A Bayesian Overlapping Coalition Formation Game for Device-to-Device Spectrum Sharing in Cellular Networks

Transcription

1 1 A Bayesian Overlapping Calitin Frmatin Game fr Device-t-Device Spectrum Sharing in Cellular Netwrks Yng Xia, Kwang-Cheng Chen, Fellw, IEEE, Chau Yuen, Senir Member, IEEE, Zhu Han, Fellw, IEEE, Luiz A. DaSilva, Senir Member, IEEE Abstract We cnsider the spectrum sharing prblem between a set f device-t-device D2D links and multiple c-lcated cellular netwrks. Each cellular netwrk is cntrlled by an peratr which can prvide service t a number f subscribers. Each D2D link can either access a sub-band ccupied by a cellular subscriber r btain an empty sub-band fr its exclusive use. We intrduce a new spectrum sharing mde fr D2D cmmunicatins in cellular netwrks by allwing tw r mre D2D links with exclusive use f sub-bands t share their sub-bands with each ther withut cnsulting the peratrs. We establish a new game theretic mdel called Bayesian nn-transferable utility verlapping calitin frmatin BOCF game. We shw that ur prpsed game can be used t mdel and analyze the abve spectrum sharing prblem. Hwever, we bserve that the cre f the BOCF game can be empty, and we derive a sufficient cnditin fr which the cre is nn-empty. We prpse a hierarchical matching algrithm which can detect whether the sufficient cnditin is satisfied and, if it is satisfied, achieve a stable and unique matching structure which cincides with the verlapping calitin agreement prfile in the cre f the BOCF game. Index Terms Device-t-device cmmunicatin, verlapping, calitin frmatin, graph, matching, spectrum sharing, cellular netwrk, stable marriage, cllege admissin, stable rmmate, game thery. I. INTRODUCTION With the prliferatin f wireless data services and applicatins, it will sn becme difficult fr the existing cellular netwrk infrastructure t supprt the demands fr mbile data services under the traditinal infrastructure-centric netwrk framewrks. One reasn is that, in infrastructure-centric netwrk framewrks, all traffic is frwarded and relayed by the cellular netwrk Sme f the results in this paper have been presented at the IEEE Internatinal Sympsium n New Frntiers in Dynamic Spectrum Access Netwrks DySPAN, April, 2014 [1]. This wrk is partially supprted by the Natinal Science Fundatin under Grants CNS , ECCS , CNS , and CNS , Natinal Science Fundatin China under Grant , the Science Fundatin Ireland under Grant N. 10/IN.1/I3007, and the Singapre University Technlgy and Design under Grant N. SUTD-ZJU/RES/02/2011, Mediatek Inc. and Ministry f Science and Technlgy f Taiwan under Grant N. MOST E Y. Xia and Z. Han are with the Electrical and Cmputer Engineering at University f Hustn, TX, USA s: xyng.2012@gmail.cm and zhan2@uh.edu. K. C. Chen is with the Graduate Institute f Cmmunicatin Engineering, Natinal Taiwan University, Taipei, Taiwan ckc@ntu.edu.tw C. Yuen is with Singapre University f Technlgy and Design, Singapre yuenchau@sutd.edu.sg L. A. DaSilva is with CTVR, Trinity Cllege Dublin, Ireland dasilval@tcd.ie. L. A. DaSilva is als with Virginia Tech, VA, USA. infrastructure e.g., base statin even when the surces and destinatins are clse t each ther. This nt nly increases cmmunicatin delay and energy cnsumptin but als reduces the reliability f the netwrks. Fr example, in cellular netwrks, failure f a base statin can lead t mbile service utage fr the entire cverage area f the crrespnding cell. Device-t-device D2D cmmunicatin withut relying n the base statin t frward the traffic prvides an efficient way t increase the netwrk capacity and reliability. Anther issue is that the traditinal exclusive spectrum wnership mdel used in existing cellular netwrks has resulted in inefficient spectrum utilizatin fr a significant prtin f the time [2], [3]. One technique that prmises t address this prblem is spectrum sharing, which allws under-utilized licensed spectrum t be shared by unlicensed devices. Allwing bth D2D cmmunicatin and spectrum sharing in cellular netwrks can imprve netwrk capacity, reliability and spectrum utilizatin efficiency. Hwever, D2D links are generally established autnmusly and cannt be fully cntrlled by the base statin. In additin, chsing the wrng spectrum sharing pair f D2D links and cellular subscribers can result in high crss-interference, which may adversely affect bth D2D links and cellular subscribers. This mtivates the wrk in this paper, where we investigate the jint ptimizatin f spectrum sharing appraches and sub-band allcatin prblem fr a set f D2D links in an area with multiple c-lcated cellular netwrks. Each cellular netwrk is cntrlled by an peratr. We prpse a general analytical framewrk in which each D2D link first chses its preferred peratr and then decides whether t apply fr the exclusive use f a cellular sub-band r t share the sub-band with existing cellular subscribers. Since D2D links are autnmus, D2D links being assigned sub-bands fr exclusive use can als share their spectrum with each ther t further increase the spectrum utilizatin efficiency. We hence intrduce a new spectrum sharing mde fr D2D cmmunicatin in cellular netwrks, referred t as the sharing mde. In this mde, D2D links being assigned vacant sub-bands can share their sub-bands withut cnsulting the peratr. The distributed nature and autnmy f D2D links make game thery a natural tl t study and analyze D2D cmmunicatin systems in cellular netwrks. We establish a new game theretic framewrk, referred t as Bayesian nn-transferable utility verlapping calitin

2 2 frmatin BOCF game, t analyze the spectrum sharing prblem between D2D links and cellular netwrks. In ur prpsed game, D2D links that perate in the spectrum f the same peratr can be regarded as a calitin. Each member f a calitin can share spectrum with the existing cellular subscribers r apply fr an exclusive sub-band t be used by itself r shared with ther D2D links. If D2D links frm different calitins decide t share spectrum with each ther, the calitins will verlap. Our prpsed framewrk is general and the payff f each D2D link can be any perfrmance measure generated frm its received signal-t-interference-and-nise rati SINR. In additin, each D2D link is nt required t knw the payffs r actins f thers. We cnsider the cncept f the cre f calitin frmatin and seek an verlapping calitin agreement prfile in the cre that maximizes the payffs f D2D links. Our prpsed game is a generalizatin f the traditinal partitin-based Bayesian calitin frmatin game [4]. As pinted ut in [5], even analyzing the partitin-based calitin frmatin game can be challenging. Finding a stable calitin structure is an NP-hard prblem and generally requires an exhaustive search f all the pssible calitins frmed by the players. Allwing verlaps amng different calitins further increases the cmplexity f the system, and the cre f the prpsed game may nt always be nn-empty. Frtunately, we bserve that ur prpsed game can be slved by expliting tls frm matching thery [6]. Specifically, we intrduce a hierarchical matching algrithm t apprach a stable verlapping calitin frmatin. Our algrithm cnsists f three individual algrithms, each f which is used t achieve a stable matching structure f a specific matching market. The first matching market is a tw-sided many-t-ne matching market with private belief, in which each D2D link selects the peratr with the spectrum that can maximize its payff. All D2D links that are accepted by the same peratr frm a calitin. Within each calitin, D2D links cmpete fr the sub-bands f the peratr. We mdel this prblem as a tw-sided ne-t-ne matching market. In this market, each D2D link applies fr sharing sub-bands with existing cellular subscribers. If sme D2D links decide t share the spectrum with ther D2D links in the netwrk, they will enter the third market, which is a ne-sided ne-t-ne matching market. We prpse a distributed belief updating algrithm fr each D2D link t search fr a unique and stable matching structure. We prve that this matching structure cincides with the verlapping calitin agreement prfile in the strict Bayesian cre f ur prpsed game. We als derive a sufficient cnditin fr which the cre f the game is nn-empty. Our prpsed distributed ptimizatin algrithm can detect whether this sufficient cnditin is satisfied and, if satisfied, t achieve an verlapping calitin structure in the cre. The rest f this paper is rganized as fllws. Related wrk is reviewed in Sectin II. The netwrk mdel is presented in Sectin III. The D2D and cellular spectrum sharing prblem is frmulated in Sectin IV. This prblem is mdeled as a BOCF game in Sectin V. The hierarchical matching algrithm is prpsed in Sectin VI. The numerical results are presented in Sectin VII, and we ffer ur cncluding remarks and future wrks in Sectin VIII. II. RELATED WORK Mst f the previusly reprted results n resurce management fr D2D cmmunicatins fcus n resurce allcatin fr a single D2D link with specific perfrmance gals. Fr example, in [7], the authrs applied pwer cntrl and multi-hp ruting discvery methds t imprve the prbability f utage fr pprtunistic D2D cmmunicatins in a cellular netwrk. The pwer cntrl prblem fr D2D links in a cellular netwrk was als studied in [8] [10]. In [11], the authrs investigated the pssible perfrmance imprvement brught by netwrk cding and user cperatin in a D2D cmmunicatin system. Observing the fact that D2D cmmunicatins have nt yet been cnsidered in LTE-Advanced systems, the authrs in [12] have prpsed a mechanism t supprt a D2D cmmunicatin sessin in existing LTE cellular netwrks. In [13], a distributed channel-aware spatial resurce allcatin algrithm, referred t as FlashLinQ, was prpsed fr ad hc netwrk systems. Mtivated by the recent bservatin that treating the interference as nise at each f the spectrum sharing D2D links is infrmatin theretically ptimal under certain cnditins, a new spectrum sharing mechanism referred t as infrmatin-theretic link scheduling ITLinQ has been prpsed in [14]. In [1], we mdel the spectrum sharing prblem between a set f D2D links and ne cellular peratr as a Bayesian nn-cperative game. In this paper, we extend ur previus wrk in [1] t the case f multiple peratrs. This extensin dramatically changes the structure f the prblem studied in [1] because different peratrs have different resurces and each peratr will nly reveal its resurce infrmatin t the D2D links being given permissin t access its spectrum. Hw D2D links can select their preferred peratr withut knwing which sub-band they will be eventually allcated by each peratr is a challenging task. Different frm the existing wrk, in this paper we study the interactin between different D2D links and between D2D links and cellular subscribers in a general multi-user D2D cmmunicatin-enabled cellular netwrk using calitinal game theretic mdels. Recently, calitinal game thery has been used t study interactins in wireless netwrks [15], [16]. Fr example, in [17], a calitin frmatin game has been applied t study the dynamic spectrum access prblem in cgnitive radi netwrks. In [16], a hierarchical game theretic framewrk has been prpsed which allws unlicensed users t cperatively share the licensed spectrum by

