Database-assisted Spectrum Access in Dynamic Networks: A Distributed Learning Solution

Transcription

1 1 Database-assisted Spectrum Access i Dyamic Networks: A Distributed Learig Solutio Yuhua Xu, Member, IEEE, Yitao Xu ad Alaga Apalaga, Seior Member, IEEE arxiv: v2 [cs.it] 3 Jul 2015 Abstract This paper ivestigates the problem of databaseassisted spectrum access i dyamic TV white spectrum etworks, i which the active user set is varyig. Sice there is o cetral cotroller ad iformatio exchage, it ecouters dyamic ad icomplete iformatio costraits. To solve this challege, we formulate a state-based spectrum access game ad a robust spectrum access game. It is proved that the two games are ordial potetial games with the expected aggregate weighted iterferece servig as the potetial fuctios. A distributed learig algorithm is proposed to achieve the pure strategy Nash equilibrium NE of the games. It is show that the best NE is almost the same with the optimal solutio ad the achievable throughput of the proposed learig algorithm is very close to the optimal oe, which validates the effectiveess of the proposed game-theoretic solutio. Idex Terms TV white spectrum, geo-locatio database, ordial potetial game, learig automata. I. INTRODUCTION EMPLOYING TV White Spectrum TVWS [1] [3] has bee regarded as a promisig approach to solve the spectrum shortage problem i future wireless etworks, as it ca effectively improve the spectrum efficiecy by allowig the ulicesed users dyamically to access the idle TV chaels. For the TVWS, it has bee show that obtaiig the spectrum availability iformatio by iquirig a geo-locatio database is more efficiet tha performig spectrum sesig aloe [4], [5]. Also, geo-locatio database has bee widely supported by the stadards bodies ad idustrial orgaizatios [6] [9]. Curretly, researchers i this field maily focused o: i costructig ad maitaiig the geo-locatio database, e.g., [10] [12], ad ii developig busiess models to aalyze the reveues of the TV spectrum holders ad the ulicesed users, e.g., [13] [15]. Sice there is o cetralized cotroller available, how to choose a chael for trasmissio i a distributed maer, aimig to avoid mutual iterferece amog the users, remais a key challege. However, oly a few prelimiary results were reported recetly [16], [17], ad hece it is urget ad importat to study efficiet database-assisted distributed spectrum access strategies. I this paper, we cosider a dyamic ad distributed TVWS etwork. Specifically, cosiderig practical applicatios of the users, they do ot access the chaels whe there is o data to This work was supported by the Natioal Sciece Foudatio of Chia uder Grat No ad No Yuhua Xu ad Yitao Xu are with the College of Commuicatios Egieerig, PLA Uiversity of Sciece ad Techology, Najig, 21007, Chia. yuhuaeator@gmail.com; yitaoxu@126.com A. Apalaga is with the Departmet of Electrical ad Computer Egieerig, Ryerso Uiversity, Toroto, Caada alaga@ee.ryerso.ca. trasmit. To capture this dyamics, it is assumed that each user becomes active/iactive accordig to a active probability i each decisio period. As a result, the active user set is varyig. Furthermore, sice there is o iformatio exchage, a user does ot kow the chose chaels, the curret state active or iactive ad the active probabilities of other users. The dyamic ad icomplete iformatio costraits make the task of developig efficiet distributed spectrum access strategies challegig. To solve this problem, we resort to game models [18] ad distributed learig techology. Specifically, we formulate a state-based spectrum access game ad a robust spectrum access game, ad propose a distributed learig to achieve desirable solutios. The mai cotributios ca be summarized as follows: 1 For a arbitrary active user set, we formulate the problem of distributed spectrum access as a state-based ocooperative game. It is proved that state-based game is a ordial potetial game with the aggregate weighted iterferece servig as the potetial fuctio. To address the challeges caused by the varyig active user set, we formulate a robust spectrum access game, which is also proved to be a ordial potetial game. Fially, we propose a distributed learig algorithm to achieve the pure strategy Nash equilibria of the formulated games. 