Incentivize Cooperative Sensing in Distributed CognitiveRadio Networks with Reputation-based Pricing

Tongjie Zhang, Zongpeng Li, Reihaneh Safavi-NainiDepartment of Computer Science, University of Calgary

tozhang, zongpeng, rei@ucalgary.ca

Abstract—In a cognitive radio network, selfish secondary usersmay not voluntarily contribute to desired cooperative sensing. Wedesign the first fully distributed scheme to incentivize participa-tion of nodes in cooperative sensing, by connecting sensing andspectrum allocation, and offering incentive from latter to theformer. Secondary users that are more active and report moreaccurate sensing values will be given higher reputation values,which results in lower prices in the spectrum allocation phase.Theoretical analysis and simulation results indicate that theproposed method effectively incentivizes sensing participation,and rewards truthful and accurate reporting. Our proposedsystem is fully distributed and does not rely on a centralauthority, and so is more applicable in dynamic cognitive radionetworks in practice. We also show how to improve the robustnessof reputation when malicious nodes report spurious reputation.Index Terms—Cognitive Radio Networks; Cooperative Sensing;Reputation; Spectrum Allocation; Incentive; Pricing

I. INTRODUCTION

As wireless devices and applications proliferate, spectrumfrequency becomes a scarce resource. Cognitive Radio Net-work (CRN) is envisioned as an intelligent wireless communi-cation system that can mitigate such spectrum scarcity problem[19]. In CRNs, the unlicensed users (secondary users) canlease spectrum from the license holders (primary users) if noharmful interference is incurred to the latter. Compared to thetraditional fixed, static spectrum allocation, CRNs bring moreefficient usage of radio frequency for wireless communication[19]. To minimize the potential interference with the primaryusers, secondary users first sense whether the spectrum ofinterests are occupied before attempting to access it.

It is challenging for a single secondary user to carry outreliable and accurate spectrum sensing, since wireless signalssuffer from fading, noise and interference, which degrade thesensing accuracy of a secondary user. Cooperative sensing isproposed to achieve more accurate decision-making, reduceamortized resource consumption at individual nodes, improvethe throughput, and overcome the performance degradation.Cooperative sensing enables multiple secondary users to col-laborate with each other in the spectrum sensing process [19].If the group decision on the spectrum state indicates thatthe primary users are idle, then the secondary users apply

This work was supported in part by NSERC (Natural Sciences andEngineering Research Council of Canada) and AITF (Alberta InnovatesTechnology Futures).

spectrum allocation protocols to decide which of them mayaccess the fallow spectrum.

Cooperative sensing protocols are subject to Spectrum Sens-ing Data Falsification (SSDF) attacks, where the adversarycorrupts a subset of secondary users to report falsified sensingresults, aiming to degrade the final group decision. A series ofstudies in the literature propose methods to improve sensingaccuracy by counter-measuring SSDF attacks. These solutionsare usually based on a centralized infrastructure, where acentral authority plays an essential role in coordinating theattack defending. However, the centralized methods usuallyincur heavy communication overhead between the centralauthority and the cognitive radios. The adversary can even aimto compromise the central authority, a single point of failurewhose capturing may paralyze the entire network. The costof constructing an infrastructure is also high. It is desirableto design secure, scalable, and distributed schemes in CRNswithout a central authority. However, the removal of the centralauthority brings a number of new challenges. A recent workintroduces the distributed method to help secondary usersobtain more accurate cooperative sensing results through aniterative update algorithm [13].

Another problem in a CRN is the existence of selfish sec-ondary users. Not all secondary users are willing to participatein the cooperative sensing process, which requires individualsensing and interaction with neighboring nodes, and henceconsumes energy and CPU cycles. In distributed CRNs, thesecondary users may belong to different operators with differ-ent base stations, potentially pursuing selfish goals and makingindependent decisions towards whether to cooperate with othersecondary users, to act alone, or even to become a free-rider. To implement fairness in the network and help honestsecondary users obtain better sensing results, effective controlof such selfish behaviour is important. How to incentivizethe non-malicious but selfish secondary users to participatein the cooperative sensing process is therefore an interestingand important topic to investigate.

The incentivizing method for cooperative sensing also needsto be fully distributed without a central authority. We modelthe spectrum sensing and spectrum allocation processes as anon-cooperative game. In our system, the reputation valuesthat reflect the sensing participation and the sensing accuracyare used to offer incentive in the pricing function used inthe spectrum allocation process. To obtain a lower price forutilizing fallow spectrum, a secondary user needs to participate978-1-4799-3360-0/14/$31.00 c©2014 Crown

more in the spectrum sensing process, and report accuratesensing reports. We propose the method to calculate globalreputation values for the secondary users, that can incentivizethem to participate in the cooperative sensing processes withmore accurate results on more channels. In the reputationfusion process, the adversary may also compromise somesecondary users to report spurious reputation values, aimingto improve their pricing factors in the spectrum allocation pro-cess. We also design a distributed algorithm to countermeasurethis kind of attacks.

The main contributions of this paper are summarized below.(1) This work is the first to address the problem of in-

centivizing cooperation in spectrum sensing together with thespectrum allocation process. We design a reputation-basedpricing method to offer strong incentive for secondary usersto pursue a lower price in the spectrum allocation process.Such connection brings more effective incentives for sec-ondary users to participate in the cooperative sensing process,compared to offering incentives from spectrum sensing only.

(2) We consider two factors of generating reputation forsecondary users, both from sensing participation and fromsensing accuracy. This method can better reflect the real worldnature of communication networks, and countermeasure SSDFattacks from malicious nodes. Secondary users are not onlyincentivized to participate in the sensing in more channels,but also to report more accurate measurement results.

(3) We design the first fully distributed algorithm to helpsecondary users compute the global reputation value on sens-ing accuracy as public knowledge. Secondary users iterativelyupdate their local reputation values to arrive at consensus,without help from any central authority, for the global rep-utation value.

