986 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 5, MAY 2015

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1 986 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 5, MAY 2015 Bayesan Herarchca Mechansm Desgn for Cogntve Rado Networks Yong Xao, Member, IEEE, Zhu Han, Feow, IEEE, Kwang-Cheng Chen, Feow, IEEE, and Luz A. DaSva, Senor Member, IEEE Abstract Ths paper consders a cogntve rado network where the censed network, referred to as the prmary user (PU) network, conssts of a herarchca structure n whch mutpe operators coexst n the same coverage area where each of the operators contros an excusve set of frequency sub-bands. Uncensed users, referred to as the secondary users (SUs), frst send ther requests to the operators, and can ony access the sub-bands controed by the operators that accept ther requests. SUs are sefsh and cannot exchange prvate nformaton wth each other. We mode the dynamc spectrum access (DSA) probem of the SUs as a Bayesan game, referred to as the DSA game. We mode the PU network as a forest where the roots represent the operators and the eaves represent the operators sub-bands. We propose a nove forest matchng market to mode the nteracton between the SUs and the PU network. In ths market, a set of SUs can be frst matched to a set of operators and the SUs matched to the same operator can then be matched to the correspondng sub-bands. We propose a dstrbuted agorthm that resuts n a stabe forest matchng structure, whch concdes wth the optma Bayesan Nash equbrum of the DSA game. We prove that the Bayesan herarchca mechansm assocated wth our proposed agorthm ncentvzes truth-teng by SUs. Our agorthm does not requre each SU to know the preference and confct-sovng rue of the PU network or the payoffs and actons of other SUs, and the compexty of each teraton n the worst case s gven by O(L 2 N 2 K) where L s the number of operators, N s the maxmum number of sub-bands of each operator, and K s the number of SUs. Index Terms Cogntve rado, stabe matchng, forest matchng, stabe marrage, coege admsson, dynamc spectrum access, herarchca, game theory, mechansm desgn, Bayesan game. I. INTRODUCTION MANY of today s networkng systems operate accordng to a herarchca structure. For exampe, n teecommuncaton networks, smart grds, coud storage systems, etc., mutpe operators (e.g., teecommuncaton operators, eectrc- Manuscrpt receved January 5, 2014; revsed May 12, 2014 and Juy 18, 2014; accepted August 23, Date of pubcaton September 30, 2014; date of current verson Apr 21, Ths work s partay supported by the Natona Scence Foundaton under Grants CNS , ECCS , CNS , and CNS , and by the Scence Foundaton Ireand under Grant 10/IN.1/I3007. Y. Xao s wth the Sngapore Unversty of Technoogy and Desgn, Sngapore (e-ma: xyong.2012@gma.com). Z. Han s wth the Department of Eectrca and Computer Engneerng, Unversty of Houston, Houston, TX USA (e-ma: zhan2@uh.edu). K.-C. Chen s wth the Graduate Insttute of Communcaton Engneerng, Natona Tawan Unversty, Tape 10617, Tawan (e-ma: chenkc@cc.ee.ntu. edu.tw). L. A. DaSva s wth CTVR, Trnty Coege Dubn, Dubn, Ireand, and aso wth Vrgna Poytechnc Insttute and State Unversty (Vrgna Tech), Backsburg, VA USA (e-ma: dasva@tcd.e). Coor versons of one or more of the fgures n ths paper are avaabe onne at Dgta Object Identfer /JSAC ty companes, coud storage provders, etc.) coexst n the same servce area. Each operator has been censed excusve use of a resource (e.g., frequency bands, eectrca grd, or coud storage nfrastructure) whch can be further dvded nto resource bocks. Each resource bock can then be used to provde an ndvdua servce, such as voce/vdeo ca, eectrcty suppy, data storage, etc., for a user (e.g., mobe servce subscrber, eectrca appance, storage appcaton, etc.), referred to as the prmary user (PU). If a set of uncensed user equpments, referred to as secondary users (SUs), can ntegenty access ths resource wthout causng ntoerabe performance degradaton to the PUs, the system w turn nto a censed resource sharng (LRS) networkng system. In ths system, SUs cannot access any resource bock uness they obtan permsson from the correspondng operator. In ths paper, we focus on a cogntve rado (CR) network n whch the spectrum censed to network operators and ther censed subscrbers (PUs) can be dynamcay accessed by the uncensed subscrbers (SUs) accordng to dfferent servce requrements and envronments [1]. We refer to the censed networkng system consstng of operators and ther correspondng sub-bands and subscrbers as the PU network.we aso use the terms frequency band (or spectrum) and sub-band to denote the resource censed to each operator and the resource bock that can be aocated to each subscrber, respectvey. We study the dynamc access of a set of SUs to the spectrum censed to a PU network wth a herarchca structure consstng of mutpe operators and ther correspondng sub-bands. The herarchca structure of the PU network makes t dffcut for SUs to decde whch operators sub-bands they want to access. More specfcay, each SU needs to send a request to an operator before accessng any sub-band. Once ts request has been accepted, the SU w stck to the operator that accepts ts request for a certan perod of tme. Each operator ony hods a cense for a mted number of sub-bands, and hence can ony aow a mted number of SUs to access ts spectrum. If the number of SUs requestng the resources of the same operator exceeds the mt for ths operator, a confct happens. The operator and sub-band fnay aocated to each SU depend not ony on the preference of the SU over the operators and sub-bands, but aso on rues apped by the PU network to sove confcts and on the benefts each operator can obtan from the popuaton of SUs. For exampe, suppose one SU beeves a sub-band controed by an operator can provde the maxmum performance and sends ts request to ths operator. However, the request of the SU can be rejected by the operator. Or even f the SU s request s accepted, ts request for the performance-maxmzng IEEE. Persona use s permtted, but repubcaton/redstrbuton requres IEEE permsson. See for more nformaton.

2 XIAO et a.: BAYESIAN HIERARCHICAL MECHANISM DESIGN FOR COGNITIVE RADIO NETWORKS 987 sub-band may be rejected because the operator aocates ths sub-band to another competng SU. In ths case, another subband of the operator w be aocated to the SU, whch may resut n performance that s even worse than that acheved by accessng sub-bands of other operators. In other words, seectng the operator wth the performance-maxmzng subband may not aways the best choce for the SUs. Furthermore, t has been observed n [2] [5] that there s no stabe mechansm that can prevent a SUs wth a genera doman of preferences from obtanng hgher benefts by msrepresentng ther true prvate nformaton. Therefore, how to desgn a truth-teng mechansm that can aso resut n the optma soca choce for the SUs s a chaengng and mportant probem. It can be observed that the nteracton among SUs and that between SUs and PUs pay a domnant roe n determnng the performance of SUs and the PU network [6] [8]. Ths motvates us to appy game theory to anayze the dynamc spectrum access probem. However, one of the most mportant souton concepts n game theory, the Nash equbrum, s generay not unque or optma [9]. For exampe, t has been shown n [10] that f we mode the spectrum access probem as a onestage non-cooperatve game, any sub-band aocaton scheme s a Nash equbrum. Furthermore, achevng the optma Nash equbrum s not aways possbe, or f possbe, t may be an NP-hard probem [9], [11]. We consder the dstrbuted optmzaton of the dynamc spectrum access (DSA) probem for SUs n a CR network. In ths probem, SUs can access the spectrum censed to mutpe operators that coexst n the area of nterest. To maxmze ther payoffs, the SUs w frst decde ther preferred operators, and then compete for the mted number of sub-bands of each operator. Each SU cannot know the preference and the confctsovng rue of operators, or observe the prvate nformaton such as preferences and payoffs of other SUs. Ths motvates us to mode the DSA probem as a Bayesan non-cooperatve game, referred to as the DSA game. We seek a sef-enforcng truth-teng mechansm desgn that can ncentvze a SUs to decde ther actons based on ther true preference and can eventuay resut n a unque and optma Bayesan Nash equbrum. It s observed that the mechansm desgn not ony ncudes deveopng rues for the operators to sove the confcts when the number of requestng SUs exceeds the mt but aso requres estabshng poces for strategc SUs to dstrbutedy compete for the mted number of operators and sub-bands. To sove the above probem, we mode the PU network as a forest structure [12] and propose a nove forest matchng market to mode the nteracton between the SUs and the PU network. The DSA probem of SUs can then be modeed as a matchng probem between a set of SUs and a forest consstng of a set of roots (operators) and ther correspondng eaves (sub-bands). We deveop a dstrbuted Bayesan herarchca agorthm that, despte the prvate nformaton and sefsh behavor of SUs, can resut n a unque and stabe forest matchng structure whch concdes wth the optma Bayesan Nash equbrum of the DSA game. Our proposed souton contans two separate agorthms for SUs to choose ther operators and sub-bands and a Bayesan beef updatng agorthm. We aso prove that the assocated Bayesan herarchca mechansm ncentvzes a SUs to seect the operators and sub-bands based on ther true prvate nformaton. Let us brefy summarze the man contrbutons of the paper as foows: 1) We formuate a Bayesan non-cooperatve game-based framework to mode the DSA probem of SUs n a CR network. 2) We ntroduce a nove Bayesan herarchca mechansm desgn framework to approach the unque and optma Bayesan Nash equbrum of our DSA game. 3) We propose a nove stabe forest matchng agorthm to acheve a stabe matchng between a set of SUs and a herarchca PU network whch concdes wth the optma Bayesan Nash equbrum of our DSA game. 4) We present numerca resuts to assess the performance of the proposed methods under dfferent stuatons. The rest of ths paper s organzed as foows. The background and reated work are revewed n Secton II. The network mode s ntroduced n Secton III. We estabsh the DSA game n Secton IV. We ntroduce the forest matchng market and the Bayesan herarchca mechansm n Secton V. Extensons and future works are dscussed n Secton VI. The numerca resuts are presented n Secton VII, and the paper s concuded n Secton VIII. II. BACKGROUND AND RELATED WORK Game theory has been wdey apped to anayze the performance of CR networks. More specfcay, n [6], [8], [13], [14], the sub-band aocaton probem for CR networks has been modeed as a non-cooperatve game to study the nteracton among the competng SUs. Coatona game theoretc modes have been apped to study the nteracton among the cooperatve users n CR networks n [15], [16]. A detaed survey of appcatons of game theory to CR networks has been presented n [17] [20]. Athough game theory has been shown to be an effectve too to study and anayze the nteracton among ndvdua payers, t s known that ts outcomes such as the Nash equbrum souton, are generay not unque or optma. Ths motvates mechansm desgn, whose man objectve s to ead the nsttutons governng the nteractons of a game to mpement a socay desrabe souton [21]. In [22], [23], an aucton mechansm has been apped to CR networks where cheatng between wreess devces has been avoded by aowng payments receved by each wreess devce to be freey transferred. However, n many practca wreess systems, payment/money transferrng between SUs s unreastc [24] [26]. In ths paper, we focus on desgnng a mechansm wthout monetary exchange where each SU ony cares about ts own prvate payoff and there s no nformaton exchange among SUs. To the best of our knowedge, ths s the frst work to consder mechansm desgn wthout monetary exchange for CR networks. We propose a nove forest matchng market whch can be regarded as a generazaton of the tradtona two-sded matchng market (aso caed stabe marrage market [27], bpartte matchng market [28], [29]). The two-sded stabe matchng probem has been wdey studed from both theoretca and

