Transmission of PAM4 Signals in ICXT-impaired Intra-datacenter

Connections with PAM2 Signal Interference

es C. Jorge

, 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, Intra-datacenter Connections, Multicore Fiber, Outage Probability, PAM4.

Abstract:

Trafﬁc in datacenters has been signiﬁcantly increasing over the last few years. As a result, it is necessary to

scale the connections of the datacenters to accommodate such an increase of trafﬁc. The solution considered

in this work is to use four-level pulse amplitude modulation (PAM4) and weakly-coupled multicore ﬁbers

(MCFs) to support intra-datacenter connections. However, transmission in weakly-coupled MCFs may be sig-

niﬁcantly degraded by inter-core crosstalk (ICXT). In this work, the impact of ICXT on the performance of

PAM4 transmission in short-haul direct-detection links is evaluated considering two-level PAM (PAM2) sig-

nals in the interfering cores. The ICXT impact on the performance of the tested core with PAM4 transmission

is evaluated using the bit error rate (BER), outage probability (OP) and eye-pattern analysis. Comparing to

PAM2 transmission in the tested core, a 7.6 dB lower ICXT level is required to achieve an acceptable OP for

a reference BER of 3.8×10

−3

in the PAM4 link.

1 INTRODUCTION

Datacenters provide an infrastructure to Internet on-

line services such as web-browsing, e-mail, video-

streaming, storage and ﬁle sharing, cloud computing

and mobile services. Due to all these services and

the emergence of 5G and Internet of Things (IoT),

trafﬁc in datacenters has been dramatically increas-

ing over the last few years (Cisco, 2018). With

the growth of capacity in datacenters, data trafﬁc,

which was mainly transmitted only from external dat-

acenters to servers, started to be transfered between

servers inside the same datacenter or anothers nearby

supported by optical ﬁber technology. One of the cur-

rent solutions to scale the capacity of datacenter con-

nections is the use of multiple wavelengths to carry

wavelength division multiplexing (WDM) channels,

each channel considering the transmission of on-off

keying modulated signals, also known as two-level

pulse amplitude modulation (PAM2) signals. In 2007,

the ﬁrst generation of intra-datacenter technology op-

erated at 10 Gb/s using a single wavelength chan-

nel, PAM2 modulation and direct-detection was re-

leased (Zhou et al., 2019). In 2010, the technol-

ogy has evolved into a second generation that oper-

ated at a 40 Gb/s aggregated bit rate with 4 WDM

channels (Zhou et al., 2019). The third generation,

from 2014, operated at 100 Gb/s with 4 WDM chan-

nels, each one at 25 Gb/s with PAM2 transmission

(Zhou et al., 2019). In 2017, a generation of 400 Gb/s

datacenter connections emerged, employing the more

bandwidth-efﬁcient four-level pulse amplitude mod-

ulation (PAM4), doubled the WDM channels in use

to 8 and the data rate in each channel from 25 Gb/s

to 50 Gb/s, leading to an aggregated rate of 400 Gb/s

(Zhou et al., 2019). The PAM4 format is foreseen as

cost-effective and efﬁcient enabler of 100G and 400G

per channel in datacenter connections (Perin et al.,

2018). So, in the future, it is expected that PAM4 sup-

ported systems can lead to data rates of 800 Gb/s and

1.6 Tb/s in the datacenters connections (Zhou et al.,

2019).

Datacenter connections can be classiﬁed into

intra-datacenter connections, which have a range up

to 10 km or inter-datacenter connections that have a

range up to 100 km (Perin et al., 2018). Intra and

inter-datacenter communication systems use typically

intensity modulation at the transmitter and direct-

detection at the receiver, to ensure lower cost (Perin

et al., 2018). Intra and inter-datacenter links have

as design priorities low cost, power consumption and

port density, and exhibit reduced propagation prob-

lems when compared to long-haul systems since non-

linear effects are usually insigniﬁcant at these short

122

Jorge, I., Rebola, J. and Cartaxo, A.

