Energy-efficient Subcarrier Allocation in SC-FDMA Wireless Networks based on Multilateral Model of Bargaining

Transcription

1 etworkng Energy-effcent Subcarrer Allocaton n SC-FDMA Wreless etworks based on Multlateral Model of Barganng Ern Elen Tsropoulou Aggelos Kapoukaks and Symeon apavasslou School of Electrcal and Computer Engneerng atonal Techncal Unversty of Athens (TUA 9 Iroon olytechnou str. Zografou 5773 Athens Greece eetsrop@netmode.ntua.gr; akapouk@netmode.ntua.gr; papavass@mal.ntua.gr Abstract In ths paper the problem of subcarrer and power allocaton n multuser sngle-carrer frequency dvson multple access (SC-FDMA wreless networks s addressed. Gven the nherent complexty of the correspondng ont optmzaton problem n ths paper we propose an approach where we treat the problem n three consecutve phases. Frst the subcarrer allocaton n terms of number of subcarrers allocated per user s obtaned by adoptng a multlateral barganng model.e. Rubnsten s barganng model. Then dfferent realstc subcarrer mappng polces are proposed towards determnng the specfc subcarrer assgnment. Subsequently an optmzaton problem wth respect to user s uplnk transmsson power s formulated and solved n order to determne the optmal power allocaton per subcarrer assgned to each user n the prevous phases. Emphaszng on energy effcency users satsfacton s formulated through a properly defned utlty-based framework that reflects the tradeoff between users actual uplnk throughput performance and ther correspondng energy consumpton. The performance evaluaton of the proposed approach s acheved va modelng and smulaton and ts superorty aganst other exstng alternatves s demonstrated. Keywords-. Subcarrer and power allocaton SC-FDMA Wreless Rubnsten barganng model. I. ITRODUCTIO Sngle Carrer Frequency Dvson Multple Access (SC- FDMA emerged as a promsng rado access technology for 4 th generaton (4G moble communcaton systems. As such t has been chosen as the uplnk multple access scheme n the Thrd Generaton artnershp roect-long Term Evoluton (3G-LTE standard []. In SC-FDMA the total bandwdth s dvded nto orthogonal subcarrers n order to be allocated to multple users. There are two types of subcarrer mappng: localzed (L-SC-FDMA and dstrbuted (D-SC-FDMA where the subcarrers are allocated to a user ether consecutve or dstrbuted respectvely []. L-SC-FDMA takes advantage of frequency selectve fadng n maxmzng throughput whle D-SC-FDMA avods allocatng subcarrers n deep fade and provdes reslence to frequency selectve fadng thus resultng n lower peak-to-average power rato (AR [3]. In our framework both dstrbuted and localzed SC-FDMA mappng are consdered. In ths paper we provde a robust and unfed framework that allows the energy effcent utlty based treatment of subcarrers and users uplnk transmsson power allocaton va a barganng model and a power optmzaton framework. As t s shown the proposed approach converges to a feasble and stable soluton whle numercal results demonstrate ts performance superorty when compared aganst exstng schemes appled n SC-FDMA. A. Related Work In [4] a utlty-based subcarrer and power allocaton scheme s proposed consderng two dfferent utlty functons: aggregate user data rate for maxmzng system capacty and aggregate logarthmc user data rate for maxmzng proportonal farness. Furthermore n [4] [5] the authors nstead of drectly treatng and solvng the optmzaton problem of resource allocaton they provde a greedy subcarrer allocaton scheme based on the mprovement of users margnal utlty. The subcarrers are organzed n chunks and the chunks are allocated to the users n order to mnmze the convergence tme of the greedy algorthm. In [6] a weghted-sum rate maxmzaton problem n SC- FDMA s consdered whch approxmates proportonal far schedulng usng udcously chosen weghts and a reformulaton of ths resource allocaton nto a pure bnarynteger problem s realzed. An extenson to [6] s proposed n [7] where two addtonal resource allocaton problems are consdered: rate constrant satsfacton wth mnmum number of subcarrers and sum-power mnmzaton subect to rate constrants. Furthermore an energy-effcent resource allocaton n multuser localzed SC-FDMA wth synchronous hybrd automatc repeat request s consdered n [8] whle a varable complexty sub-optmal approach towards mnmzng the energy n resource allocaton s proposed.