(4) To countermeasure attacks in the reputation fusionprocess with spurious reputation from malicious nodes, wedesign the first fully distributed algorithm to improve therobustness of reputation. The accuracy of the public knowledgeis improved, therefore, the incentives are more robust for non-malicious but selfish secondary users.

In the rest of the paper, Sec. II reviews related work,Sec. III introduce the network model and attack model. Sec. IVdiscusses the selfish behaviors. Sec. IV presents the reputation-based pricing method. Sec. VI is on reputation generation, andSec. VII is on defending attacks in the reputation generationprocess. Sec. VIII presents simulation results. Sec. IX con-cludes the paper.

II. RELATED WORK

Selfishness in collaborative sensing has recently attractedmuch attention. Song et al. first studied this problem andproposed incentive strategies [15]. Mukherjee further dis-cussed this problem in a partially-connected network withimperfect information [2]. However, both work consider onlythe utility (payoff) function for secondary users as improvedsensing accuracy compared to individual sensing, which isonly from the spectrum sensing process. Wang et al. studiedhow secondary users can collaborate through an evolutionary

game [16]. A recent work considers another selfish behaviorwhere secondary users report arbitrary information as theirsensing results or simply copy other secondary users’ reports,to save the sensing energy [17]. However, both work onlyconsider hard fusion with binary results of the primary userstate, which is less fine-grained compared to soft fusion wherereal values from the sensed information of the primary usersare exchanged. El-Sherif et al. discussed the joint designof spectrum sensing and spectrum allocation [23], but onlyconsidered individual spectrum sensing without cooperation.

For cooperative sensing without a central authority, Li etal. first proposed to remove the fusion center by enablingall cognitive radios to update their local measurements withneighbouring nodes iteratively towards consensus [14]. Eachsecondary user obtains local measurements of the primaryuser signals and then exchanges only with its neighbours. Asecondary user updates its value based on its own value and thereceived values from all its neighbours. The updated values arethen exchanged iteratively, until a consensus is reached amongall secondary users [18]. To countermeasure SSDF attacks ina distributed CRN, a recent work uses reputation to improvethe cooperative sensing accuracy [13].

There are a number of models for spectrum allocation.Some models assume that there exists a central authoritythat controls and coordinates the spectrum allocation [3]–[5], [7]–[9]. The problem of allocating spectrum based onthe Quality of Service (QoS) requirements of secondary usershave been recently studied [3]–[5]. Some secondary usersrequire minimum-rate guaranteed services such as Voice overIP (VoIP), while some secondary users only require besteffort service such as WiFi data services. These works allassume a single base station as the central authority to allocatespectrum resources to secondary users. A number of solutionspropose distributed spectrum allocation methods [10]–[12],where each secondary user makes its own decision about thespectrum access strategy, mainly based on local observation ofthe spectrum dynamics. A hybrid method, called distributed-centralized spectrum allocation, enables the secondary usersto elect a leader randomly from either the secondary users orthe primary users to act as the central authority [6].

III. SYSTEM MODEL

A. Network Model

We consider a hybrid network consisting of several primaryuser networks and a secondary user network. There are Nsecondary users. The total radio spectrum consists of Korthogonal frequency channels. Each primary user networkoperates over one channel. Let ΩN = 1, 2, . . . , N andΩK = 1, 2, . . . ,K denote the sets of secondary users andchannels, respectively. Each secondary user is equipped witha cognitive radio. They utilize omnidirectional antennas tocommunicate with each others. The network formed by thesecondary users is modeled as an undirected graph where allsecondary users are either directly or indirectly connected. Theset of secondary users are the nodes V , and the set of edgesis E ⊂ V ×V . Two users i and j are neighbours if (i, j) ∈ E .

Ni = j|(i, j) ∈ E ⊂ V is the set of neighbours of i.Secondary users are located within the transmission range ofthe primary users, and can individually sense the environmentto detect the existence of the primary users.

We use the energy sensing method in the cooperativesensing process for a secondary user to detect primary users’presence. An active secondary user measures the primary userenergy in a sensing session. Each sensing session is followedby a series of value update sessions, where active secondaryusers exchange local measurements with neighbors, and updatetheir own values based on received values. For the honestnodes, the initial values are the sensed values of the primaryuser energy. The malicious nodes may report arbitrary valuesaiming to achieve their malicious goals.

If the cooperative sensing results indicate that the primaryusers are not transmitting on certain channels, the secondaryusers can transmit on these unoccupied channels. The sec-ondary users are able to transmit or receive over multiplechannels simultaneously. They can also share a particularchannel with different transmission power, which leads to acorresponding level of interference. The transmission powervector of a secondary user i over all channels is denotedby Pi = (P 1

i , P2i , . . . , P

Ki ), where P ki is the transmission

power of i on channel k. There is an upper limit for the totaltransmission power of a secondary user over all the channels.

B. Adversary Model

There are three kinds of nodes in the network: (i) alwaysactive honest nodes, who participate in all the cooperativesensing processes, and report their sensed results and repu-tation vectors; (ii) honest but selfish nodes, who may choosenot to participate in the cooperative sensing process at all thechannels. When they decide to participate, they report theirsensed value to neighbors; and (iii) malicious nodes, who mayor may not participate in the cooperative sensing process, andreport falsified values when participating.

In cooperative sensing, the adversary can be either selfish,aiming to have exclusive access to the primary user spectrum,or vandalic, aiming to incur severe interferences between theprimary users and other secondary users. To achieve thesegoals, malicious nodes strategically report higher values of theprimary users when they are not transmitting, and vice versa.

We assume malicious nodes participate in the pricing gamewith fraudulent information. During the reputation fusionprocess, malicious nodes may report low reputation valuesfor honest nodes and high reputation values for themselves,aiming at lower prices in the spectrum allocation process.

