1

Social Security Aided D2D Communications:Performance Bound and Implementation

MechanismYulei Zhao, Yong Li, Member, IEEE, Lin Chen, Member, IEEE, Yang Cao, Member, IEEE,

Sheng Chen, Fellow, IEEE, and Ning Ge, Member, IEEE

Abstract—In a device-to-device (D2D) communications underlaying cellular network, any user is a potential eavesdropper for thetransmissions of others that occupy the same spectrum. Physical-layer security mechanism is typically employed to guarantee securecommunications, at the cost of reducing the system’s throughput. As hand-held devices are carried by human beings, we may leveragetheir social trust to decrease the number of potential eavesdroppers. Aiming to establish a new paradigm for solving the challengingproblem of security and efficiency tradeoff, we propose a social security aware D2D communication architecture that exploitssocial-domain trust for securing physical-domain communication. In order to understand the impact of social trust on the security oftransmissions, we analyze the system ergodic rate of social security aided communications via stochastic geometry, and our resultbased on a real dataset shows that the proposed social security aided D2D communication increases the system secrecy rate by about63% compared to the scheme without considering social trust relation. Furthermore, in order to provide implementation mechanism,we utilize matching theory to implement efficient resource allocation among multiple users. Numerical results show that our proposedmechanism increases the system secrecy rate by 28% with fast convergence over the social oblivious approach.

Index Terms—Social security, stochastic geometry, device-to-device communications, matching theory

F

1 INTRODUCTION

TO meet the increasing demands for local area services,device-to-device (D2D) communication is proposed as

a key component for next generation cellular networks [1],where user equipments (UEs) communicate with nearbydevices over direct links, instead of through a base station(BS) [2]. Licensed spectrum sharing in D2D communicationcan be categorized into two modes: overlay and underlay.Overlay assumes that the cellular and D2D users use or-thogonal spectrum resources without mutual interferencesat the cost of low efficiency. Underlay, as a more efficientway of spectrum sharing, enables users to share the samespectrum [3]. Due to this spectrum sharing, however, usershave the potential to intercept the transmission of othersthat share the same spectrum resource. Since the securityof communication is a critical issue for user privacy andmobile applications [4], mobile users may be reluctant toselect D2D communication mode, despite the considerablebenefits it brings. Therefore, academia and industry have

• Y. Zhao, Y. Li, and N. Ge are with Tsinghua National Laboratory forInformation Science and Technology (TNLIST), Department of Elec-tronic Engineering, Tsinghua University, Beijing 100084, China. (E-mails: zhao-yl12@mails.tsinghua.edu.cn, liyong07@tsinghua.edu.cn, gen-ing@tsinghua.edu.cn)

• L. Chen is with University of Paris-Sud. (E-mail: chen@lri.fr)• Y. Cao is with Huazhong University of Science and Technology. (E-mail:

ycao@hust.edu.cn)• S. Chen is with Electronics and Computer Science, University of

Southampton, Southampton SO17 1BJ, UK (E-mail: sqc@ecs.soton.ac.uk),and also with King Abdulaziz University, Jeddah 21589, Saudi Arabia.

This work was supported by the National Basic Research Program of China(973 Program) under Grant 2013CB329001, by the National Nature ScienceFoundation of China under Grant 61132002 and Grant 61301080, and by theCreative Research Group Program from NSFC (61321061).

put increasing efforts into the security problems [4], and thestandardization of D2D security communication has beenconsidered [5].

To provide confidential data transmissions, physical-layer security mechanism, which exploits the imperfectionsof wireless channel [6], is typically employed to ensure thatthe transmitter can communicate with the receiver, while thepotential eavesdroppers cannot intercept the informationat physical layer. Confidential D2D communications canbe maintained by adopting such a physical-layer securityscheme at the great cost of decreasing system transmissionrate. Therefore, it is a challenging problem to ensure secretD2D communications while sustaining the benefits of highspectrum efficiency.

Hand-held devices are carried by human beings whoform stable social structures, and social trust is a commonattribute adopted among family members, friends and col-leagues to form social groupings [7]. A natural question is‘can we leverage the social trust to improve the securityof D2D transmissions without scarifying the efficiency?’.Intuitively, social trust relations can help to reduce the num-ber of potential eavesdroppers and therefore to enhance thesecurity of communications. For example, by only sharingthe spectrum among social trusted users, the security oftransmissions can be enhanced without having to rely onphysical-layer security measure. Aiming to open up a newavenue for solving the challenging problem of security andefficiency tradeoff, we propose a social security aided D2Dcommunications architecture that exploits social trust forsecure communication. There are two key challenges inmeeting our goal. The first one is to understand the gains ofsocial security aware D2D communications, i.e., how social

2

trust can enhance social security rate, and the second one isto provide implementation mechanism to efficiently utilizesocial trust relations in system design, i.e., how to efficientlyutilize social trust to implement resource allocation amongcellular and D2D users.

Therefore, we investigate these two fundamental prob-lems. Our goal is to obtain theoretical bound and establishimplementation mechanism as the first step to understandand utilize the framework of social security aided D2D com-munications. The theoretical bound provides the potentialperformance gains of exploiting social trust among mobileusers for efficient secure transmission. We utilize stochasticgeometry to quantitatively analyze the social security ratefor D2D communications. Furthermore, we formulate theresource allocation as an optimization problem to maximizethe system social security rate and establish efficient imple-mentation mechanism based on matching theory. The socialsecurity mechanism presented here can also be applied toother wireless networks and has great potential to increasesystem secrecy rate significantly.

1.1 Summary of Main Contributions

Our contributions are summarized as follows:

• Social security aided D2D communications: We proposethis novel architecture by jointly considering socialtrust and secure communication to solve the securityproblem with ensured transmission rate. Specifically,the proposed scheme implements efficient spectrumsharing among mobile users by utilizing social trustin the social domain to achieve secure communica-tions in physical domain. To the best of our knowl-edge, this is the first study applying social trust toenhance the security of communications.

• Performance bound: We obtain the ergodic rate ofthe proposed social security aided D2D communi-cation architecture by utilizing stochastic geometry.Theoretical and numerical analysis based on a realdataset shows that the system secrecy rate increasesabout 63% by considering social trust relation. Ourresults also reveal how the D2D user density impactson the intercepted rate of cellular and D2D users,which indicates that efficient resource allocation isbeneficial in order to maximize the system secrecyrate.

• Efficient resource allocation: In order to provide prac-tical mechanism in utilizing social trust, we employmatching theory to implement efficient resource al-location by jointly considering social trust and mu-tual interference among cellular and D2D users. Ourresults show that the proposed matching algorithmsignificantly increases the system secrecy rate, andit outperforms the coalition game method withoutconsidering social trust by about 28% in the scenarioinvolving 20 D2D users.

