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Simul aneous ha es -and- ansmi ambien backsca e communica ions unde
Rayleigh ading
© The Au ho (s) 2019
Published e sion
Jameel, Fu qan; Ris aniemi, Tapani; Khan, Im an; Lee, Byong Moo
Jameel, F., Ris aniemi, T., Khan, I., & Lee, B. M. (2019). Simul aneous ha es -and- ansmi
ambien backsca e communica ions unde Rayleigh ading. EURASIP Jou nal on Wi eless
Communica ions and Ne wo king, 2019, A icle 166. h ps://doi.o g/10.1186/s13638-019-1480-
7
2019
Jameel e al. EURASIP Jou nal on Wi eless Communica ions and
Ne wo king (2019) 2019:166
h ps://doi.o g/10.1186/s13638-019-1480-7
RESEARCH Open Access
Simul aneous ha es -and- ansmi
ambien backsca e communica ions unde
Rayleigh ading
Fu qan Jameel1, Tapani Ris aniemi1, Im an Khan2and Byung Moo Lee3*
Abs ac
Ambien backsca e communica ions is an eme ging pa adigm and a key enable o pe asi e connec i i y o
low-powe ed wi eless de ices. I is p ima ily bene icial in he In e ne o hings (IoT) and he si ua ions whe e
compu ing and connec i i y capabili ies expand o senso s and minia u e de ices ha exchange da a on a low powe
budge . The p emise o he ambien backsca e communica ion is o build a ne wo k o de ices capable o ope a ing
in a ba e y- ee manne by means o sma ne wo king, adio equency (RF) ene gy ha es ing, and powe
managemen a he g anula i y o indi idual bi s and ins uc ions. Due o his inno a ion in communica ion me hods,
i is essen ial o in es iga e he pe o mance o hese de ices unde p ac ical cons ain s. To do so, his a icle
o mula es a model o wi eless-powe ed ambien backsca e de ices and de i es a closed- o m exp ession o ou age
p obabili y unde Rayleigh ading. Based on his exp ession, he a icle p o ides he powe -spli ing ac o ha
balances he adeo be ween ene gy ha es ing and achie able da a a e. Ou esul s also shed ligh on he complex
in e play o a powe -spli ing ac o , amoun o ha es ed ene gy, and he achie able da a a es.
Keywo ds: Ambien backsca e communica ions, Ene gy ha es ing, In e ne o hings (IoT), Sma ne wo king,
Wi eless-powe ed communica ions
1 In oduc ion
The g and ision o he In e ne o hings (IoT) is quickly
u ning in o eali y by b inging e e y hing o he In e -
ne [1,2]. La es de ices anging om sma phones o
implan able senso s and wea ables a e claiming o be “IoT
capable”. Al hough signi ican imp o emen s ha e been
seen om he design pe spec i e o wi eless de ices, he
objec i e o connec ing e e y hing o he In e ne is s ill
a a c y[3]. I is because se e al impo an challenges
a ise when ensu ing ubiqui ous connec i i y o de ices.
As indica ed in [4], one o he i s challenge is he lim-
i ed li e-cycle o minia u e wi eless de ices. The ene gy
cons ained na u e o de ices becomes an obs acle as he
massi e amoun o da a is ans e ed ac oss an IoT ne -
wo k and he de ices a e equi ed o be ope a ed in an
un e he ed manne . Due o which, he ene gy cons ained
na u e o de ices becomes an obs acle. Then, he e is a
*Co espondence: [email p o ec ed]
3Sejong Uni e si y, Seoul, Sou h Ko ea
Full lis o au ho in o ma ion is a ailable a he end o he a icle
equi emen o communica ion eliabili y which is e en
mo e di icul o main ain in la ge-scale wi eless sys ems
[5]. The inc eased eliabili y mos o en comes a a cos
o inc eased ene gy consump ion which canno be egu-
la ed by small ene gy ese oi s o minia u e IoT de ices.
