1
C oss-Ci y Valida ion and Re inemen o a Pa h
Loss Model o NB-IoT in U ban Scena ios
Fede ico Fe e i*, Giuseppe Caso*, Luca De Na dis, Ma co Sa elli,
Anna B uns om, Özgü Alay, Ma co Ne i, Ma ia-Gab iella Di Benede o
Abs ac —The Na owband In e ne o Things (NB-IoT) ech-
nology has an impo an ole in he mobile cellula ecosys-
em, enabling massi e Machine Type Communica ion (mMTC)
se ices. NB-IoT p opaga ion was p elimina ily analyzed ia a
measu emen campaign ca ied ou in 2020 in he ci y o Oslo,
No way. This in es iga ion esul ed in Oslo-2020, he i s NB-
IoT-speci ic Alpha-Be a-Gamma (ABG) pa h loss (PL) model,
which showed highe p edic ion accu acy compa ed o models
de eloped o di e en echnologies bu o en used o NB-IoT. In
his pape , o u he in es iga e NB-IoT PL in u ban scena ios,
we analyze new measu emen campaigns pe o med in 2020-
2021 and 2023 in he ci y o Rome, I aly. Fi s , we use he
2020-2021 measu emen s o de i e Rome-2021, a new NB-IoT-
speci ic ABG PL model. We show ha Rome-2021 p ese es
he s a is ical p ope ies o Oslo-2020 (e.g., he Gaussiani y o
he PL exponen dis ibu ion ac oss base s a ions), al hough he
momen s o he dis ibu ions a e di e en due o ci y-speci ic
en i onmen al cha ac e is ics. We also use new da a on signal
losses due o ou doo - o-indoo p opaga ion o e ine he analysis
o his scena io. Finally, we p opose a me hodology o combine
Oslo-2020 and Rome-2021 in o a mo e gene al model. Ou
me hodology uses so-called Mix u e Dis ibu ions (MDs), hus
le e aging he sha ed s a is ical p ope ies be ween Oslo-2020
and Rome-2021. By using he 2023 measu emen s, we show
ha ou MD-based app oach es ima es PL model pa ame e s
wi h highe accu acy compa ed o Oslo-2020 and Rome-2021
models used sepa a ely, hus p o iding an e ec i e solu ion o
p edic ing NB-IoT u ban PL in lack o si e-speci ic measu emen s
and in o ma ion.
Index Te ms—Cellula In e ne o Things, massi e Machine
Type Communica ion, Na owband In e ne o Things, Pa h Loss
Empi ical Models
I. INTRODUCTION
Na owband In e ne o Things (NB-IoT) is a widely
adop ed Low-Powe Wide-A ea Ne wo k (LPWAN) ech-
nology ha enables low-cos and powe -e icien massi e
Machine-Type Communica ion (mMTC) on mobile cellula
sys ems. I was i s s anda dized by he 3 d Gene a ion
Pa ne ship P ojec (3GPP) in Release 13 (Rel-13) and hen
enhanced in la e eleases, o ensu e in e -wo king in li-
censed spec um po ions wi h 4 h Gene a ion (4G) Long
Te m E olu ion (LTE) and 5 h Gene a ion (5G) New Radio
F. Fe e i and Ma co Sa elli a e wi h TIM S.p.A., Rome, I aly.
G. Caso and A. B uns om a e wi h Ka ls ad Uni e si y, Ka ls ad, Sweden.
L. De Na dis and M.-G. Di Benede o a e wi h Sapienza Uni e si y o
Rome, Rome, I aly.
Ö. Alay is wi h Uni e si y o Oslo, Oslo, No way, and Ka ls ad Uni e si y,
Ka ls ad, Sweden.
M. Ne i is wi h Rohde&Schwa z, Rome, I aly.
* These au ho s con ibu ed equally o his pape .
Co esponding au ho : G. Caso ([email p o ec ed]).
41°50'N
41°52'N
41°54'N
La i ude
12°26'E 12°28'E 12°30'E 12°32'E
Longi ude
Es i, HERE, Ga min, USGS
1 mi
2 km
Measu emen Loca ions Posi ions o BSs om Op1
Posi ions o BSs om Op2 Posi ions o BSs om Op3
Fig. 1: Rou es co e ed du ing he measu emen campaign in 2020-
2021, along wi h he es ima ed posi ions o he NB-IoT BSs o h ee
I alian MNOs (Op1, Op2, and Op3). Fo each ou e, measu emen s
we e collec ed mul iple imes, o a o al o 49 sub-campaigns (see
§III o mo e de ails on measu emen se up and me hodology).
(NR) sys ems, ha a e mos ly ocused on enhanced Mobile
B oadBand (eMBB) and Ul a-Reliable Low La ency Com-
munica ion (URLLC) use cases [1]–[3].
As o all wi eless echnologies in gene al, a p ope unde -
s anding and accu a e modeling o NB-IoT adio p opaga ion
and co e age is key owa d suppo ing, on he one hand,
mobile ne wo k ope a o s (MNOs) in e icien ly deploying and
con igu ing hei ne wo ks and, on he o he hand, esea che s
in pe o ming analyses and p oposing imp o emen s, e.g., ia
simula ions. Se e al esea ch and s anda diza ion ac i i ies a e
indeed de o ed o pa h loss (PL) modeling, wi h a ocus
on he so-called empi ical models. These es ima e PL al-
ues h ough well-es ablished, physically-g ounded equa ions
embedding speci ic pa ame e s, e.g., he PL exponen (see
§II). The alues o he pa ame e s a e ob ained by i ing he
equa ions on eal-wo ld measu emen s, aiming a minimizing
he di e ence be ween measu emen s and model es ima es.
The de i a ion o PL empi ical models is o en challenged
by he sca ci y o measu emen s, and NB-IoT makes no ex-
cep ion. In he con ex o LPWAN echnologies, empi ical PL
models we e mo e o en de i ed o p op ie a y echnologies
al e na i e o NB-IoT, i.e., Long Range (LoRa) and SigFox
(see Table I in [4] o a summa y o such wo ks). These
wo echnologies ope a e in unlicensed spec um po ions,
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con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/JIOT.2025.3557172
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2
o e dedica ed in as uc u es and using speci ic con igu a-
ions (e.g., signal bandwid h, ansmission powe , and ecei e
sensi i i y, o men ion a ew), which limi he applicabili y
o he ob ained PL models o NB-IoT, as obse ed in [5]
and also e i ied in §IV on ou measu emen s. The e o e, so
a , simula ion-based in es iga ions on NB-IoT mos ly u ilized
models de i ed o o he cellula echnologies, such as Uni-
e sal Mobile Telecommunica ions Sys em (UMTS) and LTE
(e.g., [6]–[17]). In [18], we p o ided wo empi ical models o
he NB-IoT PL in an u ban scena io, by le e aging a la ge-
scale measu emen campaign execu ed in he ci y o Oslo,
No way, in 2020 [19]. By ollowing he app oach adop ed
in [20] o o he echnologies, and using measu emen s o
a la ge numbe o Base S a ions (BSs) o ming he NB-
IoT ne wo ks o wo No wegian MNOs, he wo k in [18]
p o ided s a is ically-ex ended e sions o well-known PL
empi ical models, i.e., Close-In (CI) [21] and Alpha-Be a-
Gamma (ABG) [22] ( he la e e e ed o as Oslo-2020 in
his pape ), wi h model pa ame e s no ixed o a single alue
bu andomly gene a ed om well-known dis ibu ions. This
enables a mo e accu a e PL es ima ion o NB-IoT u ban
deploymen s wi h mul iple BSs, o e coming he limi a ion o
models de i ed ia measu emen s collec ed o a single BS,
which hus ha e ixed- alue pa ame e s [23]–[27]. Resul s in
[18] also highligh ed ha he speci ic cha ac e is ics o NB-
IoT compa ed o o he cellula echnologies, e.g., in e ms o
occupied bandwid h and con igu a ions, in oduce ema kably
di e en p opaga ion cha ac e is ics, con i ming he need o
dedica ed PL assessmen s and model alida ion/ e inemen ia
addi ional measu emen s in mul iple scena ios.
