Research ArticleGame-Theoretic Social-Aware ResourceAllocation for Device-to-Device CommunicationsUnderlaying Cellular Network

Lei Wang 12 Can Li1 Yanbin Zhang1 and Guan Gui 1

1National and Local Joint Engineering Laboratory of RF Integration and Micro-Assembly TechnologyNanjing University of Posts and Telecommunications Nanjing China2The State Key Laboratory of Integrated Services Networks Xidian University Xirsquoan China

Correspondence should be addressed to Guan Gui guiguannjupteducn

Received 25 October 2017 Accepted 20 December 2017 Published 23 January 2018

Academic Editor Mu Zhou

Copyright copy 2018 LeiWang et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Device-to-Device communication underlaying cellular network can increase the spectrum efficiency due to direct proximitycommunication and frequency reuse However such performance improvement is influenced by the power interference causedby spectrum sharing and social characteristics in each social community jointly In this investigation we present a dynamicgame theory with complete information based D2D resource allocation scheme for D2D communication underlaying cellularnetwork In this resource allocation method we quantify both the rate influence from the power interference caused by theD2D transmitter to cellular users and rate enhancement brought by the social relationships between mobile users Then theutility function maximization game is formulated to optimize the overall transmission rate performance of the network whichsynthetically measures the final influence from both power interference and sociality enhancement Simultaneously we discuss theNash Equilibrium of the proposed utility function maximization game from a theoretical point of view and further put forward autility priority searching algorithm based resource allocation scheme Simulation results show that our proposed scheme attainsbetter performance compared with the other two advanced proposals

1 Introduction

With the rapid spread of intelligence terminals and the explo-sive growth of communication capacity local area services areconsidered as a popular issue Traditional cellular networkscan not meet the explosive demands for gigantic amountof mobile users in the following years As Device-to-Device(D2D) communication enables direct communication be-tween a pair of mobile users in proximity by occupying thecellular spectrum without traversing the BS or core net-work [1 2] it becomes an important usage case through peer-to-peer scheme while nowadays mobile users in cellularnetworks need high-speed data service in which they couldpotentially be in range for direct communication [3ndash5] Forexample when friends close to each other want to exchangemusic picture or video via their ownmobile phone the D2Dcommunication can provide a reasonable solution for thelocal media service as the same interested contents can be

shared betweenmobile users In this way the throughput andspectral efficiency of the network can be highly increased [6ndash8]

In D2D communication underlaying cellular networkmobile users occupy the same licensed band of spectrumresource for cellular users to increase the system capacityHence resource allocation becomes the key issue in D2Dcommunication and appropriate resource allocation schemesare imperative to be conducted to settle this issue [9] Consid-ering the fact that the D2D communication shares the uplinkspectrum resource Xu et al utilize a reverse iterative combi-natorial auction basedmechanism to accomplish the resourceallocation [10] Ferdouse et al propose a throughput efficientsubcarrier allocation (TESA) proposal for multiclass cellularD2D systems [11] Hoang et al adopt graph-based approachto discuss the nonorthogonal dynamic spectrum sharing tomaximize the weighted system sum rate [12]

HindawiWireless Communications and Mobile ComputingVolume 2018 Article ID 5084842 12 pageshttpsdoiorg10115520185084842

2 Wireless Communications and Mobile Computing

Worth mentioning about the above studies [10ndash12] is thatmobile users in social networks usually form stable social net-works when communicating with others They are groupedby social relationships or background to form different com-munities which have the same interested contents Humanbeings in social communities share interested content throughonline social platforms such asWeibo andWeChatThemorethe interactions that take place in the community the fasterthe transmission rate the community will consider But thesestudies above all pay attention to improving the transmissionrate in an overall perspective to restrict the interferencecellular communication suffers [13] The characteristics ofhigh sociality may be able to improve the spectrum efficiencygreatly however this has not been considered

The sociality inD2Dcommunication has been extensivelystudied for resource allocation optimization problem Wanget al model the strength of sociality of D2D links by countingcontact time amongmobile users [14]Theauthors in [15] pro-pose a social-aware resource allocationmethod based on twohops communication with the BS (first hop) and extendingcommunication with another device (second hop) but withthe iterations proceeding the size of the master problem isalso increasing Li et al quantitatively analyze the benefittaken by the incorporation of social features and propose asocial-ware D2D communication framework by leveragingthese social networking characteristics this investigation hascreated the precedent for studying the problem of social-awareness based D2D resource allocation in [16]

The aforementioned works indicate that the rate perfor-mance of the network can be effectively improved by imple-menting proper interference control policy and fully usingsocial networking characteristics However how to allocatecellular resource for each D2D pairs is much more complexThe difference of our work from all the works done by thosepredecessors is that we maximize the sum transmission rateof the system by jointly paying attention to the interferencecaused by the D2D transmitter to cellular user and rateperformance enhanced by the social relationships betweenmobile users Thus we further design a priority searchingalgorithm based resource allocation scheme in D2D commu-nications underlaying cellular network

Generally D2D pairs along with cellular users may beself-interested to maximize their own benefit through coop-eration or competition in the underlaying D2D communica-tion network Consequently it is needed to develop suitablesolutions to the consideration we present above At the sametime game theory is adopted for modeling and researchingthe resource allocation problem in recent works Manykinds of game theory have been applied to the study of D2Dresource allocation problems In [17] a social-communityutilization optimization game is proposed to optimize theutility of social community for each of the D2D pairs Butmodeling the game in such a way seems quite a complextask In [18] Stackelberg game has been applied to modelthe interactions between D2D users and cellular users Sincethe Stackelberg game belongs to the category of cooperativegame its outcome is not social optimum Further cooperativegames such as Nash Bargaining Solution (NBS) are needed toimprove the results In [19] NBS is developed to tackle the

inefficiency of the scheme in [18] where the assumption is notreasonable in practical environment

Despite the popularity of game theory in recent resourceallocation related investigation the most common idea ofthese papers is to verify that any strategy that deviates fromthe Nash Equilibrium (NE) can not improve the system per-formance any moreThis one-side proof may be not convinc-ing enough when applying to resource allocation problembetween two disjoint sets influenced by mutual interferenceAccordingly the matching theory provides a distributedsolution to resource matching problem between two disjointsets In [20] the matching theory was employed to matchD2D pairs with cellular users to address the energy efficiencyoptimization problem in D2D enabled cellular networksBesides this work was extended to large-scale networks andacquired significant performance gains In [21] a 3D itera-tive matching algorithm was proposed to maximize the sumrate of D2D pairs while guaranteeing the QoS requirementof both cellular communication and D2D communicationIn [22] the matching theory was used to model the networkas a one-to-one matching market and each secondary user(SU) can maximize its utility by selecting the most suitableprimary user (PU) However it is confirmed that sociality-interference joint resource allocation problem has not beenconsidered from the perspective of matching theory

In this paper in order to jointly compare the influence ofsociality between the mobile users within the same commu-nity and power interference caused by D2D communicationwe discuss the main problem existing in current resourceallocation scheme and propose a utility function maximiza-tion (UFM) game for D2D communication underlayingcellular network by utility function construction game estab-lishment providing relative proof for the existence of NashEquilibrium Inspired by one-to-one matching theory wepropose a priority searching algorithm based resource alloca-tion scheme to acquire the final resource allocation proposalfor the UFM game We perform extensive simulations underrealistic social network to evaluate the rate performance ofour proposed scheme The result shows that our proposedscheme improves system performance obviously in terms ofincreasing the overall transmission rate and decreasing thetransmission time

The remainder of this paper is organized as followswe introduce the system model and formulate the problemin Section 2 UFM game is formulated in Section 3 Thenin Section 4 a priority searching based resource allocationalgorithm is proposed and in Section 5 simulation resultand analysis are given and finally we make the conclusionof the paper in Section 6

2 Problem Formulation

21 System Model We consider the D2D communicationunderlaying cellular network in which D2D links occupy thespectrum resource of uplink cellular communication Thereason why we choose uplink one is that when the cellularusers (CUs) are in downlink transmission they will sufferfrom sophisticated interference caused by D2D communica-tion [23] Otherwise we divide the investigation of social-awareness based resource allocation forD2D communication

Wireless Communications and Mobile Computing 3

Community 1 Community 2

Kole

Smith

Social domainCommunication domain

Mike

Sarah

Bob

Alice Jack

DT

1 DR

1

DT

nD

R

n

UE0

UEn

D2D signalCellular to D2D interferenceCellular signal

D2D to cellular interference

Figure 1 Illustration of social-aware D2D communications under-laying cellular network In physical domain wireless links aresubject to the physical interference constraints while social domainindicates the relationships between mobile users

underlaying cellular networks into two domains in our workphysical domain and virtual social domain More detailsabout these are illustrated in Figure 1

In the physical domain the system contains 119873 nodeslabelled as the set of N = 1 2 119873 Each node denotesa mobile user that can communicate with the BS or executeD2D communication with other users directly For activemobile users they can form D = 1 2 119863 D2D pairsThe remaining which is denoted by the setC = 1 2 119862can request for interested content toward BS via cellularcommunication Those D2D pairs can choose to reuse thespectrum resource of any cellular users But there existphysical constraints between mobile users and only some ofthem can form D2D pairs (including D-Tx and D-Rx) [24]

In the social domain for the reason that a communityis combined by sophisticated relationship like friendshipkinship or even classmates with each other [25] and theywere physically in close proximity we tend to make use ofthese characteristics to model the social relationship betweenthe users Users consider the strength of their social trustwithin a community and their properties of social trustbetween different communities respectively to make D2Dcommunication more secure

To ensure the practicality of our work we set the channelscene as Rayleigh fading channel Under the premise of thefree space propagation model the interference signal powerlevel of cellular user which is introduced by D2D transmitterD-Tx sharing the same spectrum resource with cellular usercan be expressed as follows according to Shannon theorem

119875int119888 = 119875119889 sdot 120577119888119889minus120572 sdot ℎ2119888119889 (1)

while the interference signal ofD2D receiverD-Rx is from theBS that establishes communication link with cellular usersThus the signal power can be expressed as

119875int119889 = 119875119861 sdot 120577119861119889minus120572 sdot ℎ2119861119889 (2)

where 119875119889 and 119875119861 are the transmitted power of BS and D2Dtransmitter respectively 120577119888119889 denotes the distance betweenthe D2D transmitter and cellular user and 120577119861119889 denotes thedistance between D2D receiver and the BS 120572 is the path lossexponent and ℎ119888119889 and ℎ119861119889 are the complexGaussian channelcoefficients

In our investigation we assume there are one D2D pairand one cellular user within a single cell By sharing cellularspectrum resource blocks with D2D pair D2D communica-tion and cellular communication can be conducted syn-chronously [26] For the purpose of maximizing the overallsystem transmission rate the Signal-to-Noise Ratio (SINR) ofthe two communicationmodes is regarded as important indi-cator Based on (1) and (2) we can obtain the SINR of cellularuser 119888 and D2D receiver 119889 as

SINR119888119894 = 119901119888119892119888119875int119888 + 1198730 SINR119889119894 = 119901119889119892119889119875int119889 + 1198730

(3)

119901119888 is the given transmission power of cellular user and 119901119889 isthe given transmission power of D2D transmitter 119892119889 and 119892119888are the channel gains of cellular link and D2D link respec-tively And1198730 is the noise power on each channel

At the same time we usually calculate the sum rate ofthe system to measure the quality of D2D communicationunderlaying cellular network For uplink direction let 119877119888119894 bethe data transmission rate between theCUand the BS and119877119889119894be the data transmission rate between D-Tx and D-Rx Sincethe transmission rate of each cellular link and D2D link canbe determined by the Shannon capacity [27]

119877119888119894 = 119861119888119894 log2 (SINR119888119894) 119877119889119894 = 119861119889119894 log2 (SINR119889119894) (4)

where SINR119889119894 and SINR119888119894 are the Signal-to-Noise Ratio(SINR) inD2D and cellular communication links and119861119888119894 and119861119889119894 are the allocated licensed band of resource for D2D andcellular communication What is imperative to mention hereis that we only consider the interference that occurred withina single cell and do not consider any influence from othermicrocells

To describe reusing relationship of spectrum resource wedenote 119909119888119889 isin [0 1] as the indicator matrix of the D2D pairsthat is 119909119888119889 = 1 when the D2D pair 119889 occupies the licensedband of resource of the cellular user 119888 otherwise 119909119888119889 =0 Thus we can acquire the transmission rate of D2D pairmultiplying the indicator 119909119888119889 by 119877119889119894 as 119877119889119894 sdot 119909119888119889 The systemperformance can be represented by the sum of 119877119888119894 and 119877119889119894

119877 = Dsum119894=1

(119877119888119894 + 119877119889119894 sdot 119909119888119889) (5)

4 Wireless Communications and Mobile Computing

We can improve the system performance by maximizingthe sum rate to judge whether our proposed optimal social-aware resource allocation scheme is effective

maxDsum119894=1

119877119888119894 + 119877119889119894 sdot 119909119888119889st sum119889119894isinD

119909119899119888119889119894 le 1 119888 isin C 119899119888 isin C

sum119899119888isinC

119909119899119888119889119894 le 1 119888 isin C 119889119894 isin D(6)

22 Problem Description

221 Power Interference In D2D communication networkwe assume the cellular users can share uplink resource withuser equipment During the D2D communication it isinevitable that D2D transmitter interference will be intro-duced to others especially to nearby CUs And since we limitthat each D2D pair can reuse the spectrum resource from atmost one cellular user by assuming there are 119863 D2D pairsand 119862 cellular users in the D2D underlaying communicationcellular network we can simplify the network as Figure 2

In the simplified networkwe establish besides the normalD2D communication we only consider the effects of both theinterference of a generic D2D transmitter introduced toothers and all other interference caused to a D2D receiverFor instance the base station (BS) introduces intratiersinterference to the D2D receivers D2D1198771 as shown in Figure 2Meanwhile due to the full frequency reuse D2D1198791 causesinterference to CU1 Considering the power interferencecaused by the transmitter of the D2D pairs to the nearby UEwe can give the definition that the interference introduced byD2D transmitter 119889 to cellular users 119888 is 119868119889rarr119888 119889 isin D 119888 isin C

119868119889rarr119888 = 119892119889119888119901119889 (7)

where 119901119889 denotes the transmission power of the correspond-ing D2D pairs 119889 119889 isin D 119892119889119888 denotes the gains of the channelbetween the transmitter of D2D pair 119889 to cellular users 119888Here the terms 119888 and 119892119889119888 are positive Hence all of the cel-lular users are assumed in the single cell and correspondinginterference is introduced by prayer 119889 119889 isin D where theplayer 119889 is called the generic D2D transmitter Meanwhilethe transmission between player 119888 119888 isin C and the BS alsointroduces interference to D2D pair 119889 where we define theintratier interference from player 119888 to player 119889 as follows

119868119888rarr119889 = 119892119888119889119901119888 (8)

where 119892119888119889 is the channel gain between the BS and the D2Dpairs 119889 119901119888 is the transmission power of cellular user 119888 Herewe assume that orthogonal channels are used for differentCUs and we do not consider any power control policy atthe macrocell layer In our investigation we pay attention tothe power interference D2D transmitter introduced to theCUs in other words a new power control policy for the D2Dtransmitters

D2D link

Cellular to D2D interferenceCellular link

D2D to cellularinterference

５1

５2

５3５4

＄2＄1

＄2＄2

＄2＄3

＄2＄4

BS

Figure 2 Interference model in the uplink

222 Social Utilization In this part we use a visualizedsocial-network graph to analyze the social relationship be-tween the mobile users and depict the social characteristic ofthe network In the virtual social network social ties aredefined to qualitatively measure the strength of social rela-tionship between D2D users and report the communicationdemands between users Besides social centrality plays a veryimportant role in D2D data transmission users with highcentrality are more likely to hold high capacity in terms ofdata transmission volume and frequency In that case forthe purpose of obtaining a visualization of the social char-acteristics existing in userrsquos daily activities we adopt theproximity social network derived from a real-world mobilitydatasetmdashKarate clubThe network contains the social data of34 members within a Karate club documenting 78 pairwiselinks between members who interact inside or outside theclub [28] By analyzing the realistic dataset and the inter-action behaviors among these members we plot the socialnetwork formed by users visualized by the trace in Figure 3where the magnitude of the node indicates the centrality ofthe specified user and the label of the node indicates thestrength of the social ties of corresponding links

In the virtual social network active mobile users in closerelationship form certain community In order to weigh theinfluence from the social relationship between the mobileusers within the same community to our resource alloca-tion scheme we define the utility of social relationship byquantifying the social characteristic Sincewe supposemobileusers in different communities have no social trust betweeneach other when cellular users download some content fromthe BS cellular users belonging to the same community candeliver the content to other interested users directly insteadof forwarding by the BS And the amount of the content is

Wireless Communications and Mobile Computing 5

140

320

230

240

210

200

220

80

80

90

340

190

330

Figure 3 Social characteristics observed from social-network trace

determined by the social closeness between the users Themore close social relationship the D2D users have the morecontent they will exchange with each other [29]

Based on the analysis mentioned above the social graphcan be denoted by119866119904 = (119881119904 119877119904)119881119904 and 119877119904 stand for the set ofall cellular users and D2D users and the set of relationshipsrespectively To be mentioned the matrix 119877119904 demonstratesthe strength of the relationship of 119881119904 in the social networkGenerally we use the form of matrix described as 120596119889119903 119889 119903 =1 2 119863 and 120585119889119888 119889 = 1 2 119863 119888 = 1 2 119862 120596119889119903denotes the intimacy coefficient between D2D users and 120585119889119888denotes the intimacy coefficient between the cellular usersand D2D users According to the definition in the dataset ofKarate club we plan to divide the closeness coefficient intotwo kinds very close and a little close The values of 120596119889119903 and120585119889119888 follow the set of [0 1] For example 120596119889119903 = 0 impliesa little close intimacy between the D2D users and 120596119889119903 =1 naturally implies a very close intimacy As illustrated inFigure 1 we construct a simple social network In community2 D2D users Jack and Alice have a very close intimacy whileBob and Jack are unfamiliar with each other Inspired by theanalysis in Part A the utility of D2D users can be representedas follows

119880119889 = log2(1 + sum119894=119866119901

119889cap119866119904119889

SINR119889119894) forall119889 isin D (9)

Approximately the utility of cellular users can be representedas follows

119880119888 = log2(1 + sum119894=119866119901119888 cap119866119904119888

SINR119888119894) forall119888 isin C (10)

By the way 119866119901 and 119866119904 denote the physical and socialrelationship of the system model mentioned above Thus 119866119901119888and 119866119904119888 denote the set of cellular users that reuse the samefrequency band of spectrum resource and maintain stableinteractionwith each other119866119901

119889and119866119904119889 denotes theD2Dusers

which reuse the same spectrum resource from cellular usersand maintain stable interaction with the cellular users 119880119889represents the influence of the social relationship to D2Dcommunication and 119880119888 represents the influence of the socialrelationship to cellular communication To sum up we candefine the social-community utility function of D2D users 119889as follows

119880119889 (119883) = sum119903119889isinD

120596119889119903119880119889 + sum119888isinC

120585119889119888119880119888 (11)

119883 denotes the correlation matrix of 119909119888119889 and in general thedegree of social utility enhancement involves two aspects theweighted sum of social utility enhancement by D2D pairshaving social connections with each other as sum119903isinD 120596119889119903119880119889and the weighted sum of utility enhancement betweenfamiliar cellular users and D2D pairs as sum119888isinC 120585119889119888119880119888 In thisway the element of social relationship is considered in theinvestigation of resource allocation in D2D communicationunderlaying cellular network

3 Game Theory-Based Framework forResource Allocation

In our investigation we tend to maximize the sum trans-mission rate of the system For example if D2D transmitterbrings about higher-than-sociality interference to cellularusers the operator would remove the D2D link So wemodelthe resource allocation issue between D2D links and cellularlinks as the utility maximization game

31 Problem Formulation The resource allocation policy ofeach of the D2D pairs 119889 depends on the power interferenceintroduced by D2D communication and social relationshipsbetween themobile users Compared to the physical relation-ship betweenmobile users the social relationship is relativelyless changeableThus we need to consider the joint influencefrom social enhancement and power interference to the D2Dpairs dynamically By that we tend to define the utility of aD2D link as the profits which are contributed by cellular usersand D2D users using spectrum resources and D2D usersusing social characteristics In this case the utility functionof the 119889th D2D links is defined as follows

Γ119889 (119883) = 120572 sdot 119877 + 120573 sdot 119880119889 (119883) minus 120574 sdot 119861119889119894 minus 120576 sdot 119868119889rarr119888iff 119880119889 (119883) ge 119868119889rarr119888 (12)

120572 and 120573 are the charging price of unit data rate supportedby the spectrum resource and the social network 120574 and 120576are the cost function of a D2D occupied resource and power

6 Wireless Communications and Mobile Computing

interference With respect to 120574 a pricing function from (12)is adopted which can be expressed as follows

120574 = 119899 + 119904 sdot (1198611198891 + sdot sdot sdot + 119861119889119894)120591 119894 = 1 2 119898 (13)

119899 119904 and 120591 denote nonnegative constants and 120591 ge 1 toguarantee that the cost function is convex In order toimprove the applicability we suppose

[1198730 + 119892119889119875119889119903] = 119901119861119889119894 (14)

where 119901 is a nonnegative constant [30] then

Γ119889 (119883) = 120572 sdot 119861119889119894 log2 (1 + SINR119889119894) + 120573 sdot sum119895isinD

120596119889119903119880119889+ sum119888isinC

120585119889119888119880119888 minus [119899 + 119904 sdot 119898sum119894=1

119861119889119894]119861119889119894 minus 120576 sdot 119868119894rarr119906iff 119880119889 (119883) ge 119868119889rarr119888

(15)

In the proposed problem in (15) each D2D pair is aimedat integrating every aspect of influence and then maximizingits own utility As the distribution of mobile equipment ischanging all the time the features of the network are varyinginstantaneously So for the purpose of exact comparison weshould implement some effective method to eliminate thiskind of dilemma

Dynamic game with complete information can modelcertain dynamic situation under the premise that the par-ticipant knows the type of the action it will take and theinformation needed for every decision of the action It canbe applied into our proposed model as every D2D paircan get to know the social utility and power interferenceand get the real-time Γ119889(119883) when D2D communication isin progress So the problem above can be regarded as adynamic game with complete social information as well assophisticated interference information In this way we canpropose a dynamic game based scheme to optimize theoverall performance of theD2D communication network dueto the two-sidesrsquo competition

32 UFM Game Formulation From the analysis above wederive the information from two-sidesrsquo action needed inour game theory And for the optimization problem weusually utilize the game theory to solve it Firstly we definecorresponding strategy adopted by each D2D user 119889 in acertain point of history as 119886119889 119886119889 isin 119860119889 where 119860119889 is theset of all available strategies of the D2D pair 119889 The choiceof strategies of all the other participants that is all theother D2D pairs in our work can be defined as 119886minus119889 =1198861 119886119889minus1 119886119889+1 119886119863 If the above assumption for theUFM game theory is perfect there must exist a strategy 119886119889 isin119860119889 to maximize its own utility function

max119886119889isin119860119889

Γ119889 (119886119889 119886minus119889) forall119889 isin D (16)

The UFM game for the resource allocation thinking from theperspective of utility function is defined by quadruple Φ =D 119860119889119889isinD Γ119889119889isinD 119868119889rarr119888119889isinD119888isinC where D denotes the

D2D pairs119883119889 denotes all of the resource allocation strategiesD2D pairs set D can take Γ119889 denotes the utility function ofeach of the D2D pairs 119889 and 119868119889rarr119888 denotes the interferenceintroduced by D2D pairs 119889 to cellular user 11988833 Nash Equilibrium Nash Equilibrium is a very importantterminology in game theory [31 32] It represents a set ofstrategies which are combined by all optimal choices takenby each participant which reflect the optimal reaction eachparticipant adopts against the other participantrsquos strategiesAccording to this if the choices chosen by all the D2D pairsare optimal the system sum rate of the D2D communicationunderlaying cellular network will reach the extreme oneThefollowing part will discuss the existence of Nash Equilibriumin UFM game theory and provide proof for it

Generally the UFM game Φ = D 119860119889119889isinD Γ119889119889isinD119868119889rarr119888119889isinD119888isinC can reach the Nash Equilibrium if each of theD2D pairs has the only optimal response to the other D2Dpairrsquos strategy

119886lowast119889 = argmax119886119889isin119860119889

Γ119889 (119886minus119889 119886119889) forall119889 isin D (17)

and 119886lowast = 119886lowast1 119886lowast2 119886lowast119863 denotes the Nash EquilibriumBecause of the same incentive of changing their strategy

for all the D2D pair we refer to the potential game theory todemonstrate the existence of NE for the UFM game In [33]Monderer and Shapley propose the definition of potentialgame and elaborate the idea in detail too In the field ofwireless resource allocation games game theory has beenapplied in a few of authorsrsquo papers for example [34ndash36] Inpotential game theory the change in individual playerrsquos gaincan be mapped to the global function which is called thepotential function By this way we can conclude if there isany change that occurred on individual player the potentialfunction will change equally in the strict potential game Γdenotes an exact potential function if and only if exist119865(119868) 119868 rarr119880 forall119894 119895 forall119868119894 119868119895 119880119894 isin 119868119894 and 119880119895 isin 119868119895

