Performance Analysis of PAM4 Signal Transmission in Inter-datacenter

Multicore Fiber Links Impaired by Inter-Core Crosstalk

Rafael A. Dias

, Jo

ao L. Rebola

1,2

and Adolfo V. T. Cartaxo

1,2

Optical Communications and Photonics Group, Instituto de Telecomunicac¸

oes, Lisboa, Portugal

Instituto Universit

ario de Lisboa (ISCTE-IUL), Lisboa, Portugal

Keywords:

Bit Error Rate, Inter-Core Crosstalk, Inter-datacenter Connections, Multicore Fiber, Outage Probability, PAM4.

Abstract:

In this work, we propose to use four-level pulse amplitude modulation (PAM4) and multicore ﬁbers (MCFs)

to support very high capacity inter-datacenter connections. The limitations imposed by inter-core crosstalk

(ICXT) on the performance of 112 Gb/s up to 80 km-long optically ampliﬁed PAM4 inter-datacenter links

with intensity-modulation and direct-detection (IM-DD) and full chromatic dispersion compensation in the

optical domain are analyzed through numerical simulation. We show that those PAM4 inter-datacenter links

achieve an outage probability (OP) of

−4

with a maximum ICXT level of

-13.9 dB

for high skew-symbol rate

products and require an ICXT level decrease of about

8.1 dB

to achieve the same OP for low skew-symbol rate

products. Due to using full dispersion compensation, the OP is not much affected by increasing the MCF length,

from

10 km

, where electrical noise signiﬁcantly contributes to the performance degradation, to

80 km

, where

signal-ampliﬁed spontaneous emission beat noise is dominant. For an OP of

−4

, the maximum acceptable

ICXT level shows only a 1.4 dB variation with the MCF length increase.

1 INTRODUCTION

Nowadays, datacenters provide a vital infrastructure

to Internet online services and in the last few years,

worldwide trafﬁc in optical networks has been in-

creasing dramatically around 30% per year (Cisco,

2018), (Klaus et al., 2017). This growth is fuelled

by the progressive development of next-generation

5G mobile broadband technologies, expansion of the

Internet of things, and increasing of high-data-rate ap-

plications such as streaming video, real-time gaming,

cloud computing, and big data analysis (Klaus et al.,

2017). This growth is demanding a higher capacity

in datacenters. To accomplish such demands, cloud

companies and content providers have built multiple

datacenters in different locations which are separated

by large distances because this approach offers mul-

tiple beneﬁts (increased availability, reduced latency

to customers) for distributed applications with a wide

range of users such as email, multimedia services,

social networks and online storage (Noormohammad-

pour and Raghavendra, 2018). Moreover, the trafﬁc

which was mainly transmitted only from external dat-

acenters to servers was surpassed by the amount of

trafﬁc exchanged between servers inside the same and

between datacenters (Cisco, 2018).

In intra-datacenter optical ﬁber links, the format

of the signals usually transmitted was the on-off key-

ing (OOK), where intensity-modulation and direct-

detection (IM-DD) ensured low cost and complex-

ity (Zhou et al., 2019). However, in 2014, OOK signal

transmission reached its limit at the data rate of 25

Gb/s (Perin et al., 2018). To surpass the limitation im-

posed by OOK modulation, PAM4 signal transmission

has been introduced for datacenter communications in

2017 (Zhou et al., 2019), (Kachris and Tomkos, 2012).

The PAM4 modulation format reduces the signal band-

width by half and doubles spectral efﬁciency in com-

parison to OOK signals. Therefore, PAM4 is expected

to be an economical and efﬁcient enabler of 100G and

400G single-channel transmission in intra and inter-

datacenter connections (Zhou et al., 2019), (Perin et al.,

2018).

Multicore ﬁbers (MCFs) have been recently pro-

posed to increase the capacity of short-haul links, such

as datacenters interconnects, and as they can be more

densely packed, space can be saved inside datacen-

ter facilities in comparison with the space occupied

by multiple bundles of single-core single-mode ﬁbers

(SC-SMF) required to achieve the same capacity (But-

ler et al., 2017). Weakly-coupled MCFs provide an

economic solution for the required capacity, as indi-

vidual cores can be used as independent channels with

similar propagation delays. However, the effect of

inter-core crosstalk (ICXT) limits the MCF reach and

performance (Rebola et al., 2019b), (Jorge et al., 2020).

Dias, R., Rebola, J. and Cartaxo, A.

Performance Analysis of PAM4 Signal Transmission in Inter-datacenter Multicore Fiber Links Impaired by Inter-Core Crosstalk.