In his pape , we ollow up on he in es iga ion in [18],
wi h he main goal o alida ing and e ining he empi ical
cha ac e iza ion o NB-IoT PL in u ban scena ios. We hus
make he ollowing con ibu ions:
•We in oduce a la ge-scale measu emen campaign exe-
cu ed in he ci y o Rome, I aly, in 2020-2021, co e ing
396 NB-IoT BSs om h ee I alian MNOs (Fig. 1). By
le e aging he collec ed measu emen s, we de i e a new
s a is ically-ex ended ABG PL model o NB-IoT, e-
e ed o as Rome-2021, which includes he dis ibu ions
o he ABG pa ame e s and o he PL shadowing e m.
Simila ly o Oslo-2020,Rome-2021 imp o es PL es ima-
ion accu acy compa ed o models de eloped o o he
echnologies bu o en used in NB-IoT in es iga ions,
hus enabling ealis ic simula ions o NB-IoT PL in u ban
a eas wi h mul iple BSs;
•We compa e Oslo-2020 and Rome-2021 and disco e ha
he s a is ical p ope ies o he o me a e p ese ed by
he la e (e.g., Gaussian dis ibu ions a e a good i o
bo h Oslo-2020 and Rome-2021 ABG model pa ame e s),
bu p esen di e en momen s (e.g., mean and s anda d
de ia ion). This alida es he analyses in [18] bu also
highligh s he impac o ci y-speci ic en i onmen al and
deploymen cha ac e is ics on signal p opaga ion;
•We e ine he analysis in [18] on he addi ional losses
due o ou doo - o-indoo p opaga ion. On he one hand,
we con i m ha deep indoo (DI) scena ios (i.e., enclosed
a eas below he g ound loo ) esul in signi ican ly highe
losses compa ed o ypical indoo scena ios (i.e., ooms
wi h windows a high loo s). On he o he hand, we high-
ligh ha such losses signi ican ly a y ac oss loca ions,
also as a unc ion o BS posi ions/heigh s, hus making
he common app oach o using a cons an loss alue
ques ionable, and opening up o model imp o emen s;
•We p opose a PL model gene aliza ion whe e we combine
Oslo-2020 and Rome-2021 models ia Mix u e Dis i-
bu ions (MDs) [28], hus le e aging he knowledge o
he pa ame e s’ dis ibu ion ac oss ci ies. We alida e
he MD-based modeling app oach by exploi ing a new
measu emen campaign ca ied ou in Rome in 2023.
In pa icula , we show ha he MD-based model can
es ima e he PL alues obse ed in Rome in 2023 wi h a
highe accu acy compa ed o using Oslo-2020 and Rome-
2021 sepa a ely, hus p o iding an e ec i e solu ion
o p edic ing NB-IoT u ban PL in lack o si e-speci ic
measu emen s and en i onmen al/deploymen in o ma-
ion and equi emen s, e.g., o simula ion-based s udies.
The pape is o ganized as ollows. The backg ound is
p o ided in §II, while §III p esen s he measu emen se up and
campaigns execu ed in Rome in 2020-2021 and 2023, along
wi h he da a p ocessing ca ied ou p io o he ollowing
analyses. The Rome-2021 model is in oduced in §IV, whe e
an in-dep h compa ison wi h he p e ious Oslo-2020 model is
also p esen ed. The MD-based modeling app oach is de ailed
and e alua ed in §V. Finally, §VI concludes he pape .
II. BACKGROUND AND RELATED WORK
This sec ion p o ides he backg ound o ou wo k, by
discussing on a high le el PL modeling solu ions o cellula
sys ems and hei applica ion o NB-IoT.
A. PL Modeling o Cellula Sys ems
In ou doo - o-ou doo p opaga ion modeling, i is assumed
ha a ansmi e (TX) and a ecei e (RX) communica e
o e an ou doo wi eless link, and he PL [dB] is commonly
ep esen ed as ollows:
PL =PL +X,(1)
whe e PL is he PL a e age e m and Xis a andom a iable
ep esen ing PL a ia ions a ound he a e age e m, ha a e
caused by slow ading phenomena, such as shadowing due o
he p esence o su ounding objec s.
CI and ABG a e mos widely used empi ical models in
es ima ing PL in cellula sys ems up o 5G [22], [26], [27].
The CI model es ima es PL as ollows:
PLCI = 10γlog10 d
d0+A,(2)
whe e dis he TX-RX dis ance, d0is a e e ence dis ance,
γis a dis ance- ela ed pa ame e usually e e ed o as PL
exponen , and Ais ei he se o he loss a d0es ima ed ia
he F ee Space (FS) model (see la e ) o op imized, along wi h
γ, ia model i ing on eal measu emen s. A single alue o
γand Acan be hen ob ained i measu emen s o a single
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3
TX-RX pai a e a ailable a di e en dis ances (e.g., one BS
and se e al measu emen poin s). Simila ly, he ABG model
es ima es PL as ollows:
PLABG = 10γlog10(d) + 10βlog10( c) + l0,(3)
whe e cis he ca ie equency, βis a equency- ela ed
exponen , and l0is a cons an loss e m.1Also in his case,
he alues o γ,β, and l0can be ob ained ia model i ing,
and a single alue o each pa ame e can be ob ained wi h
one BS and se e al measu emen poin s a di e en dis ances.
No e ha ABG gene alizes he FS model, whe e i is assumed
γ= 2,β= 2, and l0= 20 log10(4π
c), wi h cindica ing he
speed o ligh (l0≈32.44 dB i dis in km and cis in MHz).
As shown in (1), he es ima ed PL is complemen ed by a
sample ex ac ed om a andom a iable X, which quan i ies
how much PL de ia es om he eal measu emen s due
o shadowing. Xis commonly assumed o be dis ibu ed
acco ding o a Gaussian dis ibu ion wi h mean µ= 0 and
s anda d de ia ion σde e mined a e i ing he PL model,
i.e., X ∼ N (µ= 0, σ).
