Risk-aware Cooperative Spectrum Access for Multi-Channel Cognitive Radio Networks

Transcription

1 1 Rk-aware Cooperatve Spectrum Acce for Mult-Channel Cogntve Rado Network Nng Zhang, Student Member, IEEE, Nan Cheng, Student Member, IEEE, Nng Lu, Student Member, IEEE, Habo Zhou, Student Member, IEEE, Jon W. Mark, Lfe Fellow, IEEE, Xuemn (Sherman) Shen, Fellow, IEEE Abtract In th paper, rk-aware cooperatve pectrum acce cheme for cogntve rado network (CRN) wth multple channel are propoed, whereby multple prmary uer (PU) operatng over dfferent channel chooe trutworthy econdary uer (SU) a relay to mprove throughput, and n return SU gan tranmon opportunte. To tudy the mult-channel cooperatve pectrum acce, cooperaton over ngle channel nvetgated frt, whch nvolve a PU electng the utable SU and grantng a perod of acce tme to the elected SU a a reward, conderng trutworthne of SU. The above procedure modeled a a Stackelberg game, through whch acce tme allocaton and power allocaton are obtaned. Baed on the above reult, cooperaton over multple channel tuded from the perpectve of the prmary network and econdary network, repectvely. Two cheme are propoed accordngly: the prmary network-centrc matchng (PCM) cheme and the econdary network-centrc cluter-baed (SCC) cheme. In PCM cheme, cooperatng SU for each channel determned to maxmze the total utlty of the prmary network, whch formulated a a maxmum weght matchng problem. In SCC cheme, SU frt form a cluter to hare the channel tate nformaton (CSI), and the bet SU are elected for cooperaton wth PU over dfferent channel to obtan the maxmum aggregate acce tme for the econdary network. Then, SU hare the obtaned reource ung congeton game and quadrature gnallng. Numercal reult demontrate that, wth the propoed cheme, PU can acheve hgher throughput, whle SU can obtan longer average acce tme, compared wth the random channel acce approach. Index Term Cogntve rado, tackelberg game, congeton game, maxmum weght matchng. I. INTRODUCTION Wth the rapd growth n wrele applcaton and ervce, the demand for the pectrum alo rng dramatcally, whch ncreangly dffcult to meet due to the carcty of pectrum reource. Currently, pectrum agned to lcened uer on a long term ba to avod nterference among dfferent wrele ytem. However, t recognzed that the lcened pectrum underutlzed nce lcened uer typcally do not fully utlze ther allocated pectrum mot of the tme [1] []. On the other hand, unlcened uer are beng tarved for pectrum avalablty. To cope wth uch a dlemma, cogntve rado ha been ntroduced to enhance pectrum utlzaton by N. Zhang, N. Cheng, N. Lu, Jon W. Mark and X. Shen are wth the Department of Electrcal and Computer Engneerng, Unverty of Waterloo, 00 Unverty Avenue Wet, Waterloo, ON NL 3G1, Canada (e-mal:{n35zhang, n5cheng, n7lu, jwmark, hen}@uwaterloo.ca). H. Zhou wth the Department of Electrcal Engneerng, Shangha Jao Tong Unverty, Shangha, 0040, Chna (e-mal:habozhou@jtu.edu.cn). enablng unlcened uer to opportuntcally utlze the pectrum band [3] [6]. In cogntve rado networkng, lcened uer and unlcened uer are referred to a prmary uer (PU) and econdary uer (SU), repectvely. Tradtonally, SU need to dentfy dle pectrum band (or pectrum hole) va pectrum enng before commencng tranmon [7] [8]. However, pectrum enng energy-conumng and may not be accurate due to channel fadng or hadowng. Moreover, the SU ha to termnate the ongong tranmon once t detect that the pectrum band re-occuped by a PU, makng SU tranmon hghly dynamc [9] [10]. To deal wth the aforementoned ue, cooperatve pectrum acce ha been propoed n cogntve rado network (CRN) [11] [16], whereby SU cooperate wth PU to mprove latter tranmon performance, and n return gan tranmon opportunte. Therefore, both PU and SU can beneft from cooperaton, whch create a wn-wn tuaton. Wth uch cooperaton between PU and SU, cogntve rado network ha alo been referred to a cooperatve CRN (CCRN). Unlke the enng baed pectrum acce, where SU are tranparent to PU, the preence of SU can be recognzed by PU n CCRN. In [11], the PU leae a fracton of acce tme to SU n exchange for cooperaton to ncreae the tranmon rate, and durng the rewardng tme the SU tranmt multaneouly by electng utable tranmon power. In [1], SU cooperate to mprove the PU tranmon rate and hare the rewardng reource va a payment mechanm. A two-phae cooperaton cheme propoed n [13], whereby the PU tranmt t gnal to the SU n the frt phae, and then the SU decode the receved gnal and upermpoe t wth t own gnal to broadcat n the econd phae, ung dfferent power level. In [16], dfferent cooperaton cheme are propoed, whereby the PU can cooperate wth trutworthy SU to enhance t ecurty level and SU can gan tranmon opportunte. However, all the above work only conder cooperaton at the tranmon lnk,.e., one par of PU and SU(), whch mght not be uffcent to explot the cooperaton beneft n the whole network. Th becaue there ext multple lnk n the network, whch caue competton among PU when they chooe SU. In [17], the author conder multple PU performng cooperaton wth multple SU n the network, where the tranmon of PU are dvded nto dfferent frame and dfferent par of PU and SU perform cooperaton over dfferent frame. However, t tll lmted to a ngle channel. In practce, a ytem uually cont of multple channel, allowng uer to communcate multaneouly. Therefore, a

