Impact of Inter-core Crosstalk on the Performance of Multi-core
Fibers-based SDM Systems with Coherent Detection
Bruno R. P. Pinheiro, Jo
˜
ao L. Rebola and Adolfo V. T. Cartaxo
Optical Communications and Photonics Group, Instituto de Telecomunicac¸
˜
oes, Lisboa, Portugal
Instituto Universit
´
ario de Lisboa (ISCTE-IUL), Lisboa, Portugal
Keywords:
Inter-core Crosstalk, Monte-Carlo Simulation, Multi-core Fibers, Optical Coherent Detection, Space-division
Multiplexing.
Abstract:
Inter-core crosstalk (ICXT) can limit the multi-core fiber (MCF) systems performance and transmission reach.
Over the last years, the impact of the ICXT on the performance of MCF optical communication systems with
coherent detection has been investigated in several works. However, the influence of the MCF parameters
and transmitted signal characteristics on the ICXT mechanism and the degradation induced by it on the per-
formance of coherent detection MCF systems are still to be completely assessed. In this work, the impact
of the ICXT on the performance of coherent detection MCF-based transmission systems is assessed through
numerical simulation considering fiber linear propagation. The metrics used to assess the MCF system per-
formance are the bit error rate (BER) and the optical signal-to-noise ratio (OSNR) penalty due to the ICXT.
Our results show that the BER and the OSNR penalty due to the detected ICXT, in MCF-based systems with
coherent detection, are influenced by the skew, time misalignment between the transmitted signals and the
roll-off factor of the transmitted signals. In the range of skew and roll-off factors analyzed, the maximum
reduction of maximum ICXT level for a 1 dB OSNR penalty by appropriate choice of skew and roll-off factor
does not exceed 1.7 dB.
1 INTRODUCTION
Current long-haul optical networks based on stand-
ard single-mode single-core fibers (SMFs) can no
longer respond efficiently to the exponential rapid
traffic growth. Thereby, in order to respond to the
ever-growing traffic demand, new technologies are re-
quired to reach higher capacities on the optical com-
munication systems (Klaus et al., 2017). Space divi-
sion multiplexing (SDM) has been proposed as a solu-
tion to achieve higher capacity in future long-haul op-
tical networks (Klaus et al., 2017). The implementa-
tion of SDM is based on two main approaches, which
consist basically on using two different types of fiber
(Saitoh and Matsuo, 2016). The first type of fiber is
known as few-mode fiber (FMF) and makes use of
several propagation modes in the fiber as transmis-
sion channels. The main drawback of FMFs is the re-
quirement of a multi-input multi-output (MIMO) di-
gital signal processing (DSP) receiver to minimize the
group delay spread between the different modes. Fur-
thermore, the FMF limits the exploitation of the space
domain, except for enhanced capacity-transmission
reach, since all modes must be received as a single
entity (Klaus et al., 2017). The second fiber type
is the multi-core fiber (MCF), in which, independent
channels are transmitted in different cores inside the
fiber. Thereby, the signals transmitted in each core
of the MCF can have different symbol rates, differ-
ent modulation formats and different temporal mis-
alignments between them. In homogeneous MCFs,
the relative uniformity of the cores supports multi-
dimensional spatial channels that enable shared trans-
mitter and receiver hardware, simplified DSP and
switching (Cartaxo et al., 2016). The use of MCFs
has been proposed for several optical communication
networks such as access, long-haul, intra-data centers
and radio-over-fiber based networks (Puttnam et al.,
2017), and so, in this work, we restrain our studies
only to MCF-based optical communication system.
As optical coherent detection with polarization-
division multiplexing (PDM) is the selected detec-
tion technology of actual backbone optical networks
(Xia and Wellbrock, 2013), the majority of the MCF-
based SDM systems tested so far, consider coherent
detection (Puttnam et al., 2017): in 2011, a high-
capacity transmission experiment reached 112 Tbps
capacity using a MCF with 7 cores and transmitting
74
Pinheiro, B., Rebola, J. and Cartaxo, A.
Impact of Inter-core Crosstalk on the Performance of Multi-core Fibers-based SDM Systems with Coherent Detection.
DOI: 10.5220/0006623400740081
In Proceedings of the 6th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2018), pages 74-81
ISBN: 978-989-758-286-8
Copyright © 2018 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
Figure 1: Schematic of the MCF-based SDM system with Nc transmitters (TX
1
to TX
Nc
) and the respective receivers (RX
1
to RX
Nc
). The signals transmitted in each core are multiplexed on the polarization.