Γ119894 (119868119894 119880minus119894) minus Γ119895 (119868119895 119880minus119895) = 119865 (119868119894 119880minus119894) minus 119865 (119868119895 119880minus119895) (18)

In the D2D communication systemwe havemodeled thechange of power interference and social utility caused byD2Dlinks would change the utility function of the game whichis consistent with the principle of potential function On theother hand potential gamehas the following inherent proper-ties which are described in [33] (1)There must exist a pure-strategy NE and a solution for it (2) The Nash Equilibriumcorresponds to the maxima of the potential function Γ (3)Generally the convergence to Nash Equilibrium would bereached in finite improvement or searching path accordingto sequential best-response dynamics

For the condition of a single band frequency channel thepotential game is formulated by utilizing the following utility-maximizing function

Γ119894 = minus (Total utility function generated by 119894+ Total utility function experienced by 119894) (19)

Wireless Communications and Mobile Computing 7

Based on the potential game theory we can demonstratethe existence of the Nash Equilibrium of our proposed UFMgame For Γ for every 119889 isin D and for every 119886minus119889 isin 119860minus119889

119875 (119889) = Γ119889 (119886minus119889 119886119889) minus Γ119889 (119886minus119889 1198861015840119889) (20)

Theorem 1 In certain history point 119905 function 119875(119889) derivedfrom UFM game is subgame perfect

Proof We suppose strategy 119886119889 denotes occupying the spec-trum resource of cellular user 119888 which is taken by D2D pairs119889 initially Therefore the initial indicator is 119909119888119889 Once D2Dpair119889 change its strategy andmake a request for the spectrumresource of cellular user 1198881015840 the indicator changes to1199091015840119888119889Thenwe can obtain

Γ119889 minus Γ1015840119889 = 120572 sdot 119877 + 120573 sdot 119880119889 (119883) minus 120576 sdot 119868119889rarr119888 minus 120572 sdot 1198771015840 minus 120573sdot 119880119889 (119883) minus 120576 sdot 1198681015840119889rarr119888

= 120572 sdot (119877 minus 1198771015840) minus 120576 sdot (119868119889rarr119888 minus 1198681015840119889rarr119888) (21)

We denote Δ 1 = 119877 minus 1198771015840 and Δ 2 = 119868119889rarr119888 minus 1198681015840119889rarr119888 As we cansee Δ 1 ≫ Δ 2 Finally we conclude that

Γ119889 minus Γ1015840119889 gt 0 (22)

It means that no D2D pair can acquire performanceenhancement by changing its strategy so we prove that ourproposed game is subgame perfect As subgame is the restric-tion from the perspective of history circumstances it canlead to the Nash Equilibrium of the game directly

4 Resource Allocation Scheme forUFM Game Theory

41 Priority Searching Based Solution The value of the utilityfunction Γ119889 varies when D2D pair chooses to reuse spectrumresource from different cellular user and the final aim of theUFM game is to determine the order of the utility function bythe size of value According to analysis in Sections 32 and 33the resource allocation strategy 119886lowast has a Nash EquilibriumIt means that we can finally achieve an optimal strategy bysubstituting the other strategies one by one in finite times Itis similar to the establishment of preference list and iteratesuntil acquiring the best selection among different alternatives[10] Inspired by the one-to-one matching theory we willshow the main idea of the proposed resource allocationalgorithm in detail

Definition 2 For anyD2D pairs we define the binary priorityrelation set≻119894 to represent the entire set of resource allocationstrategies that each D2D pair 119894 would possibly take In ourUFM game D2D pairs can choose to reuse the resourceoccupied by the associated cellular users or not according tothe priority set For any D2D pairs 119886119894 ≻119894 1198861015840119894 means D2D pairs119894 prefer choosing 119888 as the target resource source instead of 1198881015840

Since the priority set is determined by the utility function wecan define the priority as follows

1198861015840119894 ≻119894 119886119894 lArrrArrΓ119894 (1198861015840119894 ) gt Γ119894 (119886119894)

forall119894 isin D(23)

This definition demonstrates that D2D users 119894 are likelyto reuse the spectrum resource of cellular users 119888 as no moreoptions can bring additional performance gains We can setthe highest priority for cellular user 119888 in the set belonging toD2D user 119894 By this a complete priority set can be obtainedby repeating searching operation For every D2D pair wecan also design an optimization resource allocation schemebased on the priority set In this scheme everyD2Dpair urgesfinding its own highest priority and reusing the spectrumresource shared by the corresponding cellular users

Let us present Algorithm 1Based on the definitions and priority searching operation

we can obtain a final Nash-stable resource scheme 119886fin forD2D users to solve the utility maximization problem whichis given in Algorithm 1 From the whole knowledge givenabove we can see that D2D users make switching iterationfollowing a logically standard based on an arbitrarily choseninitial resource allocation strategy 119886ini At the beginning ofeach iteration D2D user 119894 isin D is randomly chosen by thesystem in step (13) And then the selectedD2D user replacesits resource allocation strategy with 119886ini by random choosinga occupied cellular users and determine its strategies 119886119894 anduniformly selects another social-trust cellular user 1198881015840 isin CThen the D2D pair will request the base station for the chan-nel state information once establishing communication linkwith these two cellular users 119888 and 1198881015840 After acquiring specifiedinformation the BS will computes the utility function of theresource allocation strategies of 119886 and 1198861015840 and broadcast tothe participant of the game model Meanwhile making thedecision that whether to carried out the switch operationfor D2D link If 119886119894 ≻119894 1198861015840119894 the switch operation will not beexecuted Otherwise the switch operation will be executedThe iteration will continue until all of the priority searchingoperations for each D2D pair are traversed and reach a finalNash Equilibrium scheme 119886fin

Different from those conventional D2D resource allo-cation schemes our proposed scheme needs to select suit-able community detection dataset and analyze the social-community information inside And a priority based poten-tial game theory is applied in our scheme This importantinformation is taken into consideration in our proposedscheme fully

42 Uniqueness and Boundedness According to Theorem 1for a given history point 119905 the combination of strategy 119886119894 119886119894 isin119860 119894 can reach a status of being subgame perfect as reactionto the combination of strategy 119886minus119894 To prove the uniquenessand boundedness of our proposed game it is necessary toconfirm that if there exist any participant forall1006704119894 isin D and its

8 Wireless Communications and Mobile Computing

(01) Input Number of mobile users119873 and random resource allocation strategy 119886ini(02)Output A priority based resource allocation scheme 119886fin(03) Utilize the dataset of Karate Club network(04) Calculate the transmission rate of the D2D links and cellular links(05) Obtain 119880119889(119883) and 119868119889rarr119888(06) if 119880119889(119883) le 119868119889rarr119888 remove the D2D links(07) else keep the D2D links(08) Define the matrix of indicator 119909119888119889 isin [0 1](09) 119868 = find 119909119888119889 = 0 ampamp 119868 = 1(10)There is just one 119888 cellular users qualified to shareresources to D2D user 119903 = 119903119888119889(11) else if uniformly randomly choose one cellular users 119888 and 119886possible cellular users 1198881015840 and denote its associate resourcesharing as 119886119894 isin 119886ini(12) Calculate Γ(1198861015840119894 ) and Γ(119886119894) priority = 0(13) if 1198861015840119894 ≻119894 119886119894 then Priority = 1(14) else repeat (15)sim(16)(15) if Priority == 1 then(16) D2D pairs quit current resource occupying strategy of 119888 andturn to adapt the new resource allocation strategy of 1198881015840(17) substitute the current resource occupying strategy 119886 forstrategy 1198861015840 and add it to 119886cur(18)Until all of the D2D pairs complete the priority searching operation resourceoccupying strategy switching operation and reach Nash Equilibrium 119886fin

Algorithm 1 The utility function maximization D2D links redistribution algorithm

corresponding strategy 1006704119886119894 can give better reaction to thestrategy combination 119886minus119894 than 119886119894 and make 1006704119886119894 ≻119894 119886119894 availableSo we provide the following proof relative to the uniquenessand boundedness of our proposed UFM game

Theorem 3 For all of the D2D pairs whose 119909119888119889 = 1 theproposed priority searching based scheme can only obtain aunique resource allocation scheme 119886finProof Based on the description in Algorithm 1 we supposereversely that the combination of strategy 119886119894 is not subgameperfect And then there must exist certain participant 119894 thathas strategy forall1006704119894 isin D and outperforms 119886119894 Now we investigateanother strategy 119886119894 and when 119905 lt 1006704119905 1006704119886119894 is equal to 119886119894 but after1006704119905 it is equal to 119886119894Then in any subgame after the history point1006704119905 strategy forall1006704119894 isin D is at least as well as 119886119894 for the reason thatforall1006704119894 isin D has deviated from 119886119894 once We can also conclude thatstrategy forall1006704119894 isin D is at least as well as 119886119894 after the history point119905 which is contrary to the assumption that strategy forall1006704119894 isin Dimproves the strategy 119886119894 And so on we can investigate other119886119894 to prove its equal benefit with forall1006704119894 isin D until reaching theunique resource allocation scheme 119886fin

Through the above analysis we prove the uniqueness ofthe UFM game by Reduction to Absurdity In each iterationin Algorithm 1 it may lead to a new resource allocationstrategy As there is only C in the physical domain andlimitedD D2D pairs due to the limited social relationship inthe social domain each of the D2D pairs is correspondingto C types of resource allocation scheme So the prioritysearching operation will eventually end in limited steps Thisfact assures the boundedness of our proposed UFM gamebased scheme

5 Simulation Results and Discussions

In this section we implement the simulation results from dif-ferent perspective to verify the performance of our proposedUFM algorithm and elaborate some necessary explanationfor the results Main simulation parameters have been givenin Table 1 Simulations are executed in a single cell whichare within an isolated community circumstance Path lossmodels are considered for cellular and D2D links along withshadow fadingmodel According to the dataset of Karate clubwe conduct the simulation within a 500m times 500m area toguarantee most of the club memberrsquos activities are within thisarea and 34 members of the club are randomly distributedwithin the BS coverage area Meanwhile the bandwidth ofallocated resource is assigned arbitrarily within the rangelimitation We compare our proposed UFM algorithm withthe following resource allocation schemes (a) distributedresource allocation (DRA) which allocates the D2D com-munication resource by thinking in a distributed way [37]and (b) optimal social-community aware resource allocation(OSRA) which allocates the D2D communication resourceto reduce the total transmission time [38] All the results areaveraged over 10 timesrsquo trial

Without loss of generality on one hand we prescribethe pathloss model between the base station and all themobile users as COST (EuropeanCooperation in Science andTechnology) 231 Hata model [39]

PLCU = 367 + 35 times lg (119889) (24)

Meanwhile we prescribe the pathloss model betweendifferent cellular users and D2D users as Xia model [40]given as follows

Wireless Communications and Mobile Computing 9

Table 1 System simulated parameters in the performance evalua-tion

Parameter ValueCoverage radius of BS 500mDistance of D2D 20msim50mNoise figure 9 dB at deviceTransmission power BS 46 dBm device 23 dBmMaximum D2D transmitter power 23 dBmRange of bandwidth 10MHzsim20MHzCommunication demand 50WInterference threshold 56 times 10minus6W119899 119904 119911 120591 1120572 120573 20

PL = 665 + 40 times log (119889) 119889 gt 501007 + 20 times lg (119889) 119889 lt 50 (25)

Since we assume the inner distance of D2D pair remainsin close standards and relatively close the free space modelcan be given by

PL = 384 + 20 times lg (119889) (26)

Moreover we consider the case of fast fading model forRayleigh fading In different situation we adopt a differentfading model to investigate In this way the evaluation of theaverage performance is objective We also set a great numberof criterions for our simulation the maximum power state ofD2D users is set at 23 dBm and the maximum interferencewhich mobile users can tolerate is assumed to be 50 times 10minus6Before investigating the system performance based on ourproposed UFM game we tend to show the joint influenceof the power interference caused by spectrum sharing andsocial characteristics in each social community illustrated inFigure 4

In this section we analyze the sum power interferenceand sum social utility respectively as the number of cellularusers varies The case of 10 cellular users means the situationof system whose spectrum resource is in short supply Inthis situation D2D users possibly have to share the spectrumresource of the same users while the case of 30 cellular usersmeans D2D pairs have many resource-occupying choicesThe results indicate that the sumpower interference decreaseswith the trend of the number of cellular users increasing asthe sum social utility stay in quite a stable level And whenthe number of cellular users in the system exceeds 18 theinfluence from social utility will surpass the influence frompower interference And thenwe evaluate the system sum rateand sum time with different number of cellular users usingthe proposed UFM algorithm and the other two advancedschemes which is illustrated in Figures 5 and 6

Figure 5 compares the sum rate of the three algorithmsunder the isolated scenarios in which we set the number ofcellular users varied in the range of [10 30] From Figure 5we observe that by removing some interference-intolerableD2D links significant performance enhancement can be

Social utilityPower interference

0

20

40

60

80

100

120

140

(Bits

(slowast

Hz)

)

12 14 16 18 20 22 24 26 2810Number of cellular users

Figure 4 Comparison of the joint interference

Comparison of sum rate of the system times104

12 14 16 18 20 22 24 26 302810Number of cellular users

1

2

3

4

5

6

7

8

UFMOSRADRA

(Bits

(slowast

Hz)

)

Figure 5 Transmission rate comparison of different resource alloca-tion algorithms with different number of cellular users

achieved when the cellular users are relatively sufficientBut in the situation that cellular users are not sufficientperformances of the two are roughly equalThe reason is thatthe excessive reuse relationships of frequency with the samecellular user will cause unbearable interference to the cellularusers According to our algorithm the D2D link will beremoved automatically in both schemes

Figure 6 compares the sum transmission time of the threealgorithms under the isolated scenarios From Figure 6 wecan observe that in the case that someunnecessaryD2D linkshas been removed the UFM algorithm still provides quite aconsiderable reduction of transmission timeThat is because

10 Wireless Communications and Mobile Computing

Comparison of sum time of the system

UFMOSRADRA

times10minus3

05

1

15

2

25

3

35

4

45

5

55

Sum

tim

e (s

)

12 14 16 18 20 22 24 26 28 3010Number of cellular users

Figure 6 Transmission time comparison of different resource allo-cation algorithms with different number of cellular users

we allowD2Dusers to continue to acquire content via cellularcommunication when D2D communication comes acrosslink interruption So the sum transmission time will not beaffected greatly

For the purpose of evaluating the system performancewhile the number of D2D users varies within a certainrange we set geographical scope as 300m times 300m aroundthe BS and suppose the number of cellular users is 10 Asillustrated in Figures 7 and 8 the variation range of numberof D2D pairs is [5 30] the result demonstrates that ourproposed UFM game always attains the best performancewith the increase of D2D users compared to the OSRAand DRA This is because in the algorithm of DRA orOSRA there exist little coordination measures to restrictD2D pairs to select their resource and it is inevitable toestablish some high-interference links between D2D pairsand cellular users In our proposed algorithm UFM gameeffectively coordinates both social relationship and powerinterference and then decides whether to access the spectrumresource of certain cellular users not in a random way Inthese circumstances we can avoid many high-risk links andattain a better system performance in terms of the evaluationof the sum transmission rate At this point we can summarizethat our proposed scheme precedes the other two schemes ina relatively comprehensive scale

6 Conclusion and Future Work

This paper studies game-theory based social-aware resourceallocation in the D2D communication underlaying cellularnetwork based on the realistic social network By consideringthe power interference and social utility in the physical andsocial domain respectively a game-theoretic based utilityfunction maximization scheme has been proposed Also to

Comparison of sum rate of the system

UFMOSRADRA

times104

0

1

2

3

4

5

6

7

8

10 15 20 25 305Number of D2D pairs

(Bits

(slowast

Hz)

)Figure 7 Transmission rate comparison of different resource alloca-tion algorithms with different number of D2D pairs

Comparison of sum time of the system

UFMOSRADRA

times10minus3

0

1

2

3

4

5

6

7

8

9

Sum

tim

e (s

)

10 15 20 25 305Number of D2D pairs

Figure 8 Transmission time comparison of different resource allo-cation algorithms with different number of D2D pairs

demonstrate the optimality of our proposed scheme thispaper provides evidence for the existence of Nash Equilib-rium theoretically Meanwhile a priority searching operationbased resource allocation scheme is designed to implementthe Nash Equilibrium of the proposed UFM game The pro-posed UFM scheme is numerically shown having superiorityover traditional DRA and OSRA scheme the performancesof sum rate and total transmission time are better thanthe OSRA and DRA algorithm through massive simulation

Wireless Communications and Mobile Computing 11

result suggesting that the proposed scheme is more ideal forjoint social-aware resource scenarios considering the socialcharacteristics Nevertheless some issues related to furthersystem optimization remain to be addressed such as powerallocation of mobile nodes and cluster formation of socialcommunity

Notations

N Set of mobile usersC Set of cellular usersD Set of D2D pairsΦ The UFM game≻119894 Set of utility priority119868119889rarr119888 Interference from 119889th D2D to 119888th cellular signal119868119888rarr119889 Interference from 119888th cellular signal to 119889th D2D119880119889(119883) Social utility of 119889th D2D pairsΓ119889(119883) Utility function of 119889th D2D pairs119909119888119889 Indicator of resource reusing relations119909lowast119889 The Nash Equilibrium of 119889th D2D pair119883119889 Set of all feasible strategies in UFM game

Conflicts of Interest

The authors declare no conflicts of interest related to thepublication of this paper

Acknowledgments

This work is partly supported by the National NaturalScience Foundation of China (61571240 61671253) the Pri-ority Academic Program Development of Jiangsu HigherEducation Institutions the Major Projects of the NaturalScience Foundation of the Jiangsu Higher Education Insti-tutions (16KJA510004) the Open Research Fund of Nationaland Local Joint Engineering Laboratory of RF Integrationand Micro-Assembly Technology Nanjing University ofPosts and Telecommunications (KFJJ20170305) the OpenResearch Fund ofThe State Key Laboratory of Integrated Ser-vices Networks Xidian University (ISN17-04) Jiangsu Spe-cially Appointed Professor Grant (RK002STP16001) Inno-vation and Entrepreneurship of Jiangsu High-Level TalentGrant (CZ0010617002) High-Level Talent Startup Grantof Nanjing University of Posts and Telecommunications(XK0010915026) and ldquo1311 Talent Planrdquo ofNanjingUniversityof Posts and Telecommunications

References

[1] Y Cao T Jiang and C Wang ldquoCooperative device-to-devicecommunications in cellular networksrdquo IEEE Wireless Commu-nications Magazine vol 22 no 3 pp 124ndash129 2015

[2] J Liu N Kato J Ma and N Kadowaki ldquoDevice-to-devicecommunication in LTE-advanced networks a surveyrdquo IEEECommunications Surveys amp Tutorials vol 17 no 4 pp 1923ndash1940 Fourthquarter 2015

[3] A Asadi Q Wang and V Mancuso ldquoA survey on device-to-device communication in cellular networksrdquo IEEE Communi-cations Surveys amp Tutorials vol 16 no 4 pp 1801ndash1819 2014

[4] H Nishiyama M Ito and N Kato ldquoRelay-by-smartphonerealizing multihop device-to-device communicationsrdquo IEEECommunications Magazine vol 52 no 4 pp 56ndash65 2014

[5] M Zhou Y Tang Z Tian L Xie and W Nie ldquoRobust neigh-borhood graphing for semi-supervised indoor localization withlight-loaded location fingerprintingrdquo IEEE Internet of ThingsJournal vol PP no 99 pp 1-1

[6] K Doppler M Rinne C Wijting C B Ribeiro and K HugldquoDevice-to-device communication as an underlay to LTE-advanced networksrdquo IEEE Communications Magazine vol 47no 12 pp 42ndash49 2009

[7] J Liu H Nishiyama N Kato and J Guo ldquoOn the outageprobability of device-to-device-communication-enabled mul-tichannel cellular networks an RSS-threshold-based perspec-tiverdquo IEEE Journal on Selected Areas in Communications vol34 no 1 pp 163ndash175 2016

[8] M Zhou Y Tang W Nie L Xie and X Yang ldquoGrassMAgraph-based semi-supervised manifold alignment for indoorWLAN localizationrdquo IEEE Sensors Journal vol 17 no 21 pp7086ndash7095 2017

[9] J Liu S Zhang N Kato H Ujikawa and K Suzuki ldquoDevice-to-device communications for enhancing quality of experiencein software defined multi-tier LTE-A networksrdquo IEEE Networkvol 29 no 4 pp 46ndash52 2015

[10] C Xu L Song Z Han et al ldquoEfficiency resource allocation fordevice-to-device underlay communication systems a reverseiterative combinatorial auction based approachrdquo IEEE Journalon Selected Areas in Communications vol 31 no 9 pp 348ndash3582013

[11] L Ferdouse W Ejaz K Raahemifar A Anpalagan and MMarkandaier ldquoInterference and throughput aware resourceallocation for multi-class D2D in 5G networksrdquo IET Commu-nications vol 11 no 8 pp 1241ndash1250 2017

[12] T D Hoang L B Le and T Le-Ngoc ldquoCooperative device-to-device communications in cellular networksrdquo IEEE Transac-tions onWireless Communications vol 15 no 10 pp 7099ndash71132016

[13] M Andrews K Kumaran K Ramanan A Stolyar P Whitingand R Vijayakumar ldquoProviding quality of service over a sharedwireless linkrdquo IEEE Communications Magazine vol 39 no 2pp 150ndash154 2001

[14] L Wang L Liu X Cao X Tian and Y Cheng ldquoSociality-aware resource allocation for device-to-device communicationsin cellular networksrdquo IET Communications vol 9 no 3 pp342ndash349 2015

[15] V Shah andA O Fapojuwo ldquoSocially aware resource allocationfor device-to-device communication in downlinkOFDMAnet-worksrdquo in Proceedings of the 2014 IEEE Wireless Communica-tions and Networking Conference WCNC 2014 pp 1673ndash1678Istanbul Turkey April 2014

[16] Y Li T Wu P Hui D Jin and S Chen ldquoSocial-aware D2Dcommunications qualitative insights and quantitative analysisrdquoIEEE Communications Magazine vol 52 no 6 pp 150ndash1582014

[17] FWang L Song Z Han Q Zhao and XWang ldquoJoint schedul-ing and resource allocation for device-to-device underlay com-municationrdquo in Proceedings of the IEEE Wireless Communi-cations and Networking Conference (WCNC rsquo13) pp 134ndash139IEEE Shanghai China April 2013

[18] F Tang Z M Fadlullah N Kato F One and R MiuraldquoAC-POCA anti-coordination game based partially overlap-ping channels assignment in combined UAV and D2D based

12 Wireless Communications and Mobile Computing

networksrdquo IEEE Transactions on Vehicular Technology vol PPno 99 pp 1-1

[19] S M Azimi M H Manshaei and F Hendessi ldquoHybrid cellularand device-to-device communication power control Nashbargaining gamerdquo in Proceedings of the 2014 7th InternationalSymposium on Telecommunications IST 2014 pp 1077ndash1081Tehran Iran September 2014

[20] Z Zhou K Ota M Dong and C Xu ldquoEnergy-efficient match-ing for resource allocation in D2D enabled cellular networksrdquoIEEE Transactions on Vehicular Technology vol 66 no 6 pp5256ndash5268 2017

[21] C Xu C Gao Z Zhou Z Chang and Y Jia ldquoSocial network-based content delivery in device-to-device underlay cellularnetworks using matching theoryrdquo IEEE Access vol 5 pp 924ndash937 2017

[22] X Feng G Sun X Gan et al ldquoCooperative spectrum sharingin cognitive radio networks a distributed matching approachrdquoIEEE Transactions on Communications vol 62 no 8 pp 2651ndash2664 2014

[23] J Zhang ldquoThe interdisciplinary research of big data andwireless channel a cluster-nuclei based channel modelrdquo ChinaCommunications vol 13 no supplement 2 Article ID 7833457pp 14ndash26 2016

[24] S Mumtaz K M Saidul Huq J Rodriguez and V FrascollaldquoEnergy-efficient interference management in LTE-D2D com-municationrdquo IET Signal Processing vol 10 no 3 pp 197ndash2022016

[25] N Kayastha D Niyato P Wang and E Hossain ldquoApplicationsarchitectures and protocol design issues for mobile socialnetworks a surveyrdquo Proceedings of the IEEE vol 99 no 12 pp2130ndash2158 2011

[26] J Zhang L Tian Y Wang and M Liu ldquoSelection transmit-tingmaximum ratio combining for timing synchronization ofMIMO-OFDM systemsrdquo IEEE Transactions on Broadcastingvol 60 no 4 pp 626ndash636 2014

[27] M Zhou Y Wei Z Tian X Yang and L Li ldquoAchieving cost-efficient indoor fingerprint localization on wlan platform ahypothetical test approachrdquo IEEEAccess vol 5 pp 15865ndash158742017

