Spectrum Access Games for Cogitive Radio Networks Moshe T. Masota 1,2, Thomas Olwal 1,2, Mjumo Mzyece 2 ad Ntsibae Ntlatlapa 1 Meraka Istitute 1 Coucil for Idustrial ad Scietific Research 1, P. O. Box 395, Pretoria 0001 Tel: +27 12 841 2085, Fax: +27 12 841 4720 ad Frech South Africa Istitute of Techology (F SATI) Tshwae Uiversity of Techology 2 email: {mmasota, tolwal, tlatlapa}@csir.co.za 1 ; mzyecem@tut.ac.za 2 Abstract Cogitive Radio (CR) is see as a key eablig techology for addressig curret uderutilizatio ad iefficiet use of radio frequecy spectrum. The use of CR will see most of the spectrum white spaces beig used opportuistically without causig ay iterferece to the licesed or primary users. CRs ca collaborate i order to address the chael fadig ad hidde termial problems that may be experieced by a sigle radio. For modelig ad aalysis of CR etworks, the use of game theory has received a wide acceptace i ext geeratio ad itelliget wireless commuicatio systems. I this paper we make use of game theory approach to model ad aalyze cogitive radio etworks i order to allow dyamic spectrum access i broadbad wireless access etworks. We start by motivatig the use of cooperative spectrum sesig to address the chael fadig ad hidde termial problems. We show that usig repeated games ad the discout factor, players ca fairly access the uplik available chael without causig iterferece to each other. Idex Terms Cogitive Radio, Spectrum Sesig, IEEE 802.16, Game Theory I. INTRODUCTION The demad for broadbad access i the moder iformatio society is see as a driver for rapid growth ad developmet of wireless commuicatio systems. I wireless commuicatio etworks, radio frequecy spectrum is the most precious ad expesive wireless etwork resource which eed to be regulated properly for a iterferece free commuicatio. Most coutries have regulatory agecies to regulate radio spectrum by meas of reewable liceses. While this approach esured a o-iterferig commuicatio betwee radio termials, it has resulted ito a iefficiet utilizatio of the spectrum [1]. Recet literature o spectrum maagemet techiques focused maily o Cogitive Radio (CR) [2] as a techological solutio to implemet dyamic or opportuistic spectrum access approach without causig ay iterferece to the licesed users or Primary Users (PUs). The use of CR as a suitable techology for addressig spectrum scarcity based o opportuistic spectrum access has resulted ito more research by the wireless commuicatio research commuity. Research o spectrum sesig is divided o whether to perform sesig i a cooperative or sigle radio maer. Work preseted i [3]-[10] motivates the use of cooperative spectrum sesig because it esures little or o iterferece is caused to PUs by the Secodary Users (SUs) as opposed to sigle radio spectrum sesig techique. It also allows CR to exploit the diversity gai provided by associated radios. Based o this motivatio ad advatages, our work assumes cooperative spectrum sesig operatio. I this paper, by PU we refer to a radio that is licesed to operate i a give frequecy spectrum bad, ad a SU is CR that accesses the frequecy spectrum bad opportuistically, thus it has lower priority o a give bad. The use of game theory i wireless commuicatios etwork is receivig more attetio recetly due to the itelligece ad flexibility offered i Cogitive Radio Networks (CRNs). Mehta ad Kwak [11] discussed some modelig of fudametal questios o CRN as iteractive games betwee odes. Some iter-disciplie research issues o game theory ad CRN are also discussed i [11]. However, o actual modelig or results are provided i this work. MacKezie ad Wicker i [12] preseted two applicatios of game theory i wireless etworks: radom access ad power cotrol. It is also show that game theory tools ca lead to strategies i which optimal behavior emerges aturally from the selfish iterests of the agets ad the rules of the games. Nie ad Comaiciu [13] proposed a game theoretic framework to aalyze the behavior of CRs for distributed adaptive chael allocatio. They foud that ocooperative games offer a very low overhead for iformatio exchage i the etwork, while cooperative games improves the overall etwork performace at the expese of a icreased overhead. I this paper we propose a spectrum decisio model for uplik access i broadbad wireless access CRNs. I some broadbad wireless access (BWA) systems, such as IEEE 802.16, resource allocatio ad maagemet mechaisms are crucial to guaratee quality of service (QoS) requiremets. I order to trasmit data, users eed to first request badwidth from the cetralized Base Statio (BS). Cotetio based ad pollig mechaisms are used for resource allocatio. Istead of usig the cotetio based radom access mechaism; we proposed game theoretic approach for CRN users to access the uplik chael for sedig badwidth request (BW-REQ) messages. The rest of this paper is orgaized as follows: Sectio II presets spectrum maagemet approach usig CR. Some related work is preseted i Sectio III. Sectio IV presets our proposed model. The basic cocept ad brief
