Energy-Efficient and QoS-ware Resource Allocation for Relay-enhanced OFDMA Wireless Cellular Networks

Transcription

1 WSEAS TRANSACTIONS o COUNICATIONS Xiaoya Huag Supeg Leg Fa Wu Yuig ao Eergy-Efficiet ad QoS-ware Resource Allocatio for Relay-ehaced OFA Wireless Cellular Networs XIAOYAN HUANG SUPENG LENG FAN WU YUING AO School of Couicatio & Iforatio Egieerig epartet Uiversity of Electroic Sciece ad Techology of Chia No.6 Xiyua Ave. West High-tech Zoe Chegdu 673 Chia xyhuag@uestc.edu.c Abstract: - We focus o eergy-efficiet resource allocatio with quality of service (QoS) guaratee for orthogoal frequecy divisio ultiple access (OFA) based wireless cellular etwors with decode-adforward () relayig. The joit trasissio ode selectio subcarrier allocatio ad power cotrol for the eergy efficiecy (EE) axiizatio proble is forulated as a o-covex ad cobiatorial optiizatio proble with the cosideratio of both the trasit ad circuit power cosuptio QoS requireets of obile statios (Ss) as well as idividual power costraits at base statio (S) ad relay statios (RSs). To solve the global optiizatio proble a low-coplexity trasissio ode selectio ad subcarrier allocatio algorith is perfored firstly. y exploitig the properties of relayig trasissio ad oliear fractioal prograig a iterative power cotrol algorith is devised to optiize the power allocatio of S ad RSs subsequetly. Nuerical results deostrate that the proposed algorith achieves sigificat EE iproveet copared with the covetioal spectral-efficiet desig ad the eergy-efficiet desig without the assistace of relayig trasissio. Key-Words: - radio resource allocatio QoS eergy efficiecy relayig subcarrier allocatio power cotrol Itroductio With the requireet of ubiquitous coverage ad the rapid growth of high-data-rate applicatios the eergy cosuptio of wireless etwor is icreasig treedously which leads to high operatio expediture ad large aout of greehouse gas eissio []. Cosequetly EE has becoe of great cocer i the telecouicatios couity due to the rapidly icreasig eergy prices ad societal as well as political pressures o obile phoe operators to reduce their carbo footprit []. ay joit acadeic ad idustrial research efforts have bee dedicated to developig eergy efficiet techiques such as the eergy aware radio ad etwor techologies (EARTH) project [3] the GreeTouch alliace [4] ad the gree radio project [5]. The cobiatio of relayig trasissio ad OFA offers a proisig echais for providig ubiquitous high data rate coverage ad hece the high spectral efficiecy (SE) which has bee widely adopted i broadbad wireless etwors such as Log Ter Evolutio (LTE) systes ad Wi. Nevertheless fro the perspective of syste eergy efficiecy the overall power cosuptio of a relay etwor icludes ot oly the trasit power but also the circuit eergy cosuptio icurred by active circuit blocs of both the source odes ad relay odes. I this case if the SE beefit of relayig trasissio fails to copesate for the icreased eergy cosuptio it is boud to result i the reductio of the syste EE; otherwise the iproveets o both SE ad EE ca be achieved siultaeously. Therefore it is crucial to devise itelliget resource allocatio schees adaptive to the diverse etwor eviroet so as to iprove the syste EE of the relay etwors. Recetly substatial research efforts focus o eergy-efficiet desig i sigle-hop OFA etwors [6]-[]. I cotrast the study o the eergy-efficiet couicatio i OFA-based relay etwors is liited. I [] ad [3] differet relay selectio algoriths aiig to iiize trasit power cosuptio are proposed. A threeode cooperative relay etwor is cosidered i [4] ad a gae-based power allocatio algorith is proposed to axiize the efficiecy of trasit power for the case of that the power allocatio of the source ode is fixed. However the circuit power cosuptio is ot tae ito accout i these approaches. I [5] the total eergy cosuptio iiizatio proble with a give ed-to-ed data rate i ulti-hop wireless etwors is studied with the cosideratio of both trasit ad circuit power cosuptio. It is oly a siplified istace of the EE axiizatio proble where the ed-to-ed data rate should also be adapted. I [6] a E-ISSN: Volue 3 4

