C ea ing and Tuning
Mul iband Op ical T ansmission
Digi al Twin Ligh pa h Models
Sadegh Ghas izadeh 1, Nelson Cos a 2, Ma c Ruiz 1, An onio Napoli 3, Joao Ped o 2,4, and Luis Velasco 1,*
1 Uni e si a Poli ècnica de Ca alunya, Spain, 2 In ine a, Po ugal, 3 In ine a, Ge many, 4 Ins i u o de Telecomunicações, Po ugal
*email: [email p o ec ed]
Abs ac —Op ical Digi al Twins (DT) equi e p e- ained
models o es ima ing he Quali y o T ansmission (QoT) o
candida e ligh pa hs in mul iband (MB) op ical ne wo ks be o e
hey a e p o isioned. Once ligh pa hs a e es ablished, hose
models need o be uned o be used o ailu e managemen , e.g.,
deg ada ion de ec ion. In his pape , we concen a e on he MB
OCATA DT, which models op ical signal p opaga ion in he ime
domain. We i s e alua e s a egies o c ea ing end- o-end
ligh pa h models om span DNNs and hen, we implemen model
uning, as a building block o he MB OCATA DT. Simula ion
esul s show he accu acy o p e- ained models o QoT
es ima ion and how hey a e uned wi h eleme y measu emen s
and imp o ed compa ed o he ini ial p e- ained models.
Keywo ds—Op ical Digi al Twin, Mul i-band Op ical
T ansmission, Digi al Twin Ligh pa h Models
I. INTRODUCTION
Op ical laye digi al wins (DT), like OCATA [1], ha e
many applica ions o ne wo k ope a ion, om ligh pa h
p o isioning o ailu e managemen [2]. Speci ically, he
OCATA DT is able o accu a ely es ima e he p e- o wa d e o
co ec ion (FEC) bi e o a e (BER) o C+L+S mul iband
(MB) ansmission sys ems, whe e he in e -channel s imula ed
Raman sca e ing becomes a majo e ec [3]. OCATA models
he p opaga ion o in-phase (I) and quad a u e (Q) op ical
cons ella ions along op ical spans. Fi s p inciple Deep Neu al
Ne wo ks (DNN) a e p e- ained be o ehand and s o ed in a
model da abase (DB), whe e hey a e a ailable o become pa
o an end- o-end (e2e) ligh pa h model, which a e c ea ed by
conca ena ing span DNNs o he cha ac e is ics de ined by he
ou e o he ligh pa h, i.e., he span leng h, and channel. In [3],
we educed he numbe o p e- ained models o jus a selec ion
e e ence channels (RCh) and p oposed a ea u e composi ion
me hod o es ima e he ea u es o any channel in he C+L+S
bands, based on he ou pu o he models p opaga ing he
ea u es o he RChs.
In his wo k, we ace he p oblem o c ea ing accu a e e2e
ligh pa h models om p e- ained span models. Se e al sou ces
o e o can be ound in he p ocess o c ea ing e2e ligh pa h
models. We ocus on he ac ha span models a e ained o
speci ic span leng hs, which migh no ma ch wi h he ones in
he ne wo k. E en hough e2e models can be used o p e-FEC
BER es ima ion o candida e ligh pa hs du ing p o isioning,
disc epancies be ween hem and he eal op ical sys em once
he ligh pa h is es ablished can educe hei e ec i eness o
ailu e managemen . To ha end, ligh pa h models a e uned
using eleme y a e p o isioning.
II. OCATA DT MODELING AND QOT ESTIMATION
OCATA de ines IQ op ical cons ella ion samples X as
sequences o symbols xאX, wi h each symbol co esponding o
one o m cons ella ion poin s (CP) in an m-QAM op ical signal
[1]. Samples a e hen condensed in o a se o cons ella ion
ea u es Y, whe e each Yi ep esen s he cha ac e is ics o a CP
i. The ea u e ex ac ion (FeX) p ocess employs Gaussian
Mix u e Models (GMM) [4] o model a gi en sample X as a se
o bi a ia e Gaussian dis ibu ions, one pe each CP.
Consequen ly, he ec o Yi=[μI,μQ,σI,σQ,σIQ] is de ined by i e
ea u es, i.e., he mean I and Q posi ions (μ) wi hin he
cons ella ion, and he eal and imagina y a iance and
symme ic co a iance e ms (σ) expe ienced by he symbols o
CP i a ound he mean.