PDM-QPSK signals (Zhu et al., 2011). By the end
of 2012, a 12 core MCF experiment exceeded 1 Pbps
capacity (Takara et al., 2012). In 2015, it was repor-
ted that a 22-core homogeneous MCF demonstration
exceeded 2 Pbps (Puttnam et al., 2015). It is ex-
pected that MCFs can attain a transmission capacity
beyond 10 Pbps (Morioka, 2017). MCF transmission
with coherent detection is definitely the most prom-
ising transmission technology that will allow to in-
crease substantially the transmission capacities of the
actual long-haul optical networks and to implement
SDM optical networks with low complexity.
However, an important limitation of the perform-
ance of the weakly-guided MCFs is the inter-core
crosstalk (ICXT) (Fini et al., 2010; Rademacher et al.,
2017a; Hayashi et al., 2014; Rademacher et al.,
2017b). ICXT arises in homogeneous MCFs which
have cores with similar properties. ICXT can be
reduced by increasing the distance between cores.
However, maintaining the same cladding diameter,
this method can lead to the reduction of the number
of cores, thus, reducing the overall transmission ca-
pacity (Hayashi et al., 2013; Hayashi et al., 2011).
Over the last years, the ICXT has been researched
and some relevant conclusions have been drawn con-
cerning the mechanism of the ICXT and its influence
on the performance of the MCF-based SDM systems
(Hayashi et al., 2014; Cartaxo et al., 2016). In (Hay-
ashi et al., 2014), a theoretical model of ICXT is pro-
posed and the impact of the ICXT on the performance
of the MCF transmission systems is assessed theor-
etically. In (Cartaxo et al., 2016), the ICXT model
presented in (Hayashi et al., 2014) is extended, by
considering the ICXT dependence on the group ve-
locity dispersion and the skew between cores. In ad-
dition, the transfer function of the ICXT field is de-
rived for homogeneous MCF. This transfer function
helps to study the influence of the ICXT on the per-
formance degradation of MCF-based optical systems
with walk-off between fiber cores (skew), slightly dif-
ferent group velocities between cores, and by consid-
ering different modulation formats (as the typically
ones used for coherent detection) at the MCF input.
In this work, we assess numerically through
Monte-Carlo (MC) simulation, the influence of the
ICXT on the bit error rate (BER) and the optical
signal-to-noise (OSNR) penalty of the MCF-based
optical communication system with coherent detec-
tion, considering 4-Quadrature Amplitude Modula-
tion (QAM) signals, with different roll-off factors,
different skews and different signal time misalign-
ments between MCF cores.
This work is organized as follows. Section 2 de-
scribes the equivalent simulation model used to char-
acterize the MCF-based optical communication sys-
tem with coherent detection and the ICXT impact on
its performance. The validation of the transfer func-
tion used in this work to emulate the ICXT behavior
on the MCF-based SDM system is performed in sec-
tion 3. In section 4, the performance of the MCF-
based SDM system with coherent detection impaired
by ICXT estimated through MC simulation is ana-
lyzed. The conclusions are outlined in section 5.
2 MCF-BASED SDM SYSTEM
MODEL
Figure 1 depicts schematically a MCF-based optical
communication system, with dedicated transmitter
and receiver hardware for each core. On the transmit-
ter side, several different signals are launched in the
MCF by Nc different transmitters, TX
1
to TX
Nc
, with
Nc corresponding to the number of cores used. Re-
mark that it is assumed that these transmitters gener-
ate independent SDM PDM-M-QAM signals, where
M is the modulation format order. The PDM-M-QAM
signals are propagated through the MCF and are de-
tected individually by Nc optical coherent receivers,
RX
1
to RX
Nc
. Core-coded modulation or polariza-
tion core-coded modulation is not considered, since
the characterization of the ICXT impact on the per-
formance of MCFs with independent transmission of
PDM-M-QAM signals in each core is not fully un-
derstood (Rademacher et al., 2017a). On the right
Impact of Inter-core Crosstalk on the Performance of Multi-core Fibers-based SDM Systems with Coherent Detection
75
MCF
+
ASE noise
Coherent
Receiver
Decision
Circuit
BER
E
n
(t)
E
m
(t) E
x
(t)
E
r
(t)
TX
n
TX
m
F (ω)
H
n
(ω)
E
n
(t)
+
I
I
(t)
I
Q
(t)
Figure 2: Equivalent simulation model for the MCF-based SDM system, considering single polarization transmission.
hand side of Figure 1, some of the detected PDM-
M-QAM signals in each core are depicted illustrat-
ively. Since, each core works as a transmission chan-
nel independent of the other cores, each transmitted
signal can have different symbol rates, different mod-
ulation formats and different temporal misalignments
between them.