Fo ou doo - o-indoo p opaga ion, a common solu ion is
o add a e m o (1), i.e., li, o accoun o he addi ional
losses expe ienced by he signal when pene a ing walls, loo s,
and/o windows be o e eaching he RX. lican be ob ained,
empi ically, by quan i ying he di e ence be ween PL ou doo
es ima es s indoo measu emen s a simila dis ances. In
Technical Speci ica ion (TS) 38.901 [29], 3GPP p oposes
li= 0.5di, whe e diis he indoo componen o he TX-RX
pa h, om he ou e wall o he RX (in me e s).
B. PL Modeling o NB-IoT
As men ioned in §I, NB-IoT is a adio in e ace o mMTC
se ices. I uses ei he a 200 kHz Global Sys em o Mobile
Communica ions (GSM)-like channel o an LTE Physical
Resou ce Block (PRB) o 180 kHz, and adop s one ou o
h ee possible ope a ion modes: (a) s and-alone, o e a 200
kHz channel in he GSM spec um, (b) in-band, o e a single
PRB wi hin a se o LTE PRBs, (c) gua d-band, wi hin a gua d
band among di e en se s o LTE PRBs. A de ailed desc ip ion
o NB-IoT is ou o scope o his pape . We e e he in e es ed
eade o [1]–[3] and e e ences he ein o mo e de ails on his
echnology, which is being enhanced ac oss 3GPP eleases.
P opaga ion condi ions signi ican ly a ec NB-IoT ope a ions
and pe o mance, and his highligh s he need o accu a e PL
modeling. In pa icula , NB-IoT BSs ansmi he Na owband
Re e ence Signal (NRS), used by NB-IoT de ices o measu e
he (Na owband) Re e ence Signal Recei ed Powe (RSRP
[dBm]). Based on he measu ed RSRP, de ices es ima e hei
p opaga ion condi ions in e ms o Co e age Le el (CL), ul i-
ma ely using CL-dependen con igu a ions, e.g., ansmission
powe and numbe o epe i ions, o di e en ope a ions,
including da a ansmission.
Modeling op ions cu en ly a ailable o NB-IoT a e sum-
ma ized below. They ypically ex end CI and ABG models,
1A di e en no a ion uses a iables α,β, and γ o he PL exponen ,
cons an losses, and c- ela ed pa ame e s, hus explaining he name ABG
(e.g., see [26] [27]).
and we e i ed on measu emen s collec ed o UMTS and LTE
(excep o he models de i ed in [18]).
3GPP UMTS 30.03 model as pe TR 45.820 [30] [31].
O iginally p oposed o ehicula scena ios in u ban and
subu ban a eas wi h buildings o uni o m heigh , his model
has γand l0 alues depending on he BS an enna heigh
(exp essed in me e s). Mo eo e , dis in km and cis in MHz.
In 3GPP Technical Repo (TR) 45.820, he model is speci ied
by assuming a BS an enna heigh o 15 me e s and c= 900
MHz [32], i.e., in LTE Band 8, which is a ailable o NB-IoT
deploymen [1] [33]. Fo he shadowing e m, 3GPP sugges s
σ= 10 dB in UMTS 30.03 and σ= 8 dB in TR 45.820. The
model is la gely used in he NB-IoT li e a u e (e.g., [6]–[12]),
and a simple ecalcula ion allows o use i a c= 800 MHz,
i.e., in LTE Band 20, which is adop ed o NB-IoT deploymen
by he I alian MNOs conside ed in his pape (see §III).
Okumu a-Ha a (OH) model [34]. OH is a adi ional model
o cellula p opaga ion a equencies anging om 150 o
1500 MHz. Fo u ban en i onmen s, i is based on measu e-
men s collec ed in he ci y o Tokyo, Japan. γand l0 alues
depend on he BS an enna heigh (in me e s), d(in kilome e s),
and c(in MHz). A speci ic e m in he OH model depends on
cand he heigh o he mobile de ice (in me e s), and changes
as a unc ion o he conside ed scena io (e.g., small- o-medium
s. la ge ci ies). Fo NB-IoT, OH is used in [13]–[15], wi h
he la e adop ing σ= 9.4dB.
3GPP U ban Mac o (UMa) models [35]. These models
es ima e he PL o Line o Sigh (LoS) and Non LoS (NLoS)
sepa a ely, by using din me e s and cin GHz. The UMa
LoS model also de ines (a) a b eak poin dis ance, whe e
he p opaga ion is assumed o s a ha ing a sligh ly di e en
beha io , and (b) e ec i e BS and de ice heigh s, ob ained by
adjus ing he o iginal alues [18]. Fo UMa NLoS, wo u he
pa ame e s a e needed, i.e., s ee wid h and building heigh ,
bo h in me e s, wi h anges epo ed in [35] along wi h he
alues o σ(4dB o UMa LoS and 6dB o UMa NLoS).
Fo NB-IoT, UMa models a e used o example in [16] [17].
Oslo CI and ABG models [18]. These a e s a is ically-
ex ended CI and ABG models ob ained by i ing (2)(3) on
NB-IoT PL measu emen s collec ed in 2020 in Oslo o mul-
iple BSs om wo MNOs, wi h NB-IoT ne wo ks ope a ing in
he gua d bands o LTE Band 20. Fo bo h models, dis in km
and cis in MHz. Fo CI, γ alues ac oss BSs a e modeled
ia a Gaussian dis ibu ion, while A alues a e ep esen ed
by a single cons an e m. Shadowing is modeled by N(0, σ),
wi h σ alues ac oss BSs ollowing a Weibull dis ibu ion. Fo
he ABG case (i.e., Oslo-2020 in his pape ), γand β alues
ac oss BSs a e modeled ia Gaussian dis ibu ions, l0is a
cons an e m, and σ alues also ollow a Weibull dis ibu ion
(see Table I). The esul s in [18] a e used in [36], [37] o
benchma k measu emen s in Hong Kong and Chile. Mo eo e ,
ecen esul s in [37] show a good i be ween he Oslo models
and he measu emen s, wi h possible accu acy imp o emen ,
in line wi h ou insigh s epo ed in he nex sec ions.
Fo ou doo - o-indoo p opaga ion, mos simula ion-based
wo ks use li alues o 10,20, o 30 dB [31] o ep esen
di e en indoo scena ios. In [38]–[40], i is empi ically
e i ied ha he 3GPP dis ance-based model o liis ai ly
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© 2025 IEEE. All igh s ese ed, including igh s o ex and da a mining and aining o a i icial in elligence and simila echnologies. Pe sonal use is pe mi ed,
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4
TABLE I: CI and ABG models p oposed in [18] o NB-IoT PL.