IV. SELFISH BEHAVIORS AND CONSEQUENCES

Secondary users in a distributed CRN are subject to re-strictions in weight and form-factor, which in turn limitstheir power supply. Since frequent battery replacement is notalways practical, energy efficiency is in general an importantgoal. The power consumed by an active sensor is 24 mWcompared to merely 0.4 mW by an inactive sensor [1]. As aresult, a secondary user has a natural incentive not to sense

by itself, but to act as a free-rider by passively receivingthe cooperative sensing results from other honest nodes. Thatis, It can join the network and listen to the communicationchannel, without implementing the local sensing algorithm.Such selfish behavior has no direct harm to other secondaryusers. However, the lack of honest neighbors’ participationswill compromise the level of robustness and accuracy of thecooperative sensing results.

Another reason for selfish behavior of honest secondaryusers is the energy consumption and delay incurred by theiterative algorithms themselves [2]. Compared with individualsensing, the iterative algorithms proposed in the existingliterature delay the decision making process. The cost ofadditional energy consumption in reporting sensed value toa neighbor is also non-negligible. Weighting the cost anddelay from the cooperative sensing process, some honest nodesmay choose not to participate in the entire process, but toperform local sensing only. If these secondary users have bettersensing technologies by themselves, it makes sense for themnot to participate and share their data. Apparently, such selfishbehavior also has a negative impact on the overall wellbeingof the distributed CRN.

Our recent work showed that honest secondary users canobtain more accurate cooperative sensing reports in an ad-versarial environment, as long as more than half of theneighbors correctly report sensed values [13]. This was basedon the assumption that all honest secondary neighbors activelyparticipate in the entire cooperative sensing process. However,some honest neighbors may not actively participate in theprocess. More honest secondary users can help the secondaryuser network to obtain a more accurate cooperative sensingresult. The selfish behaviors of some of the honest nodeshowever may result in less accurate cooperative sensing resultsat other secondary users, which will degrade the performanceof the distributed cooperative sensing. This loss of accuracywill adversely affect all nodes and in particular the selfishsecondary users who will use the cooperative sensing resultsgenerated from the active secondary users. This can incentivizethe honest secondary users to participate in the cooperativesensing process. However, the incentive from the cooperativesensing process itself does not apply to the cases where honestnodes choose to sense by themselves but not to report.

V. THE INCENTIVE METHOD

To offer stronger incentives for honest nodes to participatein the cooperative sensing process, we connect sensing partic-ipation to the reputation in a distributed spectrum allocationprocess through a user-dependant pricing function in a spec-trum allocation game. In the distributed spectrum allocationprocess, some secondary users behave selfishly to maximizetheir own performance. A well designed pricing mechanismcan elicit social efficient behaviours from them.

We adopt the noncooperative game among secondary usersproposed in recent literature [10]. The game G is expressedas G = Ω,P, Ui, where Ω = 1, 2, . . . , N is a finiteset of players; P = P1 × P2 × · · · × PN is the action

space with Pi being the action set for player i; and Ui is theutility function of player i, which depends on the strategiesof all players, which are the secondary users. They can selectdifferent transmission powers on different channels. Highertransmission powers may bring higher achievable data rate. Atthe same time, higher prices are also incurred. Secondary usersselect their transmission powers to maximize their respectiveutility functions, and under certain conditions, they eventuallyreach a Nash Equilibrium after a number of iterations [10].

We use αA to denote the probability when the cooper-ative sensing result correctly determines that a channel kis unoccupied by the primary user in a sensing session A.The utility function of a secondary user i can be consideredas the achievable data rate received by i from the network,αAlog2(1 +

βGkiiPki∑

j∈ΩN,j 6=iGkjiP

kj +Mk

i

), subtracting the cost asso-ciated with the pricing function and the cooperative sensingprocess. Only when the primary user is not transmitting, thecost brought by the pricing function is incurred for a secondaryuser who is interested to transmit on this channel. We use alinear pricing mechanism [10] to describe the cost incurredby the pricing function, where the price αAλ

ki P

ki increases

monotonically with transmission power P ki . On each channelk, we denote the cost incurred by cooperative sensing foreach secondary user as cki . The total cost Ci from cooperativesensing for a node i depends on the number of channels itsenses Ki, Ci =

∑Kik=0 c

ki . The utility function is defined as:

Ui(Pi,P−i) =∑k∈ΩK

ui(Pki )

=∑k∈ΩK

ui(Pki )−

∑k∈ΩK

αAλki P

ki −

Ki∑k=0

cki

=∑k∈ΩK

αA[log2(1 +βGkiiP

ki∑

j∈ΩN ,j 6=iGkjiP

kj +Mk

i

)− λki P ki ]−Ki∑k=0

cki

(1)

where λiPki is the user-dependent linear pricing function

that can drive the Nash Equilibrium close to a Pareto optimalsolution. Gkii is the channel gain on channel k of the source toan intended destination, Gkji is the interference power receivedat the secondary user i from unintended user j, Mk

i is the noiseat i, β is the gap of SNR (signal-to-noise-ratio) that is neededto reach a certain capacity between practical implementationand information theoretical results [20].

The social optimization problem is to maximize a weightedsum of the achievable data rates of all secondary users:

maxP

∑i∈ΩN

Ri∑k∈ΩK

αAlog2(1 +βGkiiP

ki∑

j∈ΩN ,j 6=iGkjiP

kj +Mk

i

) (2)

where Ri is the reputation of secondary user i, assigned toi to reward active participation and to punish idle behaviors inthe cooperative sensing process. When a secondary user hasa better reputation, it shall gain a higher utility in the socialoptimization problem, and vice versa.