3 988 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 5, MAY 2015 TABLE I LIST OF NOTATIONS Fg. 1. A CR network wth 3 operators, 7 SUs, and 6 PUs. practca perspectves [27], [28], [30] [32]. In ths probem, each agent beongng to one sde of the market has a preference over the agents of the other sde, and tres to fnd a matchng that can optmze ts performance. Many extensons of these probems have been studed n the terature. More specfcay, the case of some agents on one sde wth preferences over a sub-set of the agents on the other sde has been studed n [33]. The case that the agents from one sde can have equa preference over mutpe agents of the other sde, aso caed stabe marrage wth te, has been studed n [34]. Emprca studes of the dfferent varatons of the two-sded matchng probem have been reported n [31], [35]. A survey of the stabe marrage market and ts varants has been presented n [36]. Dfferent from the exstng works, we consder the case n whch a set of agents from one sde conssts of a forest structure. We focus on the matchng probem between the set of agents of one sde and the roots and eaves n a forest of the other sde. To the best of our knowedge, ths s the frst work to study the matchng probem between a set of agents and a forest. III. NETWORK MODEL We consder a CR network n whch a set of K SUs D = {D 1,D 2,...,D K } shares the spectrum hed by a set of L co-ocated network operators O = {1, 2,...,L} as shown n Fg. 1. Each operator has been censed an excusve set of sub-bands, abeed as S = {S 1,S2,...,SN } where N s the number of sub-bands censed to operator and S S j = for j and, j O. We aso denote S = L =1 S. We abe the PU currenty occupyng sub-band S as P for P 0.If there s no PU usng sub-band S,wehaveP =0.LetP be the set of a PUs n operator,.e., P = {P : P 0, {1, 2,...,N }}. We st the man notaton adopted n ths paper n Tabe I. We assume that each sub-band (ether occuped or unoccuped by a PU) can be accessed by at most one SU. Ths assumpton s reasonabe because mposng the mt of one SU to share each sub-band aows the operator to evauate and contro the nterference caused by SUs. For exampe, f ether the PU or SU, or both, observes hgher-than-toerabe nterference, the operator can smpy remove the SU from the sub-band. If two or more SUs share the same sub-band, t w be dffcut to evauate whch SU causes the hghest nterference to the PU network, or whch SU has to be removed, and t s generay neffcent to smutaneousy remove a SUs from the sub-band whenever an operator observes hgh nterference. Our mode can be extended to the case wth more than one SU sharng each sub-band. We w provde a more detaed dscusson n Secton VI. We consder the foowng power constrants n each subband S of operator : h P D k w Dk Q, f P 0, (1) where h P D k s the channe gan between PU P and SU D k n sub-band S, w D k s the transmt power of D k and Q s the maxmum toerabe nterference eve for sub-band S.IfanSU D k cannot satsfy the above constrant, t w be excuded from sub-band S. Let the payoff obtaned by each SU D k n sub-band S be ϖ Dk [S ] for S S. We consder a genera mode and the payoff of each SU can be any performance measure or functon

4 XIAO et a.: BAYESIAN HIERARCHICAL MECHANISM DESIGN FOR COGNITIVE RADIO NETWORKS 989 generated from ts receved sgna-to-nterference-pus-nose rato (SINR). For exampe, f the SU wants to maxmze ts transmt rate per bandwdth prce, the payoff functon of SU D k when t accesses sub-band S can be wrtten as ρ [ ] ϖ Dk S = e ( ) ρ og ( [ ]) 1+SINR Dk S, (2) where ρ s the bandwdth of sub-band S and e(ρ ) s the prce of bandwdth pad to the operator and SINR Dk [S ] s the sgna to nose rato receved at SU D k n sub-band S, gven by h Dk[S ] [ ] w D k σ SINR Dk S Dk[S = ] +h P D w, f P k P 0, h Dk[S ] w (3) D k σ, f P Dk[S ] =0, where h Dk [S ] s the channe gan between the source and destnaton of SU D k n sub-band S, σ D k [S ] s the addtve nose receved by SU D k n sub-band S, and w P s the transmt power of P.Wehaveϖ D k [S ] ϖ D k [Sm] n for S Sn m and S,Sn m S. The revenue η S [D k ] obtaned by operator by aowng SU D k to access sub-band S can be a functon of the resutng nterference. For exampe, f the revenue η S [D k ] s a near functon of the receved nterference at PU P when P 0or the SINR of D k when P =0,wehave1 β h Dk P w D k, If P 0, h η S [D k ]= β Dk[S ] w D k σ, If P Dk[S ] =0, (4) where β s the prcng coeffcent of operator. Iftscear from the context that D k obtans a sub-band from operator, we use η [D k ] to denote the revenue of operator obtaned from SU D k. As mentoned prevousy, each operator has a mted number of sub-bands, and hence can ony provde servces to a mted number of SUs. We refer the maxmum number of SUs an operator can accept as ts quota, denoted as q. Note that q N needs to be satsfed when each sub-band can be occuped by at most one SU. However, f we aow mutpe SUs to share each sub-band, we w have q >N. We w dscuss ths case n deta at Secton VI. In ths paper, we set q = N for O. When the number of SUs requestng permsson to access the spectrum of operator exceeds q,aconfct w happen. In ths case, ony q SUs w be accepted and the remanng SUs w be rejected and excuded from the spectrum of operator. These rejected SUs w then send ther requests to other operators. The process w contnue unt a SUs have been aocated operators. Smary, f a set of SUs, abeed as U, has 1 Appyng a near functon of the resutng nterference as the prcng functon of the operators has been adopted n [6], [8], [37], [38]. Appyng a near functon of SINR for each SU as the prcng functon s motvated by the fact that many exstng teecommuncaton mobe systems charge accordng to ther communcaton data rates, whch are monotoncay ncreasng functons of SINR. Note that, n these prcng functons, the operator can contro the nterference of SUs to the PU network by adjustng the vaue of prcng coeffcent β [6]. been accepted by operator, these SUs w then compete for the set S of sub-bands of operator. If at east two SUs n U choose the same sub-band, ony one of them w be aowed to access ths sub-band. The rest of the requestng SUs w have to compete for the remander of sub-bands n S. We assume SUs are sefsh and aways try to maxmze ther payoff. Each SU can estabsh and mantan a preference, a ranked st, over the operators and ther correspondng sub-bands. Let the preference of each SU D k over the operators and sub-bands be R o D k and R b D k, respectvey. Note that R o D k and R b D k are cosey reated to each other. For exampe, consder a CR network wth two operators 1 and 2. If an SU D k beeves that the sub-band t can obtan from operator 2 can provde a hgher payoff than that from operator 1, the preference of SU D k over operators s gven by R o D k = 2, 1. Ifweuseĩ Dk to denote the th most preferred operator for SU D k, we can rank the operators from the most to the east preferred ones for SU D k and wrte ts preference as R o D k = 1 Dk, 2 Dk where 1 Dk =2and 2 Dk =1 n ths exampe. Smary, f we use S D n k to denote the nth most preferred sub-band for SU D k of ts chosen operator, we can wrte the preference of D k U over the set S of subbands as R b D k = S D 1 k, S D 2 k,..., S N D k. We can aso wrte the preference of each SU D k as R Dk = R o D k, R b D k. We denote R o ={R o D k }, Dk D Rb ={R b D k } and R={R Dk D D k } Dk D. We assume that each operator w ony reease sub-band nformaton to the SUs that have been gven permsson to access ts spectrum. In other words, an SU D k can ony estabsh the preference R b D k over the sub-bands of operator f the request sent by SU D k has been accepted by operator. The operator and sub-band fnay aocated to each SU D k not ony depend on the preference of SU D k but aso reate to the confct-sovng rues empoyed by the operators and the payoffs and preferences of other SUs. Therefore, estabshng a proper rue for the operators to accept or reject the requests of SUs s very mportant. We consder dstrbuted optmzaton for the DSA probem n a CR network and assume SUs cannot exchange nformaton wth each other or know the preference or confct-sovng rues of PUs. Snce each SU w send ts request sgna to the operators before accessng any sub-band, each operator can use the receved request sgna to evauate the resutng revenues and estabsh ts preference over the requestng SUs. In our mode, dfferent operators can beong to dfferent network systems and hence cannot communcate or exchange nformaton such as the preference and the revenues wth each other. Note that each operator needs to frst decde whether to grant permsson to access ts spectrum to SUs before knowng whch specfc subbands w be requested by each SU. In ths paper, we many focus on the dynamc spectrum access (DSA) of SUs, and assume the preference R of each operator over the SUs has been estabshed based on a predefned crteron unreated to the fna sub-band aocated to each SU. 2 For exampe, f the operators 2 Ths settng has aready been apped n many practca systems. For exampe, n coege admsson systems, many unverstes have genera admsson requrements, such as SAT score and hgh schoo transcrpts, for acceptng students [39]. These requrements are unreated to whch departments or programmes the students fnay choose.