[28] ldquoZacharyrsquoskarateclubrdquohttpsenwikipediaorgwikiZachary27skarate club

[29] D Wu L Zhou and Y Cai ldquoSocial-aware rate based contentsharing mode selection for D2D content sharing scenariosrdquoIEEE Transactions on Multimedia vol 19 no 11 pp 2571ndash25822017

[30] J Huang Y Yin Y Sun Y Zhao C-C Xing and Q DuanldquoGame theoretic resource allocation for multicell D2D commu-nications with incomplete informationrdquo in Proceedings of theIEEE International Conference on Communications ICC 2015pp 3039ndash3044 London UK June 2015

[31] Y Xiao K-C Chen C Yuen and L A DaSilva ldquoSpectrumsharing for device-to-device communications in cellular net-works a game theoretic approachrdquo in Proceedings of the IEEEInternational SymposiumonDynamic SpectrumAccessNetworks(DYSPAN rsquo14) pp 60ndash71 IEEE McLean Va USA April 2014

[32] D Niyato and E Hossain ldquoA game-theoretic approach tocompetitive spectrum sharing in cognitive radio networksrdquo inProceedings of the IEEEWireless Communications and Network-ing Conference (WCNC rsquo07) pp 16ndash20 Kowloon China March2007

[33] D Monderer and L S Shapley ldquoPotential gamesrdquo Games andEconomic Behavior vol 14 no 1 pp 124ndash143 1996

[34] N Nie and C Comaniciu ldquoAdaptive channel allocation spec-trum etiquette for cognitive radio networksrdquo in Proceedingsof the 1st IEEE International Symposium on New Frontiers inDynamic SpectrumAccess Networks (DySPAN rsquo05) pp 269ndash278Baltimore Md USA November 2005

[35] Y Xing C N Mathur M A Haleem R Chandramouli andK P Subbalakshmi ldquoDynamic spectrum access with QoS andinterference temperature constraintsrdquo IEEE Transactions onMobile Computing vol 6 no 4 pp 423ndash433 2007

[36] T Heikkinen ldquoA potential game approach to distributed powercontrol and schedulingrdquo Computer Networks vol 50 no 13 pp2295ndash2311 2006

[37] Y Li D Jin J Yuan and ZHan ldquoCoalitional games for resourceallocation in the device-to-device uplink underlaying cellularnetworksrdquo IEEE Transactions on Wireless Communications vol13 no 7 pp 3965ndash3977 2014

[38] H Ryu and S-H Park ldquoPerformance comparison of resourceallocation schemes for D2D communicationsrdquo in Proceedingsof the 2014 IEEE Wireless Communications and NetworkingConference Workshops WCNCW 2014 pp 266ndash270 IstanbulTurkey April 2014

[39] Y Li S Su and S Chen ldquoSocial-aware resource allocationfor device-to-device communications underlaying cellular net-worksrdquo IEEE Wireless Communications Letters vol 4 no 3 pp293ndash296 2015

[40] D I Laurenson D G M Cruickshank and G J R PoveyldquoComputationally efficient multipath channel simulator for theCOST 207 modelsrdquo in Proceedings of the IEE Colloquium onComputer Modelling of Communication Systems pp 81ndash86London UK May 1994

Wireless Communications and Mobile Computing 3

Community 1 Community 2

Kole

Smith

Social domainCommunication domain

Mike

Sarah

Bob

Alice Jack

DT

1 DR

1

DT

nD

R

n

UE0

UEn

D2D signalCellular to D2D interferenceCellular signal

D2D to cellular interference

Figure 1 Illustration of social-aware D2D communications under-laying cellular network In physical domain wireless links aresubject to the physical interference constraints while social domainindicates the relationships between mobile users

underlaying cellular networks into two domains in our workphysical domain and virtual social domain More detailsabout these are illustrated in Figure 1

In the physical domain the system contains 119873 nodeslabelled as the set of N = 1 2 119873 Each node denotesa mobile user that can communicate with the BS or executeD2D communication with other users directly For activemobile users they can form D = 1 2 119863 D2D pairsThe remaining which is denoted by the setC = 1 2 119862can request for interested content toward BS via cellularcommunication Those D2D pairs can choose to reuse thespectrum resource of any cellular users But there existphysical constraints between mobile users and only some ofthem can form D2D pairs (including D-Tx and D-Rx) [24]

In the social domain for the reason that a communityis combined by sophisticated relationship like friendshipkinship or even classmates with each other [25] and theywere physically in close proximity we tend to make use ofthese characteristics to model the social relationship betweenthe users Users consider the strength of their social trustwithin a community and their properties of social trustbetween different communities respectively to make D2Dcommunication more secure

To ensure the practicality of our work we set the channelscene as Rayleigh fading channel Under the premise of thefree space propagation model the interference signal powerlevel of cellular user which is introduced by D2D transmitterD-Tx sharing the same spectrum resource with cellular usercan be expressed as follows according to Shannon theorem

119875int119888 = 119875119889 sdot 120577119888119889minus120572 sdot ℎ2119888119889 (1)

while the interference signal ofD2D receiverD-Rx is from theBS that establishes communication link with cellular usersThus the signal power can be expressed as

119875int119889 = 119875119861 sdot 120577119861119889minus120572 sdot ℎ2119861119889 (2)

where 119875119889 and 119875119861 are the transmitted power of BS and D2Dtransmitter respectively 120577119888119889 denotes the distance betweenthe D2D transmitter and cellular user and 120577119861119889 denotes thedistance between D2D receiver and the BS 120572 is the path lossexponent and ℎ119888119889 and ℎ119861119889 are the complexGaussian channelcoefficients

In our investigation we assume there are one D2D pairand one cellular user within a single cell By sharing cellularspectrum resource blocks with D2D pair D2D communica-tion and cellular communication can be conducted syn-chronously [26] For the purpose of maximizing the overallsystem transmission rate the Signal-to-Noise Ratio (SINR) ofthe two communicationmodes is regarded as important indi-cator Based on (1) and (2) we can obtain the SINR of cellularuser 119888 and D2D receiver 119889 as

SINR119888119894 = 119901119888119892119888119875int119888 + 1198730 SINR119889119894 = 119901119889119892119889119875int119889 + 1198730

(3)

119901119888 is the given transmission power of cellular user and 119901119889 isthe given transmission power of D2D transmitter 119892119889 and 119892119888are the channel gains of cellular link and D2D link respec-tively And1198730 is the noise power on each channel

At the same time we usually calculate the sum rate ofthe system to measure the quality of D2D communicationunderlaying cellular network For uplink direction let 119877119888119894 bethe data transmission rate between theCUand the BS and119877119889119894be the data transmission rate between D-Tx and D-Rx Sincethe transmission rate of each cellular link and D2D link canbe determined by the Shannon capacity [27]

119877119888119894 = 119861119888119894 log2 (SINR119888119894) 119877119889119894 = 119861119889119894 log2 (SINR119889119894) (4)

where SINR119889119894 and SINR119888119894 are the Signal-to-Noise Ratio(SINR) inD2D and cellular communication links and119861119888119894 and119861119889119894 are the allocated licensed band of resource for D2D andcellular communication What is imperative to mention hereis that we only consider the interference that occurred withina single cell and do not consider any influence from othermicrocells

To describe reusing relationship of spectrum resource wedenote 119909119888119889 isin [0 1] as the indicator matrix of the D2D pairsthat is 119909119888119889 = 1 when the D2D pair 119889 occupies the licensedband of resource of the cellular user 119888 otherwise 119909119888119889 =0 Thus we can acquire the transmission rate of D2D pairmultiplying the indicator 119909119888119889 by 119877119889119894 as 119877119889119894 sdot 119909119888119889 The systemperformance can be represented by the sum of 119877119888119894 and 119877119889119894

119877 = Dsum119894=1

(119877119888119894 + 119877119889119894 sdot 119909119888119889) (5)

4 Wireless Communications and Mobile Computing

We can improve the system performance by maximizingthe sum rate to judge whether our proposed optimal social-aware resource allocation scheme is effective

maxDsum119894=1

119877119888119894 + 119877119889119894 sdot 119909119888119889st sum119889119894isinD

119909119899119888119889119894 le 1 119888 isin C 119899119888 isin C

sum119899119888isinC

119909119899119888119889119894 le 1 119888 isin C 119889119894 isin D(6)

22 Problem Description

221 Power Interference In D2D communication networkwe assume the cellular users can share uplink resource withuser equipment During the D2D communication it isinevitable that D2D transmitter interference will be intro-duced to others especially to nearby CUs And since we limitthat each D2D pair can reuse the spectrum resource from atmost one cellular user by assuming there are 119863 D2D pairsand 119862 cellular users in the D2D underlaying communicationcellular network we can simplify the network as Figure 2

In the simplified networkwe establish besides the normalD2D communication we only consider the effects of both theinterference of a generic D2D transmitter introduced toothers and all other interference caused to a D2D receiverFor instance the base station (BS) introduces intratiersinterference to the D2D receivers D2D1198771 as shown in Figure 2Meanwhile due to the full frequency reuse D2D1198791 causesinterference to CU1 Considering the power interferencecaused by the transmitter of the D2D pairs to the nearby UEwe can give the definition that the interference introduced byD2D transmitter 119889 to cellular users 119888 is 119868119889rarr119888 119889 isin D 119888 isin C

119868119889rarr119888 = 119892119889119888119901119889 (7)

where 119901119889 denotes the transmission power of the correspond-ing D2D pairs 119889 119889 isin D 119892119889119888 denotes the gains of the channelbetween the transmitter of D2D pair 119889 to cellular users 119888Here the terms 119888 and 119892119889119888 are positive Hence all of the cel-lular users are assumed in the single cell and correspondinginterference is introduced by prayer 119889 119889 isin D where theplayer 119889 is called the generic D2D transmitter Meanwhilethe transmission between player 119888 119888 isin C and the BS alsointroduces interference to D2D pair 119889 where we define theintratier interference from player 119888 to player 119889 as follows

119868119888rarr119889 = 119892119888119889119901119888 (8)

where 119892119888119889 is the channel gain between the BS and the D2Dpairs 119889 119901119888 is the transmission power of cellular user 119888 Herewe assume that orthogonal channels are used for differentCUs and we do not consider any power control policy atthe macrocell layer In our investigation we pay attention tothe power interference D2D transmitter introduced to theCUs in other words a new power control policy for the D2Dtransmitters

D2D link

Cellular to D2D interferenceCellular link

D2D to cellularinterference

５1

５2

５3５4

＄2＄1

＄2＄2

＄2＄3

＄2＄4

BS

Figure 2 Interference model in the uplink

222 Social Utilization In this part we use a visualizedsocial-network graph to analyze the social relationship be-tween the mobile users and depict the social characteristic ofthe network In the virtual social network social ties aredefined to qualitatively measure the strength of social rela-tionship between D2D users and report the communicationdemands between users Besides social centrality plays a veryimportant role in D2D data transmission users with highcentrality are more likely to hold high capacity in terms ofdata transmission volume and frequency In that case forthe purpose of obtaining a visualization of the social char-acteristics existing in userrsquos daily activities we adopt theproximity social network derived from a real-world mobilitydatasetmdashKarate clubThe network contains the social data of34 members within a Karate club documenting 78 pairwiselinks between members who interact inside or outside theclub [28] By analyzing the realistic dataset and the inter-action behaviors among these members we plot the socialnetwork formed by users visualized by the trace in Figure 3where the magnitude of the node indicates the centrality ofthe specified user and the label of the node indicates thestrength of the social ties of corresponding links

In the virtual social network active mobile users in closerelationship form certain community In order to weigh theinfluence from the social relationship between the mobileusers within the same community to our resource alloca-tion scheme we define the utility of social relationship byquantifying the social characteristic Sincewe supposemobileusers in different communities have no social trust betweeneach other when cellular users download some content fromthe BS cellular users belonging to the same community candeliver the content to other interested users directly insteadof forwarding by the BS And the amount of the content is

Wireless Communications and Mobile Computing 5

140

320

230

240

210

200

220

80

80

90

340

190

330

Figure 3 Social characteristics observed from social-network trace

determined by the social closeness between the users Themore close social relationship the D2D users have the morecontent they will exchange with each other [29]

Based on the analysis mentioned above the social graphcan be denoted by119866119904 = (119881119904 119877119904)119881119904 and 119877119904 stand for the set ofall cellular users and D2D users and the set of relationshipsrespectively To be mentioned the matrix 119877119904 demonstratesthe strength of the relationship of 119881119904 in the social networkGenerally we use the form of matrix described as 120596119889119903 119889 119903 =1 2 119863 and 120585119889119888 119889 = 1 2 119863 119888 = 1 2 119862 120596119889119903denotes the intimacy coefficient between D2D users and 120585119889119888denotes the intimacy coefficient between the cellular usersand D2D users According to the definition in the dataset ofKarate club we plan to divide the closeness coefficient intotwo kinds very close and a little close The values of 120596119889119903 and120585119889119888 follow the set of [0 1] For example 120596119889119903 = 0 impliesa little close intimacy between the D2D users and 120596119889119903 =1 naturally implies a very close intimacy As illustrated inFigure 1 we construct a simple social network In community2 D2D users Jack and Alice have a very close intimacy whileBob and Jack are unfamiliar with each other Inspired by theanalysis in Part A the utility of D2D users can be representedas follows

119880119889 = log2(1 + sum119894=119866119901

119889cap119866119904119889

SINR119889119894) forall119889 isin D (9)

Approximately the utility of cellular users can be representedas follows

119880119888 = log2(1 + sum119894=119866119901119888 cap119866119904119888

SINR119888119894) forall119888 isin C (10)

By the way 119866119901 and 119866119904 denote the physical and socialrelationship of the system model mentioned above Thus 119866119901119888and 119866119904119888 denote the set of cellular users that reuse the samefrequency band of spectrum resource and maintain stableinteractionwith each other119866119901

119889and119866119904119889 denotes theD2Dusers

which reuse the same spectrum resource from cellular usersand maintain stable interaction with the cellular users 119880119889represents the influence of the social relationship to D2Dcommunication and 119880119888 represents the influence of the socialrelationship to cellular communication To sum up we candefine the social-community utility function of D2D users 119889as follows

119880119889 (119883) = sum119903119889isinD

120596119889119903119880119889 + sum119888isinC

120585119889119888119880119888 (11)

119883 denotes the correlation matrix of 119909119888119889 and in general thedegree of social utility enhancement involves two aspects theweighted sum of social utility enhancement by D2D pairshaving social connections with each other as sum119903isinD 120596119889119903119880119889and the weighted sum of utility enhancement betweenfamiliar cellular users and D2D pairs as sum119888isinC 120585119889119888119880119888 In thisway the element of social relationship is considered in theinvestigation of resource allocation in D2D communicationunderlaying cellular network

3 Game Theory-Based Framework forResource Allocation

In our investigation we tend to maximize the sum trans-mission rate of the system For example if D2D transmitterbrings about higher-than-sociality interference to cellularusers the operator would remove the D2D link So wemodelthe resource allocation issue between D2D links and cellularlinks as the utility maximization game

31 Problem Formulation The resource allocation policy ofeach of the D2D pairs 119889 depends on the power interferenceintroduced by D2D communication and social relationshipsbetween themobile users Compared to the physical relation-ship betweenmobile users the social relationship is relativelyless changeableThus we need to consider the joint influencefrom social enhancement and power interference to the D2Dpairs dynamically By that we tend to define the utility of aD2D link as the profits which are contributed by cellular usersand D2D users using spectrum resources and D2D usersusing social characteristics In this case the utility functionof the 119889th D2D links is defined as follows

Γ119889 (119883) = 120572 sdot 119877 + 120573 sdot 119880119889 (119883) minus 120574 sdot 119861119889119894 minus 120576 sdot 119868119889rarr119888iff 119880119889 (119883) ge 119868119889rarr119888 (12)

120572 and 120573 are the charging price of unit data rate supportedby the spectrum resource and the social network 120574 and 120576are the cost function of a D2D occupied resource and power

6 Wireless Communications and Mobile Computing

interference With respect to 120574 a pricing function from (12)is adopted which can be expressed as follows

120574 = 119899 + 119904 sdot (1198611198891 + sdot sdot sdot + 119861119889119894)120591 119894 = 1 2 119898 (13)

119899 119904 and 120591 denote nonnegative constants and 120591 ge 1 toguarantee that the cost function is convex In order toimprove the applicability we suppose

[1198730 + 119892119889119875119889119903] = 119901119861119889119894 (14)

where 119901 is a nonnegative constant [30] then

Γ119889 (119883) = 120572 sdot 119861119889119894 log2 (1 + SINR119889119894) + 120573 sdot sum119895isinD

120596119889119903119880119889+ sum119888isinC

120585119889119888119880119888 minus [119899 + 119904 sdot 119898sum119894=1

119861119889119894]119861119889119894 minus 120576 sdot 119868119894rarr119906iff 119880119889 (119883) ge 119868119889rarr119888

(15)

In the proposed problem in (15) each D2D pair is aimedat integrating every aspect of influence and then maximizingits own utility As the distribution of mobile equipment ischanging all the time the features of the network are varyinginstantaneously So for the purpose of exact comparison weshould implement some effective method to eliminate thiskind of dilemma

Dynamic game with complete information can modelcertain dynamic situation under the premise that the par-ticipant knows the type of the action it will take and theinformation needed for every decision of the action It canbe applied into our proposed model as every D2D paircan get to know the social utility and power interferenceand get the real-time Γ119889(119883) when D2D communication isin progress So the problem above can be regarded as adynamic game with complete social information as well assophisticated interference information In this way we canpropose a dynamic game based scheme to optimize theoverall performance of theD2D communication network dueto the two-sidesrsquo competition

32 UFM Game Formulation From the analysis above wederive the information from two-sidesrsquo action needed inour game theory And for the optimization problem weusually utilize the game theory to solve it Firstly we definecorresponding strategy adopted by each D2D user 119889 in acertain point of history as 119886119889 119886119889 isin 119860119889 where 119860119889 is theset of all available strategies of the D2D pair 119889 The choiceof strategies of all the other participants that is all theother D2D pairs in our work can be defined as 119886minus119889 =1198861 119886119889minus1 119886119889+1 119886119863 If the above assumption for theUFM game theory is perfect there must exist a strategy 119886119889 isin119860119889 to maximize its own utility function

max119886119889isin119860119889

Γ119889 (119886119889 119886minus119889) forall119889 isin D (16)

The UFM game for the resource allocation thinking from theperspective of utility function is defined by quadruple Φ =D 119860119889119889isinD Γ119889119889isinD 119868119889rarr119888119889isinD119888isinC where D denotes the

D2D pairs119883119889 denotes all of the resource allocation strategiesD2D pairs set D can take Γ119889 denotes the utility function ofeach of the D2D pairs 119889 and 119868119889rarr119888 denotes the interferenceintroduced by D2D pairs 119889 to cellular user 11988833 Nash Equilibrium Nash Equilibrium is a very importantterminology in game theory [31 32] It represents a set ofstrategies which are combined by all optimal choices takenby each participant which reflect the optimal reaction eachparticipant adopts against the other participantrsquos strategiesAccording to this if the choices chosen by all the D2D pairsare optimal the system sum rate of the D2D communicationunderlaying cellular network will reach the extreme oneThefollowing part will discuss the existence of Nash Equilibriumin UFM game theory and provide proof for it

Generally the UFM game Φ = D 119860119889119889isinD Γ119889119889isinD119868119889rarr119888119889isinD119888isinC can reach the Nash Equilibrium if each of theD2D pairs has the only optimal response to the other D2Dpairrsquos strategy

119886lowast119889 = argmax119886119889isin119860119889

Γ119889 (119886minus119889 119886119889) forall119889 isin D (17)

and 119886lowast = 119886lowast1 119886lowast2 119886lowast119863 denotes the Nash EquilibriumBecause of the same incentive of changing their strategy

for all the D2D pair we refer to the potential game theory todemonstrate the existence of NE for the UFM game In [33]Monderer and Shapley propose the definition of potentialgame and elaborate the idea in detail too In the field ofwireless resource allocation games game theory has beenapplied in a few of authorsrsquo papers for example [34ndash36] Inpotential game theory the change in individual playerrsquos gaincan be mapped to the global function which is called thepotential function By this way we can conclude if there isany change that occurred on individual player the potentialfunction will change equally in the strict potential game Γdenotes an exact potential function if and only if exist119865(119868) 119868 rarr119880 forall119894 119895 forall119868119894 119868119895 119880119894 isin 119868119894 and 119880119895 isin 119868119895

Γ119894 (119868119894 119880minus119894) minus Γ119895 (119868119895 119880minus119895) = 119865 (119868119894 119880minus119894) minus 119865 (119868119895 119880minus119895) (18)

In the D2D communication systemwe havemodeled thechange of power interference and social utility caused byD2Dlinks would change the utility function of the game whichis consistent with the principle of potential function On theother hand potential gamehas the following inherent proper-ties which are described in [33] (1)There must exist a pure-strategy NE and a solution for it (2) The Nash Equilibriumcorresponds to the maxima of the potential function Γ (3)Generally the convergence to Nash Equilibrium would bereached in finite improvement or searching path accordingto sequential best-response dynamics

For the condition of a single band frequency channel thepotential game is formulated by utilizing the following utility-maximizing function

Γ119894 = minus (Total utility function generated by 119894+ Total utility function experienced by 119894) (19)

Wireless Communications and Mobile Computing 7

Based on the potential game theory we can demonstratethe existence of the Nash Equilibrium of our proposed UFMgame For Γ for every 119889 isin D and for every 119886minus119889 isin 119860minus119889

119875 (119889) = Γ119889 (119886minus119889 119886119889) minus Γ119889 (119886minus119889 1198861015840119889) (20)

Theorem 1 In certain history point 119905 function 119875(119889) derivedfrom UFM game is subgame perfect

Proof We suppose strategy 119886119889 denotes occupying the spec-trum resource of cellular user 119888 which is taken by D2D pairs119889 initially Therefore the initial indicator is 119909119888119889 Once D2Dpair119889 change its strategy andmake a request for the spectrumresource of cellular user 1198881015840 the indicator changes to1199091015840119888119889Thenwe can obtain

Γ119889 minus Γ1015840119889 = 120572 sdot 119877 + 120573 sdot 119880119889 (119883) minus 120576 sdot 119868119889rarr119888 minus 120572 sdot 1198771015840 minus 120573sdot 119880119889 (119883) minus 120576 sdot 1198681015840119889rarr119888

= 120572 sdot (119877 minus 1198771015840) minus 120576 sdot (119868119889rarr119888 minus 1198681015840119889rarr119888) (21)

We denote Δ 1 = 119877 minus 1198771015840 and Δ 2 = 119868119889rarr119888 minus 1198681015840119889rarr119888 As we cansee Δ 1 ≫ Δ 2 Finally we conclude that

Γ119889 minus Γ1015840119889 gt 0 (22)

It means that no D2D pair can acquire performanceenhancement by changing its strategy so we prove that ourproposed game is subgame perfect As subgame is the restric-tion from the perspective of history circumstances it canlead to the Nash Equilibrium of the game directly

4 Resource Allocation Scheme forUFM Game Theory

41 Priority Searching Based Solution The value of the utilityfunction Γ119889 varies when D2D pair chooses to reuse spectrumresource from different cellular user and the final aim of theUFM game is to determine the order of the utility function bythe size of value According to analysis in Sections 32 and 33the resource allocation strategy 119886lowast has a Nash EquilibriumIt means that we can finally achieve an optimal strategy bysubstituting the other strategies one by one in finite times Itis similar to the establishment of preference list and iteratesuntil acquiring the best selection among different alternatives[10] Inspired by the one-to-one matching theory we willshow the main idea of the proposed resource allocationalgorithm in detail

Definition 2 For anyD2D pairs we define the binary priorityrelation set≻119894 to represent the entire set of resource allocationstrategies that each D2D pair 119894 would possibly take In ourUFM game D2D pairs can choose to reuse the resourceoccupied by the associated cellular users or not according tothe priority set For any D2D pairs 119886119894 ≻119894 1198861015840119894 means D2D pairs119894 prefer choosing 119888 as the target resource source instead of 1198881015840

Since the priority set is determined by the utility function wecan define the priority as follows

1198861015840119894 ≻119894 119886119894 lArrrArrΓ119894 (1198861015840119894 ) gt Γ119894 (119886119894)

forall119894 isin D(23)

This definition demonstrates that D2D users 119894 are likelyto reuse the spectrum resource of cellular users 119888 as no moreoptions can bring additional performance gains We can setthe highest priority for cellular user 119888 in the set belonging toD2D user 119894 By this a complete priority set can be obtainedby repeating searching operation For every D2D pair wecan also design an optimization resource allocation schemebased on the priority set In this scheme everyD2Dpair urgesfinding its own highest priority and reusing the spectrumresource shared by the corresponding cellular users