We adopt the methodology as in [10] to derive the optimalpricing factor for the secondary users, described in (3) ontop of the next page. The calculation for (3) is given in theAppendix. The pricing factor depends on the reputation values

of all the secondary users in the network. We can observe thatthe higher reputation value a node i has, the lower reputationvalues its neighbors have (including both malicious and selfishsecondary users), the lower price i has to pay in the spectrumallocation process. This effect can offer a strong incentive fora secondary user i to improve its reputation.

After receiving transmission power P ki , the noise Mki from

the neighbors, measuring Gkii and Gkij from the received signalpower, and obtaining the reputation values (Sec. VI), eachsecondary user first adjusts its liner pricing factor over allchannels according to (3), and then determines its best action,including the optimal channel selection and the transmissionrate on each channel. The goal of user i is to maximize itsindividual utility function (1). The same procedure happens atall secondary users in the network. The Pareto optimal NashEquilibrium is reached when all secondary users converge tothe best response. The secondary users can update their bestresponses according to the best responses of their neighborsiteratively, using Jacobi (parallel), Gauss-Seidel (sequential)schemes [10] or asynchronous schemes [21], [22].

VI. GENERATE REPUTATION

When discussing the spectrum allocation game, we estab-lished a reputation-based pricing scheme for secondary usersto reach Nash Equilibrium. A user with higher reputation isassigned a lower price in the game. The next step is to designan appropriate mechanism for generating reputation.

A. Sensing Participation

A natural way of generating Ri is to make public knowledgesecondary user i’s sensing participation R

(SP )i . R(SP )

i is aparameter relevant to the number of channels a secondaryuser actively senses in a cooperative sensing session. Ki isobservable by the neighbors of i.

We use the percentage of sensed channels of i for theoptimization: R(SP )

i = KiK . The higher R(SP )

i is, the betterprice i will obtain in the spectrum allocation process, whichcan be used as an incentive for i to increase Ki by participatingin more channels. To calculate Ki, each node in the networkmonitors its neighbors’ activity on channel k. We describe thisprocess in Algorithm 1.

Algorithm 1 Calculating Sensing Participation. (Input: The chan-nels a secondary user j participates in. Output: Reputation aboutsensing participation R(SP ) for all the secondary users.)

1: j participates in a subset of all channels2: j observes the other participants in every channel3: while There is a secondary user i participating on the same

channel do4: j broadcasts its observed channel participation information

Kj,i for another node i5: j receives the observed channel participation information

K1,i,K2,i,K3,i, . . . for another node i from its neighbors6: j calculates Ki = |K1,i ∪K2,i ∪ · · · ∪Kj,i ∪ . . . |7: i calculates R(SP )

i = KiK

8: end while

λki = −

∑j∈ΩN ,j 6=iRj

∂uj(Pkj )

∂Pki

Ri=

αAβ

Riln2

∑j∈ΩN ,j 6=i

RjGkijP

kj G

kjj

(∑i∈Ωj ,i6=j G

kijP

ki +Mk

j )(∑i∈Ωj ,i6=j G

kijP

ki +Mk

j + βGjjP kj Gkij)

(3)

Fig. 1: Observation on the sensing participations of neighbors

Consider the sensing participation in Fig. 1. Player 1 partic-ipates in channels 1, 3, 5, 7. Player 2 participates in channels1, 2, 3, 4, 5. Player 3 participates in channels 2, 3, 4, 5, 6.Since channel 4 is only sensed by Player 3, Player 3 has to doindividual sensing on channel 4. The activeness of Player 3 onchannel 4 is not counted towards its participation in coopera-tive sensing. To obtain Ki, Players 2 and 3 each observes onthe channels where they are active. They each records the otherplayers on a channel: K1,2 = 1, 3, 7, K1,3 = 3, 5, K2,1 =1, 3, 7, K2,3 = 2, 3, 6, K3,1 = 3, 5, K3,2 = 2, 3, 6.They broadcast the observations to neighbors. Each player thencalculates the cardinality of the union set for each individualneighbor. K1 = |K2,1 ∪K3,1| = 4, K2 = |K1,2 ∪K3,2| = 5.In this case, K3 = |K1,3 ∪ K2,3| = 4 rather than K3 = 5.Hereby, R(SP )

1 = R(SP )3 = 4

7 , R(SP )2 = 5

7 .

B. Sensing Accuracy

The above method incentivize users with reputation to par-ticipate in channel sensing. Considering that malicious nodescan be active in the cooperative sensing process to achievetheir malicious goals, the reputation shall be further improvedto reflect the sensing accuracy, besides level of participation.

We improve the sensing accuracy and participation byboth identifying falsified sensing reports and incentivizing theparticipation of honest secondary users. This idea is similaras Elo rating system for chess and ATP (the Association ofTennis Professionals) Rankings for tennis, where the more anathlete plays, the better an athlete performs, and the higherrating an athlete has. When connecting spectrum sensing withthe spectrum allocation process, reputation can reflect bothsensing accuracy and sensing participation of the secondaryusers. If a user participates more actively, or senses and reportsthe primary user state more accurately, it is assigned a lowerprice in the spectrum allocation process as a reward.