DOI: 10.5220/0010321000940103

In Proceedings of the 9th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2021), pages 94-103

ISBN: 978-989-758-492-3

The ICXT effect is reasonably well studied in the liter-

ature (Lu

ıs et al., 2016), (Cartaxo et al., 2016), (Alves

and Cartaxo, 2019) and, due to the random evolution

of ICXT over time, ICXT-impaired systems may expe-

rience: (i) random variations of the bit error rate (BER)

over short time periods (Alves et al., 2019), (Alves and

Cartaxo, 2017), and (ii) system outage over long time

periods due to high ICXT levels (Alves et al., 2019).

Therefore, it is essential to study the outage probability

(OP) and bit error rate (BER) in PAM4 IM-DD sys-

tems supported by MCFs and limited by ICXT (Rebola

et al., 2019b).

In this work, the performance of IM-DD inter-

datacenter links with full loss and perfect dispersion

compensation and PAM4 signal transmission up to

80 km is analyzed taking the limitations imposed by

ICXT into account.

2 SYSTEM MODEL

Optical

modulatorm

Optical

modulatorn

Optical

Filter

Decision

Circuit

Receiver

Electrical

Filter

Symbol

sequence

Optical

noise

Electricalnoise

Opticaltransmittersofcoresmandn

Weakly-coupledMCF

Opticalamplification

Direct-detectionopticalreceiverofcoren

Transmitter

Electrical

Filter

Symbol

sequence

Transmitter

Electrical

Filter

Sample&

Hold

Sample&

Hold

Laser

CDC

coren

corem

ICXT

...

Laser

Figure 1: Equivalent model of an optically ampliﬁed inter-

datacenter link supported by MCFs and with CD compensa-

tion.

Inter-datacenter links can reach up to 100 km and usu-

ally operate at 1550 nm to enable ampliﬁcation using

erbium-doped ﬁber ampliﬁers (EDFAs). In these links,

due to the higher distances in comparison with shorter

intra-datacenter links, chromatic dispersion (CD) be-

comes signiﬁcant and must be reduced by using disper-

sion compensation techniques (Perin et al., 2018), (El-

Fiky et al., 2017). Typically, inter-core datacenter

links are supported by single-mode single-core ﬁbers

(SM-SCFs). In this work, our proposal to increase sig-

niﬁcantly the link capacity is to use weakly-coupled

MCFs to support such links.

The system equivalent model used in this work to

study the ICXT impact on the performance of inter-

datacenter links supported by MCFs is shown in Fig. 1.

It is composed of two transmitters (TXs), one for the

interfering core and the other for the interfered core,

each one generating a different PAM4 signal. After

symbols generation, the PAM4 symbols are sampled

and passed through an electrical ﬁlter that models the

frequency limitations of the electrical part of the trans-

mitter. Each optical modulator is assumed without

chirp and with a ﬁnite extinction ratio.

The weakly-coupled MCF model considers an in-

terfered core

and a single interfering core

, and lin-

ear signal propagation. The ICXT is described by the

dual-polarization discrete changes model (DP-DCM)

with two cores (Soeiro et al., 2017). The attenuation

coefﬁcient and dispersion parameters of the two cores

are assumed equal. At the output of the interfered core

, the ICXT induced by core

is added to the signal

transmitted in core

. As the objective of this work

is to analyze the impact of ICXT on the performance

of very high capacity inter-datacenter links, the chro-

matic dispersion compensation (CDC) module uses

a dispersion compensating ﬁber (DCF), designed to

fully compensate the dispersion induced by core

An inter-datacenter link fully supported by multicore

technology would be the most feasible and practical

solution, however to the authors’ best knowledge, MC-

DCFs are not an available technology. Our proposed

solution is to use a spatial demultiplexer at the MCF

output followed by a CDC module composed by a bun-

dle of parallel single-core DCFs, each one designed to

compensate the CD induced in a speciﬁc ﬁber core of

the MCF. After the CDC, the PAM4 signal impaired

by ICXT is optically ampliﬁed by an EDFA and an

optical ﬁlter is used to suppress ampliﬁed spontaneous

emission (ASE) noise generated by the EDFA. The

EDFA gain is designed to fully compensate the losses

introduced by the MCF and DCF. The direct-detection

optical receiver includes a PIN photodetector, electri-

cal noise addition due to circuitry of the electrical part

of the receiver, electrical ﬁltering, and the decision

circuit to decide on the transmitted PAM4 symbol. In

the following, a detailed description of these models

is presented.

2.1 PAM4 Signal Characterization

In this subsection, the generation and characterization

of the PAM4 signal generated at the output of the op-

tical transmitters is explained. In the simulator, the

PAM4 symbols sequence is generated using deBruijn

sequences of maximum length

reg

, obtained from

Galois arithmetic, where

reg

represents the length

of the offset register used to generate the sequence.