Let us present Algorithm 1Based on the definitions and priority searching operation

we can obtain a final Nash-stable resource scheme 119886fin forD2D users to solve the utility maximization problem whichis given in Algorithm 1 From the whole knowledge givenabove we can see that D2D users make switching iterationfollowing a logically standard based on an arbitrarily choseninitial resource allocation strategy 119886ini At the beginning ofeach iteration D2D user 119894 isin D is randomly chosen by thesystem in step (13) And then the selectedD2D user replacesits resource allocation strategy with 119886ini by random choosinga occupied cellular users and determine its strategies 119886119894 anduniformly selects another social-trust cellular user 1198881015840 isin CThen the D2D pair will request the base station for the chan-nel state information once establishing communication linkwith these two cellular users 119888 and 1198881015840 After acquiring specifiedinformation the BS will computes the utility function of theresource allocation strategies of 119886 and 1198861015840 and broadcast tothe participant of the game model Meanwhile making thedecision that whether to carried out the switch operationfor D2D link If 119886119894 ≻119894 1198861015840119894 the switch operation will not beexecuted Otherwise the switch operation will be executedThe iteration will continue until all of the priority searchingoperations for each D2D pair are traversed and reach a finalNash Equilibrium scheme 119886fin

Different from those conventional D2D resource allo-cation schemes our proposed scheme needs to select suit-able community detection dataset and analyze the social-community information inside And a priority based poten-tial game theory is applied in our scheme This importantinformation is taken into consideration in our proposedscheme fully

42 Uniqueness and Boundedness According to Theorem 1for a given history point 119905 the combination of strategy 119886119894 119886119894 isin119860 119894 can reach a status of being subgame perfect as reactionto the combination of strategy 119886minus119894 To prove the uniquenessand boundedness of our proposed game it is necessary toconfirm that if there exist any participant forall1006704119894 isin D and its

8 Wireless Communications and Mobile Computing

(01) Input Number of mobile users119873 and random resource allocation strategy 119886ini(02)Output A priority based resource allocation scheme 119886fin(03) Utilize the dataset of Karate Club network(04) Calculate the transmission rate of the D2D links and cellular links(05) Obtain 119880119889(119883) and 119868119889rarr119888(06) if 119880119889(119883) le 119868119889rarr119888 remove the D2D links(07) else keep the D2D links(08) Define the matrix of indicator 119909119888119889 isin [0 1](09) 119868 = find 119909119888119889 = 0 ampamp 119868 = 1(10)There is just one 119888 cellular users qualified to shareresources to D2D user 119903 = 119903119888119889(11) else if uniformly randomly choose one cellular users 119888 and 119886possible cellular users 1198881015840 and denote its associate resourcesharing as 119886119894 isin 119886ini(12) Calculate Γ(1198861015840119894 ) and Γ(119886119894) priority = 0(13) if 1198861015840119894 ≻119894 119886119894 then Priority = 1(14) else repeat (15)sim(16)(15) if Priority == 1 then(16) D2D pairs quit current resource occupying strategy of 119888 andturn to adapt the new resource allocation strategy of 1198881015840(17) substitute the current resource occupying strategy 119886 forstrategy 1198861015840 and add it to 119886cur(18)Until all of the D2D pairs complete the priority searching operation resourceoccupying strategy switching operation and reach Nash Equilibrium 119886fin

Algorithm 1 The utility function maximization D2D links redistribution algorithm

corresponding strategy 1006704119886119894 can give better reaction to thestrategy combination 119886minus119894 than 119886119894 and make 1006704119886119894 ≻119894 119886119894 availableSo we provide the following proof relative to the uniquenessand boundedness of our proposed UFM game

Theorem 3 For all of the D2D pairs whose 119909119888119889 = 1 theproposed priority searching based scheme can only obtain aunique resource allocation scheme 119886finProof Based on the description in Algorithm 1 we supposereversely that the combination of strategy 119886119894 is not subgameperfect And then there must exist certain participant 119894 thathas strategy forall1006704119894 isin D and outperforms 119886119894 Now we investigateanother strategy 119886119894 and when 119905 lt 1006704119905 1006704119886119894 is equal to 119886119894 but after1006704119905 it is equal to 119886119894Then in any subgame after the history point1006704119905 strategy forall1006704119894 isin D is at least as well as 119886119894 for the reason thatforall1006704119894 isin D has deviated from 119886119894 once We can also conclude thatstrategy forall1006704119894 isin D is at least as well as 119886119894 after the history point119905 which is contrary to the assumption that strategy forall1006704119894 isin Dimproves the strategy 119886119894 And so on we can investigate other119886119894 to prove its equal benefit with forall1006704119894 isin D until reaching theunique resource allocation scheme 119886fin

Through the above analysis we prove the uniqueness ofthe UFM game by Reduction to Absurdity In each iterationin Algorithm 1 it may lead to a new resource allocationstrategy As there is only C in the physical domain andlimitedD D2D pairs due to the limited social relationship inthe social domain each of the D2D pairs is correspondingto C types of resource allocation scheme So the prioritysearching operation will eventually end in limited steps Thisfact assures the boundedness of our proposed UFM gamebased scheme

5 Simulation Results and Discussions

In this section we implement the simulation results from dif-ferent perspective to verify the performance of our proposedUFM algorithm and elaborate some necessary explanationfor the results Main simulation parameters have been givenin Table 1 Simulations are executed in a single cell whichare within an isolated community circumstance Path lossmodels are considered for cellular and D2D links along withshadow fadingmodel According to the dataset of Karate clubwe conduct the simulation within a 500m times 500m area toguarantee most of the club memberrsquos activities are within thisarea and 34 members of the club are randomly distributedwithin the BS coverage area Meanwhile the bandwidth ofallocated resource is assigned arbitrarily within the rangelimitation We compare our proposed UFM algorithm withthe following resource allocation schemes (a) distributedresource allocation (DRA) which allocates the D2D com-munication resource by thinking in a distributed way [37]and (b) optimal social-community aware resource allocation(OSRA) which allocates the D2D communication resourceto reduce the total transmission time [38] All the results areaveraged over 10 timesrsquo trial

Without loss of generality on one hand we prescribethe pathloss model between the base station and all themobile users as COST (EuropeanCooperation in Science andTechnology) 231 Hata model [39]

PLCU = 367 + 35 times lg (119889) (24)

Meanwhile we prescribe the pathloss model betweendifferent cellular users and D2D users as Xia model [40]given as follows

Wireless Communications and Mobile Computing 9

Table 1 System simulated parameters in the performance evalua-tion

Parameter ValueCoverage radius of BS 500mDistance of D2D 20msim50mNoise figure 9 dB at deviceTransmission power BS 46 dBm device 23 dBmMaximum D2D transmitter power 23 dBmRange of bandwidth 10MHzsim20MHzCommunication demand 50WInterference threshold 56 times 10minus6W119899 119904 119911 120591 1120572 120573 20

PL = 665 + 40 times log (119889) 119889 gt 501007 + 20 times lg (119889) 119889 lt 50 (25)

Since we assume the inner distance of D2D pair remainsin close standards and relatively close the free space modelcan be given by

PL = 384 + 20 times lg (119889) (26)

Moreover we consider the case of fast fading model forRayleigh fading In different situation we adopt a differentfading model to investigate In this way the evaluation of theaverage performance is objective We also set a great numberof criterions for our simulation the maximum power state ofD2D users is set at 23 dBm and the maximum interferencewhich mobile users can tolerate is assumed to be 50 times 10minus6Before investigating the system performance based on ourproposed UFM game we tend to show the joint influenceof the power interference caused by spectrum sharing andsocial characteristics in each social community illustrated inFigure 4

In this section we analyze the sum power interferenceand sum social utility respectively as the number of cellularusers varies The case of 10 cellular users means the situationof system whose spectrum resource is in short supply Inthis situation D2D users possibly have to share the spectrumresource of the same users while the case of 30 cellular usersmeans D2D pairs have many resource-occupying choicesThe results indicate that the sumpower interference decreaseswith the trend of the number of cellular users increasing asthe sum social utility stay in quite a stable level And whenthe number of cellular users in the system exceeds 18 theinfluence from social utility will surpass the influence frompower interference And thenwe evaluate the system sum rateand sum time with different number of cellular users usingthe proposed UFM algorithm and the other two advancedschemes which is illustrated in Figures 5 and 6

Figure 5 compares the sum rate of the three algorithmsunder the isolated scenarios in which we set the number ofcellular users varied in the range of [10 30] From Figure 5we observe that by removing some interference-intolerableD2D links significant performance enhancement can be

Social utilityPower interference

0

20

40

60

80

100

120

140

(Bits

(slowast

Hz)

)

12 14 16 18 20 22 24 26 2810Number of cellular users

Figure 4 Comparison of the joint interference

Comparison of sum rate of the system times104

12 14 16 18 20 22 24 26 302810Number of cellular users

1

2

3

4

5

6

7

8

UFMOSRADRA

(Bits

(slowast

Hz)

)

Figure 5 Transmission rate comparison of different resource alloca-tion algorithms with different number of cellular users

achieved when the cellular users are relatively sufficientBut in the situation that cellular users are not sufficientperformances of the two are roughly equalThe reason is thatthe excessive reuse relationships of frequency with the samecellular user will cause unbearable interference to the cellularusers According to our algorithm the D2D link will beremoved automatically in both schemes

Figure 6 compares the sum transmission time of the threealgorithms under the isolated scenarios From Figure 6 wecan observe that in the case that someunnecessaryD2D linkshas been removed the UFM algorithm still provides quite aconsiderable reduction of transmission timeThat is because

10 Wireless Communications and Mobile Computing

Comparison of sum time of the system

UFMOSRADRA

times10minus3

05

1

15

2

25

3

35

4

45

5

55

Sum

tim

e (s

)

12 14 16 18 20 22 24 26 28 3010Number of cellular users

Figure 6 Transmission time comparison of different resource allo-cation algorithms with different number of cellular users

we allowD2Dusers to continue to acquire content via cellularcommunication when D2D communication comes acrosslink interruption So the sum transmission time will not beaffected greatly

For the purpose of evaluating the system performancewhile the number of D2D users varies within a certainrange we set geographical scope as 300m times 300m aroundthe BS and suppose the number of cellular users is 10 Asillustrated in Figures 7 and 8 the variation range of numberof D2D pairs is [5 30] the result demonstrates that ourproposed UFM game always attains the best performancewith the increase of D2D users compared to the OSRAand DRA This is because in the algorithm of DRA orOSRA there exist little coordination measures to restrictD2D pairs to select their resource and it is inevitable toestablish some high-interference links between D2D pairsand cellular users In our proposed algorithm UFM gameeffectively coordinates both social relationship and powerinterference and then decides whether to access the spectrumresource of certain cellular users not in a random way Inthese circumstances we can avoid many high-risk links andattain a better system performance in terms of the evaluationof the sum transmission rate At this point we can summarizethat our proposed scheme precedes the other two schemes ina relatively comprehensive scale

6 Conclusion and Future Work

This paper studies game-theory based social-aware resourceallocation in the D2D communication underlaying cellularnetwork based on the realistic social network By consideringthe power interference and social utility in the physical andsocial domain respectively a game-theoretic based utilityfunction maximization scheme has been proposed Also to

Comparison of sum rate of the system

UFMOSRADRA

times104

0

1

2

3

4

5

6

7

8

10 15 20 25 305Number of D2D pairs

(Bits

(slowast

Hz)

)Figure 7 Transmission rate comparison of different resource alloca-tion algorithms with different number of D2D pairs

Comparison of sum time of the system

UFMOSRADRA

times10minus3

0

1

2

3

4

5

6

7

8

9

Sum

tim

e (s

)

10 15 20 25 305Number of D2D pairs

Figure 8 Transmission time comparison of different resource allo-cation algorithms with different number of D2D pairs

demonstrate the optimality of our proposed scheme thispaper provides evidence for the existence of Nash Equilib-rium theoretically Meanwhile a priority searching operationbased resource allocation scheme is designed to implementthe Nash Equilibrium of the proposed UFM game The pro-posed UFM scheme is numerically shown having superiorityover traditional DRA and OSRA scheme the performancesof sum rate and total transmission time are better thanthe OSRA and DRA algorithm through massive simulation

Wireless Communications and Mobile Computing 11

result suggesting that the proposed scheme is more ideal forjoint social-aware resource scenarios considering the socialcharacteristics Nevertheless some issues related to furthersystem optimization remain to be addressed such as powerallocation of mobile nodes and cluster formation of socialcommunity

Notations

N Set of mobile usersC Set of cellular usersD Set of D2D pairsΦ The UFM game≻119894 Set of utility priority119868119889rarr119888 Interference from 119889th D2D to 119888th cellular signal119868119888rarr119889 Interference from 119888th cellular signal to 119889th D2D119880119889(119883) Social utility of 119889th D2D pairsΓ119889(119883) Utility function of 119889th D2D pairs119909119888119889 Indicator of resource reusing relations119909lowast119889 The Nash Equilibrium of 119889th D2D pair119883119889 Set of all feasible strategies in UFM game

Conflicts of Interest

The authors declare no conflicts of interest related to thepublication of this paper

Acknowledgments

This work is partly supported by the National NaturalScience Foundation of China (61571240 61671253) the Pri-ority Academic Program Development of Jiangsu HigherEducation Institutions the Major Projects of the NaturalScience Foundation of the Jiangsu Higher Education Insti-tutions (16KJA510004) the Open Research Fund of Nationaland Local Joint Engineering Laboratory of RF Integrationand Micro-Assembly Technology Nanjing University ofPosts and Telecommunications (KFJJ20170305) the OpenResearch Fund ofThe State Key Laboratory of Integrated Ser-vices Networks Xidian University (ISN17-04) Jiangsu Spe-cially Appointed Professor Grant (RK002STP16001) Inno-vation and Entrepreneurship of Jiangsu High-Level TalentGrant (CZ0010617002) High-Level Talent Startup Grantof Nanjing University of Posts and Telecommunications(XK0010915026) and ldquo1311 Talent Planrdquo ofNanjingUniversityof Posts and Telecommunications

References

[1] Y Cao T Jiang and C Wang ldquoCooperative device-to-devicecommunications in cellular networksrdquo IEEE Wireless Commu-nications Magazine vol 22 no 3 pp 124ndash129 2015

[2] J Liu N Kato J Ma and N Kadowaki ldquoDevice-to-devicecommunication in LTE-advanced networks a surveyrdquo IEEECommunications Surveys amp Tutorials vol 17 no 4 pp 1923ndash1940 Fourthquarter 2015

[3] A Asadi Q Wang and V Mancuso ldquoA survey on device-to-device communication in cellular networksrdquo IEEE Communi-cations Surveys amp Tutorials vol 16 no 4 pp 1801ndash1819 2014

[4] H Nishiyama M Ito and N Kato ldquoRelay-by-smartphonerealizing multihop device-to-device communicationsrdquo IEEECommunications Magazine vol 52 no 4 pp 56ndash65 2014

[5] M Zhou Y Tang Z Tian L Xie and W Nie ldquoRobust neigh-borhood graphing for semi-supervised indoor localization withlight-loaded location fingerprintingrdquo IEEE Internet of ThingsJournal vol PP no 99 pp 1-1

[6] K Doppler M Rinne C Wijting C B Ribeiro and K HugldquoDevice-to-device communication as an underlay to LTE-advanced networksrdquo IEEE Communications Magazine vol 47no 12 pp 42ndash49 2009

[7] J Liu H Nishiyama N Kato and J Guo ldquoOn the outageprobability of device-to-device-communication-enabled mul-tichannel cellular networks an RSS-threshold-based perspec-tiverdquo IEEE Journal on Selected Areas in Communications vol34 no 1 pp 163ndash175 2016

[8] M Zhou Y Tang W Nie L Xie and X Yang ldquoGrassMAgraph-based semi-supervised manifold alignment for indoorWLAN localizationrdquo IEEE Sensors Journal vol 17 no 21 pp7086ndash7095 2017

[9] J Liu S Zhang N Kato H Ujikawa and K Suzuki ldquoDevice-to-device communications for enhancing quality of experiencein software defined multi-tier LTE-A networksrdquo IEEE Networkvol 29 no 4 pp 46ndash52 2015

[10] C Xu L Song Z Han et al ldquoEfficiency resource allocation fordevice-to-device underlay communication systems a reverseiterative combinatorial auction based approachrdquo IEEE Journalon Selected Areas in Communications vol 31 no 9 pp 348ndash3582013

[11] L Ferdouse W Ejaz K Raahemifar A Anpalagan and MMarkandaier ldquoInterference and throughput aware resourceallocation for multi-class D2D in 5G networksrdquo IET Commu-nications vol 11 no 8 pp 1241ndash1250 2017

[12] T D Hoang L B Le and T Le-Ngoc ldquoCooperative device-to-device communications in cellular networksrdquo IEEE Transac-tions onWireless Communications vol 15 no 10 pp 7099ndash71132016

[13] M Andrews K Kumaran K Ramanan A Stolyar P Whitingand R Vijayakumar ldquoProviding quality of service over a sharedwireless linkrdquo IEEE Communications Magazine vol 39 no 2pp 150ndash154 2001

[14] L Wang L Liu X Cao X Tian and Y Cheng ldquoSociality-aware resource allocation for device-to-device communicationsin cellular networksrdquo IET Communications vol 9 no 3 pp342ndash349 2015

[15] V Shah andA O Fapojuwo ldquoSocially aware resource allocationfor device-to-device communication in downlinkOFDMAnet-worksrdquo in Proceedings of the 2014 IEEE Wireless Communica-tions and Networking Conference WCNC 2014 pp 1673ndash1678Istanbul Turkey April 2014

[16] Y Li T Wu P Hui D Jin and S Chen ldquoSocial-aware D2Dcommunications qualitative insights and quantitative analysisrdquoIEEE Communications Magazine vol 52 no 6 pp 150ndash1582014

[17] FWang L Song Z Han Q Zhao and XWang ldquoJoint schedul-ing and resource allocation for device-to-device underlay com-municationrdquo in Proceedings of the IEEE Wireless Communi-cations and Networking Conference (WCNC rsquo13) pp 134ndash139IEEE Shanghai China April 2013

[18] F Tang Z M Fadlullah N Kato F One and R MiuraldquoAC-POCA anti-coordination game based partially overlap-ping channels assignment in combined UAV and D2D based

12 Wireless Communications and Mobile Computing

networksrdquo IEEE Transactions on Vehicular Technology vol PPno 99 pp 1-1

[19] S M Azimi M H Manshaei and F Hendessi ldquoHybrid cellularand device-to-device communication power control Nashbargaining gamerdquo in Proceedings of the 2014 7th InternationalSymposium on Telecommunications IST 2014 pp 1077ndash1081Tehran Iran September 2014

[20] Z Zhou K Ota M Dong and C Xu ldquoEnergy-efficient match-ing for resource allocation in D2D enabled cellular networksrdquoIEEE Transactions on Vehicular Technology vol 66 no 6 pp5256ndash5268 2017

[21] C Xu C Gao Z Zhou Z Chang and Y Jia ldquoSocial network-based content delivery in device-to-device underlay cellularnetworks using matching theoryrdquo IEEE Access vol 5 pp 924ndash937 2017

[22] X Feng G Sun X Gan et al ldquoCooperative spectrum sharingin cognitive radio networks a distributed matching approachrdquoIEEE Transactions on Communications vol 62 no 8 pp 2651ndash2664 2014

[23] J Zhang ldquoThe interdisciplinary research of big data andwireless channel a cluster-nuclei based channel modelrdquo ChinaCommunications vol 13 no supplement 2 Article ID 7833457pp 14ndash26 2016

[24] S Mumtaz K M Saidul Huq J Rodriguez and V FrascollaldquoEnergy-efficient interference management in LTE-D2D com-municationrdquo IET Signal Processing vol 10 no 3 pp 197ndash2022016

[25] N Kayastha D Niyato P Wang and E Hossain ldquoApplicationsarchitectures and protocol design issues for mobile socialnetworks a surveyrdquo Proceedings of the IEEE vol 99 no 12 pp2130ndash2158 2011

[26] J Zhang L Tian Y Wang and M Liu ldquoSelection transmit-tingmaximum ratio combining for timing synchronization ofMIMO-OFDM systemsrdquo IEEE Transactions on Broadcastingvol 60 no 4 pp 626ndash636 2014

[27] M Zhou Y Wei Z Tian X Yang and L Li ldquoAchieving cost-efficient indoor fingerprint localization on wlan platform ahypothetical test approachrdquo IEEEAccess vol 5 pp 15865ndash158742017

[28] ldquoZacharyrsquoskarateclubrdquohttpsenwikipediaorgwikiZachary27skarate club

[29] D Wu L Zhou and Y Cai ldquoSocial-aware rate based contentsharing mode selection for D2D content sharing scenariosrdquoIEEE Transactions on Multimedia vol 19 no 11 pp 2571ndash25822017

[30] J Huang Y Yin Y Sun Y Zhao C-C Xing and Q DuanldquoGame theoretic resource allocation for multicell D2D commu-nications with incomplete informationrdquo in Proceedings of theIEEE International Conference on Communications ICC 2015pp 3039ndash3044 London UK June 2015

[31] Y Xiao K-C Chen C Yuen and L A DaSilva ldquoSpectrumsharing for device-to-device communications in cellular net-works a game theoretic approachrdquo in Proceedings of the IEEEInternational SymposiumonDynamic SpectrumAccessNetworks(DYSPAN rsquo14) pp 60ndash71 IEEE McLean Va USA April 2014

[32] D Niyato and E Hossain ldquoA game-theoretic approach tocompetitive spectrum sharing in cognitive radio networksrdquo inProceedings of the IEEEWireless Communications and Network-ing Conference (WCNC rsquo07) pp 16ndash20 Kowloon China March2007

[33] D Monderer and L S Shapley ldquoPotential gamesrdquo Games andEconomic Behavior vol 14 no 1 pp 124ndash143 1996

[34] N Nie and C Comaniciu ldquoAdaptive channel allocation spec-trum etiquette for cognitive radio networksrdquo in Proceedingsof the 1st IEEE International Symposium on New Frontiers inDynamic SpectrumAccess Networks (DySPAN rsquo05) pp 269ndash278Baltimore Md USA November 2005

[35] Y Xing C N Mathur M A Haleem R Chandramouli andK P Subbalakshmi ldquoDynamic spectrum access with QoS andinterference temperature constraintsrdquo IEEE Transactions onMobile Computing vol 6 no 4 pp 423ndash433 2007

[36] T Heikkinen ldquoA potential game approach to distributed powercontrol and schedulingrdquo Computer Networks vol 50 no 13 pp2295ndash2311 2006

[37] Y Li D Jin J Yuan and ZHan ldquoCoalitional games for resourceallocation in the device-to-device uplink underlaying cellularnetworksrdquo IEEE Transactions on Wireless Communications vol13 no 7 pp 3965ndash3977 2014

[38] H Ryu and S-H Park ldquoPerformance comparison of resourceallocation schemes for D2D communicationsrdquo in Proceedingsof the 2014 IEEE Wireless Communications and NetworkingConference Workshops WCNCW 2014 pp 266ndash270 IstanbulTurkey April 2014

[39] Y Li S Su and S Chen ldquoSocial-aware resource allocationfor device-to-device communications underlaying cellular net-worksrdquo IEEE Wireless Communications Letters vol 4 no 3 pp293ndash296 2015

[40] D I Laurenson D G M Cruickshank and G J R PoveyldquoComputationally efficient multipath channel simulator for theCOST 207 modelsrdquo in Proceedings of the IEE Colloquium onComputer Modelling of Communication Systems pp 81ndash86London UK May 1994

4 Wireless Communications and Mobile Computing

We can improve the system performance by maximizingthe sum rate to judge whether our proposed optimal social-aware resource allocation scheme is effective

maxDsum119894=1

119877119888119894 + 119877119889119894 sdot 119909119888119889st sum119889119894isinD

119909119899119888119889119894 le 1 119888 isin C 119899119888 isin C

sum119899119888isinC

119909119899119888119889119894 le 1 119888 isin C 119889119894 isin D(6)

22 Problem Description

221 Power Interference In D2D communication networkwe assume the cellular users can share uplink resource withuser equipment During the D2D communication it isinevitable that D2D transmitter interference will be intro-duced to others especially to nearby CUs And since we limitthat each D2D pair can reuse the spectrum resource from atmost one cellular user by assuming there are 119863 D2D pairsand 119862 cellular users in the D2D underlaying communicationcellular network we can simplify the network as Figure 2

In the simplified networkwe establish besides the normalD2D communication we only consider the effects of both theinterference of a generic D2D transmitter introduced toothers and all other interference caused to a D2D receiverFor instance the base station (BS) introduces intratiersinterference to the D2D receivers D2D1198771 as shown in Figure 2Meanwhile due to the full frequency reuse D2D1198791 causesinterference to CU1 Considering the power interferencecaused by the transmitter of the D2D pairs to the nearby UEwe can give the definition that the interference introduced byD2D transmitter 119889 to cellular users 119888 is 119868119889rarr119888 119889 isin D 119888 isin C

119868119889rarr119888 = 119892119889119888119901119889 (7)

where 119901119889 denotes the transmission power of the correspond-ing D2D pairs 119889 119889 isin D 119892119889119888 denotes the gains of the channelbetween the transmitter of D2D pair 119889 to cellular users 119888Here the terms 119888 and 119892119889119888 are positive Hence all of the cel-lular users are assumed in the single cell and correspondinginterference is introduced by prayer 119889 119889 isin D where theplayer 119889 is called the generic D2D transmitter Meanwhilethe transmission between player 119888 119888 isin C and the BS alsointroduces interference to D2D pair 119889 where we define theintratier interference from player 119888 to player 119889 as follows