In a given sensing interval, a secondary user i has mi

neighbors who report falsified values (including attackingmalicious neighbors and honest nodes sensing incorrectlydue to severe fading or system failure), and ni neighborswho report correct values (including honest nodes sensingcorrectly and non-attacking malicious nodes). We use R(SA)k

j,i

to denote the reputation of transmitter i generated by receiverj to reflect the sensing accuracy of i. Each user j main-tains a reputation vector of its neighbors, on a channel k:R(SA)k

j,1 , R(SA)kj,2 , . . . , R

(SA)kj,mj+nj

. All secondary users updatetheir values and exchange their updated values with theirneighbors. Vi,j is the value that a transmitter i sends to areceiver j. After the first round of sensing value exchange, anhonest node calculates the reputation of its neighbors based ontheir reported values and its own value. The reputation valuesreflecting sensing accuracy R

(SA)kj,i are generated on channel

k as follows:

R(SA)kj,i = 2−

(mj + nj + 1)|V ki,j − V kj |∑mj+nj+1

l=1 |V kl,j − V kj |(4)

where V kj =∑mj+nj+1

l=1 V kl,jmj+nj+1 is the average value of all the

nodes in the neighborhood on channel k [13]. The value ofR

(SA)kj,i falls into [0, 2].This reputation generating method can assign reputation

R(SA)kj,i < 1 for a neighbor that reports falsified values, and

R(SA)kj,i > 1 reputation for a neighbor that reports correct

values, which will help honest nodes obtain better cooperativesensing results than the reputation-less scheme, assuming thatthe majority of neighbors are either correctly sensing honestnodes or non-attacking malicious nodes [13].

C. Reputation Fusion

Reputation values reflecting sensing accuracy of a secondaryuser are generated individually by its peers, and are fused intoa global reputation value for use in the pricing factor of thespectrum allocation process. The reputation fusion process is adistributed scheme without a central authority. Upon detectionof an idling primary user, the secondary users exchangetheir reputation vectors with each other iteratively towardsa converged global reputation. Such agreed-upon reputationvalues become public knowledge in spectrum allocation.

Inspired by the distributed algorithm for cooperative sensing[14], we design a distributed algorithm for secondary usersto achieve consensus on global reputation, as described inAlgorithm 2. µ is a discount factor. t indicates the reputationupdate session.

In the distributed reputation fusion algorithm, the consensusreputation value R

(SA)ki for i on channel k is the average

reputation value from all secondary users in the network

R(SA)ki =

∑j∈ΩN,j 6=i

R(SA)kj,i

Ni[18]. Since a node can sense on

multiple channels, the reputation value R(SA)i about a node

i can be described as 1Ki

∑k∈ΩK ,Pki >0R

(SA)ki . The higher

R(SA)ki it obtains, the lower price i faces in the spectrum

allocation process, which can be used as another incentive fori to contribute more accurate sensing results. This statement

Algorithm 2 Distributed Reputation Fusion Algorithmon Channel k. (Input: Reputation vector of a node j:R

(SA)kj,1 , R

(SA)kj,2 , . . . , R

(SA)kj,i , . . . , R

(SA)kj,mj+nj

and received reputationvectors from j’s neighbors. Output: The converged reputation vector.)

1: while i is a neighbor of j do2: j receives reputation vectors from a neighbor i:

R(SA)ki,1 , R

(SA)ki,2 , . . . , R

(SA)ki,mi+ni

3: j sends its own reputation vector to a neighbor i:R

(SA)kj,1 , R

(SA)kj,2 , . . . , R

(SA)kj,i , . . . , R

(SA)kj,mj+nj

4: while The converged reputation vector is not obtained do5: j updates its reputation vector as

R(SA)k(t+1)j,i = R

(SA)ktj,i +

mj+nj∑l=0

µ(R(SA)ktl,i −R(SA)kt

j,i )

(5)6: end while7: end while

also implies that a malicious node is less incentivized to attackwith falsified sensing results.

The method of generating and fusing R(SP )i has been

discussed before as R(SP )i = Ki

K , which falls into the rangeof [0, 1]. The two reputation vectors can be linearly combinedtogether with parameters ε and η, to form the final globalreputation Ri to be used in the pricing factor in the spectrumallocation process. Considering the different value ranges ofR

(SA)i and R(SP )

i , the global reputation value of node i is:

Ri = εR(SA)i + 2ηR

(SP )i

= ε1

Ki

∑k∈ΩK ,P

ki >0

R(SA)ki + 2η

Ki

K

=ε

KiNi

∑k∈ΩK ,P

ki >0

∑j∈ΩN ,j 6=i

(2−(mj + nj + 1)|V ki,j − V kj |∑mj+nj+1

l=1 |V kl,j − V kj |)

+2ηKi

K(6)

where 0 < ε < 1, 0 < η < 1, ε+ η = 1.

D. The Role of Reputation

For the linear combination of R(SA)i and R

(SP )i , we now

analyze the effect of the parameters towards incentivizingsecondary user participation. In the reputation value Ri, 2ηKi

Koffers incentive for both malicious and honest neighbors,εKi

∑k∈ΩK ,Pki >0R

(SA)ki offers incentive to honest neighbors

only. To differentiate secondary users in the spectrum allo-cation process, we propose the requirement that is consistentwith the requirement for sensing accuracy. We require thatRi < 1 for a malicious neighbor i, Ri > 1 for an honestneighbor i.

For an honest neighbor i, the requirement isεKi

∑k∈ΩK ,Pki >0R

(SA)ki > K−2ηKi

K . Since ε+ η = 1, the re-

quirement translates to εKi

∑k∈ΩK ,Pki >0R

(SA)ki > K−2ηKi

K(1−η) .

Since εKi

∑k∈ΩK ,Pki >0R

(SA)ki > 1, so an honest node has to

meet the requirement of K−2ηKiK(1−η) < 1 to obtain a reputation

value Ri > 1. This requirement can be transformed toKi >

K2 . Hereby, as long as it participates in more than

half of the channels and report correctly sensed values,the requirement is satisfied. In this case, the system canincentivize the honest nodes to participate in at least half ofthe channels. Again, the more channels it participates in, thelower price it can gain in the spectrum allocation process.

For a malicious neighbor i, the requirement isεKi

∑k∈ΩK ,Pki >0R

(SA)ki < K−2ηKi

K . Since ε+ η = 1, the re-

quirement translates to εKi

∑k∈ΩK ,Pki >0R

(SA)ki < K−2ηKi

K(1−η) .