Figure 2 depicts the equivalent simulation model
of MCF-based SDM with coherent detection consid-
ering single polarization transmission and only two
cores. The interfered core is the core n and the in-
terfering core is the core m. The performance of a
PDM system with optical coherent detection can be
assessed by evaluating only one signal polarization
as long as ideal PDM is assumed (Essiambre et al.,
2010). Moreover, we assume ideal compensation of
the chromatic dispersion at the coherent receiver out-
put. The detected signals have a raised-cosine (RC)
pulse shape in order to eliminate the inter-symbol in-
terference at the decision circuit. The RC signals
can be generated by making use of the RC filter,
which transfer function, H
RC
( f ), is (Carlson and Cri-
lly, 2009)
H
RC
( f ) =
T
s
0 |f |
1β
2T
s
T
s
cos
2
h
πT
s
2β
|f |
1β
2T
s
i
1β
2T
s
|f |
1+β
2T
s
0 |f |>
1+β
2T
s
(1)
where T
s
is the symbol period and β is the roll-
off factor. Alternatively, the RC signals can be ob-
tained by having root raised-cosine (RRC) filters at
the transmitter and at the receiver, in such a way that
h
RRC
(t)h
RRC
(t) = h
RC
(t), where * is the convolution
operator (Carlson and Crilly, 2009). Hence, the trans-
fer function of the RRC filter is H
RRC
( f ) =
p
H
RC
( f ).
The transmitter output signal of the core n, E
n
(t),
with RRC pulse shape, can be expressed by
E
n
(t) =
P
n
+
i=
(a
I,i
+ ja
Q,i
)h
RRC
(t iT
s
) (2)
where a
I,i
and a
Q,i
are the amplitude of the in-phase
(I) and quadrature (Q) components of the i-th M-
QAM transmitted symbol, respectively, and P
n
is the
average power of the transmitted signal at core n. The
transmitted signal at core m, E
m
(t) is expressed as
E
m
(t) =
P
m
+
i=
(a
(m)
I,i
+ ja
(m)
Q,i
)h
RRC
(t iT
s
τ
mn
)
(3)
where P
m
is the average power of the transmitted sig-
nal at core m, a
(m)
I,i
and a
(m)
Q,i
are the I and Q com-
ponents of the i-th M-QAM transmitted symbol of
E
m
(t), respectively. The amplitude levels, a
b,i
and
a
(m)
b,i
, b {I,Q} are random variables that take on
equally likely the following values:
a
b,i
1,±3, ...,±
M 1}A (4a)
a
(m)
b,i
1,±3, ...,±
M 1}A
(m)
(4b)
where A and A
(m)
are amplitudes that are defined in
order that the powers corresponding to the fields E
n
(t)
and E
m
(t) are P
n
and P
m
, respectively. τ
mn
is the
temporal misalignment between E
m
(t) and E
n
(t), that
takes values between 0 and T
s
. The temporal mis-
alignment is the difference between the signal trans-
mission time instants of the each transmitter with ref-
erence to the interfered core, i.e., the core in which
the receiver performance is assessed.
The propagation in core n is characterized by the
transfer function H
n
(ω) = e
jβ
n
(ω)L
, where β
n
is the
propagation constant of core n and L is the length of
the MCF. The resulting signal after propagation in
the n-th core, E
0
n
(t), is described by E
0
n
(t) = E
n
(t)
F
1
[H
n
(ω)] (Agrawal, 2010), where F
1
[ ] is the in-
verse Fourier transform operator.
The equivalent simulation model of the MCF to
characterize the ICXT between cores m and n is
defined by the ICXT field transfer function F(ω)
given by (Cartaxo et al., 2016)
F(ω) = jK
nm
e
jβ
n
(ω)L
N
k=1
e
j∆β
mn
(ω)z
k
e
jφ
k
(5)
where K
nm
is the discrete coupling coefficient
between cores m and n, N is the number of phase-
matching points (PMPs), and φ
k
is the random phase
PHOTOPTICS 2018 - 6th International Conference on Photonics, Optics and Laser Technology
76
shift, introduced at the k-th center point (with longit-
udinal coordinate z
k
) between consecutive PMPs, that
is distributed uniformly between 0 and 2π (Cartaxo
and Alves, 2017). In Equation (5), ∆β
mn
is the differ-
ence between the propagation constants of core m and
n, given by
∆β
mn
(ω) = ∆β
0,mn
+ d
mn
ω
1
2
D
mn
λ
2
2πc
ω
2
(6)
In Equation (6), c is the speed of light in vacuum,
λ is the wavelength, ∆β
0,mn
is the difference of the
propagation constants at zero frequency, D
mn
is the
difference between the dispersion parameters of core
m and n, and d
mn
is the walkoff between cores m and
n, defined by d
mn
= ν
1
gm
ν
1
gn
, with ν
gm
and ν
gn
being
the group velocities in cores m and n, respectively. In
this work, we assume that ∆β
0,mn
and D
mn
are 0.