2 more realtc cenaro that cooperaton among multple PU and multple SU could be performed over dfferent channel multaneouly. However, the extng oluton mght not be applcable, nce they are degned ether for one par of PU and SU or multple PU and multple SU over one channel. Moreover, t often aumed that SU are well-behaved durng cooperaton. When there ext ome dhonet uer, or even malcou one, thoe SU can partcpate n cooperaton, and hence cooperaton may ncur rk. In th paper, we make an effort to facltate cooperaton for mult-channel CRN, where PU operatng over dfferent channel cooperate wth SU to mprove throughput and grant rewardng acce tme to cooperatng SU for ther own tranmon. To tudy the mult-channel cae, cooperaton over ngle channel tuded frt, whch modeled by Stackelberg game. To evaluate the rk of cooperaton wth certan SU, the concept of trut value ntegrated nto the game. By analyzng uch a game, the cooperaton parameter for a par of PU and SU can be obtaned, e.g., the acce tme allocaton coeffcent of the PU and the optmal tranmon power of the SU. Baed on the outcome of the Stackelberg game, cooperaton over multple channel n the network tuded to maxmze the total network utlty from dfferent perpectve. From the perpectve of the prmary network, the objectve to maxmze the PU aggregate throughput of dfferent channel. From the perpectve of the econdary network, the objectve to maxmze the aggregate rewardng acce tme of dfferent channel. Two cheme are propoed accordngly: the prmary network-centrc matchng (PCM) cheme and the econdary network-centrc cluter-baed (SCC) cheme. In PCM cheme, cooperatng SU over each channel are determned to maxmze the total utlty of the prmary network, whch formulated a a maxmum weght matchng problem. In SCC cheme, to better explot tranmon opportunte, SU frt form a cluter baed on geographc locaton, perform cooperaton wth PU to obtan the tranmon opportunte over dfferent channel ung the approach for ngle channel cae, and then hare them. To obtan the maxmum aggregate acce tme, the bet SU for cooperaton wth PU over dfferent channel are determned ung maxmum weght matchng. To hare the obtaned acce channel wth dfferent rewardng tme farly, SU follow an approach ung congeton game and quadrature gnallng. Specfcally, actve SU, whch partcpate n cooperaton wth PU a relay, tay n the current operatng channel and employ the n-phae component of quadrature ampltude modulaton (QAM) for tranmon; whle nactve SU,.e., other SU whch are not elected a relay, chooe acce channel for ther own nteret by followng Nah Equlbrum (NE) of the congeton game and employ the quadrature component of QAM for tranmon. By employng quadrature gnallng, the actve and nactve SU can acce channel multaneouly wthout nterference wth each other [18]. Wth congeton game, each nactve SU can gan certan tranmon opportunte, and more mportantly, n a far way. The contrbuton of th work can be ummarzed a follow. Frt, we tudy cooperaton for mult-channel CRN; and we argue that the extng ngle channel reult are Fgure PU 1 PU PU j SU p SU t SU Cooperatve cogntve rado network wth multple channel neffcent when applyng to mult-channel cenaro. Second, we ntegrate the trutworthne of SU n the cooperaton to facltate the degn of rk-aware cheme. Thrd, cooperaton over multple channel tuded to maxmze the total utlty of the prmary network ung maxmum weght matchng. Fnally, a cluter-baed approach for SU to explot tranmon opportunte over multple channel propoed, whch ntegrate congeton game wth quadrature gnallng for cluter member to acce the rewardng reource. The remander of the paper organzed a follow. The detaled decrpton of the ytem model gven n Secton II. Cooperaton over ngle channel and multple channel are tuded n Secton III and Secton IV, repectvely. Concludng remark are provded n Secton V. II. SYSTEM MODEL Th ecton preent the detal of the cooperatve cogntve rado networkng model under conderaton, together wth the man ytem parameter, hown n Table I. A. MAC Layer A hown n Fg. 1, the ytem cont of two component, the nfratructure-baed prmary network and the ad hoc econdary network. The prmary network wth multple channel (K channel) allow K PU to tranmt data multaneouly. Each PU communcate wth the bae taton (BS) over one channel n a tme lot wth length T, and the PU over a ceratn channel can be ndcated by the channel ndex, e.g., P U j denote the PU operatng over channel j, where j {1,,..., K}. In the econdary network, SU tranmt data to the correpondng recever. Motvated by the poor qualty of the prmary lnk or large volume of data tranmon requrement, PU may eek for the opportunte to cooperate wth SU to ncreae the throughput. For cooperaton, one PU elect one SU a a relay whch adopt the Amplfyand-Forward (AF) mode [19] to forward the PU meage to mprove the throughput 1. In return, the PU grant a perod of acce tme a a reward to the cooperatng SU. Specfcally, for a gven channel, e.g., channel j, the cooperaton between 1 The analy for Decode-and-Forward (DF) mode mlar to that of AF mode. Hence, we only focu on AF cooperatve cheme n the paper. BS

3 3 Table I THE MAIN NOTATIONS. Symbol N M K α (j) Up(j) U(j) Pc(j) h p(j) h pb (j) h b h P T r Ψ U j n ζ(n ) n(s) Decrpton The et of SU n the cluter, N = N The et of nactve SU n the cluter, M = M The et of channel n the network, K = K The acce tme allocaton coeffcent when the PU on channel j cooperate wth SU The utlty functon of the PU on channel j when cooperatng wth SU n Stackelberg game The utlty functon of SU when cooperatng wth the PU on channel j n Stackelberg game The tranmon power of the PU on channel j when cooperatng wth SU The channel gan from P U j to SU The channel gan from P U j to the bae taton The channel gan from SU to the bae taton The channel gan from SU to the correpondng econdary recever The tranmon power of SU The trut value of SU The duraton of the rewardng acce tme of channel The utlty of SU n the congeton game The total number of nactve SU choong channel n congeton game The hare of channel whch each SU electng that channel can obtan The congeton vector correpondng to trategy profle S P U j and SU carred out n the followng way. A fracton α (j) of the tme lot duraton T (0 < α (j) 1) ued for cooperatve communcaton. Note that for α (j), correpond to SU and j correpond to channel j or P U j. In the frt duraton of α(j)t, P U j tranmt data to SU, and n the ubequent duraton of α (j)t, SU relay the receved data to BS. In the lat perod of (1 α (j))t, whch the rewardng tme, the cooperatng SU tranmt t own data to the correpondng econdary recever. A common control channel aumed for exchangng nformaton among PU, SU, and BS (e.g., CSI), and for delverng the decon of the PU to the econdary network. B. Phycal Layer The channel between node are modeled a raylegh blockfadng channel, contant wthn each lot and varyng over dfferent lot. The channel gan from P U j to BS, from P U j to SU, from SU to BS, and from SU to t correpondng econdary recever are denoted by h pb (j), h p(j), h b, and h, repectvely. Smlar to [11] [13], [0], the channel tate nformaton (CSI) aumed avalable n the ytem, whch can be obtaned by perodcal plot. The bandwdth for each channel W. For cooperaton, P U j chooe power Pc(j) for the tranmon from P U j to SU. SU contraned to pend the ame power P for both the cooperaton and t own tranmon o a to enure that SU pend at leat the ame power for cooperaton a whch t wllng to pend for t own tranmon. The one-ded power pectral denty of the ndependent addtve whte Gauan noe. C. Securty Threat If all the SU are well-behaved, both PU and SU can beneft from ther cooperaton. However, when there ext ome dhonet or malcou SU, the normal operaton of CCRN cannot be guaranteed. Specfcally, the followng ecurty ue arng n CCRN need to be condered. Durng cooperaton, the malcou SU can alter the packet from the PU or fabrcate packet and then forward them to the detnaton. A legtmate SU may be compromed and mbehave when t elected to cooperate wth the PU, e.g., t may launch black or grey hole attack, etc. A dhonet SU may not obey the cooperaton rule durng cooperaton to purue more elf-beneft, e.g., t may tranmt t own packet ntead of relayng the packet from the PU. Moreover, conderng the moblty of SU, the malcou or dhonet SU may mbehave at one place and then move to other place. Snce there no record of the pat behavor, thee uer can have the ame opportunty to be elected to cooperate wth the PU, and then contnue to harm the ytem. A a ummary, we lt the potental mbehavor n CCRN a follow. 1) Selfhne: the cooperatng SU may chooe a lower tranmon power than the expected one durng cooperaton or t jut chooe not to forward the PU meage to ave energy. ) Malcoune: the malcou SU may delete, modfy or replace the bt n the DF mode. In AF mode, t may ntentonally add ome jammng gnal to corrupt the PU gnal. 3) Dhonety: the dhonet SU may provde fake CSI to gan tranmon opportunte. Wthout conderng thee ecurty threat, the PU may chooe an untrutworthy SU for cooperaton, whch may caue the falure of cooperaton and degrade the QoS of PU. III. COOPERATION OVER SINGLE CHANNEL In th ecton, we wll dcu the cooperaton between a PU and an SU over channel j. Snce we focu on a ngle channel, for eae of preentaton, the channel ndce n related notaton are omtted, e.g., α (j) become α, h p(j) become h p, and o on. Due to the poor channel condton or the traffc requrement, the PU may dere hgher throughput whch the

4 4 drect tranmon cannot acheve. In th cae, the PU can chooe an SU to act a a cooperatng relay to ncreae t throughput, whle n return grant a perod of acce tme to the SU. Therefore, the cooperaton can be performed on a ba of mutual beneft, where the PU can ncreae t throughput whle the SU can gan tranmon opportunte. To evaluate the rk of cooperaton, trut value appled and the above cooperaton procedure modeled ung Stackelberg game. In uch a game, the utlte of both the PU and the SU are preented and analyzed. By analyzng the game, the cloe-form oluton for the player bet tratege are derved, whch conttute the Stackelberg equlbrum. A. Trut Computatonal Model In an unfrendly envronment, the aforementoned ecurty ue may re, whch cannot be well mtgated by mean of cryptographc methodologe [1]. Thu, trut and reputaton ytem appled to addre thee ue []. Specfcally, trut value are agned to SU and utlzed to evaluate the behavor of SU. The prmary ytem mantan a table for recordng dentte and the correpondng trut value of t one-hop neghborng SU. In addton, BS keep the trut value of all SU n t doman. Each tme after cooperaton, the behavor of the elected SU wll be evaluated and the trut value wll be updated accordngly. Then, the trut value wll be exchanged perodcally between the PU and the BS. We ue a Bayean framework [3] [4] to evaluate the trut value: each entty aumed to behave well wth probablty p, and mbehave wth probablty (1 p),.e., the behavor of the entty follow a Bernoull dtrbuton. Through a ere of obervaton, a poteror probablty can be derved to etmate the future behavor of the entty. Poteror probablte of bnary event can be repreented a the beta dtrbuton. An expreon of the probablty denty functon (PDF) f( ˆp κ, ι) n term of the gamma functon Γ gven by: f(ˆp κ, ι) = Γ(κ + ι) Γ(κ) Γ(ι) ˆp(κ 1) (1 ˆp) (ι 1), (1) where ˆp the etmate of p, and κ, ι are the two parameter. The expectaton of beta dtrbuton gven by E(ˆp) = κ (κ+ι), whch can be ued to repreent the trut value of the relevant entty. In our ytem, a malcou or dhonet SU behave well wth probablty p and mbehave wth probablty 1 p. In order to etmate the trutworthne of SU, BS need to oberve the ongong tranmon and evaluate the actvte of SU accordng to the receved gnal. To determne whether the relayng SU mbehave or not, one approach to utlze tracng ymbol, whch are known at both the ource and the detnaton [5] [6]. Another way baed on the correlaton between gnal receved from the ource and the relay [7]. In addton, the mbehavor can alo be