Since εKi

∑k∈ΩK ,Pki >0R

(SA)ki < 1, as long as the

malicious node i is active on less than half of the channels,Ki <

K2 ⇔

K−2ηKiK(1−η) > 1, the requirement is satisfied. In this

case, the malicious node is for sure to receive Ri < 1, whichindicates a higher price in the spectrum allocation process.

For an active malicious neighbor i that attacks in morethan half of the channels Ki > K

2 , we need to analyzethe effect of parameter η. We can observe that the morechannels i actively attacks, the lower ε

Ki

∑k∈ΩK ,Pki >0R

(SA)ki

is. At the same time, the lower K−2ηKiK(1−η) also turns to be.

In the extreme situation where the malicious nodes attack allchannels, Ki = K. The requirement for Ri < 1 turns to beεKi

∑k∈ΩK ,Pki >0R

(SA)ki < 1−2η

1−η , where 1−2η1−η is the lower

bound for the system to meet the requirement.

VII. IMPROVE THE ROBUSTNESS OF REPUTATION

Malicious nodes are interested in manipulating the rep-utation values to give themselves lower prices, while givehigher prices to honest nodes. Once fused with correct data,such spurious data can lead to detrimental, unfair prices.We further assign differentiated weights to the reputationvalues about sensing accuracy. Such reputation-of-reputationserves as credibility to help honest nodes obtain more accuratereputation values their neighbours.

An honest node calculates the credibility of its neighborsbased on their reported reputation vectors and its own repu-tation vector after the first round of reputation exchange inAlgorithm 2. We use differentiated weight ω(SA)k

j,i to denotethe credibility of the transmitter i generated by the receiver j.Then, we can modify (5) to

R(SA)k(t+1)j,i = R

(SA)ktj,i +

mj+nj∑l=0

µω(SA)kj,i (R

(SA)ktl,i −R(SA)kt

j,i ).

(7)For requirements on ω(SA)k

j,i to guarantee that the reputationfusion in (7) to be better than that in (5), we have:

Proposition. Assume a node j can assign credibility ω(SA)kj,i <

1 to a neighbor that reports spurious reputation values, andω

(SA)kj,i > 1 to a neighbor that reports correct reputation

values. Then j can update the fused reputation value of aneighbor i to a higher reputation value when i reports correctsensing results, and a lower reputation value when i reportsfalsified sensing results, compared to the reputation fusionprocess without credibility ω(SA)k

j,i .Proof: Let si be the number of i’s neighbors who transmit

spurious reputation, ci be number of other neighbors. For anhonest node j, we denote the credibility of a neighbor i that

reports a correct reputation with ω(SA)kj,iC

, and the credibility

of a node i that reports a spurious reputation with ω(SA)kj,iS

.Comparing the two reputation update methods (5) and (7), wehave R

(SA)k(t+1)j,i = R

(SA)ktj,i + µ[

∑sji=0 ω

(SA)kj,iS

(R(SA)ktl,i −

R(SA)ktj,i ) +

∑sj+cji=sj+1 ω

(SA)kj,iC

(R(SA)ktl,i − R

(SA)ktj,i )] and

R(SA)k(t+1)j,i = R

(SA)ktj,i + µ[

∑sji=0(R

(SA)ktl,i − R

(SA)ktj,i ) +∑sj+cj

i=sj+1(R(SA)ktl,i − R

(SA)ktj,i )]. Therefore, the difference

between these two methods is:

µ[

sj∑i=0

(ω(SA)kj,iS

− 1)(R(SA)ktl,i −R(SA)kt

j,i )

+

sj+cj∑i=sj+1

(ω(SA)kj,iC

− 1)(R(SA)ktl,i −R(SA)kt

j,i )].

(8)

We now examine the two scenarios, when (i) an honestnode j generates the reputation of a neighbor correctly, or(ii) incorrectly, in which case the effect is the same as aspurious reputation value. In case (i), R(SA)kt

j,i ≈ R(SA)ktl,i

for a neighbor l that also generate a correct reputation value,then the difference between the two methods is approximatelyµ∑sji=0(ω

(SA)kj,iS

− 1)(R(SA)ktl,i − R

(SA)ktj,i ). While i reports

a correct sensed value, we have R(SA)ktl,i < R

(SA)ktj,i for a

neighbor l that reports a spurious reputation value. So, aslong as

∑sji=0(ω

(SA)kj,iS

− 1) < 0, (7) can help j obtain ahigher converged reputation for i than (5). While the nodei reports a falsified sensed value, R(SA)kt

l,i > R(SA)ktj,i for a

neighbor l that reports a spurious reputation value and so aslong as

∑sji=0(ω

(SA)kj,iS

− 1) < 0, (7) can help j obtain a lowerconverged reputation for i than (5). Thus the first requirementfor credibility is that

∑sji=0(ω

(SA)kj,iS

− 1) < 0 for a neighbor lreporting incorrectly.

In case (ii), R(SA)ktj,i ≈ R

(SA)ktl,i for a neighbor l that

also generate an spurious reputation value, then the differencebetween the two methods is approximately µ

∑sji=0(ω

(SA)kj,iC

−1)(R

(SA)ktl,i − R(SA)kt

j,i ). While i reports incorrectly, we haveR

(SA)ktl,i < R

(SA)ktj,i for a neighbor l that reports a correct

reputation value. So, as long as∑sji=0(ω

(SA)kj,iC

− 1) > 0, (7)can help j obtain a higher converged reputation for i than (5).While i reports a correct sensed value, R(SA)kt

l,i < R(SA)ktj,i

for a neighbor i that reports a correct reputation value andso as long as

∑sji=0(ω

(SA)kj,iC

− 1) < 0, (7) can help j obtaina lower converged reputation for i than (5). Thus the secondrequirement for credibility is that

∑sji=0(ω

(SA)kj,iC

− 1) > 0 fora neighbor l reporting a correct reputation value.