2 It is show that the best Nash equilibrium is almost the same with optimal solutio, which validates the effectiveess of the formulated game models. I additio, the achievable throughput of the proposed learig algorithm is very close to the optimal oe, which also validates the distributed learig algorithm i dyamic etworks. The most related work is [16], i which game-theoretic database-assisted spectrum sharig strategies were ivestigated. This work is differetiated i: i all users are assumed to be always active [16], while we cosider a etwork with varyig umber of active users, ad iii the spectrum access algorithms i [16] eed iformatio exchage, while the proposed learig-based spectrum access algorithm is fully distributed. Also, the problem of distributed spectrum access for miimizig the aggregate weighted iterferece was studied i [19] ad i our previous work [20], [21]. The differeces i the curret work are that we optimize the throughput directly ad the active user set i each decisio period is radomly chagig. Also, some simulatio results o the problem of distributed spectrum access with chagig active user set were prelimiarily reported i our recet work

2 2 Iquire spectrum availability Distributed spectrum access through learig Take spectrum access strategy Geo-locatio Spectrum Database Cogitive Access poit Learig Learig Iterfereces ad iteractios amog multiple users i dyamic eviromet Take spectrum access strategy Fig. 1. The illustrative diagram of database-assisted spectrum access. [22]. I this work, rigorous aalysis ad proofs are give ad more simulatio results are preseted to validate the proposed game-theoretic solutio. The rest of this paper is orgaized as follows. I Sectio II, the system model ad problem formulatio are preseted. I Sectio III, we formulate the state-based spectrum access game ad the robust spectrum game respectively, aalyze their properties, ad propose a distributed learig-based spectrum access algorithm. Fially, simulatio results ad discussio are preseted i Sectio IV ad coclusio is draw i Sectio V. II. SYSTEM MODEL AND PROBLEM FORMULATION A. System model We cosider a distributed etwork with N cogitive users ad M chaels. Note that here each cogitive user correspods to a commuicatio lik cosistig of a trasmitter ad a receiver, e.g., the cogitive access poit AP ad its servig cliets. Each cogitive user iquires the spectrum availability from the geo-locatio spectrum database, which specifies the available chael set A ad the maximum allowable trasmissio power P for each user. With the iquired iformatio o the available chaels ad maximum trasmissio power, the users take suitable spectrum access strategies through learig. A illustratio of the databaseassisted spectrum access is show i Fig. 1. To address the user traffic i practical applicatios, we cosider a etwork with a varyig umber of active users. Specifically, it is assumed that each user performs chael access i each slot with probability λ, 0 < λ 1. Such a model captures geeral kids of dyamics i wireless etworks [23], e.g., a user becomes active oly whe it has data to trasmit ad iactive otherwise; also, it ca be regarded as a high-level abstractio of the user traffic, i.e., the active probability correspods to the probability of o-empty buffer. B. Problem formulatio To capture the chagig umber of active users, we defie the system state as S = {s 1,...,s N }, where s = 1 idicates that user is active while s = 0 meas it is iactive. The system state probability is the give by µs 1,...,s N = N =1 p, where p is determied as follows: { λ, s p = = λ, s = 0 Deote a arbitrary ad o-empty active user set as