Transmission of PAM4 Signals in ICXT-impaired Intra-datacenter Connections with PAM2 Signal Interference.

DOI: 10.5220/0008976801220130

In Proceedings of the 8th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2020), pages 122-130

ISBN: 978-989-758-401-5; ISSN: 2184-4364

propagation distances (Perin et al., 2018).

The signal transmission in datacenters is usu-

ally supported by single-core single-mode ﬁbers (SC-

SMF). Recent SC-SMF transmissions have achieved

a transmission capacity of about 100 Tb/s and a

capacity-distance product over 100 Pb/s·km relying

on the use of coherent-detection allied with sophisti-

cated digital signal processing (Saitoh and Shoichiro,

2016). However, datacenter connections are still ex-

ploring direct-detection due to its lower cost and sim-

plicity, and such high transmission capacities cannot

be met in these connections. For the sake of sav-

ing space between the racks inside datacenters, re-

ducing ﬁber per area density, and to reduce inven-

tory issues, multicore ﬁbers (MCFs) are one of the

most attractive technologies to overcome the use of

SC-SMF and scale the transmission capacity in intra-

datacenter connections (Butler et al., 2017). Homo-

geneous weakly-coupled MCFs are a promise to ex-

pand these capacity limits. In these ﬁbers, each core

has similar properties, as geometry and refractive in-

dex, all the cores have the same propagation constant

and can be used as independent transmission chan-

nels (Klaus et al., 2017). However, MCFs lead to

inter-core crosstalk (ICXT), which may limit signif-

icantly the short-haul direct-detection datacenter con-

nection performance or the link reach. The ICXT re-

sults from undesired ﬁeld coupling between the cores

of the MCF. The ICXT is a stochastic process that

has a random time variation which can cause random

high levels of ICXT in a short period of time (Alves

et al., 2019), (Alves and Cartaxo, 2017). This random

behavior of ICXT can cause the system shutdown or

long time periods of outage and ﬂuctuations of the bit

error rate (BER). In this work, the impact of ICXT

on the performance of PAM4 transmission in intra-

datacenter links impaired by PAM2 transmission in

the interfering cores is analyzed through several met-

rics, such as BER, eye-pattern analysis and outage

probability (OP). This scenario will probably be en-

countered in the upgrade of a future existing intra-

datacenter link with PAM2 transmission in all cores

of the MCF (Rebola et al., 2019c) to support PAM4

transmission in some cores.

2 SIMULATION MODEL

Fig. 1 shows the system model for the intra-datacenter

link, which typically operates at a wavelength near

1310 nm, to minimize total chromatic dispersion

(CD). These links are usually unampliﬁed, resulting

in a low power margin (Perin et al., 2018).

The equivalent system model of the intra-

Figure 1: Typical intra-datacenter links. TX: transmitter,

MUX: multiplexer, DEMUX: demultiplexer, RX: receiver.

datacenter link shown in Fig. 1, supported by MCFs

with PAM signal generation at the transmitter is

shown in Fig. 2. It is composed by two optical PAM

transmitters, one for each ﬁber core. The tested core

considers PAM4 transmission and the interfering core

assumes PAM2 signalling. An ideal linearized model

without chirp for each optical transmitter is assumed.

The weakly-coupled MCF model considers an inter-

fered core n and a single interfering core m, and the

signals are propagated in the two polarization direc-

tions x and y inside the MCF (Soeiro et al., 2017).

The ICXT is described by the discrete changes model

(DCM). At the output of the interfered core n, the

ICXT induced by the core m appears added to the

signal transmitted in core n. The direct-detection op-

tical receiver model includes the PIN photodetector,

the electrical noise addition due to photodetector and

electrical ampliﬁer, electrical ﬁltering and the deci-

sion circuit to decide on the transmitted PAM4 sym-

bol. In the following subsections, detailed descrip-

tions are presented to some of these models.

PAM2

PAM4

Figure 2: Equivalent system model.

2.1 PAM4 Signal Characterization

In this subsection, the generation and the character-

ization of the PAM4 signal of the tested core is ex-

plained.