2 B. aper Contrbuton & Approach In ths paper we propose an approach where we treat the correspondng problem n three consecutve phases. Frst we adopt a multlateral barganng model.e. Rubnsten s barganng model to obtan a feasble and stable subcarrer allocaton n terms of the number of subcarrers allocated per user. Subsequently dfferent realstc subcarrer mappng polces can be followed to determne the specfc subcarrer assgnment. Fnally targetng energy effcency an optmzaton problem wth respect to user s uplnk transmsson power s formulated and solved n order to determne the optmal power allocaton per subcarrer assgned to each user n the prevous two phases. The basc features contrbutons and dfferences of our proposed approach and framework le n the followng: Users satsfacton s defned as an enhanced utlty functon of ther occuped system s resources that represents the tradeoff between users actual uplnk throughput performance and ther correspondng energy consumpton nstead of smply expressng the achevable data rate of each user usng the Shannon formula [4][5]. Based on that an Energy-effcent Utlty-based Subcarrer and ower Allocaton (EUSA non-cooperatve game s formulated towards maxmzng the personal utlty perceved by each user rather than studyng the centralzed problem of maxmzng the overall utlty of all users as n [4] [5]. A barganng model based approach s followed based on Rubnsten s -person multlateral barganng model - towards obtanng an ntal subcarrer allocaton to all users (n terms of the number of subcarrers allocated per user nstead of adoptng greedy [4] [5] or heurstc approaches whch have the drawback of hgh convergence tme to the stable outcome [6]-[8]. Three mappng polces to determne the assgnment of specfc subcarrers ID to each user are dscussed. The mappng polces consder and explot users channel gan. Gven the subcarrer allocaton and assgnment users uplnk transmsson powers are allocated n an optmal way concludng to a unque stable pont and achevng energyeffcency nstead of smply adoptng the non-energy-effcent equal-bt-equal-power (EBE allocaton for each subcarrer ([4] [5]. An teratve dstrbuted and low-complexty algorthm s proposed whch converges to the stable power allocaton and ts convergence s proven. The performance of the proposed approach s evaluated n detal n order to gan nsght about ts operatonal characterstcs whle ts superorty compared to other state of the art approaches.e. [4] [5] s llustrated. The rest of the paper s organzed as follows: Secton II ntally descrbes the system model and the adopted utlty functon. Then the optmzaton problem of the energy-effcent utlty-based subcarrer and users uplnk transmsson power allocaton s formulated. Secton III presents a feasble and stable subcarrer allocaton methodology based on a multlateral barganng model and secton IV provdes an optmzaton framework to treat the power allocaton problem. Secton V dscusses dfferent subcarrer assgnment/mappng polces whle an teratve dstrbuted algorthm to realze the overall proposed subcarrer and users uplnk transmsson power allocaton approach s descrbed. The performance evaluaton of the proposed framework s acheved va modelng and smulaton n Secton VI and fnally secton VII concludes the paper. II. SYSTEM MODEL AD BACKGROUD IFORMATIO The tme synchronzed uplnk for a sngle cell of a multple users wreless communcatons system employng SC-FDMA wth system bandwdth B Hz s consdered. The tme axs s dvded nto tmeslots (0.5 ms duraton as a basc unt of tme schedulng. The system bandwdth B Hz s dvded nto a set S = { s / = {... } =...K } where sub K denotes the number of subcarrers occuped by user and { s /...K } S = = refers to the correspondng set. The total number of users resdng n the cell s and the correspondng set s denoted by = {... } whle the overall number of subcarrers n the system s S = K. User at subcarrer s S has channel gan transmsson power s G s = and uplnk. User s total uplnk transmsson power s upper lmted by hs maxmum power due to hs physcal lmtatons.e. K = s. Furthermore the receved bt energy to nterference densty rato at the s base staton for user at subcarrer s s gven by: s G s s = ( σ s where σ s denotes the nose power of subcarrer s. In order to algn user s varous flow characterstcs under a common optmzaton framework each moble user s assocated wth a sutable utlty functon U that refers to the level of satsfacton the user receves as a result of hs actons and correspondng allocated resources. Amng at consderng utltes from the users pont of vew the unque characterstcs of the wreless transmsson envronment n terms of transmsson errors occurred at the recever (whch are strongly related wth the acheved sgnalto-nterference rato (SIR play a key role n the defnton of the utlty. On one hand hgher SIR level at the recever wll result n a lower bt-error rate and hence hgher throughput whle on the other hand achevng a hgh SIR level usually requres the user to transmt at a hgh power whch n turn results n lower battery lfetme. In ths work we consder that user s utlty represents hs degree of satsfacton at hs s

