PhD Thesis
Con ibu ions o he E alua ion and
Imp o emen o LoRaWAN
by
Lluís Casals Ibáñez
Ad iso s: Ca les Gómez Mon eneg o and Ra ael Vidal Fe é
PhD P og am o Ne wo k Enginee ing
Ne wo k Enginee ing Depa men
Uni e si a Poli ècnica de Ca alunya
Cas ellde els, Ma ch 2023
i
Abs ac
Low Powe Wide A ea Ne wo k (LPWAN) echnologies ha e gained signi ican momen um as
wi eless solu ions o implemen ing In e ne o Things (IoT) solu ions. The unique se o LPWAN ea u es,
such as long ange, low powe consump ion, and low in as uc u e cos , along wi h challenging message
sizes and message a es, has a ac ed he a en ion o he indus y, academia and s anda d de elopmen
o ganiza ions. Wi hin he LPWAN amily, LoRaWAN has become a e y popula echnology. A e he
publica ion o he LoRaWAN speci ica ion and he a ailabili y o ce i ied ha dwa e, many esea che s
ha e de o ed hei e o s o in es iga e he pe o mance o his echnology. Since he IoT is expec ed o
include a e y la ge numbe o de ices (such as senso s and ac ua o s), and LoRaWAN is expec ed o
suppo up o hund eds o housands o IoT de ices pe adio ga eway, he ene gy e iciency, pe o mance
and scalabili y o LoRaWAN a e ho esea ch a eas.
This PhD hesis ocuses i s esea ch on a se o c ucial opics a ound he a o emen ioned a eas.
Many LoRaWAN de ices, such as senso s o ac ua o s, will ypically un on ba e y powe . The e o e, i
is c ucial o in es iga e he powe consump ion cha ac e is ics o LoRaWAN. Howe e , published wo ks
only ocus on his opic o a limi ed ex en , p o iding only ough es ima es o pa ame e s ela ed o
LoRaWAN ene gy pe o mance, wi hou conside ing he ealis ic beha io o he LoRaWAN de ice
ha dwa e, as well as he impac o he main LoRaWAN pa ame e s and mechanism se ings. The e o e, one
o he objec i es o his PhD hesis is o p opose an analy ical model ha cha ac e izes de ice cu en
consump ion, li e ime and ene gy cos o da a deli e y.
On he o he hand, he s udy o he beha io o con i med da a ansmission and he e olu ion o
he Sp eading Fac o (SF) pa ame e due o he ules de ined in he LoRaWAN speci ica ion in case o
e ansmissions is also in ou in e es . Th ough simula ions, we s udy he beha io o LoRaWAN unde
con olled condi ions, o di e en load condi ions o di e en ac i e LoRaWAN unc ionali ies (e.g.
con i med e sus uncon i med da a ansmission). S a ing wi h he FLoRa simula o , based on OMNeT++,
we imp o ed and comple ed his simula o o include he unimplemen ed unc ionali ies and co ec some
beha io s ha did no con o m o he LoRaWAN speci ica ion. In a p elimina y analysis, we ealize ha
SF ends o downg ade o SF12, co esponding o he lowes da a a e and he longes da a ansmission
ime, which leads o poo ne wo k pe o mance, al hough i could be, in some condi ions, mo e eliable.
We ha e called his phenomenon he "SF12 well". In his con ex , we ha e conside ed al e na i e
mechanisms o upda e he SF pa ame e in he case o da a e ansmissions, which allows o imp o e he
ansmission in he uplink channel.
As he hi d objec i e o he p esen PhD hesis, we ocus on he impac o he packe size on he
ene gy e iciency in LoRaWAN. Fu he mo e, o unde s and he obse ed beha io , we also conside he
impac o packe size on o he pe o mance pa ame e s. Exis ing s udies on LoRaWAN ene gy e iciency
e alua ion, including hose ha conside packe size as a pa ame e , p esen signi ican limi a ions. We also
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
ii
ca y ou ou s udy by means o he simula o we de eloped o add ess he abo e objec i e, wi h addi ional
modi ica ions o compu e ene gy consump ion in a mo e de ailed p ocess. In his wo k we also apply he
ealis ic ene gy model ob ained in he i s p oposed objec i e. As a complemen a y wo k, we also e alua e
he in luence o du y cycle cons ain s on he o e all pe o mance o LoRaWAN and speci ically on he
ene gy pe o mance.
Abs ac
iii
Resum
Les ecnologies de xa xa d'à ea ex ensa de baixa po ència (LPWAN) han guanya un impuls
signi ica iu com a solucions sense il pe implemen a aplicacions i se eis d'In e ne de les coses (IoT). El
conjun de ca ac e ís iques únic de LPWAN, com a a lla g abas , baix consum d'ene gia i baix cos de la
in aes uc u a, jun amen amb els desa inamen s que ep esen en la mida dels missa ges i les axes de
missa ges, ha acapa a l'a enció de la indús ia, el món acadèmic i les o gani zacions de desen olupamen
d’es ànda ds. Dins de la amília LPWAN, LoRaWAN s'ha con e i en una ecnologia mol popula . Amb
la publicació de l'especi icació LoRaWAN i la disponibili a de maquina i ce i ica , mol s in es igado s
han dedica els seus es o ços a es udia el endimen d'aques a ecnologia. A ès que es p e eu que la IoT
inclogui un nomb e mol ele a de disposi ius (com senso s i ac uado s), i que s'espe a que LoRaWAN
adme i ins a cen ena s de mile s de disposi ius IoT pe passa el·la àdio, l'e iciència ene gè ica, el
endimen i l'escalabili a de LoRaWAN són à ees d'in es igació canden s.
Aques a esi doc o al cen e les se es in es igacions en un conjun de emes c ucials al ol an
d’aques es à ees. Mol s disposi ius LoRaWAN, no malmen , uncionen en base a una ba e ia. Pe an , és
de i al impo ància in es iga les ca ac e ís iques del consum d'ene gia de LoRaWAN. Tanma eix, els
eballs publica s només an es udis limi a s, p opo cionan només es imacions ap oximades dels
pa àme es elaciona s amb el endimen ene gè ic, sense eni en comp e el compo amen ealis a del
maquina i dels disposi ius LoRaWAN, o l'impac e dels p incipals pa àme es de LoRaWAN i la
con igu ació del mecanisme. Pe an , un objec iu del p esen eball és p oposa un model analí ic que
ca ac e i zi el consum eal dels disposi ius, la se a ida ú il i el cos ene gè ic del lliu amen de dades.
D'al a banda, ambé abo dem l'es udi del compo amen de la ansmissió de dades amb
con i mació i l'e olució del pa àme e Sp eading Fac o (SF) segons les egles de inides a l'especi icació
LoRaWAN en cas de e ansmissió. Mi jançan simulacions, hem es udia el compo amen de LoRaWAN
en condicions con olades de cà ega o de uncionali a s ac i es de LoRaWAN (p. e., ansmissió de dades
con i mada e sus no con i mada). P enen com a base el simulado FLoRa, basa en OMNeT++, hem
millo a i comple a aques simulado pe inclou e les uncionali a s no implemen ades, i co egi alguns
compo amen s que no s'ajus a en a l'especi icació de LoRaWAN. L'anàlisi dels esul a s p elimina s ens
indica que SF endeix a can ia cap a SF12, que co espon a la eloci a de dades més baixa i al majo
emps de ansmissió de dades, la qual cosa compo a un baix endimen de la xa xa, enca a que pod ia se ,
en algunes condicions, més iable. A aques enomen l'hem anomena "pou SF12". En aques con ex , hem
conside a mecanismes al e na ius a l'ho a d’ac uali za el pa àme e SF en el cas de e ansmissions de
dades, que pe me millo a la ansmissió en el canal de l'enllaç ascenden .
El e ce objec iu d'aques a esi és es udia l'impac e de la mida del paque en l'e iciència ene gè ica
de LoRaWAN. A més a més, pe en end e el compo amen obse a , ambé conside em l'impac e de la
mida del paque en al es pa àme es de endimen . Els es udis exis en s sob e l'a aluació de l'e iciència
ene gè ica de LoRaWAN, inclosos els que conside en la mida del paque com a pa àme e, p esen en

Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
i
limi acions signi ica i es. El nos e es udi ambé el eali zem mi jançan el simulado que hem desen olupa
pe abo da l'objec iu an e io , amb modi icacions addicionals pe al de calcula el consum d'ene gia d'una
mane a més de alla . En aques eball ambé apliquem el model ene gè ic ealis a ob ingu en el p ime
objec iu plan eja , i a aluem la in luència de les es iccions del cicle de eball en el endimen gene al de
LoRaWAN i en el endimen ene gè ic, en pa icula .
Ag aïmen s / Acknowledgmen s
En p ime lloc, ull ag ai la guia i l'ajuda dels meus di ec o s de esi: Ca les Gómez i Ra ael Vidal.
Si mi o en e e i obse o o el camí que hem e , es ic segu que no hau ia a iba ins aquí sense la os a
expe esa, supo i, ambé, sense la os a lexibili a en els momen s que ha calgu compagina esi,
docència i amília. To plega ha es a un pe íode mol in ens i en iquido , que ha es a possible pe la os a
àlua com a p o essionals pe ò ambé com a pe sones. Mol since amen , GRÀCIES!
A o s els companys de depa amen , especialmen a la secció de Cas ellde els-Vilano a pe la se a
col·labo ació en els momen s que ha calgu , sob e o en l'úl ima e apa d'aques eball, en possible
compa ibili za la cà ega docen que enia a l'escola i la dedicació a la esi doc o al.
Al g up de ece ca WNG, on he desen olupa o a la eina d'in es igació elacionada amb aques a
esi i al es ac i i a s al lla g dels anys, g àcies pe pe me e'm col·labo a amb o s osal es, i pe dona -
me una e e ència pe con inua eballan , i e -ho en un ambien posi iu i cons uc iu.
I would like o hank he ex e nal expe s o e iewing his PhD hesis, as well as hei commen s
and sugges ions o imp o e i . In addi ion, I also hank he membe s o he PhD disse a ion commi ee o
hei a ailabili y and ime in e iewing and e alua ing his wo k.
Vull e una menció a o es les eines (o les més impo an s) que han e possible, o han acili a , que
pogués desen olupa o es les asques elacionades amb aques a esi: Linux, Py hon (amb Ma plo lib,
Pandas, Numpy), OMNeT++, Bash, awk, sed, C, e c. No se si aques es eines hau ien sigu capaces de e
aques a esi. Del que si que n'es ic segu és que sense elles, jo enca a es a ia comp an paque s de
LoRaWAN. G àcies a o es els seus desen olupado s que han e possible que ingués una eina més
senzilla.
També ull ag ai les mos es d'in e ès i ànims de o a la amília i o s els amics que han segui el
meu camí pe aques doc o a . Això de e una esi doc o al, o a del nos e àmbi p o essional o acadèmic,
semp e é una au a de mis e i. Malg a això, es d'ag aï l'es o ç pe acos a -se a l'ocupació que m'ha ingu
abso bi du an els da e s any.
Pe acaba , i mol especialmen , ull ag ai a la Ca me i la Laia el os e supo , paciència,
lexibili a i comp ensió. A es a un lla g camí (mol lla g si ambé comp em els in en s alli s) on "la esi"
ens ha acompanya a o a eu com una male a plena de eina ex a. Espe o que el inal i el esul a us hagi
complagu ambé a osal es. MOLTES GRÀCIES pe se -hi.
ii
Con en s
Lis o Figu es ......................................................................................................................... ix
Lis o Tables ........................................................................................................................ xiii
Glossa y ................................................................................................................................ x
1. In oduc ion ....................................................................................................................... 1
1.1. Mo i a ion ......................................................................................................................................... 1
1.2. Objec i es ........................................................................................................................................ 1
1.3. Resul s and con ibu ions ................................................................................................................. 2
1.4. O ganiza ion o his PhD hesis ........................................................................................................ 3
2. LoRaWAN o e iew ............................................................................................................ 5
2.1. LoRaWAN gene al ea u es ............................................................................................................. 5
2.2. LoRaWAN physical laye ................................................................................................................. 6
2.2.1. Recei e window pa ame e s ................................................................................................. 8
2.3. LoRaWAN MAC laye ...................................................................................................................... 9
3. Modeling he ene gy pe o mance o LoRaWAN ............................................................... 11
3.1. Rela ed wo k .................................................................................................................................. 11
3.2. Modeling LoRaWAN ED cu en consump ion ............................................................................... 14
3.2.1. Unacknowledged ansmission ............................................................................................ 14
3.2.2. Acknowledged ansmission ................................................................................................ 20
3.3. E alua ion ...................................................................................................................................... 24
3.3.1. ED cu en consump ion in unacknowledged ansmission ................................................. 25
3.3.2. ED cu en consump ion in acknowledged ansmission ..................................................... 26
3.3.3. ED li e ime ........................................................................................................................... 29
3.3.4. Ene gy cos o da a deli e y ................................................................................................ 30
4. The SF12 Well in LoRaWAN: p oblem and ED solu ions ..................................................... 39
4.1. Rela ed wo k .................................................................................................................................. 39
4.2. The p oblem ................................................................................................................................... 41
4.2.1. Simula o de ails .................................................................................................................. 42
4.2.2. Simula ed scena ios ............................................................................................................ 42

x
x
Glossa y
ACK_TIMEOUT Acknowledgmen Timeou
AFLoRa Ad anced F amewo k o LoRa
ADR Adap i e Da a Ra e
BER Bi E o Ra e
BLE Blue oo h Low Ene gy
CAD Channel Ac i i y De ec ion
CED Con i med mode ED
CR Coding Ra e
CRC Cyclic Redundancy Check
CSS chi p sp ead spec um
DR Da a Ra e
ETSI Eu opean Telecommunica ions S anda ds Ins i u e
ED End-de ice
EDL End-De ice Load
EPB Ene gy consump ion Pe deli e ed da a Bi
EU Eu opean Union
FHDR F ame Heade
FLoRa F amewo k o LoRa
FPo F ame Po
FRM Payload F ame Payload
GFSK Gaussian F equency Shi Keying
IoT In e ne o Things
IP In e ne P o ocol
ISM Indus ial Scien i ic Medical
LoRa Long Range
LoRaWAN Long Range Wide A ea Ne wo k
LPWAN Low Powe Wide A ea Ne wo k
MAC Medium Access Con ol
MAX_RETR Maximum numbe o message e ansmissions by an ED
MHDR MAC Heade
MIC Message In eg i y Code
OTAA On-The-Ai Ac i a ion
PDR Packe Deli e y Ra io
PHDR Physical Heade
PHDR_CRC Physical Heade Cyclic Redundancy Check
PHY Physical
QoS Quali y o Se ice
RECEIVE_DELAY1 Delay om end o uplink ansmission o s a o 1s ecei e window
RECEIVE_DELAY2 Delay om end o uplink ansmission o s a o 2nd ecei e window
RF Radio F equency
RX1 Recei e Window 1
RX1DRO se O se o DR in he i s ecei e window, RX1
RX2 Recei e Window 2
SF Sp eading Fac o
SINR Signal o In e e ence and Noise Ra io
SPI Se ial Pe iphe al In e ace
ToA Time-on-Ai
TP Time be ween Packe s
UED Uncon i med mode ED
WFT Well Fall Time
1. In oduc ion
This chap e p o ides he mo i a ion, he con ibu ions and he o ganiza ion o his PhD hesis. We
s a wi h he mo i a ion o his wo k in Sec ion 1.1. We ollow wi h he desc ip ion o he main
con ibu ions om his PhD hesis in Sec ion 1.2. Finally, we de ail he chap e s o his PhD hesis documen
in Sec ion 1.3.
