A Comparison of Different Options to Improve PDM-QPSK
Resilience against Cross-channel Nonlinearities
Donato Sperti, Paolo Serena and Alberto Bononi
Università degli Studi di Parma, Dipartimento di Ingegneria dell’Informazione, viale G. Usberti 181/A,
43124 Parma (Italy),
B donato.sperti@nemo.unipr.it
Abstract Q-factor improvements induced by channel walk-off coming from either chromatic dispersion,
or PMD, or in-line XPM suppressors are compared in 112 Gb/s PDM-QPSK WDM transmissions with
NRZ, aligned-RZ and interleaved-RZ pulses.
Introduction
Polarization division multiplexing (PDM) - quadra-
ture phase shift keying (QPSK) has emerged
as one of the most attractive solutions for 100
Gb/s transmissions. While single-channel lin-
ear impairments can be almost completely com-
pensated by means of digital signal process-
ing (DSP) based coherent detection, the perfor-
mance of wavelength division multiplexing (WDM)
transmissions on a 50 GHz grid is set by cross-
channel fiber nonlinearities
1
. As a way to mit-
igate cross-channel effects, some experiments
2
and simulations
1
verified the benefits of the inter-
leaved return-to-zero (iRZ) pulse format, in which
the polarization tributaries are 50%-RZ shaped
and delayed by half a symbol time. Polarization
mode dispersion (PMD) should reduce the iRZ
benefits by re-aligning the polarizations. How-
ever, PMD also introduces channel depolariza-
tion, thus reducing cross-channel effects, when
linear PMD is fully compensated at the receiver
3
.
Hence a quantitative analysis of the PMD impact
on iRZ transmission is of great interest. Cross-
channel nonlinearities can also be mitigated by
the fiber group velocity dispersion (GVD), which,
especially in links without dispersion manage-
ment (noDM), induces substantial channel walk-
off
1,4
. Another efficient way to increase channel
walk-off is to use passive devices that introduce
different delays on adjacent channels at specific
points of the line: such devices were introduced
to efficiently suppress cross-phase modulation
(XPM) in on-off keying (OOK) systems
5
. XPM
suppressors based on periodic group-delay have
already been successfully tested for PDM-QPSK
systems
6
, thus proving that they are effective not
only against XPM, but also against another fun-
damental impairment of PDM systems, namely,
cross-polarization modulation (XPolM)
7
.
In this paper we compare the effectiveness of
PMD, of GVD, and of the XPM suppressor in
Fig. 1: System simulation setup.
mitigating cross-channel nonlinearities in PDM-
QPSK transmissions for three different pulse for-
mats: iRZ, non-return to zero (NRZ) and aligned
RZ (aRZ).
System Setup
We simulated with the open-source software Op-
tilux
8
the transmission of a 19-channel 112Gb/s
PDM-QPSK homogeneous WDM system with 50
GHz channel spacing. All channels were first
modulated by nested Mach-Zehnder modulators
with independent 1024 De Bruijn sequences, and
then their states of polarization (SOP) were ran-
domized on the Poincaré sphere. Before creating
the WDM comb, each channel was filtered over a
0.4 nm bandwidth. The simulated link was com-
posed of 20 × 100 km spans of single mode fiber
(SMF), with zero overall cumulated dispersion ob-
tained with a linear post-compensating fiber. Two
different setups were considered: 1) a DM link
with pre-compensation of -650 [ps/nm] and 30
[ps/nm/span] of in-line residual dispersion, and
2) a noDM link without pre- and in-line compen-
sation. PMD was emulated only in the DM link,
since in absence of dispersion management the
interaction between PMD and Kerr nonlinearity is
known to be negligible
3
.
The XPM suppressor, when used, was imple-
mented by a demultiplexer followed by a bank
of delay lines and a multiplexer, as sketched in
Fig. 1. Each channel in the suppressor was de-
layed by D [ps] with respect to its left neighbor in
wavelength.
Fiber propagation was obtained by solving the
ECOC 2010, 19-23 September, 2010, Torino, Italy
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Manakov-PMD equation through the split step
Fourier algorithm
9
. Fiber birefringence and PMD
were emulated by using 50 different random
waveplates per span. We assumed flat gain
amplifiers with 6 dB noise figure at each span
end, although the entire link noise was loaded
as a unique white noise source before detec-
tion. Such an approach neglects nonlinear phase
noise, which is here negligible
3
. Before detection
we perfectly compensated optical linear impair-
ments, i.e. GVD and PMD, which allows us to fo-
cus entirely on the extra penalty coming from the
interplay of linear and nonlinear distortions along
the link.
The central channel was detected with a stan-
dard DSP based coherent receiver including: mix-
ing with an ideal local oscillator, low pass filtering
over a bandwidth of 17 GHz, sampling, phase-
recovery with the Viterbi algorithm using 7 taps,
decision, and finally differential decoding
4
.