detected baed on the ucce or falure of tranmtted frame va acknowledgment (ACK/NACK) [8]. Baed on extng work n the lterature, t aumed that the mbehavor of relayng node can be detected. Conder a proce wth two poble outcome (mbehavor or well-behavor), and let µ and ν be the oberved number of good behavor and mbehavor, repectvely. Then, the PDF of obervng outcome n the future can be expreed a a functon of pat obervaton by ettng: κ = µ + 1 and ι = ν + 1. Thu, the expected value of ˆp can be determned from obervaton a follow: E(ˆp) = µ + 1 (µ + ν + ), () whch ued a the trut value T r of SU. When new obervaton of a partcular SU are made, e.g., δ oberved mbehavor and ξ oberved good behavor, the aocated trut value can be updated ung () by ettng ν := ν + δ and µ := µ + ξ. B. Stackelberg Game between PU and SU Snce the prmary uer and econdary uer are elfh and ratonal, they mght not have a common objectve,.e., the PU and the SU are ntereted n maxmzng ther own utlte. Thu, game theory can be appled to model the nteracton between the two uer. Moreover, conderng dfferent prorte for pectrum uage of PU and SU, Stackelberg game mot utable to model the cooperaton procedure. In the Stackelberg game, the PU act a the leader and the SU act a the follower. A the leader, the PU can chooe the bet tratege, aware of the effect of t decon on the tratege of the follower (the SU); whle the SU can jut chooe t own tratege gven the elected parameter of the PU. The utlty functon for both PU and SU are repectvely defned n the followng. By analyzng the game, the bet cooperatng SU and the optmal cooperaton parameter can be determned. 1) Prmary Uer: Gven a fxed tme duraton T, ncreang the throughput equvalent to ncreang the average tranmon rate. To th end, the PU elect the mot utable SU from the et S p of t one-hop neghbor. Suppoe that SU choen for cooperaton, the PU decde the lot allocaton parameter α and t tranmon power P c to maxmze the potental proft, on the ba of avalable ntantaneou CSI. Wthout cooperaton, the tranmon rate of the drect communcaton can be gven by R d = W log (1 + P h pb ). (3) For cooperaton, the tranmon rate R c through AF cooperatve communcaton between the PU and SU gven a follow: R c = α W where f(pc h p log [1 + P c h pb + f(pc, P h b h p, P h b h b )], (4) ) = 1 Pc h p P h b Pc h p + P. + The factor α account for the fact that α T ued for cooperatve relayng, whch further plt nto two phae. The PU chooe cooperaton only when the tranmon rate va cooperaton greater than that of the drect communcaton. Conderng the trut value T r of each neghborng SU, the

5 5 utlty functon gven by U p = T r R c, (5) whch ndcate the expected tranmon rate the PU can acheve through cooperaton wth SU. The objectve of the PU to maxmze t utlty functon and the trategy to chooe the mot utable SU from the et of t one-hop neghborng SU and the cooperaton parameter,.e., the lot allocaton parameter α and the tranmon power Pc for cooperaton wth the elected SU. ) Secondary Uer: The SU can gan tranmon opportunte through cooperaton wth the PU. In partcular, the SU relay PU data n the econd phae and tranmt t own data n the lat phae. Aumng cooperaton wth the PU, the elected SU decde t tranmon power, pertanng to the gven α. The target of the SU to maxmze throughput (equvalent to the tranmon rate) wthout expendng too much energy. Followng the cooperaton agreement, SU pend the ame power P for both cooperatve and econdary tranmon. In partcular, the tranmon rate R for econdary tranmon between SU and t correpondng recever gven by h R(α ) = (1 α )W log (1 + P ). (6) Wth energy conumpton P(1 α )T, the utlty functon of SU can be repreented by R(α )T c P(1 α )T, where c (0 < c < 1) the weght of energy conumpton n the overall utlty. Wth a maller c, the SU value throughput more than energy conumpton, and vce vera. Over the perod of T, the utlty functon of SU gven by U (α ) = W log (1 + P h )(1 α ) c(1 α )P. (7) The objectve of SU n the game to maxmze t utlty by choong the optmal tranmon power P. C. Game Analy A a equental game, the Stackelberg game can be analyzed by the backward nducton method. Frt, the optmal trategy of the SU (the follower) analyzed, aumng the trategy of the PU (the leader) fxed. Second, the PU decde the optmal trategy, aware of the outcome of the frt tep. By dong o, the bet repone functon of both the PU and the SU are derved uch that the correpondng utlte can be maxmzed. Then, the Stackelberg equlbrum of the propoed game can be acheved baed on the bet repone functon. 1) Bet Repone Functon of the SU: Aumng that the PU ue α for cooperaton, SU elect the optmal tranmon power to maxmze t utlty, whch can be formulated a the followng optmzaton problem: max P U (α ) = (1 α )W log (1 + P h.t. 0 P P max, ) c(1 α )P where P max the power contrant for SU. Solvng the above problem, the optmal tranmon power can be determned. Defnton 1: Let P (α ) be the bet repone functon of the econdary uer f the utlty of SU can acheve the maxmum value when P (α ) elected, for any gven α,,e., 0 < α < 1, U(P (α ), α ) U(P (α ), α ). Theorem 1: The bet repone functon of the econdary uer P (α ) gven by P (α ) = mn{ (1 α )W c(1 α ) ln h, P max }, when the prmary uer elect a certan α for cooperaton. Proof: Gven the tme allocaton coeffcent α, the utlty functon of SU gven a follow: U(α ) = (1 α )W log (1 + P h ) c(1 α )P. (8) From the above equaton, t eay to prove that the utlty functon frt ncreae and then decreae wth the ncreae of P wthout conderng the power contrant. Therefore, there ext an optmal power uch that U can reach the maxmum value at that tranmon power. Takng the frt order partal dervatve of the utlty functon wth repect to P yeld U P = (1 α )W h (1 + P h ) ln c(1 α ). (9) Settng (U ) (P ) = 0 yeld the optmal