5 990 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 5, MAY 2015 try to mantan a guaranteed worst case revenue from SUs, the preference of each operator j w be a st of SUs n the order of the guaranteed mnmum revenue obtaned when each SU accesses the sub-band provdng the mnmum revenue,.e., the preference of operator over SUs s gven by R ={ D 1 D, 2,..., D K} where D k s the kth most preferred SU of operator and, for any two SUs D n, D k D, n<k f ηmn [D n ]> η mn [D k ], where η mn [D k ]= mn{η S S S [D k ]}, D k D. After a set of SUs obtans permsson to access sub-bands of operator, they w compete wth each other for the set of sub-bands S. In ths case, operator can aso estabsh a preference R S for each of ts sub-band S over a the accepted SUs, 3.e., the preference for sub-band S, denoted by R S = { D 1, D 2 S S SUs D n, D k S S,..., D U }, shoud satsfy that, for any two S U, n<kmeans η S [D n ] >η S [D k ]. In a CR network, each SU needs to request permsson from an operator before accessng ts sub-bands. In many practca systems, once the request has been accepted, an agreement (e.g., a contract) between the SUs and the operators that accept ther requests w be enforced to avod SUs changng ther decsons wthn a short perod of tme and aso to prevent the operators from retractng the aocated sub-bands from SUs wthn the agreed tme perod. For exampe, n a teecommuncaton system, a mobe servce subscrber needs to sgn a fxedterm contract wth a teecommuncaton operator and cannot swtch to another operator wthn the contract perod. In ths paper, we assume the communcaton tme can be dvded nto tme sots. At the begnnng of each tme sot, a SUs decde whch operators and sub-bands to send ther request to. The SUs cannot change ther decsons durng the rest of each tme sot, but can swtch to dfferent operators and sub-bands n dfferent tme sots. In the rest of ths paper, we focus on desgnng a mechansm that can ncentvze SUs to make decsons based on ther true preference and eventuay approach a socay desrabe outcome. It s generay unreastc to assume each SU can predct the type nformaton of other SUs nstantaneousy before t makes decsons at the begnnng of each tme sot. It s however possbe for each SU to eavesdrop on the past decsons of other SUs. Therefore, we assume each SU can observe the decsons of other SUs n the prevous tme sots. Note that the beef and the decson of each SU n the current tme sot are prvate nformaton that s nnot be known by other SUs. IV. A BAYESIAN GAME FRAMEWORK AND MECHANISM DESIGN FOR DSA PROBLEM A. A Bayesan Game Framework We mode the DSA probem of SUs as a Bayesan game, referred to as the DSA game, whch s formay defned as foows. 3 As observed n Secton III, to mantan the QoS of the exstng PUs, the sub-band sharng between SUs and PUs needs to be strcty controed by the operators. Therefore, the preference of each sub-band over the SUs has to be estabshed and mantaned by the operators. To smpfy our dscusson, n ths paper, we use the term preference of sub-band to denote the preference of the operator over the access by the SUs to each of ts sub-bands. Defnton 1: The DSA game s defned by a tupe G = D, A, T, B, ϖ where D s the set of payers (.e., SUs), A = {A Dk } Dk D s the acton space of SUs, T = {T D k } Dk D s the type space of SUs, B = {B Dk } Dk D s the beef functon of SUs about types of others, and ϖ s the payoff of SUs. In DSA game, acton a Dk = a o D k,a b D k of each SU D k can be dvded nto two parts: operator seecton acton a o D k O { } specfes whch operator SU D k w send ts request to, and sub-band seecton acton a b D k S { } specfes whch sub-band SU D k w request after beng granted permsson to access the spectrum of an operator. We can wrte set A Dk of the possbe actons of each SU D k as A Dk = O { } S { }. For exampe, a o D k = means SU D k decdes to send request to operator. Ifa o D k =, t means D k does not send a request to any operator. We aso use a b D k = S to mean that D k w send a request for sub-band S after beng accepted by operator. Smary, we use a b D k = to mean D k does not send a request for any sub-band. We denote a o = {a o D k }, Dk D ab = {a b D k } and a = {a Dk D D k } Dk D. The request sent by each SU to the operators for sub-bands can be rejected accordng to the operator s confct-sovng rues. We defne the confct-sovng rue of operators as a functon Γ o such that Γ o (D k, a o )= means that operator accepts the request sent by SU D k.if D k cannot obtan permsson to access the spectrum of any operator, we wrte Γ o (D k, a o )=D k. Smary, we defne the confct-sovng rue of sub-bands 4 as a functon Γ b such that Γ b (D k, a b )=S means that D k has been gven permsson to access sub-band S of operator. WeuseΓb (D k, a b )=D k to mean that D k cannot access any sub-band of ts operator. We denote the fna operator and sub-band aocaton structure as Γ= Γ o, Γ b,.e., Γ(D k, a) =, S means D k has been assgned to operator and sub-band S. The type y D k T Dk of each SU D k whch ncudes ts preference over the possbe actons s prvate nformaton and can ony be known by tsef. Each SU cannot know the types of other SUs but can estabsh a beef functon about actons of other SUs usng ts prevous observatons. Snce each SU decdes ts acton usng ts type, we can defne a strategy functon f Dk for each SU D k to map ts type nto an acton,.e., f Dk : T Dk A Dk. In ths way, we can convert the beef B Dk (y Dk ) of each SU D k about the types of ther SUs nto the beef about the actons of other SUs, denoted as b Dk (a Dk ). From the prevous dscusson, t can be observed that the fna operator and sub-band aocaton structure can be determned by the acton profe of a SUs and the confct-sovng rues of operators and sub-bands. We can hence wrte the expected payoff of each SU D k acheved by ts acton a Dk and beef b Dk (a Dk ) for the gven confct-sovng rues of operators and sub-bands as ϖ Dk (a Dk,b Dk (a Dk )) [ = b Dk (a Dk ) ϖ Dk Γ b (D k, a b ) ], (5) a Dk A Dk 4 In most exstng wreess networkng systems, the operator contros the subband usage. Therefore, n ths paper, we use the term confct-sovng rue of sub-band to mean the acceptance and rejecton decson of the operator about the request sent by SUs for each of ts sub-bands.