Transmission of PAM4 Signals in ICXT-impaired Intra-datacenter Connections with PAM2 Signal Interference

123

Figure 3: Representation of the power levels of an optical

PAM4 signal with non-zero extinction ratio and the corre-

sponding decision thresholds for an optical receiver with

signal independent noise dominance.

The PAM4 modulation format maps two bits in

each PAM4 symbol, which reduces the bandwidth re-

quirement by half when compared to PAM2 signals

(Lv et al., 2016). In the simulator, the PAM4 sym-

bol sequence is generated using deBruijn sequences

obtained from Galois arithmetic of maximum length

, where N

represents the number of positions of

the offset register used to generate the sequence. In

this way, a deBruijn sequence is generated where the

PAM4 symbols

and

are equally likely

to occur. Fig. 3 shows a representation of the power

levels of an ideal PAM4 signal assuming a non-zero

extinction ratio, where

and

represent

the symbols of the PAM4 signal; F

, F

and F

, are

the ideal decision thresholds; P

, P

and P

are the

powers corresponding to each one of the symbols, and

r represents the extinction ratio deﬁned as in (Rebola

and Cartaxo, 2000).

r =

(1)

Eq. 1 corresponds to the inverse of the deﬁnition of

the extinction ratio as adopted by ITU-T (Telecom-

munications Standardization Section of ITU-T, 2009).

The constants A and C deﬁne the spacing between

the intermediate levels of the PAM4 signal. As the

performance in intra-datacenter links is only affected

by electrical noise, the PAM4 power levels should be

equidistant (Rebola and Cartaxo, 2000). As such, A

and C are given, respectively, by (Rebola and Cartaxo,

2000)

A =

r (2)

C =

r (3)

The average power of the generated PAM4 optical

signal is then given by

1 + A +C + r

(4)

These power levels are used to generate the PAM4

signal with rectangular-shaped pulses. Then, this

ideal PAM4 signal is ﬁltered by a 3

order Bessel

ﬁlter, in order to have a more realistic pulse shape at

the optical transmitter output. The −3 dB bandwidth

of the Bessel ﬁlter is equal to the symbol rate R

. This

ﬁltering models the frequency limitations due to the

electrical part of the PAM4 transmitter.

The PAM2 signal in the interfering core is gener-

ated as described in (Rebola et al., 2019c).

2.2 Discrete Changes Model

In this subsection, the simulation model used in this

work, known as dual polarization DCM, to charac-

terize the ICXT induced by the cores is presented

(Soeiro et al., 2017). It should be highlighted that

this model provides a very accurate characterization

of the ICXT impact in direc-detection optical com-

munication systems, as shown in (Alves et al., 2019),

by comparison with experimental results.

Linear propagation along the MCF is assumed in

the two cores, where m and n are the interfering and

tested (interfered) cores, respectively. The dual po-

larization DCM considers the power splitting of the

transmitted PAM signal by the polarization directions

x and y at the input of the MCF to obtain the ICXT in

both polarizations. The transfer functions F

x,x

(ω) and

y,x

(ω) are used to obtain the ICXT generated in the

polarization x of core n from polarizations x and y of

core m. The transfer functions F

x,y

(ω) and F

y,y

(ω) are

used to obtain the ICXT generated in the polarization

y of core n from both polarizations of core m (Soeiro

et al., 2017). The transfer functions F

a,b

(ω), model

the frequency response of the ICXT from the polar-

ization a at the input of core m to the polarization b

at the output of core n and are given by (Soeiro et al.,

2017)

a,b

(ω) = −

√

exp

−jβ

(ω)L

∑

k=1

exp

−j(β

(ω) −β

(ω))z

exp

−jφ

(a,b)

nm,k

(5)

with a ∈ {x, y}, b ∈ {x, y}, K

is the average inter-

core coupling coefﬁcient of the polarization directions

given by K

=(K

(x)

+ K

(y)

)/2 (Soeiro et al., 2017); ω

is the angular frequency; L is the MCF length; β

and

PHOTOPTICS 2020 - 8th International Conference on Photonics, Optics and Laser Technology