3 allocated subcarrer s S S sub n relaton to the expected tradeoff between hs actual uplnk throughput performance and the correspondng energy consumpton. Therefore the adopted utlty functon [9] s expressed as: Ropt f ( s U s ( s = ( s where R s user s fxed desgned transmsson rate opt dependng on user s requested servce and f ( s s hs effcency functon. The latter represents the probablty of a successful packet transmsson for user at subcarrer s and s an ncreasng functon of hs bt energy to nterference densty rato. User s effcency functon can be represented by a s sgmodal-lke functon of hs power allocaton for varous modulaton schemes [9]. Therefore user s effcency functon has the followng propertes:. f ( s s an ncreasng contnuous twce dfferentable and sgmodal functon wth respect to s.. f ( f ( =. = to ensure that U (0 = 0 when = 0. s The valdty of the above propertes has been demonstrated n several practcal scenaros wth reasonably large packet szes M.e. M 00bts [0]. Therefore the overall user satsfacton can be expressed as: s K K s s s s = U (... K U ( s = = (3 where K denotes the number of subcarrers allocated to user A. Energy-effcent Utlty-based Subcarrer and ower Allocaton (EUSA on-cooperatve Game Formulaton { } = S denote the energyeffcency utlty-based subcarrer and power allocaton (EUSA game n SC-FDMA wreless networks. Each user selects a number of subcarrers K and the correspondng transmsson power s for each of hs allocated subcarrers s S n order to maxmze hs overall expected utlty U va mnmzng hs power consumpton and n parallel satsfyng hs Qualty of Servce (QoS prerequstes. Therefore the overall optmzaton problem s formulated as: Let G S { } U( s K where K s = s K = s s s s = 0 K S K s.t. s S = K = = max U (... K U ( (4 = [0 ] denotes the set of user s feasble uplnk transmsson power whch s a compact and convex set wth maxmum and mnmum constrants. As t s observed va the EUSA optmzaton problem (4 each user may transmt wth a dfferent transmsson power s at each of hs allocated subcarrer to acheve energy-effcency. More specfcally allocatng subcarrers and users uplnk transmsson powers by solvng a standard form of the optmzaton problem (4 s extremely complex due to the followng reasons: ( The obectve functon n (4 s formulated as a complex form dependent on both subcarrer and power allocaton and ( there s an addtonal power constrant for each user.e. = [0 ]. In the followng at the frst step of our approach we determne a feasble and stable subcarrer allocaton of EUSA game (.e. a vector of users subcarrers ( K K... K... K K = based on Rubnsten s -person multlateral barganng model. As clarfed before the subcarrer allocaton procedure based on the -person multlateral barganng model determnes the total number of subcarrers that should be allocated to each user. However t does not drectly dentfy the actual subcarrers to be assgned and used by each user (.e. subcarrer IDs wthn the avalable range and spectrum. Thus at the second step of our approach dfferent assgnment (mappng polces are followed dependng on varous prortzaton factors and obectves and as a result dfferent mappngs can be obtaned and realzed. For example one such assgnment could be based on sequental subcarrer selecton followng the localzed (L-SC- FDMA mappng approach whle alternatve assgnments favorng specfc users (e.g. dstant users vs. closer ones to base staton and vce versa would allow for assgnment of subcarrers that are dstrbuted over the entre avalable frequency band (D-SC-FDMA. In Secton V several such alternatve polces are presented whle ther performance and mpact s evaluated n detal n Secton VI. After determnng the specfc subcarrer allocaton at the thrd step of our approach an optmzaton problem s formulated (secton IV where each user ams to maxmze hs utlty U ( s s at each of hs allocated subcarrer. Specfcally the optmzaton problem uses K to determne the optmal user s uplnk transmsson power allocaton. It should be noted that we follow the aforementoned sequental mult-phase approach n order to deal wth the hgh complexty of the combned problem of subcarrer and power allocaton. As a consequence our fnal soluton though results to a feasble and stable allocaton does not guarantee optmalty wth respect to the ntal ont resource allocaton problem. evertheless t guarantees optmal power assgnment to the allocated subcarrers thus achevng energy-effcency whle as demonstrated by numercal results the proposed approach prevals over greedy and heurstc alternatves. III. SUBCARRIER ALLOCATIO BASED O MULTILATERAL MODEL OF BARGAIIG To allocate the total number of subcarrers S to the users resdng at the cell per tme slot varous greedy or heurstc subcarrer allocaton schemes have been proposed [3]-[8]. 3 3