3 3 paying a certain price t licensed users. Hwever, mst f the existing studies either fcus n the cperatin amng all the wireless users r nn-verlapping calitin frmatin. In this paper, we intrduce a new Bayesian nn-transferable verlapping calitin frmatin BOCF game mdel t study spectrum sharing by D2D cmmunicatins in cellular netwrks. In this paper, we prpse a hierarchical matching algrithm t find the verlapping calitin agreement in ur prpsed game. The tw-sided stable matching prblem has been widely studied frm bth theretical and practical perspectives [6], [18] [20]. In this prblem, each agent belnging t the set f ne side f the market has a preference abut the agents belnging t the set f the ther side and tries t find a matching t ptimize its perfrmance. Many extensins f these prblems have been studied in the literature. The case f sme agents n the ne side nly having preferences ver a sub-set f the agents n the ther side was studied in [21]. The case where the agents frm ne side have equal preference ver multiple agents f the ther side, called stable marriage with tie, has been studied in [22]. Empirical studies f the different variatins f the stable marriage prblem have been reprted in [19], [23]. In mst f the previus wrks, each player cannt have any belief abut the envirnment as well as the preference f thers. In this paper, we allw each player t establish and maintain a private belief functin. One wrk that is similar t ur setting f private belief fr agents is the belief-based calitin frmatin game prpsed in [24]. Hwever, that wrk assumes the belief functins are fixed, and cannt be updated during the game, which is different frm the setting f ur paper, where we intrduce a Bayesian belief update algrithm t allw each player t search fr the ptimal matching structure. III. A GENERAL SYSTEM MODEL FOR D2D COMMUNICATIONS IN CELLULAR NETWORKS We cnsider spectrum sharing between a set f K D2D links, labeled as D = {D 1, D 2,..., D K }, and a set f L c-lcated cellular netwrk peratrs, labeled as peratrs O = {1, 2,..., L}. Each D2D link crrespnds t a cmmunicatin channel between a D2D surce and its crrespnding destinatin, and each cellular subscriber crrespnds t a dwnlink r uplink cmmunicatin channel frm the BS t the cellular subscriber as shwn in Figure 1. T avid causing interference t the neighburing cell, we assume each D2D link can nly share spectrum with the subscribers in its lcal cell. Each peratr i has been licensed an exclusive set S i f sub-bands which can be accessed by bth D2D links and cellular subscribers. Let K i be the subset f vacant sub-bands f peratr i unccupied by cellular subscribers. Let J i be the subset f sub-bands ccupied by the cellular subscribers f peratr i, i.e., we have J i K i = and S i = J i K i i O. Each D2D link can nly share sub-bands with the cellular subscribes TABLE I LIST OF NOTATION Symbl Definitin D Set f D2D links O Set f peratrs S i Set f sub-bands f peratr i J i Set f sub-bands f peratr i ccupied by cellular subscribers K i Set f sub-bands f peratr i unccupied by cellular subscribers C Set f D2D links with vacant sub-bands D k the kth D2D link Pl i Cellular subscriber in sub-band l f peratr i ϖ Dk [l] Payff f D k when accessing sub-band l ϖ Dk [l, m] Payff f D k when sharing a sub-band with D n fr l = Γ s D k, m = Γ s D n and D n, D k K ϖ Dk Expected payff f D k ηi ld k Revenue f the peratr btained frm D k in subband l R d D Preference f D k k ver ther D2D links with exclusive use f sub-bands ϕ Dk Decisin f D k t send a request t peratr, subband and D2D links with vacant sub-bands Γ Cnflict-slving rules f the peratrs, sub-bands and D2D links with sub-bands fr exclusive use a C i Actin f players in calitin C i Y Dk Type f D k B Dk Belief functin f D k abut the decisins f ther D2D links and the cnflict-slving rules b Dk Belief functin f each player D k abut the types f ther players ϕ Labeling sequence f D2D links with vacant subbands within the same cell. Since the access t licensed spectrum is expensive, the exclusive sub-band given t each D2D link may, in practice, be narrwer than the full-size sub-band allcated t the cellular subscribers. Each D2D link can either access a sub-band ccupied by a cellular subscriber r apply fr a vacant sub-band fr exclusive use if sharing the spectrum with a cellular subscriber cannt prvide sufficient quality-f-service QS. Let Pl i be the cellular subscriber ccupying sub-band l f peratr i fr l J i. We dente S = S i, J = J i and K = K i. i O i O i O Because f the cmplexity f the interference management in D2D and cellular spectrum sharing prblem, mst existing wrks assume that each D2D link can share spectrum with at mst ne cellular subscriber [7], [25] [27]. In this paper, we fllw the same line and assume that each sub-band can at mst cntain tw users either tw D2D links r ne D2D link and ne cellular subscriber. This assumptin makes the spectrum sharing between D2D links and cellular netwrks feasible t be implemented in the existing cellular telecmmunicatin system. Fr example, in Release 12 f the LTE standard, an enb Evlved Nde B can keep track f the interference received at each f its cellular subscribers in each sub-band and can simply remve the D2D link frm the sub-band nce it bserves a higher-than-tlerable interference level [28], [29]. Our mdel hwever can be directly extended t the cases with tw r mre D2D links sharing the same sub-band with each cellular

4 4 P P12 BS f Operatr 1 5 BS f Operatr BS f Operatr 3 Cellular Users D2D Links Fig. 1. System mdel fr D2D cmmunicatins in a cellular netwrk with three peratrs: D2D links D1, D2, D3 perate in mdes M1 i.e., D1 has been assigned t a dedicate sub-band fr exclusive use, M2 i.e., P11 and D2 share the same sub-band and M3 i.e., the traffic f D3 has been frwarded by enb f peratr 2, respectively. D2D links D4 and D5 perate in mde M4 i.e., D4 and D5 share their dedicated sub-bands with each ther. a mre general system in which multiple peratrs c-exist in the same cverage area and each D2D link in each specific mde btains different perfrmance in different sub-bands. We cnsider the jint ptimizatin fr bth mde selectin and the sub-band accessing/sharing. That is, each D2D link shuld nt nly chse a specific mde t perate in but als decide a specific peratr and sub-band that can maximize its perfrmance in its chsen mde. Let ϖdk [l] be the payff f D2D link Dk btained by accessing sub-band l in mde M1 if l K r M2 if l J fr Dk D and l S. Let ϖdk [l, m] be the payff f D2D link Dk when it shares its assigned sub-band l with anther D2D link which has been assigned sub-band m fr l, m K mde M4. We cnsider a general mdel and the payff f each D2D link can be any functin f its received signal-t-interference-plus-nise rati SINR. Fr example, if D2D link Dk wants t maximize its transmit rate per bandwidth price, the payff f the D2D link Dk in each mde is given as fllws. M1 and M2: When D2D link Dk accepts a dedicated subband l in mde M1 r shares a sub-band l with a cellular subscriber in mde M2, its payff is given by subscriber. We will discuss this in detail in Sectin VIII. A cmmnly adpted apprach is t divide pssible spectrum sharing schemes between D2D links and cellular subscribers int three mdes [12]: ρ[l] ϖdk [l] = E lg 1 + SINRDk [l], 1 M1. Dedicated Mde: D2D links access dedicated e[l] sub-bands that are unccupied by the cellular where ρ[l] is the bandwidth f sub-band l and e[l] is subscribers, the price paid t the peratr fr accessing sub-band M2. Reuse Mde: D2D links reuse the sub-bands ccupied l. Nte that, different frm the cellular netwrks in by cellular subscribers, which the peratr charges subscribers accrding t M3. Relay Mde: The traffic f D2D links is relayed the quality f experience QE, in D2D thrugh the BS. This mde is nrmally applied when cmmunicatins, the data traffic des nt traverse the direct cmmunicatin cannt prvide adequate netwrk infrastructure and the peratrs cannt perfrmance fr D2D links. mnitr the transmissin rate between tw devices In cellular netwrks, each D2D link can perate in ne that establish a direct link. Therefre, in this paper, f the abve three mdes with help frm the enb f the we assume each peratr charges a fixed price e[l] crrespnding peratr. The detailed implementatin f fr any D2D link t access a dedicated sub-band l. these mdes in LTE-Advanced systems has been The payff f each D2D link crrespnds t the described in [12], [26], [30]. transmissin rate per unit price btained by accessing We illustrate the D2D links and ptential interference fr the assigned sub-bands f the crrespnding peratr. the abve three mdes in Figure 1. SINRDk [l] is the signal-t-nise-and-interference Since D2D links are autnmus, t further imprve rati SINR experienced by D2D link Dk in the spectrum utilizatin efficiency, D2D links assigned sub-band l, given by [31], dedicated sub-bands fr their exclusive use can als share their sub-bands with each ther. Therefre, we intrduce SINRDk [l] = the fllwing new mde fr spectrum sharing between hdk [l]wdk l K in mde M1, ϱdk [l], D2D cmmunicatins and cellular netwrks: 2 hdk [l]wdk ϱ [l]+h M4. Sharing Mde: D2D links in mde M1 can further w, l J in mde M2, Dk P i Dk P i l l increase spectrum utilizatin efficiency by sharing where ϱdk [l] is the additive nise received by Dk in their dedicated spectrum with each ther. sub-band l, hdk [l] is the channel gain between the We als illustrate the mde M4 in Figure 1. We will surce and destinatin f D2D link Dk in sub-band l. prvide mre detailed discussin n the pssible hpli Dk is the channel gain between cellular subscriber implementatin f ur prpsed framewrk in LTE Pli and D2D link Dk. wpli and wdn are the transmit Advanced netwrk systems in Sectin VII. Different frm mst f the existing wrks, which pwers f Pli and Dn, respectively. assume each D2D link btains the same perfrmance in M3. If D2D link Dk decides t use mde M3, it will first different sub-bands under each specific mde, we cnsider transmit t the BS and then wait fr the BS t

5 5 frward the signals t the crrespnding D2D destinatin. Since, in this mde, the traffic f D2D links is transmitted in the same way as fr the cellular subscribers, this mde f peratin cannt prvide any imprvement in terms f the spectrum utilizatin efficiency and shuld be the last chice f each D2D link. In this paper, we assume each D2D link cannt btain any psitive payff in this mde, i.e., we write the payff f D k in mde M3 as ϖ Dk [D k ] = 0. M4. If tw D2D links D k and D n with dedicated sub-bands l and m, respectively, decide t share their sub-bands with each ther by transmitting at the same time ver the same aggregated sub-bands l and m [32], [33] and agree t equally share the cst f sub-bands l and m fr l, m K and i, j O, the payff f each D2D link e.g., D k in mde M4 is given by ϖ Dk [l, m] = 2 ρ[l] + ρ[m] E lg 1 + SINR Dk [l, m], 3 e[l] + e[m] h Dk [l,m]w Dk where SINR Dk [l, m] = ϱ Dk [l,m]+h D nd k [l,m]w D, n h Dk [l, m] and h Dn D k [l, m] are the channel gain between the surce and destinatin f D2D link D k and that between the surce f D2D link D k and the destinatin f D2D link D n in the frequency band frmed by aggregating sub-bands l and m, respectively. ϱ Dk [l, m] is the additive nise at the receiver f D2D link D k in the aggregated frequency band frmed by sub-bands l and m. We fllw a cmmnly adpted setting and set the revenue f each peratr in the sub-bands ccupied by cellular subscribers as a functin f the resulting interference caused by the D2D links [16], [34], [35]. We can als define the revenue f peratr i frm a D2D link D k accessing a vacant sub-band fr exclusive use, as a functin f the SINR f D k, i.e., the revenue ηi ld k btained by peratr i frm D2D link D k in sub-band l is given by ηi l D k = g EINT Dk [l] where g is the revenue functin and INT Dk [l] is given by { hdk Pl INT Dk [l] = iw D k, l J i, h Dk [l]w Dk ϱ Dk [l], l K i 4. In this setting, the price charged by each peratr t each UE sharing the sub-bands with cellular subscribers is prprtinal t the interference caused by the UE. As is bserved in [16], this allws each peratr t cntrl the resulting interference created by the UEs by adjusting the prices. Fr example, if the revenue ηi ld k is a linear functin f EINT Dk [l], we have ηi ld { k = max β i EINT Dk [l] }, where β i is the pricing l J i cefficient f peratr i [36]. It has been shwn in [37] that the peratrs can always limit the interference f the D2D links in their sub-bands by adjusting the value f the pricing cefficient. We can nw shw that the jint ptimizatin f the mde selectin and sub-band accessing/sharing prblem is Fig. 2. A Hierarchical Matching Algrithm Operatr Selectin Algrithm A Tw-Sided Many-t-One Matching Market Sub-band Selectin Algrithm A Tw-sided One-t-One Matching Market D2D Selectin Algrithm A One-sided One-t-One Matching Market An Overlapping Calitin Agreement Prfile A hierarchical matching algrithm fr BOCF game. Belief Update equivalent t the ptimizatin f the sub-band allcatin prblem fr D2D links. Fr example, if D2D link D k has been assigned t sub-band l K fr exclusive use, D k will be in mde M1. If D2D link D k has been eventually allcated sub-band l J that is ccupied by a cellular subscriber, D k perates in mde M2. If D2D link D k can access an aggregated sub-band frmed by tw sub-bands l and m fr l, m K, D k perates in mde M4. If D2D link D k cannt btain any sub-band t supprt its direct cmmunicatin, it will then ttally rely n the peratr t establish cnnectivity and frward traffic between the tw devices and hence will be in mde M3. In the rest f this paper, we fcus n ptimizatin f the sub-band allcatins fr D2D links in cellular netwrks. The list f ntatin used in this paper is prvided in Table I. IV. PROBLEM FORMULATION As mentined previusly, each peratr nly pssesses a limited number f sub-bands and hence can nly prvide service fr a limited number f D2D links. When the number f D2D links requesting t access the spectrum f an peratr exceeds this limit, a cnflict will happen. Similarly, cnflicts may als happen when mre than ne D2D link send a request fr the same sub-band f an peratr r the same D2D link t share a sub-band with. T avid pssible verlading, the peratr will have t reject the requests f sme D2D links, i.e., if the number f D2D links sending requests t peratr i exceeds S i, peratr i will nly allw S i D2D links t access its spectrum, selected accrding t the revenue that can be btained frm the requesting D2D links. We assume the spectrum sharing prcess can be divided int time slts. We fllw the same line as [13] and assume the cmmunicatin f D2D links is synchrnized using the timing signals sent by the cellular netwrks r the GPS timing signal. Each D2D link needs t make its decisins abut peratrs, sub-bands and sub-band sharing partner at the beginning f each time slt and cannt change its decisin during the rest f the time slt. The decisins f