Pa ame e Oslo CI Oslo ABG (Oslo-2020)
γN(2.36,1.15) N(2.78,3.17)
β–N(2.81,0.60)
Ao l0[dB] 81.31 32.44
X N (0, σ)N(0, σ)
σ[dB] Wbl(6.670,2.289) (a) Wbl(4.709,2.218)
(a) Wbl(x,y)s ands o Weibull dis ibu ion wi h scale xand shape y.
accu a e abo e he g ound le el, bu i pe o ms poo ly below
he g ound le el. In [18], measu emen s in a ew indoo and DI
loca ions a e used o es ima e he addi ional losses wi h espec
o he a e age models in Table I. Fo ABG, i is sugges ed ha
li∈[8,13] dB o indoo scena ios, and liis up o 50 dB o
DI. Sligh ly highe alues a e ob ained o he CI model.
III. METHODOLOGY AND DATA PROCESSING
In his sec ion, we i s desc ibe ou measu emen se up and
campaigns in 2020-2021 and 2023 (§III-A), and hen discuss
how PL measu emen s we e ex ac ed om he collec ed da a
and p epa ed o he subsequen analyses (§III-B).
A. Measu emen Se up and Campaigns
NB-IoT measu emen s we e collec ed in Rome in 2020-
2021 and 2023 by using he Rohde & Schwa z (R&S) TSMA6
sys em, embedded wi h Radio F equency (RF) and Global
Posi ioning Sys em (GPS) an ennas. In ou se up, he R&S
TSMA6sys em included a spec um scanne and an embedded
PC whe e he R&S so wa e o da a collec ion, isualiza ion,
and expo ing was unning. P io o he measu emen cam-
paigns, he se up was calib a ed owa d enabling accu a e co -
e age measu emen s o all 3GPP echnologies ope a ing in he
measu emen a eas. Fo his pape , we used i o (a) de ec ing-
and-decoding he con ol signals (e.g., NRSs) b oadcas by
NB-IoT BSs, (b) collec ing co e age measu emen s on hem
(e.g., RSRP alues), and (c) ob aining an es ima ed posi ion o
he de ec ed BSs. Knowing he posi ion o he BSs and o he
measu emen poin s ( ia GPS) allowed o e alua e he dis ance
dbe ween each de ec ed BS and measu emen poin , needed
in (2)(3). Since he posi ion was in geog aphical coo dina es,
we used he Ha e sine o mula [41] o ob ain dis ance alues.
The 2020-2021 campaign co e ed 7weeks be ween Decem-
be 2020 and Janua y 2021. We enabled he R&S TSMA6
o pe o m passi e measu emen s on se e al LTE bands. By
doing so, we de ec ed h ee I alian MNOs, deno ed Op1,
Op2, and Op3, p o iding NB-IoT se ices in he LTE Band
20 gua d bands. The campaign was di ided in o mul iple
sub-campaigns, ca ied ou in di e en a eas. We conduc ed
ou doo sub-campaigns while walking o d i ing along he
ou es depic ed in Fig. 1, o a o al o 49 sub-campaigns. We
also collec ed s a ic measu emen s in indoo and DI loca ions,
o a o al o 13 loca ions: 9o ices a he 2nd loo o
he Depa men o In o ma ion Enginee ing, Elec onics and
Telecommunica ions (DIET Dep .) o Sapienza Uni e si y, 1
la a he 6 h loo o a 7- loo esiden ial building, and 3DI
loca ions (1a DIET Dep ., 1a he pa king lo o he building,
and 1a he pa king lo o a comme cial s o e).
The 2023 campaign co e ed 4weeks be ween Ma ch and
July 2023. We con igu ed ou se up o ope a e in he same
condi ions o he 2020-2021 campaign and, also in his case,
we collec ed NB-IoT measu emen s om Op1, Op2, and Op3
in he LTE Band 20 gua d bands. The campaign was di ided
in o 6sub-campaigns ca ied ou in di e en a eas o he ci y,
pa ially o e lapping wi h he a eas co e ed in 2020-2021. Due
o ou ocus on benchma king ou doo PL models, we did no
collec indoo and DI measu emen s in 2023.2
We u he obse e ha bo h 2020-2021 and 2023 cam-
paigns we e ca ied ou o add ess he main goal o alida ing
and e ining a ci y-wide NB-IoT PL model, as a ollow up
o ou p e ious wo k in [18] and in line wi h p e ious wo ks
on o he echnologies (e.g., 5G [26], [27] and LoRa/SigFox
[5], [42]). Hence, as also epo ed in Fig. 1, ou campaigns
we e execu ed by d i ing along pa hs o se e al kilome e s,
whe e u ban en i onmen al condi ions we e ex emely a i-
able and, hus, no p ecisely ca ego izable (e.g., in e ms o
building densi y and e ain cha ac e is ics). This measu emen
me hodology and, hus, he ocus on ci y-wide PL modeling,
is also jus i ied by he na u e o he NB-IoT echnology,
which is expec ed o co e la ge u ban a eas om he same
BS – as e i ied by ou measu emen s as well as in o he
expe imen al wo ks on NB-IoT [5] – wi h he same signal
acing he e ogeneous en i onmen al condi ions.
B. PL De i a ion om Measu emen s and BS Fil e ing
Gi en a NB-IoT BS xand a measu emen poin a dis ance
d, we e alua ed he PL as ollows:
PL(d) = PNRS
TX,x −RSRP(d),(4)
whe e PNRS
TX,x [dBm] is he powe used by BS x o ansmi
he NRS. The decoding o con ol messages by he TSMA6
allowed o e ie e PNRS
TX o se e al BSs. This pa ame e
is named n s_Powe _ 13 and is b oadcas by BSs in
Sys em In o ma ion Block 2(SIB2) messages. Fo all MNOs,
we obse ed ha BSs used sligh ly di e en PNRS
TX alues,
con ined in he ange o a ew dBs. To educe a iabili y, we
used he median alue ac oss he BSs o each MNO in (4),
i.e., 21,22, and 24 dBm o Op1, Op2, and Op3, espec i ely.
Conside ing ha ou measu emen s we e collec ed unde
mobili y, we pe o med a u he il e ing o emo e as
ading e ec s. Simila ly o [18], we adop ed he ule in [43],
hus applying a ±20λmo ing a e age window o he se o
PL measu emen s o each BS. Finally, o limi he impac
o posi ioning e o s due o GPS inaccu acy, we de ined a
dis ance h eshold o 0.05 km and disca ded, o each BS, all
PL measu emen s collec ed a dis ances below his h eshold.
We also applied manual BS il e ing o emo e BSs de ec ed
by ou sys em, bu ep esen ed by oo ew measu emen s, hus
no allowing accu a e PL cha ac e iza ions. In summa y, we
pe o med he analyses epo ed in he nex sec ions on 396
BSs de ec ed in 2020-2021 (107 o Op1,143 o Op2, and 146
o Op3), and on 204 BSs de ec ed in 2023 (71 o Op1,63 o
Op2, and 70 o Op3).
2Bo h da ase s a e a ailable o u he explo a ion upon eques .
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5
IV. MODEL VALIDATION AND REFINEMENT:
FROM Oslo-2020 TO Rome-2021
In his sec ion, we p esen he s eps leading o he NB-
IoT-speci ic ABG PL model de i ed in his pape , i.e., Rome-
2021. A e assessing he accu acy o exis ing models (§IV-A),
we cha ac e ize he main e ms o Rome-2021, as in (1).