Hence, Equation (5) is rewritten as
F(ω) = jK
nm
e
jβ
n
(ω)L
N
k=1
e
jωS
mn
z
k
/L
e
jφ
k
(7)
where S
mn
denotes the skew between the cores m and
n and is given by d
mn
L.
The ICXT signal at the output of core n due to the
signal in core m, E
x
(t), is given by
E
x
(t) = jK
nm
P
m
N
k=1
[cosφ
k
j sin φ
k
]·
+
i=
h
a
(m)
I,i
+ ja
(m)
Q,i
i
h
RRC
(t iT
s
S
mn
z
k
/L τ
mn
)
F
1
[H
n
(ω)]
(8)
After the MCF, the amplified spontaneous emis-
sion (ASE) noise is added to the interfered and the
ICXT signals. The ASE noise is generated from the
optical amplification and is an additive white Gaus-
sian noise with a singlesided power spectral density in
each polarization, N
0
, defined as 2 P
n
/(OSNR B
sim
),
where 2 P
n
is the total average signal power summed
over the two states of polarization and B
sim
is the
bandwidth used in the MC simulation (Jeruchim et al.,
2000). From this definition, the optical signal-to-
noise ratio (OSNR) is defined as the ratio between the
total signal power and the total ASE noise power and
it is estimated at the coherent receiver input.
Figure 3 depicts the model of a coherent receiver
with a 2x4 90
hybrid for a single-polarization trans-
mission (Essiambre et al., 2010). The main goal of
the 2x4 90
hybrid is to combine the local oscillator
signal, E
LO
(t), with the incoming signal, E
r
(t). The
optical fields at the output of the 2x4 90
hybrid are
given by (Essiambre et al., 2010)
E
1
(t)
E
2
(t)
E
3
(t)
E
4
(t)
=
1
2
1 1
j j
j 1
1 j
E
r
(t)
E
LO
(t)
(9)
where E
r
(t) = E
0
n
(t) + E
x
(t) + E
ASE
(t). In this work,
we assume an ideal synchronization (in time, carrier
frequency, phase and polarization) between the LO
and the received signals. We also assume that the sig-
nal, ICXT and the ASE noise are perfectly aligned in
the polarization.
The coherent receiver detects the I and Q com-
ponents of the incoming signal and then, each IQ
component is filtered by H
CR
( f ), which impulse re-
sponse is h
RRC
(t) h
cdc
(t). This block has two main
goals: perform RRC filtering and ideally compensate
chromatic dispersion using the filter with impulse re-
sponse h
cdc
(t). The ideal balanced photodetectors,
placed at the 2x4 90
hybrid output, are modeled as
square-law devices. Hence, following the configura-
tion of the coherent receiver depicted in Figure 3, I
I
(t)
and I
Q
(t) are expressed by
I
I
(t) = {E
0
n
(t)E
LO
(t) + E
x
(t)E
LO
(t)+
E
ASE
(t)E
LO
(t)}h
CR
(t)
(10a)
I
Q
(t) = {E
0
n
(t)E
LO
(t) + E
x
(t)E
LO
(t)+
E
ASE
(t)E
LO
(t)}h
CR
(t)
(10b)
where {Z} and {Z} are, respectively, the real and
the imaginary parts of a complex number Z, with the
complex conjugate represented by Z
.
By examining Equations (10), we identify
three terms: the desired received electrical signal
E
n
(t)E
LO
(t), the ICXT-LO beating term E
x
(t)E
LO
(t)
and the ASE-LO beating term E
ASE
(t)E
LO
(t).
The performance of the SDM optical system rep-
resented in Figure 2 is assessed by evaluating the BER
of the detected currents I
I
(t) and I
Q
(t) at the optimum
sampling time instants and the OSNR penalty due to
the presence of ICXT. The OSNR penalty quantifies
the impact of the ICXT on the performance of the
coherent receiver and is defined as the ratio between
the required OSNR with ICXT that leads to a BER
Figure 3: Model of a coherent receiver with electrical RRC
filtering and ideal dispersion compensation.
