Energy harvesting-based spectrum access with incremental cooperation, relay selection and hardware noises

240 T. N. NGUYEN, ET AL., EH-BASED SPECTRUM ACCESS WITH INCREMENTAL COOPERATION, RELAY SELECTION . . . Ene gy Ha es ing-based Spec um Access wi h Inc emen al Coope a ion, Relay Selec ion and Ha dwa e Noises Tan N. NGUYEN 1, T an T ung DUY 2, Gia-Thien LUU 2, Phuong T. TRAN 1, Mi osla VOZNAK 1,3 1Wi eless Communica ions Resea ch G oup, Facul y o Elec ical and Elec onics Enginee ing, Ton Duc Thang Uni e si y, No. 19 Nguyen Huu Tho S ee , Tan Phong Wa d, Dis ic 7, Ho Chi Minh Ci y, Vie nam 2Pos s and Telecommunica ions Ins i u e o Technology, 11 Nguyen Dinh Chieu S ., Dis . 1, Ho Chi Minh Ci y, Vie nam 3VSB Technical Uni e si y o Os a a, 17. lis opadu 15/2172, 708 33 Os a a - Po uba, Czech Republic {nguyennha an, an hanhphuong}@ d .edu. n, { an ungduy, lg hien}@p i hcm.edu. n, mi osla . oznak@ sb.cz Submi ed Sep embe 13, 2016 / Accep ed Decembe 7, 2016 Abs ac . In his pape , we p opose an ene gy ha es - ing (EH)-based spec um access model in cogni i e adio (CR) ne wo k. In he p oposed scheme, one o a ailable sec- onda y ansmi e s (STs) helps a p ima y ansmi e (PT) o wa d p ima y signals o a p ima y ecei e (PR). Via he coope a ion, he selec ed ST inds oppo uni ies o access li- censed bands o ansmi seconda y signals o i s in ended seconda y ecei e (SR). Seconda y use s a e assumed o be mobile, hence, op imiza ion o ene gy consump ion o hese use s is in e es ed. The EH STs ha e o ha es ene gy om he PT’s adio- equency (RF) signals o se e he PT- PR communica ion as well as o ansmi hei signals. The p oposed scheme employs inc emen al elaying echnique in which he PR only equi es he assis ance om he STs when he ansmission be ween PT and PR is no success ul. Mo e- o e , we also in es iga e impac o ha dwa e impai men s on pe o mance o he p ima y and seconda y ne wo ks. Fo pe o mance e alua ion, we de i e exac and lowe -bound exp essions o ou age p obabili y (OP) o e Rayleigh ading channel. Mon e-Ca lo simula ions a e pe o med o e i y he heo e ical esul s. The esul s p esen ha he ou age pe o mance o bo h ne wo ks can be enhanced by inc eas- ing he numbe o he ST-SR pai s. In addi ion, he ou - age pe o mance o bo h p ima y and seconda y ne wo ks is se e ely deg aded wi h he inc easing o ha dwa e impai - men le el. I is also shown ha ac ion o ime used o EH and posi ions o he seconda y use s signi ican ly impac on he sys em pe o mance. Keywo ds Cogni i e adio, elay selec ion, ene gy ha es ing, ha dwa e impai men s, ou age p obabili y 1. In oduc ion Recen ly, ene gy ha es ing (EH) has been gained much a en ion as a p omising echnique o p olong li e ime o ene gy-limi ed wi eless ne wo ks wi hou echa ging ba e - ies [1]. The EH sys ems allow wi eless de ices o collec ene gy om adio equency (RF) and con e he ha es ed ene gy in o di ec cu en powe by in e nal in e e ci cui s. To enhance pe o mances o he EH ne wo ks, in e ms o ou age p obabili y, e o a e and di e si y gain, coope a- i e elaying p o ocols [2] we e conside ed as an e icien solu ion. The au ho s in [3] s udied a dual-hop elaying p o ocol wi h EH and a g eedy swi ching policy. In [4], he au ho s p oposed wo EH-based elaying p o ocols: ime swi ching-based elaying (TSR) and powe spli ing-based elaying (PSA). In [5], he ampli y-and- o wa d (AF) elay ha es s he ene gy om he sou ce, which is used o elay he sou ce da a o he des ina ion. Mo eo e , he au ho s in [5] p oposed op imiza ion me hods o maximize he end- o-end ins an aneous channel capaci y in bo h hal -duplex and ull-duplex elay modes. In [6], closed- o m exp essions o a e age channel capaci y and h oughpu o EH-based