Abo e all, hese de ices would need o demons a e
se ices like ul a- eliable low-la ency communica ions
(URLLC), enhanced mobile b oadband (eMBB), and mas-
si e machine ype communica ions (mMTC) o beyond
5G ne wo ks. Resul an ly, i has become e iden ha an
ul a low-powe ed communica ion pa adigm is essen ial
o enabling sho - ange communica ion among de ices,
wi hou comp omising he eliabili y o communica ions
[2,6].
O la e, backsca e communica ion has ga he ed he
a en ion o he esea che s as a key enabling echnology
o connec ing IoT de ices. Backsca e communica ion
allows adio de ice o ansmi hei da a by e lec ing
and modula ing an inciden adio equency (RF) signal.
I adap s he an enna impedance misma ch in o de o
© The Au ho (s). 2019 Open Access This a icle is dis ibu ed unde he e ms o he C ea i e Commons A ibu ion 4.0
In e na ional License (h p://c ea i ecommons.o g/licenses/by/4.0/), which pe mi s un es ic ed use, dis ibu ion, and
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Jameel e al. EURASIP Jou nal on Wi eless Communica ions and Ne wo king (2019) 2019:166 Page 2 o 9
change he e lec ion coe icien . Using he ecei ed RF
ene gy, backsca e de ices ha es a ac ion o ene gy
o ci cui ope a ions [7]. I is wo h highligh ing ha he
backsca e de ices do no equi e oscilla o s o gene a -
ing ca ie signals as hey ge he ca ie wa es om he
dedica ed RF sou ce. In ac , he ul a-low powe na u e
o a backsca e ansmi e (i.e., below 1 mW [8]) shows
p omise o a e y long li e cycle (i.e., 10 yea s) wi h an on-
chip ba e y. Since he ha es ed ene gy om an RF sou ce
ypically anges om 1 mW o 10s o mW, he low powe
consump ion o backsca e de ices is a pe ec ma ch o
RF ene gy ha es ing [9].
Besides he ob ious ad an ages o con en ional
backsca e communica ions, he e a e ew limi a ions
o hese de ices. The backsca e de ices equi e a dedi-
ca ed RF sou ce o ansmission o ca ie wa es. E en
hough his model has been adop ed in adio equency
iden i ica ion (RFID) ags used in lib a ies and g oce y
s o es, he powe budge o hese communica ion models
may no be sui able o ene gy-cons ained IoT de ices
[6,10]. Addi ionally, he cen alized na u e o hese com-
munica ion models is also a hu dle in pa ing he way o
la ge-scale deploymen o IoT ne wo ks. The dis ibu ed
a chi ec u e o IoT ne wo ks a o s he deploymen o
decen alized RF sou ces ha can be accessed any ime.
Besides his, ene gy ha es ing h ough wi eless powe
ansmission can ex end he li e cycle o he IoT ne -
wo ks wi h li le changes in ha dwa e implemen a ions
[11,12].
To o e come he abo emen ioned limi a ions, a new
backsca e pa adigm has eme ged ha is called ambien
backsca e communica ion [13]. An ambien backsca -
e ansmi e uses ambien RF signals in o de o
pe o m in a ba e y- ee manne . Mo e speci ically,
he ambien RF signals a e used o backsca e ing
and ene gy ha es ing. This lexibili y allows he cos -
e ec i e deploymen o ambien backsca e de ices while
a oiding dependence on a pa icula RF sou ce [14].
Howe e , owing o he no el y o he echnology, he
s udy o ambien backsca e communica ions is s ill
a i s nascen s age. A a ie y o ne wo k challenges
and da a communica ion issues a ise ha equi e u -
he explo a ion. Fu he mo e, limi ed heo e ical knowl-
edge o ambien backsca e communica ion demands
new dimensions o pe o mance e alua ion o he
ne wo k.
Mo i a ed by he a o emen ioned obse a ions, we
pe o m he analysis o backsca e communica ion
unde Rayleigh ading. Speci ically, ou con ibu ion is
wo old:
– De i a ion o closed- o m exp ession o ou age
p obabili y o wi eless-powe ed de ices ope a ing
unde Rayleigh ading.
– De i a ion o he powe -spli ing ac o ha balances
he adeo be ween ene gy ha es ing and
achie able da a a e.