The symbols ’0’, ’1’, ’2’ and ’3’ are equally likely to

occur (Rebola and Cartaxo, 2000). Fig. 2 shows a rep-

Performance Analysis of PAM4 Signal Transmission in Inter-datacenter Multicore Fiber Links Impaired by Inter-Core Crosstalk

Figure 2: Representation of the ideal power levels of an

optical PAM4 signal with non-zero extinction ratio and the

corresponding decision thresholds.

resentation of the ideal PAM4 signal power levels for a

non-zero extinction ratio where

, with

=0, 1, 2 and 3

correspond to the PAM4 signal symbols;

and

are the ideal decision thresholds;

and

are

the powers corresponding to each of the symbols

and

is the extinction ratio deﬁned as

r = P

. The

constants

and

deﬁne the intermediate levels of the

PAM4 signal (Rebola and Cartaxo, 2000). In optically

ampliﬁed links, signal-ampliﬁed spontaneous emission

(ASE) beat noise typically dominates the performance

degradation and leads to different received noise pow-

ers proportional to the different intensity levels of the

signal (Perin et al., 2018). In (Rebola and Cartaxo,

2000), the optimization of

and

is studied to min-

imize the bit error probability for optically ampliﬁed

PAM4 links where signal-ASE is dominant. The op-

timal

and

are given by

C = (1 + 4

√

r + 4r)/9

and

A = (4 + 4r + r )/9

(Rebola and Cartaxo, 2000). After

generation, the ideal PAM4 signal is ﬁltered by a 3

order Bessel ﬁlter to model the amplitude and phase

distortion induced by the ﬁltering and parasitics at the

electrical part of the transmitter. The

−3

dB band-

width of the Bessel ﬁlter is set equal to the symbol rate

2.2 Discrete Changes Model

In this subsection, the simulation model known as DP-

DCM, used to characterize the ICXT induced by the

cores of the MCF is described with more detail (Soeiro

et al., 2017). The DP-DCM characterizes the ICXT

induced by the different cores of the MCF on the

interfered core. The ICXT was reported to result

mostly from the discrete contribution of phase match-

ing points (PMPs). The PMPs are points along the lon-

gitudinal propagation direction of the ﬁber for which

the difference between the effective refractive index

of the interfering and interfered cores is zero (Soeiro

et al., 2017). These points manifest randomly along

the ﬁber and the total ICXT can be approximated as

the sum of the contributions associated with each PMP.

Each contribution is weighted by an independent ran-

dom phase shift (RPS) and the corresponding propaga-

tion delay (Rademacher et al., 2017). The RPSs model

random variations of the bending radius, twist rate, or

other conditions in the MCF (Soeiro et al., 2017), (Car-

taxo et al., 2016). It should be highlighted that this

model provides a very good characterization of the

ICXT impact in IM-DD optical communication sys-

tems, as shown in (Soeiro et al., 2017), by comparison

with experimental results (Alves et al., 2019) (Alves

and Cartaxo, 2017) (Alves and Cartaxo, 2019).

The DP-DCM describes the ICXT in the two po-

larization directions

and

. The transfer functions

a,b

(ω)

, model the frequency response of the ICXT

from the polarization

(with

a = x

) at the input

of core

to the polarization

(with

b = x

) at the

output of core

and are given by (Soeiro et al., 2017)

a,b

(ω) = −

√

exp



−jβ

(ω)L



exp



−



∑

k=1

exp

−j(β

(ω) −β

(ω))z

exp

−jφ

(a,b)

nm,k

(1)

where

is the power attenuation coefﬁcient of core

is the average inter-core coupling coefﬁcient,

which is given by the average of its contributions in

the two polarization directions (Soeiro et al., 2017),

is the angular frequency,

is the MCF length;

the number of PMPs (Cartaxo et al., 2016),

(a,b)

nm,k

rep-

resents the RPS associated with the

-th PMP, which

is modelled by an uniform distribution between 0 and

(ω)

(with

l = n

) is the average of the prop-

agation constants in the two polarization directions in

cores l, which is given by (Agrawal, 2010)

(ω) = β

0,l

+ β

1,l

ω +

2,l

3,l

(2)

where

0,l

is the propagation constant at the operating

wavelength

1,l

is the inverse of the group veloc-

ity,

2,l

is the group velocity dispersion and

3,l

the higher order dispersion, for core

. The skew be-

tween the interfering core,

and the interfered core,

, is given by

= d

, where

is the walkoff

between cores m and n deﬁned by d

= β

1,m

−β

1,n

The longitudinal coordinate of the

-th PMP,

, is

randomly distributed between two consecutive PMPs

and is given by

= [L(r

+ k −1)]/N

, where

(1 ≤ k ≤ N

)

are independent random variables with

uniform distribution in the interval [0,1[.

The DP-DCM has been developed to keep the com-

plexity and time of simulation at acceptable levels. In

such a model, the evolution of the ICXT impact on

the system performance is evaluated in time fractions

with a much shorter duration than the ICXT decorrela-

tion time. Those time fractions are separated by time

PHOTOPTICS 2021 - 9th International Conference on Photonics, Optics and Laser Technology

intervals longer than the decorrelation time of ICXT.