decode-and- o wa d (DF) ne wo ks we e de i ed. Coope a- i e elaying schemes wi h mul iple sou ce-des ina ion pai s communica ing wi h one EH elay we e p oposed in [7]. Fu he mo e, he au ho s in [7] p oposed a ious powe al- loca ion s a egies and e alua ed he pe o mances ia bo h simula ions and analyzes. Wi h he apid inc easing o wi eless de ices and sys- ems, spec um sca ci y becomes a c i ical issue due o eme - gence o wi eless se ices. To o e come his p oblem, Mi- ola [8] in oduced cogni i e adio (CR) concep , in which licensed use s (p ima y use s (PUs)) can sha e licensed bands o unlicensed use s (seconda y use s (SUs)). The basic idea o he CR echnique is ha wo wi eless sys ems coexis and ope a e a he same spec um esou ces. Howe e , hey ha e di e en p io i ies: PUs can use he licensed bands DOI: 10.13164/ e.2017.0240 APPLICATIONS OF WIRELESS COMMUNICATIONS RADIOENGINEERING, VOL. 26, NO. 1, APRIL 2017 241 any ime, while SUs can use he spec um wi h lowe p io - i y [9]. In con en ional CR me hod [10], SUs mus de ec he p esence/absence o PUs. I he e a e acan bands de- ec ed, SUs can access hem o ansmi he seconda y da a. Recen ly, esea che s ha e p oposed wo spec um sha ing me hods in which SUs can use he licensed bands wi hou de ec ing PUs’ ope a ions. In he i s me hod, named unde - lay CR [11], [12], PUs and SUs can use he licensed bands a he same ime, p o ided ha he co-channel in e e ence om he seconda y ansmission mus be lowe han a maximum h eshold equi ed by PUs. In he second me hod, named o e lay CR [13–15], SUs can use licensed bands bu hey mus help PUs enhance he quali y o se ice (QoS). In pa - icula , he seconda y ansmi e s (STs) play a ole as elays o he p ima y ne wo k and ia his assis ance, hey can ind oppo uni ies o access he licensed bands. So a , mos o he published pape s ha e assumed ha anscei e ha dwa e is pe ec . Howe e , in p ac ice, he anscei e ha dwa e o wi eless de ices is impe ec because i is a ec ed by impai men s such as ampli ie -ampli ude non-linea i y, I/Q imbalance and phase noise [16]. Hence, he ha dwa e impai men s (HI) need o be aken in o accoun when e alua ing pe o mances o wi eless elay ne wo ks. In [17], ou age p obabili y (OP) o wo-way elay ne wo ks wi h he ha dwa e noises a elay was in es iga ed. The au- ho s in [18] p oposed and e alua ed he ou age pe o mance o p oac i e elay selec ion p o ocols in co-channel in e e - ence ne wo ks. In [19], he au ho s in es iga ed he join impac o he impe ec ha dwa e and he wi eless powe ans e on he ou age pe o mance o wo-way unde lay CR. The esul s in [16–18] ha e p esen ed ha he p esence o HI deg ades he sys em pe o mances o e ading channels. In p ac ical wi eless ne wo ks, use s a e usually in mo- ion, which equi es ex a ene gy in addi ion o ene gy used o signal ansmission. Mo eo e , CR seconda y use s also consume ene gy o spec um sensing p ocess. The e o e, i is e y impe a i e ha ene gy e iciency mus be consid- e ed o seconda y use s in CR ne wo ks. To he bes o ou knowledge, he e a e se e al epo s ela ed o coope a i e CR models using he EH echnique. In pa icula , in [20], he ST is deployed wi h a echa geable ba e y which can ha es ene gy om he en i onmen . The au ho s in [21] p oposed an op imal spec um access o EH-based CR ne - wo ks, whe e he ST a he beginning o each ime slo needs o de e mine whe he o emain idle so as o conse e ene gy, o o execu e spec um sensing o acqui e knowledge o he cu en spec um occupancy s a e. In [22], [23], he au ho s s udied he pe o mance o he seconda y ne wo ks ope a - ing on unde lay mode. Published wo ks [24], [25] e alua ed he pe o mances o bo h p ima y and seconda y ne wo ks in o e lay CR en i onmen , whe