B, i.e., B = { N : s = 1}. For presetatio, deote the set of all the active user sets as Γ. The, the probability of a active user set ca deoted by µb. We have B Γ µb = 1 µb 0, where µb 0 = N =1 1 λ is the probability that all the users are iactive. With the spectrum availability iformatio obtaied from the database, user chooses a chael a A for data trasmissio. For ay active user set B ad chael selectio profile a,a, the received Sigal-to-Iterferece-plus- Noise Ratio SINR of a active user is determied by: η B,a,a = P d α i B\{}:a i=a P i d α 2 i +σ, where α is the path loss factor,d is the distace betwee user ad its dedicated receiver, d i is the distace betwee user i ad, i B\{}:a i=a P i d α i +σ is the aggregate iterferece from all other active users also choosig chael a, ad σ is the backgroud oise. The, the achievable throughput of user is give by: R B,a,a = Blog 1+η B,a,a, 3 where B is the chael badwidth. Therefore, there are two possible optimizatio goals for each user, i.e., or P1 : max a R B,a,a, B Γ, 4 P2 : max E B [R B,a,a ] = µbr B,a,a a B Γ 5 Sice the etwork is always chagig, it is ot feasible to optimize the achievable throughput for each active user

3 3 set. Thus, we pay attetio to solvig P2. However, the task of solvig P2 is challegig due to the followig imperfect iformatio costraits: Dyamic: the active user set i the system is always chagig; i particular, it may chage radomly i each decisio period. Icomplete: there is o iformatio exchage amog the users, which leads to: i a user does ot kow the active probabilities ad chose chaels of other users, ad ii the state distributio µb is ukow to the all users. Based o the above aalysis, it is see that cetralized approaches are ot available ad we eed to develop a distributed ad learig-based approach for solvig problem P2. III. SPECTRUM ACCESS GAMES AND DISTRIBUTED LEARNING ALGORITHM Sice o cetralized cotroller is available i the cosidered distributed etwork ad all the users take their spectrum access strategies distributively ad autoomously, we formulate this problem as a o-cooperative game. I the followig, we preset the formulated game models, aalyze its properties, ad propose a distributed learig algorithm to coverge to stable solutios i dyamic eviromet. A. Game formulatio ad aalysis I this subsectio, we first preset a state-based spectrum access game, i which a iheret system state specifies the active user set. Based o the state-based game, we the preset a robust game, i which the expectatios over all possible system states are cosidered. Note that the state-based game correspods to problem P1 while the robust game correspods to problem P2. 1 State-based spectrum access game: Formally, the statebased spectrum access game model is deoted as F 1 = [N,B,{A } N,{u B} N ], where N = {1,...,N} is a set of players users, B is active user set, A is a set of available actios chaels for user, ad u B is the utility fuctio of player. The utility fuctio is defied as the available trasmissio, i.e., u B,a,a = R B,a,a, N, B Γ 6 Each user is the game iteds to maximize its idividual utility, which meas that the state-based spectrum access game ca be expressed as: F 1 : max a A u B,a,a, B. 7 I order to ivestigate the properties of F 1, we first preset the followig defiitios, which is directly draw from [24]. Defiitio 1 Nash equilibrium. For a arbitrary active user set B, a spectrum access profile a = a 1,...,a B is a pure strategy NE if ad oly if o player ca improve its utility by deviatig uilaterally, i.e., u B,a,a u B,a,a, B, a A,a a 8 Defiitio 2 Ordial potetial game. A game is a ordial potetial game OPG if there exists a ordial potetial fuctio φ : A 1 A N R such that for all N, all a A, ad a A, the followig holds: u B,a,a u B,a,a > 0 φb,a,a φb,a,a > 0 That is, the chage i the utility fuctio caused by the uilateral actio chage of a arbitrary each user has the same tred with that i the ordial potetial fuctio. Followig the similar