Incentivize Cooperative Sensing in Distributed Cognitive Radio Networks with Reputation-based Pricing

Transcription

1 Incentvze Cooperatve Sensng n Dstrbuted Cogntve Rado Networs wth Reputaton-based Prcng Tongje Zhang, Zongpeng L, Rehaneh Safav-Nan Department of Computer Scence, Unversty of Calgary {tozhang, zongpeng, re}@ucalgary.ca Abstract In a cogntve rado networ, selfsh secondary users may not voluntarly contrbute to desred cooperatve sensng. We desgn the frst fully dstrbuted scheme to ncentvze partcpaton of nodes n cooperatve sensng, by connectng sensng and spectrum allocaton, and offerng ncentve from latter to the former. Secondary users that are more actve and report more accurate sensng values wll be gven hgher reputaton values, whch results n lower prces n the spectrum allocaton phase. Theoretcal analyss and smulaton results ndcate that the proposed method effectvely ncentvzes sensng partcpaton, and rewards truthful and accurate reportng. Our proposed system s fully dstrbuted and does not rely on a central authorty, and so s more applcable n dynamc cogntve rado networs n practce. We also show how to mprove the robustness of reputaton when malcous nodes report spurous reputaton. Index Terms Cogntve Rado Networs; Cooperatve Sensng; Reputaton; Spectrum Allocaton; Incentve; Prcng I. INTRODUCTION As wreless devces and applcatons prolferate, spectrum frequency becomes a scarce resource. Cogntve Rado Networ (CRN) s envsoned as an ntellgent wreless communcaton system that can mtgate such spectrum scarcty problem [9]. In CRNs, the unlcensed users (secondary users) can lease spectrum from the lcense holders (prmary users) f no harmful nterference s ncurred to the latter. Compared to the tradtonal fxed, statc spectrum allocaton, CRNs brng more effcent usage of rado frequency for wreless communcaton [9]. To mnmze the potental nterference wth the prmary users, secondary users frst sense whether the spectrum of nterests are occuped before attemptng to access t. It s challengng for a sngle secondary user to carry out relable and accurate spectrum sensng, snce wreless sgnals suffer from fadng, nose and nterference, whch degrade the sensng accuracy of a secondary user. Cooperatve sensng s proposed to acheve more accurate decson-mang, reduce amortzed resource consumpton at ndvdual nodes, mprove the throughput, and overcome the performance degradaton. Cooperatve sensng enables multple secondary users to collaborate wth each other n the spectrum sensng process [9]. If the group decson on the spectrum state ndcates that the prmary users are dle, then the secondary users apply Ths wor was supported n part by NSERC (Natural Scences and Engneerng Research Councl of Canada) and AITF (Alberta Innovates Technology Futures) /4/$3. c 4 Crown spectrum allocaton protocols to decde whch of them may access the fallow spectrum. Cooperatve sensng protocols are subject to Spectrum Sensng Data Falsfcaton (SSDF) attacs, where the adversary corrupts a subset of secondary users to report falsfed sensng results, amng to degrade the fnal group decson. A seres of studes n the lterature propose methods to mprove sensng accuracy by counter-measurng SSDF attacs. These solutons are usually based on a centralzed nfrastructure, where a central authorty plays an essental role n coordnatng the attac defendng. However, the centralzed methods usually ncur heavy communcaton overhead between the central authorty and the cogntve rados. The adversary can even am to compromse the central authorty, a sngle pont of falure whose capturng may paralyze the entre networ. The cost of constructng an nfrastructure s also hgh. It s desrable to desgn secure, scalable, and dstrbuted schemes n CRNs wthout a central authorty. However, the removal of the central authorty brngs a number of new challenges. A recent wor ntroduces the dstrbuted method to help secondary users obtan more accurate cooperatve sensng results through an teratve update algorthm [3]. Another problem n a CRN s the exstence of selfsh secondary users. Not all secondary users are wllng to partcpate n the cooperatve sensng process, whch requres ndvdual sensng and nteracton wth neghborng nodes, and hence consumes energy and CPU cycles. In dstrbuted CRNs, the secondary users may belong to dfferent operators wth dfferent base statons, potentally pursung selfsh goals and mang ndependent decsons towards whether to cooperate wth other secondary users, to act alone, or even to become a freerder. To mplement farness n the networ and help honest secondary users obtan better sensng results, effectve control of such selfsh behavour s mportant. How to ncentvze the non-malcous but selfsh secondary users to partcpate n the cooperatve sensng process s therefore an nterestng and mportant topc to nvestgate. The ncentvzng method for cooperatve sensng also needs to be fully dstrbuted wthout a central authorty. We model the spectrum sensng and spectrum allocaton processes as a non-cooperatve game. In our system, the reputaton values that reflect the sensng partcpaton and the sensng accuracy are used to offer ncentve n the prcng functon used n the spectrum allocaton process. To obtan a lower prce for utlzng fallow spectrum, a secondary user needs to partcpate