The emainde o he pape is o ganized as ol-
lows. Sec ion 2discusses he ela ed wo k on con en-
ional backsca e and ambien backsca e communica-
ions. In Sec ion 3, a de ailed desc ip ion o he sys-
em model is p o ided. Sec ion 4p o ides he pe o -
mance analysis while Sec ion 5discusses he nume i-
cal esul s. Finally, Sec ion 6p o ides key indings and
conclusions.
2 Rela ed wo k
Backsca e communica ion has been conside ed om
di e en aspec s in wi eless ne wo ks [15]. The au ho s
o [16] employed backsca e communica ion o enable
de ice- o-de ice communica ions. Besides his, se e al
de ec ion schemes o backsca e communica ion sys-
ems a e p oposed in [17–19]. A de ec o ha does no
equi e he channel s a e in o ma ion (CSI) was con-
s uc ed using a di e en ial encode in [18]. Speci ically,
hey de eloped a model and de i ed op imal de ec ion
and minimum bi -e o - a e (BER) h esholds. Mo eo e ,
he exp essions o lowe and uppe bounds on BER we e
also de i ed ha we e co obo a ed h ough simula ion
esul s. A join -ene gy de ec ion scheme is p oposed in
[19] ha equi es only channel a iances a he han spe-
ci ic CSI. The same au ho s p o ided a s udy o BER com-
pu a ion, op imal and subop imal de ec ion, and blind
pa ame e acquisi ion. The non-cohe en signal de ec ion
ou pe o med he con en ional echniques in e ms o
de ec ion accu acy and compu a ion complexi y. A suc-
cessi e in e e ence cancella ion (SIC)-based de ec o and
a maximum-likelihood (ML) de ec o wi h known CSI a e
p esen ed in [17], o eco e signals no only om ead-
e s bu also om RF sou ces. In addi ion o his, he
au ho s de i ed BER exp essions o he ML de ec o . I
was shown ha he backsca e signal can signi ican ly
enhance he pe o mance o he ML de ec o as compa ed
o con en ional single-inpu -mul iple-ou pu (SIMO)
sys ems.
Capaci y and ou age pe o mance analysis o ambi-
en backsca e communica ion sys ems was s udied in
[20–23]. The au ho s o [20] analyzed he channel capaci y
o e o hogonal equency di ision mul iplexing (OFDM)
signals. The e godic capaci y op imiza ion p oblem a he
eade wi h SIC was in es iga ed by he au ho s o [21].
Speci ically, he au ho s join ly conside ed he ansmi
sou ce powe and he e lec ion coe icien and imp o ed
he e godic capaci y. Fo ambien backsca e communi-
ca ion sys ems, he BER o an ene gy de ec o was de i ed
and he BER-based ou age p obabili y was ob ained in
[22]. In [23], he e ec i e dis ibu ion o signal- o-noise
Jameel e al. EURASIP Jou nal on Wi eless Communica ions and Ne wo king (2019) 2019:166 Page 3 o 9
a io (SNR) was de i ed and he SNR-based ou age p ob-
abili y was e alua ed o e eal Gaussian channels.
Mo e ecen ly, he au ho s in [24]in es iga edacog-
ni i e adio ne wo k ha ing ambien backsca e commu-
nica ion. In pa icula , i was conside ed ha a wi eless-
powe ed seconda y use can ei he ha es ene gy o
adop ambien backsca e ing om a p ima y use on
ansmission. A ime alloca ion p oblem was de eloped in
o de o maximize he h oughpu o he seconda y use
and o ob ain he op imal ime a io be ween ene gy ha -
es ing and ambien backsca e ing. Re e ence [25]in o-
duced a hyb id backsca e communica ion scheme as an
al e na i e access scheme o a wi eless-powe ed ans-
mi e . Speci ically, when he ambien RF signals we e no
su icien o suppo wi eless-powe ed communica ions,
he ansmi e can choose be ween bis a ic backsca e -
ing o ambien backsca e ing based on a dedica ed ca ie
emi e . A h oughpu maximiza ion p oblem was o mu-
la ed o ind he op imal ime alloca ion o he hyb id
backsca e communica ion ope a ion. Bo h [24]and[25]
s udied a de e minis ic scena ios.