This means that from time fraction to time fraction,

the ICXT is uncorrelated and, within each time frac-

tion, is totally correlated. For this reason, each time

fraction corresponds to an independent set of RPSs,

which we name MCF realization. Therefore, the dif-

ferent MCF realizations are obtained by generating

randomly different sets of

RPSs. In each iteration

of the Monte Carlo (MC) simulator, one MCF real-

ization is generated, and the symbols of the PAM4

signal transmitted in core

are randomly generated.

For equal powers at the input of the interfered and

interfering cores and identical loss in the two cores,

the ratio between the mean ICXT power and the mean

power of the signal, at the output of the interfered core

, named ICXT level,

, is related to the parameters

of Eq. 1 by X

= N

(Soeiro et al., 2017).

2.3 Chromatic Dispersion

Compensation Modeling

To compensate the dispersion introduced along the

transmission through core

, a DCF is used at the

output of the MCF to fully compensate the distor-

tion due to chromatic dispersion on the signal im-

paired by ICXT. The DCF is modelled considering

linear propagation transmission, with

DCF

charac-

terizing the DCF attenuation coefﬁcient. The DCF

length is designed to fully compensate the accu-

mulated dispersion induced by the MCF at the op-

erating wavelength, by setting the DCF length to

DCF

= −D

λ,n

L/D

λ,DCF

(Agrawal, 2010), where

λ,n

is the core

dispersion parameter and

λ,DCF

is the

DCF dispersion parameter.

2.4 Optical Ampliﬁcation and Filtering

Modelling

In this work, the EDFA gain output is designed

to fully compensate the losses introduced by the

MCF and DCF. The ASE noise is modelled as

additive white Gaussian noise with power spec-

tral density, per polarization mode, given by

ASE

= 0.5F

(g −1)hν

(Agrawal, 2010), where

the ampliﬁer gain output in linear units,

hν

is the

photon energy, and F

is the ampliﬁer noise ﬁgure.

The optical ﬁlter is modelled by a 4

order super

Gaussian (SG) ﬁlter. The transfer function of the

-th

order SG ﬁlter is given by

( f ) =

√

exp

−



f − f



√

(3)

where

and

are the optical ﬁlter central frequency

and insertion loss in linear units, and B

is the optical

ﬁlter bandwidth at -3 dB.

2.5 Optical Receiver

At the optical receiver, the PIN photodetector is mod-

elled as a square-law device with responsivity

. The

electrical ﬁlter of the optical receiver is modelled as

order Bessel ﬁlter with a

−3

dB bandwidth,

e,RX

The electrical noise power after the receiver electrical

ﬁlter is given by

= R

NEP

e,n

(Agrawal, 2010),

where

NEP

is the noise equivalent power, deﬁned as

the minimum optical power necessary to generate a

photocurrent equal to the noise current of the photo-

detector (Agrawal, 2010). The bandwidth

e,n

is the

noise equivalent bandwidth of the receiver electrical

ﬁlter.

The detected ASE noise power for the

-th received

PAM4 symbol at the electrical ﬁlter output, is given by

n,k,ASE

= 4S

ASE

e,n

(gP

+ B

o,n

ASE

)

(Rebola and

Cartaxo, 2000), where

is the symbol level corre-

sponding to the received

symbol taken from the

eye-pattern and

o,n

is the noise equivalent bandwidth

of the optical ﬁlter. At the decision circuit input, the

received signal impaired by ICXT, residual dispersion,

ASE and electrical noises is processed to estimate the

BER and OP.

2.6 BER and OP Calculation

In this subsection, the procedure for the BER and

OP estimation in IM-DD PAM4 systems impaired by

ICXT is described. The BER is calculated by the semi-

analytical method known as the exhaustive Gaussian

approach, which, for a PAM4 received signal is given

by (Rebola and Cartaxo, 2000)

BER =

2 ·4

reg

(

reg

∑

k=1



−i

0,k



reg

∑

k=1





1,k

−F

1,k



+ Q



−i

1,k



reg

∑

k=1





2,k

−F

2,k



+ Q



−i

2,k



reg

∑

k=1



3,k

−F

3,k



)

(4)

where

0,k

1,k

2,k

and

3,k

are the means of the cur-

rents at the input of the decision circuit for the symbols

’0’, ’1’, ’2’ and ’3’, respectively, at the time sampling

Performance Analysis of PAM4 Signal Transmission in Inter-datacenter Multicore Fiber Links Impaired by Inter-Core Crosstalk

instants,

= t

+ T

(k −1)

, where

is the symbol

period;

is extracted from the received eye-pattern

at the decision circuit input and

k ∈ {1,...,4

reg

}

0,k

1,k

2,k

and

3,k

are the noise standard deviations

of the same current for the different time sampling in-

stants (Rebola and Cartaxo, 2000). The

(

) function

is given by (Carlson and Crilly, 2010)

Q(x) =

∞

√

2π

−

dξ (5)