Impact of Inter-core Crosstalk on the Performance of Multi-core Fibers-based SDM Systems with Coherent Detection
77
of 10
3
and the required OSNR without ICXT for the
same BER. The ICXT level that leads to a 1 dB OSNR
penalty is a typical reference to evaluate the tolerance
to ICXT.
3 VALIDATION OF THE ICXT
TRANSFER FUNCTION
The validation of the transfer function F(ω) is per-
formed through the comparison between the empir-
ical estimations of the mean and variance of the
amplitude of the ICXT transfer function, XTTF(ω),
defined in (Cartaxo et al., 2016), and the mean and
variance obtained by simulation.
The XTTF(ω) is obtained from the fluctuations
after the photodetection of the crosstalk field at the
output of core n, and is given by (Cartaxo et al., 2016)
XTTF(ω) =
[F
(0)F(ω) +F(0)F
(ω)]
2
(11)
Since E[|XTTF(0)|] = N|K
nm
|
2
, with E[ ] denoting the
expected operator value. the normalized XTTF, X(ω),
is defined by X(ω) =XTTF(ω)/
N|K
nm
|
2
.
The empirical expressions of the mean of the
|X(ω)| is given by (Cartaxo et al., 2016)
E[|X(ω)|] =
x
2
+ sinc
2
ωS
mn
2π
1
2
x
2
+
1
2
cos
LD
n
λ
2
ω
2
2πc

1
2
(12)
where x
0.5549 (Cartaxo et al., 2016) and sinc(x)
is the sinc function, defined by sin(πx)/(πx) (Carlson
and Crilly, 2009). The variance of |X(ω)| is obtained
from (Cartaxo et al., 2016)
Var
{
|X(ω)|
}
=
1
2
x
2
+ sinc
2
ωS
mn
2π
·
·
x
2
+
1
2
cos
LD
n
λ
2
ω
2
2πc

(13)
Figure 4 shows the comparison of the numer-
ical simulation results for the mean and variance of
the normalized XTTF amplitude with those estimated
from the empirical model. The numerical simulations
consider 10
5
samples of ICXT signals with N = 1000
PMPs, which are randomly distributed along the MCF
following a uniform distribution. The parameters for
the MCF are: L=25 km, λ= 1550 nm , D
mn
= 0,
S
mn
= {25, 125} ps and D
n
= {0, 17} ps/nm/km. The
empirical estimations of the mean and variance of
X(ω) are marked with solid lines, while the mean
and variance of X(ω) obtained through simulation are
0 5 10 15 20 25 30 35 40
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Modulation Frequency [GHz]
Mean of normalized XTTF amplitude
d
mn
=1 ps/km D
n
=0 (12)
d
mn
=1 ps/km D
n
=17 ps/nm/km (12)
d
mn
=5 ps/km D
n
=17 ps/nm/km (12)
d
mn
=1 ps/km D
n
=0 (S)
d
mn
=1 ps/km D
n
=17 ps/nm/km (S)
d
mn
=5 ps/km D
n
=17 ps/nm/km (S)
(a)
0 5 10 15 20 25 30 35 40
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Modulation Frequency [GHz]
Variance of normalized XTTF amplitude
d
mn
=1 ps/km D
n
=0 (13)
d
mn
=1 ps/km D
n
=17 ps/nm/km (13)
d
mn
=5 ps/km D
n
=17 ps/nm/km(13)
d
mn
=1 ps/km D
n
=0 (S)
d
mn
=1 ps/km D
n
=17 ps/nm/km (S)
d
mn
=5 ps/km D
n
=17 ps/nm/km (S)
(b)
Figure 4: Comparison between the theoretical mean (Equa-
tion (12)) and variance (Equation (13)) and simulations (S)
results of the (a) mean and (b) variance of the normalized
XTTF as a function of the modulation frequency.
shown with dashed lines. Figure 4 shows an excellent
agreement between the theoretical and the simulation
results for the mean and the variance of X(ω), hence,
showing that the simulation model is properly imple-
mented.
4 PERFORMANCE ANALYSIS
In this section, we assess the performance of the
MCF-based SDM system with optical coherent detec-
tion using MC simulation. The performance metrics
used in this work are the BER and the OSNR pen-
alty due to the ICXT. The BER is estimated using
direct error counting (DEC) and the BER is given by
N
e
/(N
it
N
s
N
b
), where N
e
is the number of counted er-
rors at the decision circuit input, N
b
is the number of
bits per symbol given by log
2
(M), N
s
is the number
of simulated QAM symbols and N
it
is the number of
iterations of the MC simulation.
Table 1 presents the parameters used in MC simu-
lation in order to assess the performance of the MCF-
PHOTOPTICS 2018 - 6th International Conference on Photonics, Optics and Laser Technology
78
Table 1: Parameters of the MCF-based SDM system.