119868119888rarr119889 = 119892119888119889119901119888 (8)

where 119892119888119889 is the channel gain between the BS and the D2Dpairs 119889 119901119888 is the transmission power of cellular user 119888 Herewe assume that orthogonal channels are used for differentCUs and we do not consider any power control policy atthe macrocell layer In our investigation we pay attention tothe power interference D2D transmitter introduced to theCUs in other words a new power control policy for the D2Dtransmitters

D2D link

Cellular to D2D interferenceCellular link

D2D to cellularinterference

５1

５2

５3５4

＄2＄1

＄2＄2

＄2＄3

＄2＄4

BS

Figure 2 Interference model in the uplink

222 Social Utilization In this part we use a visualizedsocial-network graph to analyze the social relationship be-tween the mobile users and depict the social characteristic ofthe network In the virtual social network social ties aredefined to qualitatively measure the strength of social rela-tionship between D2D users and report the communicationdemands between users Besides social centrality plays a veryimportant role in D2D data transmission users with highcentrality are more likely to hold high capacity in terms ofdata transmission volume and frequency In that case forthe purpose of obtaining a visualization of the social char-acteristics existing in userrsquos daily activities we adopt theproximity social network derived from a real-world mobilitydatasetmdashKarate clubThe network contains the social data of34 members within a Karate club documenting 78 pairwiselinks between members who interact inside or outside theclub [28] By analyzing the realistic dataset and the inter-action behaviors among these members we plot the socialnetwork formed by users visualized by the trace in Figure 3where the magnitude of the node indicates the centrality ofthe specified user and the label of the node indicates thestrength of the social ties of corresponding links

In the virtual social network active mobile users in closerelationship form certain community In order to weigh theinfluence from the social relationship between the mobileusers within the same community to our resource alloca-tion scheme we define the utility of social relationship byquantifying the social characteristic Sincewe supposemobileusers in different communities have no social trust betweeneach other when cellular users download some content fromthe BS cellular users belonging to the same community candeliver the content to other interested users directly insteadof forwarding by the BS And the amount of the content is

Wireless Communications and Mobile Computing 5

140

320

230

240

210

200

220

80

80

90

340

190

330

Figure 3 Social characteristics observed from social-network trace

determined by the social closeness between the users Themore close social relationship the D2D users have the morecontent they will exchange with each other [29]

Based on the analysis mentioned above the social graphcan be denoted by119866119904 = (119881119904 119877119904)119881119904 and 119877119904 stand for the set ofall cellular users and D2D users and the set of relationshipsrespectively To be mentioned the matrix 119877119904 demonstratesthe strength of the relationship of 119881119904 in the social networkGenerally we use the form of matrix described as 120596119889119903 119889 119903 =1 2 119863 and 120585119889119888 119889 = 1 2 119863 119888 = 1 2 119862 120596119889119903denotes the intimacy coefficient between D2D users and 120585119889119888denotes the intimacy coefficient between the cellular usersand D2D users According to the definition in the dataset ofKarate club we plan to divide the closeness coefficient intotwo kinds very close and a little close The values of 120596119889119903 and120585119889119888 follow the set of [0 1] For example 120596119889119903 = 0 impliesa little close intimacy between the D2D users and 120596119889119903 =1 naturally implies a very close intimacy As illustrated inFigure 1 we construct a simple social network In community2 D2D users Jack and Alice have a very close intimacy whileBob and Jack are unfamiliar with each other Inspired by theanalysis in Part A the utility of D2D users can be representedas follows

119880119889 = log2(1 + sum119894=119866119901

119889cap119866119904119889

SINR119889119894) forall119889 isin D (9)

Approximately the utility of cellular users can be representedas follows

119880119888 = log2(1 + sum119894=119866119901119888 cap119866119904119888

SINR119888119894) forall119888 isin C (10)

By the way 119866119901 and 119866119904 denote the physical and socialrelationship of the system model mentioned above Thus 119866119901119888and 119866119904119888 denote the set of cellular users that reuse the samefrequency band of spectrum resource and maintain stableinteractionwith each other119866119901

119889and119866119904119889 denotes theD2Dusers

which reuse the same spectrum resource from cellular usersand maintain stable interaction with the cellular users 119880119889represents the influence of the social relationship to D2Dcommunication and 119880119888 represents the influence of the socialrelationship to cellular communication To sum up we candefine the social-community utility function of D2D users 119889as follows

119880119889 (119883) = sum119903119889isinD

120596119889119903119880119889 + sum119888isinC

120585119889119888119880119888 (11)

119883 denotes the correlation matrix of 119909119888119889 and in general thedegree of social utility enhancement involves two aspects theweighted sum of social utility enhancement by D2D pairshaving social connections with each other as sum119903isinD 120596119889119903119880119889and the weighted sum of utility enhancement betweenfamiliar cellular users and D2D pairs as sum119888isinC 120585119889119888119880119888 In thisway the element of social relationship is considered in theinvestigation of resource allocation in D2D communicationunderlaying cellular network

3 Game Theory-Based Framework forResource Allocation

In our investigation we tend to maximize the sum trans-mission rate of the system For example if D2D transmitterbrings about higher-than-sociality interference to cellularusers the operator would remove the D2D link So wemodelthe resource allocation issue between D2D links and cellularlinks as the utility maximization game

31 Problem Formulation The resource allocation policy ofeach of the D2D pairs 119889 depends on the power interferenceintroduced by D2D communication and social relationshipsbetween themobile users Compared to the physical relation-ship betweenmobile users the social relationship is relativelyless changeableThus we need to consider the joint influencefrom social enhancement and power interference to the D2Dpairs dynamically By that we tend to define the utility of aD2D link as the profits which are contributed by cellular usersand D2D users using spectrum resources and D2D usersusing social characteristics In this case the utility functionof the 119889th D2D links is defined as follows

Γ119889 (119883) = 120572 sdot 119877 + 120573 sdot 119880119889 (119883) minus 120574 sdot 119861119889119894 minus 120576 sdot 119868119889rarr119888iff 119880119889 (119883) ge 119868119889rarr119888 (12)

120572 and 120573 are the charging price of unit data rate supportedby the spectrum resource and the social network 120574 and 120576are the cost function of a D2D occupied resource and power

6 Wireless Communications and Mobile Computing

interference With respect to 120574 a pricing function from (12)is adopted which can be expressed as follows

120574 = 119899 + 119904 sdot (1198611198891 + sdot sdot sdot + 119861119889119894)120591 119894 = 1 2 119898 (13)

119899 119904 and 120591 denote nonnegative constants and 120591 ge 1 toguarantee that the cost function is convex In order toimprove the applicability we suppose

[1198730 + 119892119889119875119889119903] = 119901119861119889119894 (14)

where 119901 is a nonnegative constant [30] then

Γ119889 (119883) = 120572 sdot 119861119889119894 log2 (1 + SINR119889119894) + 120573 sdot sum119895isinD

120596119889119903119880119889+ sum119888isinC

120585119889119888119880119888 minus [119899 + 119904 sdot 119898sum119894=1

119861119889119894]119861119889119894 minus 120576 sdot 119868119894rarr119906iff 119880119889 (119883) ge 119868119889rarr119888

(15)

In the proposed problem in (15) each D2D pair is aimedat integrating every aspect of influence and then maximizingits own utility As the distribution of mobile equipment ischanging all the time the features of the network are varyinginstantaneously So for the purpose of exact comparison weshould implement some effective method to eliminate thiskind of dilemma

Dynamic game with complete information can modelcertain dynamic situation under the premise that the par-ticipant knows the type of the action it will take and theinformation needed for every decision of the action It canbe applied into our proposed model as every D2D paircan get to know the social utility and power interferenceand get the real-time Γ119889(119883) when D2D communication isin progress So the problem above can be regarded as adynamic game with complete social information as well assophisticated interference information In this way we canpropose a dynamic game based scheme to optimize theoverall performance of theD2D communication network dueto the two-sidesrsquo competition

32 UFM Game Formulation From the analysis above wederive the information from two-sidesrsquo action needed inour game theory And for the optimization problem weusually utilize the game theory to solve it Firstly we definecorresponding strategy adopted by each D2D user 119889 in acertain point of history as 119886119889 119886119889 isin 119860119889 where 119860119889 is theset of all available strategies of the D2D pair 119889 The choiceof strategies of all the other participants that is all theother D2D pairs in our work can be defined as 119886minus119889 =1198861 119886119889minus1 119886119889+1 119886119863 If the above assumption for theUFM game theory is perfect there must exist a strategy 119886119889 isin119860119889 to maximize its own utility function

max119886119889isin119860119889

Γ119889 (119886119889 119886minus119889) forall119889 isin D (16)

The UFM game for the resource allocation thinking from theperspective of utility function is defined by quadruple Φ =D 119860119889119889isinD Γ119889119889isinD 119868119889rarr119888119889isinD119888isinC where D denotes the

D2D pairs119883119889 denotes all of the resource allocation strategiesD2D pairs set D can take Γ119889 denotes the utility function ofeach of the D2D pairs 119889 and 119868119889rarr119888 denotes the interferenceintroduced by D2D pairs 119889 to cellular user 11988833 Nash Equilibrium Nash Equilibrium is a very importantterminology in game theory [31 32] It represents a set ofstrategies which are combined by all optimal choices takenby each participant which reflect the optimal reaction eachparticipant adopts against the other participantrsquos strategiesAccording to this if the choices chosen by all the D2D pairsare optimal the system sum rate of the D2D communicationunderlaying cellular network will reach the extreme oneThefollowing part will discuss the existence of Nash Equilibriumin UFM game theory and provide proof for it

Generally the UFM game Φ = D 119860119889119889isinD Γ119889119889isinD119868119889rarr119888119889isinD119888isinC can reach the Nash Equilibrium if each of theD2D pairs has the only optimal response to the other D2Dpairrsquos strategy

119886lowast119889 = argmax119886119889isin119860119889

Γ119889 (119886minus119889 119886119889) forall119889 isin D (17)

and 119886lowast = 119886lowast1 119886lowast2 119886lowast119863 denotes the Nash EquilibriumBecause of the same incentive of changing their strategy

for all the D2D pair we refer to the potential game theory todemonstrate the existence of NE for the UFM game In [33]Monderer and Shapley propose the definition of potentialgame and elaborate the idea in detail too In the field ofwireless resource allocation games game theory has beenapplied in a few of authorsrsquo papers for example [34ndash36] Inpotential game theory the change in individual playerrsquos gaincan be mapped to the global function which is called thepotential function By this way we can conclude if there isany change that occurred on individual player the potentialfunction will change equally in the strict potential game Γdenotes an exact potential function if and only if exist119865(119868) 119868 rarr119880 forall119894 119895 forall119868119894 119868119895 119880119894 isin 119868119894 and 119880119895 isin 119868119895

Γ119894 (119868119894 119880minus119894) minus Γ119895 (119868119895 119880minus119895) = 119865 (119868119894 119880minus119894) minus 119865 (119868119895 119880minus119895) (18)

In the D2D communication systemwe havemodeled thechange of power interference and social utility caused byD2Dlinks would change the utility function of the game whichis consistent with the principle of potential function On theother hand potential gamehas the following inherent proper-ties which are described in [33] (1)There must exist a pure-strategy NE and a solution for it (2) The Nash Equilibriumcorresponds to the maxima of the potential function Γ (3)Generally the convergence to Nash Equilibrium would bereached in finite improvement or searching path accordingto sequential best-response dynamics

For the condition of a single band frequency channel thepotential game is formulated by utilizing the following utility-maximizing function

Γ119894 = minus (Total utility function generated by 119894+ Total utility function experienced by 119894) (19)

Wireless Communications and Mobile Computing 7

Based on the potential game theory we can demonstratethe existence of the Nash Equilibrium of our proposed UFMgame For Γ for every 119889 isin D and for every 119886minus119889 isin 119860minus119889

119875 (119889) = Γ119889 (119886minus119889 119886119889) minus Γ119889 (119886minus119889 1198861015840119889) (20)

Theorem 1 In certain history point 119905 function 119875(119889) derivedfrom UFM game is subgame perfect

Proof We suppose strategy 119886119889 denotes occupying the spec-trum resource of cellular user 119888 which is taken by D2D pairs119889 initially Therefore the initial indicator is 119909119888119889 Once D2Dpair119889 change its strategy andmake a request for the spectrumresource of cellular user 1198881015840 the indicator changes to1199091015840119888119889Thenwe can obtain

Γ119889 minus Γ1015840119889 = 120572 sdot 119877 + 120573 sdot 119880119889 (119883) minus 120576 sdot 119868119889rarr119888 minus 120572 sdot 1198771015840 minus 120573sdot 119880119889 (119883) minus 120576 sdot 1198681015840119889rarr119888

= 120572 sdot (119877 minus 1198771015840) minus 120576 sdot (119868119889rarr119888 minus 1198681015840119889rarr119888) (21)

We denote Δ 1 = 119877 minus 1198771015840 and Δ 2 = 119868119889rarr119888 minus 1198681015840119889rarr119888 As we cansee Δ 1 ≫ Δ 2 Finally we conclude that

Γ119889 minus Γ1015840119889 gt 0 (22)

It means that no D2D pair can acquire performanceenhancement by changing its strategy so we prove that ourproposed game is subgame perfect As subgame is the restric-tion from the perspective of history circumstances it canlead to the Nash Equilibrium of the game directly

4 Resource Allocation Scheme forUFM Game Theory

41 Priority Searching Based Solution The value of the utilityfunction Γ119889 varies when D2D pair chooses to reuse spectrumresource from different cellular user and the final aim of theUFM game is to determine the order of the utility function bythe size of value According to analysis in Sections 32 and 33the resource allocation strategy 119886lowast has a Nash EquilibriumIt means that we can finally achieve an optimal strategy bysubstituting the other strategies one by one in finite times Itis similar to the establishment of preference list and iteratesuntil acquiring the best selection among different alternatives[10] Inspired by the one-to-one matching theory we willshow the main idea of the proposed resource allocationalgorithm in detail

Definition 2 For anyD2D pairs we define the binary priorityrelation set≻119894 to represent the entire set of resource allocationstrategies that each D2D pair 119894 would possibly take In ourUFM game D2D pairs can choose to reuse the resourceoccupied by the associated cellular users or not according tothe priority set For any D2D pairs 119886119894 ≻119894 1198861015840119894 means D2D pairs119894 prefer choosing 119888 as the target resource source instead of 1198881015840

Since the priority set is determined by the utility function wecan define the priority as follows

1198861015840119894 ≻119894 119886119894 lArrrArrΓ119894 (1198861015840119894 ) gt Γ119894 (119886119894)

forall119894 isin D(23)

This definition demonstrates that D2D users 119894 are likelyto reuse the spectrum resource of cellular users 119888 as no moreoptions can bring additional performance gains We can setthe highest priority for cellular user 119888 in the set belonging toD2D user 119894 By this a complete priority set can be obtainedby repeating searching operation For every D2D pair wecan also design an optimization resource allocation schemebased on the priority set In this scheme everyD2Dpair urgesfinding its own highest priority and reusing the spectrumresource shared by the corresponding cellular users

Let us present Algorithm 1Based on the definitions and priority searching operation

we can obtain a final Nash-stable resource scheme 119886fin forD2D users to solve the utility maximization problem whichis given in Algorithm 1 From the whole knowledge givenabove we can see that D2D users make switching iterationfollowing a logically standard based on an arbitrarily choseninitial resource allocation strategy 119886ini At the beginning ofeach iteration D2D user 119894 isin D is randomly chosen by thesystem in step (13) And then the selectedD2D user replacesits resource allocation strategy with 119886ini by random choosinga occupied cellular users and determine its strategies 119886119894 anduniformly selects another social-trust cellular user 1198881015840 isin CThen the D2D pair will request the base station for the chan-nel state information once establishing communication linkwith these two cellular users 119888 and 1198881015840 After acquiring specifiedinformation the BS will computes the utility function of theresource allocation strategies of 119886 and 1198861015840 and broadcast tothe participant of the game model Meanwhile making thedecision that whether to carried out the switch operationfor D2D link If 119886119894 ≻119894 1198861015840119894 the switch operation will not beexecuted Otherwise the switch operation will be executedThe iteration will continue until all of the priority searchingoperations for each D2D pair are traversed and reach a finalNash Equilibrium scheme 119886fin

Different from those conventional D2D resource allo-cation schemes our proposed scheme needs to select suit-able community detection dataset and analyze the social-community information inside And a priority based poten-tial game theory is applied in our scheme This importantinformation is taken into consideration in our proposedscheme fully

42 Uniqueness and Boundedness According to Theorem 1for a given history point 119905 the combination of strategy 119886119894 119886119894 isin119860 119894 can reach a status of being subgame perfect as reactionto the combination of strategy 119886minus119894 To prove the uniquenessand boundedness of our proposed game it is necessary toconfirm that if there exist any participant forall1006704119894 isin D and its

8 Wireless Communications and Mobile Computing

(01) Input Number of mobile users119873 and random resource allocation strategy 119886ini(02)Output A priority based resource allocation scheme 119886fin(03) Utilize the dataset of Karate Club network(04) Calculate the transmission rate of the D2D links and cellular links(05) Obtain 119880119889(119883) and 119868119889rarr119888(06) if 119880119889(119883) le 119868119889rarr119888 remove the D2D links(07) else keep the D2D links(08) Define the matrix of indicator 119909119888119889 isin [0 1](09) 119868 = find 119909119888119889 = 0 ampamp 119868 = 1(10)There is just one 119888 cellular users qualified to shareresources to D2D user 119903 = 119903119888119889(11) else if uniformly randomly choose one cellular users 119888 and 119886possible cellular users 1198881015840 and denote its associate resourcesharing as 119886119894 isin 119886ini(12) Calculate Γ(1198861015840119894 ) and Γ(119886119894) priority = 0(13) if 1198861015840119894 ≻119894 119886119894 then Priority = 1(14) else repeat (15)sim(16)(15) if Priority == 1 then(16) D2D pairs quit current resource occupying strategy of 119888 andturn to adapt the new resource allocation strategy of 1198881015840(17) substitute the current resource occupying strategy 119886 forstrategy 1198861015840 and add it to 119886cur(18)Until all of the D2D pairs complete the priority searching operation resourceoccupying strategy switching operation and reach Nash Equilibrium 119886fin

Algorithm 1 The utility function maximization D2D links redistribution algorithm

corresponding strategy 1006704119886119894 can give better reaction to thestrategy combination 119886minus119894 than 119886119894 and make 1006704119886119894 ≻119894 119886119894 availableSo we provide the following proof relative to the uniquenessand boundedness of our proposed UFM game

Theorem 3 For all of the D2D pairs whose 119909119888119889 = 1 theproposed priority searching based scheme can only obtain aunique resource allocation scheme 119886finProof Based on the description in Algorithm 1 we supposereversely that the combination of strategy 119886119894 is not subgameperfect And then there must exist certain participant 119894 thathas strategy forall1006704119894 isin D and outperforms 119886119894 Now we investigateanother strategy 119886119894 and when 119905 lt 1006704119905 1006704119886119894 is equal to 119886119894 but after1006704119905 it is equal to 119886119894Then in any subgame after the history point1006704119905 strategy forall1006704119894 isin D is at least as well as 119886119894 for the reason thatforall1006704119894 isin D has deviated from 119886119894 once We can also conclude thatstrategy forall1006704119894 isin D is at least as well as 119886119894 after the history point119905 which is contrary to the assumption that strategy forall1006704119894 isin Dimproves the strategy 119886119894 And so on we can investigate other119886119894 to prove its equal benefit with forall1006704119894 isin D until reaching theunique resource allocation scheme 119886fin

Through the above analysis we prove the uniqueness ofthe UFM game by Reduction to Absurdity In each iterationin Algorithm 1 it may lead to a new resource allocationstrategy As there is only C in the physical domain andlimitedD D2D pairs due to the limited social relationship inthe social domain each of the D2D pairs is correspondingto C types of resource allocation scheme So the prioritysearching operation will eventually end in limited steps Thisfact assures the boundedness of our proposed UFM gamebased scheme

5 Simulation Results and Discussions

In this section we implement the simulation results from dif-ferent perspective to verify the performance of our proposedUFM algorithm and elaborate some necessary explanationfor the results Main simulation parameters have been givenin Table 1 Simulations are executed in a single cell whichare within an isolated community circumstance Path lossmodels are considered for cellular and D2D links along withshadow fadingmodel According to the dataset of Karate clubwe conduct the simulation within a 500m times 500m area toguarantee most of the club memberrsquos activities are within thisarea and 34 members of the club are randomly distributedwithin the BS coverage area Meanwhile the bandwidth ofallocated resource is assigned arbitrarily within the rangelimitation We compare our proposed UFM algorithm withthe following resource allocation schemes (a) distributedresource allocation (DRA) which allocates the D2D com-munication resource by thinking in a distributed way [37]and (b) optimal social-community aware resource allocation(OSRA) which allocates the D2D communication resourceto reduce the total transmission time [38] All the results areaveraged over 10 timesrsquo trial

Without loss of generality on one hand we prescribethe pathloss model between the base station and all themobile users as COST (EuropeanCooperation in Science andTechnology) 231 Hata model [39]

PLCU = 367 + 35 times lg (119889) (24)

Meanwhile we prescribe the pathloss model betweendifferent cellular users and D2D users as Xia model [40]given as follows

Wireless Communications and Mobile Computing 9

Table 1 System simulated parameters in the performance evalua-tion

Parameter ValueCoverage radius of BS 500mDistance of D2D 20msim50mNoise figure 9 dB at deviceTransmission power BS 46 dBm device 23 dBmMaximum D2D transmitter power 23 dBmRange of bandwidth 10MHzsim20MHzCommunication demand 50WInterference threshold 56 times 10minus6W119899 119904 119911 120591 1120572 120573 20

PL = 665 + 40 times log (119889) 119889 gt 501007 + 20 times lg (119889) 119889 lt 50 (25)

Since we assume the inner distance of D2D pair remainsin close standards and relatively close the free space modelcan be given by

PL = 384 + 20 times lg (119889) (26)

Moreover we consider the case of fast fading model forRayleigh fading In different situation we adopt a differentfading model to investigate In this way the evaluation of theaverage performance is objective We also set a great numberof criterions for our simulation the maximum power state ofD2D users is set at 23 dBm and the maximum interferencewhich mobile users can tolerate is assumed to be 50 times 10minus6Before investigating the system performance based on ourproposed UFM game we tend to show the joint influenceof the power interference caused by spectrum sharing andsocial characteristics in each social community illustrated inFigure 4

In this section we analyze the sum power interferenceand sum social utility respectively as the number of cellularusers varies The case of 10 cellular users means the situationof system whose spectrum resource is in short supply Inthis situation D2D users possibly have to share the spectrumresource of the same users while the case of 30 cellular usersmeans D2D pairs have many resource-occupying choicesThe results indicate that the sumpower interference decreaseswith the trend of the number of cellular users increasing asthe sum social utility stay in quite a stable level And whenthe number of cellular users in the system exceeds 18 theinfluence from social utility will surpass the influence frompower interference And thenwe evaluate the system sum rateand sum time with different number of cellular users usingthe proposed UFM algorithm and the other two advancedschemes which is illustrated in Figures 5 and 6

Figure 5 compares the sum rate of the three algorithmsunder the isolated scenarios in which we set the number ofcellular users varied in the range of [10 30] From Figure 5we observe that by removing some interference-intolerableD2D links significant performance enhancement can be

Social utilityPower interference

0

20

40

60

80

100

120

140

(Bits

(slowast

Hz)

)

12 14 16 18 20 22 24 26 2810Number of cellular users

Figure 4 Comparison of the joint interference

Comparison of sum rate of the system times104

12 14 16 18 20 22 24 26 302810Number of cellular users

1

2

3

4

5

6

7

8

UFMOSRADRA

(Bits

(slowast

Hz)

)

Figure 5 Transmission rate comparison of different resource alloca-tion algorithms with different number of cellular users

achieved when the cellular users are relatively sufficientBut in the situation that cellular users are not sufficientperformances of the two are roughly equalThe reason is thatthe excessive reuse relationships of frequency with the samecellular user will cause unbearable interference to the cellularusers According to our algorithm the D2D link will beremoved automatically in both schemes

Figure 6 compares the sum transmission time of the threealgorithms under the isolated scenarios From Figure 6 wecan observe that in the case that someunnecessaryD2D linkshas been removed the UFM algorithm still provides quite aconsiderable reduction of transmission timeThat is because

10 Wireless Communications and Mobile Computing

Comparison of sum time of the system

UFMOSRADRA

times10minus3

05

1

15

2

25

3

35

4

45

5

55

Sum

tim

e (s

)

12 14 16 18 20 22 24 26 28 3010Number of cellular users

Figure 6 Transmission time comparison of different resource allo-cation algorithms with different number of cellular users

we allowD2Dusers to continue to acquire content via cellularcommunication when D2D communication comes acrosslink interruption So the sum transmission time will not beaffected greatly

