100 Gb/s MB-OFDM Metropolitan Networks
Employing SSBI Mitigation in Presence of Fiber
PMD Effect
Artur R. T. Duarte, Tiago M. F. Alves and Adolfo V. T. Cartaxo
Instituto de Telecomunicações, Dep. Electrical and Computer Engineering, Instituto Superior Técnico
Universidade de Lisboa, Lisbon, Portugal
[email protected], [email protected], [email protected]
Abstract—The performance of a 100 Gb/s direct-detection
(DD) multiband orthogonal frequency-division multiplexing (MBOFDM) metropolitan network employing a digital signal processing based iterative signal-signal beat interference (SSBI)
mitigation algorithm in presence of polarization mode dispersion
(PMD) is evaluated through numerical simulation. The study
comprises both the first- and second-order PMD. The MB-OFDM
signal is composed by 12 OFDM bands per wavelength where
each band slot has a 3.125 GHz bandwidth and each OFDM
band has a 2.333 GHz bandwidth. The trade-off between the
number of fiber segments considered by the PMD model and
the quality of the PMD emulation is studied. The results show
that the quality of the PMD emulation remains almost constant
for a number of fiber segments equal to 50 or higher. Also, the
results show that the impact of first- and second-order PMD
on the system performance can be neglected for standard single
mode fibers link lengths up to 400 km. The number of iterations
needed by the SSBI mitigation algorithm to converge is the same
either considering or neglecting the PMD effect.
Index Terms—orthogonal frequency-division multiplexing,
multiband, direct-detection, polarization mode dispersion, signalsignal beat interference.
I. I NTRODUCTION
Recently, the metropolitan (metro) network based on directdetection (DD) multiband orthogonal frequency-division multiplexing (MB-OFDM) signals (MORFEUS) has been proposed to provide high granularity, switching capabilities and
high spectral efficiency [1]. The MORFEUS network employs
virtual carrier (VC) assisted DD in which the VC are generated
in the electrical domain together with each OFDM band and
one virtual carrier per OFDM band is employed enabling
the use of a low-bandwidth and low-cost receiver [1]. The
performance of a 42.8 Gb/s MORFEUS network employing
a 2-band, 3-band and 4-band MB-OFDM signal has been
optimized in [2] for a 240 km optical metro link, in which a
bit error rate (BER) of 10−3 was obtained for an optical signal
to noise ratio (OSNR) equal to 24 dB. However, the impact of
polarization mode dispersion (PMD) fiber on the performance
of the MORFEUS network is yet to be assessed. In [3], the
performances of three single-receiver DD-OFDM formats at
42.7 Gb/s in presence of PMD were compared and a new
format more tolerant to PMD was proposed. However, because
a single larger OFDM band per wavelength was used, such
formats present much lower granularity than the MORFEUS
signals.
In this work, the performance of the MORFEUS network
in presence of PMD is evaluated. Despite the fact that the
performance of the MORFEUS network was evaluated for
a bit-rate of 42.8 Gb/s, the traffic growth experienced along
the last years encourage the development of next generation
systems with 100 Gb/s per wavelength to be employed in
metro networks. Therefore, a 12-band DD MB-OFDM system
at 100 Gb/s is considered.
II. S YSTEM DESCRIPTION
The MORFEUS metro network is composed by MORFEUS
nodes interconnected in a ring topology by standard single
mode fiber (SSMF) [1]. The insertion and extraction of the
OFDM bands from or to a metro ring are performed by the
MORFEUS insertion block (MIB) and MORFEUS extraction
block (MEB), respectively [1]. The band selector (BS) used
in the MEB is a 2nd order super Gaussian filter with the optimized parameters presented in table I [4]. To focus the analyses on the PMD effect, the impact of the passthrough nodes
on the MORFEUS network performance is neglected. Fig. 1
illustrates the MB-OFDM system equivalent to the MORFEUS
network under the above-mentioned conditions. Firstly, the
12-band MB-OFDM signal is generated in electrical domain
in a MB-OFDM transmitter. The electrical MB-OFDM signal
is converted to the optical domain by a dual-parallel MachZehnder modulator (DP-MZM) which generates a single side
band (SSB) signal. The MB-OFDM signal is inserted in the
metro network by a MIB. One band of the MB-OFDM signal
is extracted at a given node by a MEB. Afterwards, the OFDM
band signal enters the PIN photodetector where is converted
to the electrical domain and the electrical OFDM signal is
demodulated at the OFDM receiver.