Parameter Value
R
b
[Gbps] 56
β {0, 0.25, 0.5, 0.75, 1}
τ
mn
/T
s
[0, 1]
S
mn
[ps] [0, 35]
Modulation format 4-QAM
T
s
[ps] 35.7
Number of PMPs 1000
OSNR
0
[dB] 10.3
Number of symbols N
s
2
11
Counted errors N
e
10
4
based SDM system with optical coherent detection in
presence of ASE noise and ICXT. OSNR
0
is the re-
quired OSNR for a BER of 10
3
in absence of ICXT,
i.e. this parameter is the reference OSNR to quantify
the OSNR penalty due to the ICXT.
The validation of the simulation model of the co-
herent receiver presented in Figure 3 must be per-
formed previously without ICXT. Figure 5 depicts
the BER as a function of the OSNR estimated using
DEC (circles) and the theoretical BER (dashed line),
BER
QAM
, as a function of the OSNR obtained using
(Essiambre et al., 2010)
BER
QAM
= 4
(1 1/
M)
log
2
M
Q
s
6 ·OSNR ·B
OSA
(M 1)R
s
!
(14)
where Q(x) is the Q function, which is given by
(Carlson and Crilly, 2009)
Q(x) =
1
2π
Z
+
x
e
t
2
/2
dt (15)
B
OSA
is the optical spectrum analyzer bandwidth,
defined as 12.5 GHz (Hui and O’Sullivan, 2008) in
which the OSNR is estimated, and R
s
is the symbol
8 8.5 9 9.5 10 10.5 11 11.5 12
−4.5
−4
−3.5
−3
−2.5
−2
−1.5
OSNR [dB]
log
10
(BER)
Without ICXT (T)
Without ICXT (S)
Figure 5: log
10
(BER) as a function of the OSNR obtained
through simulation (circles) and theoretically (dashed line)
for the 4-QAM modulation format without ICXT.
0 5 10 15 20 25 30 35
0
0.2
0.4
0.6
0.8
1
1.2
S
mn
[ps]
Normalized Variance of the Detected ICXT
β = 0
β = 0.25
β = 0 5
β = 0.75
β = 1
Figure 6: Normalized variance of the detected ICXT as a
function of the skew, considering β = {0,0.25, 0.5,0.75,1}
and τ
mn
= 0.
rate. From Figure 5, a perfect agreement between
the DEC estimation and the theoretical BER is no-
ticed, which validates the coherent receiver simula-
tion model in a back-to-back configuration in pres-
ence of ASE noise and without ICXT.
In the following, we analyze the variance of the
current due to the ICXT at the decision circuit input.
Hence, we estimate the variance of the detected ICXT
using the MC simulation, for different skews, time
misalignments between the interfered and interfering
core signals, and roll-off factors.
Figure 6 depicts the variance of the detected
ICXT, normalized to N|K
nm
|
2
, as a function of the
skew and the roll-off factors of 0, 0.25, 0.5, 0.75 and
1 estimated through MC simulation.
Firstly, we consider a perfect alignment between
the interfered and the interfering signals, i.e. τ
mn
= 0,
in order to analyze solely the influence of the skew
on the ICXT variance. Figure 6 shows that the vari-
ance of the detected ICXT as a function of the skew is
constant when β is 0. For higher roll-off factors, and
considering 0 S
mn
35 ps, the lowest ICXT vari-
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
1.2
Normalized Variance of the Detected ICXT
τ
mn
/T
s
S
mn
= 0 ps
S
mn
= 10 ps
S
mn
= 20 ps
Figure 7: Normalized variance of the detected ICXT as a
function of the temporal misalignment considering β = 1
and S
mn
of 0, 10 and 20 ps.
Impact of Inter-core Crosstalk on the Performance of Multi-core Fibers-based SDM Systems with Coherent Detection
79
ance is reached when the skew is 25 ps. Figure 6 also
allows to conclude that the increase of the roll-factor
and skew leads to a reduced ICXT variance and, con-
sequently, lower degradation of the coherent receiver
performance due to the ICXT.
Figure 7 depicts the normalized variance estim-
ated through MC simulation as a function of the tem-
poral misalignment between the interfered and inter-
fering signals considering a roll-off factor of 1.
Figure 7 shows that the minimum and the max-
imum value of the ICXT variance are spaced by 0.5T
s
.
Figure 7 also shows that the change of the skew leads
to a temporal shift of the time instants that lead to the
minimum and the maximum ICXT variances and also
to a reduction of the difference between the maximum
and minimum ICXT variances.