e a single EH-based ST uses he AF o DF echnique o o wa d he combined signals o bo h p ima y ecei e (PR) and seconda y ecei e (SR). The au ho s in [26] p oposed a coope a i e spec um access p o- ocol in which he SU can ha es he ene gy om he p ima y signals and hen assis s he p ima y da a ansmission using Alamou i echnique. Li e al. [27] also p oposed a spec um sha ing me hod based on compe i i e p ice game model. In his pape , we p opose a new coope a i e spec um sha ing elaying p o ocols, whe e he bes EH-based ST is chosen o assis he da a ansmission be ween he nodes PT and PR. We also p opose an inc emen al elaying coope a- ion [2] in which he PR only equi es he help om STs when he communica ion be ween he PT and PR is no success ul. Di e en wi h he schemes p oposed in [24–26], he p oposed scheme includes mul iple ST-SR pai s and only he bes ST is selec ed o he coope a ion. Mo eo e , he impac o ha d- wa e impai men s on he ou age pe o mance o he p ima y and seconda y ne wo ks is also in es iga ed. Fo pe o - mance e alua ion, we de i e exac and lowe -bound closed- o m exp essions o ou age p obabili y o bo h ne wo ks o e Rayleigh ading channel. We hen pe o m Mon e-Ca lo sim- ula ions o e i y he heo e ical de i a ions. The es o his pape is o ganized as ollows. The sys- em model o he p oposed p o ocol is desc ibed in Sec. 2. In Sec. 3, we e alua e he pe o mance o he p oposed scheme. The simula ion esul s a e shown in Sec. 4 and Sec. 5 concludes his pape . Fig. 1. Sys em model o he p oposed p o ocol. 2. Sys em Model In Fig. 1, we p esen he sys em model o he p oposed scheme, whe e he p ima y ne wo k includes one PT-PR pai , while he e a e MST-SR pai s in he seconda y ne wo k. The PT a emp s o ansmi i s da a o he PR wi h he help o STs, i.e., STm(m=1,2, ..., M). Via coope a ion, he STm can access he licensed band o ansmi i s da a o he SRm. Assume ha all o he e minals a e equipped wi h a sin- gle an enna and ope a e on hal -duplex mode. We also as- sume ha he STs (SRs) a e close oge he and o m a clus e , and hence, he dis ances om he PT o STs (SR) a e as- sumed o be he same [11]. Le us deno e d0,d1,d2,d3and d4as he dis ances o he PT −PR,PT −STm,PT −SRm, 242 T. N. NGUYEN, ET AL., EH-BASED SPECTRUM ACCESS WITH INCREMENTAL COOPERATION, RELAY SELECTION . .. STm−PR and STm−SRmlinks, espec i ely. We also deno e hPT,PR,hPT,STm,hPT,SRm,hSTm,PR and hSTm,SRmas channel coe icien s o he PT −PR,PT −STm,PT −SRm,STm−PR and STm−SRmlinks, espec i ely. We assume ha all o he links a e modeled o be block and la Rayleigh ading chan- nels, which emain cons an du ing an in e al T and change independen ly o e di e en in e als. As men ioned in [11], channel gains γ0,γ1m,γ2m,γ3mand γ4m(γ0=|hPT,PR|2, γ1m=|hPT,STm|2,γ2m=|hPT,SRm|2,γ3m=|hSTm,PR|2, γ4m=|hSTm,SRm|2)a e exponen ial andom a iables (RVs) wi h pa ame e s λ0,λ1,λ2,λ3and λ4, espec i ely [11]. Mo eo e , o ake pa h-loss in o accoun , he pa ame e s can be exp essed as a unc ion o he dis ance and he pa h-loss exponen by [11]: λ0=dχ 0,λ1=dχ 1,λ2=dχ 2,λ3=dχ 3and λ4=dχ 4, espec i ely, whe e χis pa h-loss coe icien . We assume ha he STs a e limi ed-ene gy e minals which mus ha es ene gy om he RF signals gene a ed by he PT. I is also assumed ha he nodes STs and SRs ha e enough ene gy o p ocessing he con ol messages in se -up phases [23] as well as o decoding he ecei ed da a. The ope a ion o he p oposed p o ocol is spli in o h ee sub-blocks. Simila o he ime swi ching scheme in [23], a du a ion o αTis used o he STs o ha es he ene gy om he PT, a du a ion o (1−α)T/2 o he STs and he PR o ecei e he da a om he PT, and a du a ion o (1−α)T/2 is employed o o wa d he da a om he selec ed ST o he PR and he in ended