1.1. Mo i a ion
Low Powe Wide A ea Ne wo k (LPWAN) echnologies ha e gained signi ican momen um as
wi eless solu ions o enabling In e ne o Things (IoT) applica ions [1,2]. The unique se o LPWAN
ea u es, such as long ange, low ene gy consump ion and low in as uc u e cos , along wi h challenging
message sizes and message a es, has a ac ed he a en ion o he indus y, academia and s anda d
de elopmen o ganiza ions [2,3].
Wi hin he LPWAN amily, LoRaWAN has become a e y popula echnology [4,5]. A e he
publica ion o he LoRaWAN speci ica ion [6] and he a ailabili y o ce i ied ha dwa e [7], many
esea che s ha e de o ed hei e o s o in es iga e he pe o mance o his echnology.
Since he IoT is en isaged o in ol e a massi e numbe o de ices (such as senso s and ac ua o s),
and LoRaWAN is expec ed o suppo up o hund eds o housands o IoT de ices pe adio ga eway, ene gy
e iciency, pe o mance and scalabili y o LoRaWAN is a ho esea ch a ea [4,5,8–27]. This PhD hesis
ca ies ou esea ch in a se o c ucial opics. We nex o e iew he main esea ch objec i es o his PhD
hesis.
1.2. Objec i es
Many LoRaWAN de ices, such as senso s o ac ua o s, will ypically be ba e y-ope a ed.
The e o e, i is c ucial o in es iga e he cha ac e is ics o LoRaWAN ene gy consump ion. Howe e ,
published wo ks only ocus on his opic o a limi ed ex en , p o iding only ough es ima es on pa ame e s
ela ed wi h LoRaWAN ene gy pe o mance, while no conside ing he ealis ic beha io o LoRaWAN
de ice ha dwa e, as well as he impac o he main LoRaWAN pa ame e s and mechanism se ings
[14,23,26,27]. This will be one objec i e o he p esen wo k: o p opose an analy ical model ha
cha ac e izes de ice cu en consump ion, li e ime and ene gy cos o da a deli e y.
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
2
On he o he hand, he s udy o he beha io o con i med da a ansmission and he e olu ion o
he Sp eading Fac o (SF) pa ame e due o he ules de ined in he LoRaWAN speci ica ion in case o
e ansmissions is also in ou in e es . As we will de ail in Chap e 4, i is ad an ageous o use some kind
o simula o o s udy his beha io o LoRaWAN in con olled condi ions, in o de o se known ini ial
pa ame e s ha enable o compa e he same sys em unde di e en load condi ions o di e en LoRaWAN
ac i e unc ionali ies (e.g., con i med s uncon i med da a ansmission). We ound a se o simula o s used
in LoRaWAN e alua ion s udies, which howe e a e e y ocused on a pa ial model o LoRaWAN.
The e o e, ou choice has been o build a new simula o , by ex ending he unc ionali y o an exis ing one,
FLoRa [28], based on OMNeT++. FLoRa implemen s he mos basic unc ionali y o physical and Medium
Access Con ol (MAC) le els o LoRaWAN, and is only able o simula e ansmission in he uplink channel
and a limi ed ansmission in he downlink channel. In a p elimina y analysis, we ealize ha SF ends o
downg ade o SF12, co esponding o he lowes da a a e and g ea es da a ansmission ime, ha leads o
a low pe o mance o he ne wo k, al hough i could be, in some condi ions mo e eliable. In his con ex ,
we ha e conside ed al e na i e mechanisms o upda e he SF pa ame e , which allows o imp o e he
ansmission in he uplink channel.
As a hi d objec i e o ou PhD, we ocus on he impac o packe size on he ene gy e iciency in
LoRaWAN. Howe e , o unde s and he obse ed beha io , we also conside he impac o packe size on
se e al o he pe o mance pa ame e s. Exis ing s udies on e alua ing he ene gy e iciency o LoRaWAN,
including hose ha conside packe size as a pa ame e , p esen signi ican limi a ions. We ca y ou his
s udy by means o he simula o we de eloped o he second objec i e, wi h addi ional upda es in o de o
compu e he ene gy consump ion in a mo e de ailed p ocess. In his wo k we also apply he ealis ic ene gy
model ob ained in he i s objec i e o he PhD hesis esea ch.
As a complemen a y wo k, we e alua e he in luence o he du y cycle es ic ions on he gene al
pe o mance o LoRaWAN and, speci ically, on he ene gy pe o mance.
1.3. Resul s and con ibu ions
The main con ibu ions o his PhD hesis a e he ollowing:
A) De eloping an ene gy model o LoRaWAN ne wo ks.
B) Cha ac e izing he SF12 Well p oblem in a LoRaWAN ne wo k, and p oposing (and
e alua ing) a numbe o solu ions.
C) S udying he packe ansmission ene gy e iciency in LoRaWAN and de e mining he
op imal packe size in se e al condi ions.
D) De e mining he in luence o he du y cycle es ic ion on he ene gy pe o mance and in
he communica ion pe o mance in LoRaWAN ne wo ks.
E) Imp o ing a ne wo k simula o o LoRaWAN including acknowledged ansmission
mode, and se e al SF managemen me hods.
1. In oduc ion
3
1.4. O ganiza ion o his PhD hesis
The emainde o he documen is o ganized as ollows. Chap e 2 o e iews LoRaWAN,
desc ibing i s gene al a chi ec u e and ocusing on i s physical and MAC laye de ails. In Chap e 3, we
p esen a model o he ene gy pe o mance o LoRaWAN. Chap e 4 desc ibes and discusses he causes
o he SF12 Well p oblem, and p oposes solu ions o his phenomenon. Chap e 5 is ocused on he s udy
o packe size ene gy e iciency-op imiza ion, conside ing a wide se o ne wo k condi ions. In Chap e 6,
we p esen he conclusions and u u e wo ks om his PhD hesis.

2. LoRaWAN o e iew
In his chap e , we p esen undamen al LoRaWAN cha ac e is ics. We desc ibe he p o ocol
a chi ec u e as well as he physical and MAC laye s, highligh ing he mechanisms, p ocedu es and key
pa ame e s ha a e ele an in he scope o his PhD hesis. This chap e is o ganized in h ee sec ions. The
i s one p o ides a gene al LoRaWAN o e iew, whe eas he emaining wo sec ions ocus on LoRaWAN
physical and link laye unc ionali y, espec i ely.
2.1. LoRaWAN gene al ea u es
LoRaWAN is a wi eless communica ion echnology ha o e s long ange (o en in he o de o
kilome e s) [5] while suppo ing low ene gy consump ion (e.g., allowing mul iyea li e ime o ba e y-
ope a ed de ices) [29]. As in o he LPWAN echnologies, long ange is achie ed a he expense o educed
communica ion capaci y. Howe e , his ea u e does no pose a p oblem o many IoT use cases.
The LoRaWAN ne wo k a chi ec u e comp ises h ee main ypes o ne wo k en i ies:
end-de ices (EDs), ga eways, and a ne wo k se e (NS) (see Figu e 1a). These elemen s a e o ganized in
a opology known as s a o s a s [30]. The EDs ypically co espond o cons ained de ices such as senso s.
The EDs ansmi LoRaWAN messages o he NS as hei des ina ion endpoin h ough one o mo e
ga eways. This ype o message ansmission is known as uplink ansmission. In he downlink, he NS may
ansmi LoRaWAN messages o he EDs h ough only one ga eway. Communica ion be ween he EDs and
he ga eways is ca ied ou by means o a physical laye called LoRa. The ga eways and he NS a e
connec ed by means o an IP-based ne wo k, while he ga eways o wa d LoRaWAN messages be ween
he EDs and he NS (see Figu e 1b) [29]. The NS cen alizes da a collec ion, which allows a sepa a e
applica ion en i y (e.g., an applica ion se e ) o access he NS da a.
LoRaWAN de ines h ee classes in e ms o suppo ed ea u es and unc ionali y: class A, class B,
and class C. Class A, which is also e e ed o as basic LoRaWAN, is manda o y o all LoRaWAN de ices.
In his class, and o he sake o ene gy sa ing, downlink ansmission is only allowed in ime in e als
called ecei e windows, which a e subsequen o an uplink ansmission. Class B is de ined on he basis o
class A, o e ing addi ional downlink ansmission oppo uni ies a imes which may be scheduled a p io i.
In con as wi h class A and class B, class C o e s no cons ain s o downlink ansmission. Howe e , he
class C EDs canno u n o hei adio in e ace and a e no sui able o de ices wi h a cons ained ene gy
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
6
sou ce. Mos LoRaWAN de ices implemen only class A ea u es, as he o he classes a e op ional. In his
PhD hesis we assume ha class A is used in all he conside ed LoRaWAN scena ios.
(a)
(b)
Figu e 1. LoRaWAN sys em. (a) Gene al a chi ec u e. (b) P o ocol s ack o each ne wo k elemen .
The nex wo subsec ions o e iew he main ea u es o he class A LoRaWAN physical laye and
he MAC laye , espec i ely.
2.2. LoRaWAN physical laye
LoRaWAN suppo s wo ypes o modula ions o physical ansmission be ween an ED and a
ga eway: he LoRa modula ion and he Gaussian F equency Shi Keying (GFSK). The o me is he mos
equen ly used modula ion in many scena ios. LoRa is based on a chi p sp ead spec um (CSS) [31]. The
du a ion o a LoRa symbol depends on he SF in use, as a LoRa symbol comp ises 2SF chips [5]. Six SFs
PHY LoRa PHY LoRa
End-De ice
(ED)
Ga eway Ne wo k se e
(NS)
PHY PHY
LoRaWAN
Cus ome
applica ion
LoRa o FSK
Modula ion
E he ne ,
Wi-Fi, 4G,
e c.
MAC MAC
Enc yp ed
Enc yp ed
Backhaul
IP S ack
Backhaul
IP S ack
Cus ome
applica ion
LoRaWAN
Message o wa ding
2. LoRaWAN o e iew
7
( anging om se en o wel e) a e de ined, leading o six di e en co esponding Da a Ra es (DRs) (see
Table 1). The SFs a e o hogonal, which con ibu es o spec al e iciency. LoRa modems also use o wa d
e o co ec ion, adding a small o e head o he ansmi ed message, which p o ides eco e y ea u es
agains bi co up ion. This is implemen ed h ough di e en Coding Ra es (CRs), om 4/5 o 4/8 (deno ed
CR = 1 o CR = 4, espec i ely). On he o he hand, o a oid issues ega ding d i o he c ys al e e ence
oscilla o , a low DR op imiza ion mechanism is applied, which adds a small o e head, o inc ease
obus ness o equency a ia ion o e he imescale o he LoRa message [31]. This is done o SF = 11
and SF = 12.
LoRaWAN has been de ined o suppo ope a ion in se e al wo ld egions. In his PhD hesis, we
conside he LoRaWAN physical laye cha ac e is ics speci ied o he Eu opean Union (EU), including
he use o he 868 MHz band, whe e h ee de aul adio channels a e de ined: 868.10 MHz, 868.30 MHz,
and 868.50 MHz. These channels a e cha ac e ized by a bandwid h o 125 kHz, use he LoRa modula ion,
and o e se e al DRs, om DR0 o DR5, which co espond o 0.3 kbps o 5 kbps, espec i ely (see
Table 1). DR6 and DR7 a e op ional ( he la e is he only one based on he GFSK modula ion). In o de o
p o ide obus ness o he communica ion, equency channel hopping is used o e he se o adio equency
(RF) channels con igu ed in EDs.
Table 1. DRs, SFs, and physical laye bi a es o he EU 868 MHz band channels.
DR
Modula ion
SF
Bandwid h (kHz)
Physical Bi Ra e (bi /s)
0
LoRa
SF12
125
250
1
LoRa
SF11
125
440
2
LoRa
SF10
125
980
3
LoRa
SF9
125
1760
4
LoRa
SF8
125
3125
5
LoRa
SF7
125
5470
6
LoRa
SF7
250
11,000
7
GFSK
50,000
ETSI egula ions es ablish spec um access es ic ions on he du y cycle, including a du y cycle
limi a ion o less han 1% o he band be ween 868.0 MHz and 868.6 MHz. LoRaWAN complies wi h he
men ioned du y cycle es ic ion by in oducing an idle in e al o sui able du a ion a e he ansmission
o a message.
In class A, message exchanges be ween an ED and he NS a e ini ia ed by he o me . As we
men ioned ea lie , he NS is allowed o ansmi only in one o wo a ailable ecei e ime windows, called
RX1 and RX2 (see Figu e 2), which a e a ailable a e a message ansmission by he ED. The e o e, i he
NS has o ansmi a new downlink message, such a ansmission will wai un il he nex ecei e window is open.
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
14
Table 4. Main cu en consump ion de ails on LoRa/LoRaWAN anscei e s used by de ices in Table 3.
3.2. Modeling LoRaWAN ED cu en consump ion
In his sec ion, we p esen models o c ucial LoRaWAN ene gy pe o mance pa ame e s such as
ED cu en consump ion, ED li e ime, and ene gy e iciency o da a deli e y. We assume a class A ED ha
pe iodically ansmi s an uplink da a message (e.g., a no i ica ion ha ca ies a senso eading). In he
models, we conside he impac o bi e o s. Fo he sake o ac abili y and cla i y, we assume a uni o m
BER ha e e s o he esidual BER a e applica ion o physical laye e o co ec ing echniques,
equi alen o he esidual BER ha co esponds o message loss a e due o non-ideal link quali y. The
sec ion is di ided in wo subsec ions, which o e he a o emen ioned models o unacknowledged and
acknowledged ansmission, i.e., he ansmission o uncon i med and con i med da a messages,
espec i ely. We de elop he models o all DRs ha a e manda o y (i.e., om DR0 o DR5), as well as o
DR6.