Two cons ella ion samples (X1, X
2) can be compa ed by
compu ing he di e ence be ween hem in e ms o he
Euclidean dis ance o hei ea u es (Y1 and Y2) [1], as ollows:
݂݂݀݅ሺܺଵǡܺଶሻൌԡܻଵെܻ
ଶԡଶ
(1)
Fu he mo e, p e-FEC BER can be es ima ed om ea u es
Y. Speci ically, he pa ame e Φiou was de ined in [2] o
ep esen he p obabili y o ecei ing a symbol o iginally sen
as pa o CP i, ou o he de ec ion a ea Ai assigned o ha CP.
ߔ௨௧
ൌͳെܲቀݔؿܣ
ቚݔࣨሺܻሻቁ
(2)
Then, he es ima ed p e-FEC BER can be compu ed based
on Φiou o all he CPs as eq. (3), whe e he a e age p obabili y
Φou is in e p e ed as an es ima ion o he symbol e o a e, and
he p e-FEC BER is de i ed assuming ha 1 symbol e o
causes only 1 bi wi h e o , i.e., assuming G ay coding.
p e-FEC BER ଵ
ή୪୭మሺሻ σȰ௨௧
ୀଵ
(3)
III. LIGHTPATH MODEL COMPOSITION AND TUNING
We assume he scena io ep esen ed in Figu e 1, whe e a
MB op ical ne wo k is composed o MB op ical ansponde s
(TP) and op ical ampli ie s, and each ampli ie includes
e bium-doped ibe ampli ie (EDFA) o C and L bands and
hulium-doped ibe ampli ie (TDFA) o he S band. A
So wa e-De ined Ne wo king (SDN) con olle is in cha ge o
ligh pa h p o isioning and eleme y da a collec ion, while he
OCATA DT uns besides he SDN con olle o p o ide QoT
es ima ion and ailu e managemen . Fo illus a i e pu poses, a
ligh pa h be ween he TPs in si es A and Z is ep esen ed.
The model DB in OCATA includes p e- ained span DNNs,
so ligh pa h models can be easily c ea ed. Using p e- ained
span models in oduces some e o coming om: i) da a used
978-3-903176-67-6 © 2025 IFIP
2025 In e na ional Con e ence on Op ical Ne wo k Design and Modeling (ONDM)
TP TP
demux
mux
mux
mux
MB OA
demux
mux
MB OA
Si e A
Si e Z
Tx
Rx
Tx
Rx
Node
Agen
Node
Agen
SDN
Con olle
OCATA Digi al Twin
Teleme y /
Model DBs
Sandbox
Domain
Model Tuning
check
Tune
Model S o e
models
Ligh pa h
OCATA
Digi al Twin
Algo i hms
Figu e 1: OCATA digi al win a chi ec u e
o p e- aining can come om sligh ly di e en de ices han
he ones in he ne wo k and aging impac s also hei beha io ;
ii) span models a e ained only o RChs, which migh no
ma ch he channel alloca ed o he ligh pa h; and iii) span
models a e ained o speci ic span leng hs, which migh no
ma ch wi h he ones in he ne wo k. The i s wo sou ces o
e o impac he accu acy o he models mainly o hei use
a e he ligh pa h is es ablished, as he inal e o o QoT
es ima ion should be insigni ican [3]. Howe e , ha o he
span leng hs migh ha e a signi ican impac on he accu acy o
he models.
In his pape , we explo e and e alua e he e o o ligh pa h
models unde wo al e na i e app oaches o ligh pa h model
composi ion: i) he pe -span composi ion (Algo i hm 1) inds
he span DNNs modelling he closes as possible span leng h
o each o he spans in he links (E) o he ou e o he ligh pa h.
Howe e , his app oach can lead o signi ican inaccu acy on
he o al dis ance modelled by he esul ing conca ena ed DNN;
and ii) he dis ance-based composi ion (Algo i hm 2) selec s he
span models inding bo h he co ec pe -link span models, as
well as educing he o al dis ance e o . The algo i hm keeps
ack o he accumula ed e o in he dis ance and inds he bes
sequence o span leng hs ha esul s in minimum leng h e o .
The span models a e conca ena ed in o a single DNN ha can
be used o QoT es ima ion.
In MB op ical ansmission, he algo i hms a e execu ed o
he wo RChs adjacen o he ac ual channel alloca ed o he
ligh pa h, in he gene al case whe e he alloca ed channel is no
one o he RChs, and QoT es ima ion is pe o med by applying
eq. (3) on he ea u es esul ing om he ea u e composi ion
p ocedu e in [3]. In addi ion, he ligh pa h model c ea ed om
span models o he RCh closes o he alloca ed one is s o ed in
he model DB.