4 However these allocatons are nether optmal nor converge always to a statonary pont. In the followng the subcarrer allocaton s obtaned adoptng a multlateral barganng model. Rubnsten [] models a two-person barganng n order to share a pe of sze as an extensve game by makng use of a game structure n whch two players take turns n makng offers. The pe wll be shared only after the players reach an agreement. Each player n barganng round t offers a partton of the pe x (t and hs opponent may agree to the offer (Y or reect ( t. Acceptance of the offer ends the barganng. After reecton the reectng player then has to make a counter offer to the next barganng round and so on. Furthermore there are no rules whch bnd the players to any prevous offers they have made. Consderng the nfntehorzon game the exstence of a unque equlbrum has been proven n []: δ x = ( x x = + δ + δ (5 where δ s the same dscount factor for each player. The game can be summarzed n the followng graph: Fgure. Blateral Barganng Model In ths paper n order to allocate the pe of the total number of subcarrers S to the users an extenson of Rubnsten s alternatng-offers barganng model to the case of players s adopted and s called -person multlateral barganng model [3]. The -person barganng game G( t;... over a pe of sze S wth dentcal players s defned as: layer makes the frst offer at barganng round t= x = x x...x...x where x s user/player s offerng ( proposed share/partton and = x =. layer to player then respond sequentally each sayng ether accept (Y or reect ( to the proposal. In the case of all responders accept player s offer then the game ends wth each player obtanng a partton x. A reecton takes the game to the next barganng round where player now makes an offer and players ( 3... sequentally respond. In the case of the responders reect at barganng round t= then the game goes to the next stage wth player 3 makng the offer and so on. If the offer x s accepted by all responders n barganng round t the payoff s δ t x to player where δ< s the common dscount factor. Absence of agreement that s barganng forever leads to a payoff of 0 for all players. To overcome the obstacle of barganng forever dscount factor δ close to one s adopted correspondng to a short tme nterval between barganng rounds as n ths case the frst players advantage to the ntal offer s small. In [3] t s proven that the barganng game s ash equlbrum s gven as follows: δ δ ι δ Ν δ x = δ... δ... δ δ δ δ δ (6 In our approach we adopt the Rubnsten s -person multlateral barganng model and allocate the total number of subcarrers to the users resdng n the cell accordng to ts proven unque ash equlbrum pont. A ash equlbrum n subcarrers s formally defned as: Defnton : A subcarrer vector K ( K... K... K = s a ash equlbrum of the EUSA game G S { } { U( s K = S } where S = { s / =...K } f U ( - s K K U ( s K K- every and for all { } =...K sub ( K... K K +... K for S S where K - = s the - dmensonal vector of user subcarrers that does not contan user s subcarrers. Theorem : A ash equlbrum n subcarrers for game GS = { } { U( s K S } exsts s unque and s gven by: ( δ δ K = S0 δ (7 δ roof: The proof s a straghtforward applcaton of the correspondng proof n [3] where t s shown that the Rubnsten s -person ( multlateral barganng model concludes to a unque ash equlbrum. In our case the pe to be allocated s the total number of subcarrers and as a result the unque ash equlbrum s gven by (7. Based on theorem we obtan a closed form soluton n allocatng the total number of subcarrers to the users. However due to the fact that the subcarrers to be allocated to the users s a dscrete source n the followng we utlze the round of K thus the number of subcarrers allocated to each user s obtaned as: ( δ δ K = S 0 δ. (8 δ Based on extensve smulatons we have verfed that the dfference between usng the allocaton gven by relaton (7 and the correspondng one resultng from the roundng process s less than one percent wth respect to the total number of allocated subcarrers. Furthermore two mportant observatons are noted concernng the subcarrer allocaton: A. The earler a player has been admtted to the EUSA game the greater porton of resources he takes. Thus amng at achevng farness and party among the compettve users as well as attanng a short tme nterval between barganng rounds adoptng dscount factors close to one s the most appealng strategy. However f amng at dfferentatng the users accordng to QoS prerequstes or dfferent servce 4 4

