Energy-efficient resource allocation for OFDMA two-way relay networks with imperfect CSI

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1 Chag et al. EURASIP Joural o Wreless Commucatos a Networkg :5 DOI /s RESEARCH Ope Access Eergy-effcet resource allocato for OFDMA two-way relay etworks wth mperfect CSI Zheg Chag 1, Qaqa Zhag, Xjua Guo * a Tapa Rstaem 1 Abstract Most of the exste works o the rao resource allocato RRA problem commoly assume the chael-state formato CSI ca be perfectly obtae by the trasmsso source. However, such assumpto s ot practcal the realstc wreless systems. I ths work, we coser the practcal mplemetato ssues of resource allocato orthogoal frequecy vso multple access OFDMA two-way relay etworks: the accuracy of chael-state formato CSI avalable to the source. Istea, oly the estmate chael status s kow by the source. I ths cotext, a jot optmzato of subcarrer parg a allocato, relay selecto, a trasmt power allocato s formulate OFDMA two-way amplfy-a-forwar relay etworks. Moreover, the objectve of ths work s to mmze the eergy cosumpto of the overall system. Further, to esure the qualty of servce QoS or ata rate requremet, the eergy cosumpto must be mmze wthout compromsg the QoS. Therefore, by applyg covex optmzato techques, eergy-effcet algorthms are evelope wth the objectve to mmze the total trasmt power wth guarateeg the requre ata rates. Through smulato stues, eergy cosumpto performace of the systems uer the propose schemes s vestgate. It ca be observe that our propose scheme ca mprove the eergy cosumpto performace of the cosere system. Keywors: OFDMA; Two-way relay; Subcarrer parg; Rao resource allocato; Imperfect chael-state formato; Eergy effcecy 1 Itroucto The ema for hgh-spee ata trasmsso has bee sgfcatly crease ue to the fast-growg wreless multmea servce market the last ecae. Orthogoal frequecy vso multple access OFDMA s kow as a effectve techque explotg the features of OFDM combatg chael fag a multpath effects a provg hgh ata rate. Meawhle, relay-assste commucato s regare as a promsg techology, as t obtas better a relable system performace terms of spectrum a eergy effcecy [1, ]. Therefore, OFDMA wreless etwork wth cooperatve relays s foresee as a promsg structure for provg hghspee ata trasmsso a reachg may esrable objectves the cotext of future wreless etworks evelopmet. *Correspoece: xguo@ysu.eu.c College of Iformato Scece a Egeerg, Yasha Uversty, Qhuagao, Cha Full lst of author formato s avalable at the e of the artcle I ato, there has bee creasg atteto pa for stuyg the two-way brectoal relay etworks TWRN, where two ata oes exchage formato va several assstg relay oes RNs. Comparg wth the tratoal oe-way relay schemes that ee four tme slots to fsh formato exchage, the TWRN oly requres two tme slots [3]. I the frst tme slot, two TWRN users ca trasmt ther sgals smultaeously to the avalable RNs. The, the seco tme slot, wth the assumpto of perfect sychrozato, RNs broacast the processe verso of the receve sgal to the two users to complete formato exchage. Processg of sgal at RN reles o fferet processg fuctos, such as amplfy-a-forwar AF, ecoe-a-forwar DF, etc., amog whch AF s most lkely to be realze a most wely use practcal system. Therefore, the paper, we focus o the OFDMA wreless etworks wth AF two-way relays. Nevertheless, orer to fully realze the aforemetoe beefts, OFDMA TWRN calls for a cautous rao 015Chag et al. Ope Access Ths artcle s strbute uer the terms of the Creatve Commos Attrbuto 4.0 Iteratoal Lcese whch permts urestrcte use, strbuto, a reproucto ay meum, prove you gve approprate cret to the orgal authors a the source, prove a lk to the Creatve Commos lcese, a cate f chages were mae.