In the simulation, the decision thresholds

and

are optimized by applying the bisection method to

minimize the BER. The effect of intersymbol interfer-

ence from ﬁltering and ﬁber dispersion is taken into

account by the waveform distortion in the eye pattern

at these

sampling time instants and in Eq. 4, this

effect is included in the mean currents

0,k

1,k

2,k

and

3,k

. The effect of ICXT on the interfered core is also

taken into account in these mean currents by the wave-

form distortion induced on the receiver signal. The

effect of electrical noise, signal-ASE, and ASE-ASE

beat noises are taken into account semi-analytically in

the standard deviations of the received symbols,

0,k

1,k

, σ

2,k

and σ

3,k

The OP is the probability of a system becoming

unavailable, i.e., the probability of the BER in the pres-

ence of ICXT surpasses a given BER limit. In the sim-

ulation, the OP is estimated by

OP = N

/Nr

(Winzer

and Foschini, 2011), (Rebola et al., 2019b), where

is the number of occurrences of BER above the

BER limit and

is the number of simulated MCF

realizations necessary to reach

occurrences of BER

above the BER limit. The required outage probabil-

ity in optical communications is typically lower than

−4

(Winzer and Foschini, 2011), (Cvijetic et al.,

2008).

3 NUMERICAL RESULTS AND

DISCUSSION

In this section, the impact of ICXT on the performance

of the transmission of PAM4 signals in optically ampli-

ﬁed IM-DD links, emulating inter-datacenter connec-

tions is assessed. The system simulation parameters

used throughout these studies are presented in Table 1.

The DCF dispersion slope was set to compen-

sate for the effect of the MCF dispersion slope. The

electrical and optical receiver ﬁlters bandwidth were

optimized in a back-to-back conﬁguration to minimize

the receiver sensitivity. Then, for each link length,

the signal power at the transmitter output has been

set to achieve the BER of 3.8

−5

in absence of

ICXT, which is two orders of magnitude below the

Table 1: System and simulation parameters.

Parameters Value

Operation wavelength λ

= 1550nm

e,RX

0.85 ×R

1.6 ×R

Symbol rate R

= 56 Gbaud

Number of generated

N = 4

PAM4 symbols in each

MCF realization

Number of PMPs N

= 1000

Skew-symbol rate |S

·R

|=1000,

product |S

·R

|=0.01

MCF chromatic

λ,n

=17

nm km

dispersion parameter

MCF attenuation

=0.2 dB/km

coefﬁcient

DCF chromatic

λ,DCF

=-100

nm km

dispersion parameter

DCF attenuation

DCF

=0.5 dB/km

coefﬁcient

BER limit 3.8×10

−3

BER in absence

3.8

−5

of ICXT

BER limit in presence of ICXT. A similar assump-

tion was considered in (Rebola et al., 2019c). In this

work, we consider a target BER limit of 3.8

−3

presence of ICXT, since it is the most commonly used

for datacenters connections with forward-error correc-

tion (El-Fiky et al., 2017), (Xing et al., 2018). The

number of PMPs is chosen to be high enough (1000)

to characterize the ICXT statistics rigorously (Cartaxo

et al., 2016). Two different inter-core skews are anal-

ysed: i)

·R

| 

1, the symbol rate of the PAM4

signal is much higher than the ICXT decorrelation

bandwidth, which is proportional to the inverse of

the skew (Alves and Cartaxo, 2019) and the ICXT

creates amplitude levels in the received eye-pattern

that seem to exhibit a ”noise”-like behavior (Rebola

et al., 2019a), and ii)

·R

| 

1, where the symbol

rate of the PAM4 signal is much lower than the ICXT

decorrelation bandwidth (Alves and Cartaxo, 2019)

and well-deﬁned amplitude levels in the eye-patterns

are created due to ICXT (Rebola et al., 2019a).

In the following subsections, the impact of the

ICXT on the average BER and received eye-pattern

is assessed for a MCF length of 10 km and the OP is

assessed for a MCF length of 10, 40 and 80 km.

3.1 BER in Each MCF Realization

The average BER is computed in each MCF realization

by averaging the BERs per realization calculated in

previous MCF realizations. In Figs. 3 a) and b), the

PHOTOPTICS 2021 - 9th International Conference on Photonics, Optics and Laser Technology

0 100 200 300 400 500 600 700 800 900 1000

# MCF realizations

-5

-4

-3

-2

-1

(a) |S

·R

|=1000, X

= −14 dB

0 100 200 300 400 500 600 700 800 900 1000

# MCF realizations

-5

-4

-3

-2

-1

BER

(b) |S

·R

|=0.01, X

= −16 dB

Figure 3: BER in each MCF realization and average BER as

a function of the number of MCF realizations, for r = 0.