6 6 each D2D link, hwever, can be changed between different time slts. We use subscript t t dente the parameters and results in time slt t. T simplify ur descriptin, we can ignre the subscript t when we nly fcus n ne time slt f the decisin prcess. We can define the D2D and cellular spectrum sharing DCSS prblem as a tuple P = D, O, Φ, Γ, ϖ cnsisting f fllwing elements: 1 D is the set f D2D links. 2 O is the set f peratrs. 3 Φ = O { } S { } D { } is the set f pssible decisins made by each D2D link abut the peratr, sub-bands and sub-band sharing partner. Each D2D link D k can decide ϕ Dk = ϕ D k, ϕ s D k, ϕ d D k Φ where ϕ D k O { } is the peratr requested by D2D link D k. We use ϕ D k = t mean D k declines t send a request t any peratr e.g., D k believes sharing the spectrum f the cellular netwrk cannt result in a psitive payff. ϕ s D k S i { } is the sub-band requested by D2D link D k after being accepted by peratr i. We write ϕ s D k = if D2D link D k declines t request any sub-band f peratr i e.g., D k believes peratr i des nt pssess any sub-band that can result in a psitive payff. If D k has been assigned a sub-band fr exclusive use, D k can then send a request t anther D2D link D n with an exclusive sub-band asking t aggregate and share their sub-bands. Similarly, if D k des nt want t share its sub-band with any ther D2D link, we have ϕ d D k =. It can be easily bserved that these decisins are clsely related t each ther. Mre specifically, D2D link D k shuld decide ϕ s D k and ϕ d D k based n ϕ D k. On the ther hand, ϕ D k shuld be decided by cnsidering the pssible chices f sub-bands and sub-band sharing partners fr the D2D links. We dente the decisin prfile f all D2D links as ϕ = ϕ Dk Dk D. 4 Γ = Γ, Γ s, Γ d is the cnflict-slving rule f the peratr and D2D links with dedicated sub-bands. We use Γ D k and Γ s D k t dente the final peratr and sub-band being assigned t D2D link D k. We als use Γ D k = D k r Γ s D k = D k t mean that D k cannt directly cmmunicate with anther device but has t perate in mde M3. We als use Γ d D k t dente the D2D link which agrees t share its subband with D k. Similarly, we use Γ d D k = D k t mean D k cannt share its sub-band with any ther D2D link with an exclusive sub-band. 5 ϖ Dk is the payff f D k, which depends n the decisin prfile ϕ and the cnflict-slving rule Γ, i.e., we have ϖ Dk ϕ, Γ = 1 Γd D k =D k ϖ Dk [l = Γ s D k ] + 1 Γd D k =D n D n D\{D k } ϖ Dk [l = Γ s D k, m = Γ s D n ] fr Γ s D k D k and Γ s D n D n, where ϖ Dk [l] and ϖ Dk [l, m] are given in 1 and 3, respectively, and 1 is the indicatr functin. If tw r mre D2D links have been allcated sub-bands fr exclusive use, these D2D links can share their sub-bands with each ther t further imprve their payffs. Since the sub-band allcatin prcess has been supervised by the BS, the D2D links which are allcated dedicated sub-bands can btain the identity infrmatin f each ther frm the BSs. Each D2D link with exclusive sub-bands e.g., D k knws the set C f D2D { links with sub-bands fr exclusive use, defined as C = D k : Γ s D k } K i, D k D, and i O ϖ Dk [m, l] fr Γ s D k = m, Γ s D n = l D n C after the training perid. We prvide a mre detailed discussin f this training prcess in Sectin VI. It can be bserved that the value f ϖ Dk fr each D2D link D k can be affected by the decisins f all D2D links and the cnflict-slving rules f the peratrs and D2D links with exclusive use f sub-bands, bth f which are unknwn t D k. It is generally unrealistic t assume each device can predict all these unknwn parameters instantaneusly befre it makes decisins at the beginning f each time slt t. It is hwever pssible fr each D2D link t eavesdrp n the peratrs requested by ther D2D links during the previus time slt. As bserved in [38], D2D cmmunicatin will be mainly applied in high ppulatin density areas, where the cell sizes are generally small. This makes it pssible fr each D2D link t eavesdrp n the requests sent by nearby D2D links. Each D2D link can als btain this infrmatin frm the peratrs, i.e., each peratr can bradcast its request acceptance and rejectin message t all the D2D links. In this paper, we assume each D2D link cannt knw the instantaneus decisins f thers but can bserve the decisins f ther D2D links in previus time slts. Each D2D link can explit these bservatins t establish a belief functin abut these unknwn parameters. The selfishness and autnmy f D2D links make it natural t mdel the DCSS prblem as a game. During the rest f this paper, we fcus n slving the fllwing prblems: 1 Establish a game theretic mdel t study the interactin amng autnmus and selfish D2D links. 2 Develp a distributed algrithm fr each D2D link t ptimize its decisin t maximize its expected payff. 3 Prpse an effective cnflict-slving rule fr bth the peratr and D2D link with dedicated sub-bands t apprach a sub-band allcatin structure such that n peratr r D2D link can benefit by unilaterally deviating. 4 Develp a belief updating algrithm fr each D2D link t learn the prbabilistic features f unknwn parameters f ther D2D links and peratrs using its previus bservatins. T slve the first prblem, we prpse a Bayesian verlapping calitin frmatin game t mdel the DCSS prblem in the next sectin. We will then develp the distributed algrithm, cnflict-slving rules and belief updating apprach in Sectin VI.

7 7 V. AN OVERLAPPING COALITION FORMATION GAME In many practical resurce sharing prblems, allwing verlap between different calitins can further imprve the system perfrmance and resurce utilizatin efficiency. Fr example, if multiple wireless netwrk subscribers can access several resurce blcks e.g., frequency bands, time slts, antennas, they can be first divided int different calitins each f which cnsists f the subscribers sharing ne blck f resurce [37]. Hwever, it is pssible that, in sme calitins, the share f the resurce blcks allcated t sme subscribers is nt enugh t supprt a desired level f QS, while fr sme ther subscribers, the allcated resurce may exceed thse requirements. In this case, allwing the subscribers with insufficient resurces t als aggregate r share sme f the surplus resurces allcated t ther subscribers can further imprve the resurce utilizatin efficiency as well as the netwrk system perfrmance. We define an verlapping calitin C i frmed by a set f players {D 1, D 2,..., D K } as a vectr C i = c i D 1, c i D 2,..., c i D K where c i D k is a binary variable and c i D k = 1 means that D k is a member f calitin C i and c i D k = 0 means D k des nt belng t calitin C i. If tw calitins C i and C j verlap, there exists at least ne player D k D such that c i D k = c j D k = 1 fr i j. Let suppc i be the supprt f C i. An verlapping calitin frmatin structure with L verlapping calitins is defined as C = {C i } i {1,2,...,L}. We frmally define a BOCF game as fllws: Definitin 1: A BOCF game G = D, A, Y, b, ϖ, cnsists f the fllwing elements: 1 D is the set f players. 2 A C i = A c C i A Ci is the set f pssible actins fr the players in each calitin C i. An actin a C i = a c C, a i C f calitin C i in a BOCF game i cnsists f tw parts: the calitinal actin a c C and i the verlapping actin a C. A calitinal actin i a c C A c i C fr a calitin C i is similar t the actin i in the nn-verlapping calitin frmatin game, which specifies the jint actin mutually agreed t by every member player within a calitin C i. An verlapping actin a C A i C specifies hw the i players in calitin C interact with players in ther calitins. Fr example, in the resurce sharing prblem, the calitinal actin characterizes the resurce allcatin scheme mutually agreed t by all the subscribers t divide the resurce blck within ne calitin. The verlapping actin characterizes hw subscribers being allcated resurces f different calitins exchange r share these resurces. These tw actins may be clsely crrelated in mst applicatins. Fr example, sme players allcated resurces frm different resurce blcks can share prtins f their resurces with each ther and in this case the verlapping actins e.g., hw they negtiate and share their prtins f the allcated resurces depend n the calitinal actins e.g., hw t divide each resurce blck amng the calitin members. It can be bserved that the calitin frmatin structure and actins jintly determine the payff f each member player in a calitin. We hence can define an verlapping calitin agreement as a tuple x i = C i, a C i fr supp C i D and a C i A C i. We als dente the verlapping calitin agreement prfile x as the set f all verlapping calitinal agreements frmed by the players, i.e., x = {x i } i {1,...,L}. 3 Y = Y D1 Y D2... Y DK is the type space, where Y Dk is the set f pssible types f player D k. The type Y Dk Y Dk f each player D k specifies its preference regarding different verlapping calitin agreements. 4 b = b D1, b D2,..., b DK is the vectr f belief functins, where b Dk is the belief functin f player D k abut the types f thers. Each player D k cannt knw the types f ther players. Each player can hwever establish a belief functin abut these unknwn types by expliting the previus bservatins. 5 ϖ is the vectr f the payffs f the players. 6 is the preference relatin. The preference relatin is assumed t be cmplete and transitive [6]. We use x Dk x t dente that player D k prefers verlapping calitin agreement x t x fr x x. We als use x D n D k x t dente that player D k believes D n prefers verlapping calitin agreement x t x fr D n D k and D k, D n D. An imprtant slutin cncept in the calitinal game is the cre, which is frmally defined as fllws. Definitin 2: An verlapping calitin agreement prfile x is in the weak Bayesian verlapping calitin frmatin cre if there is n verlapping calitin agreement x = C, a C x such that every member believes it will benefit frm deviating frm the current verlapping calitin agreement x i, i.e., x = C, a C and C i C such that x Dk x i D k C i. The abve definitin can be regarded as the direct extensin f the cre fr the Bayesian nn-verlapping calitin frmatin game t the verlapping case. If we take the belief f each player int cnsideratin, we can prpse a belief-based cncept f the cre, referred t as b-cre, in the BOCF game as fllws. Definitin 3: We say an verlapping calitin agreement prfile x is in the Bayesian verlapping calitin frmatin b-cre, if the fllwing tw cnditins are satisfied: 1 there exists n verlapping calitin agreement such that every member believes it will benefit frm deviating frm the current verlapping calitin agreement, 2 there exists n verlapping calitin agreement such that at least ne member f a calitin believes that each f the ther members in the calitin believes it will benefit frm deviating frm their current verlapping calitin agreement, i.e., there des nt exist x = C, a C and C i C such that there exists a D2D link D k C i satisfying x Dn D k x D n D k, D n C i.