5 classes lower value of dscount factor can be selected gvng prorty to the frst users nserted n the barganng rounds. B. As the number of users ncrease the achevable resources allocated to each user are reduced snce the total resources are fnte and dvded among more players. In the followng we frst analyze the optmal power allocaton among the subcarrers assgned to each user assumng that both subcarrer allocaton and respectve assgnment/mappng polcy have already been performed. Then n secton V dfferent subcarrer assgnment polces are dscussed and analyzed. IV. OWER ALLOCATIO TOWARDS EERGY-EFFICIECY In ths secton for the sake of presentaton and wthout loss of generalty we assume user has been allocated a total number of K subcarrers namely K subcarrers s s...s...s. In order to acheve users power allocaton gven ther subcarrer allocaton we formulate an optmzaton problem consderng each user s satsfacton (.e. utlty per each of hs allocated subcarrers. Specfcally we formulate a pure power control optmzaton problem gven subcarrers assgnment to user : max U ( s K K = s s s s.t. Consderng the above optmzaton problem at each of user s allocated subcarrer each user computes hs optmal transmsson power vector s = K s... s s S S sub and determnes hs resultng utlty vector U ( = [U ( U (...U (...U ( ] K K s s s s s s s s In the followng we study the exstence and unqueness of an optmal stable pont n users uplnk transmsson powers for the proposed optmzaton problem. Theorem : A stable pont n user s uplnk transmsson power for the proposed optmzaton problem (9 exsts s unque and s gven by s K s... = where s s s the unque global maxmzaton pont of user s utlty functon. σ s s mn u s = s G (0 s u u=... K roof: In Secton II t was descrbed that the effcency functon f ( s s a sgmodal functon of s. Moreover the receved bt energy to nterference densty rato s at the base staton for user at subcarrer s has a strct lnear relatonshp to the correspondng uplnk transmsson power n accordance to ( thus t follows that the relably s (9 transmtted bts to the base staton.e. opt ( s R f formulate also a sgmodal functon wth respect to user s uplnk transmsson power s. Due to the fact that Ropt f ( s s a sgmodal functon wth respect to the rato R opt f ( s s = U ( s a quas-concave functon of s s s 0 followng the approach n [5]. Consderng the frst order dervatve optmzaton condton we conclude U s ( s that = 0. Thus U s ( s s maxmzed s when f ( f ( = 0 s s s s s s s ( s s due to the fact that = by (. Consderng the s s sgmodal type of f s ( s relaton ( has a unque soluton. Thus the unque uplnk transmsson power s σ s s s that maxmzes U s ( s s: s =. G s Concludng our proof we examne the case of the maxmum remanng uplnk transmsson power s less than s. Then U u s s the hghest value of U s s ( s u u=...k snce the utlty functon s ncreasng over 0 s. Thus the global maxmum of U ( s gven by relaton (0. s s V. EUSA ALGORITHM & ASSIGMET/MAIG OLICIES In ths secton based on our prevous analyss we ntroduce an teratve and dstrbuted algorthm that determnes users subcarrer and uplnk transmsson power allocaton whle ts convergence s studed. Furthermore dfferent subcarrer assgnment/mappng polces are dscussed and therefore varatons of EUSA algorthm are ntroduced accordngly. The frst algorthm varaton - n the followng we refer to as ure-eusa - allocates the subcarrers to the users based on Rubnsten s -person multlateral barganng model and the users are assgned only sequental subcarrers to transmt (.e. local mappng polcy That s user s sequentally assgned the frst K subcarrers user s assgned sequentally the next set of K subcarrers etc. Alternatvely n the second varaton - we refer to as mum Gan Selecton EUSA (MGS-EUSA - a dstrbuted subcarrer mappng polcy s followed whch prortzes users transmsson to ther 5 5

6 allocated subcarrers. More specfcally two alternatves of MGS-EUSA are studed: (A Gan Selecton-Far- EUSA (MGS-F-EUSA whch allows the more dstant users from the base staton to choose frst and transmt to those subcarrers that have the best resultng channel gan and (B Gan Selecton-ear-EUSA (MGS--EUSA whch gves prorty to the less dstant users n a smlar way. All varatons of EUSA algorthm are dvded nto two basc parts. The frst part allocates and assgns the subcarrers to all users and the second part gven the subcarrer allocaton and mappng determnes the optmal users power allocaton. EUSA Algorthm Step : (Subcarrer Allocaton At the begnnng of tme slot t the optmal subcarrer allocaton ( K K... K... K K = s determned va equaton (8 based on Rubnsten s multlateral barganng model and announced to all users. (Subcarrer Mappng Step a (Only for ure-eusa Algorthm: The user wth number ID occupes and transmts to the frst K subcarrers the user wth number ID occupes the followng K subcarrers and so on tll all users are exhausted. Step b (Only for MGS-F-EUSA Algorthm: Startng from the more dstant user the user selects and transmts to the K subcarrers wth best channel gan. Step c (Only for MGS--EUSA Algorthm: Startng from the less dstant user the user selects and transmts to the K subcarrers wth best channel gan. Step 3: (Utlty and ower Optmzaton Each user computes hs uplnk transmsson power based on equaton (0 for hs assgned subcarrer s S. Set k=0. Step 4: Set k:=k+ delete the subcarrer s n the set of ( user s avalable subcarrers.e. k + ( K k { = K s } renew user s maxmum transmsson power.e. ( k + ( k ( k + = s and f 0 or S go to step 3 otherwse stop. A. Convergence Both varatons of EUSA algorthm (.e. ure-eusa and MGS-EUSA can be characterzed as sngle-valued best response algorthm. The complexty of the proposed EUSA algorthms s low due to the smplcty of the calculatons n order to determne users subcarrer and power allocaton. Specfcally n our