Once he ligh pa h is deployed, he e2e ligh pa h model will
be in place. The e o e, i needs o be uned using eleme y da a.
Speci ically, he new Model Tuning building block is p oposed
and in eg a ed in he OCATA DT a chi ec u e. The block uns
Algo i hm 3 pe iodically o check whe he majo de ia ions a e
de ec ed, in which case, he ligh pa h model is upda ed using
eq. (1) as loss unc ion. The eason o he model upda e can be
analyzed a e wa ds o de ec deg ada ions.
Algo i hm 1. Pe -span LP model composi ion
INPUT: E, RCh
OUTPUT: e2e_dnn
1:
2:
3:
4:
5:
DNNLis ← []
o each
e in E do
o each s in e.spans do
DNNLis .add(ModelDB.ge (RCh, s.leng h))
e u n conca ena e(DNNLis )
Algo i hm 2. Dis ance-based LP model composi ion
INPUT: E, RCh
OUTPUT: e2e_dnn
1:
2:
3:
4:
5:
6:
7:
8:
9:
10:
DNNLis ← []; d a e sed ← 0; dmodels ← 0
o each
e in E do
d ← e.leng h + d a e sed – dmodels
spanLeng hs ← indOp imalSpans(d, e.spans)
o each l in spanLeng hs do
dnn ← ModelDB.ge (RCh, l))
dmodels ← dmodels + dnn.ge Leng h()
DNNLis .add(dnn)
d a e sed ← d a e sed + e.leng h
e u n conca ena e(DNNLis )
Algo i hm 3. Model Tuning
INPUT: lp
OUTPUT: Upda ed
1:
2:
3:
4:
5:
6:
7:
8:
M ← ModelDB.ge (lp))
[
X] ← Teleme yDB.ge Samples(lp, pe iod, K)
[
Y] ← FeX([X])
lpBER
← es ima eA gBER([Y])
i
RE(M.ge BER(), lpBER) ≤ MAX_ERROR do e u n
False
dnn
← SANDBOX. une(M.ge DNN(), [Y])
ModelDB
.s o e(M.se DNN(dnn), lp)
e u n T ue
Algo i hm 3 ecei es he Id o he ligh pa h and e u ns
whe he he ligh pa h e2e model has been o no upda ed. The
algo i hm i s ge s he las e sion o he model M om he
model DB (line 1). M includes he conca ena ed model oge he
wi h some addi ional me ada a. Nex , eleme y samples a e
e ie ed om he eleme y DB (line 2). K samples a e
andomly selec ed om he ones collec ed du ing he las pe iod
and ea u es a e ex ac ed (line 3). The ec o o ea u es is used
o es ima e he a e age p e-FEC BER ha he ligh pa h has
expe ienced du ing he pe iod (line 4). Tha alue is compa ed
o model es ima ion and he ela i e e o (RE) is checked
agains a maximum allowable ela i e e o and, in case he
maximum e o is no exceeded, he model is no upda ed (line
5). O he wise, he conca ena ed DNN is e ie ed om M and
sen o he Sandbox o be ained wi h he ea u es om
eleme y. The uned DNN is eplaced in M and upda ed in he
model DB, and he algo i hm e u ns model upda ed (lines 6-8).
IV. RESULTS AND DISCUSSION
To e alua e he algo i hms p oposed in he p e ious sec ion,
we use he da a om he MB op ical ansmission simula o in
[5]. 16QAM signals a 32 GBaud using pseudo andom 216-bi
sequences o each channel we e gene a ed wi h 0.06 oo -
aised cosine oll-o . Signals we e launched wi h 0 dBm in a
50 GHz g id and ansmi ed h ough s anda d single-mode
ibe . A he ecei e , IQ cons ella ions a e collec ed a e ideal
ch oma ic dispe sion compensa ion and phase eco e y. To
clea ly obse e he e o in models’ accu acy, wo e y
di e en span scena ios we e simula ed, wi h spans o 50 and
2025 In e na ional Con e ence on Op ical Ne wo k Design and Modeling (ONDM)
1.E-6
1.E-5
1.E-4
1.E-3
1.E-2
1.E-1
123456789101112
1.E-6
1.E-5
1.E-4
1.E-3
1.E-2
1.E-1
123456789101112
1.E-6
1.E-5
1.E-4
1.E-3
1.E-2
1.E-1
123456789101112
1.E-6
1.E-5
1.E-4
1.E-3
1.E-2
1.E-1
123456789101112
1.E-6
1.E-5
1.E-4
1.E-3
1.E-2
1.E-1
123456789101112
Pe -span
Dis ance-based
Teleme y
1.E-6
1.E-5
1.E-4
1.E-3
1.E-2
1.E-1
123456789101112
Tuned model
Teleme y
P e-FEC BER
T ue BER
Ch 75 Ch 245
P e-FEC BER
12 1
Ch 170
# Spans 12 1
1.E-6
1.E-1
CP [1–i]CP [–3+3i]
3 Spans 3 Spans 3 Spans
6 Spans 6 Spans 6 Spans
9 Spans 9 Spans 9 Spans
(a) Models o QoT
Es ima ion
(b) Models Tuned a e P o isioning(c) Con ou s o 2 CPs
444676
Figu e 2: P e-FEC BER s # o spans (50 km) be o e (a) and a e uning (b). (c) Con ou s o bi a ia e Gaussian dis ibu ion o wo CPs.
