUALIZATION FOR ADVANCED MODULATION FORMATS IN DISPERSION-LIMITED SYSTEMS 2557is today gaining increasing attention, due to the new opticalmarket trends.We considered an Gb/s systems using a chirp-free external Mach–Zehnder amplitude modulator (MZM) at thetransmitter side. For the three considered modulation formats,the MZM operates according to different driving schemes. Letbe the driving voltage for a minimum (maximum) ofthe MZM transfer function, and the resultingON–OFF voltage swing. In order to produce standard NRZ mod-ulation, the MZM is simply driven between and volt-ages. For the DPSK modulation format, the input digital streamis first differentially precoded, then the MZM is driven betweenthe two voltages [2]. This scheme yields a two-levelphase modulation associated to “0” and “ ” radians. To obtaina DB modulation, the input digital stream is processed by theDB precoder and then filtered using a narrow lowpass electricfilter (five-pole Bessel filter with 3-dB bandwidth equal to) [8]. The filtered sequence is used to drive the MZMbetween the two voltages [8].The modulated optical signal is sent to an optical channel af-fected by CD and ASE noise. For all modulation formats, resultswill be presented as a function of the optical signal-to-noise ratio(OSNR) (calculated over an optical bandwidth of 50 GHz) at thereceiver input.We assumed to use a standard optical receiver, based on asecond-order super-Gaussian optical filter, having a 3-dBbandwidth equal to GHz, an ideal photodiode anda typical Bessel fifth-order electrical filter 3-dB bandwidthfor NRZ and DPSK. For the DB format only,we used an electrical filter with , a value that,according to [8], optimizes DB tolerance to CD.We analyze a standard equalizer structure based on atransversal FIR filter in a feedforward equalization configura-tion [1], i.e., a filter that, when receiving an electrical signal, generates at its output the signal(1)where is the number of taps, the delay between taps,and the taps’ coefficients, which are optimized using thestrategy described in the following section.System performance was evaluated by using the factor1defined as , where BER stands for thebit-error rate and is the inverse of the complementaryerror function. In this letter, the factor is always presentedin decibel units defined as . Wespanned system parameters (OSNR and CD) in order to coverthe 9–15-dB range for the factor.III. SIMULATION AND RESULTSAs an optimization strategy, we used standard numerical op-timization routines (such as the quasi-Newton method [10] andthe simplex search method [11] implemented inside the com-mercial software Matlab) based on finding, for each system re-alization, the vector of taps coefficients that maximizes thefactor, i.e., that minimizes the BER.1The Q factor was optimized by choosing the optimum clock phase.Fig. 2. OSNR versus D at Q = 17 dB for the NRZ-OOK format.Different dotted curves refer to T = T , T =2, T =3, and N = 15.The unequalized curve is shown as comparison.Besides the tap coefficients, we also investigate differentvalues for the delay and the number of coefficients .In particular, we explored , , and (whereis the bit duration) and and .For each system setup, we performed an accurate time-do-main simulation [9] of the signal propagation, then weoptimized the equalizer FIR coefficient and obtain the resultingfactor. The simulated digital stream was a PRBSsequence. We explored accumulated CD values in the[0,4600]-ps/nm range, and OSNR dB range. Wepresented all results showing the trace connecting all pointsgiving rise to a factor equal to 17 dB (corresponding to) in the and OSNR plane. Basically, weshow a plot of the OSNR required to get dB for eachvalue of . We compared each system with and withoutequalizer.We start by investigating, for the standard NRZ format, theinfluence of the tap delay and the number of taps .Results are shown in Fig. 2; the different curves refer to the un-equalized system, and to the equalized system for(i.e., an extremely long transversal filter) and tap delays, , and . Contrary to the typical results shown forexample in [1], we show that gives poor perfor-mances, while a great improvement is obtained by using. Moving to gives only marginal improve-ment, showing that for our considered setup is agood choice. We explain these results as follows. Most standardstudies on equalization [1], [2] assume that a “matched” filterprecedes the equalizer. In most cases, an integrate-and-dumpfilter with integration time is assumed as a reference. Inthis situation, choosing a delay is useless, since thetransversal filter acts on samples that are already correlated on atime window by the filter preceding the equalizer. On the con-trary, in our scenario, we assumed typical optical and electricalfilters that are always significantly larger than a “matched” filter,and thus correlate the signal on a time window smaller than ,consequently justifying a tap delay smaller than .After setting , we investigated the performancefor different values. We show in Fig. 3 the results for thecases and . This figure shows that an FIRequalizer with more than seven taps does not increase perfor-mances. We notice here that a filter with seven taps andhas a total “memory” equal to approximately 4 bits. We2558 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 