The e o e, by using he 2020-2021 measu emen s in Rome,
we i s i he ABG model o PL es ima ion (§IV-B) and hen
analyze he shadowing e m (§IV-C). Finally, we cha ac e ize
ou doo - o-indoo addi ional losses (§IV-D). Th oughou he
sec ion, we ex ensi ely compa e Rome-2021 and Oslo-2020,
in o de o highligh bo h simila i ies and di e ences.3
A. Compa ison o Exis ing Models
As a i s s ep, we e i y how well he models p esen ed
in §II-B es ima e he PL measu emen s collec ed in Rome in
2020-2021. Fo each BS, we e alua e he oo mean squa e
e o (RMSE) be ween he PL es ima ed by he models and he
measu emen s collec ed a di e en dis ance. Fo he models
ha need speci ic se ings, we use alues commonly adop ed
in he li e a u e, i.e., 15 me e s o he BS an enna heigh , 1.5
me e s o he de ice heigh , and 25 and 12 me e s o building
heigh and s ee wid h, espec i ely. Fo Oslo-2020, we use
he mean alues o he dis ibu ions o γand β, i.e., 2.78 and
2.81, espec i ely (see Table I). We conside he FS model
o u he compa ison, as well as wo popula models de i ed
o LoRa and SigFox in [42] and [5], espec i ely. These a e
CI models i ed on LoRa and SigFox measu emen s in he
ci ies o Oulu, Finland, and B no, Czech Republic, esul ing
in γ= 2.32 and A= 128.95 dB o LoRa and γ= 3.76 and
A= 118.04 dB o SigFox.
Figu e 2 shows he boxplo o he RMSE alues ob ained
ac oss BSs. We obse e ha mos o he models esul in
a he high RMSE alues (e.g., a median abo e 25 dB o
FS and be ween 12-20 dB o OH, UMa LoS/NLoS, and
LoRa models). Due o simila γand A alues, TR 45.820
and SigFox models show simila pe o mance, wi h a median
RMSE a ound 10.5-11 dB. Finally, Oslo-2020 shows he
lowes median RMSE (9dB). This highligh s ha , on he one
hand, a model speci ically de i ed on NB-IoT measu emen s,
al hough collec ed in a di e en ci y, is mo e accu a e han
models de i ed o di e en echnologies. On he o he hand,
i hin s ha u he accu acy imp o emen s can be ob ained
by exploi ing si e-speci ic measu emen s and execu ing a ded-
ica ed i ing p ocedu e, as analyzed in he nex sec ions.
B. Cha ac e iza ion o PL
We now s a de i ing he Rome-2021 model. We hus e al-
ua e he PL e m in (3) by using he 2020-2021 measu emen s.
To de e mine i , simila ly o wha ob ained in [18], a
single alue can be associa ed o he l0 e m in (3), we i s
use an Uncons ained Fi ing (UF) app oach, i.e., we i he
ABG model on he measu emen s wi h no cons ain s on he
3No e ha we pe o med simila analyses o he CI model and ob ained
esul s in line wi h [18], i.e., a highe accu acy o he ABG model compa ed
o he CI model, which jus i y he ocus on he ABG model in his pape .
FS
TR 45.820 @ 800 MHz
TR 45.820 @ 900 MHz
OH
UMa LoS
UMa NLoS
LoRa Model
SigFox Model
Oslo-2020 (Mean)
PL Model
0
10
20
30
40
50
60
RMSE [dB]
Fig. 2: Compa ison o exis ing PL models adop ed o NB-IoT. FS
and wo models de i ed o LoRa [42] and SigFox [5] a e p esen ed
o u he compa ison. Fo each model, he boxplo o he RMSE
alues ac oss BSs is epo ed.
Fig. 3: Empi ical PDF o he alues o l0ob ained ac oss BSs o
he Rome-2021 model ia UF.
possible alues o γ,β, and l0. Figu e 3 shows he empi ical
p obabili y densi y unc ion (PDF) o he alues ob ained o l0
ac oss BSs by applying UF on (3). We obse e ha l0p esen s
a dis ibu ion ha concen a es a ound i s a e age alue o
36.37 dB. Di e en ly om Oslo-2020, he dis ibu ion o l0
alues only co e s posi i e alues, hus hin ing a a lowe
a iabili y o he 2020-2021 measu emen s in Rome compa ed
o he 2020 measu emen s in Oslo, despi e he highe amoun
o MNOs, BSs, and da a poin s in he o me case. The a e age
alue di e s by a ound 4dBs om he alue adop ed in he FS
and Oslo-2020 models, a ac ha does no allow o use he
same app oxima ion p oposed in [18]. Resul s hus con i m
ha he l0 e m can be app oxima ed o a single alue, bu
his alue is di e en om he one ob ained o Oslo-2020.
Fo Rome-2021, we ix l0= 36.37 dB and mo e on in he
PL modeling by applying a Cons ained Fi ing (CF), i.e., we
only de i e he γand β e ms in (3).
Figu e 4 shows he empi ical PDFs o γ(a) and β(b)
alues ob ained ac oss BSs ia CF. As shown in he igu e
and con i med ia he Akaike In o ma ion C i e ion (AIC),
bo h pa ame e s a e well-modeled by Gaussian dis ibu ions,
i.e., N(1.86,1.89) o γand N(2.70,0.39) o β. Simila ly
o he esul s ela ed o he l0 e m, he Gaussiani y o he
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6
-2 0 2 4 6 8
0
0.05
0.1
0.15
0.2
0.25
Empi ical PDF
(a)
1.5 2 2.5 3 3.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Empi ical PDF
(b)
Fig. 4: Empi ical PDFs o he alues o γ(a) and β(b) ob ained ac oss BSs o he Rome-2021 model ia CF. The nea es Gaussian
app oxima ion is also epo ed.
dis ibu ions o γand β alida e he indings in [18] and,
hus, he Oslo-2020 modeling app oach, whe e bo h γand β
we e al eady ound o nea ly ollow Gaussian dis ibu ions,
al hough wi h di e en means and s anda d de ia ions. Mo e
speci ically, compa ed o Oslo-2020, he inc eased l0 alue o
Rome-2021 esul s in lowe mean alues o he dis ibu ions
o γand β. The s anda d de ia ions o Rome-2021 a e also
lowe compa ed o Oslo-2020, hin ing again a less a iabili y
o he 2020-2021 measu emen s in Rome. Finally, we obse e
ha , simila ly o Oslo-2020, he dis ibu ion o γ o Rome-
2021 also includes nega i e alues, due o he p esence o
buildings ha may obs uc he signal om some BSs a sho
dis ances bu no a longe dis ance [24] [25].
We now e i y he accu acy o Oslo-2020 and Rome-2021
compa ed o o he models used in li e a u e bu no i ed
on NB-IoT measu emen s. To do so, we de ine GRMSE =
RMSEm
/RMSEABG
M, whe e m∈[TR 45.820, OH, UMa LoS,
UMa NLoS, LoRa Model [42], SigFox Model [5]]and
M∈[Rome-2021,Oslo-2020], ep esen ing he gain/loss in
e ms o a e age RMSE ac oss BSs o Rome-2021 o Oslo-
2020 compa ed o he o he models. GRMSE >1means an
accu acy gain in adop ing he model a he denomina o , as
i indica es a lowe a e age RMSE compa ed o he model
a he nume a o . Figu e 5 shows ha bo h Rome-2021 and
Oslo-2020 p o ide accu acy gains, hus u he con i ming
ha NB-IoT measu emen s and model i ing a e needed o
inc ease accu acy. Mo eo e , Rome-2021 shows highe gains
compa ed o Oslo-2020, hus also con i ming he impo ance
o si e-speci ic measu emen s.
C. Cha ac e iza ion o X
A e he analysis o PL, we now s udy he shadowing
componen X. As desc ibed in §II-A, gi en a BS, X ollows
a ze o-mean Gaussian dis ibu ion, i.e., N(µ= 0, σ), i he
PL model accu a ely es ima es he a e age e m.
In o de o e i y how well Rome-2021 pe o ms on his
aspec , we epo in Fig. 6 he boxplo o he mean µo he
Gaussian dis ibu ions ha bes app oxima e Xac oss BSs.
Fo compa ison, we epo he esul s o he models ha
pe o m ela i ely well in cha ac e izing PL, i.e., Oslo-2020
FS
TR 45.820 @ 800 MHz
TR 45.820 @ 900 MHz
OH
UMa LoS
UMa NLoS
LoRa Model
SigFox Model
0
1
2
3
4
5
6
7
8
GRMSE
Rome-2021
Oslo-2020
Fig. 5: GRMSE o Rome-2021 and Oslo-2020 compa ed o FS, TR
45.820, OH, UMA LoS/NLoS, LoRa [42] and SigFox [5] models.
Rome-2021
Oslo-2020
TR 45.820 @ 800 MHz
FS
PL Model
-20
0
20
40
[dB]
-2
0
2
10-5
Fig. 6: Boxplo o he alues o µob ained ac oss BSs o he Rome-
2021 model ia CF. Boxplo s o Oslo-2020, TR 45.820, and FS
models a e epo ed o compa ison.
and TR 45.820, along wi h he esul s o he FS model o
a wo s case compa ison. We obse e ha , o Rome-2021,
µ alues a e e y close o ze o o all BSs, hus con i ming
he accu acy in modeling PL. Fo he o he models, µ alues
sp ead mo e signi ican ly, which is in line wi h he esul s
in §IV-A. In pa icula , he posi i e median alues o 4and
2.6dB o Oslo-2020 and TR 45.820 models, espec i ely,
sugges ha hese models ha e a endency in unde es ima ing
PL; mo eo e , he ange a ound such medians also spans
o e nega i e alues (±20 dB o Oslo-2020 and sligh ly
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7
la ge o TR 45.820), hus highligh ing ha he same models
al e na i ely unde es ima e and o e es ima e PL. I can also
be obse ed ha , as expec ed, FS always unde es ima es PL,
esul ing in a high median µ alue, a ound 24.7dB (i was 19
dB o he 2020 measu emen s in Oslo), and a la ge posi i e
ange a ound such alue.
02468
0
0.05
0.1
0.15
0.2
0.25
Empi ical PDF
Fig. 7: Empi ical PDFs o he alues o σob ained ac oss BSs o
he Rome-2021 model ia CF. The nea es Weibull app oxima ion is
also epo ed.
We now analyze he dis ibu ion o he s anda d de ia ion σ
o he Gaussian dis ibu ions ha bes app oxima e Xac oss
BSs. Figu e 7 shows ha , o Rome-2021,σ ollows a le -
skewed dis ibu ion. The AIC con i ms ha he Weibull dis-
ibu ion Wbl(4.539,2.155) app oxima es well he measu ed
alues, as depic ed in Fig. 7. In line wi h he analyses p esen ed
abo e, hese esul s once again alida e he main indings
in [18], whe e a Weibull dis ibu ion was also ound o be
a good app oxima ion o he σ alues ac oss BSs. As o
he dis ibu ions o γand β, he di e en pa ame e s o he
dis ibu ions o σin Rome-2021 s. Oslo-2020 highligh once
again he impac o speci ic en i onmen al cha ac e is ics in
he wo ci ies on signal p opaga ion and, hus, PL.
D. Cha ac e iza ion o Indoo and DI Addi ional Losses
We now p o ide u he insigh s on he addi ional losses
due o ou doo - o-indoo p opaga ion (i.e., end de ices wi hin
buildings). Fo his analysis, we le e age he 2020-2021 s a ic
measu emen s in 13 loca ions, 10 iden i iable as ypical indoo
scena ios and 3as DI (see §III-A). In pa icula , o all BSs
de ec ed a each loca ion, we a e age all he measu emen s and
p o ide a unique PL alue. Then, we e alua e Din-ou [dB] as
he di e ence be ween he a e age measu ed PL and he PL
es ima ed ia Rome-2021 a same dis ance, adop ing he mean
alues o he dis ibu ions o γand β.
Figu e 8 shows Din-ou o all BSs de ec ed a each loca ion.
Se e al in e es ing insigh s can be de i ed. Fo he indoo
case, i.e., Loca ions 1-9(2nd loo o he DIET Dep .) and
Loca ion 10 (6 h loo o a esiden ial building), many BSs
(o en he majo i y) ha e Din-ou >0, hus implying he
p esence o ou doo - o-indoo addi ional losses. The median
Din-ou is be ween 10 and 20 dB o Loca ions 6–9and educes
1 2 3 4 5 6 7 8 9 10 11 12 13
Loca ion
-40
-30
-20
-10
0
10
20
30
40
50
60
Din-ou [dB]
Fig. 8: Din-ou o each BS ( ep esen ed by do s) de ec ed a indoo
(Loca ions 1–10) and DI (Loca ions 11–13) loca ions.
0 0.2 0.4 0.6 0.8 1
Dis ance [km]
60
80
100
120
140
PL [dB]
De ec ed BSs
(one pe poin )
BSs a g ea e heigh
FS
Rome-2021
(Mean)
Fig. 9: PL measu ed o each BS (black ma ke s) in indoo and
DI loca ions, as a unc ion o he a e age dis ance be ween BSs and
loca ions. Fo a BS de ec ed a mul iple loca ions, he a e age PL
and a e age dis ance ac oss loca ions a e epo ed. The PL es ima ed
by Rome-2021 and FS a e epo ed o compa ison. Fo Rome-2021,
we conside ed he mean alues o he dis ibu ions o γand β.
o less han 2dB o Loca ion 10. The la e esul e lec s a
a he a ou able p opaga ion condi ion o Loca ion 10, wi h
ou ools placed a he 6 h loo acing a se o BSs on a
isible owe . As analyzed la e in he sec ion, Loca ions 1-5
and, a leas pa ially, Loca ions 6-9, also p esen a ou able
p opaga ion condi ions o some BSs, as highligh ed by he
occu ence o nega i e Din-ou alues.