2 WSEAS TRANSACTIONS o COUNICATIONS Xiaoya Huag Supeg Leg Fa Wu Yuig ao subcarrier-power allocatio ad relay selectio schee for axiizig EE per user i a OFA cooperative relay etwor is developed. However the trasit power ad the circuit power of the relay ode are eglected which ight lead to iaccurate evaluatio of the syste EE. With a high sigal-tooise ratio (SNR) approxiatio ad oly cosiderig the su power costrait of the syste a joit power ad subcarrier allocatio algorith for a OFA-based cellular etwor with aplifyad-forward (AF) relayig is devised i [7]. I [8] authors ivestigate power allocatio for EE axiizatio proble i a cogitive radio etwor with relayig. I light of the above discussios we focus o eergy-efficiet ad QoS-aware resource allocatio i relay-ehaced OFA dowli wireless cellular etwors. I particular we study the joit trasissio ode selectio subcarrier allocatio ad power cotrol to axiize the overall syste EE where both the trasit ad circuit power cosuptio QoS requireets of Ss ad the idividual power costraits at S ad RSs are tae ito cosideratio. To address the prohibitively high coputatioal coplexity i solvig o-covex ad cobiatorial optiizatio proble we propose a suboptial schee to solve the global optiizatio proble i two steps. Firstly a low-coplexity trasissio ode selectio ad subcarrier allocatio algorith is executed. The by exploitig the properties of relayig trasissio ad oliear fractioal prograig a iterative power cotrol algorith is devised to optiize the power allocatio of S ad RSs for the syste EE axiizatio. The rest of this paper is orgaized as follows. Sectio describes the syste odel ad the atheatical forulatio of the proble uder cosideratio. I Sectio 3 the proposed resource allocatio algorith is elaborated. Sectio 4 provides the perforace evaluatio of the proposed algorith via uerical results. Fially Sectio 5 cocludes this paper. Proble Forulatio Cosider a OFA-based dowli wireless cellular etwor with relayig as illustrated i Fig. which cosists of oe cetral S fixed RSs ad K Ss. Each terial is equipped with a sigle oidirectioal atea ad operates i a half-duplexig ode. The syste badwidth is divided ito N orthogoal subcarriers whose chael ipulse respose is assued to be tieivariat withi each frae. The perfect global chael state iforatio (CSI) is assued to be ow at the S ad all coputatios are perfored i the S. Each S ca be served by the S either directly or idirectly via a servig RS. The trasissio is o a tie-frae basis with each frae further divided ito two tie slots with equal duratio as show by the solid ad dashed arrows i Fig.. For the S eployig direct trasissio the S trasits data to it directly durig the both two tie slots. While for the S eployig relayig trasissio the S trasits data to the correspodig servig RS i the first tie slot ad the servig RS decodes ad forwards the received sigals to the S i the secod tie slot. Figure Exaple relay-ehaced OFA wireless cellular etwors efie to be the relay selectio idicator where eas that the S chooses the RS as its servig RS ad otherwise. For the sae of coputatioal coplexity each S ca choose at ost oe servig RS.... K () It iplies that the S adopts direct trasissio if strict iequality holds i (). efie ad as the subcarrier allocatio idicators where (or ) eas that the S adopts direct trasissio (or relayig trasissio) o the subcarrier ad (or ) otherwise. I order to avoid itra-cell iterferece each subcarrier ca be oly allocated to at ost oe S where oly a sigle E-ISSN: Volue 3 4