2 Chag et al. EURASIP Joural o Wreless Commucatos a Networkg :5 Page of 11 resource allocato RRA esg comparg wth tratoal etwork frastructure, as there are may fferet rao resources, such as relays, subcarrers, a trasmt power. Ths volves a careful esg a coorato of the power a subcarrer allocato, selecto of relays across fferet hops. Most of the relate works otherrafortwrnassumethechael-stateformato CSI s perfectly kow to the oes the system [3 5]. However, realty, the CSI caot be perfectly obtae. Istea, the trasmsso source oly kows partal/mperfect CSI. Therefore, the evelopmet of practcal resource allocato schemes requres coserato of the accuracy of CSI. The RRA schemes wth mperfect CSI has receve much atteto whe coserg the oe-way relay ual-hop wreless etworks. I [6], authors cosere the RRA algorthm for covetoal OFDMA etworks wthout relays. The authors of [7] focuse o the relay selecto scheme for TWRN wth mperfect CSI. I ato, the author also presete a power allocato scheme that mmzes the outage probablty. Some recet work ths le, e.g., [8] a [9], vestgate the ssue of jot RRA a relay selecto wth mperfect CSI, where throughput maxmzato s the optmzato objectve. Uer the coserato of chael ucertaty, the relay selecto a power allocato schemes are propose to mmze the uplk trasmt power of the etwork by takg each user s target ata rate as the qualty of servce QoS costrat [10]. Aother recet work about RRA for OFDMA relay etworks wth mperfect CSI was trouce [11], where oly power allocato algorthm was trouce. I [1], resource allocato scheme was presete for the selecte relays. Meawhle, oly lmte research work, e.g. [13] a [14], focuse o the RRA for TWRN wth mperfect CSI. I [13], authors aalyze the outage performace of TWRN wth mperfect CSI a propose a power allocato scheme. Smlarly, authors of [14] also propose power allocato a user selecto scheme for TWRN wth outate CSI. Smlarly, the authors of [15] also propose power allocato a user selecto scheme for TWRN wth outate CSI. As oe may otce, the recet resource allocato research o oe-way or two-way relays mostly focuse o maxmzg the system capacty or e-to-e ata rate. Oly morty as [5] a [1] have take eergy coservato a cosumpto reucto as the prmary objectve a cosere the mperfect CSI. However, the creasg eergy cosumpto wreless etworks evtably leas to a large carbo footprt, whch greatly cotrbutes to evrometal polluto. To protect our evromet, cope wth global warmg, facltate sustaable evelopmet, as well as reuce the bg etwork cost from operator pot-of-vew, optmzg the eergy effcecy of wreless systems are requre for the future. Therefore, the prmer target of ths work s to preset a eergyeffcet resource allocato scheme whch jotly aress relay selecto, subcarrer parg, a power allocato OFDMA TWRN wth mperfect CSI. The ma cotrbutosofthsworkareasfollows: 1. We preset a eergy-effcet resource allocato scheme wth jot coserato of relay selecto, subcarrer parg, a power allocato. For each selecte relay, oe subcarrer par cotag two subcarrers s allocate wth the objectve to reuce the trasmt power cosumpto wth mmum ata rate guaratee.. Whe mperfect CSI s assume, the close-form expressos of optmal power allocato, relay selecto, a subcarrer parg are erve. 3. The propose scheme s valate through extesve smulatos. The performace mafests that our presete scheme s able to reuce the eergy cosumpto wth mmum ata rate guaratee. The remaer of ths paper s orgaze as follows. The system a mperfect CSI moels are gve Secto. I Secto 3, the relay selecto a resource allocato problem s formulate as a optmzato problem whch ca be ecompose to N epeet subproblems. I the Secto 4, we focuse o solvg these subproblems a by applyg Karush-Kuh-Tucker KKT cotos, the close-form expressos