6 XIAO et a.: BAYESIAN HIERARCHICAL MECHANISM DESIGN FOR COGNITIVE RADIO NETWORKS 991 where D k denotes a SUs except D k and ϖ Dk [Γ b (D k, a b )] s the payoff obtaned by D k when accessng sub-band Γ b (D k, a b ) defned n (2). Note that Γ b (D k, a b ) s the resut of the acton profe of a SUs as we as the confct-sovng rues of both operators and sub-bands. We consder a (fntey) repeated game settng n whch each SU can earn from the resutng payoffs and the observatons of the prevous tme sots and update ts beef functon at the end of each tme sot. Each SU w then use the updated beef functon to decde ts preference and acton for the next tme sot. The man souton concept n our proposed DSA game s the Bayesan Nash equbrum, whch s formay defned as foows. Defnton 2: A Bayesan Nash equbrum of the DSA game s an acton profe a = a D k Dk such that D ( ( )) ( ( )) ϖ Dk a Dk,b Dk a Dk ϖdk adk,b Dk a Dk, a Dk A Dk and D k D. (6) A Bayesan Nash equbrum a s sad to be (Pareto) optma f there s no other Bayesan Nash equbrum a such that ϖ Dk (a D k,b Dk (a D k )) ϖ Dk (a D k,b Dk (a D k )) D k D where the nequaty hods strcty for at east one SU. B. Bayesan Mechansm Desgn It has been observed [11], [30] that for an unrestrcted doman of the acton profes of SUs, at east one SU can aways mprove ts performance by msrepresentng ts true type, assumng other SUs te the truth. We hence aso seek a mechansm that prevents SUs from obtanng benefts by cheatng on ther strateges. We defne a set Λ of aternatves (canddates) as the set of a possbe operator and sub-band aocatons of SUs. As mentoned prevousy, for a gven confctsovng rue, each acton profe of SUs w resut n a sub-band aocaton scheme for SUs,.e., we use λ Λ to denote an operator and sub-band aocaton scheme. Let us defne the soca choce functon as foows. Defnton 3: A soca choce functon c : T Λ s a mappng from the type of a SUs to a snge canddate of the soca choce. The soca choce functon specfes the possbe resutng outcome of our DSA game wth each type profe y of SUs. Let us defne the Bayesan mechansm as foows. Defnton 4: [11, Chapter 9.3.2] [21, Chapter 4.1] A Bayesan (drect reveaton) mechansm for the DSA game s gven by the type space T, beef functon b, acton space A defned n Defnton 1, an aternatve set Λ, payoff ϖ Dk for each SU D k and an outcome functon u : A Λ. A Bayesan mechansm mpements a soca choce functon c f for some Bayesan Nash equbrum a of DSA game, we have c(y) =u(a ) for a y T. A Bayesan mechansm s sad to be ncentve compatbe (aso caed strategy-proof or truthfu) f the soca choce functon c(y) =λ satsfes the foowng condton for a SUs, ϖ Dk ( a Dk,b Dk (a Dk ) ) ϖ Dk (a DK,b Dk (a Dk )), D k D,a D k,a Dk A Dk, and a Dk A Dk. Fg. 2. A forest matchng structure for the CR network gven n Fg. 1. In ths paper, we seek a mechansm that pays the roe of an nvsbe hand, that s, when SUs nteract through the mechansm, despte the prvate nformaton, sef-nterested and autonomous behavor of the SUs, they w have an ncentve to make ther decsons based on ther true type nformaton, whch eventuay eads to the optma Bayesan Nash equbrum of the DSA game. V. BAYESIAN HIERARCHICAL MECHANISM DESIGN USING A FOREST MATCHING ALGORITHM To desgn a mechansm for CR networks, we need to deveop the confct-sovng rue for operators and sub-bands and, for the SUs, we shoud estabsh the competton poces that can ead to the optma Bayesan Nash equbrum. Ths motvates us to mode the nteracton between the SUs and the PU network as a two-sded matchng market. In the rest of ths secton, we propose a dstrbuted agorthm that approaches a unque and stabe matchng structure whch concdes wth the optma Bayesan Nash equbrum of the DSA game. We then ntroduce a Bayesan herarchca mechansm that can ncentvze truth-teng by a SUs. We frst mode the PU network as a two-ayer forest as foows. The PU network conssts of a forest structure wth L trees, each of whch corresponds to an operator and ts subbands. More specfcay, the roots of the forest represent the operators, and the eaves represent the operators sub-bands and assocated abty to share ther sub-bands wth SUs (.e., payoffs and channe gans assocated wth sub-band sharng). We ntroduce a forest matchng market, n whch the set of SUs w be frst parttoned nto L sub-sets, each of whch corresponds to a set of SUs matched to the same operator (root). Each SU can then request a sub-band (eaf) of ts matched operator (root). Let the forest be H = V, E where V = S O s the set of vertces consstng of both roots and eaves and E s the set of edges connectng dfferent vertces. In the PU network, ony each root (e.g., operator ) and ts correspondng eaves (e.g., sub-bands n S ) are connected wth edges. We ustrate the forest matchng market for the CR network of Fg. 1 n Fg. 2. Let us formay defne the forest matchng market as foows.

7 992 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 5, MAY 2015 Defnton 5: We defne a forest matchng market as F = D, H, where D s a set of agents, H s a forest structure, and s the preference. We many focus on a (two-sded) forest matchng market wth a two-ayer forest structure n one sde of the market. In ths market, the preference of each agent over a forest conssts of two preference sts: the preference over the roots and the preference over the eaves. Smary, each root or eaf can aso have a preference over the agents. Our mode can be extended nto more genera cases that contan a forest wth more than two ayers by ntroducng the preferences for agents (and each eement n each ayer) over eements n each ayer (and agents), whch w be dscussed n Secton VI. In the rest of ths paper, we abuse the notaton and use j and Sj to denote the jth root and the th eaf n root j, respectvey. The above defnton can be regarded as a generazaton of the tradtona two-sded stabe matchng markets [4], [11], [30] nto a forest structure. Note that f there are no roots n the forest structure (caed a zero-connecton or zero-order forest [12]), the forest matchng market becomes equvaent to the two-sded matchng market. Each agent D k D can ony obtan ts payoff after beng matched to a specfc eaf beongng to a specfc root. Let us defne the matchng between the agents and a forest as foows. Defnton 6: We defne a (2-ayer forest) matchng as M = M o,m b where 1) M o s a functon from the set D O nto the set of unordered fames of eements of D O such that M o (D k ) =1for every agent D k and M o (D k )=D k f M o (D k ) O, M o () q for every O, and M o (D k )=f and ony f D k M o (), 2) M b s a functon from the set D Sonto tsef such that f M b (D k ) D k, then M b (D k ) Sand f M b (Sj k) Sk j then M b (Sj k) D, and M b (D k )=Sj k M b (Sj k)= D k D k M o (j). In our mode, not a SUs w be accepted by the operators. We use M o (D k )=D k or M b (D k )=D k to mean that SU D k cannot be matched wth any operator or sub-band. Note that n the forest matchng market, for each agent D k, beng matched wth a root cannot guarantee that t w aso be matched wth a eaf n S,.e., even f D k satsfes M o (D k ) D k, t can st have M b (D k )=D k. Let us defne the dynamc spectrum access of SUs n a CR network as a forest matchng market F DSA = D, H, n whch the agents are the SUs. H s the forest structure of the PU network, where the operators are the roots and the sub-bands censed to the operators are the eaves. Our man objectve s to deveop an agorthm that can acheve a stabe matchng between the SUs and the PU network. We ntroduce the concept of stabty for the forest matchng market as foows. Defnton 7: A (forest) matchng M s sad to be stabe f every agent beeves that matchng M cannot be strcty mproved upon by any agent, agent-and-root, or agent-and-eaf par. Fg. 3. The reatonshp between dfferent agorthms for our stabe forest matchng market. Fndng the optma acton profe of SUs requres us to jonty optmze two sub-probems, the operator and sub-band seecton sub-probems, and the beef functon of SUs. In the remander of ths secton, we frst mode the operator seecton sub-probem as a two-sded many-to-one matchng market wth prvate beef (to be dscussed n Secton V-A) n whch the SUs w be matched to L operators. We then mode the subband seecton sub-probem as a two-sded one-to-one matchng market wth prvate beef (to be dscussed n Secton V-B). At the end of each tme sot, each SU obtans ts payoff and updates ts beef usng a Bayesan beef updatng agorthm (to be dscussed n Secton V-C). We ustrate the reatonshp between dfferent markets and correspondng agorthms n Fg. 3. A. Operator Seecton Sub-Market In ths and next subsectons, we assume that each SU D k has a fxed prvate beef functon b Dk (a Dk ). We w reax ths assumpton and dscuss the Bayesan beef updatng agorthm n Secton V-C. Each SU D k tres to be matched wth an operator whch s beeved to be abe to provde the sub-band that can maxmze the payoff of D k. We mode ths probem as a two-sded manyto-one matchng market wth prvate beef, whch s defned as foows. Defnton 8: A (two-sded many-to-one) matchng market wth prvate beef s a market G M1 = D, O, b, where D and O are two fnte and dsjont sets of agents, b s the vector of the gven beef functons, and s the preference of each agent. We defne the operator seecton sub-probem as a (two-sded many-to-one) matchng market wth prvate beef, referred to as the operator seecton sub-market, n whch D s the set of SUs, O s the set of operators and b s the beef of SUs. In the operator seecton sub-market, each SU D k w frst send a request to the operator whch, accordng to the beef functon of D k, w aocate the payoff-maxmzng sub-band to D k. However, the fna sub-band that w be aocated by each operator to SU D k s not ony reated to acton a Dk of D k but aso depends on the types and beef functons of other SUs whch are unknown to SU D k. Each SU D k needs to estmate the expected payoff obtaned from each operator usng ts beef functon,.e., for the gven beef functon b Dk (a Dk )