methodology preseted i [16], we have the followig theorem. Theorem 1. For ay active user set B, the state-based spectrum access game F 1 is a ordial potetial game. Proof: For presetatio, for ay active user set B ad a arbitrary user B, deote v B,a,a = i, 10 i B\{}:a i=a P i P d α which ca be regarded as the weighted iterferece [19] experieced by user. Defie φ : A 1 A B R as φb,a,a = v B,a,a B = P i P d α i, 11 Bi B\{}:a i=a which is the aggregate weighted iterferece experieced by all the active users. If a arbitrary player uilaterally chages its chael selectio from a to a, the the chage i v caused by this uilateral chage is as follows: v B,a,a v B,a,a = P i P d α i i B\{}:a i=a i B\{}:a i=a P i P d α i 9 12 For aalysis coveiece, deote the users choosig the same chael with user as I a,b = {i B\ : a i = a }. The, the chage i potetial fuctio φ caused by the uilateral chage of user ca be expressed as follows: φb,a,a φb,a,a = v B,a,a v B,a,a + P P i d α i I a,b i P P i d α i i I a,b = 2 v B,a,a v B,a,a Sice u ad v is related by: u B,a,a = Blog 1+ ad log follows that: 1 + Pd α x/p +σ u B,a,a u B,a,a v B,a,a v B,a,a P d α v B,a,a /P +σ 13, 14 is icreasig with respect to x, it 0, a,a A 15

4 4 For ay active user set B, combiig 13 ad 15 yields the followig: u B,a,a u B,a,a φb,a,a φb,a,a 0, a,a A 16 which satisfies the defiitio of OPG, as characterized by 9. Thus, the state-based spectrum access game F 1 is a ordial potetial game with φ servig as the potetial fuctio, which proves Theorem 1. 2 Robust spectrum access game: As discussed above, it is ot feasible to perform optimizatio for each active user set sice the etwork is always chagig. Thus, based o the state-based spectrum access game F 1, we formulate a robust spectrum game below. Specifically, the robust spectrum access game is deoted as F 2 = [N,{A } N,{ω } N ], where N = {1,...,N} is a set of players users, A is a set of available actios chaels for user, ad ω is the utility fuctio of player. The utility fuctio i robust spectrum access game is defied as the expected available trasmissio rate over all possible active user sets [22], [23], [25], i.e., ω a,a = E B [u B,a,a ] = B ΓµBu B,a,a 17 Similarly, the robust spectrum access game ca be expressed as: F 2 : max a A ω a,a, N. 18 Theorem 2. The robust spectrum access game F 2 is also a ordial potetial game. Proof: We defie the potetial fuctio as: Φa,a = E B [ φb,a,a ], 19 where φ is specified by 11. If a arbitrary player uilaterally chages its chael selectio from a to a, the the chage i w caused by this uilateral chage is as follows: ω a,a ω a,a = E B [u B,a,a u B,a,a ] Similarly, the challege i the Φ is determied by: 20 3 Discussio o the game models: Ordial potetial game OPG admits the followig two promisig features [24]: i every OPG has at least oe pure strategy Nash equilibrium, ad ii a actio profile that maximizes the ordial potetial fuctio is also a pure strategy Nash equilibrium. Some further discussios o the two spectrum game models are listed below: Both the state-based ad robust spectrum access games have at least oe pure strategy NE. For the state-based spectrum access game, the aggregate weighted iterferece serves as the potetial fuctio, as specified by 11. For the robust spectrum access game, the expected aggregate weighted iterferece serve as the potetial game, as specified by 19. Thus, it is kow all the NEs of the games miimize the expected aggregate weighted iterferece respectively. Furthermore, it has bee show that miimizig lower weighted iterferece leads to higher throughput [19] [21]. Thus, it ca be expected that the two games would also achieve high throughput. B. Distributed learig for achievig Nash equilibria As the expected aggregate iterferece serves as the potetial fuctio for the robust spectrum access game, it is desirable to develop distributed algorithms to achieve the Nash equilibria. Covetioal algorithms i the game commuity, e.g., best respose