tranmon power, whch gven by (1 α )W c(1 α ) ln h. (10) Takng the power contrant nto conderaton, the bet repone functon P (α ) wll be P (α ) = mn{ (1 α )W c(1 α ) ln h, P max}. (11) Th complete the proof. The frt order dervatve of the bet repone functon wth α repect to α gven by W, whch negatve. ( +a) c ln ) Therefore, the bet tranmon power of SU a decreang functon of α. It explaned by that the SU wllng to pend more tranmon power durng cooperaton f the PU allocate more tme for the SU tranmon. ) Bet Repone Functon of the PU: Aware of the bet repone functon of the SU, the PU decde t own bet trategy for utlty maxmzaton. Thu, the bet repone functon can be derved by olvng the followng optmzaton problem: max α,pc, α W log [1 + P c h pb + f(pc h p, P.t. 0 < Pc P max, 0 < α 1, SU S p. h b )] Defnton : Let α, Pc, be aocated wth the bet repone functon of the prmary uer f the utlty of the PU can acheve the maxmum value when th trategy elected. Theorem : The bet repone functon of the prmary uer α, Pc, can be gven by (α, Pc, ) = arg max α,pc, Up. In partcular, = arg max Up(P c, α ), where P c = P max

6 6 W (15), f α c ln N0 h < P = max max{ + c ln W (Pmax+ ), (15)}, otherwe h (1) Pc and α are the optmal tranmon power and tme allocaton coeffcent repectvely, aumng cooperaton wth SU. The optmal Pc and α correpond to the elected. Proof: Snce the frt order dervatve of the utlty functon wth repect to Pc alway potve, U p a monotoncally ncreang functon a Pc ncreae. Moreover, conderng the parameter Pc and α are ndependent, Pc hould be elected a the maxmum power o that the utlty can reach the maxmum value. Therefore, to olve the optmzaton problem, t equvalent to optmze the utlty functon when Pc = P max and SU elect the bet repone P (α ). Snce the frt term n (11) monotoncally decreae wth repect to α, t maxmum value W W c ln N0. h When c ln N0 < P h max, P (α ) alway take the value of the frt term n (11). Subttutng Pc = P max and P (α ) = (1 α )W N c(1 α 0 nto the utlty functon of PU, ) ln h the utlty can be expreed by Up = α W log [1 + P max h pb + f(p max h p, P (α ) h b )], (13) whch a functon of α. The frt order dervatve of (13) gven by U p α = A α + B α + C, (14) where A =P max h p c + W h b + c B = P max h p c 4W h b c = A C =W h b. To fnd the optmal α uch that U p can be maxmzed, et frt order dervatve of (13) equal to 0. Snce C < A, we have B 4AC > 0. Thu, the above quadratc functon ha real root(). Conderng the range of α (0 < α < 1), there ext one and only one root α r. The optmal α gven by α = α r = 1 1 C A = 1 W h 1 b P max h p c + W h b + N0 c W (15) When c ln N0 P h max, there ext α 0 n the range from 0 to 1, uch that P (α 0 ) = P max. Specfcally, α 0 = + c ln D, where D = W (P max + ). The reaon that h the range of D from 0 to 1 due to the aumpton that W c ln P h max. For α α 0, P (α ) alway take the value of P max. Hence, Up reache the maxmum value n that range when α 0 choen. For α 0 < α 1, there ext one and only one root α r for the above quadratc functon, whch n the range from 0 to 1. If α r < α 0, then Up α < 0 when α 0 < α 1. The dervatve of U p wth repect to α monotoncally decreang. Thu, the optmal α = α 0. Otherwe, the optmal α = α r. Baed on the above analy, the optmal α a (1) n the theorem. Th complete the proof. D. Extence of the Stackelberg Equlbrum can be gven In th ecton, we prove that the oluton P n (11) and α n (1) are the Stackelberg Equlbrum. For th purpoe, we dcu the two cae wth/wthout conderng the power contrant of the SU ung the followng properte. The detaled proof for the properte can be found n Appendx. Baed on the properte, we frt prove the extence of Stackelberg Equlbrum when the power contrant not condered. Property 1. The utlty functon U of the SU concave wth repect to t own power level P when the tme allocaton coeffcent α fxed. For both cae, Property 1 alway hold, whch how the concavty of the utlty functon of the SU. Due to Property 1, U concave wth repect to P. Wthout conderng the power contrant, ettng (U ) (P ) = 0 yeld the optmal tranmon power P, whch gven n (10). Wth P n (10), the SU can maxmze t utlty U. For the cae wthout conderng the power contrant, we alo have the followng properte. Property. For all SU, the optmal tranmon power P n (10) decreae wth the tme allocaton coeffcent α. Property 3. The utlty functon of the prmary uer concave wth repect to the tme allocaton coeffcent α, gven that the optmal tranmon power P of the SU n (10) fxed. Due to Property, there a trade-off for the PU to elect the tme allocaton coeffcent α. When the PU allocate le tme to the cooperatng SU for tranmon, the SU wll chooe a lower tranmon power durng cooperaton, whch reult n a reducton n the utlty of the PU. When the PU allocate more tme for the SU, the PU wll have le tme for t own tranmon, whch may alo lead to a decreae n t utlty. In other word, the PU cannot keep ncreang t utlty by ncreang α. Due to Property 3, the optmal α can be obtaned by ettng Up α = 0, nce the utlty functon of the PU concave wth repect to α. Therefore, the PU can alway fnd t optmal tme allocaton coeffcent α n (15) uch that U p (α ) U p (α). Together wth Property 1, gven the tme allocaton coeffcent α, the SU can alway fnd t optmal tranmon power P n (10). Then, P n (10) and α n (15) are the Stackelberg Equlbrum. In the followng, we wll dcu the cae wth power contrant. Due to Property, P n (10) ncreae a α decreae. For a gven value of α, P may acheve t maxmum value P max. Snce the cenaro before P approache P max the ame a the cae wthout power contrant, we only dcu the cae when P = P max. When the SU chooe P max, t optmal for the PU to chooe α 0, a n the analy of α n Secton III-C. Therefore, we conclude that the oluton P n (11) and α n (1) are the Stackelberg Equlbrum.