8 XIAO et a.: BAYESIAN HIERARCHICAL MECHANISM DESIGN FOR COGNITIVE RADIO NETWORKS 993 of SU D k, the expected payoff of D k when D k chooses acton a o D k = s gven by ( ˆϖ Dk a o Dk =, b Dk (a Dk ) ) = max a b D k S { } a Dk A Dk b Dk (a Dk ) ϖ Dk [ M b (D k ) ], (7) where ϖ Dk [M b (D k )] s gven n (2). Each SU D k can then estabsh the preference st R o D k about the operators by rankng the above expected payoffs obtaned from each operator n (7) from the hghest to the owest. We use D k D n to denote that operator prefers SU D k to SU D n,.e., η mn [D k ] >η mn [D n ], and use Dk m to denote that SU D k prefers accessng the spectrum of operator to that of operator m for m and, m O,.e., ˆϖ Dk (a o D k =, b Dk (a Dk )) > ˆϖ Dk (a o D k = m, b Dk (a Dk )). In the operator seecton sub-market, we seek a matchng M o between SUs and operators that s optma for SUs, that s, there s no stabe matchng M o such that M o (D k ) Dk M o (D k ) or M o (D k )=M o (D k ) for a D k Dwth M o (D n ) Dn M o (D n ) for at east one D n D. Note that the operator seecton sub-market s equvaent to the tradtona two-sded many-to-one matchng market [30], aso caed the coege admsson market (or the hosptas and resdents market), except that, n the atter market, there s no beef functon for each SU. Ths makes t possbe for us to appy the deferred-acceptance agorthm [5], [11] to acheve a unque and stabe matchng between SUs and operators. Before we present the detaed agorthm, et us brefy dscuss the tmng structure of CR networks. At the begnnng of each tme sot, the SUs send a request sgna to ther preferred operators and wat for confrmaton. If an SU receves the confrmaton of acceptance from the requested operator, t w then compete wth the other accepted SUs for the sub-bands of the operator. We w provde a more detaed dscusson about the sub-band seecton sub-probem n the next subsecton. Let us now present the detaed operator seecton agorthm as foows: Agorthm 1: An Operator Seecton Agorthm Input: Each SU D k estabsh a preference R o D k usng (7). Every operator estabshes a preference R. Output: a matchng M o. 1) Intzaton: EverySUD k sends a request sgna to ts most preferred operator a o D k = 1 Dk, 2) WHILE every SU s on the watng st of an operator and no operator w reject any SU ) Each SU D k that receves a rejecton message from operator removes operator from ts preference R o D k, and then sends a request sgna to the most preferred operator n the updated R o D k. )Each operator estabshes a watng st and keeps up to q most preferred SUs that send requestng sgnas to t nto ts watng st and rejects the remanng requestng SUs. ENDWHILE 3) Every operator sends acceptng message to the set of SUs n ts watng st. The above agorthm s a drect appcaton of the modfed deferred-acceptance agorthm for the two-sded matchng market ntroduced n [30]. Note that f an SU has been rejected by a operators at the end of the above agorthm, t cannot access any sub-band of the operators. From Agorthm 1, we can wrte the confct-sovng rue for the operator as foows: f the number of SUs who send request to operator exceeds q, operator w send rejecton messages to a the SUs except for the q most preferred SUs that have send requests to operator so far. We can prove the foowng resut about Agorthm 1. Proposton 1: Agorthm 1 termnates n a unque and stabe matchng and the resutng matchng M o between operators and SUs s optma for SUs. Proof: See Appendx A. We have the foowng resut about the compexty of Agorthm 1. Proposton 2: The compexty of Agorthm 1 s O(LK) n the worst case where L s the number of operators and K s the number of SUs. 5 Proof: See Appendx B. B. Sub-Band Seecton Sub-Market After a SUs have been matched to the operators, each SU can then decde whch specfc sub-band t can access. To sove ths probem, we can mode ths probem as a two-sded oneto-one matchng market wth prvate beef, whch s defned as foows. Defnton 9: Let us defne the two-sded one-to-one matchng game wth prvate beef as G M2 = U, S, b,, whch conssts of two sets of fnte and dsjont sets of agents U and S, a vector of beefs and the preference. We mode the sub-band seecton sub-probem as a two-sded one-to-one matchng market wth prvate beef, referred to as the sub-band seecton sub-market, n whch U = M o () s the set of SUs matched to operator by Agorthm 1 and S s the set of the exstng sub-bands controed by operator. The beef functon s defned n Secton IV. In the sub-band seecton submarket, the SUs accepted by the same operator (e.g., operator ) compete for set S of sub-bands. Each SU can aso estabsh an estmated verson of ts expected payoff obtaned from each of ts sub-band seecton acton as foows: supposng D k has been accepted by operator, we defne the estmated payoff of SU D k when D k sends a request for sub-band S as ( ˆϖ Dk a b Dk = S,b Dk (a Dk ) ) [ = b Dk (a Dk ) ϖ Dk M b (D k ) ]. (8) a Dk A Dk 5 f(n) We use Bachmann-Landau notaton: f = O(g) f m n g(n) < +.

9 994 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 5, MAY 2015 Each SU D k accepted by operator can then estabsh ts preference R b D k over sub-bands n S by rankng the estmated payoff n each sub-band of operator n (8) from the hghest to the owest vaues. Operator can aso evauate the preference R b of each sub-band S S over the accepted SUs usng ts receved request sgnas sent by the SUs. We abuse the notaton and use S D k S m to denote that SU D k prefers sub-band S over sub-band S m,.e., ˆϖ D k (a b D k = S,b D k (a Dk )) > ˆϖ Dk (a b D k = S m,b D k (a Dk )). Smary, D k S D n means sub-band S prefers SU D k over SU D n,.e., η S [D k ] > η S [D n ] for D k,d n M o (). Smar to the operator seecton sub-market, we seek a matchng M b between SUs and sub-bands of ther matched operator that s optma for SUs, that s, there s no stabe matchng M b between the set M o () of SUs and set S of sub-bands such that M b (D k ) Dk M b (D k ) or M b (D k )= M b (D k ) for a D k M o () wth M b (D n ) Dn M b (D n ) for at east one D n M o (). Smary, we can observe that the above matchng market s equvaent to the tradtona two-sded one-to-one matchng market [30], aso caed the stabe marrage market, wth the excepton that set U and the preference of each SU depend on ts beef. We can agan appy the deferred-acceptance agorthm to acheve a unque, optma and stabe matchng. We refer to ths agorthm as Agorthm 2: sub-band seecton agorthm. Ths agorthm s smar to the operator seecton agorthm descrbed n Agorthm 1 wth the dfference that the quota for each sub-band s 1. Smary, we can wrte the confct-sovng rue for the sub-band as foows: f there are two or more SUs who send request for sub-band S, operator w send rejecton messages to a the SUs except for the most preferred SU that sends request for sub-band S so far. We omt the detaed descrpton of the agorthm due to space mtatons. We have the foowng resuts. Proposton 3: Agorthm 2 termnates n a unque and stabe matchng and the resutng matchng M b between SUs and subbands s optma for SUs. The proof of the above proposton foows the same ne as that of Proposton 1. We omt the detaed dervaton due to the space mtatons. We have the foowng resut about the compexty of Agorthm 2. Proposton 4: The compexty of Agorthm 2 for every operator n the worst case s O(N U ). The proof of the above proposton foows the same ne as that of Proposton 2. We omt the detas. C. Bayesan Herarchca Mechansm In ths subsecton, we ntroduce a Bayesan beef updatng agorthm for a SUs to teratvey update ther beefs. We use [t] to denote the parameters n the tth tme sot. From Proposton 1 n Secton III, t can be observed that for each acton profe a, beef functon and preference of SUs, the resutng matchng M o between SUs and operators s aso determned. From Proposton 3, we can observe that for every matchng M o acheved by Agorthm 1, the preference of each SU D k over sub-bands of ts matched operator s aso fxed. Combnng these two observatons, we can cam that, for every gven preference profe R whch s cacuated by the beefs of SUs, the resutng matchngs n both operator and sub-band seecton sub-markets usng Agorthms 1 and 2 are fxed. To optmze the matchng for the operator seecton and sub-band seecton sub-markets, SUs ony need to determne ther beef functon. Foowng the same ne as Secton III, each SU s beef regardng the resutng matchngs and the preferences of other SUs foow from an unknown statonary dstrbuton [9], and hence each SU can use the foowng equaton to cacuate the beef about the operator seecton acton profe of other SUs at the begnnng of each tme sot t, b Dk (a Dk [t]) = θ D k (a Dk [t 1]) t 1 where θ Dk (a Dk [t 1]) = u {1,...,t 1} (9) Dr(a Dk [u] = a Dk [t 1]) s the number of tmes that SU D k observes actons a Dk [t 1] of other SUs durng the prevous t 1 tme sots and Dr( ) s the Drac deta functon. After updatng ts beef usng (9), each SU updates ts preference over operators and sub-bands usng (7) and (8), respectvey. The man dea of the above beef updatng rues s that each SU estmates the resutng matchng usng the frequency wth whch each matchng has been observed n the prevous hstory. Snce each SU cannot have any observaton hstory before the start of the spectrum access process, t s necessary for each SU to set a pror dstrbuton b Dk (a Dk [0]) at the begnnng of the process. Ths pror can be obtaned by aowng a SUs to go through a tranng process. More specfcay, a SUs can randomy choose ther operators to estabsh a pror dstrbuton durng the tranng perod. Note that the pror dstrbuton obtaned by each SU does not affect the ong-term earnng process of SUs because as each SU receves more and more observatons over tme, the effects of ths pror dstrbuton w be outweghed [9]. Let us present the Bayesan herarchca agorthm as foows: Agorthm 3: A Bayesan Herarchca Agorthm Intazaton: Each SU D k has a pror beef b Dk (a Dk [0]), WHILE the matchng of the forest matchng market s not stabe, 1) SUs enter the operator seecton sub-market and appy Agorthm 1 to fnd the stabe matchng M o, 2) After beng matched to the operators, SUs enter the sub-band seecton sub-market and appy Agorthm 2 to fnd the stabe matchng M b, 3) After a SUs are matched to the operators and subbands, they use equaton (9) to update ther beefs and then appy equatons (7) and (8) to update ther preferences about the operators and sub-bands at the begnnng of the next tme sot. ENDWHILE