1.2 Related Work

Security has attracted increasing attention from academiaand industry [4], especially for D2D underlaying cellu-lar networks due to spectrum sharing [8]. Physical-layer

security guarantees the secrecy of transmission from aninformation-theoretic viewpoint [6], which is conceived asa promise solution in 5G networks [9]. For example, ascheduling algorithm is proposed to maximize the physical-layer security transmission rate for future cellular networks[10]. Such a physical-layer security method typically as-sumes that all users are not trustworthy, and it ensures thesecrecy of transmissions at the cost of reducing the systemtransmission rate significantly. However, the assumptionthat all D2D users are not trustworthy is not appropriate,as users in same social grouping are often have high socialtrust [7], [11], [12], [13].

Social network features, such as social ties, communityand centrality, have been exploited to design efficient re-source allocation and mode selection for D2D communi-cation systems [11]. Social trust and reciprocity have beenutilized to design efficient cooperative strategies for D2Dcommunications [7], [12], [14], [15], [16], [17]. For example,Chen et al. [14] proposed a framework to maximize socialgroup utility, and Zhang et al. [17] designed social-awarepeer-discovery approach. These existing works however donot consider explicitly the security problem. To the best ofour knowledge, we are the first to consider the utilizationof social trust to enhance the security of D2D communica-tions. In particular, we propose a social security aided D2Dcommunication mechanism to protect user privacy and toensure spectrum sharing efficiency.

Stochastic geometry is an efficient tool to analyze spec-trum sharing relationships for large-scale wireless networks[18]. In recent years, many researches have utilized stochas-tic geometry to analyze interference and coverage proba-bility for D2D communication networks [3], [19], [20], [21].Lin et al. [3] proposed a general analytical approach withstochastic geometry to evaluate the performance of D2Dcommunication through overlay and underlay spectrumsharing schemes. Lee et al. [19] utilized stochastic geometricto analyze power control for D2D communication under-laying cellular network. Liu et al. [20] analyzed the ergodicrate for D2D overlaying multi-channel downlink cellularnetwork based on stochastic geometry. Furthermore, Maet al. [21] used stochastic geometry to model the D2D-enabled cellular network with eavesdroppers and exploitedthe interferences through a secrecy perspective.

Matching theory has been regarded as an efficient re-source allocation method for future wireless networks [22].Xu et al. [23] utilized a stable matching framework to solvenetwork problems. Gu et al. [24] introduced matching theoryto implement the efficient resource allocation for D2D com-munication underlaying cellular networks. However, thiswork only considered the scenario of one-to-one matching.Saad et al. [25] used many-to-one matching to implementuplink user association in small cell networks. By contrast,in this paper, we first utilize stochastic geometry to analyzethe critical parameters that influence the social security rate.Then, matching theory is used to determine the spectrumsharing relationships for secrecy transmissions.

The rest of this paper is organized as follows. Section 2presents the system overview and problem statement. Sec-tion 3 analyzes the theoretical physical-layer secrecy rateof the proposed social security aided D2D communicationscheme, while an efficient resource allocation is developed

3

Social Domain Social Domaiiin

Physical Domain

D2D signal 1c

2c

1 2

1 1 1( , )d d d

1 2

2 2 2( , )d d d

1 2

3 3 3( , )d d d

1 2

4 4 4( , )d d d

Alice

Bob

Smith A

Smith B

Brown A

Brown B David A

David B

Mike A

Mike B

Cellular signal D2D to D2D interference g

D2D to Cellular interference Cellular to D2D interference

Da

Social Tie

Eavesdropper

Fig. 1. A social security aided D2D communication underlaying cellularnetwork, with 2 cellular users, c1 and c2, and 4 D2D user pairs, d1 to d4.In physical domain, wireless links are subject to physical interferenceconstraints, while in social domain, social trusts among mobile usersare indicated.

in Section 4. Performance evaluations are given in Section 5,and Section 6 concludes this work.

2 SYSTEM OVERVIEW AND PROBLEM STATEMENT

2.1 System Overview

Fig. 1 illustrates the social security aided D2D communica-tions underlaying cellular network from both the physicaland social domains, where the social trust relationshipsamong mobile users are indicated in the social domain,while the wireless links are determined by the spectrumsharing relations among cellular users and D2D user pairsin the physical domain. Let C and D denote the numbersof cellular users and D2D pairs working under full-duplexmode [7], respectively. Cellular and D2D users that sharethe same spectrum resource will incur severe interferenceamong them [26].

In the social domain, social relation graph among mobileusers is denoted by G = (V,W), where V is the collection ofall the cellular users and D2D pairs with |V | = N = C + D,while W =

{ωi,j , i, j = 1, 2, · · · , N

}with binary ωi,j

denoting the social trust between users i and j. Specifically,ωi,j = 1 indicates that user i trusts user j; otherwise,ωi,j = 0. In our work, social trust relationships are undi-rected, i.e., ωi,j = ωj,i. In Fig. 1, Alice is friend of Smith andBrown, which means ωc1,d1 = 1 and ωc1,d2 = 1. They canenthusiastically share the same spectrum resource withoutworrying the secrecy problem, especially for Smith A andSmith B as well as for Brown A and Brown B which representthe D2D users of D2D pairs Smith and Brown, respectively.On the other hand, Smith and Brown have no trust of eachother with ωd1,d2 = 0, and both will worry the other’s eaves-dropping. Also Bob has no social ties with Mike and Davidwith ωc2,d3 = 0 and ωc2,d4 = 0. Thus, Bob is a potentialeavesdropper to Mike and David. We introduce social-linkprobability, denoted by ps ∈ [0, 1], to indicate the social

trust among cellular and D2D users, which is the proportionbetween social trust edges and total edges of the completegraph in the social domain, i.e., ps =

∑i,j ωi,j

/N(N − 1).

In the physical domain, proximity D2D users commu-nicating with each other can occupy the same spectrumresource of cellular users to increase the system capacity,and we need to match D2D users to cellular users to de-crease the mutual interferences. As shown in Fig. 1, thereare two cellular users, c1 and c2, as well as four D2D pairs,di(d1

i , d2i ), 1 ≤ i ≤ 4. Here we use di to denote the ith D2D

pair, with d1i representing transmitter and d2

i representingreceiver. D2D pairs d1 and d2 occupy the same spectrumresource with c1, while D2D pairs d3 and d4 share thespectrum resource with c2.

2.2 Problems and Challenges

From the above system overview, it is observed that socialtrust relations can be exploited to decrease the number ofpotential eavesdroppers and hence to improve the systemsecrecy rate. This motivates us to propose the social securityaided D2D communication to solve the challenging problemof security and efficiency tradeoff. There are two key issuesrequiring investigation in order to realize social securityaided D2D communications systems, namely, determiningthe potential gains of utilizing social trust to assist D2Dcommunications and providing practical implementationmechanism.

A major challenge in the derivation of performancebound is how to consider social trust relations to obtainthe system secrecy rate. In D2D communications, mutualinterference determines the maximum system rate. On theother hand, social trust relations of users have significantimpact on the maximum system secrecy rate. When oneadditional D2D user shares the same spectrum, it changesboth the interference and social relationships among users.

The challenge in implementation is how to efficiently al-locate the spectrum resources of cellular users to D2D usersby jointly considering social trust and mutual interferences.Traditional resource allocation in D2D communications onlyconsiders interference to divide mobile users into multiplegroups with small mutual interferences. However, in socialsecurity aided D2D communications, the users who aretrustworthy with each other may occupy the same spectrumresource, even though this may cause large mutual interfer-ences.