3.2.1. Unacknowledged ansmission
Ou i s goal is modeling he a e age cu en consump ion o an ED in he unacknowledged
app oach, deno ed Ia g_unACK. In o de o de e mine his pa ame e , we i s de i e a p o ile o he di e en
s a es a e sed by he ED, as well as he du a ion and he cu en consumed in each s a e. In o de o
ealis ically model he ED beha io , and wi hou loss o gene ali y, we de elop he model based on
measu emen s om a eal LoRaWAN es bed. We use he Mul iConnec mDo pla o m om Mul i ech
[42] as ou e e ence ED pla o m o he model, since i is a popula pla o m, and i is based on he also
widely used SX1272 anscei e [46] (see Table 3). While o he LoRaWAN ED pla o ms migh exhibi
di e ences wi h he mDo pla o m (e.g., due o hei in e nal a chi ec u e), we unde s and ha ou model
cap u es he main s a es o a LoRaWAN ED. On he o he hand, i mus be no ed ha he mDo pla o m
o e s low cu en consump ion dec ease (o ~3%, and only in he ansmi s a e) when he ol age applied
is educed om 5 V o 3.3 V, he la e being he lowes ol age ha allows he de ice o ope a e [42].
Howe e , o he pla o ms may no o e he same cu en consump ion s abili y as ba e y ol age dec eases
o e ime.
T anscei e
Cu en Consump ion
Sleep
T ansmi
Recei e
Sem ech SX1272 [46]
0.1 µA (max. 1 µA)
Min.: 18 mA (7 dBm)
Max.: 125 mA (20 dBm)
10.5 o 11.2 mA
Sem ech SX1276 [47]
0.2 µA (max. 1 µA)
Min.: 20 mA (7 dBm)
Max.: 120 mA (20 dBm)
10.8, 11.5 o 12.0 mA
HopeRF HM-TRLR-
LF/HFS [48]
2 µA
(min. 1.2 µA, max. 3 µA)
Min.: 35 mA (13 dBm)
Max.: 120 mA (20 dBm)
16 mA
(min. 15 mA,
max. 18 mA)
Mic ochip RN2483
[35,36]
Up o 100-150 µA
Min.: 17.3 mA (−4.0 dBm)
Max.: 38.9 mA (14.1 dBm)
14.2 mA

3. Modeling he ene gy pe o mance o LoRaWAN
15
In he measu emen s, he ansmi powe o he ED is se o 11 dBm, which is he de aul alue o
his pa ame e . The ga eway is a Ke link LoRa IoT S a ion pla o m [49]. Bo h he ED and he ga eway a e
loca ed in an indoo scena io, whe e he dis ance be ween he ED and he ga eway is 2 m. In he
measu emen s, da a messages ca y a ame payload o he maximum size allowed o each DR in he EU
band.
Figu e 5. Expe imen al se up o cu en measu emen s o he Mul iConnec mDo LoRaWAN ED
module (on he le ) using an Agilen N6705A powe analyze .
We assume a pe iodic beha io o he ED, he e o e we model i s cu en consump ion du ing one
pe iod. Each pe iod comp ises a da a message ansmission by he ED (including he ela ed p ocedu es
equi ed o enable such ansmission), o he wise he de ice is in sleep mode. No e ha , o an ED in
unacknowledged ansmission, cu en consump ion is independen o he BER; ha is, ega dless o
whe he channel e o s ake place in he communica ion, he ED will consume he same amoun o ene gy
o any ansmission, since he e will no be e ansmissions in unacknowledged ansmission. Time and
cu en consump ion measu emen esul s p o ided in his sec ion a e ob ained om se e al measu emen s
o each es ed con igu a ion wi hin a no i ica ion pe iod. We ound negligible di e ences wi hin each se
o measu emen s o each con igu a ion.
Figu e 6 illus a es he cu en consump ion p o ile o an unacknowledged ansmission pe o med by
he Mul iConnec mDo ED con igu ed o use DR0 (no e ha he s a es a e sed and beha io obse ed a e he
same o all DRs, excep o he du a ion o some in e als). Table 5 de ines and desc ibes he di e en s a es
in ol ed in an unacknowledged ansmission, along wi h he a iables ha ep esen he du a ion and cu en
consump ion o each s a e. Ini ially, he ED is in sleep mode, which is cha ac e ized by a cu en consump ion
h ee o de s o magni ude below ha o he es o s a es. When he ED s a s he p ocedu e o pe o m he
ansmission, i i s wakes up (s a e 1), nex he adio in e ace is p epa ed o ac i i y (s a e 2), and hen he ED
ansmi s he da a uni ia he adio in e ace (s a e 3). A e he ansmission, he ED disables adio ac i i y and
wai s (s a e 4) un il i se s he adio in o ecei e mode and emains in he same s a e o he du a ion o he i s
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
16
ecei e window (s a e 5). Since no incoming p eamble is de ec ed, he i s ecei e window is closed, and he
ED wai s (s a e 6) un il he s a o he second ecei e window. Du ing he la e , he ED adio is u ned on o
possible incoming da a uni s, un il he second ecei e window is closed due o absence o incoming da a
(s a e 7). No e ha he sho e du a ion o he second ecei e window is due o use o he CAD mechanism (see
Sec ion 2.2.1), whe eby he ED s ops p eamble de ec ion much ea lie han in he i s ecei e window i no
incoming signal is de ec ed. A e ha , he adio in e ace is u ned o (s a e 8), a pos p ocessing in e al ollows
(s a e 9), and he ED execu es a u n o sequence (s a e 10), p io o e u ning o he sleep s a e (s a e 11). One
addi ional conside a ion is ha we ha e no iden i ied any speci ic s a e due o he in e nal communica ion, which
akes place ia Se ial Pe iphe al In e ace (SPI), be ween he main mic ocon olle and he adio in e ace o he
mDo pla o m. This is consis en wi h he submillisecond la ency o payload ansmission om he
mic ocon olle o he adio in e ace, o he ange o payload sizes in LoRaWAN, ha is ypical o SPI.
Figu e 6. Cu en consump ion p o ile o a Mul iConnec mDo LoRaWAN ED pe o ming an
unacknowledged ansmission wi h DR0. The da a message ansmi ed has a FRM Payload size
o 51 by es (i.e., maximum possible size o DR0).
Table 5. S a es, a iables and hei alues o LoRaWAN unacknowledged ansmission.
S a e
Numbe
Desc ip ion
Du a ion
Cu en Consump ion
Va iable
Value (ms)
Va iable
Value (mA)
1
wake up
Twu
168.2
Iwu
22.1
2
adio p epa a ion
Tp e
83.8
Ip e
13.3
3
T ansmission
T x
(see Table 6)
I x
83.0
4
wai 1s window
Tw1w
983.3
Iw1w
27.0
5
1s ecei e window
T x1w
(see Table 6)
I1w
38.1
6
wai 2nd window
Tw2w
Equa ion (4)
Iw2w
27.1
7
2nd ecei e window
T x2w
33.0
I2w
35.0
8
adio o
To
147.4
Io
13.2
9
Pos p ocessing
Tpos
268.0
Ipos
21.0
10
u n o sequence
Tseq
38.6
Iseq
13.3
11
Sleep
Tsleep
Equa ion (2)
Isleep
45 ×!10−3
3. Modeling he ene gy pe o mance o LoRaWAN
17
Le TNo i be he ime be ween wo consecu i e pe iodic message ansmissions pe o med by he
ED, i.e., he no i ica ion pe iod. Le Ti and Ii deno e he du a ion and cu en consump ion o s a e i in Table
5. Ia g_unACK can hus be calcula ed as shown in Equa ion (1):
𝐼!"#_%&'() =# 1
𝑇*+,-.
&
𝑇-·
*!"#"$!
-/0 𝐼-
#
(1)
whe e Ns a es is 11 in unacknowledged ansmission. No e ha Tsleep can be ob ained as:
𝑇12334 =𝑇*+,-. −𝑇!5,
#
(2)
whe e Tac deno es he sum o he du a ions o all s a es ela ed wi h ansmission ac i i ies, i.e., all s a es
excep he sleep in e al:
𝑇!5, =𝑇6% +𝑇473 +𝑇,8 +𝑇606 +𝑇7806 +𝑇696 +𝑇7896 +𝑇+.. +𝑇4+1, +𝑇13:
#
(3)
The du a ions T x, T x1w, and Tw2w a e a iable and depend on he DR in use. Tw2w ac ually depends on
T x1w, and can be ob ained as:
𝑇696 =𝑅𝐸𝐶𝐸𝐼𝑉𝐸_𝐷𝐸𝐿𝐴𝑌_2−𝑅𝐸𝐶𝐸𝐼𝑉𝐸_𝐷𝐸𝐿𝐴𝑌_1−𝑇7806
#
(4)
Al hough T x2w also depends on he DR, he ED pla o m in ou expe imen s uses a ixed se ing o
he second ecei e window (which co esponds o DR0), and hus he measu ed alue o T x2w is also
cons an . We nex p o ide he models o de i e T x, T x1w and T x2w.
In o de o de e mine he ime needed o ansmi a da a message ia he adio in e ace, T x, we ake
in o acoun LoRaWAN p ocedu es, LoRa modula ion de ails and he co esponding egional pa ame e s.
T x can be exp essed in e ms o he ime equi ed o ansmi bo h he p eamble and he physical message,
deno ed Tp eamble and TPHYMessage, espec i ely, as ollows [31]:
𝑇,8;=#𝑇473!<=23;+𝑇>?@A311!#3
#
(5)
Tp eamble can be ob ained as shown nex [46]:
𝑇473!<=23 =𝑇1B< ·(𝑁473 +4.25)
#
(6)
whe e Np e is he p og ammed numbe o symbols o be used by he adio anscei e , he ac ual physical
leng h o he p eamble is (Np e + 4.25) [5], and Tsym is he ime o a symbol (in seconds), which depends on
he SF and he channel bandwid h (BW, in Hz), as ollows [31]:
𝑇𝑠𝑦𝑚 =2𝑆𝐹
𝐵𝑊
##
(7)
On he o he hand,
𝑇!"#$%&&'(%
(in seconds) can be e alua ed simila ly:
𝑇>?@A311!#3 =𝑇1B< ∗𝑁>?@
#
(8)
whe e
𝑁!"#
indica es he numbe o symbols ansmi ed as he physical message (excluding he p eamble),
and i can be de e mined as ollows [31]:
𝑁>?@ =8+𝑚𝑎𝑥?𝑐𝑒𝑖𝑙?9IJI·>LJ0M·(N(OP·QR
P·(QRO9·TU)D·(𝐶𝑅+4),0D
##
(9)
In (9), SF co esponds o he sp eading ac o and can ake alues om 7 o 12 (which co espond
o da a a es om DR5 o DR0, espec i ely); CR deno es he coding a e and can ake alues om 1 o 4,
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
18
o 4/5 o 4/8 coding a e, espec i ely; PL indica es he physical payload leng h, in by es. CRC indica es
he p esence o no o he CRC ield in he physical message (CRC is se o 0 i he CRC ield is no p esen ;
o he wise, CRC is equal o 1); inally, DE, which indica es whe he he mechanism o a oid issues ega ding
d i o he c ys al e e ence oscilla o is used o no , akes alue 1 o SF12 and SF11 (i.e., i is used o
he lowes da a a es), and alue 0 o he es o SFs. Equa ions (5)–(9) can be used o model he du a ion
o bo h uplink and downlink ansmissions (e.g., he la e may co espond o ACKs sen in esponse o
uplink da a messages, see Table 6).
Table 6. Summa y o alues o T x, T x1w and T x2w, along wi h ele an pa ame e se ings. We ha e assumed an
8-symbol p eamble leng h, a CR o 4/5 (excep o he 20-bi physical heade , o which a CR o 4/8 is
used), and a bandwid h o 125 kHz (excep o DR6, wi h a bandwid h o 250 kHz, and o DR7, which is
based on FSK). T x max is ob ained by conside ing he maximum ame payload (FRM Payload) size o
each DR, while T x min co esponds o he ime o ansmi a da a message ha ca ies no da a (e.g., an
ACK). In he la e case, he physical ame leng h is he con ibu ion o he physical heade (PHDR) and
PHDR_CRC ields, he MAC Heade (MHDR), he FHDR and he MIC ields (see Sec ion 2.2 and Sec ion
2.3), leading o a o al leng h o 14.5 by es plus 8 p eamble symbols. No e ha he CRC is only p esen in
uplink ansmissions (see Sec ion 2.2). Fo DR7, an addi ional ma gin should be added o he T x1w and
T x2w alues o accoun o possible d i s o he oscilla o used o he ime ha con ols a ecei e window
s a .
DR
SF
Tsym
Tp eamble
T x1w
T x2w
DE
FRM Payload
T x Max
T x Min
Max
Min
Uplink
Downlink
(ms)
(ms)
(ms)
(ms)
(by es)
(by es)
(ms)
(ms)
0
12
32.77
401.41
262.14
33.02
1
51
0
2793.5
991.8
1
11
16.38
200.70
131.07
16.64
1
51
0
1560.6
577.5
2
10
8.19
100.35
98.30
8.45
0
51
0
698.4
288.7
3
9
4.10
50.18
49.15
4.35
0
115
0
676.9
144.4
4
8
2.05
25.09
24.58
2.30
0
242
0
707.1
72.2
5
7
1.02
12.54
12.29
1.28
0
242
0
399.6
41.2
6
7
0.51
6.27
6.14
0.64
0
242
0
199.8
20.6
7
-
0.02
0.48
1.28
1.28
-
242
0
42.4
3.2
We nex model he beha io o he ha dwa e module used in ou expe imen s in each ecei e
window when no p eamble is de ec ed.
Fo he i s ecei e window, T x1w can be de e mined as ollows:
𝑇7806 =𝑁W1B< ·𝑇1B<
#
(10)
The ED s ays in ecei e mode o he du a ion o
𝑁)&*+
symbols.
𝑁)&*+
is 8 symbols o SF = 12
and SF = 11, and 12 symbols o he es o SFs.
Fo he second ecei e window, he ecei e is ac i e du ing a ac ion o a CAD s a e (see
Sec ion 2.2.1). This ac ion has a du a ion, deno ed T x2w, ha can be calcula ed as shown nex :
𝑇7896 =9'(JX9
YZ
#
#
(11)
3. Modeling he ene gy pe o mance o LoRaWAN
19
A e p o iding he models o de e mining T x, T x1w and T x2w, Table 6 summa izes hei main alues,
along wi h ele an pa ame e se ings used in ou ED pla o m. Fo T x2w, we include he co esponding
alues o he di e en DR se ings possible. Howe e , in ou expe imen s, only he T x2w alue
co esponding o DR0 was used.
