A Non-cooperative Game Theoretic Approach for Multi-cell OFDM Power Allocation Ali Elyasi Gorji 1, Bahman Abolhassani 2 and Kiamars Honardar 3 +

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1 29 Internatona Symposum on Computng, Communcaton, and Contro (ISCCC 29 Proc.of CSIT vo. (2 (2 IACSIT Press, Sngapore A Non-cooperatve Game Theoretc Approach for Mut-ce OFDM Power Aocaton A Eyas Gorj, Bahman Abohassan 2 and Kamars Honardar 3 +,2 Iran Unversty of Scence and Technoogy(IUST,Schoo of Eectrca Engneerng Tehran 6846, Iran 3 Shahed Unversty Abstract. In ths paper, we deveop a dstrbuted adaptve power aocaton based on game theory n the orthogona frequency dvson mutpexng (OFDM ceuar systems. In ths work, power contro probem s soved based on the dea of the Nash equbrum (NE from non-cooperatve game. In ths regard, a utty functon s proposed that each user seeks to seect a transmt power eve such that maxmzes ts own utty by adjustng the transmt power on each subchanne. In process of power contro game, the users whch have better subchanne gan use ower power for transmsson; When as the outyng users, due to encounterng hgher path oss, have ow subchanne gan and consume more power to be abe to guarantee wanted bt rate. Power contro game provdes far data rate ower power consumpton for a users n comparson wth mproved Water-fng (WF approach as smuaton resuts show. Keywords: OFDM, power contro, non-cooperatve game, NE, utty functon. Introducton In OFDM systems, Instead of transmttng symbos sequentay over the communcaton channe, the channe s spt nto many subchannes and the data symbos are transmtted n parae over these subchannes. Therefore, the mpact of nter-symbo nterference (ISI decreases (.e. the fadng per sub-channe s fat. So, OFDM s a promsng technoogy for hgh data rate transmsson n wdeband wreess systems for ts abty to mtgate the effects of fadng and combatng aganst nter-symbo nterference. Due to these speca trats, many new modern communcaton systems use OFDM to utze ts exceent advantages; for exampe WMax (IEEE 82.6e []. Resource aocaton s a fundamenta ssue n OFDM wreess networks due to the scarce resources and exstence of fadng channe. Thus the man chaenge n desgnng OFDM network s to use network resources as effcenty as possbe whe provdng the requred Quaty-of- Servce (QoS by the users. Up to now, many approaches have been presented to sove resource aocaton probem such as WF agorthm whch s a conventona we-known method. But these methods may have some mtatons. For exampe WF cannot ensure farness among users and can t support dfferent QoS requrements. A new hgh performance and dynamc method to sove resource aocaton probem s the game theory, whch s mathematca too for modeng and anayzng the nteracton of two or more decson makers. Non-cooperatve game and cooperatve game are two modes of games n game theoretc approach. In a mut-ce OFDM ceuar system, mobe users may not have any knowedge about other users condtons and act sefshy at routne state. Such fact has motvated to adopton of dstrbuted noncooperatve game theory. Non-cooperatve game can do adaptve power contro n a reasonabe extent. In [2], authors propose a new method for resource aocaton n mut-ce OFDM systems as new work.. But, we use dfferent utty functon from [2] and use nove mproved WF method nstead of conventona WF. +. E-ma address: aeyas@ee.ust.ac.r & wwwgorj@yahoo.co.uk 2. E-ma address: abohassan@ust.ac.r 3. E-ma address: kamarshonardar@gma.com 59