124

are the average of the propagation constants over

the two polarizations in cores m and n and are deﬁned

by, respectively, β

= (β

(x)

+ β

(y)

)/2 and β

= (β

(x)

+ β

(y)

)/2 (Soeiro et al., 2017); z

is the longitudinal

coordinate corresponding to the k-th phase matching

point (PMP), with N

the number of PMPs (Cartaxo

et al., 2016); φ

(a,b)

nm,k

is the random phase shift (RPS) as-

sociated with the k-th PMP, and is modelled by an uni-

form distribution between 0 and 2π. The RPSs model

the random variations of the bending radius, twist rate

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

(Cartaxo et al., 2016).

The dual-polarization DCM has been developed

to keep the complexity and time of simulation at ac-

ceptable levels. In such model, the evolution of the

ICXT impact on the system performance is evalu-

ated in time fractions (named MCF realizations) much

shorter than the ICXT decorrelation time. The MCF

realizations are separated by time intervals longer

than the decorrelation time of ICXT of the MCF. This

means that, from MCF realization to MCF realiza-

tion, the ICXT is uncorrelated and, within each MCF

realization, is totally correlated. The different MCF

realizations are obtained by generating randomly dif-

ferent sets of N

RPSs. In each iteration of the MC

simulator, one MCF realization is generated. In each

MCF realization, the bits of the interfering PAM2 sig-

nal with null extinction ratio transmitted in core m are

randomly generated. In the model shown in Fig. 2,

the effect of CD is taken into account in both MCF

cores m and n. For equal powers at the output of the

interfered and interfering cores, the ratio between the

average crosstalk power and the average power of the

signal, at the output of the tested core n, X

, is related

to the parameters of Eq. 5 by X

= N

. The

skew between the interfering core, m and the tested

core, n, is given by S

= d

L, where d

is the

walkoff between cores m and n and is related to Eq. 5

by d

= β

1,m

−β

1,n

, where β

1,m

is the inverse of the

group velocity of core m, and β

1,n

is the inverse of the

group velocity of core n.

2.3 BER and OP Calculation

In this subsection, the procedure for the BER and OP

estimation in PAM4 systems with direct-detection and

impaired by ICXT is described.

The BER is calculated by the semi-analytical

method known as the exhaustive Gaussian approach

applied to the PAM4 case, which is given by (Rebola

and Cartaxo, 2000)

BER =











∑

k=1



−i

0,k



∑

k=1





1,k

−F

1,k



+ Q



−i

1,k



∑

k=1





2,k

−F

2,k



+ Q



−i

2,k



∑

k=1



3,k

−F

3,k



(6)

where i

0,k

, i

1,k

, i

2,k

and i

3,k

correspond to the mean

of the current at the input of the decision circuit for

the symbols ’0’, ’1’, ’2’ and ’3’, respectively; and

0,k

, σ

1,k

, σ

2,k

and σ

3,k

correspond to the noise stan-

dard deviations of the same current for the different

symbols (Rebola and Cartaxo, 2000). The means of

the received currents are extracted from the simulated

eye-pattern at the optimum sampling instants. The

function Q(x) is given by (Carlson and Crilly, 2010)

Q(x) =

∞

√

2π

−

dξ (7)

In the simulation, the decision thresholds F

, F

and

are optimized by using the bisection method to

minimize the BER (Srivastava and Dixit, 2012).

By considering a PAM4 sequence with 4

sym-

bols implies 4

different levels of current at 4

sam-

pling time instants at the decision circuit input and,

in this way, 4

different contributions to the BER,

as shown in Eq. 6. The effect of intersymbol inter-

ference from ﬁltering and ﬁber dispersion is taken

into account by the waveform distortion in the eye-

pattern at these 4

sampling time instants. In Eq. 6,

this effect is included in the mean currents i

0,k

, i

1,k

2,k

and i

3,k

. Also, the effect of ICXT on the inter-

fered core is taken into account in these mean cur-

rents. The effect of noise is taken into account semi-

analytically in the standard deviations of the received

symbols. In this case, as we consider thermal noise,

0,k

= σ

1,k

= σ

2,k

= σ

3,k

= σ

, with the noise power

given by

= R

NEP

e,n

(8)

where R

is the PIN responsivity, NEP is the noise

equivalent power, deﬁned as the the minimum optical

power necessary to generate a photocurrent equal to

the noise current of the photodetector and B

e,n

is the

noise equivalent bandwidth of the electrical ﬁlter of

the optical receiver.