Once all a iables equi ed o compu e Ia g_unACK a e de e mined, we can calcula e he heo e ical
li e ime o a ba e y-ope a ed ED ha pe o ms unacknowledged ansmissions, deno ed Tli e ime_unACK, on
he basis o he ba e y capaci y, Cba e y (exp essed in mA·h), as shown nex :
𝑇2-.3,-<3_%&'() =# 𝐶=!,,37B
𝐼!"#_%&'()
#
(12)
No e ha he abo e heo e ical ED li e ime calcula ion assumes an ideal ba e y wi h a linea
beha iou , whe eas he cha ac e is ics o a eal ba e y deg ade o e ime. The e o e, he calcula ed ED
li e ime esul s p o ided in his documen p o ide an uppe bound on he ac ual ED li e ime ha can be
expec ed.
Finally, ano he impo an pe o mance pa ame e is he ene gy cos o da a deli e y, ECdeli e y_unACK,
which p o ides he ene gy consumed by he ED pe each deli e ed bi o da a payload in unacknowledged
mode, as shown below:
𝐸𝐶)%,-.%/*_12345 =&𝐼'.(_12345 · 𝑉 · 𝑇267-8
𝐸*𝑙)%,-.%/*_12345,
(13)
whe e V deno es he ol age and E[ldeli e y_unACK] indica es he expec ed amoun o da a success ully
deli e ed by he ED pe da a ame ansmi ed. No e ha in he p e ious equa ion, he nume a o compu es
he ene gy consumed by he de ice du ing Tno i .
Le lpay be he FRM Payload ield size (i.e., he amoun o da a ca ied in he payload o he da a
message sen by he ED), and le lDa a be he o al size o he da a message, including all heade s. Le b
deno e he BER as in oduced in he i s pa ag aph o Sec ion 3.1. Since in unacknowledged ansmission
he e is a single ansmission a emp , which may su e bi e o s, E[ldeli e y_unACK] is de e mined as:
𝐸*𝑙)%,-.%/*_12345, =&𝑙!'* ·(1 − 𝑏),!"#"
(14)
Finally, le us assume ha collisions may occu , i.e., an ED message ansmission may o e lap wi h
messages ansmi ed by o he EDs connec ed o he same ga eway. Le pcoll be he p obabili y ha a da a
message ansmi ed by an ED collides wi h a leas ano he message ansmission. In o de o cap u e
impac o collisions on E[ldeli e y_unACK], Equa ion (14) can be ex ended as ollows:
𝐸G𝑙W32-"37B_%&'()H=#𝑙>!B ·(1−𝑏)2)#"# ·(1−𝑝5+22)
#
(15)
No e ha , as al eady in oduced, b co esponds o he esidual BER a e applica ion o physical
laye e o co ec ing echniques, equi alen o he esidual BER ha co esponds o message loss a e due
o non-ideal link quali y. In his documen , we assume ha CR = 4/5, since i is he de aul CR in
LoRaWAN, excep o he 20-bi physical heade , whe e CR = 4/8 is used. Fo CR = 4/5, a pa i y bi is
added o each g oup o 4 bi s om he physical laye message o be ansmi ed. Assuming ha an e o -
co ec ing code is used o CR = 4/8 (e.g., a Hamming code [50]) and he ange o BER alues o

Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
20
easonably use ul links, and gi en he sho size o he physical heade , we app oxima e he ela ionship
be ween b and he physical laye BER, deno ed bphy, as shown in he nex wo equa ions. Le ploss be he
p obabili y ha a ansmi ed message is a ec ed by a leas one bi e o , and he e o e he message is los ,
and le lphy_heade be he 20-bi heade size. The e o e:
𝑝2+11 =#1−(1−𝑏)2)#"# =1−K1−𝑏4[BL
P·]2)#"#O2*+,_+$#.$/^
#
(16)
(1−𝑏)2)#"# =K1−𝑏4[BL
P·]2)#"#O2*+,_+$#.$/^
#
(17)
3.2.2. Acknowledged ansmission
We nex model ED a e age cu en consump ion in he acknowledged ansmission app oach,
based on he co esponding cu en consump ion p o ile o he same ha dwa e pla o m as in he p e ious
subsec ion.
In his app oach, he ED may beha e in wo di e en ways, since he ACK may be ansmi ed in
he i s ecei e window o in he second one. In ou model, we conside bo h op ions. We ini ially assume
BER = 0, and we subsequen ly ex end he model in o de o conside a non-ze o BER. The e o e, he
a e age cu en consump ion o an ED in acknowledged mode, deno ed Ia g_ACK, can be ob ained as shown
in he nex equa ion:
𝐼'.(_345 =&𝑝9:-2 · 𝐼'.(_345_9 + 𝑝;:-2 · 𝐼'.(_345_;
(18)
whe e Ia g_ACK_1 and Ia g_ACK_2 deno e he a e age cu en consump ion o he ED when he ACK is ecei ed
in he i s and in he second ecei e window, espec i ely, and p1win and p2win ep esen hei co esponding
p obabili ies. The LoRaWAN speci ica ion o e s eedom o ne wo k manage s and implemen e s o
apply he policy ha bes sui s he equi emen s o a speci ic deploymen . The e o e, since he e is no
speci ic p io i y by de aul o he wo ecei e windows, we assume ha an ACK may be ecei ed by an
ED in he i s o in he second ecei e window wi h he same p obabili y (i.e., p1win = 0.5 and p2win = 0.5).
We nex de i e he models o ob aining Ia g_ACK_1 and Ia g_ACK_2. Figu e 7 depic s he cu en
consump ion p o ile o an ED ha pe o ms an acknowledged ansmission in wo di e en si ua ions: in
Figu e 7a), he ACK is ecei ed in he second window, while in Figu e 7b), he ACK is ecei ed in he i s
window. (No e: in ou speci ic scena io, we obse ed ha o DR0-DR3, all ACKs we e ecei ed in he
second window, while o DR4-DR5 all ACKs we e ecei ed in he i s window.)
When he ACK is ecei ed by he ED in he i s window, he numbe o s a es in ol ed in
acknowledged ansmission dec eases in compa ison wi h unacknowledged ansmission, since he ED does
no need o wai o a second ecei e window (Table 7). On he o he hand, du a ion o he i s ecei e
window (T x1w) and adio o in e al (To ) inc ease since he ACK needs o be ecei ed and subsequen ly
p ocessed. The e o e, Ia g_ACK_1 can be de i ed by using he same equa ions used o compu e Ia g_unACK (i.e.,
Equa ions (1)–(11)), bu conside ing only he s a es ha exis when he ACK is sen in he i s ecei e
window (which is equi alen o se ing bo h Tw2w and T2w o 0 in he equa ions), and he alues in Table 7.
3. Modeling he ene gy pe o mance o LoRaWAN
21
(a)
(b)
Figu e 7. Cu en consump ion p o ile o a Mul iConnec mDo LoRaWAN ED pe o ming an
acknowledged ansmission: (a) wi h DR0 (le ), (b) wi h DR5 ( igh ). In he o me , he ACK is
ecei ed by he ED in he second window, whe eas in he la e he ACK is ecei ed in he i s
window. The da a message ansmi ed by he ED has a FRM Payload size o 51 by es (le ) and
242 by es ( igh ), espec i ely.
Table 7. S a es, a iables and hei alues o LoRaWAN acknowledged ansmission when he
ACK is sen in he i s ecei e window.
S a e
Numbe
Desc ip ion
Du a ion
Cu en Consump ion
Va iable
Value (ms)
Va iable
Value (mA)
1
wake up
Twu
169.2
Iwu
22.1
2
adio p epa a ion
Tp e
80.4
Ip e
13.7
3
ansmission
T x
(see Table 6)
I x
82.8
4
wai 1s window
Tw1w
988.4
Iw1w
27.1
5
1s ecei e window
T x1w
(T x min in Table 6)
I1w
31.8
8
adio o
To
337.8
Io
13.4
9
pos p ocessing
Tpos
272.5
Ipos
20.9
10
u n o sequence
Tseq
37.5
Iseq
13.4
11
sleep
Tsleep
Equa ion (2)
Isleep
45 × 10−3
In o de o compu e Ia g_ACK_2, we conside ha beha io o he ED is simila o ha in
unacknowledged ansmission, since s a es in ol ed in he co esponding ansmission ope a ions a e he
same, and only wo di e ences can be obse ed: du a ion o he second window (T2w) and o he subsequen
adio o in e al (To ) a e bo h la ge han in he unacknowledged ansmission. In ac , he ED needs o
s ay in he second ecei e window o he ime needed o ecei e he ACK, and subsequen ope a ions
in ol e p ocessing o he ACK. The e o e, Ia g_ACK_2 can be ob ained by means o he same equa ions used
o compu e Ia g_unACK (i.e., Equa ions (1)–(11)), bu using he T2w and To alues ha co espond o
acknowledged ansmission when an ACK is sen in he second ecei e window (Table 8).
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
22
Table 8. S a es, a iables and hei alues o LoRaWAN acknowledged ansmission when he
ACK is sen in he second ecei e window.
S a e
Numbe
Desc ip ion
Du a ion
Cu en Consump ion
Va iable
Value (ms)
Va iable
Value (mA)
7
2nd ecei e window
T x2w
(T x min in Table 6)
I2w
38.0
8
adio o
To
337.8
Io
13.4
We nex ex end he model o compu e Ia g_ACK o non-ze o BER. We assume ha bi e o s a e
unco ela ed.
Le Ik deno e he a e age cu en consumed by he ED when i pe o ms k e ansmissions ( he las
one being success ully acknowledged), since he s a o he p ocedu es o he i s ansmission a emp ,
un il he end o he p ocedu es o he k- h e ansmission. Le Iac be he a e age cu en consump ion due
o ac i i ies ela ed wi h ansmi ing a da a message (including e ansmissions), i.e., all s a es excep he
sleep in e al. Iac can be compu ed as:
𝐼!5, =∑#𝐸[𝐼_]·𝑝_
A'`_NUaN
_/b
##
(19)
whe e E[Ik] deno es he expec ed cu en consump ion o an ED when i has pe o med k da a message
e ansmissions, pk indica es he p obabili y ha he ED pe o ms k e ansmissions o a message, and
MAX_RETR deno es he maximum numbe o message e ansmissions by an ED. The la e is
ecommended as pe he LoRaWAN speci ica ion o be se o 7.
E[Ik] can be ob ained by using he nex equa ion:
𝐸[𝐼_]=𝐼c)
_·𝑇c)
_+∑P𝐼'()_ac ·K𝑇'()_ac −𝑇7896
-L+#𝐼'
-·𝑇'
-·𝑝'+𝐼Y
-·𝑇Y
-·𝑝Y+𝐼(
-·𝑇(
-·𝑝(
𝑝'+𝑝Y+𝑝(Q
_
-/b
𝑇c)
_+∑RK𝑇'()_ac −𝑇7896
-L+𝑇'
-·𝑝'+𝑇Y
-·𝑝Y+𝑇(
-·𝑝(
𝑝'+𝑝Y+𝑝(S
_
-/0
#
(20)
In he p e ious equa ion,
𝐼<5
-
and
𝑇<5
-
deno e he a e age cu en consump ion and a e age du a ion
o he ac i i ies ela ed wi h an i- h acknowledged da a ansmission a emp which is e o - ee, and can
be compu ed by using (15) and Tables 6–8. On he o he hand, IACK_TO and TACK_TO co espond o he cu en
consump ion and he a e age du a ion o he ACK_TIMEOUT in e al, espec i ely. As pe ou
measu emen s, IACK_TO has he same alue as Iw1w, whe eas ACK_TIMEOUT is a andom a iable uni o mly
dis ibu ed be ween 1 and 3 s. Va iables
𝐼=
-
,
𝑇=
-
and px, whe e x can be equal o A, B o C, co espond
espec i ely o he a e age cu en consump ion, du a ion, and p obabili y o unsuccess ul acknowledged
da a message ansmission e en s de ined as ollows: A is he e en whe eby he da a message su e s a
collision, o i does no su e a collision bu i su e s a leas one bi e o , and i is equi alen in e ms o
cu en consump ion and du a ion o he ac i e pa (i.e., all s a es minus sleep) in unacknowledged
ansmission; B is he e en whe eby he da a message is success ully ecei ed, bu he ACK, sen in he
i s ecei e window, su e s a leas one bi e o ; and C is he e en whe eby he da a message is
success ully ecei ed, bu he ACK sen in he second ecei e window, su e s a leas one bi e o (no e
ha e o s in downlink messages can be de ec ed by means o he MIC ield). E en s B and C a e equi alen
3. Modeling he ene gy pe o mance o LoRaWAN
23
in e ms o cu en consump ion and du a ion o he ac i e pa o success ul acknowledged ansmission
wi h he ACK in he i s and in he second window, espec i ely. P obabili ies pA, pB and pC a e de e mined
in Equa ions (21)–(23). Le lDa a and lAck deno e he o al size o he da a and ACK messages, espec i ely.
P obabili ies pA, pB and pC can hen be ob ained as ollows:
𝑝'=𝑝5+22 +(1−𝑝5+22)·(1−(1−𝑏)2)#"#)
#
(21)
𝑝Y=𝑝06-& ·
(
1−𝑝'
)
·
(
1−
(
1−𝑏
)
2012
)
=0.5·
(
1−𝑝'
)
·
(
1−
(
1−𝑏
)
2012
)
#
(22)
𝑝(=𝑝96-& ·
(
1−𝑝'
)
·
(
1−
(
1−𝑏
)
2012
)
=0.5·
(
1−𝑝'
)
·
(
1−
(
1−𝑏
)
2012
)
#
(23)
We nex de e mine pk. To his end, we i s de i e he p obabili y ha an ED will send an
acknowledged message wi hou pe o ming any e ansmissions, p0. Then, p0 can be compu ed as he
p obabili y ha he da a message will no su e collisions, and nei he he da a message no he ACK will
su e e o s:
𝑝b=(1−𝑏)2)#"# ·(1−𝑏)2012 ·(1−𝑝5+22)
#
(24)
Based on p0, pk can be ound as he p obabili y ha only bo h message and ACK ansmissions ha
co espond o he k- h message e ansmission a e success ul, as ollows:
𝑝_=(1−𝑝b)_·𝑝b
#
(25)
No e ha as pe Equa ion (24), when he ED eaches he maximum numbe o e ansmissions, i
he las da a message e ansmission is no success ul, he co esponding cu en consump ion is no added
o Iac compu a ion in Equa ion (19). Ne e heless, impac o his inaccu acy is negligible o
MAX_RETR = 7 and o p ac ical BER alues (e.g., up o 10−3). The e o e, we op o a o simplici y in ou
model.