of optmal power allocato, relay selecto, a subcarrer assgmet are erve. I the Secto 5, the smulato results a performace aalyss are gve. We fally coclue the paper Secto 6. Systemmoel The cosere TWRN system moel s show Fg. 1, where there are two ata oes S 1 a S, K half-uplex RNs, a N subcarrers. The applcablty of ths moel s ubqutous fferet practcal scearos, e.g., cellular etworks a wreless mesh/sesor etworks, wth the assumpto that two oes ee to exchage formato wth each other a there s o rect path betwee them. Hece, the trasmsso shoul be fshe va the RNs that are locate betwee the sources. Due to the ature of half-uplex RNs that ca ot smultaeously receve a se ata, 1/ spectrum effcecy loss s brought. Thus, ths work, we aopt physcal layer etwork cog to overcome such problem a formato exchage ca be fshe two tme slots. I the cosere system, all oes operate a tme-vso uplexg TDD maer. It ca be otce that the amout of correlato betwee fferet subcarrers reles o the relato of chael coherece bawth a subcarrer spacg. We assume that OFDM symbol urato s smaller compare

3 Chag et al. EURASIP Joural o Wreless Commucatos a Networkg :5 Page 3 of 11 Fg. 1 Two-way relay etworks wth the chael coherece tme. Therefore, we coser a quas-statc fag chael for whch the chaels are costat wth oe frame but chage epeetly from oe to aother. Assumg chael recprocty, the chael ga betwee S j a RN s the same as the chael ga betwee RN a S j o a certa subcarrer. The chael coeffcet o the subcarrer m betwee S 1 a RN, a S a RN are eote by h m 1, a hm,,respectvely, a the path loss betwee S 1 a RN,aS a RN are eote by L 1, a L,, respectvely. Meawhle, the zero mea atve Gaussa ose at S 1, S,aRN o the subcarrer are eote by ν1, ν,az. It s assume that the ose follows N 0, w. We assume that the mmum mea square error MMSE s use for estmatg the chael coto. The eotg ĥm 1, a ĥm, as the estmate chael coeffcets, we have h m 1, ĥm 1, + e 1, h m, ĥm, + e, where e 1 a e are the MMSE estmato errors a follow zero mea complex Gaussa strbuto wth varace e 1 a e, respectvely, a the estmato errors are epeet wth the chael estmato results [11]. Sce o rect lk s assume betwee two ata oes, the formato exchage must be performe va the RNs wth two tme slots. I the frst tme slot, two ata seers trasmt ther ata to the RNs at the same tme o the same subcarrer m. The trasmt power of S 1 o subcarrer m s eote as Ps,1 m, a the trasmt power of S o subcarrer m s assume to be Ps, m. Wth the assumpto of perfect sychrozato at RNs, the sgal receve at the relay oe RN s expresse as [3] y m Ps,1 m L 1, ĥm 1, + e 1 x m 1 + Ps, m L, ĥm, + e x m + zm, 1 where x m 1 a xm are the trasmtte sgals of S 1 a S o subcarrer m, respectvely. I the seco tme slot, RN aopts the AF protocol a amplfes the receve sgal by a amplfcato factor o subcarrer. The amplfcato coeffcet ca be expresse as Pr, Ps,1 m L 1, ĥ m + e 1 + Ps, m L, ĥ m + e + w 1, where Pr, s the trasmt power of RN o subcarrer. I ato, ω a ρ m, are efe as the relay selecto cator a subcarrer parg cator, respectvely,.e., { 1, f RN s selecte, ω 4 0, otherwse. { ρ m, 1, f subcarrer par m, s selecte, 5 0, otherwse. I the seco tme slot, the selecte RN broacasts the scale sgal to ther estatos. Assumg perfect sychrozato at RNs, all trasmtte sgals from the relays ca be coheretly combe together. The receve sgals at S 1 a S o the subcarrer are gve as a y S 1 y S ω ρ m, 1 ω ρ m, 1, 3 L1, ĥ 1, + e 1 y m + ν 1, 6 L, ĥ, + e y m + ν. 7 Wth the assumpto that the estmate CSI s kow, each ata oe ca omt ts ow trasmtte sgal compoet from the receve sgal. Therefore, the fal sgals at S 1 a S o the subcarrer ca be wrtte as