dyamic [24], fictitious play [26] ad spatial adaptive play [27], ca ot be applied sice they eed iformatio exchage amog the players. To elimiate the requiremet of iformatio exchage, some distributed algorithms have bee applied i wireless applicatios, e.g., MAX-logit [28] ad Q-learig [29]. However, B-logit, ad MAX-logit are oly suitable for static eviromet; although Q-learig ca be applied i dyamic etworks, its covergece i multiuser eviromet ca ot be guarateed. I this paper, we propose a learig-based distributed spectrum access algorithm, which is maily based the stochastic learig automata [30], [31]. To begi with, deote q k = {q 1 k,...,q A k} as the mixed strategy of player i the kth slot, i which q m is the probability of choosig chael m. The key ideas of the proposed distributed learig algorithm are: i the active users choose the chaels accordig to their mixed strategies, ad the update their mixed strategies based o the received payoffs, ad iii a iactive user does othig. Specifically, the learig procedure is as follows: Φa,a Φa,a = E B [φb,a,a φb,a,a ] 21 Usig the result obtaied i 16, the followig always holds: ω a,a ω a,a Φa,a Φa,a 0, a,a A 22 Thus, it is proved that the robust spectrum access game F 2 is also a ordial potetial game with Φa,a servig as the potetial fuctio. Iitializatio: set k = 1 ad set the iitial mixed strategy of each user as q m k = 1 A, N, m A. Loop for k = 1,2,... Deote Bk as the active user set i the curret slot. 1. Chael selectio: accordig to its curret mixed strategy q k, ay active user i Bk radomly chooses a chael a k from its available chael set A i slot k. 2. Chael access ad trasmit: All the active users trasmit o the chose chaels, ad they receive the istataeous trasmissio throughput R k, which is determied by Update mixed strategy: All the active users Bk

5 5 update their mixed strategies accordig to the followig rules: q m k +1 = q m k+br k1 q m k,m = a k q m k +1 = q m k br kq m k, m a k, 23 where b is the learig step size, ad r k is the ormalized received payoff defied as follows: where R max r k = R k R max, 24 is the iterferece-free trasmissio throughput of user, i.e., R max = Blog 1+ Pd α σ. All the iactive users keep their mixed strategies uchaged, i.e., q k +1 = q k, N\Bk 25 Ed loop Y m AP 2 {2 3 4} AP mw {1 2} 350 mw AP 4 AP 3 AP 5 {1 3 4} {3 4} 200 mw 150 mw {2 4} 330 mw {1 4} 100 mw AP 6 { } 280 mw {1 2 4} 300 mw AP 7 AP X m The ratioale behid the update rule 23 is as follows: whe a chael is selected ad a positive payoff is received, the probability of choosig the chael i the ext step icreases while the probabilities of choosig other chaels decrease accordigly. Whe all the players adhere to this rule, the system will fially coverge to a stable state. Note that the above learig algorithm is fully distributed sice a active user oly eeds its idividual actio-payoff iformatio. Furthermore, its asymptotical covergece property is characterized by the followig theorem. Theorem 3. Whe the learig step size goes sufficietly small, i.e., b 0, the proposed distributed learig algorithm asymptotically coverges to a pure strategy NE poit of robust spectrum access game F 2. Proof: It has bee rigorously proved that the stochastic learig automata coverges to pure strategy Nash equilibria of exact potetial games i [32]. I methodology, the differeces i this work are summarized as: i all the users are always active i [32], while they are radomly active or iactive i this work, ad ii for exact potetial games, the chage i the utility fuctio cased by the uilateral actio chage of a arbitrary user is the same with that i the potetial fuctio, i.e., u a,a u a,a = φa,a φa,a 26 Whe provig the covergece for exact potetial games, the followig iequality is vital See equatio C.40 i [32]: u a,a u a,a φa,a φa,a 0 27 Note that the above iequality also holds for ordial potetial games See equatio 16. Thus, followig similar lies for the proof give i [32] Theorem 