On he o he hand, o non-ze o BER, Tac can be calcula ed as shown nex :
𝑇!5, =
&
#𝐸
G
𝑇!5,__
H
·𝑝_
A'`_NUaN
_/b
#
(26)
whe e E[Tac _k] can be de e mined by using he nex equa ion:
𝐸
G
𝑇!5,__
H
=𝑇c)
_+
&RK
𝑇'()_ac −𝑇7896
-
L
+𝑇'
-·𝑝'+𝑇Y
-·𝑝Y+𝑇(
-·𝑝(
𝑝'+𝑝Y+𝑝(
S
_
-/0
#
(27)
Based on Equa ions (18)–(23), Ia g_ACK can be ob ained by conside ing he ac i e in e al and he
sleep in e al o e he no i ica ion pe iod, TNo i , as:
𝐼!"#_'() =𝐼!5, ·𝑇!5, +𝐼12334 ·(𝑇&+,-. −𝑇!5,)
𝑇&+,-.
#
(28)
The p e ious equa ion can be used o calcula e he heo e ical li e ime (i.e., an uppe bound on he
ac ual li e ime) o a ba e y-ope a ed ED ha pe o ms acknowledged ansmissions, deno ed Tli e ime_ACK,
on he basis o he ba e y capaci y, Cba e y (exp essed in mA·h), and Ia g_ACK, as shown nex :
𝑇2-.3,-<3_'() =#𝐶=!,,37B
𝐼!"#_'()
#
(29)
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
30
in he igu e o he sake o illus a ion cla i y. Impac o he payload size is no iceable only when TNo i is
low. Fo DR0 and TNo i = 5 min, ED li e ime anges om 0.27 up o 0.41 yea s (i.e., a ~52% ela i e
di e ence), o he payload sizes conside ed. Fo DR5 and TNo i = 1 min, ED li e ime anges om 0.18 o
0.26 yea s (i.e., a ela i e di e ence o ~49%). Howe e , impac o ame payload size dec eases when
TNo i inc eases because sleep s a e, and hus i s cu en consump ion, becomes dominan . Fo example, o
a TNo i = 60 min and DR0, ED li e ime alues ange om 2.17 o 2.90 yea s (i.e., 33.4% di e ence), and
om 3.90 o 4.44 yea s (i.e., a 13.78% di e ence) o DR5.
Figu e 13. ED li e ime in unacknowledged ansmission, as a unc ion o TNo i , and o di e en DR
se ings.
Nex , we e alua e impac o BER on ED li e ime (Figu e 16). Simila ly o he obse a ions made
in Sec ion 3.3.2, ED li e ime may dec ease by up o one o de o magni ude o DR5 and o he ange o
BER alues conside ed. Impac o BER on ED li e ime is lowe o DR0, and i dec eases wi h TNo i , since
ED li e ime ends asymp o ically o he li e ime o an always-sleeping ED as TNo i inc eases.
Finally, we also s udy he impac o pcoll on ED li e ime (Figu e 17). Collisions may signi ican ly
educe ED li e ime (e.g., by one hi d o TNo i = 30 min and pcoll = 0.3), and ha e a g ea e impac on ED
li e ime o DR5, as expec ed om he a e age cu en consump ion analysis in Sec ion 3.3.2.
3.3.4. Ene gy cos o da a deli e y
In his subsec ion, we e alua e he las conside ed pe o mance pa ame e , i.e., he ene gy cos o
da a deli e y o bo h unacknowledged and acknowledged ansmission. We nex apply Equa ions (13) and
(14) and (30) and (31) o de e mine ECdeli e y_unACK and ECdeli e y_ACK, espec i ely. We assume a ba e y
ol age o 3.6 V.
Figu e 18 p o ides he ene gy cos o da a deli e y o he unacknowledged app oach, as a unc ion
o TNo i and he DR used, o BER = 0.
0
1
2
3
4
5
6
0,1 110 100 1000
Li e ime (yea s)
No i ica ion pe iod (min)
DR0, No ACK
DR1, No ACK
DR2, No ACK
DR3, No ACK
DR4, No ACK
DR5, No ACK
DR6, No ACK

3. Modeling he ene gy pe o mance o LoRaWAN
31
Fo a gi en DR, and o BER = 0, he ela i e di e ence in ene gy cos o da a deli e y be ween
acknowledged and unacknowledged ansmission is he same as he di e ence in e ms o cu en
consump ion analyzed in Sec ion 3.3.2. Howe e , such di e ence is only signi ican o low no i ica ion
pe iods, and he e o e i is no g aphically isible in Figu e 16, he e o e he igu e se es o bo h
unacknowledged and acknowledged app oaches.
Figu e 14. ED li e ime in acknowledged and unacknowledged ansmission, as a unc ion o TNo i , and
o di e en DR se ings, BER = 0 and pcoll = 0. DR2, DR3 and DR5 a e no shown in he igu e o
he sake o illus a ion cla i y.
Figu e 15. Compa ison o he ED li e ime wi h 1-by e and maximum-sized payload da a message in
acknowledged ansmission, as a unc ion o TNo i , o BER = 0, pcoll = 0, and o di e en DR
se ings. Only DR0 and DR5 a e shown in he igu e o he sake o illus a ion cla i y.
0
1
2
3
4
5
6
0,1 110 100 1000
Li e ime (yea s)
No i ica ion pe iod (min)
DR6, No ACK
DR6, ACK
DR4, No ACK
DR4, ACK
DR1, No ACK
DR1, ACK
DR0, No ACK
0
1
2
3
4
5
6
0,01 0,1 110 100 1000
Li e ime (yea s)
No i ica ion pe iod (min)
DR0 ACK, 1-by e payload
DR5 ACK, 1-by e payload
DR0 ACK, max payload
DR5 ACK, max payload
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
32
Figu e 16. Impac o BER on ED li e ime in acknowledged ansmission, as a unc ion o TNo i , o
di e en DR se ings, and o pcoll = 0.
Figu e 17. Impac o pcoll on ED li e ime in acknowledged ansmission, as a unc ion o TNo i , o
di e en DR se ings, and o BER = 0.
As shown in Figu e 18, o BER = 0, he ene gy cos o da a deli e y ollows a linea end as a
unc ion o TNo i . As i has been p e iously shown in Figu es 8 and 9, a e age cu en consump ion, and
he e o e ene gy consump ion becomes asymp o ically cons an as a unc ion o TNo i . The e o e, as TNo i
inc eases, he ene gy consumed by he ED inc eases linea ly wi h ime, while he numbe o deli e ed bi s
emains cons an . Because we a e conside ing he maximum ame payload size allowed by each DR, no e
ha he slope o he cu es o DR0-DR2 is he same, since hese h ee DRs allow he same maximum
ame payload size (i.e., 51 by es), he slope o DR3 is lowe , since he maximum ame payload size is
g ea e (i.e., 115 by es), and inally he slope o DR4, DR5 and DR6 is he lowes , since o hese DRs he
maximum ame payload size is he la ges suppo ed by LoRaWAN (242 by es). DR0 exhibi s sligh ly
g ea e ene gy cos o da a deli e y han DR1, due o he lowe bi a e o DR0, which leads o a g ea e
da a message and ACK ansmi ime, as well as ecei e window du a ion. The same easoning applies o
0
1
2
3
4
5
6
110 100 1000
Li e ime (yea s)
No i ica ion pe iod (min)
DR0, BER=10⁻³
DR0, BER=10⁻⁴
DR0, BER=10⁻⁵
DR5, BER=10⁻³
DR5, BER=10⁻⁴
DR5, BER=10⁻⁵
0
1
2
3
4
5
6
110 100 1000
Li e ime (yea s)
No i ica ion pe iod (min)
DR0, Pcoll=0.3
DR0, Pcoll=0.2
DR0, Pcoll=0.1
DR0, Pcoll=0
DR5, Pcoll=0.3
DR5, Pcoll=0.2
DR5, Pcoll=0.1
DR5, Pcoll=0
3. Modeling he ene gy pe o mance o LoRaWAN
33
he compa ison o he ene gy cos o da a deli e y o DR1 and DR2. The ene gy cos o da a deli e y o
DR4 is ~19% and ~40% g ea e han he one o DR5 and o DR6, espec i ely, o he lowes no i ica ion
pe iod, and dec eases down o ~1% o bo h DR5 and DR6 o he highes no i ica ion pe iod conside ed
(no e ha hese di e ences a e no isible in Figu e 18).
We nex e alua e he uppe bound on he ene gy cos o da a deli e y by conside ing a ame
payload size o 1 by e. Resul s a e shown in Figu e 19, along wi h he ones ob ained o a maximum-sized
ame payload. As i can be seen, o a gi en no i ica ion pe iod and DR, he ene gy cos pe deli e ed
payload bi o a 1-by e ame payload is oughly wo o de s o magni ude g ea e han he one ob ained o
a maximum-sized ame payload.
We hen s udy he impac o non-ze o BER on he ene gy cos o da a deli e y, assuming a
maximum-sized payload o DR0, and he same payload size o DR5, and conside ing also
unacknowledged and acknowledged da a message ansmission (see Figu e 20). Acknowledged
ansmission leads o a g ea e ene gy cos , by a leas one o de o magni ude, due o he addi ional ene gy
consump ion o e ansmissions, in compa ison wi h he unacknowledged app oach. On he o he hand,
BER has a g ea e impac on DR5 han on DR0, since he o me ansmi s (and may e ansmi ) da a
messages a a highe bi a e, leading o lowe ene gy consump ion, which makes e ansmissions, and hei
ela ed o e head, ene gy-expensi e.
We nex ocus on how collisions in luence he ene gy cos o da a deli e y (see Figu e 21).
As expec ed, collisions inc ease he ene gy equi ed pe deli e ed payload bi . In acknowledged
ansmission, his e ec is emphasized, since e ansmissions a e needed. Fo example, o DR5, he ene gy
cos o da a deli e y in acknowledged ansmission o Tno i = 1 min inc eases by 60% when pcoll inc eases
om 0.1 o 0.3, while in unacknowledged mode, he ene gy cos pe deli e ed bi inc eases by 12.8%.
Figu e 18. Ene gy cos o da a deli e y as a unc ion o TNo i , o di e en DR se ings, and o
BER = 0 and pcoll = 0. Resul s o DR4, DR5 and DR6 o e lap in he igu e.
0
1
2
3
4
5
6
0200 400 600 800 1000 1200 1400
Ene gy cos (µJ/bi )
No i ica ion pe iod (min)
DR0
DR1
DR2
DR3
DR4-DR6
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
34
Figu e 19. Ene gy cos o da a deli e y as a unc ion o TNo i , o di e en DR se ings, BER = 0,
pcoll = 0, and o 1-by e payload and maximum-sized payload ha co esponds o each DR.
Figu e 20. Impac o BER on he ene gy cos o da a deli e y, as a unc ion o TNo i , o bo h
unacknowledged and acknowledged ansmission, o pcoll = 0, and o DR0 and DR5.
Figu e 21. Impac o pcoll on he ene gy cos o da a deli e y, as a unc ion o TNo i , o bo h
unacknowledged and acknowledged ansmission, o BER = 0, and o DR0 and DR5.
Finally, we analyze and discuss he impac o payload (and hus, message) size on he ene gy cos
pe deli e ed bi in a dense LoRaWAN ne wo k, whe e collisions may occu . Assuming ha EDs pe o m
0,01
0,1
1
10
100
1000
0,01 0,1 110 100 1000 10000
Ene gy cos (µJ/bi )
No i ica ion pe iod (min)
DR0, 1-by e payload
DR1, 1-by e payload
DR2, 1-by e payload
DR3, 1-by e payload
DR5, 1-by e payload
DR6, 1-by e payload
DR0, max payload
DR1, max payload
DR2, max payload
DR3, max payload
DR5, max payload
DR6, max payload
0,1
1
10
100
110 100 1000
Ene gy cos (µJ/bi )
No i ica ion pe iod (min)
No ACK, DR0, BER=10⁻³
No ACK, DR0, BER=10⁻⁴
No ACK, DR5, BER=10⁻³
No ACK, DR5, BER=10⁻⁴
ACK, DR0, BER=10⁻³
ACK, DR0, BER=10⁻⁴
ACK, DR5, BER=10⁻³
ACK, DR5, BER=10⁻⁴
0,1
1
10
100
110 100 1000
Ene gy cos (µJ/bi )
No i ica ion pe iod (min)
ACK, DR0, Pcoll=0.3
ACK, DR0, Pcoll=0.2
ACK, DR0, Pcoll=0.1
No ACK, DR0, Pcoll=0.3
No ACK, DR0, Pcoll=0.2
No ACK, DR0, Pcoll=0.1
ACK, DR5, Pcoll=0.3
ACK, DR5, Pcoll=0.2
ACK, DR5, Pcoll=0.1
No ACK, DR5, Pcoll=0.3
No ACK, DR5, Pcoll=0.2
No ACK, DR5, Pcoll=0.1
3. Modeling he ene gy pe o mance o LoRaWAN
35
acknowledged ansmissions, ne wo k beha io can be modeled by an Aloha access p o ocol, as an
app oxima ion [5]. Unde hese condi ions, he ene gy cos pe deli e ed bi can be compu ed as he esul
o di iding he ene gy cos o a message ansmission (including i s e ansmissions) by he numbe o
payload bi s ca ied. The ene gy consumed in a message ansmission (including e ansmissions) is oughly
p opo ional o he numbe o ansmission a emp s pe message. In ac , he amoun o ene gy consumed
in each e ansmission (which includes he ene gy consumed o e ACK_TIMEOUT) is much la ge han
he ene gy consumed du ing he ac ual ansmission s a e, ega dless o he message size, wi h an accu acy
ha inc eases wi h he DR since ansmission ime dec eases, and wi h he load o e ed o he ne wo k. On
he o he hand, in Aloha, he expec ed numbe o ansmission a emp s pe message is e2G, whe e G is he
o al load o e ed o he ne wo k, and hus he expec ed ene gy consumed o deli e a message is a·e2G,
whe e a is he o al amoun o ene gy consumed in each ansmission a emp . No e ha G is p opo ional
o he message size, i.e., lpay + lhead, whe e lhead deno es he o al size o he message heade s. The e o e, he
ene gy cos o da a deli e y unde he desc ibed condi ions can be app oxima ed by (32):
𝐸𝐶)%,-.%/* ≈𝑎 · 𝑒;>
𝑙?'*
=𝑎 · 𝑒@·(,$"%C,&'"()
𝑙?'*
= &𝛼 · 𝑒@·,$"%
𝑙?'*
(32)
whe e α is a cons an exp essed in Joules, ha can be compu ed by using (33), and k is a cons an exp essed
in bi −1, which depends on he ansmission bi a e and on he o al message a e o e ed o he ne wo k.