study we have consdered the nfntehorzon game [3] where essentally convergence of EUSA algorthm n subcarrer allocaton s acheved based on sngle calculaton process va equaton (8. In ths case the overall convergence of the proposed approach s domnated by the last phase of our algorthm (.e. optmal power allocaton and s dscussed n more detal below and n the numercal evaluaton secton. It s noted also that f fnte-horzon game were consdered then the convergence speed and the concludng allocaton s nfluenced by the approprate selecton of the dscount factor.e. selecton of dscount factors close to one attans a short tme nterval between barganng rounds. The convergence of EUSA algorthm n users uplnk transmsson powers can be proven va the best response approach. Based on theorem user s best response BR s denoted as follows. σ s s BR( mn u s = s G ( s u u=... K Theorem 3: EUSA algorthm converges to the unque stable pont wth respect to users uplnk transmsson powers startng from any ntal pont. roof: In theorem we have shown the unqueness of a stable pont n users uplnk transmsson powers whch s denoted by = ( s s s s. By defnton ths stable pont has to satsfy: = BR( (3 where BR( ( BR( BR (... BR ( s s s = s the best response strategy of all users. The fundamental pont to show the convergence of EUSA algorthms to the unque stable transmsson power s to show that the best response functon BR( s standard [4]. A functon s characterzed as standard f t satsfes the followng propertes for all x 0 where x = ( x x... x s a stable pont of the optmzaton problem ostvty: f ( x 0; Monotoncty: f x ' x then f( x f( x ' ; Scalablty: for all α> af ( x f ( ax. These propertes can be easly verfed for BR(. 0 thus BR( 0 ; ' f then va equaton (3 we conclude that ' BR( BR( ; for all α> then va equaton (3 we conclude that α BR( BR( α. VI. UMERICAL RESULTS AD DISCUSSIOS In ths secton we provde numercal results to evaluate the performance of the proposed framework. Intally we present some results n order to gan some nsght about the operaton and features of the proposed EUSA framework and demonstrate ts effectveness. Afterwards a comparatve study s provded amng at showng the beneft and superorty of adoptng Rubnsten s barganng model n realzng the subcarrers allocaton rather than a greedy one [4] [5]. Specfcally the uplnk of a sngle-cell tme slotted SC- FDMA system s consdered supportng =0 contnuously backlogged users that are allocated at dstances 6 6

7 d+ = d + 50 [m] wth d =300m from the base staton. Ths topology has been specfcally chosen n order to reveal the operatonal characterstcs of EUSA algorthm as t allows for better understandng and nterpretaton of the correspondng results and observatons. Smlar overall results are acheved for other random topologes as well. Therefore n our study we emulate the scenaro where users channel condtons become worse as ther ID value (.e. = 0 ncreases. Each smulaton lasts tme slots whle pathloss and shadowng effect are generated randomly and are assumed to be constant durng each tme-slot. Thus each user s assumed to be statonary or slowly movng. Moreover we assume that the mult-path fadng component s tme nvarant over the tme slot but changes ndependently at each tme slot. Therefore unless otherwse explctly ndcated we model a users path gans as G =Λ d s s where d s the dstance of user from the base staton a s the dstance loss exponent and Λ s a log-normal dstrbuted random varable wth s standard devaton 8dB whch represents the mult-path fadng effect. Moreover we set users maxmum uplnk transmsson 5 power to = Watts and σ s = 50. A. Operaton and erformance of roposed Approach For smplcty n the presentaton only the ure-eusa algorthm s consdered n ths subsecton. In addton we assume that the closest to the base staton users (.e. those wth smaller IDs are the frst ones to enter the barganng rounds (.e. n step of the algorthm whle the most dstant users (those wth larger IDs are the last ones to be mported. Fg. llustrates the number of subcarrers allocated to each of the =0 users n the cell under varous dscount factors. It s observed that as the dscount factor decreases the frst users nserted n the barganng rounds are favored compared to the rest and a larger porton of the subcarrers s allocated to them. However amng at a far allocaton among the users a dscount factor δ close to one s a more approprate choce. Fg. and Fg. 3 llustrate total user s uplnk transmsson powers and total acheved user s uplnk transmsson rates at the stable pont of the optmzaton problem (9 for each user (dfferentated by users ID under two dfferent dscount factors consderng the ure-eusa algorthm. The correspondng results reveal that users uplnk transmsson powers are nversely proportonal to ther nstantaneous channel condtons whle based on the proposed power optmzaton model users do not exhaust ther maxmum uplnk transmsson power thus extendng ther battery lfe. Furthermore due to the fact that as the dscount factor ncreases (.e. δ=0.95 more subcarrers are allocated to