3 Expe imen al sys em model design
Le us conside an IoT ne wo k ha consis s o Nnumbe
o ambien backsca e de ices. These ambien backsca -
e de ices a e conside ed o be powe ed by ambien RF
sou ce. This conside a ion is unde he assump ion ha
ambien RF sou ces (like adio signals, TV signals, and
WiFi signals) a e abundan in he en i onmen . These
backsca e de ices use he ha es ed ene gy om he
ambien RF signals and ansmi hei da a o he ga eway
asshowninFig.1.
Acco ding o [6], a ypical ambien backsca e de ice
has h ee majo ope a ions, i.e., spec um sensing, ene gy
ha es ing, and da a exchange. The ci cui model o
an ambien backsca e de ice is shown in Fig. 2.The
main pu pose o he spec um senso is o de ec sui -
able ambien RF signals, whe eas he ene gy ha es ing
ci cui enables he backsca e de ices o ope a e a sel -
sus ainable manne . This sel -sus ainabili y is essen ial o
IoT ne wo ks as hey a e expec ed o ope a e wi h mini-
mum human in e en ion. When he de ice is in ope a-
ion mode, he spec um sensing is pe o med in o de o
de ec RF signal wi h la ge powe . A e wa d, he de ec ed
signal is employed o ei he backsca e communica-
ion o ene gy ha es ing. The analog- o-digi al con e e
(ADC) uses he ha es ed ene gy and con e s i in o
di ec cu en ha is u ilized by o he modules including
a mic ocon olle . The mic ocon olle pe o ms mul iple
communica ion ope a ion including p ocessing he in o -
ma ion and ma ching he impedance o an enna o be e
ecep ion o RF signals. We conside ha he amoun o
ene gy consumed by ene gy ha es e is negligible [6]and
sa is ies he ollowing condi ion
Eh≥Eb+Es+Em.(1)
In he abo e exp ession Eh,Eb,Es,Emdeno es he ha -
es ed ene gy, ene gy consumed o backsca e commu-
nica ion, ene gy consumed o spec um sensing, and he
ene gy consumed by mic o-con olle / senso o da a
Fig. 1 Sys em model
Jameel e al. EURASIP Jou nal on Wi eless Communica ions and Ne wo king (2019) 2019:166 Page 4 o 9
Fig. 2 Ci cui design o he ambien backsca e de ice
ga he and p ocessing. Some o he key symbols used
h oughou his pape a e p o ided in Table 1.
We now cha ac e ize he ene gies ha es ed and con-
sumed du ing one ime slo . We conside ha comp essi e
sensing is pe o med in each ime slo . Thus, he ime slo
Tis di ided in o phases, i.e., comp essi e sensing du a-
ion (deno ed as α) and ene gy ha es ing/backsca e ing
du a ion (deno ed as (1 −α)). A e comp essi e sens-
ing, he ecei ed signal a he de ice is di ided in o wo
Table 1 Common symbols used in he a icle
Symbol De ini ion
EhHa es ed ene gy
EbEne gy consumed o backsca e communica ion
EsEne gy consumed o spec um sensing
EmEne gy consumed by mic o-con olle / senso
αComp essi e sensing du a ion
ρPowe -spli ing ac o
βRe lec ion coe icien o he backsca e de ices
θPa h loss exponen
N0AWGN a iance
ηEne gy con e sion e iciency
MNumbe o wideband signals
eEne gy consumed o each sample
ϕTh eshold o equi ed da a a e
ψEne gy h eshold o ope a ion o he backsca e de ice
Sampling a e
PbAmoun o ci cui powe consumed du ing backsca e ing
s eams o powe . The i s pa is used o ene gy ha es -
ing while he o he pa is used o pe o ming backsca -
e ing ope a ion. This sepa a ion is pe o med wi h a
ac o ρ,whe e0<ρ≤1. A g aphical ep esen a ion o
an in e play o ρand αis p o ided in Fig. 3. Assuming ha
an i- h backsca e de ice de ec s an ambien RF, hen he
ecei ed signal a he de ice is gi en as
yi,1 =βP
Pl,1
hi,1s1+ni,1,(2)
whe e yi,1 is he ecei ed signal, s1deno es he no mal-
ized signal, P ep esen s he ansmi powe , and Pl,1 =
dθ
1is he pa h loss expe ienced by he backsca e de ice
and θis he pa h loss exponen . Fu he mo e, hi,1 ep-
esen s he channel gain be ween he ambien RF sou ce
and backsca e de ice which is assumed o be Rayleigh
aded, ni,1 is he ze o mean addi i e whi e Gaussian noise
(AWGN) wi h N0 a iance while βis he e lec ion coe -
icien o he backsca e de ices. The ha es ed ene gy is
hen deno ed as
Eh,i=ρη(1−α)Tβ1|hi,1|2
Pl,1
,(3)
whe e 1=P
N0,ρ ep esen s he ac ion o powe used
o ene gy ha es ing, and ηis he ene gy con e sion e i-
ciency ha is conside ed o be same o all he backsca e
de ices as hey employ same ci cui y.