itroductio to game theory is preseted i Sectio V. This sectio also covers our spectrum decisio game model ad the results. Sectio VI cocludes the paper with some future work. II. COOPERATIVE SPECTRUM SENSING IN CRN Spectrum sesig is the most crucial fuctio of the CR ad it should esure adaptive trasmissio i wide badwidths without causig harmful iterferece to PUs. It ivolves idetificatio of spectrum holes ad the ability to quickly detect the oset of primary trasmissio o the spectrum hole occupied by the SU. Two approaches are commoly used for spectrum detectio [3]: 1) To employ detectio techique with high performace at idividual radios, or local detectio. 2) To coduct cooperative spectrum sesig; where the detectio results of multiple radios are combied to obtai a more detailed ad correct sesitivity. A. Spectrum Sesig Approaches Local detectio: Sesig of very weak sigals requires a CR to have sigificatly better sesitivity tha primary radios. For local spectrum detectio (for example: usig eergy detectio techique), the goal is to distiguish betwee the two hypotheses: i Η0, xi = (1) hi s + i Η1, where xi is the sigal received by the SU, s(t) is the PU s trasmitted sigal, i is the Additive White Gaussia Noise (AWGN), ad hi is the amplitude gai of the chael. Η0 deotes ull hypothesis, i.e. o PU sigal i a spectrum bad. Η 1 is a alterative hypothesis, i.e. there is some PU sigal. However, local spectrum sesig suffers from deep chael fadig ad hidde termial problem. I chael fadig eviromets, the SU is challeged to distiguish betwee a white space (i.e. available spectrum bad) ad the deep fade (where it is hard to detect the primary sigal) [7]. The hidde termial problem may occur whe the SU is shadowed withi the viciity of the active PU. As a result, a SU may ot otice the presece of the PU ad mistakely try to access the primary chael, which will lead to iterferece with the primary system [10]. To address the chael fadig ad hidde termial problems experieced i local spectrum sesig, cooperative amog differet SUs is proposed where SUs shares their idividual sesig results. Cooperative Spectrum Sesig: Cooperative spectrum sesig ad decisio ca be used over sigle radio spectrum sesig i order to reduce the probability of iterferece to PUs. To esure reliable ad efficiet spectrum sesig, it is importat to associate the detectio of multiple radios through cooperative spectrum sesig [3] [9]. A typical model for cooperative spectrum sesig i CRN setup is show i Figure 1. I the model, a CRN is operatig opportuistically withi the coverage area of a primary/licesed etwork. Figure 1: Cooperative Spectrum Sesig i CRN SUs perform idividual spectrum sesig ad forward their decisios to their cetral cotroller for a global decisio makig. The cetral cotroller will the broadcast the decisio to all the SUs attached to it for iterferece free opportuistic access of licesed spectrum. Cooperative spectrum sesig ivolves the followig geeral steps [8]: 1. Every SU performs local spectrum measuremet idepedetly ad the makes a (biary) decisio 2. All of the SUs forward their (biary) decisios to a cetral cotroller (or bad maager/fusio Ceter). 3. The cetral cotroller the combies those decisios ad makes a fial decisio to ifer the absece or presece of the PU i the observed spectrum bad. Cooperative sesig will allow CR to exploit the diversity gai provided by associated radios. Cooperative spectrum sesig advatages icludes: Diversity gai due to associated radios, improved detectio probability, ad mitigatig the sesig requiremets (high cost) o idividual radios. Oe of the mai challeges faced by cooperative spectrum sesig is the trasmissio overhead, where each radio trasmits its decisio to the cetral cotroller. The iformatio trasmitted by each SU to the cetral cotroller may be soft or hard decisios. If soft decisio is used, SUs will trasmit their decisio statistics istead of a oe-bit decisio. Ad hard decisio occurs whe oly the fial 1-bit decisio is trasmitted (0 or 1). It is geerally argued that soft decisio combiig of sesig