SR. Then, he ene gy ha he STmcan ha es is gi en as [23, eq. (13)] 1: Em=ηαTPγ1m(1) whe e η(0< η ≤1) is he ene gy con e sion e iciency ha depends on he in e nal in e e ci cui in he STs, and Pis he ansmi powe o he PT. Hence, he ansmi powe o he STmo e he ime (1−α)T/2can be ob ained by [23, eq. (14)]: Pm=Em (1−α)T/2=2ηαPγ1m 1−α =µPγ1m(2) whe e µ=2ηα/ (1−α). A he nex sub-block, he PT ansmi s i s da a o he PR, which is also ecei ed by he STmand SRm. Unde he impe ec ha dwa e, he ecei ed signal a he node X, X∈{STm,SRm,PR}, can be gi en as yX=√PhPT,XxP+η ,PT+η ,X+nX(3) whe e xPis he p ima y signal ansmi ed by he PT, nXis he addi i e whi e Gaussian noise (AWGN), η ,PT and η ,Xa e he noises caused by he ha dwa e impai men s a he ansmi e PT and he ecei e X, espec i ely. Simila o [18], nX,η ,PT and η ,Xa e modeled as ze o-mean Gaussian noises wi h a iance o N0,κ PT and κ XP|hPT,X|2, espec i ely, whe e κ PT and κ Xindica e he le el o ha dwa e impai men s a he nodes PT and X. F om (3), he achie able da a a e be ween he nodes PT and PR can be calcula ed by C0=(1−α)T 2log2*.,1+P|hPT,PR|2 κ PT +κ PRP|hPT,PR|2+N0+/-, =(1−α)T 2log2 1+ Ψγ0 κPT,PRΨγ0+1!(4) whe e Ψ=P/N0is he a e age ansmi signal- o-noise a- io (SNR), κPT,PR =κ PT +κ PR is o al ha dwa e impai men le el. Simila ly, we can ob ain he ins an aneous channel ca- paci y o he PT −STmand PT −SRmlinks, espec i ely as C1m=(1−α)T 2log2 1+ Ψγ1m κPT,STmΨγ1m+1!, C2m=(1−α)T 2log2 1+ Ψγ2m κPT,SRmΨγ2m+1!(5) whe e κPT,STm =κ PT +κ STmand κPT,SRm =κ PT +κ SRm. A he end o he second sub-block, he PR a emp s o decode he ecei ed signal. I his node can decode he sou ce signal success ully, i in o ms he decoding s a us by gene a ing an ACK message. In his case, he STs and SRs emo e he p ima y signal om hei bu e s and use he hi d sub-block o ansmi he seconda y da a 2. To op imize he pe o mance o he seconda y ne wo k, we p opose a s a egy o selec he bes ST-SR pai . A i s , le us conside he signal ecei ed a he SRmdue o he ansmission o he STm: ySRm=pPmhSTm,SRmzm+η ,STm+η ,SRm+nRm(6) whe e zmis he signal ansmi ed by he STmand η ,STmis he noise caused by he ha dwa e impai men s a he STm which can be modeled as ze o-mean Gaussian noise wi h a iance o κ STm. F om (2) and (6), he ins an aneous channel capaci y o he STm−SRmlink can be gi en as C4m=(1−α)T 2log2 1+µΨγ1mγ4m κSTm,SRmµΨγ1mγ4m+1!(7) whe e κSTm,SRm =κ STm +κ SRm. F om (7), he bes ST-SR pai can be selec ed by he ollowing me hod: STa−SRa:γ1aγ4a=max m=1,2,..., M(γ1mγ4m).(8) 1As men ioned in [19], ha dwa e impai men s a e no aken in o he ha es ed ene gy. 2Because he ansmission be ween he PT and he PR is success ul, he p ima y ne wo k allows he seconda y use s o use he hi d sub-block o ansmi hei signals. RADIOENGINEERING, VOL. 26, NO. 1, APRIL 2017 243 Equa ion (8) implies ha he ST-SR pai which p o ides he highes channel gain o he ST-SR links is selec ed o he communica ion a he hi d sub-block. Nex , le us conside he e en ha he decoding s a- us a he PR is unsuccess ul. In his case, i sends back a NACK message o eques a e ansmission om one o he STs. We deno e WSR as a se o he SRs ha can decode he p ima y signal success ully. Wi hou loss o gene ali y, we can assume ha WSR =SR1,SR2, ., SRNR, whe e NR (0≤NR≤M)is he ca dinali y o WSR. Simila ly, each SR will eedback he ACK (o NACK) message o indica e he success ul (o unsuccess ul) decoding s a us 3. I he e is a leas one SR decoding he p ima y sig- nal co ec ly (NR≥1), om he success ul STs, i.e, ST1,ST2, ., STNR, we p opose a me hod o selec he ST o he coope a ion a he nex sub-block as ollows: STb:Pb=max j=1,2,..., NRPjo γ1b=max j=1,2,..., NRγ1j(9) whe e he ST p o iding he maximum ha es ed ene gy (o he