5, ad with some additioal modificatios for processig the user active probability λ [23], this theorem ca be proved. However, to avoid uecessary repetitio, the detailed proof is omitted. IV. SIMULATION RESULTS AND DISCUSSION The simulatio sceario follows the settig give i [16]. The cogitive APs are radomly located i a 500m 500m Fig. 2. A etwork cosistig of eight cogitive APs. By iquirig the geo-locatio spectrum database, each AP kows its available chael set ad the trasmittig trasmissio power, e.g, the available chael set ad trasmissio power of AP 1 are {1,2} ad 350 mw, respectively. square area. There are M = 5 chaels with badwidth B = 6MHz, the oise power is σ = 100 dbm, ad the path loss factor is α = 4. The distace betwee AP ad its associated boudary user is d = 20 m. By iquirig the geolocatio spectrum database, each AP operates with a specific trasmissio power P ad has a differet set of available chaels. The step size for the learig algorithm is b = 0.1. A. Covergece behavior We cosider a specific etwork which is show i Fig. 2. Due to the differet locatios, the actio available chael sets of the users are differet. For example, the actio set of users 1, 2, 3 ad 4 are A 1 = {1,2}, A 2 = {2,3,4}, A 3 = {1,3,4} ad A 4 = {3,4} respectively. For presetatio, it is assumed that all the users have the same active probability λ = 0.8. The covergece behavior of the proposed distributed spectrum access algorithm is show i Fig. 3. Specifically, the chael selectio probabilities of users 2, 3 ad 4 are preseted. It is oted that the chael selectio probabilities of user 2 coverges {0,0,1} over its available chael set {2,3,4}, which meas that it fially chooses chael 4 for data trasmissio. Similarly, the selectio probabilities of users 3 ad 4 also fially coverge. The results validate the covergece of the proposed distributed learig algorithm. B. Throughput performace For compariso, we cosider four approaches: optimal, best NE, worst NE ad the distributed learig algorithm. 1 Optimal: problem P2 is solved directly i a cetralized maer. Due to the fact it is a combiatorial optimizatio problem, we apply the exhaustive search approach to obtai the optimal solutio. 2 Best NE ad worst NE: by assumig that iformatio exchage amog the users is available, the best respose algorithm [24] is applied to achieve pure strategy NE of the robust spectrum access game F 2 i a distributed

6 6 Chael selectio probabilities q 22 q 23 q 24 q 31 q 33 q 34 q 43 q 44 The expected system throughput Mbps Optimal exhaustive search Best NE Worse NE Learig Fig Iteratio time idex k The covergece of the proposed distributed learig algorithm. 0 Sceario 1 Sceario 2 Sceario 3 Sceario 4 Sceario 5 Sceario 6 Fig. 5. The throughput performace compariso for six scearios with heterogeeous active probabilities. The expected system throughput Mbps Fig Optimal Exhaustive search Best NE Worse NE Proposed Distributed Learig The user active probability λ The expected throughput versus the active probabilities of the users. maer. We carried out 500 idepedet trails ad the take the best oe ad worst oe respectively. Note that the best NE ad worst NE serve as the upper ad lower bouds of the game. 3 The proposed distributed learig: i the absece of iformatio exchage ad cetralized cotroller, all the users adhere to the proposed distributed learig algorithm. First, we evaluate the throughput performace for the specific etwork show i Fig. 2. For presetatio, all the users have the same active probability. The expected throughput whe varyig the user active probability is show i Fig. 4. The result of the proposed learig is by simulatig 200 idepedet trials ad the takig the expected results. Some importat results ca be observed from the figure: i the best NE is almost the same with the optimal solutio, while the throughput gap betwee the worse NE ad the optimal solutio is trivial, which validate the effectiveess of the proposed robust spectrum game. ii