16, NO. 11, NOVEMBER 2004Fig. 3. OSNR versus D at Q = 17 dB for the NRZ-OOK format.Different dotted curves refer to N = 3; 7; 11; and 15, and T = T =2.The unequalized curve is shown as comparison.Fig. 4. OSNR versus D at Q = 17 dB for the NRZ-OOK, DPSK, and DBformat. Equalized results are obtained with N = 7 and T = T =2 forNRZ-OOK and DPSK, and N = 15 and T = T =3. The unequalizedcurves are shown as comparison.observed that for high dispersion values, the seven taps coeffi-cients are approximately symmetric with respect to the centraltaps, as can be expected from the symmetric nature of the disper-sion impulse response. This physically means that the equalizer“handles” a time window with a range around the sam-pling time of each bit.Using these optimized parameters and, Fig. 3 shows that electronic equalization can greatly im-prove performance for the standard NRZ format. We define theCD limit as the value giving a 2-dB OSNR penalty with re-spect to the back-to-back configuration; in Fig. 3, it can be ob-served that the back-to-back configuration requires an OSNRdB (in order to give a factor equal to 17 dB), so that the2-dB OSNR penalty corresponds to the points of the curve thatcrosses the OSNR dB level. Using this reference, we ob-serve an improvement from 750 ps/nm in the unequalized caseto 1550 ps/nm in the equalized case, i.e., approximately a dou-bling of the dispersion limit.Finally, we compared in Fig. 4 all the considered modulationformats with (dashed lines) and without (solid lines) equaliza-tion. This is the fundamental result of this letter, showing that,for DPSK and DB, electronic equalization does not significantlyincrease performance. Using the same reference introduced forNRZ, it can be seen that electronic equalization improves thedispersion limit by only 250 ps/nm for both DPSK and DB. Thelimited benefit given by electronic equalization on these twomodulation formats is not easy to be intuitively interpreted. Afirst observation is that both formats generate an electrical signalthat, even without CD, shows a strong correlation over a one bittime window. This is due to the very narrow filtering at the trans-mitter side for DB, and by the receiver interferometric filter forDPSK. Moreover, in the case of DB, the format is intrinsicallyextremely robust to CD, as it has been shown in many papers,such as [8]. In fact, as shown in Fig. 4, it can be noted that the DBformat, without equalization, reaches approximately the sameperformance of the back-to-back NRZ ( dB with onlyOSNR dB) for ps/nm. The correspondingeye diagram is this situation is nearly ISI-free, and thus, it cannotbe significantly improved by equalization.Finally, we notice that for all formats, and even without dis-persion, i.e., in the back-to-back configuration, equalization im-proves performance of approximately 0.5 dB with respect to theunequalized system. This result can be explained by observingthat, since our strategy optimizes taps coefficients using /BERas a target, it minimizes both ISI and noise. Thus, the resultingreceiver equivalent filtering function tends to be closer to an ide-ally matched filter in the equalized case.IV. CONCLUSIONFor the first time, to our best knowledge, we have presenteda comprehensive analysis of electronic equalization in connec-tion to advanced modulation formats, showing that the use ofelectronic equalization based on FIR filter, while giving greatbenefit to standard NRZ, gives only limited advantages for DBand DPSK.ACKNOWLEDGMENTThe authors would like to thank RSoft Design Group, Inc. forsupplying the simulation tool OptSim.REFERENCES[1] S. Benedetto, E. Biglieri, and V. Castellani, Digital TransmissionTheory. Englewood Cliffs, NJ: Prentice-Hall, 1987.[2] J. G. Proakis and M. Salehi, Communication Systems Engineering. En-glewood Cliffs, NJ: Prentice-Hall, 1994.[3] J. H. Winters and R. D. Gitlin, “Electrical signal processing techniquesin long-haul fiber-optic systems,” IEEE Trans. Commun., vol. 38, pp.1439–1453, Sept. 1990.[4] H. Bülow, “Electronic equalization of transmission impairments,” inProc. Optical Fiber Communication (OFC 2002), pp. 24–25.[5] H. Bülow et al., “Adaptation of an electronic mitigator by maximizationof the eye opening,” presented at the Eur. Conf. Optical Communication(ECOC 2000), Munich, Germany.[6] H. Buchali et al., “Reduction of the chromatic dispersion penalty at 10Gbit/s by integrated electronic equalisers,” in Proc. Optical Fiber Com-muniation (OFC 2000), vol. 3, pp. 268–270.[7] M. Rohde et al., “Robustness of DPSK direct detection transmissionformat in standard fiber WDM systems,” Electron. Lett., vol. 36, pp.1483–1484, 2000.[8] K. Yonegana and S. Kuwano, “Dispersion tolerant optical transmissionsystem using duobinary transmitter and binary receiver,” J. LightwaveTechnol., vol. 15, pp. 1530–1537, Aug. 1997.[9] A. Carena et al., “A time-domain optical transmission system simulationpackage accounting for nonlinear and polarization-related effects in thefiber,” IEEE J. Select. Areas Commun., vol. 15, pp. 751–765, May 1997.[10] C. G. Broyden, “The convergence of a class of double-rank minimizationalgorithms,” J. Inst. Math. Application, vol. 6, pp. 76–90, 1970.[11] J. C. Lagarias et al., “Convergence properties of the Nelder-Meadsimplex method in low dimensions,” SIAM J. Optimization, vol. 9, pp.112–147, 1998.