4 Chag et al. EURASIP Joural o Wreless Commucatos a Networkg :5 Page 4 of 11 a ỹ S 1 ỹ S ω ρ m, 1 ω ρ m, 1 L1, ĥ 1, + e 1 P m s,1 L 1,e 1 x m 1 + P m s, L,h m, xm + zm L, ĥ, + e P m s, L,e x m + P m s,1 L 1,h m 1, xm 1 + zm To ths e, we ca obta the receve SNRs show as follows: + ν 1, 8 + ν 1, 9 K1 ω ρ m, L1, L, ϕ 1 ϕ Ps,1 m Ɣ 1 ϕ 4 /e 1 + K 1 ω ρ m, L1, L, Ps,1 m ϕ 1 + ϕ L, ϕ 3 ϕ L, ϕ 6Ps, m ϕ + 1, 10 a K1 ω ρ m, L1, L, θ 1 θ Ps, m Ɣ ϕ 3 /e + K 1 ω ρ m, L1, L, Ps, m θ 1 + θ L 1, ϕ 4 ϕ L 1, ϕ 5Ps,1 m ϕ 1 + 1, 11 where θ 1 ĥ 1, e 1, θ ĥ, e, ϕ 1 ĥm 1, e 1, ϕ ĥm,, ϕ e 3 w, ϕ e 4 w, ϕ 1 e 5 e 1, ϕ e 6 e, 1 e 1 3 Problem formulato a smplfcato I ths secto, we am to propose a eergy-effcet relay selecto a resource allocato scheme whe coserg mperfect CSI. The objectve s to f the optmal subcarrer parg cator varable set ρ {ρ m,, m, }, relay selecto cator set ω {ω, }, a the power allocato varables P { P m s,1, Pm s,, P r,,, m, } that are able to mmze the total trasmsso power wthout sacrfcg the requre ata rate. 3.1 Problem formulato Deotg R 1 as the requre ata rate for the ate trasmsso from S 1 to S a R as the requre mmum ata rate for trasmsso from S to S 1, the the resource allocato optmzato problem ca be expresse as m ρ,ω,p m1 subject to m N P m s,1 + Ps, K N m + ω ρ m, Pr, r1 I R 1, r I R, I I Ps,1 m 0, Pm s, 0,P r, 0,, m, ω m, 1,ω m, {0, 1}, m, N N ρ m, 1, ρ m, 1,ρ m, {0, 1}, m, r1 I a ri are the achevable rates for the ata trasmsso from S 1 to S a from S to S 1 o the subcarrer par I cotag subcarrer m the frst tme slot a the seco tme slot. The r1 I a ri ca be expresse as r I a 1 W log 1 + Ɣ a, a 1,

5 Chag et al. EURASIP Joural o Wreless Commucatos a Networkg :5 Page 5 of Problem smplfcato I orer to reuce the complexty of the formulate optmzato problem, equal rate coserato s assume o each subcarrer par [5]. Thus, o each subcarrer, we coser the achevable rate shoul be better tha the gve value of ata rate so that the overall ata rates are hgher tha the requre ata rate. Hece, the optmzato problem 13 ca be ecompose to several epeet subproblems. Let r 1 be the per-subcarrer par requre ata rate of the trasmsso that s orete by S 1 a r be the oe of the trasmsso starte by S.Thus,opersubcarrer par bass, the subproblem ca be expresse as K m ρ,ω,p Pm s,1 + Pm s, + ω ρ m, Pr, 16 subject to m 1 r1 I r 1,r I r, Ps,1 m 0, Pm s, 0,P r, 0,, m, ω m, 1,ω m, {0, 1}, m, N N ρ m, 1, ρ m, 1,ρ m, {0, 1}, m, 17 The total trasmt power s the sum of the trasmsso powers o each subcarrer par. Decomposg the problem 13 to several epeet per-subcarrer par subproblems ca guaratee the accuracy wth lower complexty. We ca observe that the optmzato problem 16 wth costrats 17 s a olear optmzato problem w.r.t. trasmt power. KKT coto ca be a vtal metho for solvg such optmzato problems wth equalty costrats [16]. To procee, we substtute 3 a 15 to 16 a the apply KKT cotos [16]; the trasmsso power of user S 1 a S o subcarrer m ca be expresse as a K1 ω ρ m, η 1 + η Ps,1 m K1 ω ρ m, L 1, L, δ1 δ δ 3 K1 ω ρ m, η 3 + η4 Ps, m K1 ω ρ m, L 1, L, δ1 δ δ where we have η 1 r 1 W 1 L 1, L, ϕ + 1 ϕ 3 δ + r W 1 ϕ 4 ϕ 6 θ 1 + 1, [ η L, r 1 W 1 r W 1 L, ϕ 6 ϕ + 1 ϕ 3 /e ] +L 1, δ ϕ 4 /e 1, η 3 r W 1 L, L 1, θ ϕ 4 δ 1 + r 1 W 1 ϕ 3 ϕ 5 ϕ + 1, [ η 4 L 1, r W 1 r 1 W 1 L 1, ϕ 5 θ 1 + 1ϕ 4 /e 1 ] +L, δ 1 ϕ 3 /e, δ 1 ϕ 1 ϕ ϕ 1 + ϕ + 1 r 1 W 1, δ θ 1 θ θ 1 + θ + 1 r W 1, δ 3 r 1 W 1 r W 1 ϕ 5 ϕ 6 θ 1 + 1ϕ The trasmt power of RN ca be expresse as 1, where [.] + max{0, [.] }. We ca otce that the power allocato at ata oes a RN epe o the estmato error e 1 a e. [ Pr, [L 1, ĥ m 1, + e 1 Ps,1 m + L, ĥ m, e Ps, w]] m +. If relay RN partcpates the trasmsso, t s observe that at least oe subcarrer par shoul be assge to relay oe RN. Therefore, the subcarrer parg a relay selecto have a certa relatoshp whe proper RN s selecte,.e. ρ m, ρ m, ω ρ m,, 1 shows that subcarrer par m, s assge to the relay RN. Hece, relay selecto cator s able to be remove, a mofe subcarrer parg cator ca be use for smplcty. The problem ca be smplfe as m,ρm, subject to P, ρ m, 3 0, ρ m, {0, 1} 4