highes channel gain be ween he PT and STs) is selec ed as he bes candida e. I he node STbcan decode he p ima y signal xPsuc- cess ully, i combines linea ly xPand i s own signal zb, ol- lows he s a egy gi en in [15] as xc=pβPbxP+p(1−β)Pbzb(10) whe e βPband (1−β)Pba e he ac ions o he o al ans- mi powe Pb, which a e alloca ed o he signals xPand zb, espec i ely. Then, he STbb oadcas s he combined signal xc, and he ecei ed signals a he PR and SRbcan be gi en, espec- i ely by yPR =pβPbhSTb,PR xP+η ,STb,1 +p(1−β)PbhSTb,PR zb+η ,STb,2+η ,PR +nPR, ySRb=pβPbhSTb,SRbxP+η ,STb,3 +p(1−β)PbhSTb,SRbzb+η ,STb,4+η ,SRb+nSRb.(11) I is no ed om (11) ha he a iances o he ha dwa e impai - men s η ,STb,u,η ,PR and η ,SRba e κ STb,κ PRPb|hSTb,PR |2 and κ SRbPb|hSTb,SRb|2, espec i ely, whe e u=1,2,3,4. Mo eo e , because he SRbob ained he signal xPbe o e, i can emo e he in e e ence componen √βPbhSTb,SRbxP om he ecei ed signal. A e canceling he in e e ence, he signal ySRbcan be ew i en by y∗ SRb =p(1−β)PbhSTb,SRbzb+η ,STb,4 +pβPbhSTb,SRbη ,STb,3+η ,SRb+nSRb.(12) Combining (2), (11) and (12), we espec i ely ob ain he achie able capaci y o he STb−PR and STb−SRblinks as C3b=(1−α)T 2log2*..., 1+βµΨγ1bγ3b 1−β+κSTb,PRµΨγ1bγ3b+1+///- , C4b=(1−α)T 2log2*,1+(1−β)µΨγ1bγ4b κSTb,SRbµΨγ1bγ4b+1+-(13) whe e κSTb,PR =κ STb +κ PR and κSTb,SRb =κ STb +κ SRb. Nex , we conside he case whe e he e is no SR e- cei ing he p ima y signal success ully, i.e., NR=0. In his case, one o he STs ha e o use he o al ha es ed ene gy o se e he PR. Le WST as a se o STs ha can decode he p ima y signal success ully. Wi hou loss o gene al- i y, we can assume ha WST =ST1,ST2, ., STNT, whe e NT(0≤NT≤M)is he ca dinali y o WST. I is ob i- ous ha i NT=0, he sys em canno selec any STs o he e ansmission, and hence he p ima y signal is d opped 4. O he wise, he bes ST is chosen by he ollowing selec ion s a egy: STc:γ3c=max j=1,2,..., NTγ3j(14) whe e he success ul ST ha ing he highes channel gain be- ween i sel and he PR is selec ed as he bes elay. Then, he ecei ed signal a he PR can be gi en by yPR =pPchSTc,PR xP+η ,STc+η ,PR +nPR.(15) Finally, he ins an aneous da a a e o he STc-PR link can be o mula ed by C3c=(1−α)T 2log2*,1+µΨγ1cγ3c κSTc,PR µΨγ1cγ3c+1+-(16) whe e κSTc,PR =κ STc +κ PR. 3. Pe o mance E alua ion Fo ease o analysis, we assume ha he o al ha d- wa e impai men le els a e he same, i.e., κY,Z=κ, o all {Y,Z}∈{PT,PR,STm,SRm}.5 3.1 Ma hema ical P elimina ies Fi s ly, i is well-known ha cumula i e densi y unc ion (CDF) and p obabili y densi y unc ion (PDF) o an exponen- ial RV Y wi h pa ame e λYcan be gi en, espec i ely as FY(y)=1−e−λYy, Y(y)=λYe−λYy.(17) 3When he SR decodes he p ima y signals co ec ly, i can emo e he p ima y signal componen om he signals ecei ed om he ST [14,15]. 4In his case, he PT would s a a new ansmission wi hou sha ing he licensed band o he seconda y ne wo k because he STs canno help he PR e ansmi he da a. 5When he ha dwa e impai men le els a e di e en , wi h he same manne we also ob ain exac and asymp o ic exp essions o ou age p obabili y o bo h ne wo ks. 244 T. N. NGUYEN, ET AL., EH-BASED SPECTRUM ACCESS WITH INCREMENTAL COOPERATION, RELAY SELECTION . . . Nex , le us conside a RV Ymax, i.e., Ymax =max i=1,2,...,K(Yi), whe e Kis a posi i e in ege and Yiis an exponen ial RV whose pa ame e is λY. Hence, he CDF o Ymax can be gi en as (see in [28, eq. (7)]) FYmax (y)= K X m=0 (−1)mCm Ke−mλYy(18) whe e Cm K=[K!/m!/(K−m)!]. Then, he co esponding PDF can be ob ained by Ymax (y)= K−1 X m=0 (−1)mCm K−1KλYe−(m+1)λYy.(19) We now conside a RV Z∗ ha is p oduc o wo expo- nen ial RVs Z1and Z2(Z∗=Z1Z2), whose pa ame e s a e Ω1and Ω2, espec i ely. The CDF o Y∗can be o mula ed by FZ∗(z)=P [Z1Z2<z]=Z+∞ 0 Z1( )FZ2(z/ )d .