the dstant users whch are the last that are mported n the barganng rounds the total dstant users uplnk transmsson power ncreases when the dscount factor ncreases. For the same reason as observed by the results n Fg. 3 when consderng lower dscount factor the frst users nserted Fgure. umber of subcarrers allocated to =0 users consderng varous dscount factors. Fgure. Total users uplnk transmsson powers wth varous dscount factors. Fgure 3. Total users uplnk transmsson rates wth varous dscount factors. Fgure 4. User s Transmsson ower Convergence. n the barganng rounds and smultaneously the ones wth better channel acheve hgher uplnk transmsson rate. Ths dfference s reversed consderng the dstant users whch occupy more subcarrers for a hgh dscount factor than for a low value of dscount factor thus achevng hgher uplnk transmsson rate. Fg. 4 llustrates user s uplnk transmsson power evoluton per each of hs allocated subcarrer as a functon of the teratons requred for ure-eusa algorthm to converge at ts equlbrum pont. We observe that the convergence of the 7 7

8 proposed algorthm s very fast snce n less than twenty teratons all subcarrers have reached the equlbrum pont. B. Comparatve Study of ure-eusa and MGS-EUSA In ths subsecton we provde a comparatve study of the ntroduced EUSA varatons.e. ure-eusa and the two versons of Gan Selecton EUSA (that s MGS-F- EUSA whch gves prorty n subcarrer selecton to the more dstant users and MGS--EUSA whch gves prorty to the less dstant users. Specfcally n Fg. 5 and Fg. 6 we compare the users average uplnk transmsson power and the correspondng total utlty-based performance of all the three algorthms. The correspondng results reveal the benefts of MGS-F-EUSA algorthm vs. ure-eusa and MGS--EUSA algorthms n terms of lower users average uplnk transmsson powers (Fg.5 and hgher users total utlty-based performance (Fg.6. Ths behavor s observed due to the fact that gvng the opportunty to the dstant users (whch are already unfavored due to ther poston n the cell to select and transmt to those subcarrers where they experence better channel gans they acheve hgh utlty and smultaneously lower uplnk transmsson powers. Ths s sgnfcant especally takng nto account the scarcty of the rado resources n wreless networks the moble nodes physcal lmtatons and users tme varyng channel condtons. Furthermore we note that smlar trend - n terms of ncreasng power consumpton and decreasng utlty - s observed for all algorthms as we move towards users wth hgher ID (.e. more dstant from the base staton. C. Tradeoff between Energy Consumpton and Rate In ths subsecton the crtcal tradeoff between user s energy consumpton and the correspondng actual uplnk transmsson rate s evaluated n more detal. The rato of user s uplnk transmsson power to the correspondng actual uplnk transmsson rate s used as a sngle-value metrc to llustrate each user s cost (n terms of power per bt/sec for hs acheved transmsson rate. Three dfferent scenaros are comnsdered: (a ure-eusa algorthm consderng a logarthmc concave utlty functon of user s sgnal-tonterference densty rato whch approxmates the capacty va the classcal Gaussan formula [] whle adoptng the equalbt-equal-power (EBE allocaton (b MGS--EUSA and (c MGS-F-EUSA algorthm both consderng the utlty functon as expressed n ( and adoptng the optmal power allocaton (descrbed n Secton IV. Specfcally Fg. 7 presents the correspondng tradeoff between the total consumed energy and the correspondng acheved actual transmsson rate by all users as a functon of the dscount factor δ. It s observed that MGS-F-EUSA algorthm consderng the utlty functon as expressed n relaton ( and adoptng the proposed optmal power allocaton acheves the lower cost.e. wth lower power consumpton acheves hgher actual transmsson rate. Ths outcome s sgnfcant due to the fact that a more effcent resource allocaton s acheved from the system s pont of vew. Fgure 5. Users average uplnk transmsson powers of MGS- -EUSA ure-eusa and MGS-F-EUSA wth δ=0.95. Fgure 6. Total users utltes of MGS--EUSA ure- EUSA and MGS-F-EUSA wth δ=0.95. Fgure 7. Tradeoff among energy consumpton and achevable rate Fgure 8. Rate sum capacty vs ncreasng number of users D. Comparatve Study to Greedy Approaches In ths subsecton a comparatve study of our ntroduced subcarrer allocaton approach based on the multlateral barganng model aganst greedy frameworks adopted n recent lterature [4] [5] where the subcarrer allocaton s based on the mprovement of users margnal utlty s provded. The man obectve of ths comparson s to support and ustfy the choce of Rubnsten's barganng model n terms of effectveness n subcarrer allocaton. For farness n the comparson and n order to have a common bass and 8 8