Fo he DI case, i.e., Loca ion 11 (basemen a DIET Dep .),
Loca ion 12 (pa king lo o a comme cial s o e), and Loca ion
13 (pa king lo o a esiden ial building), we consis en ly
obse e posi i e Din-ou alues, wi h a median be ween 30 and
40 dB o he deeply enclosed spaces a Loca ions 11 and 12.
The median educes o a ound 15 dB o Loca ion 13, as a
esul o a mo e a ou able p opaga ion condi ion, wi h ou
ools placed in a pa king lo below he g ound loo bu wi h
openings in he ceiling s ill a ou ing signal p opaga ion.
A he indoo loca ions o DIET Dep ., we also obse e
a nega i e Din-ou o some BSs, wi h Din-ou <−10 dB
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8
o 2BSs ac oss Loca ions 1–5(ano he BS also shows
mos ly nega i e Din-ou alues a hese loca ions bu wi h la ge
a iabili y, i.e., Din-ou <−10 dB a Loca ions 1and 2and
Din-ou >−10 dB a Loca ions 3–5). The PL measu ed o
hese BSs is hus lowe han he one es ima ed by he Rome-
2021 model. We u he in es iga e his aspec in Fig. 9, whe e
we epo he a e age PL o each BS (black ma ke s) as a
unc ion o he a e age dis ance be ween BSs and loca ions
(i.e., o a BS de ec ed a se e al loca ions, Fig. 9 shows he
a e age PL and a e age dis ance ac oss loca ions).
In ag eemen wi h Fig. 8, Figu e 9 shows ha , due o
ou doo - o-indoo addi ional losses, he PL measu ed o he
majo i y o BSs is highe han he one es ima ed by Rome-
2021. Howe e , o 2BSs a a ound 300 and 700 me e s
om he DIET Dep ., he measu ed PL is signi ican ly lowe .
These a e he same BSs ha , in Fig. 8, ha e Din-ou <−10
dB a Loca ions 1–5. Fu he inspec ion o he posi ion o
hese BSs, also ia he online maps a www.l ei aly.i
(accessed in May 2024), showed ha hese a e placed in
a he peculia spo s, i.e., on he oo op o a qui e high
building and on he bell owe o a chu ch ( he bell owe
is 78-me e all, he highes in Rome), bo h isible om he
DIET Dep . and in clea LoS wi h Loca ions 1–5, as isually
ep esen ed in Fig. 10. This e iden ly a ou s he p opaga ion
owa ds he DIET Dep ., esul ing in a lowe PL compa ed o
he one es ima ed by Rome-2021, which is i ed on a la ge
se o BSs wi hou accoun ing o BS heigh . Al hough no
in alida ing ou model, his esul highligh s ha knowing he
BS heigh and embedding such in o ma ion in PL models
may u he imp o e PL es ima ion accu acy, pa icula ly o
BS placemen s signi ican ly de ia ing om expec ed nominal
cases. We hus plan o ge access o in o ma ion on he BS
heigh s and u he s udy his aspec in u u e wo k, owa ds
p o iding an addi ional assessmen on he ade o be ween
model simplici y and accu acy.
In summa y, compa ed o he alues in he li e a u e and
ound in [18] (see §II-B), he ou doo - o-indoo addi ional
losses measu ed in Rome a e easonably in alignmen o
he indoo loca ions, apa o speci ic BS/loca ion pai s, wi h
median alues in be ween 10 and 20 dB. Fo he DI case,
excluding he speci ic si ua ion o Loca ion 11, we obse e
median alues highe han 30 dB (used in li e a u e). Using
a ange o 30–40 dB seems o be a easonable choice o
accoun ing such addi ional losses.
V. MODEL GENERALIZATION VIA
MIXTURE DISTRIBUTIONS
In his sec ion, we le e age p e ious esul s and mo e a s ep
o wa d, aiming a p oposing and alida ing a me hodology o
combining PL models ob ained in di e en u ban scena ios
(e.g., di e en ci ies), hus making i possible o use a mo e
gene al model o he gene a ion o PL alues in lack o
si e-speci ic measu emen s and/o en i onmen al/deploymen
in o ma ion, e.g., o simula ion-based s udies.
A. Mo i a ion and P oposed App oach
Ou analyses and esul s in §IV demons a e ha he
s a is ical p ope ies o Oslo-2020 emain alid o Rome-
Fig. 10: Rela i e posi ions be ween Loca ions 1–9and he wo BSs
de ec ed wi h he lowes PL (Fig. 9). The igu e shows ha bo h
BSs a e in LoS wi h Loca ions 1–5(s aigh lines), while a building
pa ially obs uc s he LoS wi h Loca ions 6–9(dashed lines), which
explains he lowe PL measu ed a Loca ions 1–5(Fig. 8).
2021. In pa icula , ac oss mul iple BSs, γand βcan s ill
be modeled as Gaussian dis ibu ions, and σs ill ollows
a Weibull dis ibu ion. The momen s o such dis ibu ions,
howe e , change ac oss he wo ci ies due o si e-speci ic
en i onmen al/deploymen ac o s. The need o gene a ing PL
alues unde mo e gene al se ings, e.g., o simula ion-based
s udies wi h no si e-speci ic in o ma ion and equi emen s,
would hus pose he challenge o deciding which model o
use, i.e., Oslo-2020 o Rome-2021.
Mo i a ed by he abo e obse a ion, we p opose a me hod-
ology ha enables he de ini ion o a mo e gene al PL model
s a ing om ci y-speci ic models. In pa icula , we in es iga e
a scena io whe e hi d-pa y use s need o gene a e PL alues
o hei s udies (e.g., based on simula ions), bu do no ha e
access o ci y-speci ic measu emen s and da ase s, i.e., in ou
case, such use s ha e access o nei he PL measu ed alues
no gene al s a is ics (e.g., he numbe o BSs) o he 2020
measu emen s in Oslo and he 2020-2021 measu emen s in
Rome. The e o e, hey can only access o he de i ed Oslo-
2020 and Rome-2021 PL models, i.e., he alues o l0and he
dis ibu ions o γ,β, and σ.
Wi hin he abo e scena io, one solu ion would be o simply
selec one o he a ailable PL models, i.e., ei he Oslo-
2020 o Rome-2021. This would howe e lead o syn he ic
PL alues ha closely e lec he p opaga ion cha ac e is ics
encoun e ed in he ci y associa ed o he selec ed model du ing
he speci ic measu emen campaign. Aiming a a mo e gene al
cha ac e iza ion o PL, we ins ead p opose o exploi Oslo-
2020 and Rome-2021 as ini ial componen s om which a mo e
gene al model can be de ined. In pa icula , we le e age he
concep o MDs, i.e., p obabili y dis ibu ions exp essed as
collec ions (o en ini e) o componen dis ibu ions. Gi en n
p obabili y densi y unc ions p1(x), ..., pn(x)and co espond-
ing cumula i e dis ibu ion unc ions P1(x), ..., Pn(x), a MD
can be ep esen ed as (x) = Pn
i=1 wipi(x), and simila ly
o cumula i e unc ion F, whe e he weigh s w1, ..., wna e
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con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/JIOT.2025.3557172
© 2025 IEEE. All igh s ese ed, including igh s o ex and da a mining and aining o a i icial in elligence and simila echnologies. Pe sonal use is pe mi ed,
bu epublica ion/ edis ibu ion equi es IEEE pe mission. See h ps://www.ieee.o g/publica ions/ igh s/index.h ml o mo e in o ma ion.
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9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Mixing P opo ion o Rome-2021
0
0.1
0.2
0.3
0.4
KL Dis ance om Rome-2023
GMD
Oslo-2020
Rome-2021
(a)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Mixing P opo ion o Rome-2021
0
0.1
0.2
0.3
0.4
KL Dis ance om Rome-2023
GMD
Oslo-2020
Rome-2021
(b)
Fig. 11: KL di e gence be ween he dis ibu ions in he Rome-2023 model and he ones in Oslo-2020,Rome-2021, and in he GMD be ween
hese wo, o γ(a) and β(b) pa ame e s. Fo he GMD, esul s a e p esen ed as a unc ion o he mixing p opo ion used o Rome-2021.
de ined such ha wi≥0∀iand Piwi= 1. The indi idual
dis ibu ions a e o en e e ed o as mix u e componen s,
while he weigh s associa ed o each componen a e o en
e e ed o as mixing p opo ions. The mix u e componen s
a e o en no a bi a y p obabili y dis ibu ions, bu a e ins ead
membe s o a pa ame ic amily (e.g., Gaussian dis ibu ions),
wi h di e en alues o hei s a is ical pa ame e s (e.g.,
means and s anda d de ia ions) [28].
The abo e desc ip ion highligh s he po en ial o MDs o
display non- i ial highe -o de momen s such as skewness,
ku osis, and mul i-modali y, e en in he absence o such
ea u es wi hin he componen s hemsel es. In ou speci ic
con ex , we hus p opose o use Gaussian Mix u e Dis ibu-
ions (GMDs) o γand β, and a Weibull Mix u e Dis ibu ion
(WMD) o σ, hus le e aging he ac ha , when Oslo-2020
o Rome-2021 models a e aken sepa a ely, γand β ollow
Gaussian dis ibu ions and σ ollows a Weibull dis ibu ion
ac oss BSs, espec i ely. As ega ds l0, we ins ead p opose o
use he a e age o he Oslo-2020 and Rome-2021 alues.
B. E alua ion
We e alua e ou MD-based PL modeling app oach by
le e aging he new se o measu emen s collec ed in Rome
in 2023, desc ibed in §III. As a i s s ep, we build a new
PL model, e e ed in he ollowing o as Rome-2023, by
adop ing he same p ocedu e used o de i ing Rome-2021 in
he p e ious sec ions. We ix l0 o he a e age o he alues
ob ained o Oslo-2020 (32.44 dB) and Rome-2021 (36.37 dB)
and pe o m a CF o de i e he dis ibu ions o γ,β, and σ
ac oss he BSs de ec ed in 2023. By doing so, we once again
ob ain Gaussian dis ibu ions o γ, i.e., N(1.983,3.370), and
β, i.e., N(1.392,0.343), and a Weibull dis ibu ion o σ, i.e.,
Wbl(5.766,3.011).
We use his newly de i ed model as a benchma k, in o de
o unde s and how good Oslo-2020,Rome-2021, and he MD-
based app oach pe o m in es ima ing he alues measu ed
in 2023 and included in Rome-2023. Figu e 11 shows he
Kullback-Leible (KL) di e gence be ween he dis ibu ions
in he Rome-2023 model and he ones in Oslo-2020,Rome-
2021, and in he GMD be ween hese wo, o γ(a) and
β(b) pa ame e s. Fo he GMD, esul s a e p esen ed as a
unc ion o he mixing p opo ion used o Rome-2021 (by
de ini ion, he p opo ion o Oslo-2020 is he complemen o
1). As ega ds γ(Fig. 11a), we obse e ha Rome-2021 is
close o Rome-2023 han Oslo-2020, which can be somehow
expec ed conside ing ha Rome-2021 and Rome-2023 a e
ob ained h ough measu emen s in he same ci y. In be ween
hese wo models, ou GMD solu ion pe o ms close o Oslo-
2020 when he mixing p opo ion is highe o his model,
and app oaches Rome-2021 when he wo ini ial models a e
mixed equally (i.e., by using mixing p opo ions equal o 0.5).
As he mixing p opo ion o he Rome-2021 model inc eases
beyond 0.5, GMD pe o ms be e han bo h Oslo-2020 and
Rome-2021 sepa a ely, minimizing he KL di e gence when
he mixing p opo ion o Rome-2021 is be ween 0.6and
0.9; as expec ed, he pe o mance con e ges e en ually o
he one obse ed o Rome-2021 when he co esponding
mixing p opo ion eaches 1. Simila esul s a e ob ained o
β(Fig. 11b), al hough wi h a lowe a iabili y o he KL
di e gence be ween he wo ini ial models and, in u n, a lowe
gain achie able by he GMD app oach, which s ill sligh ly
dec eases he KL di e gence owa ds Rome-2023. Finally, o
σ, we again obse e a low a ia ion be ween he ini ial wo
models and he WMD ob ained by mixing hem, wi h he KL
di e gence owa ds Rome-2023 con ined o a na ow ange
be ween 0.22 and 0.24.
As a u he example, Figu e 12 shows a compa ison
be ween he dis ibu ions o he γ alues o all models
in ol ed in ou analysis ( o he GMD app oach, we show he
dis ibu ion ob ained wi h mixing p opo ions o 0.7and 0.3
o Rome-2021 and Oslo-2020, espec i ely). In he igu e, we
obse e ha he GMD model is close han he o he models
o Rome-2023, hus being able o be e ep esen he alues
measu ed in 2023 and included in he la e . We can u he
highligh ha he GMD dis ibu ion is, in his case, unimodal,
as a esul o he closeness o he wo ini ial models in e ms
o mean alues [44].
This a icle has been accep ed o publica ion in IEEE In e ne o Things Jou nal. This is he au ho 's e sion which has no been ully edi ed and
con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/JIOT.2025.3557172
© 2025 IEEE. All igh s ese ed, including igh s o ex and da a mining and aining o a i icial in elligence and simila echnologies. Pe sonal use is pe mi ed,
bu epublica ion/ edis ibu ion equi es IEEE pe mission. See h ps://www.ieee.o g/publica ions/ igh s/index.h ml o mo e in o ma ion.
Au ho ized licensed use limi ed o: Uni e si a degli S udi di Roma La Sapienza. Downloaded on Ap il 07,2025 a 08:04:12 UTC om IEEE Xplo e. Res ic ions apply.