The amoun o ene gy consumed by he comp essi e
sensing module is a linea mul iplica ion o he numbe
o samples and sampling a e. Mo e speci ically, i can be
ep esen ed as
Es=α MeT,(4)

Jameel e al. EURASIP Jou nal on Wi eless Communica ions and Ne wo king (2019) 2019:166 Page 5 o 9
Fig. 3 Time schedule and powe spli ing
whe e Mis he numbe o wideband signals ha ha e
been de ec ed du ing he phase o spec um sensing, is
he sampling a e, and eis he ene gy consumed o each
sample.
The amoun o ene gy consumed he backsca e ing
module can be ep esen ed in e ms o ci cui powe as
Eb=(1−α)PbT,(5)
whe e Pbis he amoun o ci cui powe consumed du -
ing backsca e ing phase. Fo he sake o simplici y and
wi hou loss o gene ali y, we conside ha he powe
consumed by mic o-con olle is ixed.
As a esul o backsca e ing, he ecei ed message a he
ga eway can be w i en as:
yi,2 =(1−ρ)βPb
Pl,2
hi,2si,2 +ni,2,(6)
whe e yi,2 is he ecei ed signal a he ga eway, si,2 deno es
he no malized signal sen by he i- h backsca e ing
de ice, P ep esen s he ansmi powe , and Pl,2 =dθ
2is
he pa h loss be ween backsca e de ice and he ga eway.
Fu he mo e, hi,2 ep esen s he Rayleigh aded channel
gain be ween he backsca e de ice and he ga eway and
ni,2 is he ze o mean AWGN wi h ze o mean and N0
a iance.
4 Pe o mance analysis and me hodology
In his sec ion, we de i e he communica ion ou age and
powe sho age p obabili ies o he backsca e de ices.
Based on hese p obabili ies, we aim o ind he balancing
alue o he ρ.
4.1 Ou age pe o mance
Using he Shannon capaci y o mula, he achie able sum
a e a he ga eway can be w i en as:
Rsum =
N

i=1
Ri,(7)
whe e Riis he achie able a e o i- h backsca e ing
de ice which is gi en as:
Ri=(1−α)BT log21+(1−ρ)β2|hi,2|2
Pl,2 ,(8)
whe e 2=Pb
N0.
Conside ing he independence o channels, he like-
lihood o an ou age e en depends on ollowing wo
condi ions:
1. I he ha es ed ene gy is below he ene gy equi ed
o ope a ions o backsca e de ice.
2. I he achie able a e is below he equi ed a e a he
ga eway.
Thus, using he o al p obabili y heo em, he ou age
p obabili y can be w i en as:
Pou =P (Ri<ϕ|Eh,i<ψ)P (Eh,i<ψ)
+P (Ri<ϕ|Eh,i>ψ)P (Eh,i>ψ),(9)
whe e ϕ ep esen s he h eshold o equi ed da a a e and
ψ=Eb+Es+Emis he ene gy h eshold o ope a ion o
he backsca e de ice.