3 COVERAGE PROBABILITY AND ERGODIC RATE

We now tackle the first challenge of deriving the perfor-mance bound. Our analysis model is depicted in Fig. 2. D2Dpairs are spatially distributed according to a Poison pointprocess (PPP) Φd with density λd in the plane with radiusR [19], [20]. D2D receivers distribute randomly at fixed dis-tances away from their corresponding D2D transmitters. Wefirst study the mutual interferences among a cellular userand the D2D users that share the same spectrum resource.As illustrated in Fig. 2, D2D pairs d1, d2, d3 and d4 occupythe same spectrum resource of cellular user c. The uplinktransmission of c is interfered by D2D transmitters d1

1, d12, d1

3

and d14. D2D transmissions also interfere with each other as

4

D2D signal Cellular signal

1

3d2

3d

Base Station

Cellular user-to-D2D interf. D2D-to-Cellular user interf.

2

1d

1

1d

1

2d2

2dc

D2D-to-D2D interf.

1d

2d

3d

1

4d

2

4d

4d

Fig. 2. Illustration of interference relationship for D2D communicationunderlaying cellular network in single cell.

well as suffer the interference from the cellular user’s trans-mission. Consider for example D2D pair d3. d2

3 receives theinterference from d1

1, d12, d1

4 and c. From the eavesdropper’sperspective, d2

3 has the probability pe = 1 − ps to interceptthe transmissions of these other users.

The transmission link from node i to node j is modeledas a Rayleigh fading channel with channel impulse responsehi,j . The received power of node j from the transmission ofnode i is given by Pi,j = Pi · |hi,j |2 = Pi · ρ−α

i,j · |h0|2,where Pi is the transmit power of node i, ρi,j is the distancebetween the two nodes, α is the path-loss exponent, andh0 is the complex Gaussian channel coefficient. To completethe interference analysis, we need to consider the signal tointerference plus noise ratio (SINR) at each node in eachtime slot. The SINR at terminal j receiving the desired signalfrom transmitter i can be expressed as

γj =Piρ

−αi,j |h0|2

Pint,j + N0,

where Pint,j is the interference power received by terminalj and N0 is the noise power at the receiver.

3.1 Social Security Rate of Cellular UserThe coverage probability of cellular user c is defined byP

c

cov(Tc) = P(γc ≥ Tc), where γc denotes the SINR ofcellular user c and Tc is the SINR threshold required fordata detection. γc can be expressed as

γc =Pcρ

−αc,b |h0|2∑

d∈DPdρ

−αd,b |h0|2 + N0

, (1)

where D denotes the set of D2D users that share the spec-trum resource with c, ρc,b is the distance between c and BSand ρd,b is the distance between D2D user d and BS, whilePc is the transmit power of c and Pd is the transmit powerof d. The ergodic rate of cellular user c can be obtained as[19]

Rc =∫ ∞

0

log2(1 + x)P(γc = x)dx=∫ ∞

0

P(γc ≥ x)(1 + x) ln 2

dx. (2)

Each D2D user may act as eavesdropper to intercept thecellular user’s transmission. Let Ts denote the minimum

SINR requirement for eavesdropper to intercept the signalcorrectly. When the largest SINR at potential eavesdroppersis less than Ts, uplink information transmission of c is secret.

Definition 1 (Social security coverage probability of cellularuser). The social coverage probability of secrecy transmission forcellular user c, denoted by P

c

cov,s (Ts), is defined as

Pc

cov,s (Ts) = P(

maxd′∈Dc,e

γc,d′ ≤ Ts

), (3)

where Dc,e = {d|ωc,d = 0, d ∈ D}, and γc,d′ is the SINR atD2D receiver d′ for the transmission of c, which is given by

γc,d′ =Pcρ

−αc,d′ |h0|2∑

d∈D\{d′} Pdρ−αd,d′ |h0|2 + N0

,∀d′ ∈ D. (4)

Let Rec denote the intercepted transmission rate by D2D

users, which can be obtained as follows:

Rec =

∫ ∞

0

log2(1 + x)P(

maxd′∈Dc,e

γc,d′ = x)dx

=∫ ∞

0

P(

maxd′∈Dc,e

γc,d′ ≥ x)

(1 + x) ln 2dx

=∫ ∞

0

1− P(

maxd′∈Dc,e

γc,d′ ≤ x)

(1 + x) ln 2dx. (5)

As the information transmission of cellular user is in-dependent from the interception process of D2D users, thesocial secrecy rate of c can be defined as follows.

Definition 2 (Social security ergodic rate of cellularuser). The social security rate for cellular user c is Rs

c =max {Rc −Re

c, 0}.

From (5), Rec is determined by both mutual interference

relationship and social trust information. Therefore, Defini-tion 1 can capture this feature and reflect the impact of socialtrust on security rate.

Assuming the same transmit power Pc for every cellularuser and the same transmit power Pd for every D2D user,the coverage probability of cellular user is obtained as [19]:

Pc

cov (Tc) =1− exp

(− πλdR2

sinc(δ)

(Pd

Pc

)δ

T δc

)πλdR2

sinc(δ)

(Pd

Pc

)δ

T δc

, (6)

where δ = 2α , and the noise is neglected. Then the transmis-

sion rate of cellular user is:

Rc =∫ ∞

0

Pc

cov(x)(1 + x) ln 2

dx, (7)

which cannot guarantee the secrecy of data transmissions.

Theorem 1. If the receiver noise is negligible, the social secrecycoverage probability of cellular user is

Pc

cov,s(Ts) =

exp(−2πpeλd

∫ R

0

exp(−

πλd

(PdTs

Pc

)δ

ρ2c,z

sinc(δ)

)ρc,zdρc,z

). (8)

5

Proof. From (3), Pc

cov,s(Ts) can be derived as follows:

Pc

cov,s(Ts) = P(

maxd′∈Dc,e

γc,d′ ≤ Ts

)= P

(∩z∈Φe

γc,z ≤ Ts

)=EΦd

[ ∏z∈Φe

P (γc,z ≤ Ts)

](a)= EΦd

[ ∏z∈Φe

P(1− exp

(−P−1

c Tsραc,z

(σ2 + Id(z)

)))]

=EΦd

[ ∏z∈Φe

P(1− exp

(−P−1

c Tsραc,z (Id(z))

))](b)= EΦd

[ ∏z∈Φe

P(1− LId(z)

(−P−1

c Tsραc,z

))](c)= exp

(−2πpeλd

∫ R

0

LId(z)

(−P−1

c Tsρα0,z

)ρc,zdρc,z

), (9)

where Id(z) is the interferences at z incurred by the otherD2D users following the PPP Φd, and EΦd

[ ] denotes theexpectation with respect to Φd. According to the thinningproperty of PPP, potential eavesdroppers follow a PPP,denoted by Φe, with density peλd. Equality (a) comes fromthe fact that |h0|2 is exponentially distributed, equality (b)uses the results that LX(s) = E[exp(−sX)] and the receivernoise variance σ2 is 0, while equality (c) follows from theprobability generating functional of PPP [21]. It shouldbe noted that Id(z) can be replaced by Id, because thedistribution of PPP is unaffected by translation. LId

(s) isgiven by [19]:

LId(s) = exp

(−πλdP

δd sδ

sinc(δ)

), (10)

where s = P−1c Tsρ

αc,z . Substituting (10) into (9) leads to

(8).

From (5) and (8), we have the secrecy rate of c given by

Rec =

∫ ∞

0

1− Pc

cov,s(x)(1 + x) ln 2

dx. (11)

Finally, we obtain the social security rate of cellular user asRs

c = max {Rc −Rec, 0}.

3.2 Security Rate of D2D Users

Similarly, for D2D user pair di, its ergodic rate Rdi is:γdi =

Pdρ−αdi,di

|h0|2

Pcρ−αc,di

|h0|2+∑

d′∈D\{di}

Pdρ−α

d′,di|h0|2+N0

,

Rdi =∫∞0

log2(1 + x)P(γdi = x)dx,

(12)

where γdi is the SINR at receiver of D2D pair di and we useρdi,di to denote the distance between the transmitter andreceiver of D2D pair di.

Definition 3 (Social security coverage probability of D2Duser). The coverage probability of secrecy transmission for D2Duser di, denoted by P

di

cov,s (Ts), is

Pdi

cov,s (Ts) = P(

maxd′∈Ddi,e

γdi,d′ ≤ Ts

), (13)

where Ddi,e = {d|ωdi,d = 0, d ∈ D \ {di} ∪ {c}}.

The intercepted rate of D2D user di, denoted by Redi

, is:γdi,d′ =

Pdρ−α

di,d′ |h0|2

Pcρ−α

c,d′ |h0|2+∑

d0∈D\{di,d′}

Pdρ−α

d0,d′ |h0|2+N0,

Redi

=∫∞0

log2(1 + x)P(

maxd′∈Ddi,e

γdi,d′ = x

)dx,

(14)

where γdi,d′ is the SINR at the receiver of eavesdropper d′,and Re

diis the intercepted rate of regular transmission for

di. With Rdi and Redi

, we have the secrecy rate of D2D userdi.

Definition 4 (Social security ergodic rate of D2D user).The social security rate for D2D user di is Rs

di=

max{Rdi −Re

di, 0}

.

The coverage probability of D2D user di is given by [19]:

Pdi

cov(Td) =

exp

(− πλdT

δd

sinc(δ)ρ2

di,di

)1

1 +(

TdPc

Pd

)δ (ρdi,di

45π128R

)2 , (15)

where Td is the SINR threshold for data detection requiredby D2D receiver, and the noise is neglected. The transmis-sion rate of D2D user is given by

Rdi =∫ ∞

0

Pdi

cov(x)(1 + x) ln 2

dx. (16)

Theorem 2. If the receiver noise is negligible, the social securitycoverage probability of D2D user di is given as

Pdi

cov,s(Ts) = exp

(−2πpeλd

∫ R

0

Ld−d(sz)Ld−c(sz)ρdi,zdρdi,z

)

×

(1−

(∫ 2R

0

exp

(−

πλdTδs ρ2

di,c

sinc(δ)

)f(ρdi,c)dρdi,c

)), (17)

where

LId−d(sz) = exp

(−

πλdTδs ρ2

di,z

sinc(δ)

), (18)

LId−c(sz) = 1

/(1 +

(Pc

PdTs

)δ ρ2di,z(

128R45π

)2)

, (19)

and for 1 ≤ ρdi,c ≤ 2R,

f(ρdi,c) =2ρdi,c

R2

2π

cos−1(ρdi,c

2R

)− ρdi,c

πR

√1−

ρ2di,c

4R2

.

(20)

Proof. The secrecy coverage probability of D2D user di canbe expressed as

Pdi

cov,s(Ts) = P(

maxz∈Φe∪{c}

γedi,z < Ts

)(a)= P

(maxz∈Φe

γedi,z < Ts

)P(γe

di,c < Ts

). (21)

Equality (a) is because the secrecy probabilities for D2Dreceivers and cellular user are independent of each other.

6

The first part of (21) can be expressed as

P(

maxz∈Φe

γedi,z < Ts

)= EΦd

[ ∏z∈Φe

P (γdi,z < Ts)

](a)= EΦd

[ ∏z∈Φe

(1− LId(z)

(−P−1

d Tsραdi,z

))]

= exp

(−2πpeλd

∫ R

0

LId(z)

(−P−1

d Tsραdi,z

)ρdi,zdρdi,z

)(b)= exp

(−2πpeλd

∫ R

0

LId−d(z) (sz) LId−c(z) (sz) ρdi,zdρdi,z

),

(22)

where sz = P−1d Tsρ

αdi,z

. Equality (a) follows from σ2 = 0,and equality (b) comes from the fact that the interference ateavesdropper is from both other D2D users and cellular userso that the Laplace transformation LId(z) (sz) can be dividedinto two parts:

LId(sz) = E [exp (−szId)]

= E [exp (−szId−d)] E [exp (−szId−c)]= LId−d

(sz)LId−c(sz). (23)

From [19], we obtain the Laplace transformations, LId−d(sz)

and LId−c(sz), as given in (18) and (19), respectively.

The second part of (21) can be expressed as

P (γdi,c < Ts) = 1− E[exp

(−P−1

d Tsραdi,cIc(z)

) ]= 1− E [LIc(sc)] , (24)

where sc = P−1d Tsρ

αdi,c

and Ic(z) denotes the interferencesat c from other D2D users. Then we have the Laplacetransformation of Ic(z) as:

LIc(sc) = exp(−

πλdT2α

s ρ2di,c

sincδ

). (25)

Thus we have

P (γdi,c < Ts) =1−∫ 2R

0

exp

(−

πλdTδs ρ2

di,c

sinc

)f(ρdi,c

)dρdi,c,

(26)

where f(ρdi,c

)is the probability density function of ρdi,c

given in (20). By substituting (22) and (26) into (21), weobtain P

di

cov,s of (17).

The intercepted rate of D2D user can then be obtained as

Redi

=∫ ∞

0

P(

maxd′∈Ddi,e

γdi,d′ ≥ x

)(1 + x) ln 2

dx

=∫ ∞

0

1(1 + x) ln 2

(1− P

d

cov,s

)dx, (27)

and we have Rsdi

= max{Rdi −Re

di, 0}

,∀d ∈ D.Given the average intercepted rate Re

d, the average se-crecy rate Rs

d and the average transmission rate Rd of typicalD2D pair, we have the following theorem.

Theorem 3. The system secrecy rate Rssys = Rs

c + λdπR2 ·Rsd,

the system intercepted rate Resys = Re

c + λdπR2 · Red, and the

system transmission rate Rsys = Rc + λdπR2 ·Rd.

Proof. The system secrecy rate can be derived as:

Rssys = Rs

c + EΦd

[∑di∈D

Rsdi

]= Rs

c + λdπR2 ·Rsd (28)

Similarly, we can obtain Resys and Rsys.

3.3 Numerical ResultsTo evaluate the impact of D2D density and social linkprobability on secrecy rate, we set the simulation parametersas Pc = 100 mW, Pd = 0.4 mW, R = 500 m, and α = 4. Themaximum transmission distance of D2D pair is 50 m.

We first evaluate the performances of social obliviousmechanism by setting ps = 0. It can be observed fromFig. 3 (a) and (b) that the secrecy rates Rs

c and Rsd decrease

quickly as λd increases, while the intercepted rates Rec

and Red are affected slightly by changing λd. For example,

when the number of D2D pairs increases from 1 to 16, theaverage secrecy rates of cellular user and D2D pair decreaseby about 80% and 70%, respectively. The reason is thatlarger number of D2D users introduces more interferences,while the number of potential eavesdroppers also increases.Therefore, the intercepted rate changes slightly, and thesecrecy rate drops sharply. Similarly, the transmission ratesRc and Rd decrease quickly with the increase of λd. FromFig. 3 (c), it can be seen that the system or sum secrecy rateRs

sys first increases with the increase of D2D users, and itstarts to decrease when the number of D2D users is largerthan 10. This is because the system intercepted rate Re

sys isincreasing faster than the sum transmission rate Rsys, whenthe number of D2D users is larger than 10. Although thesystem transmission rate increases with the number of D2Dpairs, the sum secrecy rate decreases at some point, whichhas important implication for system design.

Then we evaluate the impact of social link probability.With 20 D2D users, the relationship between the systemsecrecy rate and ps is shown in Fig. 3(d). It can be seenthat the system secrecy rate increases about 200% when ps

increases from 0 to 1. It is also obvious from Fig. 3(d) thatsocial trust decreases the intercepted rate significantly.

Furthermore, we utilize the social trust relations from thereal dataset of Brightkite [27], which uses undirected edgesto represent friendships. We obtain the average number ofsocial edges of one user to represent the social link proba-bility ps, as depicted in Fig. 3 (e), which is used to obtainthe system secrecy rate Rs

sys in Fig. 3 (f). From Fig. 3 (e),it is observed that social link probability decreases as thenumber of D2D pairs increases. In Fig. 3 (f), Rp

sys is thesystem secrecy rate without considering social trust, whichshows the same trend as observed in Fig. 3 (c), while Rs

sys isthe system secrecy rate obtained by considering social trust.Observe that our proposed social D2D communication se-curity mechanism dramatically enhances the system secrecyrate, and Rs

sys outperforms Rpsys by about 63% on average.

Moreover, unlike Rpsys, Rs

sys keeps increasing as λb increases.

4 MATCHING THEORY FOR RESOURCE ALLOCA-TION

We provide the solution to maximize the secrecy rate, whichyields efficient resource allocation needed to utilize the

7

0 5 10 15 200

1

2

3

4

5

6

7

8

Number of D2D pairs

Ce

llula

r R

ate

(bit/(

s*H

z))

Rc

Rc

e

Rc

s

(a)

0 5 10 15 200.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Number of D2D pairs

D2

D R

ate

(bit/(

s*H

z))

Rd

Rd

e

Rd

s

(b)

0 5 10 15 200

5

10

15

20

25

30

35

40

45

Number of D2D pairs

Su

m R

ate

(bit/(

s*H

z))

Rsys

Rsys

e

Rsys

s

(c)

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

40

45

Social Link Probability(ps)

Su

m R

ate

s(b

it/(

s*H

z))

Rsys

Rsys

e

Rsys

s

(d)

4 6 8 10 12 14 16 18 200.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

Number of D2D pairs

So

cia

l L

ink P

rob

ab

ility

(ps)

(e)

4 6 8 10 12 14 16 18 2010

15

20

25

30

35

40

45

Number of D2D pairs

Su

m R

ate

(bit/(

s*H

z))

Rsys

Rsys

s

Rsys

p

(f)

Fig. 3. Performance analysis via stochastic geometry: (a) secrecy rate of cellular user when ps = 0, (b) secrecy rate of D2D user when ps = 0,(c) sum secrecy rate of cellular user and all D2D users when ps = 0,, (d) relationship between sum secrecy rate and social link probability given 20D2D pairs, (e) social trust based on real dataset of Brightkite [27], and (f) social security performance of real social trust.

social trust in order to attain the theoretical performancegains.

4.1 Problem Formulation4.1.1 Secrecy rate of cellular user c

Let the set of cellular users be C. To distinguish with theprevious single cellular user scenario, we use R′

c, Re′

c andRs′

c to denote the uplink channel rate, intercepted rate and

secrecy channel rate of cellular user c ∈ C, respectively.Let binary xc,d denote the spectrum sharing relationshipbetween cellular users and D2D users, namely, xc,d = 1indicates D2D user d occupies the spectrum resource ofcellular user c; otherwise xc,d = 0. The collection ofeavesdroppers for c ∈ C, denoted by D′

c,e, is given byD′

c,e = {d′|xc,d′ · (1− ωc,d′) = 1,∀d′ ∈ D}, which indicatesthat the number of potential eavesdroppers is jointly deter-

8

mined by spectrum sharing and social trust relationships.The interference at cellular user c ∈ C is incurred from

the D2D pairs sharing the same spectrum resource with cand it can be calculated as

∑d∈D

xc,dPdρ−αd,b |h0|2. The uplink

channel rate of the cellular user c is then given by

R′c = log2

1 +Pcρ

−αc,b |h0|2∑

d∈Dxc,dPdρ

−αd,b |h0|2 + N0

. (29)

The potential eavesdropper of d0 ∈ D′c,e shares the same

spectrum resource of c. Therefore, the interference at d0 canbe calculated as

∑d∈D\{d0}

xc,dPdρ−αd,d0 |h0|2. The intercepted

rate of c by the eavesdroppers is thus given by

Re′

c = maxd0∈D′

c,e

log2

1 +Pcρ

−αc,d0 |h0|2∑

d∈D\{d0}xc,dPdρ

−αd,d0 |h0|2 + N0

. (30)

The secrecy channel rate of the cellular user c is Rs′

c =max

{R′

c −Re′

c , 0}

.

4.1.2 Secrecy rate of D2D pair d

The collection of eavesdroppers for D2D user d ∈ D,denoted by D′

d,e, consisting of cellular users and D2Dusers, is given by D′

d,e = {c|xc,d · (1− ωc,d) = 1,∀c ∈ C} ∪{d′|yd′,d · (1− ωd′,d) = 1,∀d′ ∈ D}, where yd,d′ = 1 if andonly if ∃c ∈ C : xc,d = 1, xc,d′ = 1; otherwise, yd,d′ = 0. Toshow the difference with the single cellular user scenario, weuse R′

d, Re′

d and Rs′

d to denote the channel rate, interceptedrate and secrecy channel rate of the D2D user d, respectively.

The interferences at D2D pair d are incurred by the cellu-lar users and D2D users, which share the same spectrum re-source with d. These interferences can be expressed by Ic

d +∑d′∈D\{d}

yd,d′Pd′ρ−αd′,d|h0|2, where Ic

d =∑c∈C

xc,dPcρ−αc,d |h0|2.

The channel rate of D2D pair d is thus given by

R′d =log2

1 +Pdρ

−αd,d |h0|2

Icd +

∑d′∈D\{d}

yd,d′Pd′ρ−αd′,d|h0|2 + N0

. (31)

If eavesdropper d0 ∈ D′d,e is a D2D pair, the interferences at

d0 can be calculated as Icd +

∑d′∈D\{d,d0}

yd,d′Pd′ρ−αd′,d0 |h0|2. If d0

is a cellular user, the interference from other cellular usersequals to 0, i.e., Ic

d = 0. The intercepted rate of d by theeavesdroppers is therefore given by

Re′

d = maxd0∈D′

d,e

log2

1+Pdρ

−αd,d0 |h0|2

Icd +

∑d′∈D\{d,d0}

yd,d′Pd′ρ−αd′,d0 |h0|2 + N0

.

(32)The secrecy rate of D2D user d is Rs′

d = max{

R′d −Re′

d , 0}

.Combining the results of Subsections 4.1.1 and 4.1.2, we

obtain the system social security rate as

R(X) =∑c∈C

(Rs′

c +∑d∈D

xc,dRs′

d

), (33)

where X is the matrix of xc,d, ∀c ∈ C, d ∈ D. Thus, we canformulate the optimal resource allocation for social securitycommunications as the following optimization problem:

maxR(X),

s.t.

xc,d ∈ {0, 1},∀c ∈ C, d ∈ D;∑c∈C

xc,d ≤ 1,∀d ∈ D;

Rs′

c ≥ Rc,∀c ∈ C.

(34)

The second constraint is imposed since each D2D pair canonly occupy one cellular user’s resource, and the third con-straint guarantees the minimum secrecy rate Rc, required byeach cellular user to guarantee its quality of service (QoS).

Lemma 1. The optimization problem (34) is NP-hard.

Proof. The optimization objective has no concave proper-ties with xc,d. Moreover, it is a binary integer non-linearprogramming problem. Therefore, it is NP-hard in general[28].

Lemma 1 indicates that the optimization problem (34)cannot be solved by conventional algorithms. Note that thesecurity rate of cellular user and D2D users are determinedby both spectrum sharing relationships and social trustinformation. When one D2D user changes its spectrumsharing strategy, the security rate of other D2D users andcellular users may be impacted significantly. Therefore, weneed to adjust the spectrum sharing strategies of D2D userscooperatively to improve system security rate. In the fol-lowing section, matching game model is used to implementefficient resource allocation.

4.2 Matching Theory Model

Matching theory is an efficient method to implement re-source allocation, which works in a decentralized and self-organizing approach for large-scale networks [23]. Ourproblem (34) can be regarded as a two-sided many-to-onematching game, where each cellular user c ∈ C shares itsresource with multiple D2D pairs d ∈ D. Thus our resourceallocation problem can be reformulated as a many-to-onematching, denoted by the tuple (C,D,≻C ,≻D), where ≻C={≻c}c∈C and ≻D= {≻d}d∈D denote the sets of preferenceof cellular users and D2D pairs, respectively. The matchingbetween cellular users and D2D pairs can be defined asfollows.

Definition 5 (Matching of social security resource alloca-tion). A many-to-one social security matching M is defined asa function from the set C ∪ D onto the set of C ∪ D such thatc = M(d) if and only if d ∈M(c).

Each D2D user aims to improve its social security rate,and the utility of D2D user d is defined as

Ud(M) = Rs′

d . (35)

From the expression of Rs′

d , we can see that Ud(M) dependson the matching of other players, which demonstrates peereffects for matching. The utility of cellular user c on theother hand is defined as

Uc(M) = Rs′

c +∑

d∈M(c)

Rs′

d , (36)

9

which indicates that c aims to increase the sum secrecy rateof all users that occupy the same spectrum resource withit. From the utility definitions of Ud(M) and Uc(M), it isclear that each D2D user occupies the spectrum resource ofa cellular user without considering the other D2D users andcellular users, while a cellular user prefers to accept the D2Duser, which contributes to maximize the total security rateof all users sharing the same spectrum resource with it.

Definition 6 (Preference of cellular user). Cellular user cprefers d to d′, if Uc(M) > Uc(M ′), denoted by d ≻c d′, whereM ′ = M \ {(c, d)} ∪ {(c, d′)} for c ∈ C, d, d′ ∈ D.

Definition 7 (Preference of D2D pair). D2D pair d prefers cto c′, if Ud(M) > Ud(M ′), denoted by c ≻d c′, where M ′ =M \ {(c, d)} ∪ {(c′, d)}, for d ∈ D, c, c′ ∈ C.

Given the above defined matching model for social se-curity transmission, we aim to find a stable matching.

Definition 8 (Stable matching). A matching M is stable if andonly if there is no blocking pair. A pair (c, d) /∈M is regarded asa blocking pair for the matching M , if there is another matchingM ′ = M\{(M(d), d)}∪{(c, d)}, where M ′ ≻c M , M ′ ≻M(d)

M and M ′ ≻d M .

For the established matching model for resource alloca-tion, a stable matching indicates that no cellular user or D2Duser would benefit from replacing their current associationrelation. From the utility definition, it can be seen thatcellular users and D2D users may change their preferencesas the game evolves. During the evolution of matchinggame, the utility of each player may change due to mutualinterference and social trust. Therefore, the preference ofeach player is also varying, which incurs peer effects [22].From the above analysis, we can see that the proposedsocial security matching cannot be obtained based on thetraditional deferred acceptance algorithm [22]. Therefore,we need to design an efficient mechanism to obtain a stablematching.

We now analyze the property of the stable matchingqualitatively, which will provide the intuition to design ourproposed algorithm. If there exists blocking pair (c, d) ofmatching M , the new matching M ′ = M \ {(M(d), d)} ∪{(c, d)} is able to increase the system security rate underthe stable condition in Definition 8. In other words, a stablematching achieves a local optimum of the system sumsecurity rate R(X), which can be utilized to obtain a stablematching. On the other hand, as the optimization problem(34) is a binary integer programming problem, an globaloptimum matching Mopt can be obtained by exhaustivesearch. Obviously, Mopt is a stable matching. Therefore,there exists at least one stable matching for our proposedmatching game model.

4.3 Algorithm and SolutionWe propose a two-stage algorithm to achieve stable match-ing, as listed in Algorithm 1. In Stage I, we obtain the initialstable matching, which is then modified to increase systemsecrecy rate in Stage II.

4.3.1 Stage I. Initial stable matchingD2D users with their initialized preference list based ontheir utility are put into the matching queue. Then we

Algorithm 1: Proposed Social Security Matching

Input: D2D users’ preference list PLd and cellularusers’ minimum secrecy rate Rc ;Output: The stable matching Mfin;Initialize:

D2D user matching queue length: n← D;stop← false;

Stage I. Initial Stable Matching:while n ≥ 1 do

for k=1,...,C doc′ = PLd[k]; xc′,d = 1, d ∈ D;if Rs′

c′ < Rc′ or Dc′ is not stable thenxc′,d = 0; xc0,d = 1;

elsebreak;

n = n− 1;Obtain initial stable matching Mini;Stage II. Best Response Based Matching:Set the current matching as Mcur ←Mini;while stop == false do

Uniformly randomly choose one D2D user i;Choose the local best response x′

i according to (38),and update the M with M ′;if R(M ′) > R(M) then

Update Mcur ←M ′;if Matching M remains unchanged for two consecutiveoperations then

stop← true;

Return The stable matching Mfin ←Mcur .

randomly select D2D user d from the matching queue, whorequests to occupy the resource of its most preferred cellularuser c′. Whether to accept this request is determined fromtwo aspects. Firstly, c′ needs to guarantee its security rateRc′ and secondly, c′ must guarantee the stable matching ofthe other D2D usersDc′ that are already associated with it. Ifcellular user c′ refuses to accept the application, d is mappedwith empty resource c0. Then, d would be removed from thematching queue. The above operations are repeated until thematching queue is empty.

4.3.2 Stage II. Best response based iterationAlthough the initial stable matching found in Stage I doesnot exist block pair, it may not be the optimally stablematching that maximizes the system social secrecy rate.Therefore, we need to adjust this initial stable matching toimprove the system secrecy rate. From Definition 8, we havethe following observation.

Lemma 2. All local optimum points of R are stable matching.

Proof. Suppose that (c, d) is a blocking pair of matching M .We have

R(M ′)−R(M) =Uc(M ′) + UM(d)(M ′)− Uc(M)− UM(d)(M). (37)

From Definition 8, we observe that R(M ′) > R(M), whichindicates that block pair can increase the sum secrecy rate.

10

Now, suppose that matching M∗ is a local maximumpoint of R. If M∗ is not a stable matching, there exists blockpair. But from the above analysis, any block pair of M∗ mayincrease R, which contradicts the fact that R(M∗) is a localmaximum value of the system secrecy rate. Therefore, alllocal optimum points of R are stable matching.

In the light of Lemma 2, we need to adjust the initialmatching into a local maximum. The strategy of D2D useri, denoted by xi, represents the cellular user of whichD2D user i occupies the same spectrum resource. The bestresponse of D2D user i is defined as follows:

x∗i = arg max

c∈CUc(M ′) + UM(i)(M ′), (38)

where M ′ = M \ {(c,M(c))} ∪ {(c, i)}. We propose aniterative algorithm to obtain a local optimal stable matching,as listed in Stage II of Algorithm 1. The local best responseof i is adopted to select its associated partner. When thecurrent sum secrecy rate is larger than the initial matching,the new matching is maintained, and M is updated by M ′.After a finite number of iterations, the matching convergesto a local optimal stable matching Mfin.

4.4 Stability and Convergence

We now analyze the convergence and stability properties ofAlgorithm 1 in the following theorem.

Theorem 4. Starting from any initial stable matching Mini,Algorithm 1 always converges to a stable matching Mfin.

Proof. Each iteration of Algorithm 1 yields a new matchingby adopting the best response of D2D user, and the maxi-mum number of strategies for each D2D user is finite sincethere are only finite cellular and D2D users in the system.Therefore, the number of strategies for the given D2D userset D is a Bell number [26]. Thus, the system converges to astable matching Mfin after finite iterations with probability1.

We now prove that the final matching Mfin must bestable by contradiction. Suppose that Mfin obtained is notstable. Then, there exists a D2D user i ∈ D whose strategyis denoted by Mfin(i), and a new strategy M ′(i) such thatU(M ′) > U(Mfin). According to Algorithm 1, D2D user ican perform a changing matching from Mfin to M ′, whichcontradicts the fact that Mfin is the final matching.

5 PERFORMANCE EVALUATION

We evaluate the performance of the proposed matchingalgorithm for social security D2D communications basedon a real dataset and a large-scale simulated network. Themain parameters in our simulation are listed in Table 1.We uniformly and randomly distribute the cellular users

TABLE 1Main simulation parameters

Parameter ValueRadius of cell 500 m

Noise spectral density -174 dBm/HzMaximum distance of D2D 80 m

Transmission power of cellular user 200 mWTransmission power of D2D user 1 mW

and D2D users within the coverage of the BS. In particular,the transmitter of D2D link is randomly distributed in thecoverage of BS, and its corresponding receiver is randomlydistributed in the circle of transmitter with the maximumdistance. According to the solution of the proposed match-ing algorithm, we evaluate the following two performancemetrics.

1) System sum secrecy rate, which is determined by allthe D2D users and cellular users as well as the socialtrust among them.

2) The Jain’s fairness measure [29], which determineswhether the receivers of D2D users and the cel-lular users are receiving fair share of the systemresources.

In order to demonstrate the effectiveness of our stablematching algorithm, we compare the performance of ourscheme, denoted as Stable Matching (SM), with the follow-ing schemes.

a) Coalition Game (CG). It utilizes the coalition for-mation game to allocate the spectrum resources toD2D users [26]. This distributed algorithm achievesthe near-optimal solution of the system secrecy ratewithout considering social trust information and isthe current state-of-the-art solution.

b) Furthest First (FF). It allocates the D2D communica-tion resources with the resources of the cellular usersthat are furthest aways from the D2D users

c) Random Selection (RS). It uniformly and randomlyallocates the communication resources to the D2Dusers.

5.1 System Social Security RateWe first set up the simulation based on the social trust rela-tions obtained from the real dataset of Brightkite [27]. Thedataset Brightkite contains the check-in data between April2008 to October 2010, and the total number of check-ins is 4.5million. Brightkite contains an explicit social network, whichis utilized in our simulation. We first estimate the social linkprobability, which is provided in Fig. 3 (e). Then, the socialtrust among cellular users and D2D users are generated ineach simulation scenario randomly based on the obtainedreal social link probability.

Fig. 4 compares the system secrecy rate attained by ourproposed SM scheme with those of the three benchmarkschemes. In Fig. 4 (a), the number of D2D pairs is set to 10,while the number of cellular users varies from 10 to 20. Itcan be seen that the RS scheme has the worst performance,as it does not consider the mutual interference and doesnot utilize the social trust. Compared with the RS, our SMscheme increases the sum security rate about 50% given10 D2D pairs. It also can be seen that our SM clearlyoutperforms the existing state-of-the-art CG scheme.

In Fig. 4 (b), the number of cellular user is set to 5, andthe number of D2D pairs varies from 1 to 20. When thenumber of D2D pairs is more than 5, multiple D2D pairshave to share the same spectrum resource of one cellularuser. Observe from Fig. 4 (b) that the sum security rates ofthe CG, FF and RS schemes all decrease with the numberof D2D pairs, when the number of D2D pairs is no more

11

10 12 14 16 18 2050

100

150

200

250

300

Number of Celluar Users

Su

m S

ecu

rity

Ra

te(b

it/(

s*H

z))

SM

CG

RS

FF

(a)

0 5 10 15 2040

50

60

70

80

90

Number of D2D Users

Su

m S

ecu

rity

Ra

te(b

it/(

s*H

z))

SM

CG

RS

FF

(b)Fig. 4. Comparison of the system performance attained by the four schemes in a simulated network based on the real dataset [27]: (a) given 10D2D pairs and varying the number of cellular users, and (b) given 5 cellular users and varying the number of D2D pairs.