6 Chag et al. EURASIP Joural o Wreless Commucatos a Networkg :5 Page 6 of 11 [ 1,,..., ] K, ρ m, [ ρ m, 1, ρ m,,..., ρ m, ] K.By substtutg 18, 19,a to 16, we ca obta P, ρ m, as P, ρ m, ξ 1 P m s,1 + ξ P m s, + K ρ m, 1 where α 1 a α ca be expresse as follows: ξ ξ ρ m, ρ m, L1, ĥ m 1, + e 1 L, ĥ m, + e w 5 6 To ths e, we have smplfe the orgal optmzato problem wth KN N varables to the subproblem oly cotag K varables. If problem 3 s solvable, we ca reach the expressos of trasmt power of ata oes a RN o subcarrer par m,. The, the trasmt power o other subcarrer pars ca be obtae the same way, a the total power cosumpto ca be acheve by the summato of the trasmt power cosumpto o all subcarrer pars. 4 Optmzato of per-subproblem Oe ca otce that the formulate problem s a mxe teger programmg problem, whch cosers the mmum power cosumpto o the subcarrer par. It s kow that the global optmal soluto for formulate resource allocato problem ca be reache by the exhaustve searchg for the optmal value the subcarrer parg cator set { ρ m,,, m, } a the amplfcato coeffcet set {,, }. The, the optmal trasmsso power ca be acheve whe the optmal relay a subcarrer par are eterme. However, such exhaustve search or brach-a-bou metho s eee to obta the global optmal soluto whch s computatoally feasble. To reuce the computatoal complexty a make the problem tractable, we coser a opportustc subcarrer assgmet, where each subcarrer s assge to a uque RN. Therefore, each subproblem ca be solve va the jot optmzato of relay selecto, subcarrer parg, a power allocato. 4.1 Relay selecto for gve subcarrer parg The smple goal of ths relay selecto scheme s to esure that a proper RN ca be selecte. I ths work, the RN whch ca mmze the trasmsso power wth requre lk rates ca be selecte. Hece, the objectve of relay selecto s selectg oe relay amog K RNs to esure the mmum trasmsso power o the gve subcarrer parg, amely arg m 1,,...,K { P, ρ m,} 7 4. Subcarrer parg As outle, ths work, we coser fferet subcarrers are allocate for two hops. Therefore, subcarrer allocato for scheme s propose to mprove the performace of the system by reucg the eergy cosumpto. Gve the selecte relay RN, we are amg to allocate the subcarrer m at the frst tme slot for the trasmsso from source to RN a the subcarrer at the seco tme slot for the trasmsso from RN to source wth objectve of mmzg the eergy cosumpto. For the the optmal relay RN, the optmal subcarrer par ca be eterme as follows: m, { arg m P, ρ m,} 8 m,1,,...,n 4.3 Power allocato Whe the subcarrer parg m, s uquely assge to relay RN, ρ m, ca be expresse as follows: ρ m, { 1, 0, otherwse 9 From 9, we ca obta the optmal solutos of the subproblems. Therefore, after some mapulatos, the optmal amplfcato factor ca be arrve as follows: η + η 4 η 1 L 1, ĥ m 1, + e 1 + η 3 L, ĥ m, + e + w L 1, L, δ 1δ δ 3 1/4. 30

7 Chag et al. EURASIP Joural o Wreless Commucatos a Networkg :5 Page 7 of 11 Power cosumpto B e0 0.5 e e e0.5 Fg. Impact of CSI mperfecto, R 1 R, K 5, N Rate betwee S a S Mbt/s 1 Substtute 9 a 30 to 5, the optmal trasmsso power allocato o the RN ca be wrtte as [ Pr, L 1, ĥ m 1, + e 1 Ps,1 m + L, ĥ m, + + e Ps, w] m So far, we have obtae the optmal amplfcato coeffcet a the optmal trasmsso power P r, o the subcarrer parg m, for the selecte relay oe RN. Substtute the optmal amplfcato coeffcet to the amplfcato coeffcet 3 a 18, 19, the close-form expressos of trasmsso power allocate to sources S 1, S a relay RN ca be expresse as follows: [ Ps,1 m η η 3 δ1 δ δ 3 ] a P m s, [ L 