Next, we evaluate the penalty on the required
OSNR that leads to a BER of 10
3
due to the ICXT.
Figure 8 depicts the OSNR penalty due to the ICXT
as a function of the ICXT level for the 4-QAM modu-
lation format, considering τ
mn
= 0 and a roll-off factor
of (a) 0, (b) 0.5 and (c) 1 for different values of skew.
The chosen values of skew are based on the results
obtained in Figure 6. The ICXT level, X
c
, is defined
as the ratio between the ICXT signal power and the
interfered core signal power at the coherent receiver
input and is given by
X
c
=
N|K
nm
|
2
P
m
P
n
(16)
Figure 8(a) shows that, when the roll-off factor is
0, the variation of the skew has no influence on the
OSNR penalty. This conclusion is in agreement with
the results of Figure 6, since when the roll-factor is
0, the variance of the detected ICXT is independent
of the skew. Moreover, Figure 8 allows to conclude
that, when the interfering signal is aligned with the
interfered signal, i.e. τ
mn
= 0, the OSNR penalty for
a given ICXT level decreases for higher skew. For
instance, in Figure 8(c), considering an ICXT level
of 17 dB and β = 1, the OSNR penalty is 0.9, 0.7
and 0.6 dB for a skew of 0, 15 and 25 ps, respect-
ively. These results are in agreement with the conclu-
sions drawn from the analysis of Figure 6, where it
is observed that the variance of the detected ICXT is
lower when S
mn
is increased. Figure 8(c) also allows
to conclude that a roll-off factor of 1 and a skew of
25 ps leads to a tolerance gain to the ICXT of 1.7 dB,
as the ICXT level for a 1 dB OSNR penalty with a
null skew is 16.7 dB, while, for a skew of 25 ps, the
ICXT level for the same OSNR penalty is 15 dB.
−35 −33 −31 −29 −27 −25 −23 −21 −19 −17 −15
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
ICXT level [dB]
OSNR penalty [dB]
S
mn
= 0
S
mn
= 15 ps
S
mn
= 25 ps
(a) β = 0.
−35 −33 −31 −29 −27 −25 −23 −21 −19 −17 −15
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
ICXT level [dB]
OSNR penalty [dB]
S
mn
= 0
S
mn
= 15 ps
S
mn
= 25 ps
(b) β = 0.5.
−35 −33 −31 −29 −27 −25 −23 −21 −19 −17 −15
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
ICXT level [dB]
OSNR penalty [dB]
S
mn
= 25 ps
S
mn
= 15 ps
S
mn
= 0
(c) β = 1.
Figure 8: OSNR penalty due to the ICXT as a function of
the ICXT level considering the 4-QAM modulation format,
τ
mn
= 0 and (a) β = 0, (b) β = 0.5 and (c) β = 1, and for
S
mn
= 0, S
mn
= 15 ps and S
mn
= 25 ps.
5 CONCLUSION
In this work, we assess the impact of ICXT on the
BER and OSNR penalty of a MCF communication
system with optical coherent detection for signals
PHOTOPTICS 2018 - 6th International Conference on Photonics, Optics and Laser Technology
80
with 4-QAM modulation. The impact is assessed for
different skew between the signals transmitted in the
interfered and interfering cores, different time mis-
alignments and by varying the signals roll-off factors.
To complement our results, the variance of the detec-
ted ICXT is also studied.
Our results show that the roll-off factor of the RC
pulse shape and the skew has a significant influence
on the variance of the detected ICXT. Considering a
null roll-off factor, the variance of the detected ICXT
is constant as a function of the skew. In presence
of skew and with a roll-off factor higher than 0, the
variance of the detected ICXT signal decreases with
the increase of the roll-off factor. For a roll-off factor
higher than 0 and a skew of 25 ps, the variance of the
ICXT reaches its lowest value.
The temporal misalignment has also influence on
the variance of the ICXT signal at the coherent re-
ceiver. Our results reveal that for a given skew, the
variation of the temporal misalignment leads to a ”si-
nusoidal” behavior of the detected ICXT variance.
When the skew is reduced, the difference between
the highest and the lowest variance becomes smal-
ler. Without skew, our results reveal that the OSNR
penalty is independent of the roll-off factor and the 1
dB OSNR penalty is reached with a 16.7 dB ICXT
level. With skew between the cores, the ICXT level
that leads to a 1 dB OSNR penalty is higher for skew
of 25 ps: for β = 0, the ICXT level is 16.7 dB; for
β = 1, the ICXT level for the same OSNR penalty is
15 dB, due to the reduction of the ICXT variance.