Transmission of PAM4 Signals in ICXT-impaired Intra-datacenter Connections with PAM2 Signal Interference

125

The OP is the probability of the system becoming

unavailable when a target BER limit is reached (Re-

bola et al., 2019b), (Winzer and Foschini, 2011). In

this work, the system is considered unavailable, i.e.,

it is in an outage period, when the BER in presence

of ICXT surpasses the BER limit of 3.8×10

−3

. In

the simulation, the OP is estimated by (Rebola et al.,

2019c)

OP =

(9)

where N

is the number of occurrences of BER above

the BER limit and N

is the number of simulated MCF

realizations necessary to reach this number of occur-

rences. An acceptable outage probability in optical

communications is typically lower than 10

−4

(Winzer

and Foschini, 2011), (Cvijetic et al., 2008).

3 NUMERICAL RESULTS AND

DISCUSSION

In this section, the impact of ICXT on the perfor-

mance of PAM4 signals transmission in short-haul

links with direct-detection, considering the transmis-

sion of a PAM2 signal in the interfering core, is as-

sessed. The simulation parameters used throughout

this work to perform this study are presented in Ta-

ble 1.

Table 1: Simulation parameters and values.

Simulation parameter Value

1 A/W

NEP 10

−12

√

e,n

0.75×R

Symbol rate R

= 56 Gbaud

Fiber length L = 2 km

Number of generated

PAM4 symbols in each N = 4

MCF realization

Carrier wavelength λ = 1550 nm

Chromatic D

= 17 ps/(nm·km)

dispersion parameter

Number of PMPs N

= 1000

Skew-symbol rate |S

·R

|=1000,

product |S

·R

|=0.01

Reference BER 3.8×10

−3

BER in absence of ICXT 3.8×10

−5

The number of PMPs is chosen to be high enough

to characterize the ICXT mechanism rigorously (Car-

taxo et al., 2016). Two different skews, |S

·R

|=1000

and |S

·R

|=0.01, are also chosen according to the

conditions i) |S

·R

|1, where the symbol rate of

the PAM signal is much higher than the ICXT decor-

relation bandwidth (which is proportional to the in-

verse of the skew) (Alves and Cartaxo, 2019) and the

ICXT creates amplitude levels that seem to exhibit a

“noise” like-behavior (Rebola et al., 2019b), and ii)

·R

|1, where the symbol rate of the PAM signal

is much lower than the ICXT decorrelation bandwidth

and well-deﬁned amplitude levels in the eye-patterns

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

and Cartaxo, 2019). Although intra-datacenters oper-

ate at a typical 1310 nm wavelength, the wavelength

may need to be extended to 1550 nm to increase the

transmission capacity. Furthermore, this wavelength

allows to study the limitations induced by the interac-

tion of CD with ICXT.

3.1 BER in Each MCF Realization

Figure 4: BER in each MCF realization and average BER as

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

= −25 dB, for a) |S

·R

|=1000 and b) |S

·R

|=0.01.

The BER limit of 3.8×10

−3

is also depicted.