1, L, L 1, L, η η4 33 δ1 δ δ 3 ] 4.4 Algorthm escrpto We have propose a eergy-effcet rao resource allocato scheme whch jotly cosers relay selecto, subcarrer parg, a power allocato problem the OFDMA TWRNs. The objectve s to f the optmal RNs a subcarrer pargs uer mmum ata rate costrats orer to mmze the power cosumpto of mutual commucato betwee two sources. The complexty of solvg problem of relay selecto a subcarrer parg at two hops s OKN. Realzato of the resource allocato s gve Algorthm 1. Algorthm 1 Descrpto of propose resource allocato algorthm 1: for m 1,..., N o : talze P m to a large value 3: for 1,..., N o 4: for 1,..., K o 5: obta P m, by 31 6: f P m, < P m the 7: P m P m,,, m m,. 8: e f 9: e for 10: e for 11: obta P r,, P s,1 m, P s, m by : e for 13: total power cosumpto s P total P m. 5 Performace aalyss 5.1 Smulato settg The path loss moel s L,j 0 log,j + 0 log f c 8, where,j s the stace betwee oe, a oe j a f c s the ceter carrer frequecy, whch cosere to be GHz the smulato. We assume that the spectral esty of ose s equal to 174 Bm/Hz a the bawth of oe subcarrer s 15 KHz. The stace betwee two sources s 0.5 km, a RNs are raomly strbute betwee them. We scuss the performace ga of the propose resource allocato algorthm wth symmetrc lk rate a asymmetrc lk rate; meawhle, we also

8 Chag et al. EURASIP Joural o Wreless Commucatos a Networkg :5 Page 8 of 11 Power cosumpto B e0 5 Relays 0.5 e0.5 5 Relays 0 e0 8 Relays 0.5 e0.5 8 Relays 0 e0 10 Relays 0.5 e Relays Rate betwee S a S Mbt/s 1 Fg. 3 Impact of umber of RNs a CSI mperfecto o eergy cosumpto performace exame the mpact of the mperfect CSI as well as the umber of RNs o the system performace. I ato to the pure eergy cosumpto performace, to capture the eergy effcecy perspectve the aalyss, the eergy cosumpto ex ECI s employe from EARTH project [17]. ECI proves the eergy per bt, whch s efe as the eergy cosumpto urg the observato pero ve by the total umber of bts that were correctly elvere the etwork urg the same tme pero. For cosere system moel, ECI ca be expresse as Eergy cosumpto execi Joule/bt ECI 1/P total [ J/bt]. 34 R 1 + R.8 x e 1 0, e 0, 5 Relays e 1 0.5, e 0.5, 5 Relays e 1 0, e 0, 10 Relays e 1 0.5, e 0.5, 10 Relays Rate betwee S a S Mbt/s 1 Fg. 4 Impact of umber of RNs a CSI mperfecto o ECI performace where P total s the overall trasmt power uer requre lk rate; the coeffcet 1/ stas for the requre two tme slots for completg the trasmsso. 5. Smulato results I Fg., the mpact of estmato error s show compare to the oe wth perfect CSI wth assumpto of lk rate symmetry,.e., R 1 R.Weassumetheumberof RNs s 5 a umber of subcarrrers s 3,.e., K 5, N 64. As oe ca observe, whe ata rate creases, the cosume eergy goes hgher as well. The eergy cosumpto s relatvely hgh whe the varace of chael estmato error s gettg stroger. For example, whe e 1 0.1, e 0.5, the eergy cosumpto s about 1 B hgher tha the oe whe there s perfect CSI at source. Itcabealsootcethatwhe R 1 R 1.8 Mbps, the power cosumpto fferece betwee CSI perfecto a mperfect s up to 0.6 B. However, the fferece s crease to.5 B whe R 1 R Mbps. Therefore, from Fg., we ca coclue that the mperfect CSI at source leas to a hgher eergy cosumpto a wth the crease of the lk rate, CSI mperfecto requres more eergy cosumpto. Fgures 3 a 4 preset how the umber of RNs a the CSI mperfecto affect the power cosumpto a ECI performace whe symmetrc ata rate s cosere. We varytheumberofrnsfrom5to10athecsiestmato error from 0 to 0.5. The umber of subcarrer s stll assume to be 64. Frst from Fg. 3, we ca see that eployg more RNs the system results a lower power cosumpto. Whe perfect CSI s avalable,.e., e 1 e 0, eployg 10 RNs ca reuce the power cosumpto up to.8 B compare wth eployg 5 RNs.