7 7 1.3 Throughput of PU (bp/hz) c=0. c=0.5 Expected throughput (bp/hz) wthout trut value wth trut value Normlzed dtance Poton of SU Fgure. Throughput of PU, averaged over fadng, veru the normalzed dtance d. Fgure 3. The mpact of trut value on SU electon. E. Numercal Reult In th part, we preent numercal reult o a to provde nght nto the propoed cooperatve framework. Smlar to [11], by normalzng the dtance between PU and BS, the SU approxmately placed at the dtance d (0, 1) from the PU and 1 d from the BS. Conderng a path lo model, the average power gan between the PU and SU, and between the SU and BS, are h p = 1 and h d ζ b = 1, repectvely, (1 d) ζ where ζ = 3.5 the path lo coeffcent. Amng at reducng the ytem parameter, the maxmum econdary tranmon power P max normalzed to 1 and we chooe P max / = 0 db. Fg. how the the PU throughput on certan channel, averaged over fadng, veru the normalzed dtance d, for c = 0. and 0.5. It een that there ext a cooperaton range n whch the PU can cooperate wth the SU to acheve a hgher throughput than that of drect tranmon. Further, a maller weght c reult n a larger cooperaton range. Fg. 3 how the mpact of trut value on the SU electon. A number of SU ( = 1,, 3, 4, 5) wth aocated trut value 0.75, 0.99, 0.85, 0.9, and 0.95, are located at the normalzed dtance d = 0.3, 0.4, 0.5, 0.6, and 0.7, repectvely. Wthout conderng trut value, the PU hould elect SU 3 nce the PU can acheve the hghet throughput va cooperaton wth SU 3. Conderng trut value of SU, SU the bet choce nce the PU can attan hghet expected throughput va cooperaton wth SU. IV. COOPERATION OVER MULTIPLE CHANNELS For cooperaton over multple channel, whch nvolve multple PU and SU, the approach aforementoned for the ngle channel cannot brng the maxmum beneft to the whole network becaue t only optmze the nteret of ndvdual uer. Therefore, t neceary to conder the cooperaton n the whole network to explot the cooperaton beneft. To th end, we tudy the cooperaton over multple channel n th ecton, from the perpectve of the prmary network and econdary network, repectvely. Two cheme are propoed accordngly: PCM cheme and SCC cheme, to better explot the overall cooperaton beneft n the whole network. A. Prmary Network-Centrc Matchng Scheme From the perpectve of the prmary network, nce the cooperaton can be carred out between multple PU and mul- tple SU multaneouly, there may ext competton among PU when electng SU. Moreover, the bet SU electon for one ngle channel mght not be optmal for the whole prmary network. Conderng above, PCM cheme propoed, wth the objectve of maxmzng the total utlty of the prmary network, whch defned a the aggregate throughput of PU over dfferent channel. Note that the throughput of a ceratn channel obtaned when the PU over that channel cooperate wth a certan SU ung the Stackelberg Equlbrum trategy. Specfcally, a the central controller, the bae taton condered to have the global nformaton n t doman, e.g., CSI. Wth the nformaton, the bae taton can gude the PU to elect the utable SU, wth the objectve of maxmzng the total utlty of the prmary network. Conder that there are K PU multaneouly operatng over dfferent channel and N SU eekng for tranmon opportunte. Denote by I,j the ndcator whch ndcate whether P U j cooperate wth SU or not. Then, we have I,j = { 1 f P U j cooperate wth SU 0 otherwe. (16) Selectng SU equvalent to determnng all the ndcator I,j, where {1,,..., N} and j {1,,..., K}. Such a problem can be formulated a follow: max N =1 j=1 K I,j Up(j).t. I,j 1, = 1,,..., N I,j 1, j = 1,,..., K j I,j {0, 1}, {1,,..., N}, j {1,,..., K} (17) Note that U p(j) the utlty of the PU on channel j when cooperatng wth SU, whch gven by (5). The above problem can be tranformed nto the maxmum weght bpartte matchng problem, whch can be olved n polynomal tme [9]. Fg. 4 how the bpartte graph, where the weght w,j on each edge repreent the expected tranmon rate,.e., U p(j) n (5), f the correpondng P U j and SU (repreented by vertce) cooperate wth each other. Fndng the optmal partner equvalent to fndng the maxmum weght matchng n Fg. 4. To olve the maxmum weght bpartte matchng problem, Hungaran algorthm [30] can be

8 8 Fgure 4. Bpartte graph for PCM cheme. ued whch a well known algorthm to fnd the matchng uch that the um of the weght can be maxmzed. By dong o, the bet matchng can be found uch that the aggregate throughput of the prmary network maxmzed. B. Secondary Network-Centrc Cluter-Baed Scheme From the perpectve of the econdary network, for a certan SU, t can only elect one channel one tme to perform cooperaton over that channel. It poble that multple SU compete wth each other over ome channel to gan the tranmon opportunte, whle no utable SU ext to explot the tranmon opportunte over the other channel. Therefore, for the whole econdary network, the tranmon opportunte are not effcently utlzed; for the ndvdual SU, t not guaranteed that the SU can gan the chance to acce the channel nce t alo depend on other SU electng the ame channel. To explot the tranmon opportunte effcently, SCC cheme propoed wth the objectve of maxmzng the total utlty of the econdary network, whch defned a the aggregate rewardng acce tme of dfferent channel. Note that the rewardng acce tme of a gven channel obtaned when the SU cooperate wth the PU over that channel ung the Stackelberg Equlbrum trategy. Snce the econdary network ad hoc network, to maxmze the total network utlty and the average acce tme per uer, SU form a cluter and perform cooperaton wth PU to gan tranmon