the proposed distributed learig is very close to the optimal oe. Note that some similar umerical results o the throughput compariso were reported i [22]. Secodly, we also cosider the specific etwork show i Fig. 2, but the active probabilities of the users are differet. Specifically, the active probabilities of the users are set to {0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8} tagged as Sceario 1, {0.3, 0.3, 0.3, 0.6, 0.6, 0.9, 0.9, 0.9} tagged as Sceario 2, {0.3, 0.4, 0.5, 0.5, 0.5, 0.6, 0.7, 0.8} tagged as Sceario 3, {0.4, 0.4, 0.4, 0.6, 0.6, 0.6, 0.6, 0.6} tagged as Sceario 4, {0.3, 0.6, 0.6, 0.6, 0.6, 0.6, 0.6, 0.7} tagged as Sceario 5, {0.6, 0.6, 0.6, 0.6, 0.6, 0.6, 0.6, 0.7} tagged as Sceario 6, respectively. The throughput compariso results are show i Fig. 5. It also oted from the figure that for the scearios with heterogeeous active probabilities, the best NE is almost the same with the optimal solutio ad the proposed distributed learig is close to the optimal oe. These results validate the effectiveess of the formulated spectrum access game as well as the proposed distributed learig algorithm, i both homogeeous ad heterogeeous scearios. Thirdly, we evaluate the throughput performace for geeral etworks. Specifically, the cogitive APs are radomly located i the square regio. Each chael is idepedetly vacat with probability θ = 0.7 for each AP, ad the trasmissio power of each AP is radomly chose from the set {100, 200, 250, 300, 350, 280, 400}mW. The throughput compariso whe varyig the umber of cogitive APs is show i Fig. 6. For each umber of APs, e.g., N = 10, we simulate 100 idepedet topologies ad take the average result. Whe the etwork scales up, exhaustive search is ot feasible due to the heavy computatioal complexity. However, it is believed that the best NE would be very close to the optimal oe. It is show from the figure that the proposed distributed learig is close to the best NE, which agai validates the proposed game-theoretic solutio. Also, as the etwork scales up, the ormalized throughput decreases due to the icrease i the mutual iterferece, as ca be expected. To summarize, the simulatio results show that the best NE is almost the same with optimal solutio, ad the proposed distributed learig algorithm is very close to the optimal oe. Recallig the dyamic ad icomplete iformatio costraits i the cosidered system, we believe that the proposed gametheoretic learig solutio is desirable for practical applicatios.

7 7 The expected ormalized throughput Mbps Best NE Worse NE Proposed Distributed Learig The umber of cogitive APs N Fig. 6. The throughput performace compariso for geeral etworks the active probabilities of all the users are λ = 0.8. V. CONCLUSION This paper ivestigated the problem of database-assisted spectrum access i dyamic etworks, i which the active user set is varyig. Sice there is o cetral cotroller, it ecouters dyamic ad icomplete iformatio costraits. To solve this challege, we formulated a state-based spectrum access game ad a robust spectrum access game. We proved that the two games are ordial potetial games with the expected aggregate iterferece servig as the potetial fuctios, ad proposed a distributed learig algorithm without iformatio exchage to achieve the pure strategy Nash equilibrium NE of the games. Simulatio results show that the best NE is almost the same with the optimal solutio ad the achievable throughput of the proposed learig algorithm is very close to the optimal oe, which validates the effectiveess of the proposed game-theoretic solutio. Note that there are still some ew challeges ad ope issues to be studied. For example, users ca access more tha oe chael whe equipped with the multiple radio techology. A game-theoretic carrier aggregatio i ulicesed spectrum bads is ogoig ad will be reported soo. REFERENCES [1] FCC , Secod Memoradum Opiio ad Order, [2] OFCOM, TV White Spaces - A Cosultatio o White Space Device