9 Chag et al. EURASIP Joural o Wreless Commucatos a Networkg :5 Page 9 of 11 Power cosumpto B e0 8 Relays 0.1 e0.5 8 Relays 0.5 e0.5 8 Relays 0 e0 10 Relays 0.1 e Relays 0.5 e Relays Fg. 5 Dversty ga wth asymmetrc rate The performace fferece creases to 4 B whe there s estmato error,.e., e 1 e 0.5. Smlarly, eployg more RNs ca mprove the ECI performace, especally f the CSI caot be obtae perfectly. For example, Fg. 4, eployg 10 RNs ca acheve 50 % performace ga whe e 1 e 0.5. It ca be also well observe that as the umber of RNs creases, the CSI mperfecto has less mpact o the power cosumpto as well as ECI performace performace. For example, whe there are 10 RNs the system, the power cosumpto gap s less tha 0.3 B betwee the cases of mperfect CSI a perfect CSI, whle such gap creases to more tha 1 B whe there are oly 5 RNs. Same pheomea ca also be observe Fg. 4, whch s maly ue to the fact that there are more choces for relay selecto. IFgs.5a6,wepresetthempactoftheumber of RNs a CSI mperfecto uer asymmetrc lk rate coserato,.e., R 1 R. I ths settg, we vary the value of requre ata rate betwee S 1 a RNs. Smlarly, the results also show that the eergy cosumpto a ECI performace ca be mprove alog wth the crease of the umber of RNs, whch aga cofrms that eployg more RNs ca sgfcatly reuce the eergy cosumpto. For stace, whe e 1 e 0.5, the system wth 10 RNs has about 0.5 B less 4 Eergy cosumpto execi Joule/bt x e 1 0, e 0, 5 Relays e 1 0.5, e 0.5, 5 Relays e 1 0, e 0, 10 Relays e 1 0.5, e 0.5, 10 Relays Fg. 6 ECI, versty ga wth asymmetrc rate Average Power cosumpto B PERA 15 ERA FRA Fg. 7 Subcarrer a power allocato wth asymmetrc rate, R 1 + R 3.8 Mbps, K 5, N 64

10 Chag et al. EURASIP Joural o Wreless Commucatos a Networkg :5 Page 10 of 11 Power cosumpto B e0 0.1 e e Normalze Noe Relay Dstace Fg. 8 Power allocato wth asymmetrc rate, R 1 + R 3.8 Mbps, K 5, N 64 power cosumpto tha the oe wth 8 RNs. I ato, the optmal performace s obtae whle R 1 R, whch cates that the effcecy of symmetrc rate s better tha asymmetrc rate. Hece, for the sake of eergy coservato a effcecy, we ee to esure the cosstece of brectoal lk rate the practcal trasmsso. I orer to see the avatages of propose subcarrer a power allocato schemes, we compare our propose resource algorthm PERA wth the fxe subcarrer parg scheme FRA [5] a equal power allocato scheme ERA Fg. 7. The power cosumpto performace at two ata oes a RNs wth asymmetrc lk rate s show Fg. 7. Beses the smlar observatos from Fg. 5, we ca see our propose scheme s able to reuce the eergy cosumpto to about 7 B, whch cates our propose scheme ca ramatcally reuce the eergy cosumpto the cosere system. Moreover, t ca be also otce that f the lk asymmetry s cosere, our propose scheme ca obta better eergy effcecy performace comparg wth other scheme. Such observato cofrms that the use of subcarrer allocato scheme across two hops ca obta atoal performace ga. Therefore, Fg. 7 emostrates the sgfcace of avace resource allocato scheme the OFDMA TWRN as well as the avatage of our propose scheme over other recet preset schemes. Fgure 8 epcts the mpact of the stace betwee ata oes a RNs. The stace betwee S 1 a RNs s ormalze to the stace betwee ata oes a vares from 0.1 to 0.9. I ato, we also coser fferet estmato error varaces. It ca be fou the power cosumpto reaches ts lowest whe the RNs are eploye roughly the mle of ata oes. Moreover, the fluece of mperfect CSI ca be easly observe. 6 Coclusos I ths paper, we have stue the rao resource allocato scheme a OFDMA two-way relay etworks wth mperfect CSI. The relays aopt AF protocol a ca assst the trasmsso betwee two source oes the system. Dfferet from most of the exste works, we coser a realstc settg: the mperfecto of CSI. Wthout coserg rect lk betwee two ata source oes, a eergy-effcet resource allocato wth jot relay selecto, subcarrer parg a allocato, a power allocato s propose to acheve the mmum trasmt power cosumpto wth requre ata rate. Through theoretcal aalyss, the resource allocato problem ths paper ca be ecompose to several epeet subproblems, a the close-form expressos of power allocato at two ata oes a relays are erve. The smulatos llustrate the mpact of mperfect CSI o the system performace a show that the scheme propose ths paper ca obta performace mprovemet terms of eergy effcecy compare wth other recet propose schemes. Competg terests The authors eclare that they have o competg terests. Ackowlegemets Ths work s partally supporte by the Acaemy of Fla Decso No , The authors also woul lke to thak the etor a the aoymous revewers for ther k commets. Author etals 1 Departmet of Mathematcal Iformato Techology, Uversty of Jyväkylä, P.O. Box 35Agora, FIN Jyväkylä, Fla. College of Iformato Scece a Egeerg, Yasha Uversty, Qhuagao, Cha.