8 8 Nte that bth cncepts f the cre defined abve are different frm the cre related t the grand calitin used in many calitinal game-based wireless netwrk mdels [39] [41]. The latter cre cncept can nly be nn-empty when all the players in the game agree t frm the grand calitin, that is, the calitin that cntains all the players [4]. The cncept f the cre in Definitin 2 can be in sme sense regarded as an extensin f the a-cre prpsed in [42] int the BOCF game. It is different frm the Aubin cre fr the cperative fuzzy game in [43] as well as the -cre and r-cre cncepts prpsed fr the transferable utility verlapping calitin frmatin game in [42]. We can mdel the DCSS prblem as a BOCF game, referred t as DCSS game, G SS = D, Y, Γ, b, ϖ, as fllws: the players are the D2D links. The calitinal actin f a calitin C i crrespnds t the sub-band allcatin scheme achieved by all the D2D links being accepted by the same peratr i. Mre specifically, the calitinal actin a c C is determined by the decisins made i by D2D links in calitin C i as well as the cnflict-slving rules f peratr i. The verlapping actin crrespnds t the sub-band sharing scheme between the D2D links with exclusive use f sub-bands frm different calitins. The type Y Dk f each player D k is its preference ver all the pssible verlapping calitin agreements. Each D2D link cannt knw the types f ther D2D links and it is generally difficult fr each D2D link t establish a belief functin ver thers types. Frtunately, we can shw that the uncertainty f each D2D link abut types f ther D2D links can be cnverted int the uncertainty abut the decisins f thers and cnflict-slving rules f the peratrs and D2D links with vacant sub-bands. It can be bserved that, fr a given cnflict-slving rule Γ, the final verlapping calitin frmatin structure C is determined by the decisins ϕ f all D2D links. By intrducing a functin F mapping frm Γ and ϕ t an verlapping calitin frmatin structure C, we have C = F Γ, ϕ. Fr each f the calitin frmatin structures, the calitinal actin a c C in calitin C i specifies the sub-band allcatin i between D2D links being accepted by peratr i and the set S i f sub-bands. Since the sub-band assigned t each D2D link D k C i is given by Γ s D k, we can bserve that the calitin actin a c C is determined by Γ s and ϕ s i C i where ϕ s C = { ϕ s i D k. If we intrduce a functin G }D k C i mapping frm ϕ s C and i Γs int a c C, we can write i a c C = G Γ s, Γ d, ϕ s i C. Similarly, fr each verlapping i calitin frmatin structure, the set C f D2D links with sub-bands fr their exclusive use is fixed. Als, since the verlapping actin f each D2D link D k C i C in a calitin C i is determined by the decisin ϕ d D k and the cnflict-slving rule Γ, we can define a functin H mapping frm the decisins f D2D links with exclusive sub-bands and the cnflict-slving rules f these D2D links int the verlapping actin, i.e., we have Γ d, ϕ d C a C i = H. Therefre, we can write each verlapping calitin agreement x i = C i, a C i = F Γ, ϕ, G Γ s, ϕ s C i, H Γ d, ϕ d C. In ther wrds, the preference f each D2D link abut the calitinal agreements can be cnverted int its preference ver different decisins fr a given cnflict-slving rule. In the DCSS game, each D2D link can bserve the decisins f ther D2D links and the peratr and sub-band it has been allcated during the previus time slts and hence can explit these bservatins t establish a belief functin abut the decisins f ther D2D links. The belief functin B Dk ϕ Dk, Γ = Pr Γ D k, Γ s D k, Γ d D k, ϕ Dk ϕ Dk f each D2D link D k can be divided int six parts: the first three belief functins crrespnd t the beliefs f D k abut the decisins f ther D2D links regarding peratrs, sub-bands and the D2D sub-band sharing partner, i.e., B Dk ϕ Dk = Pr ϕ D k ϕ D k, BDk ϕ s Dk = Pr ϕ s D k Γ D k, ϕ s D k and B Dk ϕ d D k = ϕ d Dk Γ D k, Γ s D k, ϕ d, and the remaining three Dk belief functins crrespnd t the beliefs f D k abut the cnflict-slving rules f peratrs, sub-bands and D2D links with sub-bands fr exclusive use, i.e., B Dk Γ = Pr Γ D k ϕ D k, ϕ D k, BDk Γ s = Pr Γ s D k ϕ D k, ϕ D k, Γ, ϕ s D k, ϕ s D k, and BDk Γ d = Pr We have Γ d D k ϕ Dk, ϕ Dk, Γ, ϕ s Dk, ϕ s Dk, Γ s, ϕ d Dk, ϕ d Dk. B Dk ϕ Dk, Γ = Pr Γ D k, Γ s D k, Γ d D k, ϕ D k, ϕ s D k, ϕ d D k ϕ D k, ϕ s D k, ϕ d D k = Pr ϕ D k ϕ D k Pr Γ D k ϕ Pr ϕ s D k Γ D k, ϕ s D k Pr Γ s D k Γ D k, ϕ s Pr ϕ d Dk Γ D k, Γ s D k, ϕ d Dk Pr Γ d D k Γ D k, Γ s D k, ϕ d = B Dk ϕ Dk BDk Γ D k B Dk ϕ s Dk B Dk Γ s D k B Dk ϕ d D k B Dk Γ d D k. 5 The expected payff ϖ Dk f each D2D link D k achieved by its decisin ϕ Dk and belief B Dk ϕ Dk, Γ can be written as ϖ Dk BDk ϕ Dk, Γ, ϕ Dk = ϖ Dk B Dk ϕ Dk, BDk ϕ s Dk, BDk ϕ d D k, B Dk Γ, B Dk Γ s, B Dk Γ d, ϕ D k, ϕ s D k, ϕ d D k = ϕ Dk, Γ ϕ Dk Φ K 1 B Dk {1 Γd D k =D k ϖ Dk [l = Γ s D k ] +1 Γd D k =D n ϖ Dk [l = Γ s D k, m = Γ s D n ] }.6 Since each D2D link always chses the decisin that maximizes its expected payff based n its belief, the

9 9 decisin ϕ Dk f D2D link D k fr a given belief b Dk is given by ϕ Dk = arg max ϕ Dk Φ ϖ D k BDk ϕ Dk, Γ, ϕ Dk. 7 As mentined previusly, allwing verlaps amng different calitins greatly increases the cmplexity f the traditinal nn-verlapping calitin frmatin game. Fr example, the verlap between calitins may cause instability and emptiness f the cre as shwn in the fllwing example. Example 1: Let us fcus n the verlapping actins f fur players in tw calitins C 1 and C 2. Let D 1 and D 2 r D 3 and D 4 be tw members f calitin C 1 r C 2 with exclusive use f the resurce in their crrespnding calitins fr {D 1, D 2 } C 1 and {D 3, D 4 } C 2. Here we use the term exclusive t simplify ur discussin. It means that resurce sharing between D 1 r D 2 and any ther D2D links in the netwrk des nt affect the payffs f ther members in calitin C 1. This can be extended int a mre general case. Fr example, if the spectrum sharing between D 1 and ther D2D links in the netwrk can als affect the payff f sme ther members in C 1, we can then use D 1 t dente the cmbined set f all D2D links in calitin C 1 that will be affected by the verlapping actin. If D 1 r D 2 can share its resurce with D 3 r D 4, calitins C 1 and C 2 will verlap with each ther. Hwever, if the preference f D 1, D 2, D 3 and D 4 satisfies D 3 D1 D 2 D1 D 4, D 1 D2 D 3 D2 D 4, D 2 D3 D 1 D3 D 4 and D 1 D4 D 2 D4 D 3 where we use t dente D j s preference f a player ver different verlapping actins, i.e., D i Dj D k means that D j C 1 prefers t verlap with player D i than D k fr D i, D k C 2, then we can shw that the verlapping {D 1, D 2, D 3, D 4 } between calitins C 1 and C 2 is nt stable. The situatin bserved in the abve example is called a rtatin r cycle, which is frmally defined as fllws. Definitin 4: A rtatin fr a sequence f D2D link preferences is a sequence f D2D links ˆD 0, ˆD 0, ˆD 1, ˆD 1,..., ˆD k 1, ˆD k 1 such that ˆD i ˆD j fr i j and ˆD i, ˆD j C, and ˆD i is the mst preferred D2D link fr ˆD i and ˆD i+1 is the secnd mst preferred D2D link fr ˆD i fr all i {1, 2,..., k}, where the subscripts are taken mdul k. As bserved in the abve example, bth f the cres defined in Definitins 2 and 3 can be empty. Finding an effective methd t detect the emptiness f the cre fr a general BOCF game is still an pen prblem. In the rest f this paper, we can explit the structure f the cellular netwrks t find a distributed algrithm t search fr the stable and ptimal verlapping calitin agreement prfile that is in the b-cre. VI. A HIERARCHICAL MATCHING ALGORITHM As bserved frm the previus sectin, an ptimal verlapping calitin agreement prfile is generally difficult t find and it is impssible t enumerate and cmpare all the pssible candidate structures [5]. In this sectin, we prpse a hierarchical matching algrithm t search fr the verlapping calitin agreement prfile f ur game. We divide the DCSS game int different stages. By mdeling each stage as a matching market, each D2D link nly needs t fcus n searching fr its ptimal decisin in each stage. In the beginning, all the D2D links will be first partitined int L nn-verlapping calitins, each f which crrespnds t a grup f D2D links that can access the spectrum f the same peratr. We can mdel this prblem as a tw-sided many-t-ne matching market, als called a cllege admissin market, in which a set f students is partitined and admitted int a limited number f clleges t be discussed in Sectin VI-A. After being accepted by the peratrs, the D2D links accepted by the same peratr will then cmpete fr sub-bands. We can mdel this prblem as a tw-sided ne-t-ne matching market, als called a stable marriage market, in which a set f men will be matched with a set f wmen t be discussed in Sectin VI-B. Finally, D2D links with exclusive use f sub-bands in different calitins can aggregate and share their sub-bands t further imprve their payffs. We mdel this prblem as a ne-sided ne-t-ne matching market, als called a rmmate market, in which a set f students will be paired with each ther t share the same drmitry. In ur prpsed game, the D2D links cannt predict which sub-bands will be finally allcated by each peratr r which D2D sub-band sharing partner it will chse. We, hwever, allw each D2D link t maintain a belief functin. We prpse a belief updating algrithm in Sectin VI-D. The relatinship f different markets is illustrated in Figure 2. Let us give a detailed discussin fr each f these markets as fllws. A. Operatr Selectin Algrithm In this subsectin, we assume that each player D k D can have a fixed private belief functin B Dk ϕ Dk, Γ abut the decisins f ther D2D links, and the cnflict-slving rules. We will relax this assumptin in Sectin VI-D. Each D2D link first chses an peratr which, accrding t its belief functin, is likely t result in the sub-band allcatin that maximizes its payff. We slve this prblem by mdeling the peratr selectin by the D2D links as a tw-sided many-t-ne matching market with private belief. In this market, a set f D2D links applies fr a set f peratrs. Each D2D link can nly chse ne peratr and each peratr i can nly prvide a limited number f sub-bands called a quta, labeled as q i = S i, fr D2D links t access. Let us nw frmally define the peratr selectin market as fllws: Definitin 5: An peratr selectin market is a tw-sided many-t-ne matching market with private belief G = D, O, B, cnsisting f fur elements: a set D f D2D links, a set O f peratrs, a vectr

10 10 B = B Dk Dk D f belief functins, and the preference f each D2D link r peratr ver the peratrs r D2D links. Since the set f D2D links being matched with each peratr crrespnds t a calitin, the preference relatin in the abve market cincides with the preference relatin f ur DCSS game defined in Sectin V. We use D k i D n t dente that peratr i prefers accepting D2D link D k t D n and use i Dk j t dente that D2D link D k prefers t send a request t peratr i ver sending a request t peratr j. Let us define a matching between D2D links and peratrs as fllws: Definitin 6: A tw-sided many-t-ne matching Γ is a functin frm the set D O int the set f unrdered families f elements f D O such that Γ D k = 1, Γ i q i and Γ D k = i if and nly if D k is in Γ i, fr every i O and D k D. It is wrth nting that the peratr selectin market defined in Definitin 5 can als be regarded as a calitinal game [39]. If we let all D2D links fully cmpete fr the cellular sub-bands, the game will turn int a nn-cperative game in which the main slutin cncept is the Nash equilibrium NE. As pinted ut in [44] [47], the number f NEs may be large and the NEs are nt generally reachable by simple cmpetitin amng players. An imprtant cncept in matching thery is stability, which is defined as fllws. Definitin 7: A matching Γ is said t be m-stable if the fllwing cnditins are satisfied: 1 each player believes that matching Γ cannt be strictly imprved upn by any individual player r pair f players, 2 each player believes that each f the ther players believes matching Γ cannt be strictly imprved upn by any player r pair. Nte that the cncept f stable matching is generally different frm the stability f the calitin frmatin structure in the calitinal game. Mre specifically, if we say a matching between a D2D link D k and an peratr i is stable, it means that D k r peratr i r bth D k and peratr i cannt chse any ther matching partner t imprve their payffs. Hwever, we say a calitin frmatin structure is stable if n calitin f any size f D2D links can benefit frm deviating and jin r frm ther calitins. T differentiate between these tw cncepts, we use m-stable t refer t the stability f a matching with private belief. Several different cncepts f the cre have als been intrduced fr the matching market in [18], [48]. The cre f matching is generally different frm the cre defined in ur calitin frmatin game in Definitin 2. T avid cnfusin, in this paper, we nly use the term cre t dente the cre f ur calitin frmatin game prpsed in Sectin V. T find a matching that is m-stable, each D2D link needs t send a request t the peratr that accrding t its beliefs can prvide the highest payff. Hwever, it can be bserved in 6 that the payff f each D2D link depends n its final allcated peratr, sub-band and D2D sub-band sharing partner. Therefre, a D2D link cannt knw which peratr can prvide the highest payff withut knwing which sub-band will be eventually allcated by each peratr r which D2D sub-band sharing partner it will chse. Frtunately, we can shw that each D2D link D k can establish an estimated versin f its resulting payff btained frm each peratr i using its belief functin B Dk. Mre specifically, the estimated payff f D2D link D k when it sends the request t peratr i is given by ϖ Dk BDk ϕ Dk, Γ, ϕ D k = i = max ϖ Dk BDk ϕ Dk, ϕ s D S { },ϕ d k D D { } k ϕ D k = i, ϕ s D k, ϕ d D k, 8 where ϖ Dk BDk ϕ Dk, ϕ Dk = i, ϕ s D k, ϕ d D k is given in 6. Using the abve result, each D2D link will chse the peratr that can maximize its estimated payff, i.e., ϕ D k is given by ϕ D k = arg max i O { } ϖ D k BDk ϕ Dk, Γ, ϕ D k = i. 9 We refer t the abve equatin as the peratr selectin algrithm. Nte that each peratr needs t decide whether t allw the requesting D2D links t access its spectrum befre knwing which specific sub-band will be requested by each D2D link. We hence assume each peratr can accept r reject the requests f the D2D links based n a predefined criterin unrelated t the final sub-band allcated t each D2D link. Fr example, each peratr can evaluate the minimum revenue each D2D link can prvide, e.g., we can define the minimum revenue brught by each D2D link { D k t each peratr i as η i D k = min β i l J i Dk EINT Dk [l] }. We describe the cnflict-slving rule fr peratr i as fllws: If mre than q i D2D links send requests t the same peratr i, a cnflict will happen. T reslve this cnflict, the peratr will nly accept the q i requesting D2D links that can prvide the highest minimum revenues. We can prve the fllwing results abut the peratr selectin algrithm. Prpsitin 1: Suppse the belief f every D2D link is fixed. The peratr selectin algrithm and the cnflictslving rule f peratrs result in a unique and m-stable matching between D2D links and peratrs. This result fllws immediately frm the definitin f m- stability in Definitin 7. We hence mit the details f the prf. B. Sub-band Selectin Algrithm Each D2D link will decide which specific sub-band t request after being accepted by ne peratr. We mdel this prblem as a tw-sided ne-t-ne matching market. In this game, a set f D2D links send requests fr a set f sub-bands cntrlled by an peratr, and the peratr can then decide whether r nt t accept the request frm each