𝛼 = 𝑎 · 𝑒@·,&'"(
(33)
No e ha he model p esen ed canno accu a ely cap u e he DR dec ease mechanism o
e ansmissions (see Sec ion 2.3), when used, since Aloha assumes all packe ansmissions ha e he same
du a ion. Ne e heless, i allows o quali a i ely cap u e beha io o he ene gy cos o da a deli e y as a
unc ion o packe size. As shown in Figu e 22, impac o payload size on he ene gy cos pe deli e ed bi
depends on he alue o k. All cu es ollow a “U” shape wi h an op imal payload size ha minimizes he
ene gy cos pe deli e ed bi . The “U” shape o he cu es can be explained, on he one hand, by he ac
ha e y la ge messages will lead o high ene gy cos pe deli e ed bi due o a high numbe o collisions.
On he o he hand, messages wi h e y small payload will also lead o high ene gy cos pe deli e ed bi ,
because while he numbe o collisions will be ela i ely low, he ene gy cos will be ela i e o a low
amoun o deli e ed bi s. As k inc eases, impac o collisions becomes dominan and he payload size ha
minimizes he ene gy cos pe deli e ed bi dec eases. No e ha o su icien ly low, o su icien ly high,
k alues, he op imal payload size alls ou o he egion o alid payload sizes. Fo example, o a high
enough k (e.g., k = 0.1), he co esponding ene gy cos pe deli e ed bi cu e in Figu e 21 is a unc ion
ha g ows s eadily wi h payload size.

Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
36
Figu e 22. Impac o message payload, lpay, on he ene gy cos o da a deli e y, assuming a dense
LoRaWAN ne wo k, o , α = 0.4 J and DR = 5.
3.4. Conclusions
In his i s s udy, we ha e modeled he ene gy consump ion o a class A LoRaWAN ED
ansmi ing da a messages pe iodically, conside ing impac o unacknowledged and acknowledged
ansmission, DRs, ame payload size and BER. Pe o mance pa ame e s ha e been ED a e age cu en
consump ion and li e ime, and ene gy cos o da a deli e y. The models ha e been de eloped based on
measu emen s pe o med on p e alen LoRaWAN ha dwa e.
Fo BER = 0, acknowledged ansmission educes LoRaWAN ED a e age cu en consump ion.
This happens because an ACK may be sen in he i s ecei e window, whe eas unacknowledged
ansmission in ol es wo ecei e windows and a la ge a e age cu en consump ion han a ansmission
ACK in he i s ecei e window. No e ha he quan i a i e di e ence be ween ene gy consump ion in
acknowledged and unacknowledged ansmission o BER = 0 may be pla o m-speci ic. In ac , in con as
wi h he beha io obse ed wi h he pla o m used in his wo k, he ED ha dwa e pla o m migh s ay in a
low consump ion mode (e.g., such as he sleep s a e) du ing he in e al be ween he i s and he second
ecei e windows. On he o he hand, o a non-negligible BER, acknowledged ansmission leads o g ea e
cu en consump ion han unacknowledged ansmission, due o message e ies.
Fo a no i ica ion pe iod o 5 min, DR5 leads o a cu en consump ion lowe han ha o DR0 by
a maximum ac o o 2.8, whe eas a 1-by e ame payload size educes cu en consump ion by up o a
maximum ac o o 1.59. Fo he same no i ica ion pe iod, using DR6 (which is no manda o y as pe he
LoRaWAN speci ica ion), cu en consump ion dec eases by a ac o o 3.18, compa ed o using DR0. Non-
ze o BER up o 10−3 may inc ease cu en consump ion by up o one o de o magni ude in acknowledged
ansmission. Cu en consump ion di e ences due o he se ings conside ed end o dec ease wi h he
no i ica ion pe iod, since sleep cu en consump ion hen becomes dominan .
0,001
0,01
0,1
1
110 100
Ene gy cos (J/bi )
Payload size (by es)
k=0.1 k=0.05 k=0.01 k=0.003
3. Modeling he ene gy pe o mance o LoRaWAN
37
An ED unning on a 2400 mAh ba e y and sending one message e e y 5 min can achie e a 1-yea
li e ime. As he no i ica ion pe iod inc eases, he heo e ical ED li e ime ends asymp o ically o oughly
6 yea s unde he condi ions conside ed. Howe e , om ou s a e o he a analysis, ha a he ime o his
s udy LoRaWAN ha dwa e is no as well op imized as ha o o he low-powe echnologies. In he la e ,
sleep cu en in he o de o (o e en below) 1 µA is common, which allows mul iyea de ice li e imes wi h
a bu on cell ba e y, o 1 o de o magni ude less capaci y han he one conside ed in his s udy. In con as ,
cu en ba e ies used o LoRaWAN ha dwa e ha e a la ge size and weigh , which in u n has an impac
on he physical dimensions and weigh o cu en LoRaWAN de ices and limi s applicabili y o cu en
LoRaWAN de ices o domains whe e such dimensions a e ele an , such as wea ables.
Finally, he ene gy cos pe deli e ed bi o maximum-sized ame payload ansmission is oughly
wo o de s o magni ude lowe han he one ob ained o he sho payload o 1 by e pe ame. An ED
ope a ing as a senso will hus bene i signi ican ly om accumula ing eadings and sending hem a he
highes no i ica ion pe iod possible. Fo non-ze o BER up o 10−3, acknowledged ansmission inc eases
he ene gy cos o da a deli e y by up o oughly one and wo o de s o magni ude, o DR0 and DR5,
espec i ely. The in luence o he ame payload o e he ene gy cos , o BER = 0, will be s udied in dep h
in Chap e 5, by means o simula ions.
4. The SF12 Well in LoRaWAN: p oblem and ED solu ions
Since he ini ial speci ica ion o LoRaWAN was published, many esea che s ha e de o ed hei
e o s o in es iga ing he pe o mance o his echnology [1,5,51-56]. Howe e , LoRaWAN ne wo k
pe o mance may become comp omised as he numbe o connec ed ED inc eases, e en o a ela i ely low
numbe o such de ices.
LoRaWAN o e s op ional link-laye eliabili y, based on link-laye ACKs and e ansmissions
(see Sec ion 2.3). When ACKs a e no ecei ed by a sende a e ansmi ing a ame in eliable mode, he
sende ypically ends o educe i s physical laye bi a e. Howe e , his eac ion inc eases uplink and, e en
wo se, downlink channel u iliza ion. As a esul , ne wo k pe o mance may deg ade s eadily in o
conges ion collapse.
In his chap e , we iden i y and illus a e a p oblem which we call he Sp eading Fac o 12 (SF12)
Well in a ange o scena ios, and e alua e a numbe o solu ions o coun e i . We show ha i is possible
o mi iga e i , main aining good pe o mance as he o e ed load inc eases by using di e en SF
managemen echniques.
In o de o ca y ou he s udy, we de eloped and used a simula o called Ad anced F amewo k o
LoRa (AFLoRa), a LoRaWAN simula ion en i onmen ha uses he FLoRa simula o [57] as a basis, albei
wi h signi ican enhancemen s and addi ions. As a side-con ibu ion o his chap e , we o e he simula o
publicly [58].
The p esen chap e is o ganized as ollows. Fi s , in he nex sec ion, we e iew ela ed wo k.
Sec ion 4.2 illus a es he SF12 Well p oblem in di e en scena ios in e ms o he o e ed load and he
a io o acknowledged a ic. Sec ion 4.3 p oposes and e alua es a numbe o echniques in ended o
coun e he SF12 Well p oblem, showing hei pe o mances and ade-o s. Finally, Sec ion 4.4 p o ides
he main ema ks om his wo k.
4.1. Rela ed wo k
P e ious wo k has poin ed ou ha con i med a ic in LoRaWAN may be impai ed by du y cycle
es ic ions ha limi downlink capaci y, ende ing ga eways as bo lenecks ha cause packe deli e y a io
(PDR) dec ease [52-54,59-61]. Howe e , he consequen p oblem o conges ion collapse emained
unexplo ed be o e his w i ing.
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
46
(a)
(b)
Figu e 27. E olu ion o cumula i e packe d ops a he EDs due o du y cycle es ic ions o e ime.
(a) Lowes load: 30 CEDs, using an EDL o 0.9 packe s/h. (b) Highes load: 100 CEDs, using an
EDL o 18 packe s/h.
Finally, Figu e 28 p esen s he ins an aneous PDR o e ime. No e ha he ins an aneous PDR
co esponds o he a io o packe s ecei ed by he NS a he applica ion laye di ided by he o al numbe
o applica ion-laye packe s gene a ed by he EDs wi hin a ela i ely small in e al (o 4 h and 0.2 h in
Figu es 28a and 28b, espec i ely) ha s a s a ha gi en ime. A e he WFT, his pe o mance pa ame e
e lec s he s eady-s a e ne wo k pe o mance. As a o emen ioned, in bo h scena ios, all he CEDs use SF12
a e he WFT. Howe e , o low loads, he PDR alue a e he WFT is nea 100%, while in hea y load
condi ions he PDR is e y low, a ound 10%. In ha case, he SF12 Well p oblem has a d ama ic impac
on ne wo k pe o mance.
Figu e 29 shows he WFT as a unc ion o he node load. As he o e ed a ic dec eases, he WFT
inc eases quickly. The g ea es WFT alue is ob ained o 30 CEDs and EDL = 0.9 packe s/h, wi h an
a e age WFT equal o 65.3 days. On he o he hand, he lowes WFT alue is ound o 100 CEDs and he
EDL = 18 packe s/h, wi h an a e age WFT equal o 76.7 min (and a maximum alue o 93.9 min).
The e o e, he WFT depends g ea ly on he numbe o CEDs and on he EDL. As he EDL dec eases, he
mean WFT inc eases e y quickly (no e he loga i hmic scale o he e ical axis in Figu e 29). The WFT
di e ences o he di e en numbe s o CEDs inc ease as well.

4. SF12 well in LoRaAWAN: p oblem and ED solu ions
47
(a)
(b)
Figu e 28. Ins an aneous PDR a e WFT. (a) Lowes load: 30 CEDs, using an EDL o 0.9 packe s/h.
(b) Highes load: 100 CEDs, using an EDL o 18 packe s/h.
We nex s udy he impac o he EDL and he numbe o CEDs on he PDR (see Figu e 30). I can
be obse ed how such an impac is signi ican . Fo low EDL alues, as he EDL inc eases, he PDR
dec eases quickly, especially o a high numbe o CEDs. Howe e , he dec ease slows down as he EDL
inc eases. This beha io can be unde s ood by looking a he PDR esul s co esponding o he CED and
UED ansmissions (see Figu e 31 and Figu e 32, espec i ely). While in he o me he PDR exhibi s a
s eady deg ada ion wi h he EDL, he la e shows only a sligh PDR dec ease wi h he EDL, e en o high
EDL alues.
Figu e 29. Mean and s anda d de ia ion o WFT as a unc ion o EDL, o se e al numbe s o CEDs.
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
48
Figu e 30. PDR s EDL, om all EDs.
Figu e 31 also shows ha he EDL has a d ama ic e ec on he PDR, while he numbe o CEDs
gene ally has a lowe in luence on he PDR. Howe e , o medium loads, he numbe o CEDs becomes
mo e ele an . This esul can be a ibu ed o he highe impac o he uncon i med ansmissions a high
loads when he numbe o CEDs is low.
On he o he hand, he high PDR o uncon i med ansmissions shown in Figu e 32 indica es ha ,
in con as wi h he CEDs, he UEDs a e no a ec ed by ne wo k conges ion, e en unde a high UED load.
Fu he mo e, he UEDs’ PDR is almos no in luenced by he CED ansmissions o by he numbe o
CEDs. This beha iou is due o he cons an use o SF7 (i.e., he ini ial SF alue o all he EDs in ou
conside ed scena ios) by he UEDs, which yields he lowes possible ame ToA.
Figu e 31. PDR o CEDs s EDL.
4. SF12 well in LoRaAWAN: p oblem and ED solu ions
49
Figu e 32. PDR o EDs in uncon i med ansmission mode s EDL.
In o de o u he analyze he easons o he ne wo k PDR beha io , we nex ocus on he
addi ional pe o mance pa ame e s. Figu e 33 illus a es he numbe o MAC ame collisions o e he o al
numbe o ansmi ed ames, along wi h he numbe o d opped packe s due o du y cycle es ic ions o e
he o al numbe o packe s in ended o be ansmi ed by he EDs and by he ga eway, espec i ely, in he
conside ed scena ios. No e ha in hose scena ios, he downlink a ic o wa ded by he ga eway comp ises
only he ACKs sen by he NS. As load inc eases, he numbe o collided ames and d opped packe s also
inc eases quickly o low loads. Howe e , o a high EDL, his inc ease slows down, e en becoming a
dec ease, excep o scena ios wi h 100 CEDs (see Figu es 33a and 33c). The e a e wo main easons o
his dec ease. Fi s , as he CEDs inc ease hei SF, he ame ToA inc eases, he e o e he numbe o du y
cycle losses inc eases. Consequen ly, o high EDL he CED collisions do no inc ease as much as o he
low EDL because he e is a educed numbe o CED ansmissions. Second, he UED ansmissions
con ibu e a low numbe o collisions due o hei use o SF7, as discussed ea lie . On he o he hand, he
packe d ops a he EDs a ec he PDR o bo h ypes o EDs, while packe d ops a he ga eway ha e a
nega i e e ec , mainly on he CEDs’ PDR. All hese beha io s ha e a g ea impac on he PDR (see Figu e
30), leading o a PDR dec ease wi h he EDL ha slows down as he EDL inc eases.
The obse a ions om Figu e 33 a e also ele an o unde s and he possible impac o he numbe
o channels on he SF12 Well p oblem. Fo a g ea e numbe o channels (e.g., 8 channels), a lowe numbe
o da a ame collisions and ED packe d ops, and hus a PDR inc ease, is expec ed. While he numbe o
ED e ies migh appea o dec ease as a esul , hus delaying he SF12 Well p oblem, ano he consequence
o he PDR inc ease is a g ea e numbe o ACKs o be sen by he ga eway, inc easing packe (i.e., ACK)
d ops a he ga eway. The EDs awai ing he ACKs ha will no be ecei ed will anyway pe o m e ies,
and inc ease hei SF, o he co esponding packe s (e en i such packe s ha e ac ually been success ully
deli e ed).
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
50
(a)
(b)
(c)
Figu e 33. (a) Collision a io a he ga eway. (b) Packe d op a io a EDs due o du y cycle
es ic ions. (c) Packe d op a io a he ga eway due o du y cycle es ic ions.
4.3. ED-based solu ions
The analysis in he p e ious sec ion has shown ha all he CEDs e ol e o use SF12 a a gi en
WFT in he scena ios conside ed. The ea e , he EDs use he wo s SF con igu a ion in e ms o ne wo k
conges ion. In his sec ion, we p opose h ee al e na i e SF managemen echniques based on simple
changes o how he SF pa ame e is managed by he ED. Then, we p esen and discuss an e alua ion o
hese solu ions.