average BER is stabilized at 3.4

−3

and 2.7

−3

respectively, after 1000 MCF realizations. This num-

ber of MCF realizations is a conservative choice to

achieve stabilized values of the average BER. A simi-

lar conclusion was shown in (Rebola et al., 2019c), for

OOK systems. Fig. 3 shows that, with low

·R

and

= −

16 dB, the BER limit is exceeded about 187

times, i.e., there are 187 occurrences of the BER that

lead to system outage. The OP, in this case, is approx-

imately 0.187. With high

·R

and

= −

14 dB,

the BER limit is exceeded about 145 times, which

indicates an approximated OP of 0.145. After this

analysis, it is possible to infer that for

·R

=1000,

the performance of the PAM4 inter-datacenter link is

less impaired by ICXT, than for

·R

=0.01, since a

2 dB higher ICXT level is required to achieve a similar

OP. Similar conclusions regarding the average BER

have been obtained for links with 20 km, for OOK sig-

nalling on the interfered and interfering cores (Rebola

et al., 2019c) and for PAM4 signalling in the interfered

core and OOK signalling in the interfering core (Jorge

et al., 2020).

The results shown in Fig. 3 indicate that, for these

ICXT levels, the average BER is kept below the BER

limit. However, the BER in each MCF realization

surpasses the BER limit several times, which leads to

system outage. The OPs estimated in Fig. 3 are consid-

erably above the typically required OP (not exceeding

−4

). This demonstrates that the OP is a more im-

portant performance metric than the average BER in

these optical systems. Therefore, it is essential to study

the OP in PAM4 IM-DD systems supported by MCFs

impaired by ICXT.

3.2 Eye-pattern Analysis

Through the eye-pattern analysis, it is also possible

to draw some conclusions regarding the impact of

the ICXT on the performance of an optically ampli-

ﬁed PAM4 IM-DD system with full loss and chro-

matic dispersion compensation. Fig. 4 shows the re-

ceived eye-patterns at the decision circuit input for

·R

=1000,

r = 0

and

= −

14 dB, for a) the best

BER (4.29

−5

) and b) the worst BER (8.30

−2

)

per MCF realization shown in Fig. 3 a). Fig. 5 shows

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.5

1.5

2.5

-5

(a) BER=4.29×10

−5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

-5

(b) BER=8.30×10

−2

Figure 4: Eye-Patterns at the decision circuit input for

·R

=1000,

r = 0

and

= −

14 dB, for a) best BER

and b) worst BER per MCF realization shown in Fig. 3 (a).

the received eye-patterns for

·R

=0.01,

r = 0

and

= −

16 dB, for a) the best BER (1.85

−5

) and

b) the worst BER (1.175

−1

) per MCF realization

shown in

Fig. 3 b)

. These eye patterns do not include

Performance Analysis of PAM4 Signal Transmission in Inter-datacenter Multicore Fiber Links Impaired by Inter-Core Crosstalk

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.5

1.5

2.5

-5

(a) BER=1.85×10

−5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.5

1.5

2.5

-5

(b) BER=1.175×10

−1

Figure 5: Eye-Patterns at the decision circuit input for

·R

=0.01,

r = 0

and

= −

16 dB, for a) best BER

and b) worst BER per MCF realization shown in Fig. 3 (b).

the effect of noise (electrical or optical) to make the

effect of ICXT on the eye pattern more perceptible.

Fig. 4 b)

and

5 b)

, for the worst BER, due to the

severe degradation caused by ICXT, the eye is fully

closed. For the best BER,

Fig. 5 a)

exhibits much more

”well-deﬁned” amplitude levels caused by ICXT than

in the eye-pattern shown in

Fig. 4 a)

, especially in the

part of the eye where more symbol transitions occur.

There are two main reasons for this behavior: i) the

ICXT level is 2 dB lower in

Fig. 5 a)

, for low

·R

ii) for low

·R

(Fig. 5 a), only one symbol in

the interfering core is contributing to ICXT, while for

high

·R

(Fig. 4 a), several symbols in the inter-

fering core are contributing to ICXT. A similar effect

was observed for OOK systems (Rebola et al., 2019c)

and PAM4 signals transmission impaired by ICXT in-

duced by OOK signals in the interfered core (Jorge

et al., 2020). Similar results and conclusions have been

obtained for

r = 0.1

. Furthermore, it has been found

that, for

r = 0.1

, the ICXT degrades less the average

BER and received eye-patterns than for r = 0.

3.3 Outage Probability

In this section, the dependence of the OP on the num-

ber of MCF realizations, MCF length, skew-symbol

rate product and ICXT level is assessed.