Electronic equalization for advanced modulation formats in dispersion-limited systems

PORTO Publications Open Repository TOrino

2556 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 16, NO. 11, NOVEMBER 2004
Electronic Equalization for Advanced Modulation
Formats in Dispersion-Limited Systems
V. Curri, Member, IEEE, R. Gaudino, Member, IEEE, A. Napoli, and P. Poggiolini, Member, IEEE
Abstract—We investigate in this letter the use of electronic
equalization on dispersion-limited systems for different mod-
ulation formats. Besides analyzing equalization on standard
nonreturn-to-zero (NRZ) intensity modulation as a reference,
we focus on two advanced modulation formats, duobinary (DB)
and differential phase-shift keying (DPSK) which are recently
gaining a lot of attention. We demonstrate that the introduction of
an electronic equalizer strongly improves standard NRZ perfor-
mance, whereas, it has a limited effect on DB and DPSK formats.
Moreover, we give rules for the optimal choice of the equalizer
transversal filter parameters, i.e., the number of taps and the
delay between taps.
Index Terms—Adaptive equalization, dispersion equalization,
intersymbol interference (ISI), modulation, optical fiber commu-
nications, factor.
I. INTRODUCTION
THE USE of electronic equalization as a way to mitigatethe effects of intersymbol interference (ISI) in traditional
communications systems (i.e., wireless and copper wireline sys-
tems) has been deeply studied, and an extremely large amount
of literature is available [1], [2]. In general, all these techniques
are based on the use of a transversal digital filter (which acts
as a finite impulse response (FIR) filter) at the receiver with
a proper choice of taps parameter. In early 1990s, Winters et
al. [3] proposed for the first time the use of electronic equal-
ization in optical communication system. This approach has re-
cently gained momentum, as it is today seen as a cheaper (even
though less performing) alternative to all-optical equalization.
Several solutions have been proposed, mainly in order to reduce
the system impact of chromatic dispersion (CD) [4], [6] and po-
larization-mode dispersion (PMD) [5].
Electronic compensation in optical systems still lacks a com-
plete theoretical understanding. This is mainly due to the fact
that the analysis carried out for equalization of linear channels
in traditional communication systems [1], [2] cannot be directly
applied to the optical environment, where CD and PMD are
linear at the “optical” level, but (particularly for CD) become
nonlinear at the receiver side after the photodiode “square-law”
conversion [4]–[6].
In this letter, we focus on CD electrical compensation for sys-
tems limited by amplified spontaneous emission (ASE) noise,
Manuscript received March 29, 2004; revised June 30, 2004.
V. Curri is with the Dipartimento di Elettronica, OCG-PhotonLab, Politec-
nico di Torino, Torino 10129, Italy, and also with ATS Srl, Torino 10129, Italy
(e-mail: vittorio.curri@polito.it).
R. Gaudino, A. Napoli, and P. Poggiolini are with the Dipartimento di Elet-
tronica, OCG-PhotonLab, Politecnico di Torino, Torino 10129, Italy.
Digital Object Identifier 10.1109/LPT.2004.835192
Fig. 1. Block diagram of the analyzed system setup.
focusing on advanced modulation formats. Recently, alterna-
tive modulation formats have been proposed in order to over-
come linear and nonlinear propagation limits of standard NRZ.
Among these formats, the most promising for an advantageous
implementation seem to be the differential phase-shift keying
(DPSK) [7] and the optical duobinary (DB) [8]. Anyway, the
combination of advanced modulation formats with electronic
equalization has not been deeply studied yet, at least to the best
of our knowledge.
The purpose of this work is, thus, twofold. On one side, we
analyze the impact of electronic equalization on DB and DPSK