2 more n the spectrum sensng process, and report accurate sensng reports. We propose the method to calculate global reputaton values for the secondary users, that can ncentvze them to partcpate n the cooperatve sensng processes wth more accurate results on more channels. In the reputaton fuson process, the adversary may also compromse some secondary users to report spurous reputaton values, amng to mprove ther prcng factors n the spectrum allocaton process. We also desgn a dstrbuted algorthm to countermeasure ths nd of attacs. The man contrbutons of ths paper are summarzed below. () Ths wor s the frst to address the problem of ncentvzng cooperaton n spectrum sensng together wth the spectrum allocaton process. We desgn a reputaton-based prcng method to offer strong ncentve for secondary users to pursue a lower prce n the spectrum allocaton process. Such connecton brngs more effectve ncentves for secondary users to partcpate n the cooperatve sensng process, compared to offerng ncentves from spectrum sensng only. () We consder two factors of generatng reputaton for secondary users, both from sensng partcpaton and from sensng accuracy. Ths method can better reflect the real world nature of communcaton networs, and countermeasure SSDF attacs from malcous nodes. Secondary users are not only ncentvzed to partcpate n the sensng n more channels, but also to report more accurate measurement results. (3) We desgn the frst fully dstrbuted algorthm to help secondary users compute the global reputaton value on sensng accuracy as publc nowledge. Secondary users teratvely update ther local reputaton values to arrve at consensus, wthout help from any central authorty, for the global reputaton value. (4) To countermeasure attacs n the reputaton fuson process wth spurous reputaton from malcous nodes, we desgn the frst fully dstrbuted algorthm to mprove the robustness of reputaton. The accuracy of the publc nowledge s mproved, therefore, the ncentves are more robust for nonmalcous but selfsh secondary users. In the rest of the paper, Sec. II revews related wor, Sec. III ntroduce the networ model and attac model. Sec. IV dscusses the selfsh behavors. Sec. IV presents the reputatonbased prcng method. Sec. VI s on reputaton generaton, and Sec. VII s on defendng attacs n the reputaton generaton process. Sec. VIII presents smulaton results. Sec. IX concludes the paper. II. RELATED WOR Selfshness n collaboratve sensng has recently attracted much attenton. Song et al. frst studed ths problem and proposed ncentve strateges [5]. Muherjee further dscussed ths problem n a partally-connected networ wth mperfect nformaton []. However, both wor consder only the utlty (payoff) functon for secondary users as mproved sensng accuracy compared to ndvdual sensng, whch s only from the spectrum sensng process. Wang et al. studed how secondary users can collaborate through an evolutonary game [6]. A recent wor consders another selfsh behavor where secondary users report arbtrary nformaton as ther sensng results or smply copy other secondary users reports, to save the sensng energy [7]. However, both wor only consder hard fuson wth bnary results of the prmary user state, whch s less fne-graned compared to soft fuson where real values from the sensed nformaton of the prmary users are exchanged. El-Sherf et al. dscussed the jont desgn of spectrum sensng and spectrum allocaton [3], but only consdered ndvdual spectrum sensng wthout cooperaton. For cooperatve sensng wthout a central authorty, L et al. frst proposed to remove the fuson center by enablng all cogntve rados to update ther local measurements wth neghbourng nodes teratvely towards consensus [4]. Each secondary user obtans local measurements of the prmary user sgnals and then exchanges only wth ts neghbours. A secondary user updates ts value based on ts own value and the receved values from all ts neghbours. The updated values are then exchanged teratvely, untl a consensus s reached among all secondary users [8]. To countermeasure SSDF attacs n a dstrbuted CRN, a recent wor uses reputaton to mprove the cooperatve sensng accuracy [3]. There are a number of models for spectrum allocaton. Some models assume that there exsts a central authorty that controls and coordnates the spectrum allocaton [3] [5], [7] [9]. The problem of allocatng spectrum based on the Qualty of Servce (QoS) requrements of secondary users have been recently studed [3] [5]. Some secondary users requre mnmum-rate guaranteed servces such as Voce over IP (VoIP), whle some secondary users only requre best effort servce such as WF data servces. These wors all assume a sngle base staton as the central authorty to allocate spectrum resources to secondary users. A number of solutons propose dstrbuted spectrum allocaton methods [] [], where each secondary user maes ts own decson about the spectrum access strategy, manly based on local observaton of the spectrum dynamcs. A hybrd method, called dstrbutedcentralzed spectrum allocaton, enables the secondary users to elect a leader randomly from ether the secondary users or the prmary users to act as the central authorty [6]. A. Networ Model III. SYSTEM MODEL We consder a hybrd networ consstng of several prmary user networs and a secondary user networ. There are N secondary users. The total rado spectrum conssts of orthogonal frequency channels. Each prmary user networ operates over one channel. Let Ω N = {,,..., N} and Ω = {,,..., } denote the sets of secondary users and channels, respectvely. Each secondary user s equpped wth a cogntve rado. They utlze omndrectonal antennas to communcate wth each others. The networ formed by the secondary users s modeled as an undrected graph where all secondary users are ether drectly or ndrectly connected. The set of secondary users are the nodes V, and the set of edges s E V V. Two users and j are neghbours f (, j) E.