For the purpose of evaluating the system performancewhile the number of D2D users varies within a certainrange we set geographical scope as 300m times 300m aroundthe BS and suppose the number of cellular users is 10 Asillustrated in Figures 7 and 8 the variation range of numberof D2D pairs is [5 30] the result demonstrates that ourproposed UFM game always attains the best performancewith the increase of D2D users compared to the OSRAand DRA This is because in the algorithm of DRA orOSRA there exist little coordination measures to restrictD2D pairs to select their resource and it is inevitable toestablish some high-interference links between D2D pairsand cellular users In our proposed algorithm UFM gameeffectively coordinates both social relationship and powerinterference and then decides whether to access the spectrumresource of certain cellular users not in a random way Inthese circumstances we can avoid many high-risk links andattain a better system performance in terms of the evaluationof the sum transmission rate At this point we can summarizethat our proposed scheme precedes the other two schemes ina relatively comprehensive scale

6 Conclusion and Future Work

This paper studies game-theory based social-aware resourceallocation in the D2D communication underlaying cellularnetwork based on the realistic social network By consideringthe power interference and social utility in the physical andsocial domain respectively a game-theoretic based utilityfunction maximization scheme has been proposed Also to

Comparison of sum rate of the system

UFMOSRADRA

times104

0

1

2

3

4

5

6

7

8

10 15 20 25 305Number of D2D pairs

(Bits

(slowast

Hz)

)Figure 7 Transmission rate comparison of different resource alloca-tion algorithms with different number of D2D pairs

Comparison of sum time of the system

UFMOSRADRA

times10minus3

0

1

2

3

4

5

6

7

8

9

Sum

tim

e (s

)

10 15 20 25 305Number of D2D pairs

Figure 8 Transmission time comparison of different resource allo-cation algorithms with different number of D2D pairs

demonstrate the optimality of our proposed scheme thispaper provides evidence for the existence of Nash Equilib-rium theoretically Meanwhile a priority searching operationbased resource allocation scheme is designed to implementthe Nash Equilibrium of the proposed UFM game The pro-posed UFM scheme is numerically shown having superiorityover traditional DRA and OSRA scheme the performancesof sum rate and total transmission time are better thanthe OSRA and DRA algorithm through massive simulation

Wireless Communications and Mobile Computing 11

result suggesting that the proposed scheme is more ideal forjoint social-aware resource scenarios considering the socialcharacteristics Nevertheless some issues related to furthersystem optimization remain to be addressed such as powerallocation of mobile nodes and cluster formation of socialcommunity

Notations

N Set of mobile usersC Set of cellular usersD Set of D2D pairsΦ The UFM game≻119894 Set of utility priority119868119889rarr119888 Interference from 119889th D2D to 119888th cellular signal119868119888rarr119889 Interference from 119888th cellular signal to 119889th D2D119880119889(119883) Social utility of 119889th D2D pairsΓ119889(119883) Utility function of 119889th D2D pairs119909119888119889 Indicator of resource reusing relations119909lowast119889 The Nash Equilibrium of 119889th D2D pair119883119889 Set of all feasible strategies in UFM game

Conflicts of Interest

The authors declare no conflicts of interest related to thepublication of this paper

Acknowledgments

This work is partly supported by the National NaturalScience Foundation of China (61571240 61671253) the Pri-ority Academic Program Development of Jiangsu HigherEducation Institutions the Major Projects of the NaturalScience Foundation of the Jiangsu Higher Education Insti-tutions (16KJA510004) the Open Research Fund of Nationaland Local Joint Engineering Laboratory of RF Integrationand Micro-Assembly Technology Nanjing University ofPosts and Telecommunications (KFJJ20170305) the OpenResearch Fund ofThe State Key Laboratory of Integrated Ser-vices Networks Xidian University (ISN17-04) Jiangsu Spe-cially Appointed Professor Grant (RK002STP16001) Inno-vation and Entrepreneurship of Jiangsu High-Level TalentGrant (CZ0010617002) High-Level Talent Startup Grantof Nanjing University of Posts and Telecommunications(XK0010915026) and ldquo1311 Talent Planrdquo ofNanjingUniversityof Posts and Telecommunications

References

[1] Y Cao T Jiang and C Wang ldquoCooperative device-to-devicecommunications in cellular networksrdquo IEEE Wireless Commu-nications Magazine vol 22 no 3 pp 124ndash129 2015

[2] J Liu N Kato J Ma and N Kadowaki ldquoDevice-to-devicecommunication in LTE-advanced networks a surveyrdquo IEEECommunications Surveys amp Tutorials vol 17 no 4 pp 1923ndash1940 Fourthquarter 2015

[3] A Asadi Q Wang and V Mancuso ldquoA survey on device-to-device communication in cellular networksrdquo IEEE Communi-cations Surveys amp Tutorials vol 16 no 4 pp 1801ndash1819 2014

[4] H Nishiyama M Ito and N Kato ldquoRelay-by-smartphonerealizing multihop device-to-device communicationsrdquo IEEECommunications Magazine vol 52 no 4 pp 56ndash65 2014

[5] M Zhou Y Tang Z Tian L Xie and W Nie ldquoRobust neigh-borhood graphing for semi-supervised indoor localization withlight-loaded location fingerprintingrdquo IEEE Internet of ThingsJournal vol PP no 99 pp 1-1

[6] K Doppler M Rinne C Wijting C B Ribeiro and K HugldquoDevice-to-device communication as an underlay to LTE-advanced networksrdquo IEEE Communications Magazine vol 47no 12 pp 42ndash49 2009

[7] J Liu H Nishiyama N Kato and J Guo ldquoOn the outageprobability of device-to-device-communication-enabled mul-tichannel cellular networks an RSS-threshold-based perspec-tiverdquo IEEE Journal on Selected Areas in Communications vol34 no 1 pp 163ndash175 2016

[8] M Zhou Y Tang W Nie L Xie and X Yang ldquoGrassMAgraph-based semi-supervised manifold alignment for indoorWLAN localizationrdquo IEEE Sensors Journal vol 17 no 21 pp7086ndash7095 2017

[9] J Liu S Zhang N Kato H Ujikawa and K Suzuki ldquoDevice-to-device communications for enhancing quality of experiencein software defined multi-tier LTE-A networksrdquo IEEE Networkvol 29 no 4 pp 46ndash52 2015

[10] C Xu L Song Z Han et al ldquoEfficiency resource allocation fordevice-to-device underlay communication systems a reverseiterative combinatorial auction based approachrdquo IEEE Journalon Selected Areas in Communications vol 31 no 9 pp 348ndash3582013

[11] L Ferdouse W Ejaz K Raahemifar A Anpalagan and MMarkandaier ldquoInterference and throughput aware resourceallocation for multi-class D2D in 5G networksrdquo IET Commu-nications vol 11 no 8 pp 1241ndash1250 2017

[12] T D Hoang L B Le and T Le-Ngoc ldquoCooperative device-to-device communications in cellular networksrdquo IEEE Transac-tions onWireless Communications vol 15 no 10 pp 7099ndash71132016

[13] M Andrews K Kumaran K Ramanan A Stolyar P Whitingand R Vijayakumar ldquoProviding quality of service over a sharedwireless linkrdquo IEEE Communications Magazine vol 39 no 2pp 150ndash154 2001

[14] L Wang L Liu X Cao X Tian and Y Cheng ldquoSociality-aware resource allocation for device-to-device communicationsin cellular networksrdquo IET Communications vol 9 no 3 pp342ndash349 2015

[15] V Shah andA O Fapojuwo ldquoSocially aware resource allocationfor device-to-device communication in downlinkOFDMAnet-worksrdquo in Proceedings of the 2014 IEEE Wireless Communica-tions and Networking Conference WCNC 2014 pp 1673ndash1678Istanbul Turkey April 2014

[16] Y Li T Wu P Hui D Jin and S Chen ldquoSocial-aware D2Dcommunications qualitative insights and quantitative analysisrdquoIEEE Communications Magazine vol 52 no 6 pp 150ndash1582014

[17] FWang L Song Z Han Q Zhao and XWang ldquoJoint schedul-ing and resource allocation for device-to-device underlay com-municationrdquo in Proceedings of the IEEE Wireless Communi-cations and Networking Conference (WCNC rsquo13) pp 134ndash139IEEE Shanghai China April 2013

[18] F Tang Z M Fadlullah N Kato F One and R MiuraldquoAC-POCA anti-coordination game based partially overlap-ping channels assignment in combined UAV and D2D based

12 Wireless Communications and Mobile Computing

networksrdquo IEEE Transactions on Vehicular Technology vol PPno 99 pp 1-1

[19] S M Azimi M H Manshaei and F Hendessi ldquoHybrid cellularand device-to-device communication power control Nashbargaining gamerdquo in Proceedings of the 2014 7th InternationalSymposium on Telecommunications IST 2014 pp 1077ndash1081Tehran Iran September 2014

[20] Z Zhou K Ota M Dong and C Xu ldquoEnergy-efficient match-ing for resource allocation in D2D enabled cellular networksrdquoIEEE Transactions on Vehicular Technology vol 66 no 6 pp5256ndash5268 2017

[21] C Xu C Gao Z Zhou Z Chang and Y Jia ldquoSocial network-based content delivery in device-to-device underlay cellularnetworks using matching theoryrdquo IEEE Access vol 5 pp 924ndash937 2017

[22] X Feng G Sun X Gan et al ldquoCooperative spectrum sharingin cognitive radio networks a distributed matching approachrdquoIEEE Transactions on Communications vol 62 no 8 pp 2651ndash2664 2014

[23] J Zhang ldquoThe interdisciplinary research of big data andwireless channel a cluster-nuclei based channel modelrdquo ChinaCommunications vol 13 no supplement 2 Article ID 7833457pp 14ndash26 2016

[24] S Mumtaz K M Saidul Huq J Rodriguez and V FrascollaldquoEnergy-efficient interference management in LTE-D2D com-municationrdquo IET Signal Processing vol 10 no 3 pp 197ndash2022016

[25] N Kayastha D Niyato P Wang and E Hossain ldquoApplicationsarchitectures and protocol design issues for mobile socialnetworks a surveyrdquo Proceedings of the IEEE vol 99 no 12 pp2130ndash2158 2011

[26] J Zhang L Tian Y Wang and M Liu ldquoSelection transmit-tingmaximum ratio combining for timing synchronization ofMIMO-OFDM systemsrdquo IEEE Transactions on Broadcastingvol 60 no 4 pp 626ndash636 2014

[27] M Zhou Y Wei Z Tian X Yang and L Li ldquoAchieving cost-efficient indoor fingerprint localization on wlan platform ahypothetical test approachrdquo IEEEAccess vol 5 pp 15865ndash158742017

[28] ldquoZacharyrsquoskarateclubrdquohttpsenwikipediaorgwikiZachary27skarate club

[29] D Wu L Zhou and Y Cai ldquoSocial-aware rate based contentsharing mode selection for D2D content sharing scenariosrdquoIEEE Transactions on Multimedia vol 19 no 11 pp 2571ndash25822017

[30] J Huang Y Yin Y Sun Y Zhao C-C Xing and Q DuanldquoGame theoretic resource allocation for multicell D2D commu-nications with incomplete informationrdquo in Proceedings of theIEEE International Conference on Communications ICC 2015pp 3039ndash3044 London UK June 2015

[31] Y Xiao K-C Chen C Yuen and L A DaSilva ldquoSpectrumsharing for device-to-device communications in cellular net-works a game theoretic approachrdquo in Proceedings of the IEEEInternational SymposiumonDynamic SpectrumAccessNetworks(DYSPAN rsquo14) pp 60ndash71 IEEE McLean Va USA April 2014

[32] D Niyato and E Hossain ldquoA game-theoretic approach tocompetitive spectrum sharing in cognitive radio networksrdquo inProceedings of the IEEEWireless Communications and Network-ing Conference (WCNC rsquo07) pp 16ndash20 Kowloon China March2007

[33] D Monderer and L S Shapley ldquoPotential gamesrdquo Games andEconomic Behavior vol 14 no 1 pp 124ndash143 1996

[34] N Nie and C Comaniciu ldquoAdaptive channel allocation spec-trum etiquette for cognitive radio networksrdquo in Proceedingsof the 1st IEEE International Symposium on New Frontiers inDynamic SpectrumAccess Networks (DySPAN rsquo05) pp 269ndash278Baltimore Md USA November 2005

[35] Y Xing C N Mathur M A Haleem R Chandramouli andK P Subbalakshmi ldquoDynamic spectrum access with QoS andinterference temperature constraintsrdquo IEEE Transactions onMobile Computing vol 6 no 4 pp 423ndash433 2007

[36] T Heikkinen ldquoA potential game approach to distributed powercontrol and schedulingrdquo Computer Networks vol 50 no 13 pp2295ndash2311 2006

[37] Y Li D Jin J Yuan and ZHan ldquoCoalitional games for resourceallocation in the device-to-device uplink underlaying cellularnetworksrdquo IEEE Transactions on Wireless Communications vol13 no 7 pp 3965ndash3977 2014

[38] H Ryu and S-H Park ldquoPerformance comparison of resourceallocation schemes for D2D communicationsrdquo in Proceedingsof the 2014 IEEE Wireless Communications and NetworkingConference Workshops WCNCW 2014 pp 266ndash270 IstanbulTurkey April 2014

[39] Y Li S Su and S Chen ldquoSocial-aware resource allocationfor device-to-device communications underlaying cellular net-worksrdquo IEEE Wireless Communications Letters vol 4 no 3 pp293ndash296 2015

[40] D I Laurenson D G M Cruickshank and G J R PoveyldquoComputationally efficient multipath channel simulator for theCOST 207 modelsrdquo in Proceedings of the IEE Colloquium onComputer Modelling of Communication Systems pp 81ndash86London UK May 1994

Wireless Communications and Mobile Computing 5

140

320

230

240

210

200

220

80

80

90

340

190

330

Figure 3 Social characteristics observed from social-network trace

determined by the social closeness between the users Themore close social relationship the D2D users have the morecontent they will exchange with each other [29]

Based on the analysis mentioned above the social graphcan be denoted by119866119904 = (119881119904 119877119904)119881119904 and 119877119904 stand for the set ofall cellular users and D2D users and the set of relationshipsrespectively To be mentioned the matrix 119877119904 demonstratesthe strength of the relationship of 119881119904 in the social networkGenerally we use the form of matrix described as 120596119889119903 119889 119903 =1 2 119863 and 120585119889119888 119889 = 1 2 119863 119888 = 1 2 119862 120596119889119903denotes the intimacy coefficient between D2D users and 120585119889119888denotes the intimacy coefficient between the cellular usersand D2D users According to the definition in the dataset ofKarate club we plan to divide the closeness coefficient intotwo kinds very close and a little close The values of 120596119889119903 and120585119889119888 follow the set of [0 1] For example 120596119889119903 = 0 impliesa little close intimacy between the D2D users and 120596119889119903 =1 naturally implies a very close intimacy As illustrated inFigure 1 we construct a simple social network In community2 D2D users Jack and Alice have a very close intimacy whileBob and Jack are unfamiliar with each other Inspired by theanalysis in Part A the utility of D2D users can be representedas follows

119880119889 = log2(1 + sum119894=119866119901

119889cap119866119904119889

SINR119889119894) forall119889 isin D (9)

Approximately the utility of cellular users can be representedas follows

119880119888 = log2(1 + sum119894=119866119901119888 cap119866119904119888

SINR119888119894) forall119888 isin C (10)

By the way 119866119901 and 119866119904 denote the physical and socialrelationship of the system model mentioned above Thus 119866119901119888and 119866119904119888 denote the set of cellular users that reuse the samefrequency band of spectrum resource and maintain stableinteractionwith each other119866119901

119889and119866119904119889 denotes theD2Dusers

which reuse the same spectrum resource from cellular usersand maintain stable interaction with the cellular users 119880119889represents the influence of the social relationship to D2Dcommunication and 119880119888 represents the influence of the socialrelationship to cellular communication To sum up we candefine the social-community utility function of D2D users 119889as follows

119880119889 (119883) = sum119903119889isinD

120596119889119903119880119889 + sum119888isinC

120585119889119888119880119888 (11)

119883 denotes the correlation matrix of 119909119888119889 and in general thedegree of social utility enhancement involves two aspects theweighted sum of social utility enhancement by D2D pairshaving social connections with each other as sum119903isinD 120596119889119903119880119889and the weighted sum of utility enhancement betweenfamiliar cellular users and D2D pairs as sum119888isinC 120585119889119888119880119888 In thisway the element of social relationship is considered in theinvestigation of resource allocation in D2D communicationunderlaying cellular network

3 Game Theory-Based Framework forResource Allocation

In our investigation we tend to maximize the sum trans-mission rate of the system For example if D2D transmitterbrings about higher-than-sociality interference to cellularusers the operator would remove the D2D link So wemodelthe resource allocation issue between D2D links and cellularlinks as the utility maximization game

31 Problem Formulation The resource allocation policy ofeach of the D2D pairs 119889 depends on the power interferenceintroduced by D2D communication and social relationshipsbetween themobile users Compared to the physical relation-ship betweenmobile users the social relationship is relativelyless changeableThus we need to consider the joint influencefrom social enhancement and power interference to the D2Dpairs dynamically By that we tend to define the utility of aD2D link as the profits which are contributed by cellular usersand D2D users using spectrum resources and D2D usersusing social characteristics In this case the utility functionof the 119889th D2D links is defined as follows

Γ119889 (119883) = 120572 sdot 119877 + 120573 sdot 119880119889 (119883) minus 120574 sdot 119861119889119894 minus 120576 sdot 119868119889rarr119888iff 119880119889 (119883) ge 119868119889rarr119888 (12)

120572 and 120573 are the charging price of unit data rate supportedby the spectrum resource and the social network 120574 and 120576are the cost function of a D2D occupied resource and power

6 Wireless Communications and Mobile Computing

interference With respect to 120574 a pricing function from (12)is adopted which can be expressed as follows

120574 = 119899 + 119904 sdot (1198611198891 + sdot sdot sdot + 119861119889119894)120591 119894 = 1 2 119898 (13)

119899 119904 and 120591 denote nonnegative constants and 120591 ge 1 toguarantee that the cost function is convex In order toimprove the applicability we suppose

[1198730 + 119892119889119875119889119903] = 119901119861119889119894 (14)

where 119901 is a nonnegative constant [30] then

Γ119889 (119883) = 120572 sdot 119861119889119894 log2 (1 + SINR119889119894) + 120573 sdot sum119895isinD

120596119889119903119880119889+ sum119888isinC

120585119889119888119880119888 minus [119899 + 119904 sdot 119898sum119894=1

119861119889119894]119861119889119894 minus 120576 sdot 119868119894rarr119906iff 119880119889 (119883) ge 119868119889rarr119888

(15)

In the proposed problem in (15) each D2D pair is aimedat integrating every aspect of influence and then maximizingits own utility As the distribution of mobile equipment ischanging all the time the features of the network are varyinginstantaneously So for the purpose of exact comparison weshould implement some effective method to eliminate thiskind of dilemma

Dynamic game with complete information can modelcertain dynamic situation under the premise that the par-ticipant knows the type of the action it will take and theinformation needed for every decision of the action It canbe applied into our proposed model as every D2D paircan get to know the social utility and power interferenceand get the real-time Γ119889(119883) when D2D communication isin progress So the problem above can be regarded as adynamic game with complete social information as well assophisticated interference information In this way we canpropose a dynamic game based scheme to optimize theoverall performance of theD2D communication network dueto the two-sidesrsquo competition

32 UFM Game Formulation From the analysis above wederive the information from two-sidesrsquo action needed inour game theory And for the optimization problem weusually utilize the game theory to solve it Firstly we definecorresponding strategy adopted by each D2D user 119889 in acertain point of history as 119886119889 119886119889 isin 119860119889 where 119860119889 is theset of all available strategies of the D2D pair 119889 The choiceof strategies of all the other participants that is all theother D2D pairs in our work can be defined as 119886minus119889 =1198861 119886119889minus1 119886119889+1 119886119863 If the above assumption for theUFM game theory is perfect there must exist a strategy 119886119889 isin119860119889 to maximize its own utility function

max119886119889isin119860119889

Γ119889 (119886119889 119886minus119889) forall119889 isin D (16)

The UFM game for the resource allocation thinking from theperspective of utility function is defined by quadruple Φ =D 119860119889119889isinD Γ119889119889isinD 119868119889rarr119888119889isinD119888isinC where D denotes the

D2D pairs119883119889 denotes all of the resource allocation strategiesD2D pairs set D can take Γ119889 denotes the utility function ofeach of the D2D pairs 119889 and 119868119889rarr119888 denotes the interferenceintroduced by D2D pairs 119889 to cellular user 11988833 Nash Equilibrium Nash Equilibrium is a very importantterminology in game theory [31 32] It represents a set ofstrategies which are combined by all optimal choices takenby each participant which reflect the optimal reaction eachparticipant adopts against the other participantrsquos strategiesAccording to this if the choices chosen by all the D2D pairsare optimal the system sum rate of the D2D communicationunderlaying cellular network will reach the extreme oneThefollowing part will discuss the existence of Nash Equilibriumin UFM game theory and provide proof for it

Generally the UFM game Φ = D 119860119889119889isinD Γ119889119889isinD119868119889rarr119888119889isinD119888isinC can reach the Nash Equilibrium if each of theD2D pairs has the only optimal response to the other D2Dpairrsquos strategy

119886lowast119889 = argmax119886119889isin119860119889

Γ119889 (119886minus119889 119886119889) forall119889 isin D (17)

and 119886lowast = 119886lowast1 119886lowast2 119886lowast119863 denotes the Nash EquilibriumBecause of the same incentive of changing their strategy

for all the D2D pair we refer to the potential game theory todemonstrate the existence of NE for the UFM game In [33]Monderer and Shapley propose the definition of potentialgame and elaborate the idea in detail too In the field ofwireless resource allocation games game theory has beenapplied in a few of authorsrsquo papers for example [34ndash36] Inpotential game theory the change in individual playerrsquos gaincan be mapped to the global function which is called thepotential function By this way we can conclude if there isany change that occurred on individual player the potentialfunction will change equally in the strict potential game Γdenotes an exact potential function if and only if exist119865(119868) 119868 rarr119880 forall119894 119895 forall119868119894 119868119895 119880119894 isin 119868119894 and 119880119895 isin 119868119895

Γ119894 (119868119894 119880minus119894) minus Γ119895 (119868119895 119880minus119895) = 119865 (119868119894 119880minus119894) minus 119865 (119868119895 119880minus119895) (18)

In the D2D communication systemwe havemodeled thechange of power interference and social utility caused byD2Dlinks would change the utility function of the game whichis consistent with the principle of potential function On theother hand potential gamehas the following inherent proper-ties which are described in [33] (1)There must exist a pure-strategy NE and a solution for it (2) The Nash Equilibriumcorresponds to the maxima of the potential function Γ (3)Generally the convergence to Nash Equilibrium would bereached in finite improvement or searching path accordingto sequential best-response dynamics

For the condition of a single band frequency channel thepotential game is formulated by utilizing the following utility-maximizing function

Γ119894 = minus (Total utility function generated by 119894+ Total utility function experienced by 119894) (19)

Wireless Communications and Mobile Computing 7

Based on the potential game theory we can demonstratethe existence of the Nash Equilibrium of our proposed UFMgame For Γ for every 119889 isin D and for every 119886minus119889 isin 119860minus119889

119875 (119889) = Γ119889 (119886minus119889 119886119889) minus Γ119889 (119886minus119889 1198861015840119889) (20)

Theorem 1 In certain history point 119905 function 119875(119889) derivedfrom UFM game is subgame perfect

Proof We suppose strategy 119886119889 denotes occupying the spec-trum resource of cellular user 119888 which is taken by D2D pairs119889 initially Therefore the initial indicator is 119909119888119889 Once D2Dpair119889 change its strategy andmake a request for the spectrumresource of cellular user 1198881015840 the indicator changes to1199091015840119888119889Thenwe can obtain

Γ119889 minus Γ1015840119889 = 120572 sdot 119877 + 120573 sdot 119880119889 (119883) minus 120576 sdot 119868119889rarr119888 minus 120572 sdot 1198771015840 minus 120573sdot 119880119889 (119883) minus 120576 sdot 1198681015840119889rarr119888

= 120572 sdot (119877 minus 1198771015840) minus 120576 sdot (119868119889rarr119888 minus 1198681015840119889rarr119888) (21)

We denote Δ 1 = 119877 minus 1198771015840 and Δ 2 = 119868119889rarr119888 minus 1198681015840119889rarr119888 As we cansee Δ 1 ≫ Δ 2 Finally we conclude that

Γ119889 minus Γ1015840119889 gt 0 (22)

It means that no D2D pair can acquire performanceenhancement by changing its strategy so we prove that ourproposed game is subgame perfect As subgame is the restric-tion from the perspective of history circumstances it canlead to the Nash Equilibrium of the game directly