10 XIAO et a.: BAYESIAN HIERARCHICAL MECHANISM DESIGN FOR COGNITIVE RADIO NETWORKS 995 Theorem 1: We have the foowng resuts about Agorthm 3: 1) For the resutng beefs of SUs, Agorthm 3 termnates n a unque and stabe matchng M, and the Bayesan herarchca mechansm assocated wth Agorthm 3 s ncentve compatbe for SUs. 2) Suppose the beef of each SU converges to a stabe probabty dstrbuton before tme sot t and matchng M[t] satsfes M[t] =M where M s the stabe matchng wth the resutng beef. Then M[τ] =M for a τ>t usng Agorthm 3. 3) The acton profe a acheved by Agorthm 3 s the unque and optma Bayesan Nash equbrum of the DSA game wth the resutng beefs. Proof: See Appendx C. In the rest of ths sub-secton, we derve the worst case compexty of Agorthm 3 n each teraton. Proposton 5: The compexty of Agorthm 3 n each teraton n the worst case s gven by O(L 2 N 2 K) for N =max {N }. =O Proof: See Appendx D. Note that, n practce, the number of operators n each specfc oca area s aways mted, e.g., most countres ony have three or four major teecommuncaton operators (e.g., there are 4 major mobe teecommuncaton operators that provde servces to cover most of the popuaton n n the Unted States.). Therefore, f we can regard L as a sma fxed nteger, the compexty of each teraton of Agorthm 3 n the worst case can be rewrtten as O(N 2 K). VI. EXTENSIONS AND FUTURE WORKS Our proposed Bayesan herarchca mechansm desgn and stabe forest matchng framework can be extended to more compex network systems. In ths secton, we descrbe how to extend our proposed framework nto the case wth PU networks consstng of more than two ayers (to be dscussed n Secton VI-A) and the case wth mutpe PUs and SUs sharng the same sub-band (to be dscussed n Secton VI-B). We w aso dscuss the possbe drectons of our future work n Secton VI-C. A. Bayesan Herarchca Mechansm Desgn for Systems Wth More Than Two Layers Some practca networks can consst of a herarchca structure wth more than two ayers. For exampe, the PU network can be a heterogenous network n whch each operator possesses mutpe co-ocated macro-ces, mcro-ces, and/or femto-ces. Each ce conssts of a base staton that contros the sub-band aocaton. In ths case, f each SU tres to access a sub-band, t needs to frst send the request to an operator and, once ts request s accepted, send the request to a base staton. The SUs can ony access the sub-bands after beng accepted by both the requestng operator and base staton. Snce the SUs cannot exchange nformaton wth each other, we can agan defne the nteractons of competng SUs as a Bayesan game. To desgn a dstrbuted mechansm that can approach the optma Bayesan Nash equbrum, we can mode the nteracton be- Fg. 4. A stabe forest matchng agorthm between SUs and the PU network wth more than two ayers. tween the SUs and the PU network as a forest matchng market. Specfcay, we can mode the PU network as a 3-ayer forest wth operators as roots and each base staton and ts correspondng sub-bands as a branch. A unque and stabe matchng between the SUs and each ayer of the forest structure can be acheved by the same two-sded matchng agorthms as dscussed n Sectons V-A and V-B. Each SU w update ts beef functon after beng matched wth a sub-band. We ustrate the reatonshp between dfferent matchng agorthms for a 3-ayer forest matchng mechansm n Fg. 4. Smary, we can appy our Bayesan herarcha mechansm desgn framework to optmze the system wth a forest structure consstng of more ayers. B. Aowng Mutpe SUs to Share the Same Sub-Band It can be observed that the spectrum utzaton effcency can be further mproved by aowng mutpe SUs to share the same sub-band. As mentoned prevousy, aowng mutpe SUs to access the same sub-band requres carefu desgn of the nterference contro rue for both SUs and PUs because even one SU wth hgh transmt power can cause ntoerabe nterference to a other SUs and PUs sharng the same sub-band. One way to support mut-su sub-band sharng n a CR network s to mpose a centrazed nterference contro mechansm by the operators. More specfcay, each operator can aow more SUs to access ts sub-bands,.e., q N, and keep montorng the nterference eve for each of the sub-band sharng PUs and SUs. We defne the set of sub-band sharng structures n each operator as the set of a aocaton schemes of q SUs to subbands n S. Each operator w need to frst evauate the resutng revenues for a N possbe sub-band sharng structures q and then choose the structure that can maxmze ts revenue. We can repace the confct-sovng rue defned n Secton V wth the above revenue-maxmzng sub-band sharng rues for each operator. We can then appy the same beef updatng methods n (9) for each SU to update ts beef functon after beng matched wth a sub-band and use equatons (7) and (8) to decde ts preferences over operators and sub-bands at the begnnng of the next tme sot.

11 996 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 5, MAY 2015 Fg. 5. A stabe forest matchng agorthm wth mutpe SUs sharng the same sub-band each of whch conssts of mutpe component carrers (CC) seecton agorthm. Another way s to ntroduce a dstrbuted coaton formaton agorthm for the SUs to form dfferent groups, each of whch corresponds to a set of SUs sharng the same sub-band. More specfcay, each SU after beng accepted by operator w not just estabsh a preference over a sub-bands n S but shoud estabsh a preference over a the possbe sub-band sharng structures. SUs can then form dfferent coatons accordng to ther preferences usng dstrbuted coaton formaton agorthms [17], [40], [41]. Note that, dfferent from Agorthm 2, for each SU to estabsh a preference over a the sub-band sharng structures, the SUs beng matched wth the same operator w need to coordnate and exchange nformaton before accessng any sub-bands of the operator. Our prevousy proposed herarchca matchng framework [42] can aso be apped to enforce mutpe SUs to share the same sub-band. To appy ths framework, each operator w further dvde each sub-band nto mutpe unts, referred to as component carrers (CC). Each SU w be frst aocated a CC usng the same sub-band seecton agorthm descrbed n Agorthm 2 (sub-band n Agorthm 2 shoud be repaced by CC). After beng aocated a CC, each SU can then decde whether to aggregate ts aocated CC wth the CCs of other SUs to further mprove ts performance. If mutpe SUs agree to form a subband sharng par, they w aggregate ther CCs nto a sub-band and share the sub-band wth each other. We can then mode the sub-band sharng probem as a roommate market where a SUs can be parttoned nto groups usng the stabe partton/ matchng agorthm proposed n [43], [44]. We descrbe the reatonshp of dfferent markets and correspondng agorthms of ths method n Fg. 5. C. Future Works From the prevous dscusson, t can be observed that our proposed stabe forest matchng agorthm s genera and can be apped to more compex systems. Our resuts aso pont towards some new drectons for future research. For exampe, n our mode, we many focus on the dstrbuted optmzaton of SUs and assume the confct-sovng rues of the operators are fxed. It has aready been proved n [30], [45], for a twosded matchng market that, f a operators can know each Fg. 6. Smuaton setup: we smuate the PU network as a ceuar network wth mutpe operators and the correspondng sub-bands. Each SU s a communcaton nk from a transmtter to a recever. We use to denote operators, to denote PUs and green coored and bue coored to denote the transmtter and recever of each SU, respectvey. other s preference as we as preferences of the SUs, they can adjust ther confct-sovng rues to further mprove ther performance. Therefore, one future drecton of our research s to study whether t s possbe for the operators to aso estabsh and mantan a beef functon to further mprove ther expected revenues n a dstrbuted fashon. Another potenta drecton for future work s to study the effect of aowng parta monetary transfers between PUs or SUs on the performance of CR networks [46], [47]. VII. NUMERICAL RESULTS In ths secton, we present numerca resuts to assess the performance of our agorthms and mechansms. Our proposed Bayesan herarchca agorthm s genera n the sense that each separate agorthm proposed for each of the sub-probems,.e., the operator and sub-band seecton sub-probems, can be ndvduay apped to optmze CR networks under dfferent condtons. More specfcay, f SUs cannot estabsh a preference over the operators but are randomy matched to the avaabe operators, they can st use the sub-band seecton agorthm and the assocated mechansm ntroduced n Secton V-B to optmze ther performance. We consder a CR network n Fg. 6 to smuate the nteracton between the SUs and the PU network wth a herarchca structure. We mode each SU as a transmsson nk (denoted as bue nes n Fg. 6) from a source (denoted as a bue crce n Fg. 6) to a destnaton (denoted as a green crce n Fg. 6), and the PU network as a ceuar system wth a number of operators randomy ocated around the center of the coverage area (denoted as back rectanges n Fg. 6) each of whch conssts of a fxed number of sub-bands and PUs (denoted as red tranges n Fg. 6). In a practca system, a communcaton nk between the source and destnaton shoud ony be enabed when the source and destnaton are cose enough. We hence assume the sources of the SUs are unformy randomy ocated n the coverage area and each destnaton s unformy randomy ocated