3 N = {j(, j) E} V s the set of neghbours of. Secondary users are located wthn the transmsson range of the prmary users, and can ndvdually sense the envronment to detect the exstence of the prmary users. We use the energy sensng method n the cooperatve sensng process for a secondary user to detect prmary users presence. An actve secondary user measures the prmary user energy n a sensng sesson. Each sensng sesson s followed by a seres of value update sessons, where actve secondary users exchange local measurements wth neghbors, and update ther own values based on receved values. For the honest nodes, the ntal values are the sensed values of the prmary user energy. The malcous nodes may report arbtrary values amng to acheve ther malcous goals. If the cooperatve sensng results ndcate that the prmary users are not transmttng on certan channels, the secondary users can transmt on these unoccuped channels. The secondary users are able to transmt or receve over multple channels smultaneously. They can also share a partcular channel wth dfferent transmsson power, whch leads to a correspondng level of nterference. The transmsson power vector of a secondary user over all channels s denoted by P = (P, P,..., P ), where P s the transmsson power of on channel. There s an upper lmt for the total transmsson power of a secondary user over all the channels. B. Adversary Model There are three nds of nodes n the networ: () always actve honest nodes, who partcpate n all the cooperatve sensng processes, and report ther sensed results and reputaton vectors; () honest but selfsh nodes, who may choose not to partcpate n the cooperatve sensng process at all the channels. When they decde to partcpate, they report ther sensed value to neghbors; and () malcous nodes, who may or may not partcpate n the cooperatve sensng process, and report falsfed values when partcpatng. In cooperatve sensng, the adversary can be ether selfsh, amng to have exclusve access to the prmary user spectrum, or vandalc, amng to ncur severe nterferences between the prmary users and other secondary users. To acheve these goals, malcous nodes strategcally report hgher values of the prmary users when they are not transmttng, and vce versa. We assume malcous nodes partcpate n the prcng game wth fraudulent nformaton. Durng the reputaton fuson process, malcous nodes may report low reputaton values for honest nodes and hgh reputaton values for themselves, amng at lower prces n the spectrum allocaton process. IV. SELFISH BEHAVIORS AND CONSEQUENCES Secondary users n a dstrbuted CRN are subject to restrctons n weght and form-factor, whch n turn lmts ther power supply. Snce frequent battery replacement s not always practcal, energy effcency s n general an mportant goal. The power consumed by an actve sensor s 4 mw compared to merely.4 mw by an nactve sensor []. As a result, a secondary user has a natural ncentve not to sense by tself, but to act as a free-rder by passvely recevng the cooperatve sensng results from other honest nodes. That s, It can jon the networ and lsten to the communcaton channel, wthout mplementng the local sensng algorthm. Such selfsh behavor has no drect harm to other secondary users. However, the lac of honest neghbors partcpatons wll compromse the level of robustness and accuracy of the cooperatve sensng results. Another reason for selfsh behavor of honest secondary users s the energy consumpton and delay ncurred by the teratve algorthms themselves []. Compared wth ndvdual sensng, the teratve algorthms proposed n the exstng lterature delay the decson mang process. The cost of addtonal energy consumpton n reportng sensed value to a neghbor s also non-neglgble. Weghtng the cost and delay from the cooperatve sensng process, some honest nodes may choose not to partcpate n the entre process, but to perform local sensng only. If these secondary users have better sensng technologes by themselves, t maes sense for them not to partcpate and share ther data. Apparently, such selfsh behavor also has a negatve mpact on the overall wellbeng of the dstrbuted CRN. Our recent wor showed that honest secondary users can obtan more accurate cooperatve sensng reports n an adversaral envronment, as long as more than half of the neghbors correctly report sensed values [3]. Ths was based on the assumpton that all honest secondary neghbors actvely partcpate n the entre cooperatve sensng process. However, some honest neghbors may not actvely partcpate n the process. More honest secondary users can help the secondary user networ to obtan a more accurate cooperatve sensng result. The selfsh behavors of some of the honest nodes however may result n less accurate cooperatve sensng results at other secondary users, whch wll degrade the performance of the dstrbuted cooperatve sensng. Ths loss of accuracy wll adversely affect all nodes and n partcular the selfsh secondary users who wll use the cooperatve sensng results generated from the actve secondary users. Ths can ncentvze the honest secondary users to partcpate n the cooperatve sensng process. However, the ncentve from the cooperatve sensng process tself does not apply to the cases where honest nodes choose to sense by themselves but not to report. V. THE INCENTIVE METHOD To offer stronger ncentves for honest nodes to partcpate n the cooperatve sensng process, we connect sensng partcpaton to the reputaton n a dstrbuted spectrum allocaton process through a user-dependant prcng functon n a spectrum allocaton game. In the dstrbuted spectrum allocaton process, some secondary users behave selfshly to maxmze ther own performance. A well desgned prcng mechansm can elct socal effcent behavours from them. We adopt the noncooperatve game among secondary users proposed n recent lterature []. The game G s expressed as G = {Ω, P, {U }}, where Ω = {,,..., N} s a fnte set of players; P = P P P N s the acton

4 space wth P beng the acton set for player ; and U s the utlty functon of player, whch depends on the strateges of all players, whch are the secondary users. They can select dfferent transmsson powers on dfferent channels. Hgher transmsson powers may brng hgher achevable data rate. At the same tme, hgher prces are also ncurred. Secondary users select ther transmsson powers to maxmze ther respectve utlty functons, and under certan condtons, they eventually reach a Nash Equlbrum after a number of teratons []. We use α A to denote the probablty when the cooperatve sensng result correctly determnes that a channel s unoccuped by the prmary user n a sensng sesson A. The utlty functon of a secondary user can be consdered as the achevable data rate receved by from the networ, α Alog ( + βg P j Ω N,j G j +M ), subtractng the cost assocated wth the prcng functon and the cooperatve sensng process. Only when the prmary user s not transmttng, the cost brought by the prcng functon s ncurred for a secondary user who s nterested to transmt on ths channel. We use a lnear prcng mechansm [] to descrbe the cost ncurred by the prcng functon, where the prce α A λ P ncreases monotoncally wth transmsson power P. On each channel, we denote the cost ncurred by cooperatve sensng for each secondary user as c. The total cost C from cooperatve sensng for a node depends on the number of channels t senses, C = = c Ũ (P, P ) =. The utlty functon s defned as: ũ (P ) Ω = u (P ) α Aλ P c Ω Ω = = βg α A[log ( + P Ω j Ω N,j G j + M ) λ P ] = () where λ P s the user-dependent lnear prcng functon that can drve the Nash Equlbrum close to a Pareto optmal soluton. G s the channel gan on channel of the source to an ntended destnaton, G j s the nterference power receved at the secondary user from unntended user j, M s the nose at, β s the gap of SNR (sgnal-to-nose-rato) that s needed to reach a certan capacty between practcal mplementaton and nformaton theoretcal results []. The socal optmzaton problem s to maxmze a weghted sum of the achevable data rates of all secondary users: βg max P R α Alog ( + P Ω N Ω j Ω N,j G j + M ) () where R s the reputaton of secondary user, assgned to to reward actve partcpaton and to punsh dle behavors n the cooperatve sensng process. When a secondary user has a better reputaton, t shall gan a hgher utlty n the socal optmzaton problem, and vce versa. We adopt the methodology as n [] to derve the optmal prcng factor for the secondary users, descrbed n (3) on top of the next page. The calculaton for (3) s gven n the Appendx. The prcng factor depends on the reputaton values c of all the secondary users n the networ. We can observe that the hgher reputaton value a node has, the lower reputaton values ts neghbors have (ncludng both malcous and selfsh secondary users), the lower prce has to pay n the spectrum allocaton process. Ths effect can offer a strong ncentve for a secondary user to mprove ts reputaton. After recevng transmsson power P, the nose M from the neghbors, measurng G and G j from the receved sgnal power, and obtanng the reputaton values (Sec. VI), each secondary user frst adjusts ts lner prcng factor over all channels accordng to (3), and then determnes ts best acton, ncludng the optmal channel selecton and the transmsson rate on each channel. The goal of user s to maxmze ts ndvdual utlty functon (). The same procedure happens at all secondary users n the networ. The Pareto optmal Nash Equlbrum s reached when all secondary users converge to the best response. The secondary users can update ther best responses accordng to the best responses of ther neghbors teratvely, usng Jacob (parallel), Gauss-Sedel (sequental) schemes [] or asynchronous schemes [], []. VI. GENERATE REPUTATION When dscussng the spectrum allocaton game, we establshed a reputaton-based prcng scheme for secondary users to reach Nash Equlbrum. A user wth hgher reputaton s assgned a lower prce n the game. The next step s to desgn an approprate mechansm for generatng reputaton. A. Sensng Partcpaton A natural way of generatng R s to mae publc nowledge secondary user s sensng partcpaton R (SP ). R (SP ) s a parameter relevant to the number of channels a secondary user actvely senses n a cooperatve sensng sesson. s observable by the neghbors of. We use the percentage of sensed channels of for the optmzaton: R (SP ) = ). The hgher R(SP s, the better prce wll obtan n the spectrum allocaton process, whch can be used as an ncentve for to ncrease by partcpatng n more channels. To calculate, each node n the networ montors ts neghbors actvty on channel. We descrbe ths process n Algorthm. Algorthm Calculatng Sensng Partcpaton. (Input: The channels a secondary user j partcpates n. Output: Reputaton about sensng partcpaton R (SP ) for all the secondary users.) : j partcpates n a subset of all channels : j observes the other partcpants n every channel 3: whle There s a secondary user partcpatng on the same channel do 4: j broadcasts ts observed channel partcpaton nformaton j, for another node 5: j receves the observed channel partcpaton nformaton,,,, 3,,... for another node from ts neghbors 6: j calculates =,, j,... 7: calculates R (SP ) 8: end whle =

5 λ j Ω N,j R u j(p j ) j P = R = α Aβ R ln j Ω N,j R j G j P j G jj ( Ω j, j G j P + M j )( Ω j, j G j P + M j + βg jjp j G j ) (3) Fg. : Observaton on the sensng partcpatons of neghbors Consder the sensng partcpaton n Fg.. Player partcpates n channels {, 3, 5, 7}. Player partcpates n channels {,, 3, 4, 5}. Player 3 partcpates n channels {, 3, 4, 5, 6}. Snce channel 4 s only sensed by Player 3, Player 3 has to do ndvdual sensng on channel 4. The actveness of Player 3 on channel 4 s not counted towards ts partcpaton n cooperatve sensng. To obtan, Players and 3 each observes on the channels where they are actve. They each records the other players on a channel:, = {, 3, 7},,3 = {3, 5},, = {, 3, 7},,3 = {, 3, 6}, 3, = {3, 5}, 3, = {, 3, 6}. They broadcast the observatons to neghbors. Each player then calculates the cardnalty of the unon set for each ndvdual neghbor. =, 3, = 4, =, 3, = 5. In ths case, 3 =,3,3 = 4 rather than 3 = 5. Hereby, R (SP ) = R (SP ) 3 = 4 7, R(SP ) = 5 7. B. Sensng Accuracy The above method ncentvze users wth reputaton to partcpate n channel sensng. Consderng that malcous nodes can be actve n the cooperatve sensng process to acheve ther malcous goals, the reputaton shall be further mproved to reflect the sensng accuracy, besdes level of partcpaton. We mprove the sensng accuracy and partcpaton by both dentfyng falsfed sensng reports and ncentvzng the partcpaton of honest secondary users. Ths dea s smlar as Elo ratng system for chess and ATP (the Assocaton of Tenns Professonals) Ranngs for tenns, where the more an athlete plays, the better an athlete performs, and the hgher ratng an athlete has. When connectng spectrum sensng wth the spectrum allocaton process, reputaton can reflect both sensng accuracy and sensng partcpaton of the secondary users. If a user partcpates more actvely, or senses and reports the prmary user state more accurately, t s assgned a lower prce n the spectrum allocaton process as a reward. In a gven sensng nterval, a secondary user has m neghbors who report falsfed values (ncludng attacng malcous neghbors and honest nodes sensng ncorrectly due to severe fadng or system falure), and n neghbors who report correct values (ncludng honest nodes sensng correctly and non-attacng malcous nodes). We use R (SA) j, to denote the reputaton of transmtter generated by recever j to reflect the sensng accuracy of. Each user j mantans a reputaton vector of ts neghbors, on a channel : {R (SA) j,, R (SA) j,,..., R (SA) j,m j+n j }. All secondary users update ther values and exchange ther updated values wth ther neghbors. V,j s the value that a transmtter sends to a recever j. After the frst round of sensng value exchange, an honest node calculates the reputaton of ts neghbors based on ther reported values and ts own value. The reputaton values reflectng sensng accuracy R (SA) j, are generated on channel as follows: R (SA) j, (mj + nj + )V,j = Ṽ j mj +n j + Vl,j Ṽ j (4) m j +n j + V l,j where Ṽ j = m j+n j+ s the average value of all the nodes n the neghborhood on channel [3]. The value of R (SA) j, falls nto [, ]. Ths reputaton generatng method can assgn reputaton R (SA) j, R (SA) j, < for a neghbor that reports falsfed values, and > reputaton for a neghbor that reports correct values, whch wll help honest nodes obtan better cooperatve sensng results than the reputaton-less scheme, assumng that the majorty of neghbors are ether correctly sensng honest nodes or non-attacng malcous nodes [3]. C. Reputaton Fuson Reputaton values reflectng sensng accuracy of a secondary user are generated ndvdually by ts peers, and are fused nto a global reputaton value for use n the prcng factor of the spectrum allocaton process. The reputaton fuson process s a dstrbuted scheme wthout a central authorty. Upon detecton of an dlng prmary user, the secondary users exchange ther reputaton vectors wth each other teratvely towards a converged global reputaton. Such agreed-upon reputaton values become publc nowledge n spectrum allocaton. Inspred by the dstrbuted algorthm for cooperatve sensng [4], we desgn a dstrbuted algorthm for secondary users to acheve consensus on global reputaton, as descrbed n Algorthm. µ s a dscount factor. t ndcates the reputaton update sesson. In the dstrbuted reputaton fuson algorthm, the consensus reputaton value R (SA) for on channel s the average reputaton value from all secondary users n the networ R (SA) = j Ω N,j R(SA) j, N [8]. Snce a node can sense on multple channels, the reputaton value R (SA) can be descrbed as R (SA) Ω,P > R(SA) about a node. The hgher t obtans, the lower prce faces n the spectrum allocaton process, whch can be used as another ncentve for to contrbute more accurate sensng results. Ths statement

6 Algorthm Dstrbuted Reputaton Fuson Algorthm on Channel. (Input: Reputaton vector of a node j: R (SA) j,, R (SA) j,,..., R (SA) j,,..., R (SA) j,m j +n j and receved reputaton vectors from j s neghbors. Output: The converged reputaton vector.) : whle s a neghbor of j do : j receves reputaton vectors from a neghbor : R (SA),, R (SA),,..., R (SA),m +n 3: j sends ts own reputaton vector to a neghbor : R (SA) j,, R (SA) j,,..., R (SA) j,,..., R (SA) j,m j +n j 4: whle The converged reputaton vector s not obtaned do 5: j updates ts reputaton vector as R (SA)(t+) j, 6: end whle 7: end whle m j +n j = R (SA)t j, + l= µ(r (SA)t l, R (SA)t j, ) also mples that a malcous node s less ncentvzed to attac wth falsfed sensng results. The method of generatng and fusng R (SP ) has been dscussed before as R (SP ) =, whch falls nto the range of [, ]. The two reputaton vectors can be lnearly combned together wth parameters and η, to form the fnal global reputaton R to be used n the prcng factor n the spectrum allocaton process. Consderng the dfferent value ranges of R (SA) and R (SP ), the global reputaton value of node s: R = R (SA) + ηr (SP ) = = N + η R (SA) Ω,P > Ω,P > j Ω N,j + η where < <, < η <, + η =. D. The Role of Reputaton (5) (mj + nj + )V,j ( Ṽ j mj +n j + Vl,j Ṽ j ) For the lnear combnaton of R (SA) and R (SP ), we now analyze the effect of the parameters towards ncentvzng secondary user partcpaton. In the reputaton value R, η offers ncentve for both malcous and honest neghbors, Ω,P > R(SA) offers ncentve to honest neghbors only. To dfferentate secondary users n the spectrum allocaton process, we propose the requrement that s consstent wth the requrement for sensng accuracy. We requre that R < for a malcous neghbor, R > for an honest neghbor. For an honest neghbor, the requrement s Ω,P > R(SA). Snce + η =, the requrement translates to Snce Ω,P > R(SA) (6) > η Ω,P > R(SA) > η ( η). >, so an honest node has to meet the requrement of η ( η) < to obtan a reputaton value R >. Ths requrement can be transformed to. Hereby, as long as t partcpates n more than > half of the channels and report correctly sensed values, the requrement s satsfed. In ths case, the system can ncentvze the honest nodes to partcpate n at least half of the channels. Agan, the more channels t partcpates n, the lower prce t can gan n the spectrum allocaton process. For a malcous neghbor, the requrement s Ω,P > R(SA). Snce + η =, the requrement translates to < η Ω,P > R(SA) < η ( η). Snce Ω,P > R(SA) <, as long as the malcous node s actve on less than half of the channels, < η ( η) >, the requrement s satsfed. In ths case, the malcous node s for sure to receve R <, whch ndcates a hgher prce n the spectrum allocaton process. For an actve malcous neghbor that attacs n more than half of the channels >, we need to analyze the effect of parameter η. We can observe that the more channels actvely attacs, the lower Ω,P > R(SA) s. At the same tme, the lower η ( η) also turns to be. In the extreme stuaton where the malcous nodes attac all channels, =. The requrement for R < turns to be Ω,P > R(SA) < η η η, where η s the lower bound for the system to meet the requrement. VII. IMPROVE THE ROBUSTNESS OF REPUTATION Malcous nodes are nterested n manpulatng the reputaton values to gve themselves lower prces, whle gve hgher prces to honest nodes. Once fused wth correct data, such spurous data can lead to detrmental, unfar prces. We further assgn dfferentated weghts to the reputaton values about sensng accuracy. Such reputaton-of-reputaton serves as credblty to help honest nodes obtan more accurate reputaton