0
0.01
0.02
0.03
0.04
0.05
0.06
5 10 20 50 100 200 500 1000
9 Spans
6 Spans
3 Spans
0
0.01
0.02
0.03
0.04
0.05
0.06
5 10 20 50 100 200 500 1000
K1000 5
(a) Ch 75 (b) Ch 170 (c) Ch 245
0
0.01
0.02
0.03
0.04
0.05
0.06
5 10 20 50 100 200 500 1000
1000 5
di
Y
(X
1
,X
2
)
Figu e 3: A e age e o be ween model and eleme y ea u es s numbe o samples K o h ee non- e e ence channels.
80 km. Samples om 80 km span scena ios we e used o
modelling spans o 7 RChs, as in [3], whe eas ligh pa hs we e
e alua ed and es ablished on 50 km span scena ios using non-
e e ence channels 75, 170, and 245, in he S, C and L bands,
espec i ely.
Figu e 2a shows he es ima ed QoT when e2e model
composi ion is ca ied ou using he pe -span and he dis ance-
based app oaches o he h ee Chs s he numbe o spans o
he ligh pa h (each o 50 km). We obse e ha he pe -span
ends o o e es ima e he QoT, which esul s in p o isioning
eques s ejec ed o ligh pa h exceeding 4 spans in all he
bands, i.e., 2-3 spans sho e , when compa ed wi h he ue
BER. On he opposi e, he dis ance-based app oach is much
mo e accu a e, wi h he le el o accu acy depending on he
numbe o a e sed spans, which is a esul o he di e ence o
span leng hs be ween he eal ones (50 km) and he ones used
o modelling (80 km). E en hough he esul s show poo
pe o mance o bo h app oaches in se e al cases, he p oposed
algo i hms a e s ill powe ul ools o op imize he
cha ac e is ics o he models o be p e- ained, so o minimize
he e o in he QoT es ima ion o candida e ligh pa h.
Figu e 2b shows he QoT es ima ion o he e2e models a e
model uning. In his case, we obse e ema kable accu acy in
he QoT es ima ion o all h ee Chs. Figu e 3 plo s he
e olu ion o eq. (1) wi h he numbe o samples du ing model
uning in he sandbox domain. In all he cases, 200 samples a e
enough o p oduce e y low di e ence be ween he samples
om eleme y and he model. Finally, Figu e 2c shows he
con ou s o one ex e nal and one in e nal CP o he models
a e composi ion and a e uning. I is clea , in he iew he
no iceable simila i y, he obse ed imp o emen in he
accu acy o he models.
ACKNOWLEDGEMENT
The esea ch leading o hese esul s has ecei ed unding om he
EC MSCA-DN NESTOR (G.A.101119983), om he SNS JU unde
he Ho izon Eu ope SEASON (G.A. 101096120), and om ICREA.
[1] D. Sequei a e al., “OCATA: A Deep Lea ning-based Digi al Twin o he
Op ical Time Domain,” JOCN, ol. 15, pp. 87-97, 2023.
[2] M. De igili e al., “Applica ions o he OCATA Time Domain Digi al
Twin: om QoT Es ima ion o Failu e Managemen ,” JOCN, ol. 16, 2024.
[3] S. Ghas izadeh e al., “DT-Assis ed Ligh pa h P o isioning and Nonlinea
Mi iga ion in C+L+S MB Op ical Ne wo ks,” Senso s, ol. 24, 2024.
[4] N. Bouguila and W. Fao, Mix u e Models and Applica ions, Sp inge , 2020.
[5] P. Kha e e al., “SSMS: A Spli S ep MB Simula ion So wa e,” ICTON,
2023.
2025 In e na ional Con e ence on Op ical Ne wo k Design and Modeling (ONDM)