12 XIAO et a.: BAYESIAN HIERARCHICAL MECHANISM DESIGN FOR COGNITIVE RADIO NETWORKS 997 wthn a fxed radus of ts correspondng source. We aso assume a PUs are unformy randomy ocated n the coverage area. We focus on the upnk transmsson for the PU network and each PU corresponds to a transmsson nk from the PU to the correspondng operator. We consder the payoff and revenue functons defned n (2) and (4) n Sectons III and IV. Let the channe gan between the source and destnaton of SU D k n sub-band S be h Dk [S ] = h Dk [S ] d ξ D k [S ] where h Dk [S ] s a fxed channe fadng coeffcent, d Dk s the dstance between the source and destnaton of SU D k and ξ s the pathoss exponent. We aso consder the channe gan hdk between SU D k and PU P to be h Dk P = P where d ξ D k P h Dk P s the channe fadng coeffcent and d ξ s the D k P dstance between D k and P. In the remander of ths secton, we present numerca resuts to ustrate the performance of our proposed agorthm under dfferent condtons. We many compare the foowng four agorthms: 1) Random Seecton: SUs are randomy matched to the operators and sub-bands. 2) Operator Seecton: SUs are frst matched to the operators usng Agorthm 1 dscussed n Secton V-A. The SUs are then randomy matched to the sub-bands of ther operators. Ths corresponds to the stuaton that each operator refuses to reease a of ts sub-band nformaton to SUs. In ths case, each operator pre-seects a sub-band for each of the requestng SUs and ony aows each SU to evauate ts payoff n ts desgnated sub-band. Knowng the sub-band and the payoff that can obtan from the operators, each SU can then estabsh a preference over operators and then use Agorthm 1 to seect ts operator. 3) Sub-band Seecton: SUs are frst randomy matched to the operators. A SUs that are matched to the same operator w then try to be matched to the sub-bands usng Agorthm 2 ntroduced n Secton V-B. Ths may correspond to the case that the SUs cannot remember/store any prevous observatons about the sub-bands of the operators,.e., a memoryess system. 4) Herarchca Mechansm: SUs are matched to the operators and sub-bands by usng the Bayesan herarchca agorthm proposed n Secton V-C. Note that, as we have shown n Secton V-C, f the SUs can update ther beef functons usng (9), the acton profes of SUs can aways converge to the Bayesan Nash equbrum for the resutng beefs. In the rest of ths secton, we many focus on the case that SUs have aready obtaned ther beef functons. In Fg. 7, we fx the number of operators and compare the payoff sum of SUs under dfferent engths of the squareshaped coverage area, wth a range from 200 to 2000 meters. Our consdered coverage area covers the femtoce, pco-ce (< 200 meters), mcro-ce (> 200 meters) and macro-ce (> 1000 meters) systems [48]. We observe that the random seecton acheves the worst payoff among a mechansms. We fnd that ony mted payoff mprovement can be acheved f Fg. 7. The payoff sum of SUs for dfferent szed networks wth 50 SUs and 5 operators, each of whch contros 10 sub-bands. Every sub-band contans a PU whch s randomy ocated n the coverage area. Fg. 8. The number of spectrum sharng pars formed between SUs and PUs for dfferent szed networks wth 50 SUs and 5 operators, each of whch contros 10 sub-bands. Every sub-band contans a PU whch s randomy ocated n the coverage area. each SU ony appes the operator seecton agorthm. Ths s because, n our smuaton, the number of operators s mted and s much smaer than the number of sub-bands. Hence, the payoffs obtaned by randomy seectng sub-bands n dfferent operators are smar. However, f we appy sub-band seecton agorthm for SUs to fnd ther matchngs, the payoff can be sgnfcanty mproved. In other words, aso optmzng the subband seecton sub-probem among SUs provdes much hgher payoff mprovement than just optmzng the operator seecton sub-probem. We can aso observe that further performance mprovement can be acheved by appyng Bayesan herarchca mechansm proposed n Secton V-C. In Fg. 8, we consder the same settng as that of Fg. 7 and assume that a spectrum sharng par can ony be formed between an SU and a PU f both of ther payoffs and revenues exceed a fxed threshod. Agan, we observe that, comparng to the random seecton, the sub-band seecton aows more spectrum sharng pars to be formed between SUs and PUs.

13 998 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 5, MAY 2015 Fg. 9. The payoff sum of SUs under dfferent numbers of SUs where the system conssts of 5 operators, each of whch contros 10 sub-bands. Every sub-band contans a PU whch s randomy ocated n the coverage area. Fg. 11. The number of teratons requred for a SUs to converge to the optma Bayesan Nash equbrum. equbrum n Fg. 11. We observe that the convergence performance of our proposed agorthms n many practca systems can be much better than the worst case convergence performance dscussed n Secton V-C. In many practca CR networks, dfferent SUs have dfferent reatve dstances to PUs and hence aways resut n dfferent payoffs when accessng dfferent sub-bands and operators. Ony a mted number of SUs may choose the same preferred sub-band, and the chance of more than q SUs choosng the same operator s aso ow, even when the number of SUs grows arge. Therefore, our proposed mechansm has the potenta to sgnfcanty mprove the performance wth a fast convergence rate n some practca systems. VIII. CONCLUSION Fg. 10. The payoff sum of SUs under dfferent numbers of operators. We consder a system wth 120 PUs and 120 SUs, and each operator has 120 L PUs. In Fg. 9, we compare the payoff of SUs for dfferent numbers of SUs. We observe that f the number of SUs s sma, aowng SUs to use our proposed herarchca mechansm cannot provde much payoff mprovement compared to the random seecton. However, contnuousy ncreasng the number of SUs ncreases the competton among SUs for operators and subbands, and hence aowng SUs to use our proposed agorthm to optmze ther sub-bands, or operators, or both can sgnfcanty mprove ther payoffs. In Fg. 10, we fx the number of SUs and PUs and compare the payoff sum of SUs under dfferent numbers of operators. We observe that, by appyng the operator seecton agorthm, the payoff sum of SUs ncreases wth the number of operators. However, the payoff sum acheved by sub-band seecton decreases wth the number of operators. To study the convergence performance of our proposed herarchca mechansm, we present the number of requred teratons for SUs to approach the optma Bayesan Nash In ths paper, we study CR networks n whch the PU network has a herarchca structure consstng of a set of operators, each of whch has been censed a set of sub-bands. We mode the dynamc spectrum access of SUs n ths CR network as a Bayesan non-cooperatve game, caed DSA game. To deveop a dstrbuted mechansm for our proposed game, we propose a nove forest matchng market to mode the nteracton between the SUs and the PU network. We dvde the dynamc spectrum access probem for SUs nto two sub-probems: the operator and sub-band seecton sub-probems, and then propose operator and sub-band seecton agorthms to optmze these sub-probems. We combne these agorthms wth a Bayesan beef updatng agorthm and propose a Bayesan herarchca agorthm that can resut n a unque and stabe matchng that concdes wth the optma Bayesan Nash equbrum of our proposed DSA game. We prove that the Bayesan herarchca mechansm assocated wth our proposed agorthm can ncentvze true-teng by a SUs. APPENDIX A. Proof of Proposton 1 The proof of the above Proposton foows the same ne as that n [30]. We provde a bref descrpton of the proof

14 XIAO et a.: BAYESIAN HIERARCHICAL MECHANISM DESIGN FOR COGNITIVE RADIO NETWORKS 999 for competeness. From Step 2) n Agorthm 1, we can easy show that f an SU D k has been rejected by an operator, there mustexstateastq other SUs whch are strcty preferred by operator over SU D k, and hence any matchng between SU D k and operator must not be stabe. Usng ths observaton, we can aso estabsh that f an SU D k has been rejected by operator, a the SUs that are ess preferabe to operator than SU D k w aso be rejected by operator. Combnng the above two observatons, f q SUs and an operator are matched at the end of Agorthm 1, we can cam that there s no other SU that s more preferred by operator than the q SUs n the resutng matchng structure. Ths s from the fact that f such an SU, say D n, exsts, at east one of the SUs n the fna set of q SUs matched to operator w be rejected by operator n Agorthm 1. And, smary, each SU matched to operator cannot fnd another operator j that s more preferabe than operator n the resutng matchng structure, because f such an operator j exsts these SUs w not send a request message to operator. B. Proof of Proposton 2 In Agorthm 1, the worst case happens when a SUs can ony choose the east preferred operator after recevng (L 1) rejectons from the operators. In ths worst case, every SU w frst send requests to (L 1) most preferred operators and then receve rejectons from a of them. In ths case, the number of requests sent by K SUs s K(L 1), whch resuts n compexty of O(KL). C. Proof of Theorem 1 Frst, et us consder the frst part of resut 1). Combnng Propostons 1 and 3, we can cam that for the gven beefs at SUs, the matchngs resuted from both operator and sub-band seecton agorthms are unque and stabe. Snce Step 1 2) n Agorthm 3 s equvaent to Agorthms 1 and 2, the matchng acheved by Agorthm 3 s aso unque and stabe for the resutng beefs of SUs. We w present the proof of the second part of resut 1) at the end of ths proof. We now consder resut 2). If M[t] =M = M o,m b n tme sot t, we then have ϖ Dk (a D k,b Dk (a D k )) > ϖ Dk (a D k,b Dk (a Dk )) n tme sot t. Let us show that n the next tme sot t +1, each SU w stck wth M and w not change to other actons. In tme sot t +1,SUD k w update ts beef as foows: b Dk (a Dk [t +1])=αb Dk (a Dk [t]) +(1 α)dr (a Dk [t +1]), (10). We can then rewrte the updated payoff func- where α = ton of D k as t t+1 ϖ Dk (a Dk [t +1],b Dk (a Dk [t +1])) = α ϖ Dk (a Dk [t],b Dk (a Dk [t])) +(1 α) ϖ Dk (a Dk [t +1],b Dk (a Dk [t +1])), whch s a near combnaton of ϖ Dk [t] and ϖ Dk [t +1].Itcan be easy observed that choosng a Dk [t +1]=a Dk [t] =a D k maxmzes both payoff functons of SU D k. Ths process s repeated n the foowng tme sots. Let us consder resut 3). Frst, from the defnton of stabe matchng n Defnton 7, we can cam that for a gven stabe matchng M o or M b, no SU has the ntenton to devate from M o or M b by choosng another operator or sub-band. In addton, accordng to the defnton of stabe matchng, f M o s stabe, there s no other matchng M o such that D k and D n are matched to and j, respectvey, and aso satsfes j Dk and D k j D n. In other words, f two SUs can swtch ther seected operators or sub-bands to mprove ther payoffs, they are not n a stabe matchng. However, they may st be n the Bayesan Nash equbrum [10]. We hence can cam that, for both operator and sub-band seecton sub-markets, the payoff sum of SUs acheved by the acton profe of SUs n a stabe matchng equas or s greater than that acheved by the acton profe n a Bayesan Nash equbrum but not a stabe matchng. We can aso observe that Agorthms 1 and 2 are equvaent to a specfc deferred-acceptance agorthm n whch SUs send ther requests for the operators and sub-bands frst. Ths specfc agorthm s aso caed a deferred-acceptance agorthm wth SU proposng, whch has the foowng property. Proposton 6: If M o and M b are the resutng matchngs of the deferred-acceptance agorthm wth SU proposng for operator and sub-band seecton sub-markets, then we have the foowng resuts: 1) For the operator seecton sub-market, there s no other matchng M o such that M o (D k ) Dk M o (D k ) wth M o (D n ) Dn M o (D n ) for at east one D n D,2)For the sub-band seecton sub-market, there s no other matchng M b such that M b (D k ) Dk M b (D k ) wth M b (D n ) Dn M b (D n ) for at east one D n U where = M o (D n ).From the above resuts, we can cam that the matchng acheved by Agorthms 1 and 2 obtans the optma Bayesan Nash equbra. Let us consder the second part of resut 1). Usng the above resuts, we can show that f each beef profe of SUs corresponds to a unque acton profe, we can use the same method as n Proposton 1 to prove that there s no other acton profe for SUs that w provde hgher payoffs for SUs. In other words, msrepresentng the acton for each SU cannot provde any mprovement for ts payoff. Ths concudes the proof. D. Proof of Proposton 5 In each tme sot, a SUs needs to go through Steps 1) to 3) n Agorthm 3, whch contans Agorthm 1 wth a compexty of O(KL) and Agorthm 2 wth a compexty of O(N U ). O Usng the fact that N <N and U N, we can cam that each teraton of Agorthm 3 has a compexty of O(KLLN 2 ). ACKNOWLEDGMENT Yong Xao woud ke to thank Dr. Jean Honoro at the Massachusetts Insttute of Technoogy for hs hepfu dscusson n the eary stage of ths work.