Fig. 4 show the BERs obtained in each MCF re-

alization and the average BER as a function of the

MCF realizations, for r = 0 and X

= −25 dB, for

PHOTOPTICS 2020 - 8th International Conference on Photonics, Optics and Laser Technology

126

a) |S

·R

|=1000 and b) |S

·R

|=0.01. The average

BER is computed in each MCF realization by averag-

ing the BERs per realization calculated in the previ-

ous MCF realizations. In Figs. 4 a) and b), the average

BER is stabilized at 6.5×10

−4

and 8.4×10

−4

, respec-

tively, after 1000 MCF realizations. This number of

MCF realizations is a conservative choice to achieve

stabilized values of the average BER, as already con-

cluded in (Rebola et al., 2019c). Comparatively to

PAM2 transmission in the tested core (Rebola et al.,

2019c), a much lower crosstalk level in PAM4 sys-

tems degrades much more the average BER in pres-

ence of ICXT than in PAM2 systems. In (Rebola

et al., 2019c), for a crosstalk level of X

= −15 dB and

for |S

·R

|=10 and |S

·R

|=0.2, after 1000 MCF re-

alizations, the average BER is stabilized near 10

−3

Fig. 4 shows that in a PAM4 system, this average BER

is almost reached with a crosstalk level about 10 dB

lower than the one predicted for the same average

BER in a PAM2 transmission in the tested core. Thus,

the performance of PAM4 transmission in the tested

core is much more sensitive to ICXT than PAM2 sig-

nal transmission. Regarding the OP, according to

Fig. 4, we conclude that, with |S

·R

|=0.01, in 1000

MCF realizations, the BER limit is overcomed more

times when compared with |S

·R

|=1000. In Fig. 4

a), the BER limit is exceeded about 15 times, i.e, there

are 15 occurrences of the BER that lead to system out-

age. The OP, in this case, is approximately 0.015. In

Fig. 4 b), the BER limit is exceeded about 48 times,

which indicates an approximated OP of 0.048. Simi-

lar conclusions regarding the number of MCF realiza-

tions to achieve an average BER and the lower toler-

ance of PAM4 signals to ICXT have been found for

r = 0.1.

3.2 Eye-pattern Analysis

Through the eye-pattern analysis, it is also possi-

ble to draw some conclusions regarding the impact

of the ICXT induced by the transmission of PAM2

signals in the interfering core on the PAM4 sig-

nals performance in direct-detection links. Fig. 5

shows the eye-patterns at the decision circuit input

for |S

·R

|=1000, r = 0 and X

= −25 dB, for a)

the worst BER (7×10

−3

) in each MCF realization

and b) the best BER (2.2×10

−5

) in each MCF real-

ization obtained in Fig. 4 a). Fig. 6 show the eye-

patterns for |S

·R

|=0.01, r = 0 and X

= −25 dB,

for a) the worst BER (2.5×10

−2

) in each MCF real-

ization and b) the best BER (1.5×10

−5

) in each MCF

realization obtained in Fig. 4 b). From Figs. 5 and

6, it can be observed that the eye-pattern in Fig. 6 a)

shows a greater degradation due to ICXT when com-

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

·R

|=1000, r = 0 and X

= −25 dB, for a) worst BER

(7×10

−3

) and b) best BER (2.2×10

−5

) obtained in each

MCF realization in Fig. 4 a).

pared with the eye-pattern in Fig. 5 a), especially in

the superior eye concerning the symbols ’2’ and ’3’,

since the eye opening is much lower. Figs. 5 b) and 6

b) present much similar eye openings which are much

larger than the eye openings shown in Figs. 5 a) and

6 a) due to the lower inﬂuence of ICXT for the MCF

realization that leads to the best BER. Also, Fig. 6

b) exhibits more ”well-deﬁned” amplitude levels due

to ICXT than in the eye-pattern represented in Fig. 5

b), especially in the part of the eye where more sym-

bol transitions occur. This effect happens because, for

low |S

·R

| (Fig. 6 b)), only one symbol in the inter-

fering core is contributing to ICXT, while, for high

·R

| (Fig. 5 b)), several symbols in the interfering

core are contributing to ICXT. This effect has been

already observed for PAM2 signal transmission in the

tested core (Rebola et al., 2019c). The same studies

were done for r = 0.1, and similar results and conclu-

sions were obtained.

Transmission of PAM4 Signals in ICXT-impaired Intra-datacenter Connections with PAM2 Signal Interference

127

Figure 6: Eye-patterns at the decision circuit input for

·R

|=0.01, r = 0 and X

= −25 dB, for a) worst BER

(2.5×10

−2

) and b) best BER (1.5×10

−5

) obtained in each

MCF realization in Fig. 4 b).

3.3 Outage Probability

The dependence of the OP estimation on the num-

ber of MCF realizations, for several |S

·R

|, ex-

tinction ratios and crosstalk levels is studied in the

following. Fig. 7 shows the OP estimates as a

function of the number of MCF realizations, for

r = 0, and a) |S

·R

|=1000 and X

= −26 dB; b)

·R

|=0.01 and X

=-26 dB and c) |S

·R

|=0.01

and X

= −28.2 dB. The BER is estimated in each

MCF realization and the simulation is stopped when

the number of occurrences of BER above the BER

limit reaches 200, where we consider that the OP has

been estimated with sufﬁcient accuracy (Rebola et al.,

2019c), (Rebola et al., 2019b). In Figs. 7 a) and c), the

ﬂuctuations of the OP estimates extend over a higher

number of MCF realizations than in Fig. 7 b). Ac-

cording to Figs. 7 a) and b), it is possible to observe

that, for the same crosstalk level and extinction ra-

tio, a higher number of MCF realizations is needed to

Figure 7: Outage probability estimate as a function of the

number of MCF realizations, for r = 0 and a) |S

·R

|=1000

and X

= −26 dB; b) |S

·R

|=0.01 and X

= −26 dB and

c) |S

·R

|=0.01 and X

= −28.2 dB.

reach 200 occurrences of BER above the BER limit,

with |S

·R

|=1000 than with |S

·R

|=0.01, since

the OP of the system with the higher |S

·R

|, about

4×10

−3

, is one order of magnitude lower than the one

shown in Fig. 7 b) of about 2×10

−2

. In Fig. 7 c), with

·R

|=0.01 and X

= −28.2 dB, it is possible to

PHOTOPTICS 2020 - 8th International Conference on Photonics, Optics and Laser Technology

128

observe that the number of MCF realizations is nearly

the same as in Fig. 7 a), since the values of OP reached

after 200 occurrences in both ﬁgures are very similar.

Fig. 7 indicates that the number of MCF realizations

necessary to estimate the OP with sufﬁcient accuracy

only depends on the order of magnitude of the OP as

already hinted in other works (Rebola et al., 2019c),

(Rebola et al., 2019b). In (Rebola et al., 2019c), the

number of occurrences for which it is possible to ob-

tain an OP of the optical communication system with

very small ﬂuctuations has been assessed for a PAM2

transmission in the tested core, and it has been con-

cluded that 200 occurrences are more than enough to

achieve this goal, which is in accordance with our re-

sults shown in Fig. 7. Thus, in this work, in all studies

involving the OP estimation, N

=200 is considered.

Figure 8: Outage probability as a function of X

, for

·R

|=1000 and r = 0; |S

·R

|=0.01 and r = 0;

·R

|=1000 and r = 0.1 and |S

·R

|=0.01 and r = 0.1.

The dashed lines represent a cubic interpolation of the log

of the outage probability.

Then, the OP in PAM4 transmission in the tested

core, for a single interfering core with PAM2 trans-

mission, for low and high |S

·R

| and r = 0 and

r = 0.1, has been obtained. Fig. 8 shows the OP

obtained by simulation as a function of the ICXT

level, for |S

·R

| = 1000 and r = 0; |S

·R

| =

0.01 and r = 0; |S

·R

| = 1000 and r = 0.1 and

·R

| = 0.01 and r = 0.1. For X

≥ −22 dB,

the system is unavailable with a very high OP above

−1

. Hence, for PAM4 systems impaired by ICXT

induced by one interfering core, ICXT levels above

this value are prohibitive. For lower crosstalk levels,

with |S

·R

| = 1000, for a BER limit of 10

−3

, for

example, a higher crosstalk level is needed to achieve

this OP than with |S

·R

| = 0.01, regardless the ex-

tinction ratio. So, for high |S

·R

|, Fig. 8 indicates

that the PAM4 system is more robust to outage than

for lower |S

·R

|, as already concluded in (Rebola

et al., 2019c), (Rebola et al., 2019b) for PAM2 sig-

nalling. For |S

·R

| = 0.01, comparing r = 0 with

r = 0.1, the higher extinction ratio presents slightly

higher OPs for the same crosstalk level. This suggests

that, for low |S

·R

|, the inﬂuence of the extinction

ratio on the OP is not much relevant. By comparing

with PAM2 transmission in the tested core (Rebola

et al., 2019c), a much lower ICXT level is needed to

achieve the same outage probability with PAM4 sig-

nal transmission. For example, the crosstalk levels of

= −18 dB and X

= −22 dB (Rebola et al., 2019c),

lead to an outage probability of 10

−3

, in PAM2 sys-

tems, with r = 0 and |S

·R

|=10 and |S

·R

|=0.02,

respectively. As can be seen in Fig. 8, in PAM4 sys-

tems, the ICXT level that leads to this OP is much

lower, X

= −26.9 dB, for the higher |S

·R

|, which

is 8.9 dB lower than in PAM2 systems, and X

−29.6 dB, for the lower |S

·R

|, which is 7.6 dB

lower than in PAM2 systems. Since the simulation

takes a long time to reach lower OPs, around 10

−4

the OP obtained for X

= −28 dB, |S

·R

|=1000 and

r = 0, has been obtained with only 100 occurrences

and, for X

= −27 dB, |S

·R

|=1000 and r = 0.1,

the OP has been obtained with 47 occurrences. In

this case, these simulations took more than one week

to achieve 100 and 47 occurrences, respectively. As

very low OPs ( 10

−4

) are computationally heavy

to achieve using computer simulation, we have per-

formed a cubic interpolation of log

(OP) to achieve

such lows OPs, similarly to what has been done in

(Rebola et al., 2019c).

4 CONCLUSIONS

In this work, the impact of ICXT on the performance

of PAM4 signals in short direct-detection links sup-

ported by MCFs has been studied through simulation.

The inﬂuence of PAM2 signal transmission in the in-

terfering core on the performance of PAM4 signal in

the tested core has been assessed. We have shown

that a number of MCF realizations of 1000 is more

than enough to obtain a stabilized average BER of the

PAM4 system. The impact of ICXT on the received

PAM4 signals has been also studied through the eye-

pattern analysis. For both high and low |S

·R

|, and

concerning the best achievable BER in one MCF re-

alization, the eye openings are much similar to the

one obtained in back-to-back conﬁguration, due to

the lower inﬂuence of ICXT for the MCF realiza-

tion that leads to the best BER. Regarding the worst

BER, for low |S

·R

|, the eye-patterns exhibit more

”well-deﬁned” amplitude levels due to ICXT. Also,

the OP of the PAM4 system with direct-detection has

been assessed. First, it was concluded that, for the

Transmission of PAM4 Signals in ICXT-impaired Intra-datacenter Connections with PAM2 Signal Interference

129

same reference OP, high |S

·R

| tolerates a higher

ICXT level above about 2.3 dB than low |S

·R

independently of the extinction ratio. Regarding the

extinction ratio, r = 0 requires a lower ICXT level

of about 1.4 dB than r = 0.1, for the same reference

OP. Comparing to PAM2 transmission in the tested

core, a much lower ICXT level of about 8.9 dB and

7.6 dB, for high and low |S

·R

|, respectively, is

required to achieve the same OP in the PAM4 sys-

tem. Hence, we have shown that short-haul links with

direct-detection, typical of intra-datacenter connec-

tions, with PAM4 transmission are much less tolerant

to the ICXT impairment than PAM2 systems.

ACKNOWLEDGEMENTS

This work is funded by FCT/MCTES through na-

tional funds and when applicable co-funded EU

funds under the project UIDB/EEA/50008/2020 and

MALEFICO project.

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