11 Chag et al. EURASIP Joural o Wreless Commucatos a Networkg :5 Page 11 of 11 Receve: 18 November 014 Accepte: 3 September 015 Refereces 1. R Pabst, B Walk, D Schultz, Relay-base eploymet cocepts for wreless a moble broaba rao. IEEE Commu. Mag. 49, X Zhag, X Tao, Y L, J Lu, QoS-aware scheulg wth optmzato of base-stato power allocato owlk cooperatve OFDMA systems. EURASIP J. Wrel. Commu. Netw. 013, o: / M Zhou, Q Cu, R Jatt, R Tao, Eergy-effcet relay selecto a power allocato for two-way relay chael wth aalog etwork cog. IEEE Commu. Lett. 166, K Jtvachphabool, R Zhag, YC Lag, Optmal resource allocato for two-way relay-assste OFDMA. IEEE Tras. Veh. Techol. 587, M Zhou, Q Cu, M Valkama, X Tao, Eergy-effcet resource allocato for OFDMA-base two-way relay chael wth physcal-layer etwork cog. EURASIP J. Wreless Comm. a Networkg. 01, MK Awa, V Mahtha, M Mehrjoo, X She, JW Mark, A ual-ecomposto-base resource allocato for OFDMA etworks wth mperfect CSI. IEEE Tras. Veh. Techol. 595, MJ Taghyar, S Muhaat, Relay selecto wth mperfect CSI brectoal cooperatve etworks. IEEE Commu. Lett. 161, Z Chag, T Rstaem, 01 IEEE Mltory Commucatos Coferece. Resource Allocato for Cooperatve Relay-assste OFDMA Networks wth Imperfect CSI IEEE Orlao, FL, 01, pp o: /milcom Z Chag, T Rstaem, Z Nu, Rao resource allocato for collaboratve OFDMA relay etworks wth mperfect chael state formato. IEEE Tras. Wrel. Commu. 135, S Mallck, MM Rash, VK Bhargava, Jot relay selecto power allocato for ecoe-a-forwar cellular relay etwork wth chael ucertaty. IEEE Tras. Wrel. Commu. 1110, R Devaraja, A Puchhewa, VK Bhargava, Eergy-aware power allocato cooperatve commucato systems wth mperfect CSI. IEEE Tras. Wrel. Commu. 615, S Mallck, R Devaraja, MM Rash, VK Bhargava, Resource allocato for selectve relayg base cellular wreless system wth mperfect CSI. IEEE Tras. Wrel. Commu. 615, Y Ja, A Vosough, Outage probablty a power allocato of two-way amplfy-a-forwar relayg wth chael estmato errors. IEEE Tras. Wrel. Commu. 116, L Fa, X Le, P Fa, RQ Hu, Outage probablty aalyss a power allocato for two-way relay etworks wth user selecto a outate chael state formato. IEEE Commu. Lett. 645, A Rao, MD Nsar, MS Alou, Robust power allocato for multcarrer amplfy-a-forwar relayg systems. IEEE Tras. Veh. Techol. 67, S Boy, L Vaeberghe, Covex Optmzato. Cambrge Uversty Press, Cambrge UK, G Auer, O Blume, V Ga, I Goor, M Imra, Y Jag, E Katraaras, M Olsso, D Sabella, P Skllermark, W Waja, Eergy effcecy aalyss of the referece systems, areas of Improvemets a target breakow. EARTH Proj. D.3, Submt your mauscrpt to a joural a beeft from: 7 Coveet ole submsso 7 Rgorous peer revew 7 Immeate publcato o acceptace 7 Ope access: artcles freely avalable ole 7 Hgh vsblty wth the fel 7 Retag the copyrght to your artcle Submt your ext mauscrpt at 7 sprgerope.com

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