values ther neghbours. An honest node calculates the credblty of ts neghbors based on ther reported reputaton vectors and ts own reputaton vector after the frst round of reputaton exchange n Algorthm. We use dfferentated weght ω (SA) j, to denote the credblty of the transmtter generated by the recever j. Then, we can modfy (5) to R (SA)(t+) j, m j +n j = R (SA)t j, + l= µω (SA) j, (R (SA)t l, R (SA)t j, ). (7) For requrements on ω (SA) j, to guarantee that the reputaton fuson n (7) to be better than that n (5), we have: Proposton. Assume a node j can assgn credblty ω (SA) j, < to a neghbor that reports spurous reputaton values, and ω (SA) j, > to a neghbor that reports correct reputaton values. Then j can update the fused reputaton value of a neghbor to a hgher reputaton value when reports correct sensng results, and a lower reputaton value when reports falsfed sensng results, compared to the reputaton fuson process wthout credblty ω (SA) j,. Proof: Let s be the number of s neghbors who transmt spurous reputaton, c be number of other neghbors. For an honest node j, we denote the credblty of a neghbor that

7 reports a correct reputaton wth ω (SA) j, C, and the credblty of a node that reports a spurous reputaton wth ω (SA) j, S. Comparng the two reputaton update methods (5) and (7), we have R (SA)(t+) j, = R (SA)t j, + µ[ s j = ω(sa) j, S (R (SA)t l, ) + s j+c j =s j+ ω(sa) j, C (R (SA)t l, R (SA)t j, )] and R (SA)(t+) j, = R (SA)t j, + µ[ s j = (R(SA)t l, R (SA)t j, ) + sj+c j =s j+ (R(SA)t l, R (SA)t j, )]. Therefore, the dfference between these two methods s: R (SA)t j, µ[ + )(R (SA)t l, s j (ω (SA) j, S = s j +c j (ω (SA) j, C =s j + )(R (SA)t l, )(R (SA)t l, R (SA)t j, ) R (SA)t j, )]. We now examne the two scenaros, when () an honest node j generates the reputaton of a neghbor correctly, or () ncorrectly, n whch case the effect s the same as a spurous reputaton value. In case (), R (SA)t j, R (SA)t l, for a neghbor l that also generate a correct reputaton value, then the dfference between the two methods s approxmately µ s j = (ω(sa) j, S )(R (SA)t l, R (SA)t j, ). Whle reports a correct sensed value, we have R (SA)t l, < R (SA)t j, for a neghbor l that reports a spurous reputaton value. So, as long as s j = (ω(sa) j, S ) <, (7) can help j obtan a hgher converged reputaton for than (5). Whle the node reports a falsfed sensed value, R (SA)t l, > R (SA)t j, for a neghbor l that reports a spurous reputaton value and so as long as s j = (ω(sa) j, S ) <, (7) can help j obtan a lower converged reputaton for than (5). Thus the frst requrement for credblty s that s j = (ω(sa) j, S ) < for a neghbor l reportng ncorrectly. In case (), R (SA)t j, R (SA)t l, for a neghbor l that also generate an spurous reputaton value, then the dfference between the two methods s approxmately µ s j = (ω(sa) j, C R (SA)t j, ). Whle reports ncorrectly, we have R (SA)t l, < R (SA)t j, (8) for a neghbor l that reports a correct reputaton value. So, as long as s j = (ω(sa) j, C ) >, (7) can help j obtan a hgher converged reputaton for than (5). Whle reports a correct sensed value, R (SA)t l, < R (SA)t j, for a neghbor that reports a correct reputaton value and so as long as s j = (ω(sa) j, C ) <, (7) can help j obtan a lower converged reputaton for than (5). Thus the second requrement for credblty s that s j = (ω(sa) j, C ) > for a neghbor l reportng a correct reputaton value. To generate the credblty ω (SA) j, that can meet the two requrements, we propose the method of: ω (SA) j, = R(SA)t (SA)t j, R j, s j +c j R (SA)t l, s j +c j (sj + cj)r(sa)t j, = sj +c j R (SA)t l, s j +c j R (SA)t j, s j +c j (SA)t R j, R (SA)t j, (SA)t R j, (SA)t where R j, = s the average reputaton value of from neghbors of j. We have ω (SA) j,. (9) The ratonale for ths method les n the observaton about the dstances to the average reputaton value. As long as there are more neghbors that report correct reputaton values for, the dstance from the reputaton value of a node that reports correctly to the average reputaton value wll be smaller than the average dstance to the average reputaton value, and vce versa. That leads to the followng theorem: Theorem.. The credblty-generatng method n (9) enables honest nodes to assgn ω (SA) j, < for neghbors reportng spurous reputaton, ω (SA) j, > for neghbors reportng correct reputaton, for the reputaton fuson method n (7). Therefore, (7) and (9) can help honest nodes obtan hgher reputaton values for other honest nodes, lower reputaton values for the malcous nodes, gven the condton that more neghbors report correct reputaton values. Ths mprovement of the reputaton robustness can assgn hgher prces to the malcous nodes, lower prces to honest nodes n the spectrum allocaton process. Proof: For a neghbor that reports spurous reputaton values, the dstance to the average reputaton value s above average: R (SA)t j, both s j + c j can have (s j +c j )R (SA)t j, s j +c j (s j +c j )R (SA)t j, s j +c j s j +c j (SA)t R j, > > and s j +c j R (SA)t l, R (SA)t j, R (SA)t (SA)t R l, j, (SA)t R j, R (SA)t (SA)t R l, j, R (SA)t (SA)t R l, j, s j +c j (SA)t R j,. Snce >, we >, whch s equvalent to <. Accordng to (9), we have ω (SA) j, S <. The proof for the case where a neghbor who reports correct reputaton values s smlar, and s omtted due to space constrants. Combnng these two cases wth the requrements on credblty, we can verfy the valdty of the theorem. VIII. PERFORMANCE EVALUATION We now present smulaton results for verfyng the effcacy of the proposed ncentve mechansms. In our smulatons, the SNR gap β s set to.3. Each secondary user has the same capacty to communcate wth other secondary users n ts proxmty. The parameters for channel gan are set as G = and G j =.. The noses are M = W, Ω N, Ω. The transmsson power of secondary users are P = W, Ω N, Ω. Prmary users transmt wth a unform probablty α A = on all channels. We smulate secondary users, to observe: () the prcng factor values generated from both sensng accuracy and sensng partcpaton; () the reputaton fuson process under attacs from malcous nodes. We examne the extreme stuaton where malcous nodes attac on all channels, reportng falsfed sensed values n the cooperatve sensng process and spurous reputaton values n the reputaton update process. The honest but selfsh secondary users partcpate n dfferent channels, reportng correctly sensed values n the cooperatve sensng process and correct reputaton values n the reputaton update process.