Requiremets, Nov [3] Ofcom, Implemetig Geolocatio, Nov [4] R. Murty, R. Chadra, T. Moscibroda, ad P. Bahl, Seseless: A database-drive white spaces etwork, i Proc. IEEE DySPAN, [5] S. Deb, V. Sriivasa ad R. Maheshwari, Dyamic spectrum access i DTV whitespaces: Desig rules, architecture ad algorithms, i Proc. ACM MobiCom, [6] J. Stie, D. Swai-Walsh ad M. Sherma, IEEE eabled whitespace database architecture evolutio, i Proc. IEEE DySPAN, [7] Google Spectrum Database, [8] Whitespace Alliace, [Olie] [9] Microsoft Reserach WhiteFiService, [10] J. Ojaiemi1, J. Poikoe, ad R. Wichma, Effect of geolocatio database update algorithms to the use of TV white spaces, 7th Iteratioal ICST Coferece o Cogitive Radio Orieted Wireless Networks ad Commuicatios CROWNCOM, [11] H. Yilmaz ad T. Tugcu, Locatio estimatio-based radio eviromet map costructio i fadig chaels, Wirel. Commu. Mob. Comput, vol. 15, o. 3, pp , [12] X. Yig, J. Zhag, L. Ya et al., Explorig idoor white spaces i metropolises, i Proc. ACM MobiCom, [13] X. Feg, Q. Zhag, ad J. Zhag, A hybrid pricig framework for TV white space database, IEEE Tras. Wireless Commu., vol. 13, o. 5, pp , [14] Y. Luo, L. Gao, ad J. Huag, Price ad ivetory competitio i oligopoly TV white space markets, IEEE J. Sel. Areas Commu., vol. 33, o. 5, pp , [15] Y. Luo, L. Gao, ad J. Huag, Trade iformatio, ot spectrum: A ovel TV white space iformatio market model, i Proc. IEEE WiOpt, [16] X. Che ad J. Huag, Database-assisted distributed spectrum sharig, IEEE J. Sel. Areas Commu., vol. 31, o. 11, pp , [17] Y. Liu R. Yu, M. Pa et al., Adaptive chael access i spectrum database-drive cogitive radio etworks, i Proc. IEEE ICC, [18] R. Myerso, Game Theory: Aalysis of Coflict. Cambridge, MA: Harvard Uiv. Press, [19] B. Babadi ad V. Tarokh, GADIA: A greedy asychroous distributed iterferece avoidace algorithm, IEEE Tras. If. Theory, vol. 56, o. 12, pp , 2010 [20] Q. Wu, Y. Xu, J. Wag, et al, Distributed chael selectio i timevaryig radio eviromet: Iterferece mitigatio game with ucoupled stochastic learig, IEEE Tras. o Veh. Techol., vol. 62, o. 9, pp , Nov [21] J. Wag, Y. Xu, Q. Wu ad Z. Gao, Optimal distributed iterferece avoidace: Potetial game ad learig, Trasactios o Emergig Telecommuicatios Techologies, vol. 23, o. 4, pp , [22] Y. Xu, J. Wag, Q. Wu, Z. Du, L. She ad A. Apalaga, A game theoretic perspective o self-orgaizig optimizatio for cogitive small cells, IEEE Commuicatios Magazie, to appear. [23] Y. Xu, Q. Wu, L. She, et al, Robust multiuser sequetial chael sesig ad access i dyamic cogitive radio etworks: Potetial games ad stochastic learig, IEEE Trasactios o Vehicular Techology, to appear. [24] D. Moderer. ad L. S. Shapley, Potetial games, Games ad Ecoomic Behavior, vol. 14, pp , [25] H. Tembie, Distributed strategic learig for wireless egieers, CRC Press, [26] J. Marde, G. Arsla, ad J. Shamma, Joit strategy fictitious play with iertia for potetial games, IEEE Tras. Autom. Cotrol, vol. 54, o. 2, pp , [27] Y. Xu, J. Wag, Q. Wu, et al, Opportuistic spectrum access i cogitive radio etworks: Global optimizatio usig local iteractio games, IEEE J. Sel. Topics Sigal Process., vol. 6, o. 2, pp , [28] Y. Sog, S. Wog, ad K.-W., Lee, Optimal gateway selectio i multidomai wireless etworks: A potetial game perspective, i Proc. ACM MobiCom, [29] H. Li, Multi-aget Q-learig for Aloha-like spectrum access i cogitive radio systems, EURASIP Joural o Wireless Commuicatios ad Networkig, vol. 2010, pp [30] K. Verbeeck ad A. Nowé, Coloies of learig automata, IEEE Tras. Syst., Ma, Cyber. B, vol. 32, o. 6, pp , [31] P. Sastry, V. Phasalkar ad M. Thathachar, Decetralized learig of ash equilibria i multi-perso stochastic games with icomplete iformatio, IEEE Tras. Syst., Ma, Cyber. B, vol. 24, o. 5, pp , May [32] Y. Xu, J. Wag, Q. Wu, et al, Opportuistic spectrum access i ukow dyamic eviromet: A game-theoretic stochastic learig solutio, IEEE Tras. Wireless Commu., vol. 11, o. 4, pp , 2012.