(20) Using he CDF and PDF ob ained in (17) o (20), and hen applying [29, eq. (3.324.1)] o he co esponding in eg al, we ob ain FZ∗(z)=1−p4Ω1Ω2zK1p4Ω1Ω2z(21) whe e K1(.)is modi ied Bessel unc ion o he second kind [29]. 3.2 Ou age P obabili y Analysis Ou age p obabili y is de ined by he p obabili y ha he achie able a e a a ecei e is below a a ge a e, i.e., R h. Mo eo e , he ecei e can be assumed o co ec ly decode ecei ed signals i he da a a e is highe han R h. A i s , no a ions used in his sub-sec ion can be lis ed as ollows: θ=2 2R h (1−α)T−1, ρ0=θ (1−κθ)Ψ, ρ1=θ β−(1−β+κ)θΨ, ρ2=θ (1−β−κθ)Ψ.(22) Now, he ou age p obabili y o he p ima y ne wo k can be o mula ed by Pou PR =P [C0<R h]P [NR=0]× *..,P [NT=0]+ M X u=1 Cu MP  NT=u−1 C1c≥R h C3c<R h +//- + P [C0<R h] M X m=1 Cm MP [NR=m]P [C1b<R h]+ P [C0<R h] M X m=1 Cm MP [NR=m]P  C1b≥R h C3b<R h . (23) In (23), P [NT=x]and P NR=ya e p obabili ies ha he numbe o he success ul SRs and STs equals xand y, espec i ely. P oposi ion 1: The ou age p obabili y Pou PR can be calcu- la ed by Pou PR = OP1 PR,i θ < β/ (1−β+κ) OP2 PR,i β/ (1−β+κ)≤θ < 1/κ 1,i θ≥1/κ (24) whe e OP1 PR and OP2 PR a e gi en by (31) and (32). P oo : see Appendix A. F om (24)-(32), we can obse e ha he exac exp es- sions o he ou age p obabili y a e s ill in in eg al o m, which is di icul o use o design and op imize he conside ed sys- em. Hence, ou nex objec i e is o de i e app oxima e closed- o m exp essions o he ou age pe o mance a high ansmi SNR. P oposi ion 2: A high SNR alues, i.e., Ψ=P/N0→+∞, he ou age p obabili y Pou PR can be app oxima ed by closed- o m exp essions as ollows: Pou PR Ψ→+∞ ≈(OP1,∞ PR ,i θ < β/ (1−β+κ) OP1,∞ PR ,i β/ (1−β+κ)≤θ < 1/κ (25) whe e, OP1,∞ PR and OP2,∞ PR a e calcula ed as in (33) and (34). P oo : a high Ψ egimes, we ob ain he ollowing app oxi- ma ion: Z+∞ ρ0 e−axe−b xdx Ψ→+∞ ≈Z+∞ 0 e−axe−b xdxΨ→+∞ ≈ 4b aK1*, 4b a+-(26) whe e aand ba e posi i e eal numbe s. Then, using (26) o he co esponding in eg als in (31) and (32), we espec i ely ob ain (33) and (34). Simila ly, he ou age p obabili y o he seconda y ne - wo k can be o mula ed by he ollowing o mula: Pou SR =P [C0≥R h]P [C4a<R h] +P [C0<R h]P [NR=0] +P [C0<R h] M X m=1 Cm MP [NR=m]P [C1b<R h] +P [C0<R h] M X m=1 Cm MP [NR=m] ×P [C1b≥R h,C4b<R h].(27) P oposi ion 3: The exac ou age p obabili y o he seconda y ne wo k can be compu ed by Pou SR = OP1 SR,i θ < (1−β)/κ OP2 PR,i (1−β)/κ ≤θ < 1/κ 1,i θ≥1/κ (28) RADIOENGINEERING, VOL. 26, NO. 1, APRIL 2017 245 whe e OP1 SR and OP2 SR can be ound om (35) and (36). P oo : see Appendix B. Also, he ou age p obabili y OP1 SR is s ill in in eg al o m. Hence, we a emp o ind an app oxima e closed- o m o OP1 SR as below. P oposi ion 4: The ou age p obabili y OP1 SR can be app oxi- ma ed a high Ψ egion as in (37). P oo : simila o he p oo o P oposi ion 2. Fo pe o mance compa ison, we in oduce he di ec ansmission (DT) p o ocol, in which he PT communica es wi h he PR wi hou he help o he STs. In his p o ocol, he da a a e o he PT-PR link is gi en by CDT PT−PR =log2 1+ Ψγ0 κΨγ0+1!.(29) The ou age p obabili y o DT p o ocol can be exp essed by Pou DT =P CDT PT−PR <R hg = 1,i ϑ≥1/κ 1−e−λ0ϑ 1−κϑ ,i ϑ < 1/κ (30) whe e ϑ=2R h -1. OP1 PR =1−e−λ0ρ01−e−λ2ρ0M1−e−λ1ρ0M +1−e−λ0ρ01−e−λ2ρ0MM X u=1 Cu M1−e−λ1ρ0M−ue−(u−1)λ1ρ0 u X =0 (−1) C uZ+∞ ρ0 λ1e−λ1xe− λ3ρ0 µxdx +1−e−λ0ρ0 M X m=1 Cm M1−e−λ2ρ0M−me−mλ2ρ01−e−λ1ρ0m +1−e−λ0ρ0 M X m=1 Cm M1−e−λ2ρ0M−me−mλ2ρ0 m−1 X =0 (−1) C m−1mλ1"e−( +1)λ1ρ0 ( +1)λ1−Z+∞ ρ0 e−( +1)λ1xe−λ3ρ1 µxdx#,(31) OP2 PR =1−e−λ0ρ01−e−λ2ρ0M1−e−λ1ρ0M +1−e−λ0ρ01−e−λ2ρ0MM X u=1 Cu M1−e−λ1ρ0M−ue−(u−1)λ1ρ0 u X =0 (−1) C uZ+∞ ρ0 λ1e−λ1xe− λ3ρ0 µxdx +1−e−λ0ρ0 M X m=1 Cm M1−e−λ2ρ0M−me−mλ2ρ0.