We measured the bit error rate (BER) through
the Monte Carlo algorithm by counting 100 er-
rors
10
, and then converting the estimated BER
to Q-factor. To take into account the stochastic
nature of PMD, each BER was averaged over 40
different runs with different random seeds. Each
seed corresponded to a different random pattern,
SOP, and fiber waveplates realization. For a fair
comparison, we used the same random realiza-
tions when testing different setups.
Results and Discussions
We first measured the impact of the XPM sup-
pressor on the performance of the NRZ, aRZ or
iRZ-based system in a DM link without PMD. To
this aim we measured the Q-factor for each pulse
format by varying the delay D. For a fair compar-
ison, in the NRZ and aRZ case we set the power
to -1 dBm while for iRZ we used 2 dBm. With
this choice all formats experience similar nonlin-
ear effects
2
. Fig. 2(a) shows the Q-factor vs. de-
lay D. The error bars indicate the Q-factor stan-
dard deviation. We note that the XPM suppressor
is effective for all formats, with an increasing Q-
factor for increasing D, so that the best option is
to maximize the decorrelation among channels. A
complete decorrelation is reached after a delay of
roughly 10 symbols (357 ps).
We next studied the impact of PMD on the
same three pulse formats in a DM link without
suppressor. Here we set the power to -2 dBm for
NRZ and aRZ and to 1 dBm for iRZ. In Fig. 2(b)
we show the Q-factor vs. average DGD.
Fig. 2: Q-factor vs. suppressor delay at DGD=0 (a) and
vs. average DGD without suppressor (b) for the 20x100
km DM link with pulse formats NRZ, aRZ and iRZ.
This figure shows that the DGD improves the Q-
factor for all pulse formats, and that it saturates for
an average DGD larger than 20 ps, in agreement
with
3
.
We note that an average DGD of 5 ps improves
NRZ and aRZ Q-factor by 2 dB compared with
DGD=0, while for iRZ the improvement is of only 1
dB. The stochastic fluctuations of the Q-factor are
mostly due to XPolM and are related to the ran-
dom, symbol-dependent SOP orientation of the
PDM-QPSK signals. In fact, the standard de-
viation is larger at small DGD, where XPolM is
expected to be larger
3
. It is worth noting that
iRZ has a smaller standard deviation than aRZ
and NRZ at DGD=0, since iRZ is more tolerant
to XPolM in absence of PMD
1
. Note that the
iRZ Q-factor increases for increasing DGD, even
if PMD degrades the iRZ pulse-interleaving, be-
cause PMD-induced depolarization is more effec-
tive in reducing XPolM.
For the DM link and each pulse format, we also
report in Fig. 3 the Q-factor vs. power in ab-
sence/presence of either PMD (average DGD=0
or 22.5 ps) or XPM-suppressor (delay D equal to
0 or 10 symbols). As a reference, in the same
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Fig. 3: Q-factor vs. power for different pulse formats and DGD.
graphs we also report the single channel DM-
case and the WDM noDM-case, both in absence
of DGD. The figure confirms that in absence of
DGD the noDM link largely outperforms the DM
one. However, PMD improves the DM perfor-
mance yielding Q-factors very close to the noDM
case, and even better with iRZ pulses. Again, we
note for iRZ that the PMD-induced depolarization
compensates for the degraded time-interleaving.
From the figures, we also note that for aRZ and
NRZ the DM link with XPM suppressor has similar
performance as the noDM link, while for iRZ the
DM link with XPM suppressor is superior to the
noDM link, with a Q-factor very close to the single-
channel case. Reason is that the XPM suppres-
sor reduces cross-channel interactions, but does
not degrade pulse time-interleaving. It is thus the
best option for a PDM-QPSK link with iRZ pulses.
In a final test we investigated the performance
of the DM link with XPM suppressor in presence
or absence of PMD. The Q-factor vs. power is re-
ported in Fig.
4 for all pulse formats. We used
the same average DGD and suppressor delay of
Fig. 3. From Fig. 4 we note that PMD improves
performance except for iRZ, where we observe
a small decrease of the Q-factor in the nonlin-
ear regime (descending region of Q-factor) mak-
ing iRZ performance similar to aRZ. We ascribe
such a worsening to the PMD-induced deteriora-
tion of the pulses’ time-interleaving.
Conclusions
We investigated different solutions to mitigate
cross-channel nonlinearities in 112 Gb/s PDM-
QPSK transmissions. We showed that decor-
relating the channels, through either PMD, or
delay-line XPM suppressor, or by removing dis-
persion management, improves performance and
reduces the gap among iRZ, NRZ, and aRZ pulse
Fig. 4: Q-factor vs. power for a DM link with XPM sup-
pressor (10-symbol delay) with average DGD=0 (solid
line) and 22.5 ps (dotted line).
formats. We also showed that in iRZ-PDM-QPSK
the worsening of the pulses’ time-interleaving due
to PMD is more than offset by the positive PMD-
induced depolarization effect that reduces XPolM.
We find that the best option is to use iRZ-PDM-
QPSK in a DM link with an XPM suppressor at
each span to decorrelate channels without neither
compromising the time-orthogonality of the PDM
tributaries, as with PMD, nor inducing more non-
linear self-effects, as with noDM.
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