4.3.1. P oposed solu ions
As explained in Sec ion 2.3, LoRaWAN de ices ypically inc ease he SF a e wo consecu i e
ACKs no ecei ed. This beha io will hence o h be e e ed o as SF Mode 0 (SFM0). As al e na i es,
we in oduce h ee new SF pa ame e managemen echniques, namely SF Mode 1 (SFM1), SF Mode 2
(SFM2), and SF Mode 3 (SFM3).
They a e de ined as ollows:
1. SFM1. SF7, which co esponds o he g ea es DR alue, is always used. No SF change is
conduc ed e en i he da a o he ACK ames a e los .
2. SFM2. This echnique adds an ex a s ep o SFM0. When he SF eaches he SF12 alue, i he
co esponding ACK is no ecei ed a e wo ansmission oppo uni ies, he SF is ese o SF7.
The a ionale o his app oach is ha a e unsuccess ul ansmission using SF12 i may be
be e o swi ch o SF7 as conges ion migh be he eason o he ame losses. Hence, SFM2
leads o a cyclic use o all he SF alues.
3. SFM3: The basis o his echnique is also SFM0. Howe e , wi h his echnique, i an ACK is
ecei ed, he ED will dec ease i s SF alue. Hence, his op ion b ings he oppo uni y o
inc ease he DR, wi h an expec a ion o educe he ame ToA and hus educe ne wo k
conges ion.
4. SF12 well in LoRaAWAN: p oblem and ED solu ions
51
No e ha we conside SFM1 as a benchma k o ou simula ion scena ios as i minimizes he ame
ToA. Ob iously, i canno be conside ed a gene al solu ion (i.e., o any ype o LoRaWAN ne wo k)
because i s pe o mance will be se e ely a ec ed o high numbe s o CEDs, due o collisions, o i he
adio link quali y is no good enough.
4.3.2. E alua ion
In his subsec ion, we e alua e he pe o mance o he p esen ed al e na i e SF managemen
echniques (i.e., SFM1, SFM2, and SFM3) in he same condi ions conside ed o SFM0 in Sec ion 4.2.
We ocus on he ne wo k PDR as he main pe o mance me ic (Figu e 34). Howe e , in o de o
be e unde s and he ne wo k pe o mance and beha io , we also s udy he numbe o collisions (Figu e
35), he numbe o losses due o du y cycle es ic ions a bo h he ED (Figu e 36) and he ga eway (Figu e
37), and he dis ibu ion o he SF alues used o each mode, and o each conside ed numbe o CEDs
(Figu e 38).
Figu e 34 illus a es he o al PDR o a ic including con i med and uncon i med ansmission
modes, as a unc ion o he EDL. SFM1 (see Figu e 34a) yields he highes PDR among he conside ed SF
managemen modes, e en in high load condi ions. Fo SFM1, he PDR is always abo e 80% in he
conside ed scena ios. SFM1 also o e s he bes beha io in e ms o losses due o du y cycle es ic ions
(see Figu e 36a and Figu e 37a). This bes pe o mance unde conges ion is due o he ac ha SF7 leads
o he minimum ToA, which minimizes channel u iliza ion and he impac o he du y cycle limi a ion on
ne wo k pe o mance. This occu s despi e he ac ha he collision a io o SFM1 is no he bes among
he conside ed SF managemen echniques, excep o a e y low packe load (see Figu e 35). The obse ed
collision a io is a consequence o he app oach in SFM1 based on always using he same SF alue
(i.e., SF7), which p ecludes exploi ing he o hogonali y ha s ems om using di e en SF alues.
I is in e es ing o compa e he high PDR achie ed by using SFM1 (Figu e 34a), wi h he low PDR
ob ained by he CEDs when using SFM0 (Figu e 31) o he same ange o EDL alues and numbe o
CEDs. The low PDR o SFM0 is mainly due o he use o high SF alues (equal o SF12 o all CEDs a e
he WFT), which lead o high ToA alues and p oduce a high numbe o collisions a he ga eway
(Figu e 33a) and packe d ops a he EDs (Figu e 33b). The ga eway is also unable o ansmi all he ACKs
o he co esponding CEDs due o du y cycle es ic ions (Figu e 33c), leading o unnecessa y e ies by
hose CEDs which inc ease he o e ed load and con ibu e o he dec ease o he PDR. In con as , in SFM1
all nodes use SF7, which minimizes he ToA and yields a high PDR.
Howe e , we hypo hesize ha he e exis s a highe numbe o CEDs and/o a ic load ha will
c ea e a low PDR p oblem equi alen o he one ound o SFM0, ega dless o he SF alues used by he
EDs.

Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
52
(a)
(b)
(c)
Figu e 34. PDR s EDL o (a) SFM1, (b) SFM2, and (c) SFM3.
In con as wi h he SFM1 beha io , SFM3 leads o a quick PDR dec ease as he o e ed load
inc eases, especially o a high numbe o CEDs (Figu e 34c). This is due o an inc ease in he numbe o
CEDs ha use SF12 o an SF alue close o his one (see Figu e 38i), leading o g ea e ToA alues and
con ibu ing o highe collision p obabili y (see Figu e 35c), which esul s in low PDR alues. On he o he
hand, o a low numbe o CEDs, he PDR ob ained wi h SFM3 ends o be he highes among all o he
conside ed SF managemen modes. This is, again, ela ed o he dis ibu ion o he SF alues used by he
CEDs: hey mainly use SF7 o a low numbe o CEDs, e en o high EDL (see Figu e 38i). This SF alue
dis ibu ion leads o a low collision a io (see Figu e 35c) and a e y low numbe o losses due o du y cycle
es ic ions, a bo h he EDs (see Figu e 36c) and he ga eway (see Figu e 37c). Finally, SFM3 o e s a
highe PDR compa ed wi h SFM0 by a ac o o up o 2.44, wi hin he s udy condi ions.
(a)
(b)
(c)
Figu e 35. F ame collisions a he ga eway s EDL o (a) SFM1, (b) SFM2, and (c) SFM3.
4. SF12 well in LoRaAWAN: p oblem and ED solu ions
53
(a)
(b)
(c)
Figu e 36. Packe losses due o du y cycle es ic ions a he EDs s EDL o (a) SFM1, (b) SFM2,
and (c) SFM3.
SFM2 leads o in e media e PDR esul s (see Figu e 34b) because i p oduces a dis ibu ion o SF
alues used by he CEDs ha is a he uni o m (see Figu e 38b, 38e and 38h). Only a signi ican SF alue
dis ibu ion di e ence exis s o a e y low EDL, bu e en in his case, he p obabili y o using he mos
likely SF alue (i.e., SF7) is below 41% o all numbe s o he CEDs conside ed (see Figu e 38b). The
mo e e en dis ibu ion o SF alues achie ed by SFM2 (see Figu e 38h) exploi s he o hogonali y o
di e en SF alues and leads o less collisions han he es o he conside ed SFMs, especially o a high
load (see Figu e 34). Howe e , he numbe o losses due o du y cycle es ic ions o SFM2 is g ea e han
he one ob ained o SFM1 (a bo h he CEDs and he ga eway), and, o high EDL and a high numbe o
CEDs, i is also g ea e han he SFM3 one, ega ding losses a he ga eway (see Figu e 36b and Figu e 37b,
espec i ely). Such beha io o SFM2 is due o i s endency o lead o g ea e ame ToA, because o i s
g ea e p obabili y o using g ea e SF alues han hose o SFM1 and SFM3 ( ega ding he la e , one
excep ion is he high EDL and he high numbe o CEDs). Ne e heless, SFM2 yields a PDR inc ease,
compa ed wi h SFM0 (Figu e 30), by a ac o o up o 4.7 o he ange o scena ios conside ed.
(a)
(b)
(c)
Figu e 37. Packe losses due o du y cycle a he ga eway s EDL o (a) SFM1, (b) SFM2, and (c) SFM3.
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
54
On he o he hand, compa ing losses due o du y cycle es ic ions a he ga eway o SFM0, SFM2,
and SFM3 schemes (Figu es 33c, 37b and 37c), we can app ecia e an inc ease in hose losses o he
men ioned al e na i e SFMs. Fo SFM0, he lowe numbe o packe (ACK) d ops a he ga eway is due o
a lowe PDR (which is due o a g ea e numbe o packe losses due o collisions, and he du y cycle
es ic ions a he EDs) and hus a lowe numbe o ACKs o be sen . Fo he al e na i e SF managemen
schemes, he PDR is g ea e han o SFM0, which inc eases he ACK a ic, and he numbe o packe
d ops a he ga eway. The e o e, he ga eway becomes a limi a ion o he al e na i e SF managemen
echniques.
F om he abo e analysis, i can be highligh ed ha any o he conside ed al e na i e SF
managemen echniques allows he a oidance o he SF12 Well and imp o es he ne wo k PDR. SFM1
o e s he bes pe o mance in e ms o he PDR and packe losses due o du y cycle es ic ions, al hough,
as a o emen ioned, his SF managemen echnique is only included in he e alua ion as a benchma k. Bo h
SFM2 and SFM3 ou pe o m SFM0 bu o e di e en ade-o s. In e ms o collisions a he ga eway,
SFM2 is he bes op ion because i p esen s a mo e e en SF alue dis ibu ion. Howe e , o low loads,
SFM3 o e s a lowe numbe o du y-cycle-induced packe d ops, due o a highe ac ion o de ices using
low SF alues. In consequence, SFM2 ends o o e a g ea e PDR han SFM3 o high EDL and a high
numbe o CEDs, whe eas SFM3 yields a highe PDR han SFM2 o a low EDL and a low numbe o
CEDs.
4. SF12 well in LoRaAWAN: p oblem and ED solu ions
55
SFM1
SFM2
SFM3
(a)
(b)
(c)
0.9
packe s/h
(d)
(e)
( )
3.6
packe s/h
(g)
(h)
(i)
18
packe s/h
Figu e 38. CED SF alues dis ibu ion when SF mode is (a, d, and g) SFM1; (b, e, and h) SFM2; and
(c, , and i) SFM3 and o (a, b, and c) EDL equal o 0.9 packe s/h, (d, e and ) 3.6 packe s/h, and
(g, h and i) 18 packe s/h.
4.4. Conclusions
In his chap e , we iden i ied and cha ac e ized by simula ion a o me ly unexplo ed LoRaWAN
ne wo k condi ion, which we call he SF12 Well. This phenomenon may a ise due o he p esence o e en
a ela i ely low numbe o CEDs, which will end o inc ease hei SF and hus he numbe o collisions
and packe d ops due o du y cycle cons ain s. In consequence, he SF12 Well may signi ican ly deg ade
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
62
Fo SF12 (see Figu es 39b, 40b and 41b), he EPB is g ea e han ha ob ained o SF7, due o he
g ea e ansmission ime. The la e also impac s o he pe o mance pa ame e s, such as he numbe o
collisions and ame d ops, which u he inc ease ene gy consump ion. Howe e , EPB dec eases s eadily
wi h packe size wi hin he ange o alid packe sizes, and hus, i does no show he “U” shape ound in
some cases o SF7.
In o de o de e mine he easons behind he ob ained EPB esul s as a unc ion o packe size, we
nex ocus on he ollowing addi ional pe o mance pa ame e s om he same e alua ed scena ios: i)
collision a io (Figu e 42), ii) he downlink ame d op a io a he ga eway –he eina e e e ed o as
ga eway d op a io– (Figu e 43), iii) he packe d op a io a EDs –he eina e e e ed o as ED d op a io–
(Figu e 44), i ) he ame e ansmission a io (Figu e 45), and ) PDR (Figu es 46 and 47). In each igu e,
we p esen esul s o wo TP alues: 1000 s, and 4000 s.
(a)
(b)
Figu e 41. EPB as a unc ion o packe size, o TP = 4000 s: (a) SF7, (b) SF12.
Fi s , we analyze he pe o mance o SF7, and N alues o 1000 and 2000 (i.e., he SF and N alues
o which EPB as a unc ion o packe size shows an “asymme ic U” shape), in e ms o collision a io,
ED d op a io, and ga eway d op a io.
Fo low packe sizes, he collision p obabili y and ED d op a io a e ela i ely low (see Figu e 42a
and 8a), while he ga eway d op a io is high (see Figu e 43a). The la e is due o he du y cycle es ic ion
(i.e., 1% in he used equency band in he downlink channel) and he high numbe o EDs (all o hem
CEDs) ha equi e ACKs in esponse. In consequence, EPB is high due o a high numbe o unnecessa y
ED e ansmissions, and also due o he low packe size i sel .
When packe size inc eases, ini ially, EPB dec eases due o he dominan e ec o a g ea e amoun
o deli e ed bi s o e cons an ene gy o e heads. Howe e , he collision a io inc eases quickly, and he
ED d op a io also inc eases; in consequence, he ga eway d op a io dec eases, since he NS ecei es a

5. Ene gy e iciency-op imal packe size in LoRaWAN
63
lowe numbe o ames, and he e o e i sends a lowe numbe o ACKs in esponse o he EDs. Fo high
packe sizes, ED e ansmissions (Figu e 45a) inc ease due o he e y high collision a io and ED d op
a io, leading o an EPB inc ease. Howe e , such inc ease is mi iga ed by he g ea e packe size, leading
o a low slope and an "asymme ic U” shape o N = 1000 and N = 2000, and SF7, as shown p e iously in
Figu es 39a, 40a and 41a. In con as , o SF12, and o he same N alues, he e is a highe collision a io
and ED d op a io no only o high packe sizes, bu also o low ones (see Figu es 42b and 44b). The
collision a io is close o 1, due o he high ame ansmission ime o SF12 and he high numbe o EDs
compe ing o ansmission esou ces. The high collision and ED d op a ios, combined wi h a dec easing
ga eway d op a io (see Figu e 43b) lead o a ela i ely cons an numbe o e ansmissions (see Figu e
45b), yielding a mono onically dec easing EPB as a unc ion o packe size (see Figu es 39b, 40b and 41b).
Fo SF7 and N = 100, as illus a ed in Figu es 39a, 40a, and 41a, EPB dec eases mono onically
wi h packe size. This occu s because, in his scena io, he lowe amoun o EDs p oduces lowe o e ed
a ic load. While he collision a io and he ED d op a io inc ease wi h packe size, hey emain low
(compa ed o hose ob ained o g ea e N alues, see Figu es 42a and 44a). No e ha , in consequence, he
ga eway d op a io emains low and nea -independen o packe size (see Figu e 43a), whe eas PDR is high
and almos cons an as well as a unc ion o packe size (see Figu es 46a and 47a). As a esul , he numbe
o ED e ansmissions emains ela i ely low, i inc eases only sligh ly wi h packe size, and packe size
i sel domina es he dec ease o EPB in his case (Figu es 39a, 40a, and 41a). Fo SF12 and N = 100, he
e ansmission a io emains cons an wi h packe size, he e o e EPB dec eases mono onically wi h packe
size (Figu es 39a, 40a, and 41a).