11 11 D2D link accrding t its cnflict-slving rule. T simplify ur descriptin, we use C i = Γ i t dente the set f D2D links that have been accepted by peratr i. Let us frmally define the sub-band selectin market as fllws: Definitin 8: A cellular sub-band selectin market is a tw-sided ne-t-ne matching market with private belief G = C i, S i, B, which cnsists f a set C i f D2D links, a set S i f sub-bands cntrlled by peratr i, a vectr B = B Dk Dk D f belief functins, and the preference f each D2D link r sub-band ver the sub-bands r D2D links. Nte that, as bserved in Sectin III, t maintain the QS f the existing cellular subscribers, the accessing f D2D links in each f the sub-bands needs t be strictly cntrlled by the peratrs. Therefre, the cnflict-slving rule f each sub-band ver the D2D links has t be established and maintained by the peratrs. T simplify ur discussin, in this paper, we use the term cnflict-slving rule f each sub-band t dente the cnflict-slving rule f the peratr ver the sub-bands t be accessed by each D2D link. We use l Dk m t dente that D2D link D k prefers accessing sub-band l ver sub-band m accrding t B Dk. Similarly, D k l D n means peratr i prefers t let D2D link D k as ppsed t D n access sub-band l. We define a matching between D2D links and cellular subscribers in the spectrum f an peratr i as fllws. Definitin 9: A tw-sided ne-t-ne matching with private belief Γ s between D2D links and sub-bands is a ne-t-ne crrespndence frm set C i S i nt itself such that Γ s D k S i {D k }, Γ s l C i {l} and Γ s D k = l Γ s l = D k fr every l S i and D k C i. The tw-sided ne-t-ne matching market can be regarded as a special case f the tw-sided many-t-ne matching market, where a player frm either side f the market can nly match with ne player in the ther side f the market. Therefre, we can use exactly the same algrithm t achieve a stable allcatin between the D2D links and the sub-bands. That is, similar t the peratr selectin algrithm, each D2D link shuld always send the request fr the sub-band that can prvide the highest payff. Hwever, each D2D link cannt knw its payff withut knwing which sub-band will accept its request r which D2D link will be its D2D sub-band sharing partner. Fr example, it is pssible that a D2D link D k C i can btain a higher payff by sharing the sub-band ccupied by a cellular subscriber than accessing a vacant sub-band withut sharing with any ther D2D links, i.e., ϖ Dk [l] ϖ Dk [m] fr m K i and l J i. Hwever, this D2D link D k may achieve a higher payff by first accessing a vacant sub-band m and then sharing with anther D2D link D n with a sub-band fr exclusive use, i.e., ϖ Dk [m, n] ϖ Dk [l] fr m = Γ s D k, n = Γ s D j and D j, D k C. In ther wrds, if D2D link D k fails t realize that the pssible sub-band sharing with D n can further imprve its payff, it will chse sub-band l, which is nt the sub-band that can prvide the highest payff fr D k. T slve this prblem, each D2D link shuld again explit its belief functin t derive an estimated payff fr each f the sub-bands f its matched peratr, i.e., suppse the request sent by D k t peratr i has been accepted. the estimated payff f D2D link D k when it decides t send a request t sub-band l S i is given by ϖ Dk BDk ϕ Dk, Γ, ϕ s D k = l, ϕ D k = i = max ϖ Dk BDk ϕ Dk, Γ, ϕ ϕ d D D C k = i, ϕ s D k = l, ϕ d D k, k where ϖ Dk BDk ϕ Dk, Γ, ϕ D k = i, ϕ s D k = l, ϕ d D k is given in 6. Fllwing the same lines as the peratr selectin algrithm, each D2D link D k will decide its sub-band l by ϕ s D k = 10 arg max ϖ D BDk ϕ Dk l S i k, ϕ s Dk = l, ϕ D { } k = i. We refer t the abve equatin as the sub-band selectin algrithm. We als intrduce the cnflict-slving rule f the subband fr each peratr as fllws: If tw r mre D2D links send a request fr the same sub-band, a cnflict will happen. T slve this cnflict, the sub-band r peratr will nly allw the D2D link that can prvide the higher revenue t access the requested sub-band. We have the fllwing results fr the sub-band selectin algrithm. Prpsitin 2: The sub-band selectin algrithm and the cnflict-slving rule f sub-bands result in a unique and m- stable matching between D2D links and sub-bands f their chsen peratr. The abve prpsitin fllws the same line as Prpsitin 1, and we mit the detailed prf. C. D2D Selectin Algrithm If sharing sub-bands with cellular subscribers cannt prvide adequate payff fr sme D2D links e.g., sme D2D links are clsely lcated t sme cellular subscribers, they will be given a sub-band fr exclusive use and decide whether r nt t share the sub-band with ther D2D links. In this case, the market will n lnger be a tw-sided matching market, because each D2D link can find a match with any ther D2D link with exclusive use f a sub-band in the entire netwrk. We can then mdel the prblem as a ne-sided ne-t-ne matching market which is defined as fllws: Definitin 10: We define the D2D selectin market as a ne-sided ne-t-ne matching market with private belief G = C, B, where B is the belief functin, and is the preference f each D2D link ver ther D2D links with exclusive sub-bands. We use D m Dn D k t dente that D n prefers D m t D k. Definitin 11: A ne-sided ne-t-ne matching Γ d between tw D2D links is a functin frm the set C t

12 12 itself such that Γ d D k C, Γ d D n C, and Γ d D k = D n Γ d D n = D k fr every D n, D k C. Let us nw discuss hw t establish the preference fr each D2D link when spectrum sharing between tw D2D links is allwed in the cellular netwrk. In this case, each D2D link will als need t evaluate and rank its resulting payffs when sharing a sub-band with anther D2D link that als has exclusive access t a sub-band. One way t achieve this is t allw the peratrs t help the D2D links with vacant sub-bands t discver the existence f each ther. As each BS always keeps track f the sub-band allcatin f D2D links, it always knws which D2D links have been assigned t vacant sub-bands. The BS can then bradcast this infrmatin t all the D2D links. Each D2D link D k C ccupying a previusly vacant sub-band can then use its belief functin defined in 5 t calculate the estimated payff ϖ Dk BDk ϕ Dk, Γ, ϕ D k = i, ϕ s D k = l, ϕ d D k = D n when it shares its sub-band l with each f ther D2D links e.g., D n with exclusive use f sub-band m fr D k D n and D k, D n C. Each D2D link can establish its preference abut ther D2D links with exclusive-use sub-bands by ranking the estimated payffs frm the highest t the lwest values. Let us dente the preference f each D2D link D k ver ther D2D links with exclusive use f sub-bands as R d D k. We use ṽd m k t dente the mth preferred D2D link with exclusive sub-band fr D k fr ṽd m k C. We can write R d D k as R d D k = ṽd 1 k, ṽd 2 k,..., ṽ C D k where ϖ Dk BDk ϕ Dk, Γ, ϕ D k = i, ϕ s D k = l, ϕ d D k = ṽd m k > ϖ Dk BDk ϕ Dk, Γ, ϕ D k = i, ϕ s D k = l, ϕ d D k = ṽ m+1 D k 1 m C 1. Nte that if ṽ m D k = D k fr m C 1, it means that D k cannt btain any payff imprvement by sharing its sub-band with any D2D link in the set {ṽ m+1 D k, ṽ m+2 D k,..., ṽ C D k }. As described in Example 1, in the D2D selectin market, there may nt always exist an m-stable matching amng all D2D links with sub-bands fr exclusive use. One f the main reasns fr this is the pssible existence f rtatins in the resulting preferences. We hence need t find a way t remve the rtatins frm the pssible verlapping calitin agreements. As bserved in [6], [18], [22], [49], a stable matching is assciated with a unique set f rtatins referred as the bservable rtatins. Therefre, if the rtatin detectin and remval sequence can be uniquely decided, the set f bservable rtatins as well as the stable matching will als be fixed. This prblem can be slved by taking advantage f the labeled identity f each D2D link. Mre specifically, in a D2D cmmunicatin netwrk, each D2D link has a specific cmmnly knwn identificatin number, referred t as a label, that is used by ther D2D links t recgnize it. We can then rder all D2D links with exclusive sub-bands accrding t a fixed sequence f their labels, i.e., we dente the ith rdered D2D link as ϕ i and the vectr f all the D2D links in C can be dented as ϕ = ϕ 1, ϕ 2,..., ϕ C fr ϕ i C. Remving the rtatins als requires cmmunicatin amng D2D links with exclusive sub-bands. Mre specifically, each D2D link will sequentially bradcast a rtatin detectin signal t determine if a rtatin-like sequence can be detected [6], [18], [22], [49]. If a rtatin has been detected, all D2D links in the sequence f rtatin will remve the rtatin frm their preference list. If nne f the preference lists f the D2D links becmes empty after remving the rtatins, each D2D link can then match with its mst preferred D2D link in its preference list. Otherwise, n stable matching structure exists. We refer t this algrithm as D2D Selectin Algrithm. A detailed pseud-cde f the rmmate algrithm is given in [6, Figure 4.16]. We have the fllwing results. Prpsitin 3: Suppse ϕ and the set C f D2D links being allcated vacant sub-bands fr exclusive use are fixed. The D2D selectin algrithm either reprts n m-stable matching exists r generates a unique and m-stable matching structure. Prf: See the prf f Prpsitin 3 in [1]. Frm the abve prpsitin, if the D2D selectin algrithm reprts a stable matching structure, we can claim the existence f at least ne stable matching structure. This can be regarded as a sufficient cnditin fr the existence f a stable matching fr the D2D spectrum sharing market. Nte that this cnditin is nt necessary because if we change the labeling sequence f D2D links, the resulting matching may als be changed. D. A Belief Updating Algrithm The three algrithms discussed in Sectins VI-A t VI-C are clsely related t each ther. Mre specifically, the matching frmed in the peratr selectin algrithm directly affects the sub-band selectin and D2D sub-band sharing amng D2D links. Mrever, the results f sub-band and D2D selectin algrithms als affect the peratr selectin f the D2D links. In additin, it is bserved in Prpsitin 1 that if the decisin f every D2D link abut which peratr t send its request t is fixed, the matching between the D2D links and peratrs will be fixed t. Accrding t Prpsitin 3, fr each f the fixed matchings between D2D link and peratrs, the sub-band allcatin that results frm the sub-band selectin algrithm is als determined. Finally, if the sub-band allcatin amng D2D links is fixed, the set f D2D links with exclusive use f sub-bands will be fixed, t. In this case, the results f the D2D selectin algrithm will als be fixed. It is the belief functins f all the D2D links that cnnect these three matching results. In this subsectin, we relax the previus assumptin abut the fixed belief functin f D2D links. We fcus n a learning algrithm fr each D2D link t iteratively update its belief functin accrding t its previus bservatins. In ur mdel, each D2D link can eavesdrp n the peratrs, sub-band and D2D links requested by