4 Resource Allocation Scheme forUFM Game Theory

41 Priority Searching Based Solution The value of the utilityfunction Γ119889 varies when D2D pair chooses to reuse spectrumresource from different cellular user and the final aim of theUFM game is to determine the order of the utility function bythe size of value According to analysis in Sections 32 and 33the resource allocation strategy 119886lowast has a Nash EquilibriumIt means that we can finally achieve an optimal strategy bysubstituting the other strategies one by one in finite times Itis similar to the establishment of preference list and iteratesuntil acquiring the best selection among different alternatives[10] Inspired by the one-to-one matching theory we willshow the main idea of the proposed resource allocationalgorithm in detail

Definition 2 For anyD2D pairs we define the binary priorityrelation set≻119894 to represent the entire set of resource allocationstrategies that each D2D pair 119894 would possibly take In ourUFM game D2D pairs can choose to reuse the resourceoccupied by the associated cellular users or not according tothe priority set For any D2D pairs 119886119894 ≻119894 1198861015840119894 means D2D pairs119894 prefer choosing 119888 as the target resource source instead of 1198881015840

Since the priority set is determined by the utility function wecan define the priority as follows

1198861015840119894 ≻119894 119886119894 lArrrArrΓ119894 (1198861015840119894 ) gt Γ119894 (119886119894)

forall119894 isin D(23)

This definition demonstrates that D2D users 119894 are likelyto reuse the spectrum resource of cellular users 119888 as no moreoptions can bring additional performance gains We can setthe highest priority for cellular user 119888 in the set belonging toD2D user 119894 By this a complete priority set can be obtainedby repeating searching operation For every D2D pair wecan also design an optimization resource allocation schemebased on the priority set In this scheme everyD2Dpair urgesfinding its own highest priority and reusing the spectrumresource shared by the corresponding cellular users

Let us present Algorithm 1Based on the definitions and priority searching operation

we can obtain a final Nash-stable resource scheme 119886fin forD2D users to solve the utility maximization problem whichis given in Algorithm 1 From the whole knowledge givenabove we can see that D2D users make switching iterationfollowing a logically standard based on an arbitrarily choseninitial resource allocation strategy 119886ini At the beginning ofeach iteration D2D user 119894 isin D is randomly chosen by thesystem in step (13) And then the selectedD2D user replacesits resource allocation strategy with 119886ini by random choosinga occupied cellular users and determine its strategies 119886119894 anduniformly selects another social-trust cellular user 1198881015840 isin CThen the D2D pair will request the base station for the chan-nel state information once establishing communication linkwith these two cellular users 119888 and 1198881015840 After acquiring specifiedinformation the BS will computes the utility function of theresource allocation strategies of 119886 and 1198861015840 and broadcast tothe participant of the game model Meanwhile making thedecision that whether to carried out the switch operationfor D2D link If 119886119894 ≻119894 1198861015840119894 the switch operation will not beexecuted Otherwise the switch operation will be executedThe iteration will continue until all of the priority searchingoperations for each D2D pair are traversed and reach a finalNash Equilibrium scheme 119886fin

Different from those conventional D2D resource allo-cation schemes our proposed scheme needs to select suit-able community detection dataset and analyze the social-community information inside And a priority based poten-tial game theory is applied in our scheme This importantinformation is taken into consideration in our proposedscheme fully

42 Uniqueness and Boundedness According to Theorem 1for a given history point 119905 the combination of strategy 119886119894 119886119894 isin119860 119894 can reach a status of being subgame perfect as reactionto the combination of strategy 119886minus119894 To prove the uniquenessand boundedness of our proposed game it is necessary toconfirm that if there exist any participant forall1006704119894 isin D and its

8 Wireless Communications and Mobile Computing

(01) Input Number of mobile users119873 and random resource allocation strategy 119886ini(02)Output A priority based resource allocation scheme 119886fin(03) Utilize the dataset of Karate Club network(04) Calculate the transmission rate of the D2D links and cellular links(05) Obtain 119880119889(119883) and 119868119889rarr119888(06) if 119880119889(119883) le 119868119889rarr119888 remove the D2D links(07) else keep the D2D links(08) Define the matrix of indicator 119909119888119889 isin [0 1](09) 119868 = find 119909119888119889 = 0 ampamp 119868 = 1(10)There is just one 119888 cellular users qualified to shareresources to D2D user 119903 = 119903119888119889(11) else if uniformly randomly choose one cellular users 119888 and 119886possible cellular users 1198881015840 and denote its associate resourcesharing as 119886119894 isin 119886ini(12) Calculate Γ(1198861015840119894 ) and Γ(119886119894) priority = 0(13) if 1198861015840119894 ≻119894 119886119894 then Priority = 1(14) else repeat (15)sim(16)(15) if Priority == 1 then(16) D2D pairs quit current resource occupying strategy of 119888 andturn to adapt the new resource allocation strategy of 1198881015840(17) substitute the current resource occupying strategy 119886 forstrategy 1198861015840 and add it to 119886cur(18)Until all of the D2D pairs complete the priority searching operation resourceoccupying strategy switching operation and reach Nash Equilibrium 119886fin

Algorithm 1 The utility function maximization D2D links redistribution algorithm

corresponding strategy 1006704119886119894 can give better reaction to thestrategy combination 119886minus119894 than 119886119894 and make 1006704119886119894 ≻119894 119886119894 availableSo we provide the following proof relative to the uniquenessand boundedness of our proposed UFM game

Theorem 3 For all of the D2D pairs whose 119909119888119889 = 1 theproposed priority searching based scheme can only obtain aunique resource allocation scheme 119886finProof Based on the description in Algorithm 1 we supposereversely that the combination of strategy 119886119894 is not subgameperfect And then there must exist certain participant 119894 thathas strategy forall1006704119894 isin D and outperforms 119886119894 Now we investigateanother strategy 119886119894 and when 119905 lt 1006704119905 1006704119886119894 is equal to 119886119894 but after1006704119905 it is equal to 119886119894Then in any subgame after the history point1006704119905 strategy forall1006704119894 isin D is at least as well as 119886119894 for the reason thatforall1006704119894 isin D has deviated from 119886119894 once We can also conclude thatstrategy forall1006704119894 isin D is at least as well as 119886119894 after the history point119905 which is contrary to the assumption that strategy forall1006704119894 isin Dimproves the strategy 119886119894 And so on we can investigate other119886119894 to prove its equal benefit with forall1006704119894 isin D until reaching theunique resource allocation scheme 119886fin

Through the above analysis we prove the uniqueness ofthe UFM game by Reduction to Absurdity In each iterationin Algorithm 1 it may lead to a new resource allocationstrategy As there is only C in the physical domain andlimitedD D2D pairs due to the limited social relationship inthe social domain each of the D2D pairs is correspondingto C types of resource allocation scheme So the prioritysearching operation will eventually end in limited steps Thisfact assures the boundedness of our proposed UFM gamebased scheme

5 Simulation Results and Discussions

In this section we implement the simulation results from dif-ferent perspective to verify the performance of our proposedUFM algorithm and elaborate some necessary explanationfor the results Main simulation parameters have been givenin Table 1 Simulations are executed in a single cell whichare within an isolated community circumstance Path lossmodels are considered for cellular and D2D links along withshadow fadingmodel According to the dataset of Karate clubwe conduct the simulation within a 500m times 500m area toguarantee most of the club memberrsquos activities are within thisarea and 34 members of the club are randomly distributedwithin the BS coverage area Meanwhile the bandwidth ofallocated resource is assigned arbitrarily within the rangelimitation We compare our proposed UFM algorithm withthe following resource allocation schemes (a) distributedresource allocation (DRA) which allocates the D2D com-munication resource by thinking in a distributed way [37]and (b) optimal social-community aware resource allocation(OSRA) which allocates the D2D communication resourceto reduce the total transmission time [38] All the results areaveraged over 10 timesrsquo trial

Without loss of generality on one hand we prescribethe pathloss model between the base station and all themobile users as COST (EuropeanCooperation in Science andTechnology) 231 Hata model [39]

PLCU = 367 + 35 times lg (119889) (24)

Meanwhile we prescribe the pathloss model betweendifferent cellular users and D2D users as Xia model [40]given as follows

Wireless Communications and Mobile Computing 9

Table 1 System simulated parameters in the performance evalua-tion

Parameter ValueCoverage radius of BS 500mDistance of D2D 20msim50mNoise figure 9 dB at deviceTransmission power BS 46 dBm device 23 dBmMaximum D2D transmitter power 23 dBmRange of bandwidth 10MHzsim20MHzCommunication demand 50WInterference threshold 56 times 10minus6W119899 119904 119911 120591 1120572 120573 20

PL = 665 + 40 times log (119889) 119889 gt 501007 + 20 times lg (119889) 119889 lt 50 (25)

Since we assume the inner distance of D2D pair remainsin close standards and relatively close the free space modelcan be given by

PL = 384 + 20 times lg (119889) (26)

Moreover we consider the case of fast fading model forRayleigh fading In different situation we adopt a differentfading model to investigate In this way the evaluation of theaverage performance is objective We also set a great numberof criterions for our simulation the maximum power state ofD2D users is set at 23 dBm and the maximum interferencewhich mobile users can tolerate is assumed to be 50 times 10minus6Before investigating the system performance based on ourproposed UFM game we tend to show the joint influenceof the power interference caused by spectrum sharing andsocial characteristics in each social community illustrated inFigure 4

In this section we analyze the sum power interferenceand sum social utility respectively as the number of cellularusers varies The case of 10 cellular users means the situationof system whose spectrum resource is in short supply Inthis situation D2D users possibly have to share the spectrumresource of the same users while the case of 30 cellular usersmeans D2D pairs have many resource-occupying choicesThe results indicate that the sumpower interference decreaseswith the trend of the number of cellular users increasing asthe sum social utility stay in quite a stable level And whenthe number of cellular users in the system exceeds 18 theinfluence from social utility will surpass the influence frompower interference And thenwe evaluate the system sum rateand sum time with different number of cellular users usingthe proposed UFM algorithm and the other two advancedschemes which is illustrated in Figures 5 and 6

Figure 5 compares the sum rate of the three algorithmsunder the isolated scenarios in which we set the number ofcellular users varied in the range of [10 30] From Figure 5we observe that by removing some interference-intolerableD2D links significant performance enhancement can be

Social utilityPower interference

0

20

40

60

80

100

120

140

(Bits

(slowast

Hz)

)

12 14 16 18 20 22 24 26 2810Number of cellular users

Figure 4 Comparison of the joint interference

Comparison of sum rate of the system times104

12 14 16 18 20 22 24 26 302810Number of cellular users

1

2

3

4

5

6

7

8

UFMOSRADRA

(Bits

(slowast

Hz)

)

Figure 5 Transmission rate comparison of different resource alloca-tion algorithms with different number of cellular users

achieved when the cellular users are relatively sufficientBut in the situation that cellular users are not sufficientperformances of the two are roughly equalThe reason is thatthe excessive reuse relationships of frequency with the samecellular user will cause unbearable interference to the cellularusers According to our algorithm the D2D link will beremoved automatically in both schemes

Figure 6 compares the sum transmission time of the threealgorithms under the isolated scenarios From Figure 6 wecan observe that in the case that someunnecessaryD2D linkshas been removed the UFM algorithm still provides quite aconsiderable reduction of transmission timeThat is because

10 Wireless Communications and Mobile Computing

Comparison of sum time of the system

UFMOSRADRA

times10minus3

05

1

15

2

25

3

35

4

45

5

55

Sum

tim

e (s

)

12 14 16 18 20 22 24 26 28 3010Number of cellular users

Figure 6 Transmission time comparison of different resource allo-cation algorithms with different number of cellular users

we allowD2Dusers to continue to acquire content via cellularcommunication when D2D communication comes acrosslink interruption So the sum transmission time will not beaffected greatly

For the purpose of evaluating the system performancewhile the number of D2D users varies within a certainrange we set geographical scope as 300m times 300m aroundthe BS and suppose the number of cellular users is 10 Asillustrated in Figures 7 and 8 the variation range of numberof D2D pairs is [5 30] the result demonstrates that ourproposed UFM game always attains the best performancewith the increase of D2D users compared to the OSRAand DRA This is because in the algorithm of DRA orOSRA there exist little coordination measures to restrictD2D pairs to select their resource and it is inevitable toestablish some high-interference links between D2D pairsand cellular users In our proposed algorithm UFM gameeffectively coordinates both social relationship and powerinterference and then decides whether to access the spectrumresource of certain cellular users not in a random way Inthese circumstances we can avoid many high-risk links andattain a better system performance in terms of the evaluationof the sum transmission rate At this point we can summarizethat our proposed scheme precedes the other two schemes ina relatively comprehensive scale

6 Conclusion and Future Work

This paper studies game-theory based social-aware resourceallocation in the D2D communication underlaying cellularnetwork based on the realistic social network By consideringthe power interference and social utility in the physical andsocial domain respectively a game-theoretic based utilityfunction maximization scheme has been proposed Also to

Comparison of sum rate of the system

UFMOSRADRA

times104

0

1

2

3

4

5

6

7

8

10 15 20 25 305Number of D2D pairs

(Bits

(slowast

Hz)

)Figure 7 Transmission rate comparison of different resource alloca-tion algorithms with different number of D2D pairs

Comparison of sum time of the system

UFMOSRADRA

times10minus3

0

1

2

3

4

5

6

7

8

9

Sum

tim

e (s

)

10 15 20 25 305Number of D2D pairs

Figure 8 Transmission time comparison of different resource allo-cation algorithms with different number of D2D pairs

demonstrate the optimality of our proposed scheme thispaper provides evidence for the existence of Nash Equilib-rium theoretically Meanwhile a priority searching operationbased resource allocation scheme is designed to implementthe Nash Equilibrium of the proposed UFM game The pro-posed UFM scheme is numerically shown having superiorityover traditional DRA and OSRA scheme the performancesof sum rate and total transmission time are better thanthe OSRA and DRA algorithm through massive simulation

Wireless Communications and Mobile Computing 11

result suggesting that the proposed scheme is more ideal forjoint social-aware resource scenarios considering the socialcharacteristics Nevertheless some issues related to furthersystem optimization remain to be addressed such as powerallocation of mobile nodes and cluster formation of socialcommunity

Notations

N Set of mobile usersC Set of cellular usersD Set of D2D pairsΦ The UFM game≻119894 Set of utility priority119868119889rarr119888 Interference from 119889th D2D to 119888th cellular signal119868119888rarr119889 Interference from 119888th cellular signal to 119889th D2D119880119889(119883) Social utility of 119889th D2D pairsΓ119889(119883) Utility function of 119889th D2D pairs119909119888119889 Indicator of resource reusing relations119909lowast119889 The Nash Equilibrium of 119889th D2D pair119883119889 Set of all feasible strategies in UFM game

Conflicts of Interest

The authors declare no conflicts of interest related to thepublication of this paper

Acknowledgments

This work is partly supported by the National NaturalScience Foundation of China (61571240 61671253) the Pri-ority Academic Program Development of Jiangsu HigherEducation Institutions the Major Projects of the NaturalScience Foundation of the Jiangsu Higher Education Insti-tutions (16KJA510004) the Open Research Fund of Nationaland Local Joint Engineering Laboratory of RF Integrationand Micro-Assembly Technology Nanjing University ofPosts and Telecommunications (KFJJ20170305) the OpenResearch Fund ofThe State Key Laboratory of Integrated Ser-vices Networks Xidian University (ISN17-04) Jiangsu Spe-cially Appointed Professor Grant (RK002STP16001) Inno-vation and Entrepreneurship of Jiangsu High-Level TalentGrant (CZ0010617002) High-Level Talent Startup Grantof Nanjing University of Posts and Telecommunications(XK0010915026) and ldquo1311 Talent Planrdquo ofNanjingUniversityof Posts and Telecommunications

References

[1] Y Cao T Jiang and C Wang ldquoCooperative device-to-devicecommunications in cellular networksrdquo IEEE Wireless Commu-nications Magazine vol 22 no 3 pp 124ndash129 2015

[2] J Liu N Kato J Ma and N Kadowaki ldquoDevice-to-devicecommunication in LTE-advanced networks a surveyrdquo IEEECommunications Surveys amp Tutorials vol 17 no 4 pp 1923ndash1940 Fourthquarter 2015

[3] A Asadi Q Wang and V Mancuso ldquoA survey on device-to-device communication in cellular networksrdquo IEEE Communi-cations Surveys amp Tutorials vol 16 no 4 pp 1801ndash1819 2014

[4] H Nishiyama M Ito and N Kato ldquoRelay-by-smartphonerealizing multihop device-to-device communicationsrdquo IEEECommunications Magazine vol 52 no 4 pp 56ndash65 2014

[5] M Zhou Y Tang Z Tian L Xie and W Nie ldquoRobust neigh-borhood graphing for semi-supervised indoor localization withlight-loaded location fingerprintingrdquo IEEE Internet of ThingsJournal vol PP no 99 pp 1-1

[6] K Doppler M Rinne C Wijting C B Ribeiro and K HugldquoDevice-to-device communication as an underlay to LTE-advanced networksrdquo IEEE Communications Magazine vol 47no 12 pp 42ndash49 2009

[7] J Liu H Nishiyama N Kato and J Guo ldquoOn the outageprobability of device-to-device-communication-enabled mul-tichannel cellular networks an RSS-threshold-based perspec-tiverdquo IEEE Journal on Selected Areas in Communications vol34 no 1 pp 163ndash175 2016

[8] M Zhou Y Tang W Nie L Xie and X Yang ldquoGrassMAgraph-based semi-supervised manifold alignment for indoorWLAN localizationrdquo IEEE Sensors Journal vol 17 no 21 pp7086ndash7095 2017

[9] J Liu S Zhang N Kato H Ujikawa and K Suzuki ldquoDevice-to-device communications for enhancing quality of experiencein software defined multi-tier LTE-A networksrdquo IEEE Networkvol 29 no 4 pp 46ndash52 2015

[10] C Xu L Song Z Han et al ldquoEfficiency resource allocation fordevice-to-device underlay communication systems a reverseiterative combinatorial auction based approachrdquo IEEE Journalon Selected Areas in Communications vol 31 no 9 pp 348ndash3582013

[11] L Ferdouse W Ejaz K Raahemifar A Anpalagan and MMarkandaier ldquoInterference and throughput aware resourceallocation for multi-class D2D in 5G networksrdquo IET Commu-nications vol 11 no 8 pp 1241ndash1250 2017

[12] T D Hoang L B Le and T Le-Ngoc ldquoCooperative device-to-device communications in cellular networksrdquo IEEE Transac-tions onWireless Communications vol 15 no 10 pp 7099ndash71132016

[13] M Andrews K Kumaran K Ramanan A Stolyar P Whitingand R Vijayakumar ldquoProviding quality of service over a sharedwireless linkrdquo IEEE Communications Magazine vol 39 no 2pp 150ndash154 2001

[14] L Wang L Liu X Cao X Tian and Y Cheng ldquoSociality-aware resource allocation for device-to-device communicationsin cellular networksrdquo IET Communications vol 9 no 3 pp342ndash349 2015

[15] V Shah andA O Fapojuwo ldquoSocially aware resource allocationfor device-to-device communication in downlinkOFDMAnet-worksrdquo in Proceedings of the 2014 IEEE Wireless Communica-tions and Networking Conference WCNC 2014 pp 1673ndash1678Istanbul Turkey April 2014

[16] Y Li T Wu P Hui D Jin and S Chen ldquoSocial-aware D2Dcommunications qualitative insights and quantitative analysisrdquoIEEE Communications Magazine vol 52 no 6 pp 150ndash1582014

[17] FWang L Song Z Han Q Zhao and XWang ldquoJoint schedul-ing and resource allocation for device-to-device underlay com-municationrdquo in Proceedings of the IEEE Wireless Communi-cations and Networking Conference (WCNC rsquo13) pp 134ndash139IEEE Shanghai China April 2013

[18] F Tang Z M Fadlullah N Kato F One and R MiuraldquoAC-POCA anti-coordination game based partially overlap-ping channels assignment in combined UAV and D2D based

12 Wireless Communications and Mobile Computing

networksrdquo IEEE Transactions on Vehicular Technology vol PPno 99 pp 1-1

[19] S M Azimi M H Manshaei and F Hendessi ldquoHybrid cellularand device-to-device communication power control Nashbargaining gamerdquo in Proceedings of the 2014 7th InternationalSymposium on Telecommunications IST 2014 pp 1077ndash1081Tehran Iran September 2014

[20] Z Zhou K Ota M Dong and C Xu ldquoEnergy-efficient match-ing for resource allocation in D2D enabled cellular networksrdquoIEEE Transactions on Vehicular Technology vol 66 no 6 pp5256ndash5268 2017

[21] C Xu C Gao Z Zhou Z Chang and Y Jia ldquoSocial network-based content delivery in device-to-device underlay cellularnetworks using matching theoryrdquo IEEE Access vol 5 pp 924ndash937 2017

[22] X Feng G Sun X Gan et al ldquoCooperative spectrum sharingin cognitive radio networks a distributed matching approachrdquoIEEE Transactions on Communications vol 62 no 8 pp 2651ndash2664 2014

[23] J Zhang ldquoThe interdisciplinary research of big data andwireless channel a cluster-nuclei based channel modelrdquo ChinaCommunications vol 13 no supplement 2 Article ID 7833457pp 14ndash26 2016

[24] S Mumtaz K M Saidul Huq J Rodriguez and V FrascollaldquoEnergy-efficient interference management in LTE-D2D com-municationrdquo IET Signal Processing vol 10 no 3 pp 197ndash2022016

[25] N Kayastha D Niyato P Wang and E Hossain ldquoApplicationsarchitectures and protocol design issues for mobile socialnetworks a surveyrdquo Proceedings of the IEEE vol 99 no 12 pp2130ndash2158 2011

[26] J Zhang L Tian Y Wang and M Liu ldquoSelection transmit-tingmaximum ratio combining for timing synchronization ofMIMO-OFDM systemsrdquo IEEE Transactions on Broadcastingvol 60 no 4 pp 626ndash636 2014

[27] M Zhou Y Wei Z Tian X Yang and L Li ldquoAchieving cost-efficient indoor fingerprint localization on wlan platform ahypothetical test approachrdquo IEEEAccess vol 5 pp 15865ndash158742017

[28] ldquoZacharyrsquoskarateclubrdquohttpsenwikipediaorgwikiZachary27skarate club

[29] D Wu L Zhou and Y Cai ldquoSocial-aware rate based contentsharing mode selection for D2D content sharing scenariosrdquoIEEE Transactions on Multimedia vol 19 no 11 pp 2571ndash25822017

[30] J Huang Y Yin Y Sun Y Zhao C-C Xing and Q DuanldquoGame theoretic resource allocation for multicell D2D commu-nications with incomplete informationrdquo in Proceedings of theIEEE International Conference on Communications ICC 2015pp 3039ndash3044 London UK June 2015

[31] Y Xiao K-C Chen C Yuen and L A DaSilva ldquoSpectrumsharing for device-to-device communications in cellular net-works a game theoretic approachrdquo in Proceedings of the IEEEInternational SymposiumonDynamic SpectrumAccessNetworks(DYSPAN rsquo14) pp 60ndash71 IEEE McLean Va USA April 2014

[32] D Niyato and E Hossain ldquoA game-theoretic approach tocompetitive spectrum sharing in cognitive radio networksrdquo inProceedings of the IEEEWireless Communications and Network-ing Conference (WCNC rsquo07) pp 16ndash20 Kowloon China March2007

[33] D Monderer and L S Shapley ldquoPotential gamesrdquo Games andEconomic Behavior vol 14 no 1 pp 124ndash143 1996

[34] N Nie and C Comaniciu ldquoAdaptive channel allocation spec-trum etiquette for cognitive radio networksrdquo in Proceedingsof the 1st IEEE International Symposium on New Frontiers inDynamic SpectrumAccess Networks (DySPAN rsquo05) pp 269ndash278Baltimore Md USA November 2005

[35] Y Xing C N Mathur M A Haleem R Chandramouli andK P Subbalakshmi ldquoDynamic spectrum access with QoS andinterference temperature constraintsrdquo IEEE Transactions onMobile Computing vol 6 no 4 pp 423ndash433 2007

[36] T Heikkinen ldquoA potential game approach to distributed powercontrol and schedulingrdquo Computer Networks vol 50 no 13 pp2295ndash2311 2006

[37] Y Li D Jin J Yuan and ZHan ldquoCoalitional games for resourceallocation in the device-to-device uplink underlaying cellularnetworksrdquo IEEE Transactions on Wireless Communications vol13 no 7 pp 3965ndash3977 2014

[38] H Ryu and S-H Park ldquoPerformance comparison of resourceallocation schemes for D2D communicationsrdquo in Proceedingsof the 2014 IEEE Wireless Communications and NetworkingConference Workshops WCNCW 2014 pp 266ndash270 IstanbulTurkey April 2014

[39] Y Li S Su and S Chen ldquoSocial-aware resource allocationfor device-to-device communications underlaying cellular net-worksrdquo IEEE Wireless Communications Letters vol 4 no 3 pp293ndash296 2015