results yields much better gais tha hard decisio combiig [9]. Cooperatio allows idepedetly faded radios to collectively achieve robustess to severe fades while keepig idividual sesitivity levels close to the omial path loss [9]. However, [10] argues that whe oe radio has higher sigal-to-oise ratio (SNR) compared to other radios, cooperative spectrum sesig performs worse tha the idividual spectrum sesig. III. GAME THEORY OVERVIEW Game theory is a set of tools origially developed i ecoomics for the purposes of aalyzig the complexities o huma iteractios. It is cocered with strategic iteractios where two or more players have to make a decisio. The deregulatio of the telecommuicatio idustry ad the improvemets i computatio power, which allows etwork termials to make idepedet ad selfish
operatioal decisios, motivates the use of game theoretic approaches [15]. Recetly game theory has bee applied i commuicatio systems as a aalyzig ad modelig tool [11] [13] to address wireless commuicatio problems such as spectrum maagemet, power cotrol, cogestio cotrol, topology cotrol ad routig, amog others. Game theory, therefore, offers a suite of tools that, if used effectively, ca model the iteractio amog idepedet odes i a CRN. A. Basic Elemets of Game Theory The fudametal compoet of game theory is the otio of a game, ad every game should at least have three elemets: a set of players, a set of actios for each player, ad a set of prefereces. Players are the decisio makers, actios are the alteratives available to each player, ad prefereces are utility fuctios mappig actio profiles ito the real umbers. Table 1 relates a typical game with a CRN. A game ca be expressed as G = S, A,{ u i } where G is a particular game, S deote a fiite set of players{1, 2, 3,..., s }. Ai is the set of possible actios available to player i for each player i S, ad A = A1 A2 A3... Ah deotes the actio space. Ad fially { ui} = { u1, u2, u3,..., us} deotes player i s utility fuctio, which is a objective fuctio the players wish to maximize. For every player i, the utility fuctio u is a fuctio of the particular actio chose by i the player i, a i, ad the particular actios chose by all of the other players i the game, a i. Based o this model, Nash Equilibria are idetified wherei o player would ratioally choose to deviate from their chose actio as this would dimiish their payoff, ui ( ai ) ui ( bi, a i ) for all bi Ai. The actio tuples (i.e. a uique choice of actios by each player) correspodig to the Nash Equilibria are the predicted as the most probable outcomes. Of most importace i game theory is the celebrated cocept of Nash Equilibrium. Nash Equilibrium is a actio profile at which o user may gai by uilaterally deviatig. It is a stable operatig poit because o user has ay icetive to chage strategy. IV. PROPOSED SYSTEM MODEL We cosider a CRN cosistig of oe cetral cotroller ad N SUs operatig opportuistically withi a IEEE 802.16 [16] poit-to-multipoit (PMP) primary etwork. The SUs are CR users ad they periodically perform spectrum sesig i order to fid the spectrum holes or uused spectrum bads for uplik access o the primary etwork. The SUs wish to access the primary etwork BS opportuistically, followig the stadardized method [16]. They have to do this with miimum or o iterferece to the PUs. If a SU has data to sed, it must first check which uplik chael is available, ad the sed a badwidth request (BW-REQ). A. Assumptios I our model above, the followig assumptios are made: - Cooperative spectrum sesig is employed by the SUs. Each SU perform spectrum sesig ad sed the results to a cetral cotroller. - The cetral cotroller will make the fial decisio o the available spectrum bad ad broadcast to all the SUs. - We assume o-real time ad best effort traffic exchage betwee the SUs. - We assume that all SUs are attached to the BS, meaig they already performed iitial ragig. B. Uplik Chael Access i IEEE 802.16 The IEEE 802.16 or WiMAX stadard [16] is based o coectio-orieted Medium Access Cotrol (MAC). The MAC frame i PMP architecture is modelled as a stream of mii-slots, ad it is divided ito Uplik (UL) sub-frame ad Dowlik (DL) sub-frame. Figure 2 shows a sigle MAC frame i PMP Time Divisio Access Multiple (TDMA) operatio. The DL subframe is used by the BS to broadcast to all subscriber statios (SSs). It begis with a frame cotrol sectio that cotais a preamble, a DL-MAP ad a UL-MAP. Resource maagemet ad allocatio mechaisms are crucial to guaratee QoS requiremets i 802.16 etworks. The IEEE 802.16 stadard suit defies