ACKNOWLEDGEMENTS
This work was supported in part by Fundac¸
˜
ao para
a Ci
ˆ
encia e a Tecnologia (FCT) from Portugal un-
der the project of Instituto de Telecomunicac¸
˜
oes
AMEN-UID/EEA/50008/2013 and the ISCTE-IUL
Merit Scholarship BM-ISCTE-2016.
REFERENCES
Agrawal, G. (2010). Fiber-Optic Communication Systems.
John Wiley & Sons, 4 edition.
Carlson, A. and Crilly, P. (2009). Communication Systems.
McGraw-Hill, Boston, 5. ed edition.
Cartaxo, A. and Alves, T. (2017). Discrete Changes Model
of Inter-core Crosstalk of Real Homogeneous Multi-
core Fibers. J. Lightwave Technol., 35(12):2398–
2408.
Cartaxo, A. et al. (2016). Dispersion Impact on
the Crosstalk Amplitude Response of Homogeneous
Multi-Core Fibers. IEEE Photon. Technol. Lett.,
28(17):1858–1861.
Essiambre, R. et al. (2010). Capacity limits of optical fiber
networks. J. Lightwave Technol., 28(4):662–701.
Fini, J. M. et al. (2010). Statistics of Crosstalk in Bent Mul-
ticore Fibers. Opt. Express, 18(14):15122–15129.
Hayashi, T. et al. (2011). Design and Fabrication of Ultra-
Low Crosstalk and Low-Loss Multi-core Fiber. Opt.
Express, 19(17):16576–16592.
Hayashi, T. et al. (2013). Physical Interpretation of Inter-
core Crosstalk in Multicore Fiber: Effects of Mac-
robend, Structure Fluctuation, and Microbend. Opt.
Express, 21(5):5401.
Hayashi, T., Sasaki, T., and Sasaoka, E. (2014). Behavior
of Inter-Core Crosstalk as a Noise and Its Effect on Q
-Factor in Multi-Core Fiber. IEICE Trans. Commun,
(5):936–944.
Hui, R. and O’Sullivan, M. (2008). Fiber Optic Measure-
ment Techniques. Elsevier Academic Press.
Jeruchim, M., Balaban, P., and Shanmugan, K. (2000). Sim-
ulation of communication systems: modeling, method-
ology and techniques. Kluwer Academic Publishers,
Norwell, MA, 2nd edition.
Klaus, W. et al. (2017). Advanced Space Division Multi-
plexing Technologies for Optical Networks. J. Opt.
Commun. Netw., 9(4):C1–C11.
Morioka, T. (2017). High-Capacity Transmission Using
High-Density Multicore Fiber. In Optical Fiber Com-
munication Conference, page Th1C.3.
Puttnam, B. J. et al. (2015). 2.15 Pb/s Transmission Us-
ing a 22 Core Homogeneous Single-Mode Multi-Core
Fiber and Wideband Optical Comb. In European Con-
ference on Optical Communication (ECOC), pages 1–
3.
Puttnam, B. J. et al. (2017). High Capacity Transmission
Systems Using Homogeneous Multi-Core Fibers. J.
Lightwave Technol., 35(6):1157–1167.
Rademacher, G. et al. (2017a). Crosstalk Dynamics in
Multi-Core Fibers. In Opt. Express, pages 12020–
12028.
Rademacher, G. et al. (2017b). Time-Dependent Crosstalk
from Multiple Cores in a Homogeneous Multi-Core
Fiber. In Optical Fiber Communications Conference
and Exhibition (OFC), pages 1–3.
Saitoh, K. and Matsuo, S. (2016). Multicore Fiber Techno-
logy. J. Lightwave Technol., 34(1):55–66.
Takara, H. et al. (2012). 1.01-Pb/s (12 SDM/222 WDM/456
Gb/s) Crosstalk-managed Transmission with 91.4-
b/s/Hz Aggregate Spectral Efficiency. In European
Conference and Exhibition on Optical Communica-
tion (ECOC), page Th.3.C.1.
Xia, T. and Wellbrock, G. (2013). Commercial 100-Gbit/s
Coherent Transmission Systems. In Optical Fiber
Telecommunications, chapter 2, pages 45 82. Aca-
demic Press, Boston, 6 edition.
Zhu, B. et al. (2011). 112-Tb/s Space-Division Multiplexed
DWDM transmission with 14-b/s/Hz Aggregate Spec-
tral Efficiency over a 76.8-km Seven-Core Fiber. Opt.
Express, 19(17):16665–16671.
Impact of Inter-core Crosstalk on the Performance of Multi-core Fibers-based SDM Systems with Coherent Detection
81