To generate the credibility ω(SA)kj,i that can meet the two

requirements, we propose the method of:

ω(SA)kj,i = 2−

|R(SA)ktj,i − R(SA)kt

j,i |∑sj+cjl=1

|R(SA)ktl,i

−R(SA)ktj,i |

sj+cj

= 2−(sj + cj)|R(SA)kt

j,i − R(SA)tj,i |∑sj+cj

l=1 |R(SA)tl,i − R(SA)t

j,i |

(9)

where R(SA)ktj,k =

∑sj+cjl=1

R(SA)ktj,i

sj+cjis the average reputation

value of i from neighbors of j. We have 0 ≤ ω(SA)kj,i ≤ 2.

The rationale for this method lies in the observation aboutthe distances to the average reputation value. As long as thereare more neighbors that report correct reputation values for i,the distance from the reputation value of a node that reportscorrectly to the average reputation value will be smaller thanthe average distance to the average reputation value, and viceversa. That leads to the following theorem:

Theorem. 1. The credibility-generating method in (9) enableshonest nodes to assign ω

(SA)kj,i < 1 for neighbors reporting

spurious reputation, ω(SA)kj,i > 1 for neighbors reporting

correct reputation, for the reputation fusion method in (7).Therefore, (7) and (9) can help honest nodes obtain higherreputation values for other honest nodes, lower reputationvalues for the malicious nodes, given the condition that moreneighbors report correct reputation values. This improvementof the reputation robustness can assign higher prices to themalicious nodes, lower prices to honest nodes in the spectrumallocation process.

Proof: For a neighbor that reports spurious reputationvalues, the distance to the average reputation value is above

average: |R(SA)ktj,i − R(SA)kt

j,i | >∑sj+cjl=1

|R(SA)ktl,i

−R(SA)ktj,i |

sj+cj. Since

both sj + cj > 0 and∑sj+cjl=1 |R(SA)kt

l,i − R(SA)ktj,i | > 0, we

can have(sj+cj)|R

(SA)ktj,i −R(SA)t

j,i |∑sj+cjl=1

|R(SA)tl,i

−R(SA)tj,i |

> 1, which is equivalent to

2 −(sj+cj)|R

(SA)ktj,i −R(SA)t

j,i |∑sj+cjl=1

|R(SA)tl,i

−R(SA)tj,i |

< 1. According to (9), we have

ω(SA)kj,iS

< 1.The proof for the case where a neighbor who reports correct

reputation values is similar, and is omitted due to spaceconstraints. Combining these two cases with the requirementson credibility, we can verify the validity of the theorem.

VIII. PERFORMANCE EVALUATION

We now present simulation results for verifying the efficacyof the proposed incentive mechanisms. In our simulations,the SNR gap β is set to 0.3. Each secondary user has thesame capacity to communicate with other secondary usersin its proximity. The parameters for channel gain are set asGkii = 1 and Gkij = 0.1. The noises are Mk

i = 10−11W, ∀i ∈ΩN ,∀k ∈ ΩK . The transmission power of secondary usersare P ki = 10−1W, ∀i ∈ ΩN ,∀k ∈ ΩK . Primary users transmitwith a uniform probability αA = 0.5 on all channels. Wesimulate 10 secondary users, to observe: (1) the pricing factorvalues generated from both sensing accuracy and sensingparticipation; (2) the reputation fusion process under attacksfrom malicious nodes.

We examine the extreme situation where malicious nodesattack on all channels, reporting falsified sensed values in thecooperative sensing process and spurious reputation values inthe reputation update process. The honest but selfish secondaryusers participate in 10 different channels, reporting correctlysensed values in the cooperative sensing process and correctreputation values in the reputation update process.

1 2 3 4 5 6 7 8 9 1000.51

1.52

2.53

3.54

Malicious Node

Always Active Honest NodeSelfish Node

Number of Active Channels(a)

Pric

ing

Fact

or λ

1 2 3 4 5 6 7 8 9 100

0.51

1.52

2.53

3.54

4.5

Malicious Node

Always Active Honest NodeSelfish Node

Number of Active Channels(b)

Pric

ing

Fact

or λ

1 2 3 4 5 6 7 8 9 100.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Number of Active Channels

Pric

ing

Fact

or λ

(c)

Malicious Node

Always Active Honest NodeSelfish Node

1 2 3 4 5 6 7 8 9 100.10.150.20.250.30.350.40.450.50.550.6

Number of Active Sessions of Number of Active Channels(d)

Malicious Node

Always Active Honest NodeSelfish Node

1 2 3 4 5 6 7 8 9 100.10.20.30.40.50.60.70.80.9

Pric

ing

Fact

or λ

(e)Number of Active Channels

1 2 3 4 5 6 7 8 9 100123456789

Pric

ing

Fact

or λ

(f)Number of Active Channels

Pric

ing

Fact

or λ

1 2 3 4 5 6 7 8 9 100.20.30.40.50.60.70.80.91

Always Active Honest NodeSelfish NodeMalicious Node

Always Active Honest NodeSelfish NodeMalicious Node

Always Active Honest NodeSelfish NodeMalicious Node

1 2 3 4 5 6 7 8 9 10012345678910

Always Active Honest NodeSelfish NodeMalicious Node

Number of Active Channels

Number of Active Channels

Pric

ing

Fact

or λ

Pric

ing

Fact

or λ

(g)

(h)

Fig. 2: Pricing Factors for an always active node, a selfish node and a malicious node. Parameters:(a) 6, 1, 3, 0.5, 0.5. (b) 5, 1, 4, 0.5, 0.5.(c) 4, 3, 3, 0.5, 0.5. (d) 2, 5, 3, 0.5, 0.5. (e) 6, 1, 3, 0.9, 0.1. (f): 6, 1, 3, 0.1, 0.9. (g) 5, 1, 4, 0.9, 0.1. (h) 5, 1, 4, 0.1, 0.9.