reservatio-based badwidth allocatio mechaisms sice multiple SSs share a commo UL to the BS o a demad basis. If a SS eeds some amout of badwidth for commuicatio, it has to make a reservatio with the BS by sedig a BW-REQ. Two methods are suggested i order to determie which SS is allowed to trasmit its BW-REQ from multiple cadidates: Cotetio-based radom access ad cotetio-free cetralized pollig. I cotetio-based radom access, a SS trasmits a BW-REQ durig a predefied cotetio period ad a radom back-off mechaism is used to resolve cotetio amog BW-REQ from multiple SSs. C. Spectrum Decisio Modelig As opposed to the cotetio-based radom access, SUs will use their itelligece to access the UL chael. Sice the umber of SUs for a give CRN may be large eough (more tha oe), it might happe that oe SU decides to be greedy ad use the available spectrum selfishly. This will mea that other users may ever have a opportuity to access the spectrum, as a result, they are deprived a opportuity to commuicate. I order to address the selfish ad greedy behavior by some users, we propose a game theoretic approach, whereby the decisio to access the spectrum will have either coflictig cosequeces. Table 1. Typical Compoets for Wireless Network Game [11] Compoets of Elemets of CRN Game A set of players Nodes i wireless etwork A set of actios A modulatio scheme, power cotrol, waveforms, spectrum A set of prefereces Performace metrics (e.g. SINR, delay)
Figure 2: IEEE 802.16 MAC Frame i PMP TDMA [17] V. SPECTRUM DECISION GAME A. Spectrum Decisio Game Modelig For a simplified decisio model, we assume that players (SUs) kow the umber of other users wishig to trasmit o the same available bad,. Let G( ) be the game i which there are curretly SUs wishig to trasmit or sed. I each stage of G( ), each of the players must decide whether to sed (S) or wait (W). If oe player decides to trasmit ad the rest decide to wait, the player who trasmits will receive a payoff of 1, ad each of the other ( 1) players will play G( 1) i the ext period. If o player (SU) trasmit or more tha oe player trasmits, all players will play G( ) agai i the ext period. Players place a lower value o payoffs i later stages tha o curret payoffs. This is represeted by a per period discout factor q < 1. Let u represet user i s utility from playig G( ) ad let K be a radom variable deotig the umber of other users withi the CRN, but ot participatig i the game (i.e. ot havig data to trasmit). For = 1, the player should trasmit ad achieve the utility of 1 ( u 1 = 1 ) ad for > 1 we express u as a fuctio of player i s actio (S) or wait (W) recursively: u ( S) = P[ K = 0] + q u P[ K > 0] (2) B. Results Discussio We focus our results to the calculatio of the utility fuctio achievable by players i a give game. Show i Figure 3 is the utility by players i a give game G( ). It is show that for a game, G( ) with oe player, = 1, a utility of 1 is achieved. As the umber of players icreases, the utility decreases rapidly to the poit where the umber of players approaches half the total users, ad the icreases agai. As metioed earlier, the highest discout factor (q) a trasmittig user ca receive is 1 if oe user trasmits ad others wait. Therefore each player s goal is to maximize its utility. We varied the q betwee 0.9 ad 0.99. It ca be observed from our first results, i Figure 3, that as the umber of users i the games icreases, the utility starts by decreasig, ad the it icreases agai. These are sort of strage results that we aim at addressig i our ogoig research. If we adopt the strategy i [12], ad cosider mobile SUs, where users are battery powered. Power savig mechaisms are itroduced i [16] for mobile WiMAX. Therefore for a battery powered SU, we have to itroduce some cost, c. The SU cost will represet the battery usage of a device as it access the UL chael for BW-REQ ad also for data trasmissio. This will chage equatio (4) to become equatio (6), as show below. u P[ K = 0] c ( S) = (6) 1 q P[ K > 0] Figure 4 shows a ew utility fuctio with varyig trasmissio cost, c, ad fixed discout factor. There are some simple asymmetric Nash Equilibrium strategies i our games. For istace, if SUs are havig traffic to trasmit, SU 1 ca trasmit i period 1, SU 2 i period 2, ad so o util SU trasmits i period. For a strategy i which each player selects a vector of trasmit probabilities ca be played i order to achieve a symmetric equilibrium, where each player s decisio of whether to trasmit or ot is idepedet of all other players decisios. u ( W ) = q u P[ K = 1] + q u P[ K 1] (3) 1 So, for > 1, we ca simplify (2) as follows: u ( S) q u P[ K 0] = P[ K = 0] [ ] u ( S) 1 q P[ K 0] = P[ K = 0] u P[ K = 0] ( S) = (4) 1 q P[ K 0] Similarly, (3) ca also be simplified as represeted i (5) q P[ K = 1] u ( W ) = u 1 (5) 1 q P[ K 1] Figure 3: User utilities for playig G( )