modulation formats, comparing the results to standard NRZ,
which is taken as a reference. On the other side, we present a
set of results on the optimization of equalizer transversal filter
number of taps and delay between taps (for each modulation
format).
This letter is organized as follows. In Section II, we describe
the reference scenario and the equalizer scheme together with
the algorithm used for the evaluation of the FIR filter coeffi-
cients. In Section III, we present the simulation results, demon-
strating that the electronic equalization may strongly improve
NRZ performance, but has a limited effect on systems based on
DB and DPSK modulation formats. Finally, in Section IV, we
draw the conclusions and envision possible evolutions of this
work.
II. SYSTEM SETUP
We analyzed and simulated [9] the system scenario shown
in Fig. 1, corresponding to an externally modulated system
limited by the accumulation of ASE noise and by CD-induced
ISI, while we neglect other effects, such as fiber nonlinearities.
These assumptions are reasonable for high-capacity metro and
extended metro links using single-mode fibers, a scenario that
1041-1135/04$20.00 © 2004 IEEE
CURRI et al.: ELECTRONIC EQUALIZATION FOR ADVANCED MODULATION FORMATS IN DISPERSION-LIMITED SYSTEMS 2557
is today gaining increasing attention, due to the new optical
market trends.
We considered an Gb/s systems using a chirp-
free external Mach–Zehnder amplitude modulator (MZM) at the
transmitter side. For the three considered modulation formats,
the MZM operates according to different driving schemes. Let
be the driving voltage for a minimum (maximum) of
the MZM transfer function, and the resulting
ON–OFF voltage swing. In order to produce standard NRZ mod-
ulation, the MZM is simply driven between and volt-
ages. For the DPSK modulation format, the input digital stream
is first differentially precoded, then the MZM is driven between
the two voltages [2]. This scheme yields a two-level
phase modulation associated to “0” and “ ” radians. To obtain
a DB modulation, the input digital stream is processed by the
DB precoder and then filtered using a narrow lowpass electric
filter (five-pole Bessel filter with 3-dB bandwidth equal to
) [8]. The filtered sequence is used to drive the MZM
between the two voltages [8].
The modulated optical signal is sent to an optical channel af-
fected by CD and ASE noise. For all modulation formats, results
will be presented as a function of the optical signal-to-noise ratio
(OSNR) (calculated over an optical bandwidth of 50 GHz) at the
receiver input.
We assumed to use a standard optical receiver, based on a
second-order super-Gaussian optical filter, having a 3-dB
bandwidth equal to GHz, an ideal photodiode and
a typical Bessel fifth-order electrical filter 3-dB bandwidth
for NRZ and DPSK. For the DB format only,
we used an electrical filter with , a value that,
according to [8], optimizes DB tolerance to CD.
We analyze a standard equalizer structure based on a
transversal FIR filter in a feedforward equalization configura-
tion [1], i.e., a filter that, when receiving an electrical signal
, generates at its output the signal
(1)
where is the number of taps, the delay between taps,
and the taps’ coefficients, which are optimized using the
strategy described in the following section.
System performance was evaluated by using the factor1
defined as , where BER stands for the
bit-error rate and is the inverse of the complementary
error function. In this letter, the factor is always presented
in decibel units defined as . We
spanned system parameters (OSNR and CD) in order to cover
the 9–15-dB range for the factor.
III. SIMULATION AND RESULTS
As an optimization strategy, we used standard numerical op-
timization routines (such as the quasi-Newton method [10] and
the simplex search method [11] implemented inside the com-