13 13 each f the ther D2D links. We assume each D2D link is mypic and hence can use a Dirichlet distributin t mdel the uncertainty abut the decisins f ther D2D links as well as the cnflict-slving rules f peratrs and ther D2D links with sub-bands fr exclusive use. We can hence apply Bayesian reinfrcement learning and use the fllwing equatin t calculate the belief abut each actin f ther D2D links at the beginning f each time slt t, ϕ Dk = Pr ϕ Dk ϕ D k = i B Dk,t = θ D k ϕ Dk,t 1 = ϕ D k ϕ D k,t 1 = i θ Dk ϕ D k,t 1 = i, 11 where θ Dk ϕ Dk,t 1 = ϕ D k ϕ D k,t 1 = i = 1 ϕ D k [u] = ϕ D k ϕ D k [u] = i is the u {1,...,t 1} number f times that D2D link D k bserves the decisins f ther D2D links are equivalent t ϕ D k when its wn decisin is ϕ D k = i during the previus t 1 time slts. θ Dk ϕ Dk,t 1 = i = 1 ϕ D k [u] = i is the u {1,...,t 1} number f times D k sends a request t peratr i during the previus t 1 time slts. Similarly, we can write the belief updating algrithm fr B Dk Γ as fllws: B Dk,t Γ = Pr Γ D k ϕ D k, ϕ D k = i 12 = θ Dk Γ t 1 D k = Γ D k ϕ D k,t 1 = ϕ D k, ϕ D k,t 1 = i θ Dk ϕ D k,t 1 = ϕ D k, ϕ D k,t 1 = i, where θ Dk Γ t 1 D k = Γ D k ϕ D k,t 1 = ϕ D k, ϕ D k,t 1 = i is the number f times that D k has been assigned peratr Γ D k when the decisin f D k is ϕ D k = i and the decisins f ther D2D links are equivalent t ϕ D k during the previus t 1 time slts. The rest f the belief updating algrithm can be written in a similar fashin: B Dk,t ϕ s Dk = 13 θ Dk ϕ s Dk,t 1 = ϕ s D k Γ t 1D k, ϕ s D k,t 1 = ϕs D k θ Dk Γ t 1 D k, ϕ s D k,t 1 = ϕs D k, B Dk,t Γ s Dk = 14 B Dk,t θ Dk Γ s t 1 D k = Γ s D k Γ t 1D k, ϕ s D k,t 1 = ϕs D k, ϕ s D k,t 1 = ϕ s D k θ Dk Γ t 1 D k, ϕ s D k,t 1 =, ϕs D k, ϕ s D k,t 1 = ϕ s D k ϕ d Dk = 15 θ Dk ϕ d D k,t 1 = ϕ d D k Γ t 1D k, Γ s t 1D k, ϕ d D k,t 1 = ϕd D k θ Dk Γ t 1 D k = i, Γ s t 1D k, ϕ d D k,t 1 = ϕd D k, 16 B Dk,t Γ d Dk = 17 θ Dk Γ d t 1 D k = Γ d D k Γ t 1D k, Γ s t 1D k, ϕ d D k,t 1 = ϕd D k,, ϕd D k,t 1 = ϕ d D k θ Dk Γ t 1 D k, Γ s t 1D k, ϕ d D k,t 1 = ϕd D k,, ϕ d D k,t 1 = ϕ d D k After updating its beliefs, each D2D link uses equatin 7 t chse its actin. We can nw describe the hierarchical matching algrithm as fllws: At the beginning f each time slt, every D2D link chses ϕ D k using 9. After being matched with the peratrs, each D2D link chses ϕ s D k using 10. If a D2D link has been matched with a sub-band fr exclusive use, it uses the D2D sub-band sharing algrithm t decide its sub-band sharing partner. After all D2D links chse their sub-bands and sub-band sharing partners, they use t update their beliefs and then use the updated belief functin t find their matching during the next time slt. We nw shw that the results in Prpsitin 3 als hld if all the D2D links use the belief updating algrithm in 7. We have the fllwing result abut the prpsed hierarchical matching algrithm. Therem 1: We have the fllwing results: 1 Fr the resulting belief functin f each D2D link, the matching structure achieved by the hierarchical matching algrithm is equivalent t the verlapping calitin agreement x that is in the b-cre f ur prpsed DCSS game in Sectin V. 2 Suppse, in sme time slt t, the verlapping calitin agreement x[t] satisfies x[t] = x where x is the verlapping calitin agreement prfile in the b-cre based n the true belief the belief f each D2D link cincides with the true prbabilistic features f decisins made by ther D2D links and cnflict-slving rules f peratrs and D2D links with exclusive sub-bands f every D2D link. Then x[τ] = x, τ > t. Prf: First, let us cnsider the first result. It can be easily bserved that if every D2D link D k can predict the true beliefs f ther D2D links, all D2D links can establish the true preferences and use the peratr selectin algrithm t btain a unique and stable matching. The D2D links can then use the D2D selectin algrithm t generate the unique and stable verlapping calitin agreement. In ther wrds, the resulting calitin frmatin structure is stable and deterministic fr every resulting belief functin f D2D links. We nw cnsider the secnd result. If x[t] = x in time slt t, we then have ϖ Dk x > ϖ Dk x fr x is nt in the cre where ϖ Dk x is the payff f D k btained in the sub-band allcated in verlapping calitin agreement x. Let us shw that in the next time slt t + 1, each D2D link will stick with x and will nt change t ther decisins. In time slt t + 1, D2D link D k will update its belief by B Dk,t+1ϕ Dk, Γ = αb Dk,t α = ϕ Dk, Γ +1 α1 ϕ Dk,t+1 = ϕ D k, where and ϕ D k is the decisin f D k that results in t t+1.

14 14 x. We then can rewrite the updated payff functin f D k as ϖ Dk,t+1 = α ϖ Dk ϕdk,t, ϕ Dk,t, B Dk,t +1 α ϖ Dk,t+1 ϕdk,t+1, ϕ Dk,t+1, B Dk,t+1, which is a linear cmbinatin f ϖ Dk,t and ϖ Dk,t+1. It can be easily bserved that chsing ϕ Dk,t+1 = ϕ Dk,t = ϕ D k maximizes bth payff functins f D2D link D k. This prcess will be repeated in each f the remaining time slts. Prpsitin 4: Fr each resulting belief functin, the cmplexity f ur hierarchical matching algrithm in the wrst case is ONK 4 L 2 where N = max i O { K i }. Prf: Suppse the belief functin f each D2D link has been updated. All D2D links need t first send requests t their preferred peratrs. Accrding t the cnflict-slving rules f the peratr, the request sent by a D2D link D k t peratr i can be rejected if peratr i has already received q i r mre requests frm ther D2D links that are preferred by peratr i. In the wrst case, each f the K D2D links will send requests and be rejected by each f its mst preferred L 1 peratrs befre an peratr accepts its request. This results in KL 1 cmplexity. Similarly, accrding t the cnflict-slving rule fr the sub-bands, each D2D link being accepted by each peratr i can als be rejected fr each f the S i 1 sub-bands. This results in anther C i S i 1 cmplexity fr each peratr. Accrding t [6], the D2D selectin algrithm fr D2D links in set C will result in a cmplexity f O C 2. We hence can claim that the final cmplexity fr each resulting belief functin is given by OKL 1 i O { Ci S i 1 } C 2. Using the fact that C i K, S i N and C K, we btain the cmplexity ONK 4 L 2 fr ur prpsed algrithm fr each resulting belief functin. VII. NUMERICAL RESULTS In this sectin, we first describe hw t implement ur prpsed algrithm in LTE-Advanced netwrk systems and then present the numerical results t verify the perfrmance imprvement that can be brught by ur prpsed algrithms. In a D2D cmmunicatin system, it is critical fr the surce and destinatin f each D2D link t determine each ther s availability and ensure they are lcated within direct cmmunicatin range. This requires all the ptential D2D surces and destinatins t first g thrugh a peer device discvery prcess [26]. This peer device discvery can be either implemented with limited r full cntrl frm the peratrs thrugh the BS as described in [30]. In the limited cntrl apprach, each BS peridically bradcasts the set f available vacant and ccupied sub-bands that can be used by the D2D links. Each D2D link can then use the received bradcast signal t establish its preference abut the peratrs and then submit a request fr the peratr and sub-band accrding t its preference. In the full cntrl apprach, each D2D link will simply send a D2D cmmunicatin request t the BS and the BS will decide the required mdes and cmmunicatin parameters fr each D2D link. In this sectin, we cmpare the fllwing fur D2D spectrum sharing appraches. 1 Randm Allcatin: D2D links randmly chse peratrs, mdes and sub-bands. In this case, we nly allw each D2D link t use mdes M1 M3. This is equivalent t the existing D2D cmmunicatins in cellular netwrks withut using the ptimal mde selectin apprach studied in [26]. 2 Randm Operatr Allcatin: each D2D link D k randmly picks an peratr and then uses the sub-band selectin algrithm t decide its mdes and sub-bands. We again limit each D2D link t chse frm mdes M1 M3. Therefre, this methd is equivalent t the existing D2D cmmunicatins in cellular netwrks where each D2D link randmly chses an peratr and then selects the ptimal mde intrduced in [26]. 3 Hierarchical Allcatin: all D2D links use the peratr selectin algrithm t chse the ptimal peratrs and then use the sub-band selectin algrithm t decide the mde and sub-bands. Again, we assume each D2D link can nly chse frm mdes M1 M3. This methd is equivalent t the existing D2D cmmunicatins in cellular netwrks where each D2D link chses the ptimal peratr and then chses the ptimal mde. 4 Hierarchical Allcatin with Overlaps: D2D links use the hierarchical matching algrithm t decide their ptimal peratr, mde and sub-band. Nte that in this apprach, each D2D link can chse frm mdes M1 M4. Nte that, as we have prved in Sectin VI-D, if the D2D links can update their belief functins using 11 17, the verlapping calitin agreement f D2D links can cnverge t a unique and stable structure. In the rest f this sectin, we fcus n the case where D2D links have already updated their belief functins. We will discuss the cnvergence rate f the belief updating algrithm at the end f this sectin. Let us cnsider a cellular system cnsisting f multiple peratrs randmly lcated in the center regin f a square-shaped cverage area, as shwn in Figure 3. Each peratr has a set f cellular subscribers using its spectrum, which can als be shared with a number f D2D links. D2D links and cellular subscribers are unifrmly randmly lcated in the entire cverage area. T simplify ur discussin, we fcus n the dwnlink transmissin and assume each D2D link cnsists f a surce and a destinatin. In a practical system, D2D cmmunicatin shuld nly be enabled when the surce and destinatin are clse t each ther. We hence assume each destinatin is unifrmly randmly lcated within a fixed radius 20 meters in ur simulatin f the crrespnding surce. We cnsider the payff f D2D

15 meter meter Fig. 3. Simulatin setup: we use t dente peratrs, t dente cellular subscribers, blue lines t dente the D2D links, blue t dente D2D transmitters and black t dente D2D receivers. Number f Valid Spectrum Sharing Pairs Hierachical Allcatin with Overlaps Hierachical Allcatin Randm Operatr Allcatin Randm Allcatin Length f the Side f Simulatin Area Payff Hierachical Allcatin with Overlaps Hierachical Allcatin Randm Operatr Allcatin Randm Allcatin Length f the Side f Simulatin Area Fig. 4. The ttal payff f D2D links under different cverage area sizes L = 5, K = 100, J i = 20 i O. links defined in 1-3 and let the channel gain between tw D2D links D k and D n and ne D2D link D k and ne cellular subscriber Pj i be h Dn D k = h D nd k and d σ D nd k h P id h P i j D k = j k, respectively, where h d σ Dn D k and h P i j D k P j id k are the channel fading cefficients fllwing the Rayleigh randm distributin, d Dn D k and d σ Pj id are the distance k between D n and D k and Pj i and D k, respectively, and σ is the pathlss expnent. In Figure 4, we fix the number f peratrs, cellular subscribers and D2D links and present the ttal payff f D2D links under different lengths f the side f the square-shaped cverage area with a range frm 100 t 1000 meters. Our cnsidered cverage area cvers femtcell, pic-cellular < 200 meters, micr-cellular > 200 meters, and macr-cellular > 1000 meters systems [31]. We bserve that the randm allcatin methd achieves the wrst payff amng all the methds. Even under the case that each D2D link cannt establish a preference list fr the peratrs but chses its peratr randmly, the payff f the D2D link can be imprved by applying the sub-band allcatin algrithm sub-band selectin algrithm in Sectin VI-B. If we further allw Fig. 5. The number f D2D and cellular r D2D and D2D spectrum sharing pairs fr different cverage area sizes L = 5, K = 100, J i = 20 i O. Number f Valid Spectrum Sharing Pairs Hierachical Allcatin with Overlaps Hierachical Allcatin Randm Operatr Allcatin Randm Allcatin Minimum Required Data Rate bpsk per Spectrum Price Fig. 6. The number f D2D and cellular r D2D and D2D spectrum sharing pairs fr different minimum required data rate kbits per secnd L = 5, K = 100, J i = 20 i O. Payff Hierachical Allcatin with Overlaps Hierachical Allcatin Randm Operatr Allcatin Randm Allcatin Number f Operatrs Fig. 7. The ttal payff f D2D links fr different numbers f peratrs K = 120, J = 120.