8 Prcng Factor λ Prcng Factor λ Always Actve Selfsh Node Malcous Node Number of Actve Channels (a) Always Actve Selfsh Node Malcous Node Number of Actve Channels 8 9 (b) Prcng Factor λ Prcng Factor λ Number of Actve Channels (c) Always Actve Selfsh Node Malcous Node Always Actve Selfsh Node Malcous Node Number of Actve Channels 8 9 (d) Prcng Factor λ Number of Actve Channels Prcng Factor λ (e) Number of Actve Channels (f) Always Actve Selfsh Node Malcous Node Always Actve Selfsh Node Malcous Node Prcng Factor λ Always Actve Selfsh Node Malcous Node Number of Actve Channels Prcng Factor λ (g) Always Actve Selfsh Node Malcous Node Number of Actve Channels Fg. : Prcng Factors for an always actve node, a selfsh node and a malcous node. Parameters:(a) {6,, 3,, }. (b) {5,, 4,, }. (c) {4, 3, 3,, }. (d) {, 5, 3,, }. (e) {6,, 3,.9,.}. (f): {6,, 3,.,.9}. (g) {5,, 4,.9,.}. (h) {5,, 4,.,.9}. (h) ) Prcng Factor: We frst smulate the prcng factor for dfferent nds of secondary users n dfferent stuatons. In Fg., the x-axs ndcates the number of channels a selfsh node partcpates n, the y-axs s the prcng factor for an honest node, a malcous node or a selfsh node. We use the tuple {# of always actve nodes, # of selfsh nodes, # of malcous nodes,, η} to denote the dfferent parameters. We can observe that the always actve nodes have lower prcng factors compared to the malcous nodes. As the number of actve channels ncreases, the prcng factors of the selfsh nodes are eventually lowered to the same level of an always actve honest node. The more actve channels the selfsh nodes partcpate n, the lower prces they can obtan. Fg. (a) and (b) depct scenaros wth dfferent numbers of malcous nodes. Snce malcous nodes are all actvely spreadng falsfed sensng results on all the channels, the selfsh node needs to partcpate n at least fve channels when there are three malcous nodes, eght channels when there are four malcous nodes, to obtan a lower prce than the malcous nodes. As the number of malcous nodes ncreases, the dfferences between the prcng factors of an always actve honest node and a malcous node shrns. Fg. (a), (c) and (d) depct the scenaros wth dfferent numbers of selfsh nodes. As the number ncreases, the prcng factor for a selfsh node decreases. Ths s because the prcng factor depends on the comparable reputaton values of all the nodes n the networ. If other nodes have lower reputaton values, the prcng factor for the selfsh nodes can ncrease. Fg. (a), (b), (e), (f), (g) and (h) depct the scenaros wth dfferent selecton of parameters and η. We can observe that the hgher value η s, the hgher dfferences between the selfsh node and an always actve honest node. The reason s that the hgher η amplfes the role of sensng partcpaton n the prcng factor. In ths case, the secondary users can be ncentvzed to partcpate on more channels. However, the mportance of sensng accuracy s downplayed. Ths s the tradeoff between the two parameters and η. These observatons ndcate that the system can assgn lower prces to more actve honest nodes, and hgher prces to malcous nodes. Updated Reputaton Use Credblty ω No Credblty 5 5 Reputaton Fuson Update Sessons (a) Updated Reputaton Use Credblty ω No Credblty. 5 5 Reputaton Fuson Update Sessons (b) Fg. 3: Reputaton Fuson Process. The reputaton fuson for the R (SA) of (a) an honest node; (b) a malcous node. ) Credblty: Fg. 3 depcts the dfferences credblty ω brngs to the system performance for an honest node and a malcous node. For an honest node, the malcous nodes report the lowest reputaton. Wth the help of credblty ω, the converged reputaton value R (SA) of another honest node for the vctm honest node s approxmately.3 hgher than the scenaro wthout credblty. For a malcous node, the other malcous nodes report extremely hgh reputaton values. Wth the help of credblty ω, the converged reputaton value R (SA) of an honest node for the malcous node s approxmately.4 lower than the scenaro wthout credblty. These observatons ndcate that the system can mprove the robustness of reputaton by reducng the effect of spurous reputaton values.

9 IX. CONCLUSION We propose to use reputaton as a prcng factor n the spectrum allocaton process to ncentvze cooperatve sensng n dstrbuted CRNs. The reputaton values are generated from both sensng accuracy and sensng partcpaton. Both theoretcal analyss and smulaton results ndcate that ths method can ncentvze secondary users to partcpate n more channels and report more accurate sensng reports, n order to obtan lower prces n the spectrum allocaton process. To countermeasure attacs n the reputaton fuson process where malcous nodes report spurous reputaton values, we proposed a method wth the help of other honest neghbors. Our methods, from cooperatve spectrum sensng to reputaton fuson then to spectrum allocaton, are entrely dstrbuted wthout a central authorty, and thus more applcable to dstrbuted CRNs. APPENDIX The calculaton of the optmal prcng factor as shown n (3) s: = = = λ = j