F om he abo e equa ion, we no e ha i he ha es ed
ene gy is below he h eshold, hen he backsca e de ice
wouldno beable o ans e anyda a o hega eway.
In his case, he p obabili y ha he a e alls below a
equi ed h eshold would always be 1. Thus, we can w i e:
P (Ri<ϕ|Eh,i<ψ)=1. (10)
The p obabili y ha he ha es ed ene gy would all
below a speci ied h eshold can be w i en as:
P (Eh,i<ψ)=P ρη(1−α)Tβ1|hi,1|2
Pl,1
<ψ
. (11)
Jameel e al. EURASIP Jou nal on Wi eless Communica ions and Ne wo king (2019) 2019:166 Page 6 o 9
A e some simpli ica ions, i can be ep esen ed as:
P (Eh,i<ψ)=P |hi,1|2<Pl,1ψ
ρη(1−α)Tβ1
=1−exp −Pl,1ψ
¯γ1ρη(1−α)Tβ1.
(12)
In con as , he p obabili y o ene gy ha es ing inc eas-
ing beyond he h eshold can be ep esen ed as:
P (Eh,i>ψ)=exp −Pl,1ψ
¯γ1ρη(1−α)Tβ1, (13)
whe e ¯γ1is he a e age channel gain be ween RF sou ce
and he backsca e ing de ice. Le us now conside he
case when he ha es ed ene gy is g ea e han ψ.In his
case, he p obabili y ha he achie able da a a e alls
below a p e-de e mined h eshold can be w i en as:
P (Ri<ϕ|Eh,i>ψ)=P (1−α)BT
×log21+(1−ρ)β2|hi,2|2
Pl,2 <ϕ|Eh,i>ψ
.
(14)
A e some s aigh o wa d simpli ica ions, we ob ain:
P (Ri<ϕ|Eh,i>ψ)=P ⎛
⎝|hi,2|2<
Pl,2 2
ϕ
(1−α)BT −1
(1−ρ)β2⎞
⎠
=1−exp ⎧
⎨
⎩
−
Pl,2 2
ϕ
(1−α)BT −1
¯γ2(1−ρ)β2⎫
⎬
⎭
,
(15)
whe e ¯γ2is he a e age channel gain be ween backsca e -
ing de ice and he ga eway. Subs i u ing he Eqs. (10), (12),
(13), and (15)in(9), we ob ain:
Pou =1−exp −Pl,1ψ
¯γ1ρη(1−α)Tβ1
+exp −Pl,1ψ
¯γ1ρη(1−α)Tβ1
×⎡
⎣1−exp ⎧
⎨
⎩
−
Pl,2 2
ϕ
(1−α)BT −1
¯γ2(1−ρ)β2⎫
⎬
⎭⎤
⎦.
(16)
A e sol ing 16,weha e:
Pou =1−exp ⎛
⎜
⎜
⎝
−
Pl,2 2
ϕ
(1−α)BT −1
¯γ2(1−ρ)β2
−Pl,1ψ
¯γ1ρη(1−α)Tβ1⎞
⎟
⎟
⎠
.(17)
4.2 Balancing communica ion ou age and powe
sho age
In his sec ion, we aim o ind he alues o ρ ha balances
he adeo be ween communica ion ou age and powe
sho age. In pa icula , we no e ha di e en alues o
ρha e a di e en impac on communica ion ou age and
powe sho age. F om (3), we can obse e ha he amoun
o ene gy ha es ed is he inc easing unc ion o ρ.In
o he wo ds, as he alue o ρinc eases, he amoun o
ha es ed ene gy also inc eases, whe eas i dec eases wi h
a dec ease in he alue o ρ. In con as , he achie able
a e o any i- h backsca e ing de ice is a dec easing unc-
ion o ρ. Since he achie able a e is dependen on he
ecei ed SNR, he e o e, inc easing he alue o ρ esul s
in inc easing he SNR while a educ ion in ρcauses an
inc ease in he alues o SNR which in u n inc eases he
achie able a e.