opportunte, and then hare the obtaned reource farly. Specfcally, SU frt form a cluter N wth the ze of N baed on the geographc locaton, and contrbute to hare the nformaton, e.g., CSI. Then, the bet SU can be elected for each channel to cooperate wth PU n order to obtan the maxmum aggregate rewardng acce tme of dfferent channel. To th end, a mlar matchng approach a n the prevou ecton can be appled. The dfference are a follow: ) the weght are the rewardng tme, e.g., the correpondng weght (1 α (j))t, f SU chooe to cooperate wth P U j ; and ) the objectve to maxmze the aggregate rewardng tme by fndng the bet matchng. After that, the elected SU cooperate wth the correpondng PU to obtan the rewardng acce tme. Fnally, SU n the cluter hare the obtaned rewardng tme farly. To do th, SU can be clafed nto two group: actve SU (the elected SU for performng cooperaton wth PU a relay) and nactve SU (wth the ze of M). Snce actve SU devote the tranmon power durng cooperaton, they hould have a larger hare of the rewardng tme. To th end, two group of uer frt hare the reource ung quadrature gnalng,.e., the actve SU tay n the current operatng channel and ue the n-phae component of QAM, whle the nactve SU elect one channel to acce and employ the quadrature component. By leveragng quadrature gnalng, actve and nactve SU can tranmt multaneouly wthout nterference wth each other [0]. Then, nactve SU have to decde whch channel to acce to maxmze ther own utlte,.e., the hare of rewardng tme for acceng the channel. The decon proce modeled a a congeton game and the hare that each nactve SU can obtan determned by the Nah Equlbrum (NE) of the congeton game. By dong o, each SU can be guaranteed to gan certan acce tme. Moreover, the average acce tme obtaned ung the cluter baed approach longer than that ung the random channel acce approach, a hown n the numercal reult. Each nactve SU elect one channel to acce among multple channel wth dfferent rewardng tme, to maxmze t own utlty. The decon proce modeled a a congeton game, whch defned by the tuple {M, K, ( ) M, (U j ) M,j K}, where M = {1,,..., M} denote the et of nactve SU, K = {1,,..., K} denote the et of channel, repreent the trategy pace of SU, and U j the utlty functon of SU for electng channel j. The utlty functon a functon of the total number of SU choong the ame channel, whch a decreang functon due to competton or congeton. In other word, more SU elect the ame channel, le hare each SU can obtan. SU am to maxmze t utlty by decdng whch channel to acce and the utlty functon of SU can be gven by U j = Ψ jζ(n j ), (18) where Ψ j the duraton of the rewardng tme on channel j, ζ(n j ) the hare of the rewardng tme on channel j whch SU obtan, and n j the total number of nactve SU choong the channel j. Therefore, Uj repreent the acce tme that SU obtan. For mplcty, the nactve SU electng the ame channel hare the rewardng tme equally ung TDMA, and then ζ(n ) = 1/n. In the above congeton game, each SU chooe a ngle channel to acce for maxmzng t utlty. If each one ha choen a trategy and no SU can ncreae t utlty by changng trategy whle the tratege of other keep unchanged, the current et of tratege conttute an NE. Defnton 3: A trategy profle S = ( 1,,..., M ) an NE f and only f U (, ) U (, ), M, S, (19) where and are the tratege elected by SU and all of t opponent, repectvely. NE mean no one can ncreae t utlty unlaterally. It known that the congeton game alway ext pure NE. The condton for NE n the congeton game can be gven a

9 9 Algorthm 1 1: // Intalzaton: Form the cluter baed on geographc locaton : // Procedure 1: Bet SU Selecton 3: for each SU N do 4: for P U j on channel j, j K do 5: Calculate acce tme allocaton α,j ung (1) 6: Calculate rewardng perod Ψ,j = 1 α,j. 7: end for 8: end for 9: Run Hungaran algorthm to fnd the bet SU for cooperaton 10: // Procedure : Rewardng Acce Tme Sharng 11: Set congeton vector n(s) = (n 1,..., n K ) = (0, 0,..., 0). 1: Order the rewardng perod on each channel [Ψ 1, Ψ,..., Ψ K ] decreangly accordng to the length. 13: for each SU N do 14: f SU actve SU then 15: SU tay n the current operatng channel. 16: SU employ the n-phae component for tranmon. 17: ele 18: for each Ψ j, where j K do 19: Calculate Ψ j ζ(n j + 1). 0: end for 1: SU elect the channel wth maxmum Ψ j ζ(n j +1). : SU employ the quadrature component for tranmon. 3: n j = n j : end f 5: end for 6: return follow: n = Ψ M j,j K Ψ j j K Ψ + n, (0) j where n {0, 1,,..., ΨM+Ψ(K 1) k K Ψ k 1}. The detaled proof can be Ψ M k,k K Ψ k k K Ψ k found n [31]. Any trategy profle whch atfe the above condton n (0) wll conttute an NE. However, there ext multple NE n our congeton game. In order for the SU to elect an NE trategy, the procedure n algorthm 1 can be ued for SU to determne whch channel to acce. The whole procedure of SCC cheme preented n Algorthm 1, whch cont of two man part: the bet SU electon and rewardng acce tme harng. C. Numercal Reult Smlar to the work n [3], we et up the mulaton cenaro a follow: The bae taton located at the orgn (0, 0) and PU are randomly located between (0, d p,mn ) and (0, d p,max ); whle SU are randomly located between (0, d,mn ) and (0, d,max ). The number of PU et to 5. The dtance between node are normalzed by d p,max and Throughput of prmary network (bp/hz) PCM cheme Random acce Number of SU Fgure 5. Throughput of the prmary network averaged over fadng veru number of SU Throughput of prmary network (bp/hz) PCM cheme Random acce Poton of the cluter Fgure 6. Throughput of the prmary