2 In ths paper, we propose a new dstrbuted non-cooperatve game theoretc based power contro for resource aocaton n mut-ce OFDM systems. The ntroduced utty functon has a new formuaton, whch s dfferent from other prevous works n OFDM. NE s acheved n mpementaton of the game. The proposed approach affords feasbty and farness. It s aso showed that the game conduct user to use ower power n contrast wth mproved WF method. The content of the paper s organzed as foows: In Secton 2, we descrbe the system mode. In Secton 3, we formuate the probem as a non-cooperatve game. Numerca resuts are gven n Secton 4, foowed by the concusons n Secton System Mode 2.. SINR and Rate n OFDM Systems In a mut-ce OFDM system, whch has N co-channe ces and L OFDM subchannes n each ce are reused among mutpe ces; the th user s Sgna to Interference pus Nose Rato (SINR at subchanne th ( =, 2,, L can be expressed as [3]: h. p γ =, =,2,3,..., N ( h. p + ξ j j j where p s the transmt power of the th user at ts th subchanne and h j denotes channe power gan from the jth user to the base staton of th user on the th subchanne. p j s the transmt power of jth nterferer on the th subchanne. ξ s the therma nose power for a the users and subchannes. Rate adaptaton such as adaptve moduaton provdes each sub-channe wth the abty to match the effectve bt rates, accordng to the nterference and channe condtons. Quadrature Amptude Moduaton (QAM s a moduaton method wth hgh spectrum effcency. Wthout oss of generaty, we assume that the output of the dfferent adaptve moduaton consteaton has unt power [4]. Gven a desrabe rate r of M-ary Quadrature Amptude Moduaton (MQAM, the BER of the th sub-channe of the th user can be approxmated as a functon of the receved SINR γ by (2 [5]. ( β2. γ r 2 (2 BER β. e Wth some manpuatons and settng β.2 and β 2.5 we have β = -.6/n(5 BER that s very we known and conventona form n most of references and named SINR gap. We note that the BER s equa for a users and subchannes; therefore we can express BER of a and wth BER and hence β wth β. Seectng the approprate vaue of β s very mportant and nfuenced n a smuatons. For exampe f BER= -6 then β=.3. Thus, we can extract r equaton from (2 that ndcates the achevabe data rate per second per Hz of th user at the th subchanne: r = og ( + β. γ (3 2 Our system s OFDM and each user can use a subchannes n ts transreceve program, therefore tota data rate of th user on a subchannes s expressed as (4: L = r (4 = r 3. Non-cooperatve Power Aocaton Game 3.. Game Theory Game theory s a study of how to mathematcay determne the best strategy for gven condtons n order to optmze the outcome. The users nteracton n a wreess network can be modeed as a game n whch the users termnas are the payers n the game competng for network resources. Trpet G = N,(S,( u represent a game where N= {,,,,N} s the set of payers/users, S s the fnte set of actons (strateges avaabe to user and u s preference reaton of payer that s caed utty functon for user. In a non-cooperatve game, each users target s to choose ts strategy n such a way to maxmze ts own utty,.e.: 6

3 ( Max u for =,,N (5 s S We defne reated mportant concepts, namey, a Nash Equbrum and utty functon for such game n the foowng [6] Nash equbrum and ts mpementaton on non-cooperatve power contro game scheme A NE s a state of the game where no payer prefers a dfferent acton f the current actons of the other payers are fxed. On the other word, a NE s a set of strateges,(,..., NE NE s s such that no user can unateray mprove ts own N utty. NE NE NE NE NE NE NE NE NE u s,..., s, s, s,..., s u s,..., s, s, s,..., s s S and =,, N (6 ( + ( + for a N N At NE, no user has any ncentve to change ts strategy. We can ook at a NE as the best acton that each payer can pay based on the gven set of actons of the other payers. A NE s a stabe outcome of G. Each payer can t proft from changng hs acton, and because the payers are ratona, ths s a steady state. However, n deveopng non-cooperatve power contro game scheme, a power vector ( p NE, p NE,..., p NE N s defned as a NE for short, f for every user for N and for a p: (,...,,,,..., NE NE NE NE NE NE NE NE NE NE NE NE NE p p p p p Ω u + N ( p,..., p, p, p,..., p u ( p,..., p, p, p,..., p (7 + N + N Max( u (8 for =,,N p P where Ω s set of strategy set of game Utty functon and Power Contro Utty functon s mportant and essenta part n deveopment of non-cooperatve game theory. It s a quantfcaton of a payer s /user s preferences wth respect to certan objects. Here, we defned users utty functon as a rato of tota throughput to tota power that s expressed as: λ. f ( r u( Ρ =, p α (9 λ2 + λ3 ( p where p s the power summaton (tota power of th user over a sub-channes that s expressed as: p L = p ( = where P (P ={p,,p L } denote the power aocaton vector of a users at a subchannes. f s a functon of r. Here f ( r = r. α s a non-negatve rea vaue that we can ca t gan scang parameter whch s assocated wth power and data rate. Seecton of α depends on the appcaton. Choosng α >paces more emphass on power usage and choosng α < paces more emphass on the QoS and frame error rate. Ths approach used n [7], too. However, n (9, λs( λ, λ 2, λ 3 are constant coeffcent whch are caed baancng factor. To fnd NE pont t s necessary to deveop condton (: u = p ( Wth some mathematca manpuatons we w have: βγ. p ( f ( r r α f ( r = n 2 + βγ. p (2 Equaton (2 s the NE equaton of the non-cooperatve game scheme of (8. A users try to choose approprate power contro strategy to maxmze ther own utty to earn NE. In NE pont of the Power contro game, no snge user can mprove ts power eve by unatera changes n ts power. 4. Smuaton and Numerca Resuts In ths secton, we demonstrate the performance of our method n power aocaton usng our proposed utty functon. In our desgnaton, sx hexagona ces are ocated far away from the centre of 7th centra ce wth dstance of 2Km. We suppose that every ce has 5m radus and conssts of a base transrecever 6