3 WSEAS TRANSACTIONS o COUNICATIONS Xiaoya Huag Supeg Leg Fa Wu Yuig ao trasissio ode either direct or relayig ca be eployed. K... N () Let represet the badwidth of each subcarrier ad deote the average power of additive white Gaussia oise (AWGN) of each li. Let h ad g deote the chael gai o the subcarrier of the li betwee the S( )/RS ad the S ad the li betwee the S ad the RS respectively. Let p represet the trasit power of the S allocated o the subcarrier for the S i direct trasissio ode. Ad p ad p represet the trasit power of the S ad RS allocated o the subcarrier i the first ad secod tie slot for the trasissio to the S i relayig trasissio ode respectively. Accordigly the achievable ed-to-ed data rate (bit/s) of the S o the subcarrier eployig direct ad relayig trasissio are respectively calculated as r log p (3) ad r logi p p (4) where h ad g are the oralized chael gais. The factor / i (4) accouts for the fact that two tie slots are required for the two-hop relayig trasissio. Cosequetly the su throughput of the syste is give by R K N r r. (5) Ad the total trasit power of the syste icludes the trasit power of both the S ad RSs that is K N R PT p p p (6) where ad R deote the reciprocal of the drai efficiecies of the power aplifiers eployed at the S ad RSs respectively. I additio to the trasit power the eergy cosuptio of the syste also cosist of the circuit eergy cosuptio icurred by active circuit blocs which is relatively idepedet of the trasissio rate [9]. Let PC ad P R C represet the circuit power of the S ad each RS respectively. The the overall power cosuptio of the syste is give by R P PT PC PC. (7) I suary the EE is defied as the trasitted bits per uit eergy which ca be expressed as EE RP[9]. For the sae of the syste EE ad flexible QoS support for Ss it is essetial to optiize the Ss trasissio ode selectio subcarrier allocatio ad power cotrol joitly. I this wor the desig of eergy-efficiet ad QoSaware resource allocatio for the relay-ehaced OFA dowli wireless cellular etwors is forulated as a costraied optiizatio proble with the objective of axiizig the syste EE subject to the iiu data rate requireets of Ss as well as the separate axiu trasit power costraits at the S ad RSs. P: ax RP st.. N i C: r r R K N p p P K N p PR K C: C3: C4: C5: (8) C6: C7: p p p where R ad P i the objective fuctio are give by (5) ad (7) respectively. R i is the iiu data rate requireet of the S ; P ad P R are the axiu trasit power budget of the S ad the RS respectively. The variables to be optiized i P cotais the biary variables i.e. ad ad the cotiuous variables i.e. p p ad p. 3 Eergy-Efficiet ad QoS-aware Resource Allocatio Algorith Apparetly P i (8) is a o-covex ad cobiatorial optiizatio proble which ivolves a prohibitively high coputatioal coplexity. To this ed we propose to solve it i two steps as a suboptial solutio where the first step is to perfor the trasissio ode selectio ad subcarrier allocatio ad the secod step is to optiize the trasit power of the S ad the RSs for eergy efficiecy axiizatio. 3. Trasissio ode Selectio ad Subcarrier Allocatio I the cosidered etwor sceario fixed RSs are uiforly distributed o a circle with a specific distace away fro the S so that the cell ca be cosidered as beig divided ito sectors ad each sector is served by oe of the RSs. Obviously E-ISSN: Volue 3 4

4 WSEAS TRANSACTIONS o COUNICATIONS Xiaoya Huag Supeg Leg Fa Wu Yuig ao the path-loss has a substatial effect o the Ss receivig SNR ad hece the syste EE. Therefore a siple but effective schee is that each S chooses the correspodig sector s RS as its servig RS i case of adoptig relayig trasissio. oreover if the li betwee the S ad the S is better tha the weaer oe of the li betwee the S ad the S s servig RS ad the li betwee the servig RS ad the S the S will eploy direct trasissio; ad relayig trasissio otherwise. To be specific let ( ) be the idex of the servig RS of the S ad