VI. CONCLUSION I this paper we preseted the use of game theory i CRNs to aalyze ad model the spectrum access decisio i broadbad wireless access etworks. Secodary users must first perform spectrum sesig i order to idetify uoccupied uplik chaels. We used the game theory to compute the utility fuctio, ad plotted it versus the umber of SUs. There are still more challeges to be addressed i spectrum access decisio games i CRNs. While this work covers our prelimiary results, more research work is still uderway i our research group to ehace this model so we ca be able to use the potetial game approach to compute the equilibrium access probability. I future we aim at fidig reliable ad efficiet techiques to perform spectrum characterizatio ad PU activity to allow a ehaced spectrum decisio modelig. Our future work will also iclude buildig a outdoor CRN testbed to allow real-life simulatios ad experimetatios for the verificatio of our aalytical results. REFERENCES [1] FCC, ET docket No. 03-322, Notice of proposed rulemakig ad order, December 2003. [2] J. Mitola III ad G.Q. Maguire, Cogitive radio: makig software radios more persoal, IEEE Persoal Commuicatio, August 1999. [3] X. Che, Z. S, Bie ad W. L. Wu, Detectio efficiecy of cooperative spectrum sesig i cogitive radio etwork, Sciece-Direct, Elsevier, vol. 15, o. 3, pp. 1 7, Sept. 2008 [4] B. She, L. Huag, C. Zhao, K. Kwak ad Z. Zhou, Weighted cooperative spectrum sesig i cogitive radio etworks, i Proceedigs of IEEE Third Iteratioal Coferece o Covergece ad Hybrid Iformatio Techology, pp. 1074 1079, 2008. [5] Y.-C. Liag, Y. Zeg, E.C.Y. Peh ad A.T. Hoag, Sesig-throughput tradeoff for cogitive radio etwork, IEEE Trasactios o Wireless Commuicatios, vol.7, o.4, April 2008, pp.1326-1337. [6] V. Sharma & A. Jayaprakasam, A efficiet algorithm for cooperative spectrum sesig i cogitive radio etworks, [Olie] Available from: http://arxiv.org/abs/0809.2931 (Accessed: 20/01/2009). [7] A. Ghasemi ad E.S. Sousa, Spectrum sesig i cogitive radio etworks: the cooperatio-processig tradeoff, IterSciece Trasactios o Wireless Commuicatio ad Mobile Computig, pp. 1049-1060, 2007. [8] W. Zhag, R.K. Mallik ad K.B. Letaief, Cooperative spectrum sesig optimizatio i cogitive radio etworks, Proceedigs of IEEE ICC, pp. 3411 3415, 2008. [9] S. M. Mishra, A. Sahai ad R. W. Broderse, Cooperative sesig amog cogitive radios, I Proceedigs of IEEE Iteratioal Coferece o Commuicatio, Jue 2006. [10] A. Saha N. Hove, ad R. Tadra, Some fudametal limits o cogitive radio, i: Proc. of Allerto Coferece, Sept Oct 2004. Figure 4: User Utilities with trasmissio cost, c [11] S. Mehta ad K.S, Kwak, Game theory ad cogitive radio based wireless etworks, i Aget ad Multi- Aget Systems: Techologies ad Applicatios, vol. 5559/2009, A. Hakasso, Ed. Spriger-Verlag Berl pp. 803-812, 2009. [12] A. B. MacKezie ad S.B. Wicker, Game theory ad the desig of self-cofigurig, adaptive wireless etworks, IEEE Commuicatios Magazie, pp. 126 131, Nov. 2001. [13] N. Nie ad C. Comaiciu, Adaptive chael allocatio spectrum etiquette for cogitive radio etworks, i Mobile Networks ad Applicatios, Spriger, vol. 11, pp. 779-797, 2006. [14] I.F. Akyildiz, W.Y. Lee ad K.R. Chowdhury, CHRANS: cogitive radio ad hoc etworks, Elsevier Tras. Ad Hoc Networks, vol. 7, pp. 810-836, Ja. 2009. [15] J. Huag, D.P. Palomar, N. Madayam, S.T. Wicker, J. Walrad ad T. Basar, Guest Editorial: Game theory i commuicatio systems, IEEE Joural o Selected Areas i Commuicatios, Vol. 26, No.7, pp. 1042 1046, Sept. 2008. [16] IEEE Std 802.16-2009, IEEE stadard for Local ad Metropolita Area Networks - Part 16: Air iterface for broadbad wireless access systems, May 2009. [17] C. Eklud, R.B. Marks, K.L. Stawood ad S. Wag, IEEE stadard 802.16: a techical overview of the wirelessman air iterface broadbad wireless access, i IEEE Commuicatios Magazie, pp. 98-107, Jue 2002. Moshe Masota received his M. Tech degree ad MSc degree i 2008 from Tshwae Uiversity of Techology (TUT) ad Ecole Supérieure d Igéieurs e Electrotechique et Electroique (ESIEE) de Paris, respectively. He is presetly studyig towards the D. Tech degree at TUT. His research iterests iclude cogitive radios, spectrum maagemet ad eergy efficiecy i broadbad wireless etworks.