No e ha , o SF7, he e ansmission a io is be ween 82.1% and 87.3% (see Figu e 45a), o
N ³ 1000 and o all packe sizes conside ed, which means ha almos all ansmissions a e e ansmissions
and sugges s ha he sys em is in a sa u a ion s a e. In he wo s case, o each packe o be ansmi ed,
he e is one i s a emp and 7 ame e ansmissions, which leads o an uppe bound o he e ansmission
a io o 87.5 %. This is also he case o SF12 and all he conside ed N alues, whe e he e ansmission
a io is a ound 87.4% (see Figu e 45b).
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
64
(a)
(b)
Figu e 42. Collision a io, o N = NC: (a) SF7, (b) SF12.
(a)
(b)
Figu e 43. Ga eway d op a io, o N = NC: (a) SF7, (b) SF12.
5. Ene gy e iciency-op imal packe size in LoRaWAN
65
(a)
(b)
Figu e 44. ED d op a io, o N = NC: (a) SF7, (b) SF12.
5.2.3. PDR in con i med ansmission mode
We nex discuss he ob ained PDR esul s in conjunc ion wi h EPB pe o mance. As shown in
Figu e 10a, o SF7 and TP = 1000 s, PDR dec eases wi h packe size. This is mainly due o he inc easing
collision a io and ED d op a io (Figu es 42a and 44a), and i is agg a a ed by ga eway d ops (Figu e 43a).
Fo SF7 and TP = 4000 s (see Figu e 47a), PDR dec eases mo e slowly wi h packe size, due o he lowe
o e ed ne wo k load.
(a)
(b)
Figu e 45. Re ansmission a io om EDs, o N = NC: (a) SF7, (b) SF12.
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
66
(a)
(b)
Figu e 46. PDR and EPB o TP = 1000 s: (a) SF7, (b) SF12.
Fo SF7 and N = 100, EPB dec eases as well wi h packe size, showing a ade-o be ween PDR
and EPB in he conside ed scena ios (Figu es 10a and 11a). Howe e , o N = 1000 and N = 2000, and o
TP = 1000 s (Figu e 10a), due o he “U” shape o EPB, he la e dec eases wi h packe size only up o a
packe size o ~80 by es and ~40 by es, espec i ely. These packe sizes ep esen h eshold alues ha
mus no be exceeded o he sake o PDR and EPB, since u he inc easing packe size ha ms bo h
pe o mance pa ame e s. Simila beha io occu s o TP = 4000 s and N = 2000 (Figu e 47a), whe e he
h eshold packe size is ~100 by es.
Use o SF12 (Figu e 10b and 47b) leads o signi ican ly lowe PDR han ha achie ed o SF7
(Figu e 46a and 47a), especially o N ³ 1000, whe e PDR app oaches ze o. Excep o N = 100, modi ying
he packe size does no a y he PDR signi ican ly, al hough inc easing packe size (up o 51 by es o
SF12) dec eases EPB.
5.2.4. Mixed CED and UED scena ios
In his subsec ion, we e alua e mixed scena ios wi h NC CEDs, and N – NC UEDs. Ou aim is o
s udy ne wo k pe o mance in scena ios whe e a leas a subse o he EDs (i.e., he UEDs) con ibu e less
a ic load o he ne wo k, since hey do no pe o m e ansmissions.
We analyze wo main cases: NC = 100 and NC =1000, o di e en N alues. Fo all o hem, we
also conside SF7 and SF12, and TP = 4000 s. Figu es 48a and 49a show EPB o NC = 100 and
NC = 1000, espec i ely, o SF7, and o di e en N alues. Fo NC = 100 (Figu e 48a), EPB dec eases
d ama ically wi h packe size, e en o high numbe s o UEDs. In con as , NC = 1000 (Figu e 49a) shows
a di e en beha io , wi h a sligh EPB inc ease o high packe size and high N alues, which p oduces an
“asymme ic U” shape cu e wi h a minimum o a medium packe size alue.
5. Ene gy e iciency-op imal packe size in LoRaWAN
67
The EPB inc ease in Figu e 49a, o high packe sizes, is due o a high collision a io, e en g ea e
han 80% (see Figu e 50a). The la e is due o he high numbe o EDs ( om N = 1000 o
N = 5000) and because a signi ican pa o hem (NC = 1000) use CTM. The g ea e numbe o collisions
inc eases he amoun o e ansmissions pe o med by CEDs. This also causes a ga eway d op a io dec ease
(see Figu e 51a) because a lowe numbe o ACK ames need o be ansmi ed by he NS (due o a lowe
numbe o uplink ames eaching i ).
(a)
(b)
Figu e 47. PDR and EPB o TP = 4000 s: (a) SF7, (b) SF12.
(a)
(b)
Figu e 48. EPB as a unc ion o packe size, o TP = 4000 s, NC = 100 and se e al N alues:
(a) SF7, (b) SF12.

Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
68
(a)
(b)
Figu e 49. EPB as a unc ion o packe size, o TP = 4000 s, NC = 1000 and se e al N alues:
(a) SF7, (b) SF12.
(a)
(b)
Figu e 50. Collision a io in he ga eway o TP = 4000 s, NC = 1000 and se e al N alues: (a) SF7,
(b) SF12.
On he o he hand, o SF7, packe d op a io a EDs is low in all cases (below 10%, see Figu e
52a) due o he ela i ely low load o each ED o a packe ansmission e e y 4000 s, and he low
ansmission imes due o SF7, in ela ion o du y cycle limi a ions.
5. Ene gy e iciency-op imal packe size in LoRaWAN
69
(a)
(b)
Figu e 51. Ga eway d op a io o TP = 4000 s, NC = 1000 and se e al N alues: (a) SF7, (b) SF12.
(a)
(b)
Figu e 52. ED d op a io o TP = 4000 s, NC = 1000 and se e al N alues: (a) SF7, (b) SF12.
When SF12 is used (see Figu es 48b and 49b), he EPB is g ea e han o SF7 as expec ed, due o
he g ea e ansmission ime. Fo NC = 1000, EPB ends o dec ease wi h packe size (Figu e 49b).
Howe e , o NC = 100 and high N alues (i.e., N = 2000), see Figu e 48b, EPB ollows an “asymme ic
U” shape, wi h an op imal packe size ( ha minimizes EPB) o ~40 by es. On he o he hand, EPB dec eases
wi h N, om N = 120 o N = 500, while o g ea e N alues (N ³ 1000), EPB inc eases wi h N
(Figu e 48b). We nex explain he easons o such beha io . Fo he lowe N alues conside ed, as N
inc eases, he collision a io does no a y signi ican ly (Figu e 53b). Howe e , he ED d op a io dec eases
wi h N (Figu e 54b), due o he g ea e numbe o UEDs, which a e less a ec ed by he du y cycle
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
70
es ic ions han CEDs. As a esul , o low N alues, EPB dec eases wi h N. As N inc eases u he
(e.g., N ≥ 500), he collision a io inc eases ema kably, which despi e he ED d op a io dec ease wi h N,
p oduces he obse ed EPB inc ease wi h N o N ≥ 1000.
Fo NC = 1000, we can also highligh ha he ga eway d op a io is simila o he one o SF7
(Figu e 51), mainly due o a e y high collision p obabili y o SF12 (see Figu e 50b), as a esul o i s
g ea e ansmission ime compa ed wi h SF7. This educes he amoun o ACK ames o be ansmi ed
o EDs om he NS, which a e less a ec ed by du y cycle es ic ions a he ga eway. Fo SF12, ED packe
d ops (see Figu e 52b) show g ea e alues han o SF7, due o he g ea e ansmission ime o he o me .
Finally, we ocus on PDR and EPB in he mixed CED and UED scena ios. Fo SF7 and NC = 1000,
since bo h PDR (Figu e 55) and EPB (Figu e 48a) dec ease wi h packe size, a ade-o be ween PDR and
EPB exis s. CEDs ou pe o m UEDs by 10%-20% (see Figu e 55). Fo SF12 and NC = 1000, PDR is e y
low, below 5% in mos cases, o bo h CEDs and UEDs, which illus a es ha he o e ed load signi ican ly
exceeds he ne wo k capaci y o he conside ed scena io in his case (Figu e 56).
Fo NC = 100 (Figu es 57 and 58), he PDR is g ea e han ha achie ed o NC = 1000 (Figu es
55 and 56) in he s udied scena ios, due o he lowe numbe o CEDs. Fo SF7 and NC = 100, CEDs show
a PDR close o 100% o almos all packe sizes conside ed (Figu e 57a). Howe e , UEDs exhibi a PDR
wi h a ema kable dependency on packe size o high N alues (e.g., N > 500), which can all o ~0.6 in
he wo s case (see Figu e 57b).
Fo SF12 and NC = 100, simila PDR is ob ained by bo h CEDs and UEDs o low N alues
(e.g., N < 500), see Figu e 58. Fo N ≥ 500, CEDs ha e a be e PDR by 10%-25% (Figu e 58). Since o
SF12 and high N alues EPB ollows an “asymme ic U” shape (Figu e 48b), a packe size g ea e han he
EPB-op imal one (i.e., ~40 by es o N = 2000) should no be exceeded, as PDR dec eases wi h packe size.
(a)
(b)
Figu e 53. Collision a io o TP = 4000 s, NC = 100 and se e al N alues: (a) SF7, (b) SF12.
5. Ene gy e iciency-op imal packe size in LoRaWAN
71
(a)
(b)
Figu e 54. ED d op a io o TP = 4000 s, NC = 100 and se e al N alues: (a) SF7, (b) SF12.
(a)
(b)
Figu e 55. PDR o TP = 4000, NC = 1000 and se e al N alues, and SF7: (a) CEDs, (b) UEDs.
Con ibu ions o he E alua ion and Imp o emen o LoRaWAN
78
6.2.1. Ex ending he ene gy consump ion empi ical analysis o o he LoRaWAN
ED ha dwa e pla o ms and ne wo k beha io s
In he las yea s, he a ie y o a ailable LoRaWAN ED ha dwa e pla o ms has inc eased, wi h
imp o ed cha ac e is ics in e ms o ene gy consump ion and ansmission e iciency. We p opose o ex end
he ene gy consump ion empi ical analysis o o he popula LoRaWAN ED pla o ms in he ma ke , in
o de o cha ac e ize each model and p oduce an a e age model, in ended o be mo e gene al and
ep esen a i e. On he o he hand, he e exis LoRaWAN ne wo ks which use pa ame e se ings di e en
om he adi ionally ypical ones (e.g., TTN ne wo ks cu en ly use RECEIVE_DELAY1 and
RECEIVE_DELAY2 o 5 and 6 seconds, espec i ely [90]).
6.2.2. Conside ing a g ea e se o ansmission channels
The numbe o ansmission channels can be a key pa ame e in he pe o mance o LoRaWAN in
e ms o ene gy modelling, SF12 Well beha io o in ene gy e iciency e sus packe size. We p opose o
ex end ou s udy o 8 channels and beyond, as he majo i y o nowadays LoRaWAN EDs and ga eways can
wo k wi h, a leas , 8 channels.
6.2.3. Analyzing he beha io o SF12 Well in a channel wi h losses
In Chap e 4 we analyzed he SF12 Well phenomenon in a con olled channel wi h no e o s o
losses. In hose condi ions, he SF12 Well is ela ed o a conges ion si ua ion. Howe e , conside ing mo e
ealis ic channel condi ions, we p opose o e alua e he in luence o non-ze o loss a e o e he SF12 Well,
and how o balance i wi h PDR.
6.2.4. Conside ing new s a egies o imp o ing EPB e iciency
In Chap e 4 we conside ed some basic s a egies in ended o ace he SF12 Well p oblem. The
s a egies we e based on how SF is used and how he e ansmission mechanism is applied. We p opose o
explo e some al e na i es ha can balance complexi y and ene gy e iciency imp o emen . The al e na i es
consis on he use o a limi ed numbe o SFs ( o example, he 2 o 3 lowes SF alues), applied o he
h ee SFM p oposed me hods. We expec ha he collision a io will dec ease enough o o e come he
ene gy cos penal y due o ToA inc ease.
6.2.5. Imp o ing PHY laye implemen a ion in AFLoRa
The s udy done in Chap e s 4 and 5 is based on simula ions using he AFLoRa amewo k, o e he
OMNeT++ pla o m simula o . The AFLoRa amewo k is buil wi h a wi eless module comp ising a
physical laye ha applies a gene al beha io in e ms o collision condi ion de e mina ion. We p opose o
imp o e he simula o wi h a mo e accu a e physical laye implemen a ion, aking in o accoun he
echniques used in eal ED pla o ms in o de o de e mine whe he a packe has been ecei ed o no .

Con ibu ions
The main con ibu ions o he p esen PhD hesis can be summa ized in he ollowing publica ions.
Published jou nal pape s:
1. L. Casals, B. Mi , R. Vidal, and C. Gomez, “Modeling he Ene gy Pe o mance o
LoRaWAN,” Senso s, ol. 17, no. 10, p. 2364, Oc . 2017, doi: 10.3390/s17102364. A ailable
online: h p://dx.doi.o g/10.3390/s17102364.
2. L. Casals, C. Gomez, and R. Vidal, “The SF12 Well in LoRaWAN: P oblem and End-De ice-
Based Solu ions,” Senso s, ol. 21, no. 19, p. 6478, Sep. 2021, doi: 10.3390/s21196478.
A ailable online: h p://dx.doi.o g/10.3390/s21196478.
Submi ed jou nal pape s:
1. L. Casals, C. Gomez, and R. Vidal, “Unde s anding he Impac o Packe Size on he Ene gy
E iciency o LoRaWAN”, Jou nal o Communica ions and Ne wo ks, submi ed: 2-3-2023.
O he con ibu ions om he p esen PhD hesis a e he ollowing imp o emen s o FLoRa
simula o (so ed by elease da e):
1. AFLoRa 0.9, Ad anced F amewo k o LoRaWAN ( 0.9). A ailable on Gi hub:
h ps://gi hub.com/lluiscas/AFLoRa, 2021 (accessed on 30 Decembe 2022).
2. AFLoRa 1.0, Ad anced F amewo k o LoRaWAN 1.0. A ailable on Gi hub:
h ps://gi hub.com/lluiscas/AFLoRa- 1, 2022 (accessed on 30 Decembe 2022).
Re e ences
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