the equivalet chael gais of the S-S li the RS-S li ad the S-RS li are defied as H ( h... h ) H ( ) ( h ( )... h ( ) N ) N ad G ( ) ( g... gn ) respectively. The the S selects relayig trasissio if the iequality i H ( ) G ( ) H holds such that ( ) ad for ay ( ). Otherwise direct trasissio is chose so that for ay. Table The subcarrier allocatio algorith Algorith : Subcarrier Allocatio Algorith : Assuig that p P N ad pr PR N o each i i i subcarrier ad R R RK. Get the trasissio ode idex T { }( ) accordig to { }. Iitialize α α R PT the subcarrier set {... N} the allocated data rate R ad the differece i R ( ). : for the S : K while T Calculate ˆ arg i r ; T Update ˆ ad \ ˆ ; Update T i R R r ˆ ad R R ; Update T T R Rr ˆ ad P T PT p ˆ where R p ˆ p ad p ˆ p pr ; ed while ed for 3: if the for each subcarrier T R r Calculate arg ax K ; R T P P P p T C C T Update ad \ ; T Update R R r ad P T T PT p ; ed for ed if After the trasissio ode selectio for each S subcarriers are allocated while assuig that the total trasit power budget of the S ad RSs is evely allocated to each subcarrier. The ai idea is that the Ss are allocated with subcarriers sequetially accordig to the descedig order of their iiu data rate requireets. Each S is successively assiged the subcarrier with a capacity closest to its required data rate util the iiu data rate requireet of the S is satisfied. If there are residual subcarriers after fulfillig all the Ss deads the each reaiig subcarrier is allocated to the S achievig the highest EE icreet o it. The proposed subcarrier allocatio algorith is suarized i Table. 3. Power Cotrol of the S ad RSs Accordig to (4) the achievable data rate utilizig two-hop relayig trasissio depeds o the saller oe of p ( ) ad p ( ) ( ). If these two ites are ot equal to each other the surplus part of the bigger oe is useless for iprovig the data rate of the S but results i a waste of the power resource ad hece deterioratig the syste EE. Accordigly we ca decrease the correspodig trasit power util the two ites beig equal so as to reduce the power cosuptio further while without affectig the achievable data rate of the S. Therefore it is reasoable to assue that p ( ) p ( ) ( ) holds for ay S eployig relayig trasissio. The we ca get p ( ) p ( ) (9) is a costat for the where ( ) ( ) ( ) specified S ad subcarrier. Furtherore give the{ } { } ad{ } the su throughput i (5) ad the overall power cosuptio i (7) ca be rewritte as ˆ R log p l l log p ( ) l l () ad R ˆ R ( ) P PC PC p l p l l () where ad are the sets of Ss selectig direct trasissio ad relayig trasissio respectively; is the set of subcarriers assiged to the S. Accordigly P i (8) ca be rewritte as P: ax Rˆ Pˆ st.. i C: log p R l l i ( ) p l p P l l ( ) p PR l l l C: log p R () C3: C4: where is the set of Ss selectig the RS as servig RS. The optiizatio variables of P are E-ISSN: Volue 3 4

5 WSEAS TRANSACTIONS o COUNICATIONS Xiaoya Huag Supeg Leg Fa Wu Yuig ao p l ad p. Apparetly P is still a o-covex optiizatio proble due to the fractioal objective fuctio. Fortuately accordig to the oliear fractioal prograig theory [8] P ca be solved as a sequece of paraeterized optiizatio probles as forulated i (3) by the ielbach s ethod []. P3: ax Rˆ q ˆ ip st.. i C: log p R l l i ( ) p l p P l l ( ) p PR l l l C: log p R C3: C4: (3) where qi is the attaied EE i the previous iteratio. Sice logarith is a o-decreasig cocave fuctio it is straightforward to prove that ˆR i () is a cocave fuctio with respect to the optiizatio variables due to the fact that the perspective fuctio of a cocave fuctio is cocave ad the oegative weighted sus of cocave fuctios is cocave[]. I the eawhile it is clear that ˆP i () is a positive affie fuctio with respect to the optiizatio variables. Cosequetly the objective fuctio of P3 is cocave. Additioally all the iequality costrait