16 16 Ttal Payff Hierachical Allcatin with Overlaps Hierachical Allcatin Randm Operatr Allcatin Randm Allcatin Number f Cellular Subscribers fr each Operatr Fig. 8. The ttal payff f D2D links fr different numbers f cellular subscribers fr each peratr L = 5, K = 100. Ttal Payff Randm Allcatin Randm Operatr Allcatin Hierachical Allcatin with Overlaps Number f D2D Links Fig. 9. The ttal payff f D2D links fr different numbers f D2D links L = 5, J i = 20 i O. Payff f D2D link D2D link1 D2D link Number f iteratins Fig. 10. The cnvergence rate f payffs f tw D2D links using the belief updating algrithm. each D2D link t decide its peratr using the peratr selectin market prpsed in Sectin VI-A, the payff f each D2D link can be further imprved. We als bserve significant perfrmance imprvement by allwing spectrum sharing amng D2D links with exclusive sub-bands. This is because the chance fr each D2D link with an exclusive-use sub-band t find a suitable sub-band sharing partner increases with the ttal number f D2D links with sub-bands fr exclusive use. If tw D2D links with small r even negligible crss-interference can be matched with each ther e.g., tw D2D links that are far frm each ther, the payff btained by each f the matching D2D links can be significantly imprved. In ther wrds, in a large cverage area with unifrmly randmly lcated D2D links, each D2D link will learn the fact that applying fr a exclusive-use sub-band fr exclusive use at first and then sharing with anther D2D link with vacant sub-bands with small crss-interference can maximize its payff. Nte that in ur simulatin, we assume each D2D link can always btain a dedicated sub-band fr exclusive use if sharing sub-bands with cellular subscribers cannt achieve a higher payff. Hwever, in many practical scenaris, the number f vacant sub-bands is limited. In this case, sme f the D2D links can nly chse between mde M2 and mde M3. In ther wrds, ur simulatin results f hierarchical allcatin with verlaps can be regarded as the upper bund f the payff achieved by D2D links when they share sub-bands with the cellular netwrks. T cmpare the spectrum sharing capacity in terms f the ttal number f D2D links that can be supprted by the existing cellular system, we present the number f valid spectrum sharing pairs frmed between a D2D link and a cellular subscriber r tw D2D links in Figure 5. We bserve that the hierarchical allcatin appraches with and withut verlaps can almst duble the spectrum sharing capacity, especially in the femtcell r pic-cell cases cverage length < 200 meters. This is because when the cverage area becmes small, the crss-interference between the spectrum sharing D2D links and cellular subscribers becmes critical and, in this case, chsing the peratr serving the cellular subscribers that are far frm each D2D link becmes imprtant t imprve the spectrum sharing capacity f the systems. We study the spectrum sharing capacity f the DCSS system under different minimum required data rate per spectrum price in Figure 6. We bserve that if each D2D link nly requires a data rate belw 64 kbps, almst every D2D link can find anther cellular subscriber r D2D link t share the spectrum with. Hwever, the spectrum sharing capacity is dramatically decreased when the required data rate fr each D2D link exceeds 96 kbps. Furthermre, using the hierarchical allcatin with verlaps apprach cannt prvide any extra capacity imprvement fr hierarchical allcatin if the required minimum data rate becmes larger than 128 kbps. This is because the crss interference between D2D and cellular

17 17 cmmunicatin becmes significant when bth D2D links and cellular subscriber raise their transmit pwers t supprt high transmit data rates. Nte that, in ur simulatin, we assume the transmit pwers f bth D2D links and cellular subscribers are cnstants and hence the perfrmance f D2D links can be further imprved by using ptimal transmit pwers as shwn in [9], [31], [50], [51]. In Figure 7, we fix the number f D2D links and cellular subscribers and cnsider the payffs f D2D links under different numbers f peratrs. It is bserved that the payffs f the D2D links increase with the number f peratrs when using the hierarchical allcatin methd. This is because with the increasing number f peratrs, selecting the prper peratrs becmes mre and mre imprtant fr each D2D link. Hwever, if we nly allw each D2D link t randmly select the peratrs, the payff f the D2D links with the randm peratr selectin will apprach that f a randm allcatin methd withut any ptimizatin. We fix the number f peratrs and cellular subscribers t cmpare the payffs f D2D links with different numbers f cellular subscribers in Figure 8. It is bserved that the payff f the D2D links increases with the number f cellular subscribers. This is because the cst t the D2D links f accessing an exclusive-use sub-band is higher than that f sharing a sub-band with a cellular subscriber. As the number f subscribers increases, there are mre pprtunities fr D2D links t pair with such subscribers. In additin, the payff f the hierarchical allcatin increases at a faster speed than that f randm peratr allcatin when the number f cellular subscribers t each peratr increases. In Figure 9, we fix the number f peratrs and cellular subscribers and cnsider the ttal payff f D2D links, varying the number f D2D links in the cverage area. We bserve that if the number f D2D links is small, mst f the D2D links can find cellular subscribers t share spectrum with and hence allwing spectrum sharing between D2D links with exclusive sub-bands i.e., hierarchical allcatin with verlaps cannt prvide any payff imprvement. Hwever, cntinuusly increasing the number f D2D links prvides mre chices fr each D2D link with an exclusive sub-band when it wants t share its sub-band with ther D2D links using the D2D selectin market. The cnvergence f the belief updating algrithm is illustrated in Figure 10, where we select tw D2D links and present their payffs with hierarchical allcatin with verlaps fr different iteratins. It can be bserved that the payffs f the chsen D2D links can cnverge t a relatively stable state after the initial fluctuatins f the training perid. VIII. CONCLUDING REMARKS AND FUTURE WORKS In this paper, we have cnsidered the spectrum sharing prblem between multiple D2D links and a cellular netwrk with multiple peratrs. We have develped a BOCF game framewrk t analyze this prblem. In ur prpsed framewrk, each D2D link will first decide which peratr s spectrum it wants t access. All the D2D links being assigned the same peratr can be regarded as a calitin and then cmpete fr the available sub-bands cntrlled by the crrespnding peratr. Each D2D link can als apply fr a vacant sub-band fr exclusive use. If there are tw r mre D2D links with sub-bands fr exclusive use, they can further imprve their perfrmance by sharing their sub-bands with each ther. We prpse a hierarchical framewrk based n a stable matching market t derive a sufficient cnditin fr the cre f the BOCF game t be nn-empty. We intrduce a distributed hierarchical matching algrithm t detect whether the sufficient cnditin is satisfied and, if satisfied, leads t an verlapping calitin agreement prfile that is in the b-cre f the game. Numerical results shw that ur prpsed hierarchical matching algrithm can achieve significant perfrmance imprvement especially in a large cverage area with a large number f D2D links. Bth the BOCF game framewrk and the hierarchical matching algrithm can be directly applied t mre cmplex systems. Fr example, if we als allw three r mre D2D links with exclusive sub-bands t share their sub-bands with each ther, the verlapping actins f each calitin shuld cnsist f all the cmbinatins amng the D2D links with vacant sub-bands. Each D2D link will then need t establish a belief functin ver all the pssible cmbinatins between itself and subsets f ther D2D links with exclusive sub-bands. Using this belief functin, each D2D link will then send the sub-band sharing requests t a grup f D2D links which, accrding t their belief functins, will accept the request and share their sub-band with each ther. Anther case that can be directly extended frm ur prpsed hierarchical matching algrithm is that f tw r mre D2D links sharing the same sub-band with cellular subscribers. In ur mdel, we mdel the sub-band selectin prblem as a ne-sided ne-t-ne matching market in which each D2D link can nly be matched with ne sub-band. Hwever, if we mdel the sub-band selectin prblem as a ne-sided many-t-ne matching market as discussed in Sectin VI-A, each sub-band and its assciated cellular subscribers can then be matched with multiple D2D links. Our wrk in this paper als pens multiple future directins. One future directin f ur research is t study whether it is pssible fr the peratrs t als establish and maintain the beliefs abut D2D links t further imprve their revenues. Mre specifically, in ur mdel, we mainly fcus n the distributed ptimizatin f D2D links and assume the cnflict-slving rules f the peratrs and the D2D links with vacant sub-bands fr exclusive use are fixed. It has already been prved in [18], [52], fr a tw-sided matching market that it is pssible fr the peratrs t adjust their cnflict-slving rules t further imprve their perfrmance. Anther

18 18 ptential directin fr future research is t study the effects f allwing partial payment transfers between peratrs r D2D links n the perfrmance f bth D2D links and cellular netwrk systems [53], [54]. REFERENCES [1] Y. Xia, K. C. Chen, C. Yuen, and L. A. DaSilva, Spectrum sharing fr device-t-device cmmunicatins in cellular netwrks: A game theretic apprach, in IEEE Internatinal Sympsium n New Frntiers in Dynamic Spectrum Access Netwrks DySPAN, Apr., [2] D. Willkmm, S. Machiraju, J. Blt, and A. Wlisz, Primary user behavir in cellular netwrks and implicatins fr dynamic spectrum access, IEEE Cmmunicatins Magazine, vl. 47, n. 3, pp , Mar [3] U. Paul, A. P. Subramanian, M. M. Buddhikt, and S. R. Das, Understanding traffic dynamics in cellular data netwrks, in IEEE INFOCOM, Shanghai, China, Apr [4] R. Myersn, Game thery: analysis f cnflict. Harvard Univ. Press, [5] K. Apt and A. Witzel, A generic apprach t calitin frmatin, Internatinal Game Thery Review IGTR, vl. 11, n. 3, pp , [6] D. Gusfield and R. W. Irving, The stable marriage prblem: structure and algrithms. MIT press Cambridge, [7] B. Kaufman, J. Lilleberg, and B. Aazhang, Spectrum sharing scheme between cellular users and ad-hc device-t-device users, IEEE Trans. Wireless Cmmun., vl. 12, n. 3, pp , Mar [8] A. Mukherjee and A. Httinen, Energy-efficient device-tdevice MIMO underlay netwrk with interference cnstraints, in Internatinal ITG Wrkshp n Smart Antennas WSA, Dresden, Germany, Mar [9] M. G. d. S. Reg, T. F. Maciel, H. d. H. Barrs, F. R. Cavalcanti, and G. Fdr, Perfrmance analysis f pwer cntrl fr device-tdevice cmmunicatin in cellular MIMO systems, in Internatinal Sympsium n Wireless Cmmunicatin Systems ISWCS, Paris, France, Aug [10] P. Phunchngharn, E. Hssain, and D. I. Kim, Resurce allcatin fr device-t-device cmmunicatins underlaying LTE-Advanced netwrks, IEEE Wireless Cmmunicatins, vl. 20, n. 4, pp , Sep [11] A. Osseiran, K. Dppler, C. Ribeir, M. Xia, M. Skglund, and J. Manssur, Advances in device-t-device cmmunicatins and netwrk cding fr IMT-Advanced, ICT-Mbile Summit, Santander, Spain, Jun [12] K. Dppler, M. Rinne, C. Wijting, C. Ribeir, and K. Hugl, Devicet-device cmmunicatin as an underlay t LTE-advanced netwrks, IEEE Cmmunicatins Magazine, vl. 47, n. 12, pp , Dec [13] X. Wu, S. Tavildar, S. Shakkttai, T. Richardsn, J. Li, R. Laria, and A. Jvicic, Flashlinq: A synchrnus distributed scheduler fr peert-peer ad hc netwrks, IEEE/ACM Transactins n Netwrking, vl. 21, n. 4, pp , Aug [14] N. Naderializadeh and A. S. Avestimehr, Itlinq: A new apprach fr spectrum sharing in device-t-device cmmunicatin systems, t appear in IEEE JSAC Special Issue n 5G Wireless Cmmunicatin Systems, [15] Z. Han and V. Pr, Calitin games with cperative transmissin: a cure fr the curse f bundary ndes in selfish packet-frwarding wireless netwrks, IEEE Trans. n Cmmun., vl. 57, n. 1, pp , Jan [16] Y. Xia, G. Bi, D. Niyat, and L. A. DaSilva, A hierarchical game theretic framewrk fr cgnitive radi netwrks, IEEE J. Sel. Area Cmmun.: Cgnitive Radi Series, vl. 30, n. 10, pp , Nv [17] W. Saad, Z. Han, R. Zheng, A. Hjrungnes, T. Basar, and H. V. Pr, Calitinal games in partitin frm fr jint spectrum sensing and access in cgnitive radi netwrks, IEEE Jurnal f Selected Tpics in Signal Prcessing, vl. 6, n. 2, pp , Apr [18] A. E. Rth and M. A. O. Stmayr, Tw-sided matching: A study in game-theretic mdeling and analysis. Cambridge University Press, [19] D. E. Knuth, Stable marriage and its relatin t ther cmbinatrial prblems: An intrductin t the mathematical analysis f algrithms. CRM Prceedings and Lecture Ntes, vl. 10, [20] A. E. Rth, Deferred acceptance algrithms: Histry, thery, practice, and pen questins, Internatinal Jurnal f Game Thery, vl. 36, n. 3, pp , Mar [21] K. Iwama, S. Miyazaki, Y. Mrita, and D. Manlve, Stable marriage with incmplete lists and ties, in the 26th Internatinal Cllquium n Autmata, Languages and Prgramming ICALP, ser. Lecture Ntes in Cmputer Science, vl. 1644, pp , Prague, Czech Republic, July [22] R. W. Irving and D. F. Manlve, The stable rmmates prblem with ties, Jurnal f Algrithms, vl. 43, n. 1, pp , Apr [23] I. P. Gent and P. Prsser, An empirical study f the stable marriage prblem with ties and incmplete lists, in the 15th Eurpean Cnference n Artificial Intelligence ECAI, July [24] C.-K. Chan and H.-F. Leung, Belief-based stability in nntransferable utility calitin frmatin with uncertainty, Intelligent Decisin Technlgies, vl. 5, n. 2, pp , Jun [25] C.-H. Yu, O. Tirkknen, K. Dppler, and C. Ribeir, Pwer ptimizatin f device-t-device cmmunicatin underlaying cellular cmmunicatin, in IEEE Internatinal Cnference n Cmmunicatins ICC, Dresen, Germany, Jun [26] K. Dppler, C.-H. Yu, C. B. Ribeir, and P. Janis, Mde selectin fr device-t-device cmmunicatin underlaying an lte-advanced netwrk, in IEEE Wireless Cmmunicatins and Netwrking Cnference WCNC, Sydney, Australia, Apr [27] A. Asadi, Q. Wang, and V. Mancus, A survey n device-tdevice cmmunicatin in cellular netwrks, t appear in IEEE Cmmunicatins Surveys & Tutrials, [28] G. Fdr, E. Dahlman, G. Mildh, S. Parkvall, N. Reider, G. Miklós, and Z. Turányi, Design aspects f netwrk assisted device-t-device cmmunicatins, IEEE Cmmunicatins Magazine, vl. 50, n. 3, pp , Mar [29] X. Lin, J. G. Andrews, A. Ghsh, and R. Ratasuk, An verview f 3GPP device-t-device prximity services, IEEE Cmmunicatins Magazine, vl. 52, n. 4, pp , [30] L. Lei, Z. Zhng, C. Lin, and X. Shen, Operatr cntrlled device-t-device cmmunicatins in LTE-advanced netwrks, IEEE Wireless Cmmunicatins, vl. 19, n. 3, pp , Jun [31] A. Gldsmith, Wireless cmmunicatins. Cambridge University Press, [32] L. Chen, S. Lw, and J. Dyle, Randm access game and medium access cntrl design, IEEE/ACM Trans. Netwrking, vl. 18, n. 4, pp , Aug [33] L. Tng, V. Naware, and P. Venkitasubramaniam, Signal prcessing in randm access, IEEE Signal Prcessing Magazine, vl. 21, n. 5, pp , Sep [34] A. Al Daud, T. Alpcan, S. Agarwal, and M. Alanyali, A stackelberg game fr pricing uplink pwer in wide-band cgnitive radi netwrks, in IEEE Cnference n Decisin and Cntrl, Cancun, Mexic, Dec [35] M. Razaviyayn, M. Ya, and L. Zhi-Quan, A Stackelberg game apprach t distributed spectrum management, in IEEE Internatinal Cnference n Acustics Speech and Signal Prcessing ICASSP, Dallas, TX, Mar [36] Y. Xia, Z. Han, K. C. Chen, and L. A. DaSilva, Bayesian hierarchical mechanism design fr cgnitive radi netwrks, t appear at IEEE J. Sel. Area Cmmun.: Cgnitive Radi Series, vl. 33, n. 4, April [37] Y. Xia, D. Niyat, Z. Han, and K. C. Chen, Secndary users entering the pl: A jint ptimizatin framewrk fr spectrum pling, IEEE J. Sel. Area Cmmun.: Cgnitive Radi Series, vl. 32, n. 3, pp , Mar [38] S. Mumtaz, K. M. S. Huq, and J. Rdriguez, Direct mbilet-mbile cmmunicatin: paradigm fr 5g, IEEE Wireless Cmmunicatins, vl. 21, n. 5, pp , Oct [39] W. Saad, Z. Han, T. Başar, M. Debbah, and A. Hjrungnes, Hednic calitin frmatin fr distributed task allcatin amng wireless agents, IEEE Trans. Mbile Cmputing, vl. 10, n. 9, pp , Sep [40] K. Akkarajitsakul, E. Hssain, and D. Niyat, Distributed resurce allcatin in wireless netwrks under uncertainty and applicatin f Bayesian game, IEEE Cmmunicatins Magazine, vl. 49, n. 8, pp , 2011.