3.3.1 Dependence on the Number of MCF

Realizations

Fig. 6 shows the OP estimate as a function of the num-

ber of MCF realizations, for

r = 0

, and and three differ-

ent situations: a)

·R

|=1000

and

= −18 dB

; b)

·R

|=0.01

and

= −

18 dB and c)

·R

|=0.01

and

= −22 dB

. To estimate the OP, the BER is

obtained in each MCF realization and the simulation

is stopped when the number of occurrences of BER

above the BER limit reaches 200. According to Figs. 6

a) and b), it is possible to observe that for the same

ICXT level and extinction ratio, a higher number of

MCF realizations is required to reach 200 occurrences

of BER above the BER limit, with

·R

=1000 than

with

·R

=0.01, since the OP with

·R

=1000

is about 1

−2

and is lower than the OP of about

−2

shown in Fig. 6 b), for

·R

=0.01. In

Figs. 6 a) and c), the number of MCF realizations to

reach 200 BER occurrences above the BER limit is

more than ﬁve times higher, in comparison to Fig. 6 b),

and the oscillations of the OP estimates tend to dimin-

ish and stabilize above

MCF realizations, while in

Fig. 6 b), the stabilization is reached after about 4000

realizations. Notice that in Fig. 6 c), the number of

MCF realizations is considerably higher in comparison

to Fig. 6 a) and b) cases, due to the lower OP (about

one order of magnitude) that must be estimated. Fig. 6

indicates that the number of MCF realizations neces-

sary to estimate the OP with sufﬁcient accuracy only

depends on the order of magnitude of the OP. A similar

conclusion was shown in other works, for PAM4 and

OOK signalling (Rebola et al., 2019c), (Jorge et al.,

2020).

The number of occurrences for which it is possible

to obtain an OP of the optical communication system

with very small ﬂuctuations has been assessed for this

system, and it has been concluded that 200 occurrences

of BER above the BER limit seem more than enough

to achieve a stabilized estimate of outage probabil-

ity. Thus, in all subsequent studies involving the OP

estimation,

=200, are considered. The simulation

results presented in this work only reach OPs around

−4

because lower OPs are computationally heavy

to achieve using computer simulation. To achieve an

OP of

−4

with 200 BER occurrences above the BER

limit, around 2 million MCF realizations are required.

As the estimation of the BER for one MCF realization

takes around 0.6 seconds, around 2 weeks of simula-

PHOTOPTICS 2021 - 9th International Conference on Photonics, Optics and Laser Technology

100

0 0.5 1 1.5 2 2.5

# MCF realizations

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

0.024

Outage Probability Estimate

(a)

0 500 1000 1500 2000 2500 3000 3500 4000 4500

# MCF realizations

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

(b)

0 1 2 3 4 5 6 7 8 9 10

# MCF realizations

1.5

2.5

3.5

4.5

Outage Probability Estimate

-3

(c)

Figure 6: OP estimate as a function of the number of

MCF realizations, for a MCF length of 10 km,

r = 0

and

·R

|=1000

and

= −18 dB

; b)

·R

|=0.01

and

= −18 dB and c) |S

·R

|=0.01 and X

= −22 dB.

tion, in a 16 GB RAM with a 3.2 GHz processor are

necessary to reach such low OPs. Therefore, for an

OP of 10

−6

, it would be necessary around 200 weeks.

Similarly, we have performed a cubic interpolation

and extrapolation of log

(OP), to achieve such low

OPs, similarly to what has been done in (Rebola et al.,

2019c), (Jorge et al., 2020).

3.3.2 Dependence on the Skew-Symbol Rate

Product

The dependence of the OP on the skew-symbol rate

product is studied with more detail in this subsection,

for a MCF length of 80 km and r = 0.1.

-2

-1

-4.1

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

Figure 7: OP as a function of

·R

for a MCF length of

80 km,

r = 0.1

, and

=-12 dB, -14 dB, -16 dB and -18 dB.

For

·R

|  0.1

, the ICXT is highly correlated

along the signal bandwidth (Alves and Cartaxo, 2019),

only one PAM4 symbol is contributing to ICXT, and

the ICXT behaves as static coupling (Alves and Car-

taxo, 2019). Hence, the ICXT effect is enhanced and

the OP reaches its worst-case value, concerning the

skew-symbol rate product, for all ICXT levels stud-

ied. For

·R

|  100

, the ICXT is decorrelated

along the signal bandwidth (Alves and Cartaxo, 2019)

and several PAM4 symbols are contributing to ICXT,

leading to a similar ”noise”-like behavior (Alves and

Cartaxo, 2019). Hence, a signiﬁcant decrease of the

OP is observed (Rebola et al., 2019c), (Rebola et al.,

2019b), reaching a minimum for very high

·R

For intermediate values of the skew-symbol rate prod-

uct, a transition between the two ICXT behaviors is

observed, similarly to what has been reported in (Re-

bola et al., 2019b).

Fig. 7 also shows that, for

=-12 dB, the decrease

of the OP is less than one order of magnitude when

increasing the

·R

. For

=-14

-16

and

-18 dB

the OP decreases several orders of magnitude. These

results show that, the OP improvement observed for

high

·R

is smaller when the ICXT level increases,

similarly to what has been concluded in (Rebola et al.,

2019b), for an OOK system.