mercial software Matlab) based on finding, for each system re-
alization, the vector of taps coefficients that maximizes the
factor, i.e., that minimizes the BER.
1The Q factor was optimized by choosing the optimum clock phase.
Fig. 2. OSNR versus D at Q = 17 dB for the NRZ-OOK format.
Different dotted curves refer to T = T , T =2, T =3, and N = 15.
The unequalized curve is shown as comparison.
Besides the tap coefficients, we also investigate different
values for the delay and the number of coefficients .
In particular, we explored , , and (where
is the bit duration) and and .
For each system setup, we performed an accurate time-do-
main simulation [9] of the signal propagation, then we
optimized the equalizer FIR coefficient and obtain the resulting
factor. The simulated digital stream was a PRBS
sequence. We explored accumulated CD values in the
[0,4600]-ps/nm range, and OSNR dB range. We
presented all results showing the trace connecting all points
giving rise to a factor equal to 17 dB (corresponding to
) in the and OSNR plane. Basically, we
show a plot of the OSNR required to get dB for each
value of . We compared each system with and without
equalizer.
We start by investigating, for the standard NRZ format, the
influence of the tap delay and the number of taps .
Results are shown in Fig. 2; the different curves refer to the un-
equalized system, and to the equalized system for
(i.e., an extremely long transversal filter) and tap delays
, , and . Contrary to the typical results shown for
example in [1], we show that gives poor perfor-
mances, while a great improvement is obtained by using
. Moving to gives only marginal improve-
ment, showing that for our considered setup is a
good choice. We explain these results as follows. Most standard
studies on equalization [1], [2] assume that a “matched” filter
precedes the equalizer. In most cases, an integrate-and-dump
filter with integration time is assumed as a reference. In
this situation, choosing a delay is useless, since the
transversal filter acts on samples that are already correlated on a
time window by the filter preceding the equalizer. On the con-
trary, in our scenario, we assumed typical optical and electrical
filters that are always significantly larger than a “matched” filter,
and thus correlate the signal on a time window smaller than ,
consequently justifying a tap delay smaller than .
After setting , we investigated the performance
for different values. We show in Fig. 3 the results for the
cases and . This figure shows that an FIR
equalizer with more than seven taps does not increase perfor-
mances. We notice here that a filter with seven taps and
has a total “memory” equal to approximately 4 bits. We
2558 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 16, NO. 11, NOVEMBER 2004
Fig. 3. OSNR versus D at Q = 17 dB for the NRZ-OOK format.
Different dotted curves refer to N = 3; 7; 11; and 15, and T = T =2.
The unequalized curve is shown as comparison.
Fig. 4. OSNR versus D at Q = 17 dB for the NRZ-OOK, DPSK, and DB
format. Equalized results are obtained with N = 7 and T = T =2 for
NRZ-OOK and DPSK, and N = 15 and T = T =3. The unequalized
curves are shown as comparison.
observed that for high dispersion values, the seven taps coeffi-
cients are approximately symmetric with respect to the central
taps, as can be expected from the symmetric nature of the disper-
sion impulse response. This physically means that the equalizer
“handles” a time window with a range around the sam-
pling time of each bit.
Using these optimized parameters and
, Fig. 3 shows that electronic equalization can greatly im-
prove performance for the standard NRZ format. We define the
CD limit as the value giving a 2-dB OSNR penalty with re-
spect to the back-to-back configuration; in Fig. 3, it can be ob-
served that the back-to-back configuration requires an OSNR