19 19 [41] A. Leshem and E. Zehavi, Game thery and the frequency selective interference channel, IEEE Signal Prcessing Magazine, vl. 26, n. 5, pp , Sep [42] G. Chalkiadakis, E. Elkind, E. Markakis, M. Plukarv, and N. R. Jennings, Cperative games with verlapping calitins, Jurnal f Artificial Intelligence Research, vl. 39, n. 1, pp , [43] J.-P. Aubin, Cperative fuzzy games, Mathematics f Operatins Research, vl. 6, n. 1, pp. 1 13, Feb [44] D. P. Fster and H. Yung, Learning, hypthesis testing, and nash equilibrium, Games and Ecnmic Behavir, vl. 45, n. 1, pp , Mar [45] M. Bwling and M. Vels, Ratinal and cnvergent learning in stchastic games, in Internatinal jint cnference n artificial intelligence, vl. 17, n. 1, Seattle, WA, Aug [46] E. Kalai and E. Lehrer, Ratinal learning leads t nash equilibrium, Ecnmetrica: Jurnal f the Ecnmetric Sciety, pp , Sep [47] A. Leshem, E. Zehavi, and Y. Yaffe, Multichannel pprtunistic carrier sensing fr stable channel access cntrl in cgnitive radi systems, IEEE J. Select. Areas Cmmun., vl. 30, n. 1, pp , Jan [48] A. E. Rth, The evlutin f the labr market fr medical interns and residents: a case study in game thery, The Jurnal f Plitical Ecnmy, vl. Y2, n. 6, pp , [49] T. Fleiner, R. W. Irving, and D. F. Manlve, Efficient algrithms fr generalized stable marriage and rmmates prblems, Theretical cmputer science, vl. 381, n. 1, pp , Aug [50] Y. Xia, G. Bi, and D. Niyat, A simple distributed pwer cntrl algrithm fr cgnitive radi netwrks, IEEE Trans. Wireless Cmmun.,, vl. 10, n. 11, pp , Nv [51] R. Knpp and P. Humblet, Infrmatin capacity and pwer cntrl in single-cell multiuser cmmunicatins, in IEEE Internatinal Cnference n Cmmunicatins ICC, Seattle, WA, Jun [52] P. Biró and G. Nrman, Analysis f stchastic matching markets, Internatinal Jurnal f Game Thery, vl. 42, n. 4, pp , Nv [53] T. Fleiner, A fixed-pint apprach t stable matchings and sme applicatins, Mathematics f Operatins Research, vl. 28, n. 1, pp , Feb [54] J. W. Hatfield and P. R. Milgrm, Matching with cntracts, American Ecnmic Review, pp , Sep Kwang-Cheng Chen M. 89-SM. 94-F. 07 received the B.S. frm the Natinal Taiwan University in 1983, and the M.S. and Ph.D frm the University f Maryland, Cllege Park, United States, in 1987 and 1989, all in electrical engineering. Frm 1987 t 1998, Dr. Chen wrked with SSE, COMSAT, IBM Thmas J. Watsn Research Center, and Natinal Tsing Hua University, in mbile cmmunicatins and netwrks. Since 1998, Dr. Chen has been with Natinal Taiwan University, Taipei, Taiwan, ROC, and is the Distinguished Prfessr and Assciate Dean in academic affairs fr the Cllege f Electrical Engineering and Cmputer Science, Natinal Taiwan University. Dr. Chen has been actively invlved in the rganizatin f varius IEEE cnferences as General/TPC chair/c-chair. He has served in editrships with a few IEEE jurnals and many internatinal jurnals and has served in varius psitins within IEEE. Dr. Chen als actively participates in and has cntributed essential technlgy t varius IEEE 802, Bluetth, and 3GPP wireless standards. He has authred and c-authred ver 250 technical papers and mre than 20 granted US patents. He c-edited with R. DeMarca the bk Mbile WiMAX published by Wiley in 2008, and authred the bk Principles f Cmmunicatins published by River in 2009, and c-authred with R. Prasad anther bk Cgnitive Radi Netwrks published by Wiley in Dr. Chen is an IEEE Fellw and has received a number f awards including the 2011 IEEE COMSOC WTC Recgnitin Award and has c-authred a few award-winning papers published in the IEEE CmSc jurnals and cnferences. Dr. Chen s research interests include wireless cmmunicatins and netwrk science. Yng Xia S 11-M 13 received his B.S. degree in electrical engineering frm China University f Gesciences, Wuhan, China in 2002, M.Sc. degree in telecmmunicatin frm Hng Kng University f Science and Technlgy in 2006, and his Ph. D degree in electrical and electrnic engineering frm Nanyang Technlgical University, Singapre in Frm August 2010 t April 2011, he was a research assciate in schl f electrical and electrnic engineering, Nanyang Technlgical University, Singapre. Frm May 2011 t Octber 2012, he was a research fellw at CTVR, schl f cmputer science and statistics, Trinity Cllege Dublin, Ireland. Frm Nvember 2012 t December 2013, he was a pstdctral fellw at Massachusetts Institute f Technlgy. Frm December 2013 t Nvember 2014, he was a MIT-SUTD pstdctral fellw with Singapre University f Technlgy and Design and Massachusetts Institute f Technlgy. Currently, he is a pstdctral fellw II at Department f Electrical and Cmputer Engineering at University f Hustn. His research interests include machine learning, game thery and their applicatins in cmmunicatin netwrks. Chau Yuen received the B.Eng. and Ph.D. degrees frm Nanyang Technlgical University, Singapre, in 2000 and 2004, respectively. In 2005, he was a Pstdctral Fellw with Bell Labs, Alcatel-Lucent, Murray Hill, NJ, USA. Frm 2006 t 2010, he was a Senir Research Engineer with the Institute fr Infcmm Research, Singapre, where he was invlved in an industrial prject n develping an n wireless lcal area netwrk system and participated actively in the Third-Generatin Partnership Prject Lng-Term Evlutin and LTE Advanced standardizatin. In 2008, he was a Visiting Assistant Prfessr with The Hng Kng Plytechnic University, Kwln, Hng Kng. Since June 2010, he has been an Assistant Prfessr with the Department f Engineering Prduct Develpment, Singapre University f Technlgy and Design, Singapre. Dr. Yuen serves as an Assciate Editr fr the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY. He received the Lee Kuan Yew Gld Medal, the Institutin f Electrical Engineers Bk Prize, the Institute f Engineering f Singapre Gld Medal, the Merck Sharp & Dhme Gld Medal, the Hewlett Packard Prize twice, and the 2012 IEEE Asia-Pacific Outstanding Yung Researcher Award.

20 20 Zhu Han S 01-M 04-SM 09 received the B.S. degree in electrnic engineering frm Tsinghua University, in 1997, and the M.S. and Ph.D. degrees in electrical engineering frm the University f Maryland, Cllege Park, in 1999 and 2003, respectively. Frm 2000 t 2002, he was an R&D Engineer f JDSU, Germantwn, Maryland. Frm 2003 t 2006, he was a Research Assciate at the University f Maryland. Frm 2006 t 2008, he was an assistant prfessr in Bise State University, Idah. Currently, he is an Assciate Prfessr in Electrical and Cmputer Engineering Department at the University f Hustn, Texas. His research interests include wireless resurce allcatin and management, wireless cmmunicatins and netwrking, game thery, wireless multimedia, security, and smart grid cmmunicatin. Dr. Han is an Assciate Editr f IEEE Transactins n Wireless Cmmunicatins since Dr. Han is the winner f IEEE Fred W. Ellersick Prize Dr. Han is an NSF CAREER award recipient Luiz A. DaSilva SM is the Prfessr f Telecmmunicatins at Trinity Cllege Dublin. He als hlds a research prfessr appintment in the Bradley Department f Electrical and Cmputer Engineering at Virginia Tech, USA. His research fcuses n distributed and adaptive resurce management in wireless netwrks, and in particular wireless resurce sharing, dynamic spectrum access, and the applicatin f game thery t wireless netwrks. He is currently a Principal Investigatr n research prjects funded by the Natinal Science Fundatin in the United States, the Science Fundatin Ireland, and the Eurpean Cmmissin under Hrizn 2020 and Framewrk Prgramme 7. He is a C-principal Investigatr f CONNECT, the Telecmmunicatins Research Centre in Ireland. Prf DaSilva is an IEEE Cmmunicatins Sciety Distinguished Lecturer.