F om he abo e a gumen s, we can obse e ha he
balancing alue o ρcan be ound by sol ing he ene gy
ha es ing and SNR exp essions simul aneously. Thus, we
can w i e:
ρη(1−α)Tβ1|hi,1|2
Pl,1
=(1−ρ)β2|hi,2|2
Pl,2
. (18)
A e c oss mul iplica ion and aking leas common
mul iple, we ob ain he ρ∗as:
ρ∗=|hi,2|22Pl,1
|hi,2|22Pl,1 +η(1−α)Tβ1|hi,1|2Pl,2
. (19)
F om he abo e exp ession, we can obse e ha ρ∗is
in e sely p opo ional o he 1.Mo eo e ,i Pl,1 =Pl,2,
hen he balancing alue o ρ∗ishal ed.Wealsono e ha
he alue o ρ∗inc eases wi h an inc ease in αindica ing
he di ec ela ionship be ween ρ∗and α.
5 Resul s and discussions
In his sec ion, we p o ide esul s and ele an discussion
on he abo emen ioned analysis. Unless men ioned o he -
wise, ollowing pa ame e s ha e been used o gene a ing
Fig. 4 Ou age p obabili y as a unc ion o SNR
Jameel e al. EURASIP Jou nal on Wi eless Communica ions and Ne wo king (2019) 2019:166 Page 7 o 9
simula ion and analy ical esul s: η=0.5, B=1MHz,
β=0.5, d1=d2=5m, ϕ=2kbps, θ=2, and ρ=0.3.
Figu e 4illus a es he ou age p obabili y as a unc-
ion o inc easing alues o SNR. I can be seen ha
he ou age p obabili y dec eases wi h an inc ease in
he SNR. Howe e , he impac o αon Pou is di e -
en o di e en alues o SNR. Speci ically, we obse e
ha an inc ease in he α esul sinaninc easein he
ou age p obabili y. I is because wi h an inc ease in α
which p o ides mo e ime o comp essi e sensing and
less ime o ene gy ha es ing and backsca e ing. On
he o he hand, an inc ease in ρcauses an inc ease in
ou age p obabili y. This esul is caused by alloca ing
mo e ac ion o ecei ed powe o ene gy ha es ing
and less o pe o ming backsca e communica ions. In
addi ion, he simula ion esul s closely ollow he analy -
ical cu es which indica es he alidi y o ou heo e ical
model.
(a)
(b)
Fig. 5 Achie able a e agains di e en alues o αwhe e (a)
d1=d2=5m, (b)d1=d2=10m
Figu e 5a shows he achie able a e as a unc ion o
inc eased SNR. As an icipa ed by he analy ical exp es-
sion, he inc ease in SNR imp o es he achie able a e.
Howe e , an inc ease in αdec eases he achie able a e. In
ac , he impac o αbecomes mo e p ominen a highe
alues o SNR showing a apid ise in he cu es. Whe e
Fig. 5aisplo ed o d1=d2=5m, he cu es o Fig. 5b
a e plo ed agains d1=d2=10m. This inc ease in
dis ance has a c i ical impac on he achie able a e. In
pa icula , o he same alues o SNR and α(e.g., SNR=0
dB and α=0.1), he achie able a e d ops om 20 kbps o
5 kbps when he dis ance is inc eased.
Figu e 6plo s he ha es ed ene gy agains inc easing
alues o d1. Indeed, hese esul s highligh he signi i-
canceo dis ancebe ween heRFsou ceand hebacksca -
e de ice. I can be seen ha an inc ease in d1 esul s in
dec easing he ha es ed ene gy. Addi ionally, he inc eas-
ing alues o αdec ease he ha es ed amoun o ene gy
due o comp essi e sensing. This dec ease in ha es ed
ene gy, agains di e en alues o α,islessp ominen
when 1=5 dB. This indica es ha he ime scheduling is
mo e e ec i e o la ge ansmi powe o he ambien RF
sou ce. Fu he mo e, his inc ease in 1allows de ices o
ha es powe up o a signi ican ly la ge dis ance which
in luences he li e-cycle o de ices.