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Jackson, Mechansm theory, optmzaton, and operatons research, n Encycopeda of Lfe Support Systems, U. Dergs, Ed. Oxford, U.K.: EOLSS, [22] B. Wang, Y. Wu, Z. J, K. R. Lu, and T. C. Cancy, Game theoretca mechansm desgn methods, IEEE Sgna Process. Mag., vo. 25, no. 6, pp , Nov [23] S. Sodagar, A. Attar, and S. Ben, Strateges to acheve truthfu spectrum auctons for cogntve rado networks based on mechansm desgn, n Proc. IEEE Symp. New Fronters DySPAN, Sngapore, Apr. 2010, pp [24] A. Gershkov, B. Modovanu, and X. Sh, Optma mechansm desgn wthout money, Unv. Toronto, Toronto, ON, Canada, Tech. Rep., [25] A. D. Procacca and M. Tennenhotz, Approxmate mechansm desgn wthout money, ACM Trans. Econ. Comput., vo. 1, no. 4, p. 18, Dec [26] R. Coe, V. Gkatzes, and G. Goe, Postve resuts for mechansm desgn wthout money, n Proc. Int. Conf. Auton. Agents Mut-Agent Syst., 2013, pp [27] D. Gusfed and R. W. Irvng, The Stabe Marrage Probem: Structure and Agorthms. Cambrdge, MA, USA: MIT Press, [28] D. 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Hjorungnes, Hedonc coaton formaton for dstrbuted task aocaton among wreess agents, IEEE Trans. Mobe Comput., vo. 10, no. 9, pp , Sep [42] Y. Xao, K. C. Chen, C. Yuen, and L. A. DaSva, Spectrum sharng for devce-to-devce communcatons n ceuar networks: A game theoretc approach, n Proc. IEEE Int. Symp. New Fronters DySPAN, Apr. 2014, pp [43] K. Cechárová and T. Fener, On a generazaton of the stabe roommates probem, ACM Trans. Agorthms, vo. 1, no. 1, pp , Ju [44] J. J. Tan, A necessary and suffcent condton for the exstence of a compete stabe matchng, J. Agorthms, vo. 12, no. 1, pp , Mar [45] P. Bró and G. Norman, Anayss of stochastc matchng markets, Int. J. Game Theory, vo. 42, no. 4, pp , Nov [46] T. Fener, A fxed-pont approach to stabe matchngs and some appcatons, Math. Oper. Res., vo. 28, no. 1, pp , Feb [47] J. W. Hatfed and P. R. Mgrom, Matchng wth contracts, Amer. Econ. Rev., vo. 95, no. 4, pp , Sep [48] A. Godsmth, Wreess Communcatons. Cambrdge, U.K.: Cambrdge Unv. Press, Yong Xao (S 11 M 13) receved the B.S. degree n eectrca engneerng from Chna Unversty of Geoscences, Wuhan, Chna, n 2002, the M.Sc. degree n teecommuncaton from Hong Kong Unversty of Scence and Technoogy n 2006, and the Ph.D degree n eectrca and eectronc engneerng from Nanyang Technoogca Unversty, Sngapore, n From August 2010 to Apr 2011, he was a Research Assocate at the Schoo of Eectrca and Eectronc Engneerng, Nanyang Technoogca Unversty, Sngapore. From May 2011 to October 2012, he was a Research Feow at CTVR, Schoo of Computer Scence and Statstcs, Trnty Coege Dubn, Ireand. Currenty, he s a MIT-SUTD Postdoctora Feow wth Sngapore Unversty of Technoogy and Desgn and Massachusetts Insttute of Technoogy. Hs research nterests ncude machne earnng, economc modes and ther appcatons n communcaton networks.

16 XIAO et a.: BAYESIAN HIERARCHICAL MECHANISM DESIGN FOR COGNITIVE RADIO NETWORKS 1001 Zhu Han (S 01 M 04 SM 09 F 14) receved the B.S. degree n eectronc engneerng from Tsnghua Unversty, n 1997, and the M.S. and Ph.D. degrees n eectrca engneerng from the Unversty of Maryand, Coege Park, MD, USA, n 1999 and 2003, respectvey. From 2000 to 2002, he was an R&D Engneer at JDSU, Germantown, MD, USA. From 2003 to 2006, he was a Research Assocate at the Unversty of Maryand. From 2006 to 2008, he was an Assstant Professor at Bose State Unversty, Bose, ID, USA. Currenty, he s an Assocate Professor n the Eectrca and Computer Engneerng Department, Unversty of Houston, Houston, TX, USA. Hs research nterests ncude wreess resource aocaton and management, wreess communcatons and networkng, game theory, wreess mutmeda, securty, and smart grd communcaton. He s an Assocate Edtor of IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS snce He s the wnner of the 2011 IEEE Fred W. Eersck Prze. He receved the NSF Career Award n Luz A. DaSva (SM 14) currenty hods the Stokes Professorshp n Teecommuncatons n the Department of Eectronc and Eectrca Engneerng, Trnty Coege Dubn. He has aso been a facuty member n the Bradey Department of Eectrca and Computer Engneerng at Vrgna Tech snce Hs research focuses on dstrbuted and adaptve resource management n wreess networks, and n partcuar cogntve rado networks and the appcaton of game theory to wreess networks. He s currenty a Prncpa Investgator on research projects funded by the Natona Scence Foundaton n the Unted States, the Scence Foundaton Ireand, and the European Commsson under Framework Programme 7. He s a Coprncpa Investgator of CTVR, the Teecommuncatons Research Centre n Ireand. He has co-authored two books on wreess communcatons and over 150 peer-revewed papers n eadng journas and conferences on communcatons and networks. In 2006, he was named a Coege of Engneerng Facuty Feow at Vrgna Tech. Kwang-Cheng Chen (M 89 SM 94 F 07) receved the B.S. degree from the Natona Tawan Unversty n 1983, and the M.S. and Ph.D. degrees from the Unversty of Maryand, Coege Park, MD, USA, n 1987 and 1989, a n eectrca engneerng. From 1987 to 1998, he worked wth SSE, COMSAT, IBM Thomas J. Watson Research Center, and Natona Tsng Hua Unversty, n mobe communcatons and networks. Snce 1998, he has been wth Natona Tawan Unversty, Tape, Tawan, ROC, and s the Dstngushed Professor and Assocate Dean n academc affars for the Coege of Eectrca Engneerng and Computer Scence, Natona Tawan Unversty. He has been actvey nvoved n the organzaton of varous IEEE conferences as Genera/TPC char/co-char. He has served n edtorshps wth a few IEEE journas and many nternatona journas and has served n varous postons wthn IEEE. He aso actvey partcpates n and has contrbuted essenta technoogy to varous IEEE 802, Buetooth, and 3GPP wreess standards. He has authored and co-authored over 250 technca papers and more than 20 granted US patents. He co-edted (wth R. DeMarca) the book Mobe WMAX (Wey, 2008) and authored the book Prncpes of Communcatons (Rver, 2009) and co-authored (wth R. Prasad) another book Cogntve Rado Networks (Wey, 2009). Hs research nterests ncude wreess communcatons and network scence. He s an IEEE Feow and has receved a number of awards ncudng the 2011 IEEE COMSOC WTC Recognton Award and has co-authored a few award-wnnng papers pubshed n the IEEE Communcatons Socety journas and conferences.

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