dB (in order to give a factor equal to 17 dB), so that the
2-dB OSNR penalty corresponds to the points of the curve that
crosses the OSNR dB level. Using this reference, we ob-
serve an improvement from 750 ps/nm in the unequalized case
to 1550 ps/nm in the equalized case, i.e., approximately a dou-
bling of the dispersion limit.
Finally, we compared in Fig. 4 all the considered modulation
formats with (dashed lines) and without (solid lines) equaliza-
tion. This is the fundamental result of this letter, showing that,
for DPSK and DB, electronic equalization does not significantly
increase performance. Using the same reference introduced for
NRZ, it can be seen that electronic equalization improves the
dispersion limit by only 250 ps/nm for both DPSK and DB. The
limited benefit given by electronic equalization on these two
modulation formats is not easy to be intuitively interpreted. A
first observation is that both formats generate an electrical signal
that, even without CD, shows a strong correlation over a one bit
time window. This is due to the very narrow filtering at the trans-
mitter side for DB, and by the receiver interferometric filter for
DPSK. Moreover, in the case of DB, the format is intrinsically
extremely robust to CD, as it has been shown in many papers,
such as [8]. In fact, as shown in Fig. 4, it can be noted that the DB
format, without equalization, reaches approximately the same
performance of the back-to-back NRZ ( dB with only
OSNR dB) for ps/nm. The corresponding
eye diagram is this situation is nearly ISI-free, and thus, it cannot
be significantly improved by equalization.
Finally, we notice that for all formats, and even without dis-
persion, i.e., in the back-to-back configuration, equalization im-
proves performance of approximately 0.5 dB with respect to the
unequalized system. This result can be explained by observing
that, since our strategy optimizes taps coefficients using /BER
as a target, it minimizes both ISI and noise. Thus, the resulting
receiver equivalent filtering function tends to be closer to an ide-
ally matched filter in the equalized case.
IV. CONCLUSION
For the first time, to our best knowledge, we have presented
a comprehensive analysis of electronic equalization in connec-
tion to advanced modulation formats, showing that the use of
electronic equalization based on FIR filter, while giving great
benefit to standard NRZ, gives only limited advantages for DB
and DPSK.
ACKNOWLEDGMENT
The authors would like to thank RSoft Design Group, Inc. for
supplying the simulation tool OptSim.
REFERENCES
[1] S. Benedetto, E. Biglieri, and V. Castellani, Digital Transmission
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A.Carenaetal.,“Atime-domainopticaltransmissionsystemsimulation package accounting for nonlinear and polarization-related effects in the ﬁber,”

Adaptation of an electronic mitigator by maximization of the eye opening,” presented at the

Cliffs,

Digital Transmission Theory. Englewood Cliffs,

Dispersion tolerant optical transmission system using duobinary transmitter and binary receiver,”

Electrical signal processing techniques in long-haul ﬁber-optic systems,”

Electronic equalization of transmission impairments,” in

Lagarias et al., “Convergence properties of the Nelder-Mead simplex method in low dimensions,”

Reduction of the chromatic dispersion penalty at 10 Gbit/s by integrated electronic equalisers,” in

Robustness of DPSK direct detection transmission format in standard ﬁber

V. Curri

R. Gaudino

A. Napoli

P. Poggiolini

Crossref

Electronic Equalization for Advanced Modulation Formats in Dispersion-Limited Systems

https://iris.polito.it/retrieve/handle/11583/1403866/45390/10347_UPLOAD.pdf

Electronic equalization for advanced modulation formats in dispersion-limited systems

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