20 25 30 35 40200

250

300

350

400

450

500

550

600

650

Number of Celluar Users

Sum

Security

Rate

(bit/(

s*H

z))

SM

CG

RS

FF

(a)

0 10 20 30 4040

60

80

100

120

140

Number of D2D Users

Su

m S

ecu

rity

Ra

te(b

it/(

s*H

z))

SM

CG

RS

FF

(b)Fig. 5. Comparison of the system performance attained by the four schemes in a large-scale simulated network: (a) given 10 D2D pairs and varyingthe number of cellular users, and (b) given 5 cellular users and varying the number of D2D pairs..

than 10. This is because withing this range, the interferenceis relatively small, and social trust has dominant influenceon the sum security rate but the CG, FF and RS schemes allcannot utilize this information. When the number of D2Dpairs is more than 10, the mutual interference increasesconsiderably and has serious influence on the achievablesystem security rate. Therefore, the sum security rate of theCG scheme becomes increasing with the number of D2Dpairs, as the CG scheme can effectively take into account themutual interference. By contrast, our SM scheme effectivelynot only considers the mutual interference but also utilizesthe social trust information. Consequently, its achievablesystem security rate increases with the number of D2D pairsacross the whole range of D2D pairs, and it significantlyoutperforms the existing state-of-the-art CG scheme, as canbe clearly seen from Fig. 4 (b).

We also simulate a large-scale network with the sociallink probability ps = 0.8. Fig. 5 compares the system secrecyrate of our SM scheme with those of the three benchmarkschemes. In Fig. 5 (a), the number of D2D pairs is 10, and thenumber of cellular users varies from 20 to 40. This representsthe scenario of sufficient spectrum resource, where D2Dusers do not need to share the resource of a same cellular

user and, therefore, there may exist no interference amongD2D users. It can be seen from Fig. 5 (a) that our SM schemeachieves the best performance, and it clearly outperformsthe CG scheme. This is because our SM scheme can effec-tively consider the social trust information among D2D pairsand cellular users to achieve better resource allocation.

In Fig. 5 (b), the number of cellular users is 5, andthe number of D2D pairs varies from 0 to 40. When thenumber of D2D users is more than 20, both the social trustand mutual interference have serious influence on the sumsecurity rate. For example, the FF scheme only considersthe interference of each D2D pair and its performance isworse than that of the RS scheme when the number ofD2D pairs is above 30. Clearly, our SM scheme attains thebest performance among all the algorithms evaluated. Forexample, given 20 D2D pairs, our SM scheme increases thesum secrecy rate by about 25%, compared with the currentstate-of-the-art CG, as can be seen from Fig. 5 (b).

5.2 Impact of Social Link ProbabilityTo observe the impact of the social link probability on thesystem secrecy rate, we set the numbers of cellular users andD2D pairs to 5 and 20, respectively. Fig. 6 depicts the system

12

0 0.2 0.4 0.6 0.8 180

85

90

95

100

105

Social Link Probability(ps)

Sum

Security

Rate

(bit/(

s*H

z))

Social Security

No Security

Social Oblivious

Fig. 6. System secrecy rate performance as the functions of social linkprobability obtained by three different approaches, given 5 cellular usersand 20 D2D pairs.

Fig. 7. Comparison of the convergence rates, in terms of the averagenumber of iterations, required by our SM algorithm and the exhaustivesearch.

5 10 15 200.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

Number of Celluar Users

Fai

rnes

s

SMCGRSFF

(a)

0 5 10 15 200.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of D2D Users

Fai

rnes

s

SMCGRSFF

(b)Fig. 8. Comparison of the system fairness for the four schemes in a simulated network based on the real dataset [27]: (a) given 10 D2D pairs andvarying the number of cellular users, and (b) given 5 cellular users and varying the number of D2D users.

secrecy rates as the functions of the social link probability forthe three different approaches, where the ‘Social Security’denotes our SM approach, and the ‘No Security’ approachcorresponds to the best case that cellular users and D2Dusers all trust each other and there is no need to considersecurity transmission, while the ‘Social Oblivious’ approachrepresents the worst case that cellular users and D2D usersare social oblivious and they do not trust each other atall. In reality, social trust information exists among cellularuser and D2D users, and our Social Security approach caneffectively exploit this inherent relationship.

For each simulation scenario, we generate the social trustinformation among the cellular users and D2D users basedon ps randomly. With ps = 0, the system secrecy rate ofour SM approach has the smallest value equal to that of theSocial Oblivious approach, as in this situation cellular usersand D2D users are social oblivious. Thus, each user is thepotential eavesdropper of the transmissions of other users.With ps = 1, the SM approach attains the maximum systemsecrecy rate, as cellular users and D2D users trust eachother completely. It can be seen that with ps = 1, our SMincreases the system secrecy rate by about 28%, comparedto the Social Oblivious approach. When ps varies from 0to 1, the sum security rate of our scheme increases from

the smallest value to the largest value. The results of Fig. 6again confirm that our SM approach jointly considers thesocial trust information and mutual interference in resourceallocation effectively.

5.3 Computation ComplexityTo investigate the convergence rate of our proposed SMalgorithm, we set the numbers of cellular users to 4 and8, respectively, and vary the number of D2D users D. Theaverage number of iterations required by the SM algorithmto converge to the final matching is shown in Fig. 7, incomparison to that required by the exhaustive search. Theaverage number of iterations increases linearly by our algo-rithm to find the solution as D increases. By contrast, theexhaustive search needs 8D iterations to find the optimalsolution with 8 cellular users. Compared with the exhaus-tive search, our SM algorithm reduces the computationcomplexity dramatically.

5.4 System FairnessTo gain some insights on how the secrecy data transmissionis actually shared among the D2D users and cellular users,in Fig. 8, we depict the Jain’s fairness indexes obtained by

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the four schemes under the same simulated network en-vironment of Section 5.1. Among all the schemes evaluated,our proposed SM scheme achieves the best fairness resourcesharing among the cellular users and D2D users. Fig. 8 (b)also indicates that varying the number of D2D users has anon-obvious influence on the fairness of data transmissionfor these four schemes.

6 CONCLUSION AND FUTURE WORK

This paper has proposed the novel idea of social securityaided D2D communication underlaying cellular networks.We have quantitatively analyzed the impact of social truston the social secrecy rate utilizing stochastic theory. It hasbeen observed that the system secrecy rate increases byabout 63% when considering social trust relations basedon a real dataset. We have also used matching theory toallocate the resources of multiple cellular users to D2Dusers efficiently, which increases the system secrecy rate byabout 28%, compared to the social oblivious approach, in thecase involving 20 D2D user pairs. This study has opened anew paradigm for designing security D2D communicationsand has provided effective implementation mechanism forrealizing social security aided D2D communications.

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