Figu e 7a demons a es he adeo be ween ha es ed
ene gy and achie able a e. We ha e plo ed di e en
cu es o achie able a e and ha es ed ene gy agains he
inc easing alues o ρ. I can be obse ed ha an inc ease
in ρcauses an inc ease in he amoun o ha es ed ene gy
while simul aneously educing he achie able a e. Since
he alue o αin luences bo h a e and ha es ed ene gy,
he lowe alues o αdec eases he con e ging poin o
he cu es o a e and ene gy cu es. Simila ends can
beshowninFig.7b; howe e , he con e ging poin o he
Fig. 6 Ha es ed ene gy agains inc easing alues o d1
Jameel e al. EURASIP Jou nal on Wi eless Communica ions and Ne wo king (2019) 2019:166 Page 8 o 9
(a)
(b)
Fig. 7 Achie able a e and ha es ed ene gy e sus inc easing alues
o ρ,whe eη=0.3 and (a)d1=d2=5m, (b)d1=d2=10m
cu es now shi s owa ds he igh -hand side while educ-
ing bo h he ha es ed ene gy and a e. This end can be
a ibu ed o he inc ease in d1and d2. This shi in balanc-
ing poin shows ha a highe alue o ρis equi ed wi h
an inc ease in dis ance. This also indica es ha ene gy
ha es ing becomes a c i ical ac o when he dis ance is
inc eased be ween ambien RF sou ce and he de ice and
ha be ween de ice and ga eway.
6Conclusion
Ambien backsca e communica ions p o ide i ually
endless oppo uni ies o connec wi eless de ices. We
an icipa e ha wea able de ices, connec ed homes, indus-
ial In e ne , and minia u e embeddable a e some o he
a eas whe e ambien backsca e communica ions would
be adap ed o p o ide pe asi e connec i i y. Thus, o be -
e analyze he u ili y o hese low-powe ed de ices, his
a icle has p o ided a comp ehensi e analysis o ambien
backsca e ing model om he pe spec i e o achie able
da a a es and he amoun o ha es ed ene gy. In addi ion
o de i ing closed- o m exp essions o ou age p obabil-
i y and balancing powe -spli ing ac o , we ha e shown
ha he dis ance be ween ambien RF sou ce and he
de ice plays a c i ical ole in de e mining he li e-cycle o
de ices and he ou age p obabili y a he ga eway. In ac ,
we ha e demons a ed ha an inc ease in dis ance shi s
he balancing powe -spli ing poin o he igh -hand side.
Besides his, we ha e obse ed ha when he dis ance is
inc eased om 5 m o 10 m agains ixed alues o SNR
and α, he achie able a e a ga eway d ops om 20 o
5 kbps. These esul s can ac as a undamen al building
block o designing and la ge-scale deploymen o ambien
backsca e de ices in he u u e.
Abb e ia ions
ADC: Analog- o-digi al con e e ; BER: Bi -e o - a e; CSI: Channel s a e
in o ma ion; IoT: In e ne o hings; ML: Maximum-likelihood; OFDMA:
O hogonal equency di ision mul iplexing; SIC: Successi e in e e ence
cancella ion; SIMO: Single-inpu -mul iple-ou pu ; SNR: Signal- o-noise a io
Au ho s’ con ibu ions
FJ con ibu ed o he concep ion and de elopmen o he analy ical model o
he s udy. FJ, TR, IK, and BML con ibu ed o he acquisi ion o simula ion
esul s. All au ho s ead and app o ed he inal manusc ip .
Funding
This wo k was suppo ed by Basic Science Resea ch P og am h ough he
Na ional Resea ch Founda ion o Ko ea (NRF) unded by he Minis y o
Educa ion (g an numbe : NRF-2017R1D1A1B03028350).
A ailabili y o da a and ma e ials
Da a sha ing is no applicable o his a icle as no da a se s we e gene a ed o
analyzed du ing he cu en s udy.
Compe ing in e es s
The au ho s decla e ha hey ha e no compe ing in e es s.
Au ho de ails
1Uni e si y o Jy äskylä, Jy äskylä, Finland. 2Uni e si y o Enginee ing and
Technology, Peshawa , Pakis an. 3Sejong Uni e si y, Seoul, Sou h Ko ea.
Recei ed: 1 Decembe 2018 Accep ed: 29 May 2019
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