4 staton (BTS at the centre of the ce and one mobe staton (MS/user s nsde the ce, as seen n Fg.. Upnk and downnk exst between MS and BTS. 2th user has mnmum dstance from hs BTS and th user has maxmum dstance from hs BTS among a users. We defne d as the dstance from the th user to the correspondng BTS and as seen n Fg. d 2 < d 3 < d 4 < d 5 < d 6 < d 7 < d. Due to ths reason, path oss s exst and can be acheved accordng to g =.97/d 4 formuaton. Thus, tota path gan eve of each user w decrease by ncreasng the dstance between BTS and MS. Hence, the nearest user to the BTS w have the best path gans. Due to usng the same frequency n nonadjacent ces, co-channe nterference exsts among ces. The channe has one-path Rayegh dstrbuton mode wth sow fat fadng. Fg. 2 shows the path gan n a subchannes. It s notabe that the path gan ncudes both path oss and sow fat fadng. Background nose ξ to be 2-5 W and tota subchannes are 8. Aso, SINR gap s.3and α=2. In our noncooperatve game scenaro, the NE of the game s attaned after severa teratons. The mut-ce OFDM systems requre strngent power contro to mantan a desrabe eve sgna power from each user. When we deveoped non-cooperatve game approach, desrabe eve s obtaned when NE s attaned. Aso, strength of each sgna (powers of subchannes of each user effects on harm and payoff of user n the game. Strong sgnas due to coser users act as co-channe nterference and degrade the quaty of other sgnas. Thus, the force of a sgna s a payoff for t, but s a detrment for other user n game. The power gan eve of subchannes of each user showed n Fg. 2. When NE s obtaned after some teraton, the game s over and as showed n Fg. 3, the power s aocated accordng to nverse of summaton of subchanne gan eve of each user (or nverse of the dstance of each user. In other word, after reachng NE, non-cooperatve power contro game assgns arger power to users whch have ow tota subchanne gan and ow power to users whch have arge tota subchanne gan. We can see from our smuaton, the user wth ower d s capabe to consume ower transmttng power and s capabe to have better SINR and thus s capabe to have better bt rate. Ths showes game theoretc approach can ncrease the abtes of far user (user wth ow subchanne gan eve. Aso, the n ths power contro game, when NE s satsfed, each user assgns hs best or near the best subchanne for transmsson. Fg. 4, shows the mproved WF method power aocaton. 6 x - 5 Path Gan Leve Fg. : Arrangement of mobe statons and BTSs Fg. 2: Path gans of dfferent subchannes of every user From Fg. 4, It can be seen that, n each subchanne of every user, the aocated power eve s hgh when users gan s arge and descend when users gan s tte; but, tota power can be assgned accordng to the nverse manner of the subchanne, such as game method. Aso, t can be seen from Fg.4, that 2th user has the most user gan and east Interference pus Nose to Sgna/carrer Rato (INSR. To comparson of WF acton and non-cooperatve game theoretc method, t can be seen from Fg. 5, a users have the same data rate at NE,.e. are far and our proposed utty based non-cooperatve power contro game guarantees far data rate for a users, regardess of ther dstances from the BTS. It s showed that our proposed new smpe utty functon satsfes the power aocaton demand n power aocaton scenaro. But WF n genera use more power for each user and doesn t abe to far users rate. 62

5 .9.8 f 35 amount of aocated power to each subchanne of every user.7 3 Aocated Power Leve Power Leve Fg. 3: aocated power n game theoretc method Fg. 4: WF power aocaton 7 6 Waterfng rate NE rate Rate vaue (bt/s/hz Fg. 5: Comparson between tota data rate n non-cooperatve power contro game at NE and WF method. The NE rate s far (equa for a users. 5. Concuson In ths paper, we modeed a dstrbuted non-cooperatve game for power contro n mut-ce OFDM systems. The NE acheved n the game. Smuatons resuts show that the proposa acheves much better power aocaton and rate n contrast wth mproved WF method. Game method forms far desrabe rate among users wth ower power consumpton. 6. References [] Mathas Bohge, James Gross, Mchae Meyer, Adam Wosz. Dynamc Resource Aocaton n OFDM Systems: An Overvew of Cross-Layer Effcentzaton Prncpes and Technques. 27 Journa of IEEE Network,, Vo. 2, No., pp: [2] Lan Wang, Zhsheng NIU. Adaptve Power Contro n Mut-ce OFDM: A non-cooperatve Game wth Power Unt Based Utty. IEICE Commun. Trans., Vo. E89-B, No.6, June 26, pp [3] Andrea Godsmth. Wreess Communcatons. pubshed by Cambrdge Unversty Press. 25. [4] S. T. Chung and A. J. Godsmth. Degrees of freedom n adaptve moduaton: a unfed vew. IEEE Trans. on Commununcatons, Vo.49, pp.56-57, September 2. [5] an C. Wong, Zukang Shen, Bran L. Evans and Jeffrey G. Andrews, A Low Compexty Agorthm for Proportona Resource Aocaton n OFDMA Systems. IEEE SIPS 24. [6] Thomas S. Ferguson. Game Theory. Unversty of Caforna at Los Angees, 25. [7] Sarah Koske, Zoran Gajc. A Nash Game Agorthm for SIR-Based Power Contro n 3G Wreess CDMA Networks. IEEE/ACM Trans. on Networkng, Vo. 3, No. 5, October 25, pp: