Simultaneous harvest-and-transmit ambient backscatter communications under Rayleigh fading

This is a sel -a chi ed e sion o an o iginal a icle. This e sion may di e om he o iginal in pagina ion and ypog aphic de ails. Au ho (s): Ti le: Yea : Ve sion: Copy igh : Righ s: Righ s u l: Please ci e he o iginal e sion: CC BY 4.0 h ps://c ea i ecommons.o g/licenses/by/4.0/ 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 ep oduc ion in any medium, p o ided you gi e app op ia e c edi o he o iginal au ho (s) and he sou ce, p o ide a link o he C ea i e Commons license, and indica e i changes we e made. 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 Re e ences 1. E. Siow, T. Ti opanis, W. Hall, Analy ics o he In e ne o hings: A su ey. ACM Compu . Su . (CSUR). 51(4), 74 (2018) 2. P. Kamalinejad, C. Mahapa a, Z. Sheng, S. Mi abbasi, V. C. Leung, Y. L. Guan, Wi eless ene gy ha es ing o he In e ne o hings. IEEE Commun. Mag. 53(6), 102–108 (2015) 3. F. Jameel, S. Kuma , Z. Chang, T. Hamalainan, T. Ris aniemi, in 2018 IEEE Con e ence on S anda ds o Communica ions and Ne wo king (CSCN). Ope a o e enue analysis o de ice- o-de ice communica ions o e laying cellula ne wo k, (2018), pp. 1–6. h ps://doi.o g/10.1109/ CSCN.2018.8581856 4. D. Muni , S. T. Shah, K. W. Choi, T.-J. Lee, M. Y. Chung, Pe o mance analysis o wi eless-powe ed cogni i e adio ne wo ks wi h ambien backsca e . EURASIP J. Wi el. Commun. Ne w. 2019(1), 45 (2019). h ps://doi.o g/10. 1186/s13638-019-1367-7 5. F. Jameel, Z. Hamid, F. Jabeen, S. Zeadally, M. A. Ja ed, A su ey o de ice- o-de ice communica ions: Resea ch issues and challenges. IEEE Commun. Su . Tu o . 20(3), 2133–2168 (2018). h ps://doi.o g/10.1109/ COMST.2018.2828120 6. X. Liu, Y. Gao, F. Hu, Op imal ime scheduling scheme o wi eless powe ed ambien backsca e communica ions in io ne wo ks. IEEE In e ne o Things J., 1–1 (2019). h ps://doi.o g/10.1109/JIOT.2018.2889700 7. C. Boye , S. Roy, Backsca e Communica ion and RFID: Coding, Ene gy, and MIMO Analysis. IEEE T ans. Commun. 62(3), 770–785 (2014)