The photodetection process generates signal-signal beat
interference (SSBI). When the frequency gap between the
VC and the OFDM band is reduced (to increase spectral
efficiency), the SSBI causes signal distortion and it must be
mitigated. The SSBI mitigation technique considered consists
MB-OFDM
transmitter
DP-MZM
SSMF
MIB
(1)
OFDM
receiver
MEB
PIN
TABLE I: MB-OFDM system parameters and values.
Number of bands
Data bit rate
Line bit rate (12% overhead)
Number of subcarriers
Bb
Bslot
Central frequency of the 1st OFDM band
VBG
VC-to-band power ratio
Mapping scheme
BS -3 dB bandwidth
BS detuning
12
100 Gb/s
112 Gb/s
128
2.333 GHz
3.125 GHz
1.563 GHz
18.23 MHz
7 dB
16 QAM
2.2 GHz
300 MHz
III. T HEORETICAL M ODEL OF PMD
As a consequence of fiber asymmetry, signals propagating
in different polarizations propagate at different speeds causing
a delay between polarizations at the receiver [5]. This effect
is called PMD. In order to study a fiber link where both firstand second-order PMD are considered, the optical fiber can
be viewed as a concatenation of short fiber segments with a
given mean birefringence and random coupling angles between
consecutive segments. Fig. 2 illustrates the concatenation of
Nseg fiber segments. The angle αn is the coupling angle
between the (n − 1)th and nth segments, and hn is the length
of the nth segment.
It is possible to calculate the optical field at the output of
~ b (ω) =
the fiber for a given optical field at the input as E
~
T (ω)Ea (ω) [6] where T (ω) is the Jones matrix that describes
~ a (ω) and E
~ b (ω) are the
a concatenation of Nseg segments, E
α2
(3)
h2
α3
(Nseg)
...
h3
αN
h
seg
Nseg
Fig. 2: Illustration of the concatenation of Nseg fiber segments.
Fig. 1: Illustration of the MB-OFDM system.
of a digital signal processing (DSP) based iterative algorithm,
similar to the one used in [1]. The goal of the SSBI mitigation
algorithm is to estimate the SSBI term and subtract it from the
photodetected signal, with the objective of obtaining a SSBIfree signal.
The main parameters of the MB-OFDM system are summarized in table I. A detailed definition of those parameters can
be found in [1]. The MB-OFDM signal is composed by 12
OFDM bands, each one with bandwidth equal to Bb wherein
each band is positioned at the center of each the 12 band slots
with bandwidth equal to Bslot . In order to choose a suitable
value for VC-to-band gap (VBG), it is important to take into
account that the virtual carrier must not interfere with the
OFDM band. The optimal value of the VBG was found to
be equal to the subcarrier frequency spacing between adjacent
subcarriers of the OFDM band.
h1
α1
(2)
principal states of polarization (PSP) representations of the
signal in frequency domain at the input and output of the fiber,
respectively.
The Jones matrix T (ω) can be calculated as [7]
Nseg
T (ω) =
Nseg
=
Y
Bn (ω)R(αn )
n=1
 √
√
j
3π/8 bω hn /2+φn
Y e

n=1
"
0
cos(αn )
sin(αn )
− sin(αn )
cos(αn )

e
−j
√
0


√
3π/8 bω hn /2+φn
#
(1)
where Bn (ω) is the birefringence matrix of the nth segment,
R(αn ) is the rotation matrix that emulates the coupling between the (n−1)th and
√ nth segments, b is the PMD coefficient
of the fiber in ps/ km and ω is the optical frequency in
rad/s. The phase φn accounts for small temperature fluctuations along the fiber which can be described by an uniform
distribution between 0 and 2π. The coupling angle αn is also
described by an uniform distribution between 0 and 2π.
The length of the segments are randomly generated from a
Gaussian distribution around a given mean length per segment
with standard deviation equal to 30% of the mean length per
segment, as suggested in [7].
IV. O PTIMIZATION OF THE NUMBER OF SEGMENTS OF THE
PMD EMULATION
The PMD emulation is accomplished by employing the
theoretical model of PMD described in section III through
numerical simulation. Due to the complexity of the computation required to perform such simulation for a wide range
of frequencies, the very long simulation time is a concern.
Since the simulation time depends linearly on the number of
fiber segments considered for the PMD emulation, a study of
the trade-off between the number of segments and the quality
of the PMD emulation is performed. Fig. 3 represents the
histogram of the differential group delay (DGD) resulting from
10000 T (ω) matrix realizations considering 800 segments and
a specific (optical) frequency.
A SSMF with a PMD coefficient
√
of DP M D = 0.5 ps/ km and fiber length of 400 km is
considered. Fig. 3 shows that the statistical distribution of the
DGD follows closely the Maxwellian distribution [8] [9]. A
similar histogram was obtained for only 5 segments. Such
result may wrongly lead to the conclusion that the quality
of the PMD emulation is similar if a number of segments
−10
12
10
8
6
4
5
10
15
20
25
8
6
4
2
0
0
2
0
0
x 10
|dDGD/df | [ps/Hz]
|dDGD/df | [ps/Hz]
norm. frequency [x10 −2]
−10
8
14
30
0.5
1
f [THz]
1.5
4
2
0.5
1
1.5
2
f [THz]
(a) For Nseg = 5
(b) For Nseg = 10
−10
8
−10
x 10
|dDGD/df | [ps/Hz]
8
|dDGD/df | [ps/Hz]
between 5 and 800 is considered. However, that might not be
true since the analysis based on the histograms does not take
into account the fluctuations of the DGD along the frequency.
In order to extend the study to analyze such fluctuations, it
is important to make a comparison between the fluctuations of
the DGD along frequency when different numbers of segments
are considered. The absolute value of the slope of the DGD as
a function of the equivalent baseband frequency is presented
in fig. 4 for Nseg equal to 5, 10, 50 and 300. Fig. 4 shows that
when the number of segments considered is 5 or 10, the slope
values of the DGD are small. This means that the fluctuations
of the DGD along the frequency are smooth. On the other
hand, when the number of segments considered is higher than
50, such fluctuations are stronger and seems to remain similar
for values up to Nseg = 300. Assuming that the higher the
number of segments, the more realistic is the PMD model,
then the best choice would be 300 segments. However, due to
long simulation times required to evaluate the PMD in case of
higher number of segments, which are unacceptable for this
work purpose, the choice of Nseg = 100 offers a good tradeoff between simulation time and PMD emulation quality.
6
0
0
2
DGD [ps]
Fig. 3: Histogram of the DGD resulting from 10000 T (ω) matrix realizations. Continuous line: theoretical Maxwellian probability density
function. Nseg = 800.
x 10
6
4
2
0
0
0.5
1
1.5
2
x 10
6
4
2
0
0
0.5
1
1.5
2
f [THz]
f [THz]
(c) For Nseg = 50
(d) For Nseg = 300
Fig. 4: Absolute value of the slope of the DGD as a function of the
equivalent baseband frequency for a fiber length equal to 400 km.
Then, each T (ω) matrix is organized into the DGD categories.
Notice that, due to the very low probability of high DGD
values, some DGD categories may end up empty. One T (ω)
matrix from each DGD category is chosen to serve as sample,
and it is used as a channel transfer function. The BER resulting
from each one of the DGD categories is multiplied by the
occurrence probability of that same category to obtain the
contribution to the overall weighted mean BER of each DGD
category. The overall weighted mean BER calculation is given
by
hBERi =
100
X
BERn P [(n − 1)∆τ ≤ DGD < n∆τ ]
(2)
n=1
V. S YSTEM PERFORMANCE EVALUATION IN PRESENCE OF
FIRST- AND SECOND - ORDER PMD
In this section, the performance of the 100 Gb/s DD MBOFDM system employing SSBI mitigation in presence of
PMD is evaluated. Also, the study assumes that the time
interval between two consecutive sequences of OFDM training
symbols is very short when compared with the PMD variations
along time. In this way, time fluctuations of the channel transfer function are properly followed by the equalizer estimated
from the training symbols.
A. Description of the performance evaluation method
In order to evaluate the system performance taking into
account the DGD, the following method was used. The DGD
range of values is divided in ∆τ width intervals from 0 ps up to
100∆τ . These intervals are denominated as DGD categories.
From a set of approximately 2500 T (ω) matrices randomly
generated (for a given fiber length), the DGD value at the
frequency where the center of the OFDM band to be selected
is positioned, is calculated using the method described in [6].
where n identifies the DGD category and BERn is the BER
resulting from the nth DGD category. P [τ1 ≤ DGD < τ2 ]
stands for the probability of the DGD being between τ1 and τ2
and is calculated from the theoretical Maxwellian PDF. Notice
that Maxwellian distribution mean depends on the fiber length
considered.
B. Results of the performance evaluation
In order to obtain results as much comparable to real system
as possible, the CD effect is included by multiplying T (ω) by
the transfer function of the CD. Simulations, where CD alone
is considered, showed that the equalizer of the OFDM receiver perfectly compensates for the CD. This is an important
conclusion that allows a proper analysis of the PMD impact.
Also, simulations in back-to-back configuration showed that
the 11th band has the worst performance, with a required
OSNR = 31.3 dB to achieve BER = 10−3 . Therefore, 11th
band is the one to be demodulated at the OFDM receiver. The
BER is calculated from 100 noise runs using the exhaustive
Gaussian approach proposed in [10]. This remarkable increase
−2.4
0.06
−2.8
0.04
−3.2
0.02
0
1
−3.6
26
51
76
DGD category
log 10 (weigthed BER n )
−2
log 10 BER n
Prob [DGD category]
0.08
−4
100
to conclude that the performance of the 100 Gb/s DD MBOFDM network employing SSBI mitigation is not affected by
first- and second-order PMD for SSMF lengths up to 400 km.
−3
−4
−5
−6
VI. C ONCLUSION
−7
−8
−9
1
26
51
76
100
DGD category
(a)
(b)
Fig. 5: (a) BER of the system and occurrence probability of each
DGD category; (b) weighted BER of each DGD category. In both
plots, fiber link with 400 km length.
of required OSNR in comparison with the one reported in [1]
is attributed to the higher bit-rate considered in this
√ work.
A SSMF with PMD parameter DP M D = 0.5 ps/ km is
considered. This is a ”worst-case” of DP M D for modern fibers
[11]. The method described in V-A is applied for a width of
the DGD intervals of ∆τ = 0.4 ps.
Fig. 5a shows the BER of the system resulting from each
DGD category, superimposed with the occurrence probability
of each DGD category for a 400 km fiber link. The BERn is
almost the same for all DGD categories, therefore, the impact
of DGD on BER along the range of the DGD shown in fig.
5a is very reduced. Fig. 5b shows the weighted BER of each
DGD category which is calculated using the argument of the
summation from equation 2. We can see that the contribution
of each DGD category for the hBERi is progressively lower
(exponential decaying) for higher values of DGD. This is an
important remark because, despite the DGD categories higher
than n = 76 are empty (as seen in fig. 5a), the hBERi remains
almost unaffected. Fig. 6 represents the hBERi as a function
of the fiber length in presence of CD, optical noise, first- and
second-order PMD. The number of iterations required for the
SSBI mitigation algorithm to stabilize is 5. The same number
of iterations was obtained for a simulation were the PMD is
neglected. As can be seen in fig. 6, the hBERi of the system
remains almost constant, with slight non-relevant fluctuations,
for fiber lengths from 0 up to 400 km. Therefore, it is possible
log 10 <BER>
−2
−2.5
−3
−3.5
−4
0
100
200
300
400
Lf [km]
Fig. 6: Overall weighted mean BER, hBERi, as a function of the
fiber length in presence of first- and second-order PMD, CD and
optical noise.
The impact of PMD on 100 Gb/s DD MB-OFDM metropolitan networks employing SSBI mitigation was evaluated thorough numerical simulation. The trade-off between the number
of fiber segments considered for the PMD model and the
quality of the PMD emulation was studied.
The results showed that the quality of the PMD emulation
remains almost constant for a number of fiber segments equal
to 50 or higher. It was shown that the first- and second-order
PMD do not affect the performance for SSMF lengths up to
400 km. The number of iterations needed for the DSP-based
iterative SSBI mitigation algorithm to converge is the same
either considering or neglecting the PMD effect.
ACKNOWLEDGMENT
This work was supported by Fundação para a
Ciência e a Tecnologia (FCT) from Portugal through
Project MORFEUSPTDC/EEITEL/2573/2012. The project
UID/EEA/50008/2013 is also acknowledged.
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