Ω N,j Rj j Ω N,j Rj u j (P j ) R [α A log (+ P βg jj Ω N, j G j P +M j P R βg [α A log jj (+ G j Ω N,j Rj j P + l Ω N,l j, j G j P )] +M j P R βg jj ( ) = j Ω N,j Rj α A ln = j Ω N,j Rj α A ln j Ω N,j Rj α A G j P + l Ω N,l j, j G j P +M j P βg jj + G j P + l Ω N,l j, j G j P +M j R G j βg jj (G j P + l Ω N,l j, j G j P +M j ) ln j Ω N,j Rj α A βg jj + G j P + l Ω N,l j, j G j P +M j R G j βg jj ( Ω N, j G j P +M j ) βg jj + Ω N, j G j P +M j R G j βg jj Ω N, j G j P +M j ln Ω = N, j G j P +M j +βg jj, R whch can be easly transformed to the fnal result of λ. REFERENCES [] V. rshnamurthy, M. Masery, and G. Yn, Decentralzed Adaptve Flterng Algorthms for Sensor Actvaton n An Unattended Ground Sensor Networ, IEEE Transactons on Sgnal Processng, vol. 56, no., pp , Dec. 8. [] A. Muherjee, Dffuson of Cooperatve Behavor n Decentralzed Cogntve Rado Networs wth Selfsh Spectrum Sensors, IEEE Journal of Selected Topcs n Sgnal Processng, vol. 7, no., pp , Aprl 3. [3] T. Jang, H. Wang, and A. Athanasos, QoE-Drven Channel Allocaton Schemes for Multmeda Transmsson of Prorty-Based Secondary Users over Cogntve Rado Networs, IEEE Journal on Selected Areas n Communcatons, vol. 3, no. 7, pp. 5-4, Aug.. )] [4] R. Xe, F. R. Yu, and H. J, Dynamc Resource Allocaton for Heterogeneous Servces n Cogntve Rado Networs wth Imperfect Channel Sensng. IEEE Transactons on Vehcular Technology, vol. 6, no., pp , Feb.. [5] R. Xe, F. R. Yu, H. J, and Y. L, Energy-Effcent Resource Allocaton for Heterogeneous Cogntve Rado Networs wth Femtocells. IEEE Transactons on Wreless Communcatons, vol., no., pp , Nov.. [6] Q. Lang, S. Han, F. Yang, G. Sun, and X. Wang, A Dstrbuted- Centralzed Scheme for Short- and Long- Term Spectrum Sharng wth a Random Leader n Cogntve Rado Networs, IEEE Journal on Selected Areas n Communcatons, vol. 3, no., pp , Dec.. [7] L. T. Tan, and L. B. Le, Channel Assgnment wth Access Contenton Resoluton for Cogntve Rado Networs, IEEE Transactons on Vehcular Technology, vol. 6, no. 6, pp , July. [8] S. Wang, Z, -H. Zhou, M. Ge, and C. Wang, Resource Allocaton for Heterogeneous Cogntve Rado Networs wth Imperfect Spectrum Sensng, IEEE Journal on Selected Areas n Communcatons, vol. 3, no. 3, pp , March 3. [9] Y. Tachwal, B. F. Lo, I. F. Ayldz, and R. Augustí, Multuser Resource Allocaton Optmzaton Usng Bandwdth-Power Product n Cogntve Rado Networs, IEEE Journal on Selected Areas n Communcatons, vol. 3, no. 3, pp , March 3. [] F. Wang, M, runz, and S. Cu, Prce-Based Spectrum Management n Cogntve Rado Networs, IEEE Journal of Selected Topcs n Sgnal Processng, vol., no., pp , Feb. 8. [] H, -P, Shang, and M. van der Schaar, Dstrbuted Resource Management n Mult-hop Cogntve Rado Networs for Delay Senstve Transmsson, IEEE Transactons on Vehcular Technology, vol. 58, no., pp , Feb. 9. [] L. Cao, and H. Zheng, Dstrbuted Rule-Regulated Spectrum Sharng, IEEE Journal on Selected Areas n Communcatons, vol. 6, no., pp. 3-45, Jan. 8. [3] T. Zhang, R. Safav-Nan, and Z. L, ReDSen: Reputaton-based Secure Cooperatve Sensng n Dstrbuted Cogntve Rado Networs, Proceedngs of the 3 IEEE Internatonal Conference on Communcatons (ICC), pp , June 3. [4] Z. L, F. R. Yu, and M. Huang, A Dstrbuted Consensus-Based Cooperatve Spectrum-Sensng Scheme n Cogntve Rados, IEEE Transactons on Vehcular Technology, vol. 59, no., pp , Jan.. [5] C. Song, and Q. Zhang, Achevng Cooperatve Spectrum Sensng n Wreless Cogntve Rado Networs, ACM SIGMOBILE Moble Computng and Communcatons Revew, vol. 3, no., pp. 4-5, Aprl 9. [6] B. Wang,. Lu, and T. Clancy, Evolutonary Cooperatve Spectrum Sensng Game: How to Collaborate? IEEE Transactons on Communcatons, vol. 58, no. 3, pp. 89-9, March. [7] S. L, H. Zhu, Z. Gao, X. Guan, and. Xng, YouSense: Mtgatng Entropy Selfshness n Dstrbuted Collaboratve Spectrum Sensng, Proceedngs of the 3nd IEEE Internatonal Conference on Computer Communcatons (INFOCOM 3), pp , Aprl 3. [8] R. Olfat-Saber, J. A. Fax, and R. M. Murray, Consensus and Cooperaton n Networed Mult-Agent Systems, Proceedngs of the IEEE, vol. 95, no., pp. 5-33, Jan. 7. [9] I. F. Ayldz, B. F. Lo, and R.Balarshnan, Cooperatve spectrum sensng n cogntve rado networs: A survey, Physcal Communcaton vol. 4, no., pp. 4-6, March. [] J. W. Mwangoa,. B. Letaef, and Z. Cao, Jont Power Control and Specturm Allocaton for Cogntve Rado Networs va Prcng, Physcal Communcaton vol., no. -, pp.3-5, March - June 9. [] I. Atzen, L. G. Ordóñez, G. Scutar, D. P. Palomar, and J. R. Fonollosa, Noncooperatve and Cooperatve Optmzaton of Dstrbuted Energy Generaton and Storage n the Demand-Sde of the Smart Grd, IEEE Transactons on Sgnal Processng, vol. 6, no., pp , May 3. [] D. A. Schmdt, C. Sh, R. A. Berry, M. L. Hong, and W. Utschc, Dstrbuted Resource Allocaton Schemes, IEEE Sgnal Processng Magazne, vol. 6, no. 5, pp.53-63, Sept. 9. [3] A. A. El-Sherf, and. J. R. Lu, Jont Desgn of Spectrum Sensng and Channel Access n Cogntve Rado Networs, IEEE Transactons on Wreless Communcatons, vol., no. 6, pp , June.