(32) OP1,∞ PR =1−e−λ0ρ01−e−λ2ρ0M1−e−λ1ρ0M +1−e−λ0ρ01−e−λ2ρ0M. M X u=1 Cu M1−e−λ1ρ0M−ue−(u−1)λ1ρ0.*.,e−λ1ρ0+ u X =1 (−1) C us4 λ1λ3ρ0 µK1*.,s4 λ1λ3ρ0 µ+/-+/- +1−e−λ0ρ0 M X m=1 Cm M1−e−λ2ρ0M−m.e−mλ2ρ01−e−λ1ρ0m +1−e−λ0ρ0 M X m=1 Cm M1−e−λ2ρ0M−m.e−mλ2ρ0 m−1 X =0 (−1) C m−1m*., e−( +1)λ1ρ0 +1−s4λ1λ3ρ1 µ(1+ )K1*.,s4(1+ )λ1λ3ρ1 µ+/-+/-, (33) OP2,∞ PR =1−e−λ0ρ01−e−λ2ρ0M1−e−λ1ρ0M +1−e−λ0ρ01−e−λ2ρ0MM X u=1 Cu M1−e−λ1ρ0M−ue−(u−1)λ1ρ0*.,e−λ1ρ0+ u X =1 (−1) C us4 λ1λ3ρ0 µK1*.,s4 λ1λ3ρ0 µ+/-+/- +1−e−λ0ρ0 M X m=1 Cm M1−e−λ2ρ0M−me−mλ2ρ0.(34) 246 T. N. NGUYEN, ET AL., EH-BASED SPECTRUM ACCESS WITH INCREMENTAL COOPERATION, RELAY SELECTION . . . OP1 SR =e−λ0ρ0*.,1−s4λ1λ4ρ0 µK1*.,s4λ1λ4ρ0 µ+/-+/- M +1−e−λ0ρ01−e−λ2ρ0M +1−e−λ0ρ0 M X m=1 Cm M1−e−λ2ρ0M−me−mλ2ρ01−e−λ1ρ0m +1−e−λ0ρ0 M X m=1 Cm M1−e−λ2ρ0M−me−mλ2ρ0 m−1 X =0 (−1) C m−1mλ1"e−( +1)λ1ρ0 ( +1)λ1−Z+∞ ρ0 e−( +1)λ1xe−λ4ρ2 µxdx#,(35) OP2 SR =e−λ0ρ0*.,1−s4λ1λ4ρ0 µK1*.,s4λ1λ4ρ0 µ+/-+/- M +1−e−λ0ρ0.(36) OP1 SR Ψ→+∞ ≈e−λ0ρ0*.,1−s4λ1λ4ρ0 µK1*.,s4λ1λ4ρ0 µ+/-+/- M +1−e−λ0ρ01−e−λ2ρ0M +1−e−λ0ρ0 M X m=1 Cm M1−e−λ2ρ0M−me−mλ2ρ01−e−λ1ρ0m +1−e−λ0ρ0 M X m=1 Cm M1−e−λ2ρ0M−me−mλ2ρ0 m−1 X =0 (−1) C m−1mλ1*., e−( +1)λ1ρ0 +1−s4λ1λ4ρ2 µ(1+ )K1*.,s4(1+ )λ1λ4ρ2 µ+/-+/-. (37) 4. Nume ical Resul s and Discussion In his sec ion, we p esen Mon e Ca lo simula ions o e i y he de i a ions in Sec. 3. Fo he simula ion en i on- men , we conside a wo-dimensional X-Y ne wo ks in which PT, PR, STs, SRs a e espec i ely placed a (0,0),(1,0), (xST,0)and (xST,0.25), espec i ely, whe e 0<xST <1. In all o he simula ions, he ime block is no malized by 1 (T=1) and he pa h-loss exponen is ixed by 4 (χ=4). In Figu es 2 and 3, we espec i ely p esen he ou - age p obabili y o he p ima y and seconda y ne wo ks as a unc ion o Ψin dB. The pa ame e s o hese igu es a e ixed by R h =1,xST =0.5,κ=0.01,α=0.1,β=0.95, η=0.5and M∈{1,2,3,6}. F om Fig. 2, we can see ha he ou age pe o mance o he p ima y ne wo k signi ican ly en- hances, as compa ed wi h he DT p o ocol. Mo eo e , i can be obse ed ha he ou age p obabili y dec eases wi h he inc easing he numbe o he ST-SR pai s. As obse ed om Fig. 3, he ou age pe o mance o he seconda y ne wo k is also be e wi h high M alues. I is wo hy no ing om Figu es 2–3 ha he simula ion esul s ma ch e y well wi h he exac heo e ical esul s and he app oxima e heo e ical esul s apidly con e ge o he exac ones. Figu e 4 illus a es he ou age pe o mance o bo h ne wo ks as a unc ion o he co-o dina e xST when R h ∈ {1.5,2},κ=0,α=0.1,β=0.95,η=0.5,M=2and Ψ=0dB. We can obse e om Fig. 4 ha he ou age p obabili y apidly inc eases wi h he inc easing o R h. I is also seen ha he ou age pe o mance o he seconda y ne wo k in he p oposed p o ocol dec eases when he alue o xST inc eases. I is due o he ac ha he link dis ances, i.e., PT-ST and PT-SR, inc ease when xST inc eases, which educes he p obabili y ha he nodes ST and SR can decode he p ima y da a success ully (o dec eases he p obabili y ha STs can access he licensed bands as well as he p oba- bili y ha SRs can emo e he in e e ence componen om he p ima y da a). Mo eo e , he posi ion o he nodes ST also impac s on he pe o mance o he p ima y ne wo k in he p oposed scheme. In pa icula , when R h =1.5, he ou - age p obabili y inc eases when he alue o xST changes om 0.05 o 0.95. Mo e in e es ing, wi h R h =2, he e exis s an op imal alue o xST a which he ou age p obabili y o he p ima y ne wo k is lowes . In almos o he alues o xST and R h, he p ima y ne wo k in ou scheme ou pe o ms ha in he DT p o ocol. This igu e also p esen s ha by placing he nodes ST a app op ia e posi ions, he p oposed me hod will p o ide high pe o mance gain, as compa ed wi h he DT one. Again, he