9 metrc for all scenaros consdered here the non-energyeffcent equal-bt-equal-power (EBE allocaton s used whle user s maxmum uplnk transmsson power s assumed to be: = 0.5 Watts. Furthermore towards maxmzng spectral effcency a logarthmc concave utlty functon of user s sgnal-to-nterference densty rato s adopted [] whch approxmates the capacty va the classcal Gaussan channel formula. Fg. 8 presents the rate sum capacty where the sum of users data rates s the consdered utlty functon as a functon of ncreasng number of users. Fve scenaros have been assumed: ( R-L-FDMA: L-FDMA wth users selected by round-robn [4] ( S-L-FDMA: L-FDMA wth the channel dependent schedulng (CDS proposed n [4] ( R-I-FDMA: Interleaved-FDMA.e. users selected subcarrers are equdstant from each other wth users selected by round-robn (v S-I-FDMA: I-FDMA wth the CDS method proposed n [4] and (v Rubnsten s multlateral barganng model n order to allocate the total subcarrers to the users. The correspondng results clearly reveal the superorty of the proposed approach resultng n sgnfcantly hgher rate sum capacty. VII. COCLUSIOS In ths paper we ntroduced an energy-effcent utlty-based subcarrer and power allocaton framework for applcaton n the next generaton SC-FDMA wreless networks. The proposed approach ntally determnes the subcarrer allocaton va Rubnsten s -person multlateral barganng model thus decomposng the orgnal ont resource allocaton and then realstc mappng polces are used towards specfyng the subcarrers ID assgnment va consderng users channel gan condtons. Afterwards an optmzaton problem s formulated and solved amng at maxmzng users utltes per each of ther allocated subcarrer and achevng energy-effcency. The obtaned numercal results demonstrate that such an approach sgnfcantly outperforms exstng resource allocaton methods. Its superor performance stems from the approprate choce of the order that the users enter the barganng game as well as the appled subcarrer mappng polcy (.e. favourng the users closer to the base staton for achevng hgher rate-sum-capacty (MGS-- EUSA or favourng the ones wth worse channel gans (MGS-F-EUSA. It should be noted that among the key features of our approach s the ntroducton of a holstc and flexble common framework that allows for: a the support of heterogeneous servces and users wth dfferent QoS b the mplementaton of dfferent users prortes n accessng the avalable resources (.e. through the use of dfferent dscount factors δ c the realzaton of dfferent performance obectve functons and metrcs (.e. maxmze rate-sum-capacty farness etc.. Towards ths drecton the performance evaluaton study and analyss of the mpact of the use of dfferent subcarrer mappng polces along wth the use of dfferent dscount factors δ under varous realstc network topologes and user dstrbutons s of hgh research and practcal mportance and part of our current research. ACKOWLEDGEMETS Ths research s co-fnanced by the European Unon (European Socal Fund and Hellenc natonal funds through the Operatonal rogram 'Educaton and Lfelong Learnng' (SRF REFERECES [] Hyung G. Myung Davd J. Goodman Sngle Carrer FDMA: A ew Ar Interface for Long Term Evoluton John Wley & Sons Ltd 008. [] Hyung G. Myung Junsung Lm Davd J. Goodman Sngle carrer FDMA for uplnk wreless transmsson IEEE Vehcular Technology Magazne Vol. Issue 3 pp Feb [3] H.G. Myung J. Lm and D.J. Goodman eak-to- Average ower Rato of Sngle Carrer FDMA Sgnals wth ulse Shapng IEEE Internatonal Symposum on ersonal Indoor and Moble Rado Communcatons (IMRC pp. -5 Helsnk Fnland Sep [4] Junsung Lm H.G. Myung Oh Kyungn D.J. Goodman roportonal Far Schedulng of Uplnk Sngle-Carrer FDMA Systems IEEE 7th Int. Symp. on ersonal Indoor and Moble Rado Communcatons pp [5] Junsung Lm H.G. Myung Oh Kyungn D.J. Goodman Channel-Dependent Schedulng of Uplnk Sngle Carrer FDMA Systems IEEE Vehcular Technology Conference pp [6] I.C. Wong O. Oter W. Mccoy Optmal resource allocaton n uplnk SC-FDMA systems IEEE Transactons on Wreless Communcatons vol. 8 ssue 5 pp [7] F.I. Sokmen T. Grc Uplnk resource allocaton algorthms for Sngle-Carrer FDMA systems European Wreless Conference (EW pp [8] D.J. Dechene A. Sham Energy Effcent Resource Allocaton n SC-FDMA Uplnk wth Synchronous HARQ Constrants IEEE Internatonal Conference on Communcatons (ICC pp [9] C. U. Saraydar. B. Mandayam and D. J. Goodman Effcent power control va prcng n wreless data networks IEEE Trans. on Commun. vol. 50 pp Feb. 00. [0] E. E. Tsropoulou T. Kastrnoganns and S. apavasslou QoS-Drven Uplnk ower Control n Mult-Servce CDMA Wreless etworks - A Game Theoretc Framework Journal of Communcatons Academy ublsher vol. 4 o 9 pp Oct [] S. Guntur and F. agann Game theoretc approach to power control n cellular CDMA n roc. of 58th IEEE Vehcular Technology Conference (VTC pp Orlando FL Oct [] Arel Rubnsten erfect Equlbrum n a Barganng Model Econometrca Econometrc Socety vol. 50 no. pp January 98. [3] Ger B. Ashem A unque soluton to n-person sequental barganng Games and Economc Behavor Elsever vol. 4 no. pp Aprl 99. [4] R.D. Yates A framework for uplnk power control n cellular rado systems IEEE J. Select. Areas Commun. vol. 3 pp Sept [5] V. Rodrguez An analytcal foundaton for resource management n wreless communcaton n: roc. of IEEE Global Telecom. Conf. 003 (GLOBECOM 03 vol. no. pp Dec