1) Pricing Factor: We first simulate the pricing factor fordifferent kinds of secondary users in different situations. InFig. 2, the x-axis indicates the number of channels a selfishnode participates in, the y-axis is the pricing factor for anhonest node, a malicious node or a selfish node. We use thetuple # of always active nodes, # of selfish nodes, # ofmalicious nodes, ε, η to denote the different parameters.

We can observe that the always active nodes have lowerpricing factors compared to the malicious nodes. As thenumber of active channels increases, the pricing factors ofthe selfish nodes are eventually lowered to the same level ofan always active honest node. The more active channels theselfish nodes participate in, the lower prices they can obtain.Fig. 2 (a) and (b) depict scenarios with different numbersof malicious nodes. Since malicious nodes are all activelyspreading falsified sensing results on all the channels, theselfish node needs to participate in at least five channels whenthere are three malicious nodes, eight channels when thereare four malicious nodes, to obtain a lower price than themalicious nodes. As the number of malicious nodes increases,the differences between the pricing factors of an always activehonest node and a malicious node shrinks. Fig. 2 (a), (c)and (d) depict the scenarios with different numbers of selfishnodes. As the number increases, the pricing factor for a selfishnode decreases. This is because the pricing factor dependson the comparable reputation values of all the nodes in thenetwork. If other nodes have lower reputation values, thepricing factor for the selfish nodes can increase. Fig. 2 (a),(b), (e), (f), (g) and (h) depict the scenarios with differentselection of parameters ε and η. We can observe that the highervalue η is, the higher differences between the selfish node andan always active honest node. The reason is that the higherη amplifies the role of sensing participation in the pricing

factor. In this case, the secondary users can be incentivizedto participate on more channels. However, the importance ofsensing accuracy is downplayed. This is the tradeoff betweenthe two parameters ε and η. These observations indicate thatthe system can assign lower prices to more active honestnodes, and higher prices to malicious nodes.

0 50 100 1500

0.2

0.4

0.6

0.8

1

1.2

1.4

0 50 100 1500.20.40.60.81

1.21.41.61.82

No CredibilityUse Credibility ω

No CredibilityUse Credibility ω

Reputation Fusion Update Sessions Reputation Fusion Update Sessions

Upd

ated

Rep

utat

ion

Upd

ated

Rep

utat

ion

(a) (b)

Fig. 3: Reputation Fusion Process. The reputation fusion for theR(SA) of (a) an honest node; (b) a malicious node.

2) Credibility: Fig. 3 depicts the differences credibility ωbrings to the system performance for an honest node anda malicious node. For an honest node, the malicious nodesreport the lowest reputation 0. With the help of credibilityω, the converged reputation value R(SA) of another honestnode for the victim honest node is approximately 0.3 higherthan the scenario without credibility. For a malicious node, theother malicious nodes report extremely high reputation values2. With the help of credibility ω, the converged reputationvalue R(SA) of an honest node for the malicious node isapproximately 0.4 lower than the scenario without credibility.These observations indicate that the system can improve therobustness of reputation by reducing the effect of spuriousreputation values.

IX. CONCLUSION

We propose to use reputation as a pricing factor in thespectrum allocation process to incentivize cooperative sensingin distributed CRNs. The reputation values are generatedfrom both sensing accuracy and sensing participation. Boththeoretical analysis and simulation results indicate that thismethod can incentivize secondary users to participate in morechannels and report more accurate sensing reports, in orderto obtain lower prices in the spectrum allocation process.To countermeasure attacks in the reputation fusion processwhere malicious nodes report spurious reputation values, weproposed a method with the help of other honest neighbors.Our methods, from cooperative spectrum sensing to reputationfusion then to spectrum allocation, are entirely distributedwithout a central authority, and thus more applicable todistributed CRNs.

APPENDIX

The calculation of the optimal pricing factor as shown in(3) is:

λki = −

∑j∈ΩN ,j 6=i

Rj∂uj(P

kj )

∂Pki

Ri

= −

∑j∈ΩN ,j 6=i

Rj

∂[αAlog2(1+βGkjjP

kj∑

i∈ΩN,i 6=jGkijPki

+Mkj

)]

∂Pki

Ri

= −

∑j∈ΩN ,j 6=i

Rj

∂[αAlog2(1+βGkjjP

kj

GkijPki

+∑l∈ΩN,l 6=j,i6=j

GkijPki

+Mkj

)]

∂Pki

Ri

= −

∑j∈ΩN ,j 6=i

RjαAln2

∂(βGkjjP

kj

GkijPki

+∑l∈ΩN,l 6=j,i6=j

GkijPki

+Mkj

)

∂Pki

1+βGk

jjPkj

GkijPki

+∑l∈ΩN,l 6=j,i 6=j

GkijPki

+Mkj

Ri

=

∑j∈ΩN ,j 6=i

RjαAln2

GkijβGkjjP

kj

(GkijPki

+∑l∈ΩN,l 6=j,i6=j

GkijPki

+Mkj

)2

1+βGk

jjPkj

GkijPki

+∑l∈ΩN,l 6=j,i6=j

GkijPki

+Mkj

Ri

=

∑j∈ΩN ,j 6=i

RjαAln2

GkijβGkjjP

kj

(∑i∈ΩN,i 6=j

GkijPki

+Mkj

)2

1+βGk

jjPkj∑

i∈ΩN,i 6=jGkijPki

+Mkj

Ri

=

∑j∈ΩN ,j 6=i

RjαAln2

GkijβGkjjP

kj∑

i∈ΩN,i 6=jGkijPki

+Mkj∑

i∈ΩN,i 6=jGkijP

ki +Mk

j +βGkjjPkj

Ri,

which can be easily transformed to the final result of λki .

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