fuctios of P3 are covex. Therefore P3 is a covex optiizatio proble so that the Lagrage dual ethod ca be eployed. Upo rearragig ters the Lagragia of P3 ca be writte as L νθ μ log p l l l l l l l log p q p i l ( ) q R i ( ) i ( ) p lrl l i R P PR R qi PC PC (4) where ν θ ad μ are the Lagragia ultipliers associated with the costraits C C C3 ad C4 of P3 respectively. deotes the power p allocatio policy of the syste. Accordig to the Karush-Kuh-Tucer (KKT) coditios [] the closed-for optial power allocatio of the S for the give paraeter qi ad Lagragia ultipliers is obtaied as l l p (5) qi ad l p R qi ( ) ( ) ( ) ( ) (6) The the optial power allocatio of the RSs i.e. p ( ) ca be readily obtaied fro (9) ad (6). O the other had to solve the dual proble of the prial proble P3 i.e. to fid ν θ ad μ for a give the gradiet ethod [] ca be used sice the dual fuctio is differetiable. Specifically the gradiet update equatios are give by ( t ) ( t ) ( t ) log i l l p l l Rl (7) l log p R ( t ) ( t ) ( t ) i ( ) ( t) ( t) ( t) P p p ad l l l (8) (9) ( ) ( ) ( ) t t t PR ( ) p () () t where t is the iteratio idex.5 t is the positive step size. Note that the process of coputig the optial power allocatio ad subsequetly updatig the Lagragia ultipliers is iterated util covergece is attaied which idicates that the optial poit of the prial proble P3 has bee reached. To su up the power cotrol procedure for EE axiizatio is suarized i Table. Table The iterative power cotrol algorith Algorith : Iterative Power Cotrol Algorith : Iitialize the iteratio idex i the syste EE q 5 ad the error tolerace. : do while qi qi Update i i ; Solve P3 to obtai the power allocatio policy ; Update q ˆ ˆ i R P ; ed do 4 Perforace Evaluatio I this sectio the perforace of the proposed algorith is evaluated via ote Carlo siulatios. E-ISSN: Volue 3 4

6 WSEAS TRANSACTIONS o COUNICATIONS Xiaoya Huag Supeg Leg Fa Wu Yuig ao A relay-ehaced OFA wireless cellular etwor with a radius of is cosidered which cosists of a cetral S three RSs ad ultiple Ss with a iiu data rate requireet uiforly distributed i a rage of 3~Kbps. There are 64 subcarriers each with a badwidth of 5Hz. The wireless chael is odelled by the Ouura-Hata path-loss ad bloc Rayleigh fadig. The AWGN spectral desity is 74 d/hz. We assue that S-RS li has lie-of-sight (LOS) propagatio while S-S ad RS-S lis do ot. The axiu trasit power ad static circuit power cosuptio of the S are set to P 4 W ad PC W while PR 5 W ad R PC 3 W for each RS. The reciprocal of the power aplifier s drai efficiecy of the S ad each RS R are.6 ad 5 respectively []. I order to verify the effectiveess of the proposed algorith we cosider other two resource allocatio algoriths i.e. ) SE w. relay algorith targetig to axiize the syste throughput of the relay-aided OFA wireless cellular etwor; ) EE w.o. relay algorith aiig to axiize the syste EE of the OFA wireless cellular etwor without deployig RSs. Firstly Fig. ad Fig.3 show the effect of the distace betwee the S ad RSs o the average EE ad syste throughput respectively. I this experiet three fixed RSs are evely placed o a circle aroud the S with a radius of r. Te Ss are uiforly distributed i a zoe of 6~ away fro the S. As illustrated i Fig. ad Fig.3 both the attaiable EE ad syste throughput first icrease ad the decrease with the distace betwee the S ad RSs for the give locatios ad iiu data rate requireets of Ss. This is due to the fact that the ed-to-ed perforace of twohop relayig trasissio depeds o the weaer oe betwee the S-RS ad RS-S lis. As the S-RS li has LOS propagatio the li is stregtheed gradually whe the RSs approach to the Ss ad hece iprovig both the attaiable EE ad SE. However the RSs caot be placed too close to the Ss sice the beefits gleaed fro havig a stroger RS-S li are the outweighed by havig a ore hostile S-RS li. ore iportatly it is