Performance Analysis of PAM4 Signal Transmission in Inter-datacenter Multicore Fiber Links Impaired by Inter-Core Crosstalk

101

3.3.3 Dependence on the MCF Length

-24 -22 -20 -18 -16 -14 -12 -10

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

Figure 8: OP as a function of the ICXT level, for

·R

|=0.01

and

·R

|=1000

, for

r = 0.1

. The dashed

lines represent a cubic interpolation of

log

( )

of the outage

probability.

The dependence of the OP on the MCF length, and

consequently, on the noise type dominance, i.e., elec-

trical noise dominance or ASE noise dominance, for

·R

=0.01 and

·R

=1000,

r = 0.1

, and several

ICXT levels, is studied in this subsection. In this study,

we aim to analyse the effect of the ICXT on these en-

vironments. Therefore, the ICXT level is set constant

for each ﬁber length, i. e., the ICXT level is consid-

ered independent of the MCF length. Fig. 8 shows the

OP as a function of the ICXT level, for

·R

=0.01

and

·R

=1000, for

r = 0.1

and

=10 km,

=40

km and

=80 km. In Fig. 8, for high

·R

, longer

MCF lengths lead to an increased tolerance to ICXT,

while for low

·R

, the ICXT tolerance is not sig-

niﬁcantly affected by the MCF length. Hence, for

high

·R

, the difference between the dominance

of signal-ASE beat noise on the performance, for 80

km, and the enhanced contribution of electrical noise

to the performance, for 10 km, inﬂuences the tolerance

to ICXT. For low

·R

, the tolerated ICXT level is

not particularly affected by the different noise regimes.

The ICXT levels that lead to an OP of

−4

, for

each intercore skew and MCF length combination, ex-

tracted from Fig. 8, are presented in Table 2. In Table 2,

for

·R

=0.01, the ICXT level required to achieve

an OP of

−4

increases slightly less than

0.5 dB

, with

the MCF length increase. For

·R

|=1000

, the max-

imum acceptable ICXT level required to achieve the

OP of

−4

diminishes with the MCF length increase,

showing a

0.8 dB

and

1.4 dB

reduction from

40 km

and

80 km

, respectively, to

10 km

. For

80 km

, for an

OP of

−4

, a higher tolerance to ICXT exceeding

8.1 dB

is observed for high

·R

in comparison to

Table 2: Maximum acceptable ICXT level (dB) for an OP of

−4

and r = 0.1.

L=10 km L=40 km L=80 km

|=0.01 -21.8 -22.1 -22

|=1000 -15.3 -14.5 -13.9

low

·R

. The way dispersion from the MCF and

DCF affects the ICXT mechanism for the different

link lengths might provide some explanation for these

results. Even though, for an OP of

−4

, the maxi-

mum acceptable ICXT level shows only a variation

not exceeding

1.4 dB

with the increase of the MCF

length.

4 CONCLUSIONS

In this work, the impact of ICXT induced by one in-

terfering core on the performance of an optically am-

pliﬁed PAM4 IM-DD system with full loss and chro-

matic dispersion compensation was studied through

MC simulation by assessing the average BER, eye-

pattern degradation, and OP.

We have shown that 1000 MCF realizations are

more than enough to obtain stabilized average BERs

and that is essential to study the OP for IM-DD sys-

tems supported by MCFs impaired by ICXT. For low

·R

, the eye-patterns exhibit more ”well-deﬁned”

amplitude levels due to ICXT in comparison to high

·R

. Furthermore, for

r = 0.1

, the ICXT degrades

less the average BER and received eye-patterns than

for

r = 0

. For an OP of

−4

, numerical results have

shown a higher tolerance to ICXT exceeding

8.1 dB

is observed for high

·R

. It has also been shown

that, with the ICXT level independent from the MCF

length, the OP is not much affected by increasing

the MCF length, from 10 km, where electrical noise

signiﬁcantly contributes to the performance degrada-

tion, to 80 km, where signal-ASE beat noise is dom-

inant. From a MCF length of 10 to 80 km, and to

achieve the typical OP of

−4

, the maximum accept-

able ICXT level varies only

1.4

and

0.2 dB

, respec-

tively, for |S

·R

|=1000 and |S

·R

|=0.01.

This work demonstrates that in optically ampliﬁed

PAM4 IM-DD system supported by MCFs, the ICXT

level must be kept below

-22 dB

to guarantee an OP

≤

−4

. If the ICXT level exceeds this threshold, ICXT

mitigation techniques should be developed to maintain

the quality of transmission.

PHOTOPTICS 2021 - 9th International Conference on Photonics, Optics and Laser Technology

102

ACKNOWLEDGEMENTS

This work is funded by FCT/MCTES through national

funds and when applicable co-funded EU funds un-

der the project UIDB/EEA/50008/2020 and project

DigCore/UIDP/50008/2020.

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