network, averaged over fadng, veru the poton of the cluter the prevou path lo model utlzed to calculate average power gan. Fg. 5 how the throughput of the prmary network, averaged over fadng, veru the number of SU where d p,mn = 15, d p,max = 0, d,mn = 5, and d,max = 10, repectvely. It can be een that the propoed cheme outperform the random channel acce approach whereby each SU randomly elect one channel to eek tranmon opportunte through cooperaton. The reult of random acce approach obtaned by Monte Carlo mulaton contng of 1000 tral. Fg. 6 how the throughput of the prmary network, averaged over fadng, wth repect to the poton of the cluter. We fx the range of the SU locaton (.e., d,max d,mn ) and change d,mn. The poton etmated by the relatve dtance from d,mn to d p,mn normalzed by d p,max. It can be een that the throughput frt ncreae and then drop when the cluter move cloely to PU. The reaon that when the cluter too cloe to PU, the channel between SU and the bae taton become poor; and when the cluter too far away from PU, the channel between SU and PU are poor. A a reult, the cooperaton gan lmted. Fg. 7 how the mpact of the number of nactve SU (M) on the NE of the congeton game. Defne channel electon ndcator of channel a the number of nactve SU choong channel dvded by the total number of nactve SU,.e., n /M, whch reflect the popularty of the channel. When M mall, ome channel() may not be choen by any SU. For example, there no nactve SU choong channel 1 when M = 8. When M become hgher, all channel are elected by at leat one SU and the electon ndcator of each channel alo change to atfy the NE condton.

10 10 channel electon ndcator M=8 M=16 Farne among SU SCC cheme Random acce channel ndex Number of SU Fgure 7. Impact of the number of nactve SU on Nah Equlbrum Fgure 9. Farne among SU veru the number of SU Average rewardng tme per SU SCC cheme Random acce Average rewardng tme per SU SCC cheme PCM cheme Number of SU Number of SU Fgure 8. Average acce tme per SU averaged over fadng for SCC cheme and random channel acce Fgure 10. Average acce tme per SU averaged over fadng for PCM cheme and SCC cheme Fg. 8 how the average acce tme per uer, averaged over fadng, veru the ze of the cluter. We compare the propoed cheme wth the random channel acce approach. It can be een that each SU can obtan longer acce tme ung the propoed cheme, compared wth the random channel acce approach. Fg. 9 how the farne among SU, averaged over fadng. Smlar to [33], the farne defned a ( U) N U, where U the acce tme obtaned by SU. It can be een that the farne of the propoed cheme outperform the random acce approach. Th becaue each SU can obtan a certan hare of acce tme ung SCC cheme, whle only a few SU can excluvely acce the channel ung the random channel acce approach. Fg. 10 how the average acce tme per SU, averaged over fadng, when ung PCM cheme and SCC cheme, repectvely. It reveal that the average acce tme ung SCC cheme greater than that ung PCM cheme. The reaon that PCM cheme baed on the perpectve of the prmary network to maxmze PU utlty whle SCC cheme am to maxmze SU utlty. V. CONCLUSIONS In th paper, we have propoed rk-aware cooperatve pectrum acce cheme for mult-channel CRN. We have tuded cooperaton on a ngle channel by Stackelberg game. Baed on the reult of the ngle channel cenaro, we have propoed two cheme for the cooperaton on multple channel cenaro,.e., PCM cheme and SCC cheme, from the perpectve of prmary and econdary network, repectvely. In PCM cheme, to maxmze the total utlty of the prmary network, cooperatng SU on each channel determned ung maxmum weght matchng. In SCC cheme, SU form a cluter to maxmze the total utlty of the econdary network and hare the obtaned reource baed on congeton game and quadrature gnalng. Numercal reult have demontrated that, wth the propoed cheme, the PU can acheve hgher throughput, whle the SU can obtan longer average acce tme, compared wth the random channel acce approach. For future work, we wll degn a mbehavor detecton mechanm dedcated to CCRN. In addton, we wll explot the channel tattc nformaton to make the propoed cheme more effcent. The effect of mperfect CSI on cooperaton wll be tuded a well. VI. ACKNOWLEDGEMENT Th work ha been upported by The Natural Scence and Engneerng Reearch Councl (NSERC) of Canada under Grant No. RGPIN7779. A. Proof of Property 1 APPENDIX Takng the frt order partal dervatve of the utlty functon wth repect to P yeld Then, we have U = (1 α)w h P (1 + P h ) ln c(1 α ). (1) U P = (1 α)w h 4 (1 + P h ) N 0 ln. ()

11 11 From the above equaton, we can ee that U P < 0. Therefore, the utlty functon U of SU concave n t own power level P when the tme allocaton fxed. B. Proof of Property For a gven SU, the optmal tranmon power gven by P (α) = (1 α)w c(1 α ) ln h. (3) Takng the frt dervatve of P wth repect to α, we have P α = αw ( + α) c ln. (4) The denomnator alway potve, whle the numerator negatve. Then, P α < 0. Therefore, the optmal tranmon power P decreae wth α. C. Proof of Property 3 Snce P contnuou wth α, the utlty functon U p of the PU alo contnuou wth α. Subttutng P (α) = (1 α)w c(1 α N0 ) ln nto U h p, the utlty can be gven by (13), whch a functon of α. Takng frt order dervatve of (13) wthe repect to α yeld (14). Then, takng econd order dervatve of (13) wth repect to α yeld U p α = Aα + B. (5) Snce A > 0, B = A, and 0 < α < 1, we have U p α < 0. Therefore, the utlty functon of the prmary uer concave n the tme allocaton coeffcent α. 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