evidet that the proposed algorith obtais rearable EE gai copared with the covetioal SE desig. ifferet fro the aggressive eergy cosuptio i the SE desig the proposed eergy-efficiet algorith does ot cotiue to icrease the syste throughput after achievig the axiu EE ad satisfyig the data rate requireets of Ss. As a result it suffers fro a certai aout of syste throughput loss. Average eergy efficiecy (Kbit/Joule) Average syste throughput (bps) SE w. relay istace betwee the S ad RSs () Figure Average EE versus the distace betwee the S ad RSs (i.e. ) SE w. relay istace betwee the S ad RSs () Figure 3 Average syste throughput versus the distace betwee the S ad Ss (i.e. ) O the other had Fig.4 ad Fig.5 show the effect of the distace betwee the S ad Ss o the average EE ad syste throughput respectively. I this experiet three RSs are evely placed o a circle aroud the S with a radius of 7 ad te Ss are located o a circle aroud the S with a radius of. As depicted i Fig.4 ad Fig.5 it is obvious that both the attaiable EE ad syste throughput decrease with the distace betwee the S ad Ss. Particularly both the two EE desigs outperfor the covetioal SE desig sigificatly. Furtherore it ca be foud that the proposed algorith obtais higher syste throughput tha the EE w.o. relay algorith owig to beefitig fro the relayig trasissio. Especially the gai is ore evidet whe the Ss are close to the RSs. O the other had the EE of the proposed algorith is superior to that of the EE w.o. relay algorith whe the Ss are located i the outer zoe of the cell. This stes fro the fact that the EE is defied as a ratio betwee the r r E-ISSN: Volue 3 4

7 WSEAS TRANSACTIONS o COUNICATIONS Xiaoya Huag Supeg Leg Fa Wu Yuig ao syste throughput ad the overall power cosuptio ad the overall power cosuptio of a relay etwor icludes ot oly the trasit power ad circuit power cosuptio of the S but also that of the RSs. Whe the Ss are closer to the S the S-S li is always strog eough to satisfy the Ss data rate requireets with lower power cosuptio which aturally leads to high syste EE despite without the assistace of RSs. I cotrast the syste throughput gai of the relayig trasissio is offset by the icreased overall power cosuptio such that the EE of the proposed algorith is lower tha that of the EE w.o. relay algorith i this case. O the cotrary whe the Ss gradually approach the cell edge the S- S li deteriorates greatly whereas the advatage of relayig trasissio is icreasigly proiet so that the EE of the proposed algorith overtaes that of the EE w.o. relay algorith accordigly. the Ss at the border of the cell. I this experiet three RSs are evely placed o a circle aroud the S with a radius of 7 ad eight Ss are uiforly distributed i a zoe of 8~ away fro the S with a fixed iiu data rate requireet of Kbps. Fig.6 ad Fig.7 illustrate the cuulative distributio fuctio (C) of the EE ad syste throughput usig differet algoriths respectively. Copared with the SE w. relay algorith the proposed algorith achieves up to 53.88% EE gai o average although it suffers fro a syste throughput loss of 44.7%. Furtherore the sae as eergy efficiet desig the proposed algorith outperfors the EE w.o. relay algorith by 49.87% ad 4.4% i ters of the EE ad syste throughput respectively SE w. relay EE w.o. relay F(x).5 Average syste throughput (bps) SE w. relay EE w.o. relay Eergy Efficiecy (Kbit/Joule) Figure 6 The C of eergy efficiecy istace betwee the S ad Ss () Figure 4 Average syste throughput versus the distace betwee the S ad Ss (i.e. ) SE w. relay EE w.o. relay F(x) Average eergy efficiecy (Kbit/Joule) istace betwee the S ad Ss () Figure 5 Average EE versus the distace betwee the S ad Ss (i.e. ) I additio Fig.6 ad Fig.7 are also provided to copleet Fig.4 ad Fig.5 to show the superiority of the proposed algorith for the case of.3.. SE w. relay EE w.o. relay Syste Throuthput (bps) Figure 7 The C of syste throughput 5 Coclusio This paper ivestigates resource allocatio for the EE axiizatio proble i OFA-based cellular relay etwors. A suboptial eergyefficiet ad QoS-aware resource allocatio algorith is proposed to solve the joit trasissio ode selectio subcarrier allocatio ad power cotrol proble i two steps. Nuerical results E-ISSN: Volue 3 4