simula ion and analy ical esul s a e in good ag eemen , which alida es he co ec ion o ou de i a ions. In Fig. 5, we in es iga e he impac o he ha dwa e impai men s on he pe o mance o bo h ne wo ks. In his simula ion, we assign he alues o he pa ame e s as ol- lows: R h =1,xST =0.15,α=0.2,β=0.9,η=0.75, M=3and Ψ=5dB. We can see ha he ou age p obabili y o he conside ed p o ocols inc eases wi h he inc easing o he alue κ. Mo eo e , he ou age pe o mance o he DT RADIOENGINEERING, VOL. 26, NO. 1, APRIL 2017 247 Fig. 2. Ou age p obabili y o he p ima y ne wo k as a unc- ion o he ansmi SNR (Ψ) in dB when R h =1, xST =0.5,κ=0.01,α=0.1,β=0.95,η=0.5 and M∈{1,2,3,6}. Fig. 3. Ou age p obabili y o he seconda y ne wo k as a unc- ion o he ansmi SNR (Ψ) in dB when R h =1, xST =0.5,κ=0.01,α=0.1,β=0.95,η=0.5 and M∈{1,2,3,6}. Fig. 4. Ou age p obabili y o he p ima y and seconda y ne - wo ks as a unc ion o xST when R h ∈{1.5,2},κ=0, α=0.1,β=0.95,η=0.5,M=2and Ψ=0dB. Fig. 5. Ou age p obabili y o he p ima y and seconda y ne - wo ks as a unc ion o κwhen R h =1,xST =0.15, α=0.2,β=0.9,η=0.75,M=3and Ψ=5dB. Fig. 6. Ou age p obabili y o he p ima y and seconda y ne - wo ks as a unc ion o αwhen R h =1.5,xST =0.1, κ=0,β=0.95,η=1,M=3and Ψ=0dB. Fig. 7. Ou age p obabili y o he p ima y and seconda y ne - wo ks as a unc ion o βwhen R h =1.5,xST =0.25, κ=0.01,α=0.1,η=0.25,M=2and Ψ=5dB. 248 T. N. NGUYEN, ET AL., EH-BASED SPECTRUM ACCESS WITH INCREMENTAL COOPERATION, RELAY SELECTION . . . p o ocol only changes sligh ly, while ha o he p oposed scena io signi ican ly deg ades. Figu e 6 shows he impac o he ac ion o ime used o he ene gy ha es ing ime slo (α) on he ou age pe o - mance wi h R h =1.5,xST =0.1,κ=0,β=0.95,η=1, M=3and Ψ=0dB. As seen om his igu e, he pe o - mance o he p ima y and seconda y ne wo ks a ies wi h he change o he α. Howe e , i can be obse ed ha he e exis s he op imal alue α∗so ha he pe o mance o he p ima y and seconda y ne wo ks is bes . In Fig. 7, we in es iga e he impac o he ac ion o he ansmi powe alloca ed o he p ima y signal (β) on he sys em pe o mance. The simula ion pa ame e s o his ig- u e a e R h =1.5,xST =0.25,κ=0.01,α=0.1,η=0.25, M=2and Ψ=5dB. We can see ha he pe o mance o he p ima y (seconda y) ne wo k is be e (wo se) wi h high (low) β alues. In his igu e, he ou age p obabili y o he p ima y ne wo k (seconda y) ne wo k almos equals 1 when βis less (highe ) han 0.93 (0.91). 5. Conclusions In his pape , we p oposed an o e lay spec um access p o ocol o enhance he pe o mance o he p ima y and sec- onda y ne wo ks. The main con ibu ion o his pape is o de i e exac and lowe -bound closed- o m exp essions o he ou age p obabili y, which we e e i ied by compu e simula- ions. The esul s p esen ed ha by selec ing app op ia e pa- ame e s, he ou age pe o mance o bo h ne wo ks could be imp o ed signi ican ly. In pa icula , he p oposed sys- em can be op imized by app op ia ely designing he ac ion o ime block used o he ene gy ha es ing p ocess and he ac ion o he ansmi powe alloca ed o he p ima y signal. In addi ion, inc easing he numbe o he ST-SR pai s and se- lec ing he STs wi h he op imal posi ion could also enhance pe o mance o bo h p ima y and seconda y ne wo ks. Acknowledgmen s This esea ch is unded by Vie nam Na ional Founda- ion o Science and Technology De elopmen (NAFOSTED) unde g an numbe 102.01-2014.33. Re e ences [1] ZHOU, X.,ZHANG, R., HO, C. K. Wi eless in o ma ion and powe ans e : A chi ec u e design and a e-ene gy adeo . IEEE T ansac- ions on Communica ions, No . 2013, ol. 61, no. 11, p. 4754–4767. DOI: 10.1109/TCOMM.2013.13.120855 [2] LANEMAN, J. N., TSE, D. N. C, WORNELL, G. W. 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