8 WSEAS TRANSACTIONS o COUNICATIONS Xiaoya Huag Supeg Leg Fa Wu Yuig ao deostrate that the proposed algorith sigificatly outperfors the SE desig i ters of syste EE at a cost of certai aout of syste throughput loss. oreover it also idicates that icorporatig with relayig trasissio effectively helps to further iprove the EE ad syste throughput of the EE resource allocatio desig especially whe the Ss are located at the cell edge. Refereces: [] G. Y. Che S. Zhag S. Xu ad G. Y. Li Fudaetal tradeoffs o gree wireless etwors IEEE Cou. ag. vol.49 o.6 pp Jue. [] L. Correia. Zeller O. lue. Ferlig Y. Jadig I. Gódor G. Auer ad L. Va er Perre Challeges ad eablig techologies for eergy aware obile radio etwors IEEE Cou. ag. vol. 48 o. pp Nov.. [3] EARTH (Eergy Aware Radio ad etwor techologies) EU Fuded Research Project FP7-ICT EARTH. Available: [4] L. Collis Greeig the global etwor Egieer. Techol. vol. 5 o. 4 pp ar.. [5] C. Ha T. Harrold S. Arour I. Kriidis S. Videv P. Grat H. Haas J. Thopso I. Ku C.-X. Wag T. A. Le. Nahai J. Zhag ad L. Hazo Gree radio: radio techiques to eable eergy-efficiet wireless etwors IEEE Cou. ag. vol. 49 o. 6 pp Ju.. [6] G. iao N. Hiayat ad G. Y. Li Eergyefficiet li adaptio i frequecy-selective chaels IEEE Tras. Cou. vol.58 o. pp [7] G. iao N. Hiayat G. Y. Li S. Talwar istributed iterferece-aware eergy-efficiet power optiizatio IEEE Tras. Wireless Cou. vol. o.4 pp [8] G. iao N. Hiayat G. Y. Li S. Talwar Low-coplexity eergy-efficiet schedulig for upli OFA IEEE Tras. Wireless Cou. vol.6 o. pp.-. [9] C. Xiog G. Y. Li S. Zhag Y. Che ad S. Xu Eergy- ad spectral-efficiecy tradeoff i dowli OFA etwors. IEEE Tras. Wireless Cou. vol. o. pp [] C. Xiog G. Y. Li S. Zhag Y. Che S. Xu Eergy-efficiet resource allocatio i OFA etwors i Proc. IEEE Global Telecou. Cof. (GLOECO ) Housto pp.-5. [] F. Chu K. Che G. Fettweis Gree resource allocatio to iiize receivig eergy i OFA cellular systes IEEE Cou. Letters vol.6 o.3 pp [] Z. Zhou S. Zhou J. Cui S. Cui Eergy efficiet cooperative couicatio based o power cotrol ad selective sigle-relay i wireless sesor etwors IEEE Tras. Wireless Cou. vol.7 o.8 pp [3] R. ada N. ehta A. olisch J. Zhag Eergy-efficiet cooperative relayig over fadig chaels with siple relay selectio IEEE Tras. Wireless Cou. vol.7 o.8 pp [4]. Noleby. Aazhag User Cooperatio for Eergy-Efficiet Cellular Couicatios i Proc. IEEE It. Cof..Cou. (ICC ) Cape Tow pp.-5. [5] C. ae W. E. Star Ed-to-ed eergybadwidth tradeoff i ultihop wireless etwors IEEE Tras. Ifo. Theory vol.55 o.9 pp [6] C. Y. Ho ad C. Huag Eergy efficiet subcarrier-power allocatio ad relay selectio schee for OFA-based cooperative relay etwors i Proc. IEEE It. Cof..Cou. (ICC ) Kyoto Japa pp.-6. [7] K.T.K. Cheug S. Yag L. Hazo. Achievig axiu eergy-efficiecy i ulti-relay OFA cellular etwors: a fractioal prograig approach IEEE Trasactios o Couicatios 3 6(7): [8]. Naee K. Illao A.K Karoar et al.. Power allocatio i decode ad forward relayig for gree cooperative cogitive radio systes I Proc. IEEE Wireless Couicatios ad Networig Coferece (WCNC) Shaghai [9] S. Schaible. Fractioal prograig Zeitschrift fr Operatios Research 983 7: [] W. ielbach. O oliear fractioal prograig aageet Sciece 967 3: [] S. oyd L. Vadeberghe. Covex Optiizatio. Cabridge: Cabridge Uiversity Press [] O. Arold F. Richter G. Fettweis ad O. lue Power cosuptio odelig of differet base statio types i heterogeeous cellular etwors i Proc. Future Netw. obile Suit pp. -8. E-ISSN: Volue 3 4