[40] D I Laurenson D G M Cruickshank and G J R PoveyldquoComputationally efficient multipath channel simulator for theCOST 207 modelsrdquo in Proceedings of the IEE Colloquium onComputer Modelling of Communication Systems pp 81ndash86London UK May 1994

6 Wireless Communications and Mobile Computing

interference With respect to 120574 a pricing function from (12)is adopted which can be expressed as follows

120574 = 119899 + 119904 sdot (1198611198891 + sdot sdot sdot + 119861119889119894)120591 119894 = 1 2 119898 (13)

119899 119904 and 120591 denote nonnegative constants and 120591 ge 1 toguarantee that the cost function is convex In order toimprove the applicability we suppose

[1198730 + 119892119889119875119889119903] = 119901119861119889119894 (14)

where 119901 is a nonnegative constant [30] then

Γ119889 (119883) = 120572 sdot 119861119889119894 log2 (1 + SINR119889119894) + 120573 sdot sum119895isinD

120596119889119903119880119889+ sum119888isinC

120585119889119888119880119888 minus [119899 + 119904 sdot 119898sum119894=1

119861119889119894]119861119889119894 minus 120576 sdot 119868119894rarr119906iff 119880119889 (119883) ge 119868119889rarr119888

(15)

In the proposed problem in (15) each D2D pair is aimedat integrating every aspect of influence and then maximizingits own utility As the distribution of mobile equipment ischanging all the time the features of the network are varyinginstantaneously So for the purpose of exact comparison weshould implement some effective method to eliminate thiskind of dilemma

Dynamic game with complete information can modelcertain dynamic situation under the premise that the par-ticipant knows the type of the action it will take and theinformation needed for every decision of the action It canbe applied into our proposed model as every D2D paircan get to know the social utility and power interferenceand get the real-time Γ119889(119883) when D2D communication isin progress So the problem above can be regarded as adynamic game with complete social information as well assophisticated interference information In this way we canpropose a dynamic game based scheme to optimize theoverall performance of theD2D communication network dueto the two-sidesrsquo competition

32 UFM Game Formulation From the analysis above wederive the information from two-sidesrsquo action needed inour game theory And for the optimization problem weusually utilize the game theory to solve it Firstly we definecorresponding strategy adopted by each D2D user 119889 in acertain point of history as 119886119889 119886119889 isin 119860119889 where 119860119889 is theset of all available strategies of the D2D pair 119889 The choiceof strategies of all the other participants that is all theother D2D pairs in our work can be defined as 119886minus119889 =1198861 119886119889minus1 119886119889+1 119886119863 If the above assumption for theUFM game theory is perfect there must exist a strategy 119886119889 isin119860119889 to maximize its own utility function

max119886119889isin119860119889

Γ119889 (119886119889 119886minus119889) forall119889 isin D (16)

The UFM game for the resource allocation thinking from theperspective of utility function is defined by quadruple Φ =D 119860119889119889isinD Γ119889119889isinD 119868119889rarr119888119889isinD119888isinC where D denotes the

D2D pairs119883119889 denotes all of the resource allocation strategiesD2D pairs set D can take Γ119889 denotes the utility function ofeach of the D2D pairs 119889 and 119868119889rarr119888 denotes the interferenceintroduced by D2D pairs 119889 to cellular user 11988833 Nash Equilibrium Nash Equilibrium is a very importantterminology in game theory [31 32] It represents a set ofstrategies which are combined by all optimal choices takenby each participant which reflect the optimal reaction eachparticipant adopts against the other participantrsquos strategiesAccording to this if the choices chosen by all the D2D pairsare optimal the system sum rate of the D2D communicationunderlaying cellular network will reach the extreme oneThefollowing part will discuss the existence of Nash Equilibriumin UFM game theory and provide proof for it

Generally the UFM game Φ = D 119860119889119889isinD Γ119889119889isinD119868119889rarr119888119889isinD119888isinC can reach the Nash Equilibrium if each of theD2D pairs has the only optimal response to the other D2Dpairrsquos strategy

119886lowast119889 = argmax119886119889isin119860119889

Γ119889 (119886minus119889 119886119889) forall119889 isin D (17)

and 119886lowast = 119886lowast1 119886lowast2 119886lowast119863 denotes the Nash EquilibriumBecause of the same incentive of changing their strategy

for all the D2D pair we refer to the potential game theory todemonstrate the existence of NE for the UFM game In [33]Monderer and Shapley propose the definition of potentialgame and elaborate the idea in detail too In the field ofwireless resource allocation games game theory has beenapplied in a few of authorsrsquo papers for example [34ndash36] Inpotential game theory the change in individual playerrsquos gaincan be mapped to the global function which is called thepotential function By this way we can conclude if there isany change that occurred on individual player the potentialfunction will change equally in the strict potential game Γdenotes an exact potential function if and only if exist119865(119868) 119868 rarr119880 forall119894 119895 forall119868119894 119868119895 119880119894 isin 119868119894 and 119880119895 isin 119868119895

Γ119894 (119868119894 119880minus119894) minus Γ119895 (119868119895 119880minus119895) = 119865 (119868119894 119880minus119894) minus 119865 (119868119895 119880minus119895) (18)

In the D2D communication systemwe havemodeled thechange of power interference and social utility caused byD2Dlinks would change the utility function of the game whichis consistent with the principle of potential function On theother hand potential gamehas the following inherent proper-ties which are described in [33] (1)There must exist a pure-strategy NE and a solution for it (2) The Nash Equilibriumcorresponds to the maxima of the potential function Γ (3)Generally the convergence to Nash Equilibrium would bereached in finite improvement or searching path accordingto sequential best-response dynamics

For the condition of a single band frequency channel thepotential game is formulated by utilizing the following utility-maximizing function

Γ119894 = minus (Total utility function generated by 119894+ Total utility function experienced by 119894) (19)

Wireless Communications and Mobile Computing 7

Based on the potential game theory we can demonstratethe existence of the Nash Equilibrium of our proposed UFMgame For Γ for every 119889 isin D and for every 119886minus119889 isin 119860minus119889

119875 (119889) = Γ119889 (119886minus119889 119886119889) minus Γ119889 (119886minus119889 1198861015840119889) (20)

Theorem 1 In certain history point 119905 function 119875(119889) derivedfrom UFM game is subgame perfect

Proof We suppose strategy 119886119889 denotes occupying the spec-trum resource of cellular user 119888 which is taken by D2D pairs119889 initially Therefore the initial indicator is 119909119888119889 Once D2Dpair119889 change its strategy andmake a request for the spectrumresource of cellular user 1198881015840 the indicator changes to1199091015840119888119889Thenwe can obtain

Γ119889 minus Γ1015840119889 = 120572 sdot 119877 + 120573 sdot 119880119889 (119883) minus 120576 sdot 119868119889rarr119888 minus 120572 sdot 1198771015840 minus 120573sdot 119880119889 (119883) minus 120576 sdot 1198681015840119889rarr119888

= 120572 sdot (119877 minus 1198771015840) minus 120576 sdot (119868119889rarr119888 minus 1198681015840119889rarr119888) (21)

We denote Δ 1 = 119877 minus 1198771015840 and Δ 2 = 119868119889rarr119888 minus 1198681015840119889rarr119888 As we cansee Δ 1 ≫ Δ 2 Finally we conclude that

Γ119889 minus Γ1015840119889 gt 0 (22)

It means that no D2D pair can acquire performanceenhancement by changing its strategy so we prove that ourproposed game is subgame perfect As subgame is the restric-tion from the perspective of history circumstances it canlead to the Nash Equilibrium of the game directly

4 Resource Allocation Scheme forUFM Game Theory

41 Priority Searching Based Solution The value of the utilityfunction Γ119889 varies when D2D pair chooses to reuse spectrumresource from different cellular user and the final aim of theUFM game is to determine the order of the utility function bythe size of value According to analysis in Sections 32 and 33the resource allocation strategy 119886lowast has a Nash EquilibriumIt means that we can finally achieve an optimal strategy bysubstituting the other strategies one by one in finite times Itis similar to the establishment of preference list and iteratesuntil acquiring the best selection among different alternatives[10] Inspired by the one-to-one matching theory we willshow the main idea of the proposed resource allocationalgorithm in detail

Definition 2 For anyD2D pairs we define the binary priorityrelation set≻119894 to represent the entire set of resource allocationstrategies that each D2D pair 119894 would possibly take In ourUFM game D2D pairs can choose to reuse the resourceoccupied by the associated cellular users or not according tothe priority set For any D2D pairs 119886119894 ≻119894 1198861015840119894 means D2D pairs119894 prefer choosing 119888 as the target resource source instead of 1198881015840

Since the priority set is determined by the utility function wecan define the priority as follows

1198861015840119894 ≻119894 119886119894 lArrrArrΓ119894 (1198861015840119894 ) gt Γ119894 (119886119894)

forall119894 isin D(23)

This definition demonstrates that D2D users 119894 are likelyto reuse the spectrum resource of cellular users 119888 as no moreoptions can bring additional performance gains We can setthe highest priority for cellular user 119888 in the set belonging toD2D user 119894 By this a complete priority set can be obtainedby repeating searching operation For every D2D pair wecan also design an optimization resource allocation schemebased on the priority set In this scheme everyD2Dpair urgesfinding its own highest priority and reusing the spectrumresource shared by the corresponding cellular users

Let us present Algorithm 1Based on the definitions and priority searching operation

we can obtain a final Nash-stable resource scheme 119886fin forD2D users to solve the utility maximization problem whichis given in Algorithm 1 From the whole knowledge givenabove we can see that D2D users make switching iterationfollowing a logically standard based on an arbitrarily choseninitial resource allocation strategy 119886ini At the beginning ofeach iteration D2D user 119894 isin D is randomly chosen by thesystem in step (13) And then the selectedD2D user replacesits resource allocation strategy with 119886ini by random choosinga occupied cellular users and determine its strategies 119886119894 anduniformly selects another social-trust cellular user 1198881015840 isin CThen the D2D pair will request the base station for the chan-nel state information once establishing communication linkwith these two cellular users 119888 and 1198881015840 After acquiring specifiedinformation the BS will computes the utility function of theresource allocation strategies of 119886 and 1198861015840 and broadcast tothe participant of the game model Meanwhile making thedecision that whether to carried out the switch operationfor D2D link If 119886119894 ≻119894 1198861015840119894 the switch operation will not beexecuted Otherwise the switch operation will be executedThe iteration will continue until all of the priority searchingoperations for each D2D pair are traversed and reach a finalNash Equilibrium scheme 119886fin

Different from those conventional D2D resource allo-cation schemes our proposed scheme needs to select suit-able community detection dataset and analyze the social-community information inside And a priority based poten-tial game theory is applied in our scheme This importantinformation is taken into consideration in our proposedscheme fully

42 Uniqueness and Boundedness According to Theorem 1for a given history point 119905 the combination of strategy 119886119894 119886119894 isin119860 119894 can reach a status of being subgame perfect as reactionto the combination of strategy 119886minus119894 To prove the uniquenessand boundedness of our proposed game it is necessary toconfirm that if there exist any participant forall1006704119894 isin D and its

8 Wireless Communications and Mobile Computing

(01) Input Number of mobile users119873 and random resource allocation strategy 119886ini(02)Output A priority based resource allocation scheme 119886fin(03) Utilize the dataset of Karate Club network(04) Calculate the transmission rate of the D2D links and cellular links(05) Obtain 119880119889(119883) and 119868119889rarr119888(06) if 119880119889(119883) le 119868119889rarr119888 remove the D2D links(07) else keep the D2D links(08) Define the matrix of indicator 119909119888119889 isin [0 1](09) 119868 = find 119909119888119889 = 0 ampamp 119868 = 1(10)There is just one 119888 cellular users qualified to shareresources to D2D user 119903 = 119903119888119889(11) else if uniformly randomly choose one cellular users 119888 and 119886possible cellular users 1198881015840 and denote its associate resourcesharing as 119886119894 isin 119886ini(12) Calculate Γ(1198861015840119894 ) and Γ(119886119894) priority = 0(13) if 1198861015840119894 ≻119894 119886119894 then Priority = 1(14) else repeat (15)sim(16)(15) if Priority == 1 then(16) D2D pairs quit current resource occupying strategy of 119888 andturn to adapt the new resource allocation strategy of 1198881015840(17) substitute the current resource occupying strategy 119886 forstrategy 1198861015840 and add it to 119886cur(18)Until all of the D2D pairs complete the priority searching operation resourceoccupying strategy switching operation and reach Nash Equilibrium 119886fin

Algorithm 1 The utility function maximization D2D links redistribution algorithm

corresponding strategy 1006704119886119894 can give better reaction to thestrategy combination 119886minus119894 than 119886119894 and make 1006704119886119894 ≻119894 119886119894 availableSo we provide the following proof relative to the uniquenessand boundedness of our proposed UFM game

Theorem 3 For all of the D2D pairs whose 119909119888119889 = 1 theproposed priority searching based scheme can only obtain aunique resource allocation scheme 119886finProof Based on the description in Algorithm 1 we supposereversely that the combination of strategy 119886119894 is not subgameperfect And then there must exist certain participant 119894 thathas strategy forall1006704119894 isin D and outperforms 119886119894 Now we investigateanother strategy 119886119894 and when 119905 lt 1006704119905 1006704119886119894 is equal to 119886119894 but after1006704119905 it is equal to 119886119894Then in any subgame after the history point1006704119905 strategy forall1006704119894 isin D is at least as well as 119886119894 for the reason thatforall1006704119894 isin D has deviated from 119886119894 once We can also conclude thatstrategy forall1006704119894 isin D is at least as well as 119886119894 after the history point119905 which is contrary to the assumption that strategy forall1006704119894 isin Dimproves the strategy 119886119894 And so on we can investigate other119886119894 to prove its equal benefit with forall1006704119894 isin D until reaching theunique resource allocation scheme 119886fin

Through the above analysis we prove the uniqueness ofthe UFM game by Reduction to Absurdity In each iterationin Algorithm 1 it may lead to a new resource allocationstrategy As there is only C in the physical domain andlimitedD D2D pairs due to the limited social relationship inthe social domain each of the D2D pairs is correspondingto C types of resource allocation scheme So the prioritysearching operation will eventually end in limited steps Thisfact assures the boundedness of our proposed UFM gamebased scheme

5 Simulation Results and Discussions

In this section we implement the simulation results from dif-ferent perspective to verify the performance of our proposedUFM algorithm and elaborate some necessary explanationfor the results Main simulation parameters have been givenin Table 1 Simulations are executed in a single cell whichare within an isolated community circumstance Path lossmodels are considered for cellular and D2D links along withshadow fadingmodel According to the dataset of Karate clubwe conduct the simulation within a 500m times 500m area toguarantee most of the club memberrsquos activities are within thisarea and 34 members of the club are randomly distributedwithin the BS coverage area Meanwhile the bandwidth ofallocated resource is assigned arbitrarily within the rangelimitation We compare our proposed UFM algorithm withthe following resource allocation schemes (a) distributedresource allocation (DRA) which allocates the D2D com-munication resource by thinking in a distributed way [37]and (b) optimal social-community aware resource allocation(OSRA) which allocates the D2D communication resourceto reduce the total transmission time [38] All the results areaveraged over 10 timesrsquo trial

Without loss of generality on one hand we prescribethe pathloss model between the base station and all themobile users as COST (EuropeanCooperation in Science andTechnology) 231 Hata model [39]

PLCU = 367 + 35 times lg (119889) (24)

Meanwhile we prescribe the pathloss model betweendifferent cellular users and D2D users as Xia model [40]given as follows

Wireless Communications and Mobile Computing 9

Table 1 System simulated parameters in the performance evalua-tion

Parameter ValueCoverage radius of BS 500mDistance of D2D 20msim50mNoise figure 9 dB at deviceTransmission power BS 46 dBm device 23 dBmMaximum D2D transmitter power 23 dBmRange of bandwidth 10MHzsim20MHzCommunication demand 50WInterference threshold 56 times 10minus6W119899 119904 119911 120591 1120572 120573 20

PL = 665 + 40 times log (119889) 119889 gt 501007 + 20 times lg (119889) 119889 lt 50 (25)

Since we assume the inner distance of D2D pair remainsin close standards and relatively close the free space modelcan be given by

PL = 384 + 20 times lg (119889) (26)

Moreover we consider the case of fast fading model forRayleigh fading In different situation we adopt a differentfading model to investigate In this way the evaluation of theaverage performance is objective We also set a great numberof criterions for our simulation the maximum power state ofD2D users is set at 23 dBm and the maximum interferencewhich mobile users can tolerate is assumed to be 50 times 10minus6Before investigating the system performance based on ourproposed UFM game we tend to show the joint influenceof the power interference caused by spectrum sharing andsocial characteristics in each social community illustrated inFigure 4

In this section we analyze the sum power interferenceand sum social utility respectively as the number of cellularusers varies The case of 10 cellular users means the situationof system whose spectrum resource is in short supply Inthis situation D2D users possibly have to share the spectrumresource of the same users while the case of 30 cellular usersmeans D2D pairs have many resource-occupying choicesThe results indicate that the sumpower interference decreaseswith the trend of the number of cellular users increasing asthe sum social utility stay in quite a stable level And whenthe number of cellular users in the system exceeds 18 theinfluence from social utility will surpass the influence frompower interference And thenwe evaluate the system sum rateand sum time with different number of cellular users usingthe proposed UFM algorithm and the other two advancedschemes which is illustrated in Figures 5 and 6

Figure 5 compares the sum rate of the three algorithmsunder the isolated scenarios in which we set the number ofcellular users varied in the range of [10 30] From Figure 5we observe that by removing some interference-intolerableD2D links significant performance enhancement can be

Social utilityPower interference

0

20

40

60

80

100

120

140

(Bits

(slowast

Hz)

)

12 14 16 18 20 22 24 26 2810Number of cellular users

Figure 4 Comparison of the joint interference

Comparison of sum rate of the system times104

12 14 16 18 20 22 24 26 302810Number of cellular users

1

2

3

4

5

6

7

8

UFMOSRADRA

(Bits

(slowast

Hz)

)

Figure 5 Transmission rate comparison of different resource alloca-tion algorithms with different number of cellular users

achieved when the cellular users are relatively sufficientBut in the situation that cellular users are not sufficientperformances of the two are roughly equalThe reason is thatthe excessive reuse relationships of frequency with the samecellular user will cause unbearable interference to the cellularusers According to our algorithm the D2D link will beremoved automatically in both schemes

Figure 6 compares the sum transmission time of the threealgorithms under the isolated scenarios From Figure 6 wecan observe that in the case that someunnecessaryD2D linkshas been removed the UFM algorithm still provides quite aconsiderable reduction of transmission timeThat is because

10 Wireless Communications and Mobile Computing

Comparison of sum time of the system

UFMOSRADRA

times10minus3

05

1

15

2

25

3

35

4

45

5

55

Sum

tim

e (s

)

12 14 16 18 20 22 24 26 28 3010Number of cellular users

Figure 6 Transmission time comparison of different resource allo-cation algorithms with different number of cellular users

we allowD2Dusers to continue to acquire content via cellularcommunication when D2D communication comes acrosslink interruption So the sum transmission time will not beaffected greatly

For the purpose of evaluating the system performancewhile the number of D2D users varies within a certainrange we set geographical scope as 300m times 300m aroundthe BS and suppose the number of cellular users is 10 Asillustrated in Figures 7 and 8 the variation range of numberof D2D pairs is [5 30] the result demonstrates that ourproposed UFM game always attains the best performancewith the increase of D2D users compared to the OSRAand DRA This is because in the algorithm of DRA orOSRA there exist little coordination measures to restrictD2D pairs to select their resource and it is inevitable toestablish some high-interference links between D2D pairsand cellular users In our proposed algorithm UFM gameeffectively coordinates both social relationship and powerinterference and then decides whether to access the spectrumresource of certain cellular users not in a random way Inthese circumstances we can avoid many high-risk links andattain a better system performance in terms of the evaluationof the sum transmission rate At this point we can summarizethat our proposed scheme precedes the other two schemes ina relatively comprehensive scale

6 Conclusion and Future Work

This paper studies game-theory based social-aware resourceallocation in the D2D communication underlaying cellularnetwork based on the realistic social network By consideringthe power interference and social utility in the physical andsocial domain respectively a game-theoretic based utilityfunction maximization scheme has been proposed Also to

Comparison of sum rate of the system

UFMOSRADRA

times104

0

1

2

3

4

5

6

7

8

10 15 20 25 305Number of D2D pairs

(Bits

(slowast

Hz)

)Figure 7 Transmission rate comparison of different resource alloca-tion algorithms with different number of D2D pairs

Comparison of sum time of the system

UFMOSRADRA

times10minus3

0

1

2

3

4

5

6

7

8

9

Sum

tim

e (s

)

10 15 20 25 305Number of D2D pairs

Figure 8 Transmission time comparison of different resource allo-cation algorithms with different number of D2D pairs

demonstrate the optimality of our proposed scheme thispaper provides evidence for the existence of Nash Equilib-rium theoretically Meanwhile a priority searching operationbased resource allocation scheme is designed to implementthe Nash Equilibrium of the proposed UFM game The pro-posed UFM scheme is numerically shown having superiorityover traditional DRA and OSRA scheme the performancesof sum rate and total transmission time are better thanthe OSRA and DRA algorithm through massive simulation

Wireless Communications and Mobile Computing 11

result suggesting that the proposed scheme is more ideal forjoint social-aware resource scenarios considering the socialcharacteristics Nevertheless some issues related to furthersystem optimization remain to be addressed such as powerallocation of mobile nodes and cluster formation of socialcommunity

Notations

N Set of mobile usersC Set of cellular usersD Set of D2D pairsΦ The UFM game≻119894 Set of utility priority119868119889rarr119888 Interference from 119889th D2D to 119888th cellular signal119868119888rarr119889 Interference from 119888th cellular signal to 119889th D2D119880119889(119883) Social utility of 119889th D2D pairsΓ119889(119883) Utility function of 119889th D2D pairs119909119888119889 Indicator of resource reusing relations119909lowast119889 The Nash Equilibrium of 119889th D2D pair119883119889 Set of all feasible strategies in UFM game

Conflicts of Interest

The authors declare no conflicts of interest related to thepublication of this paper

Acknowledgments

This work is partly supported by the National NaturalScience Foundation of China (61571240 61671253) the Pri-ority Academic Program Development of Jiangsu HigherEducation Institutions the Major Projects of the NaturalScience Foundation of the Jiangsu Higher Education Insti-tutions (16KJA510004) the Open Research Fund of Nationaland Local Joint Engineering Laboratory of RF Integrationand Micro-Assembly Technology Nanjing University ofPosts and Telecommunications (KFJJ20170305) the OpenResearch Fund ofThe State Key Laboratory of Integrated Ser-vices Networks Xidian University (ISN17-04) Jiangsu Spe-cially Appointed Professor Grant (RK002STP16001) Inno-vation and Entrepreneurship of Jiangsu High-Level TalentGrant (CZ0010617002) High-Level Talent Startup Grantof Nanjing University of Posts and Telecommunications(XK0010915026) and ldquo1311 Talent Planrdquo ofNanjingUniversityof Posts and Telecommunications

References

[1] Y Cao T Jiang and C Wang ldquoCooperative device-to-devicecommunications in cellular networksrdquo IEEE Wireless Commu-nications Magazine vol 22 no 3 pp 124ndash129 2015

[2] J Liu N Kato J Ma and N Kadowaki ldquoDevice-to-devicecommunication in LTE-advanced networks a surveyrdquo IEEECommunications Surveys amp Tutorials vol 17 no 4 pp 1923ndash1940 Fourthquarter 2015

[3] A Asadi Q Wang and V Mancuso ldquoA survey on device-to-device communication in cellular networksrdquo IEEE Communi-cations Surveys amp Tutorials vol 16 no 4 pp 1801ndash1819 2014

[4] H Nishiyama M Ito and N Kato ldquoRelay-by-smartphonerealizing multihop device-to-device communicationsrdquo IEEECommunications Magazine vol 52 no 4 pp 56ndash65 2014

[5] M Zhou Y Tang Z Tian L Xie and W Nie ldquoRobust neigh-borhood graphing for semi-supervised indoor localization withlight-loaded location fingerprintingrdquo IEEE Internet of ThingsJournal vol PP no 99 pp 1-1

[6] K Doppler M Rinne C Wijting C B Ribeiro and K HugldquoDevice-to-device communication as an underlay to LTE-advanced networksrdquo IEEE Communications Magazine vol 47no 12 pp 42ndash49 2009

[7] J Liu H Nishiyama N Kato and J Guo ldquoOn the outageprobability of device-to-device-communication-enabled mul-tichannel cellular networks an RSS-threshold-based perspec-tiverdquo IEEE Journal on Selected Areas in Communications vol34 no 1 pp 163ndash175 2016

[8] M Zhou Y Tang W Nie L Xie and X Yang ldquoGrassMAgraph-based semi-supervised manifold alignment for indoorWLAN localizationrdquo IEEE Sensors Journal vol 17 no 21 pp7086ndash7095 2017

[9] J Liu S Zhang N Kato H Ujikawa and K Suzuki ldquoDevice-to-device communications for enhancing quality of experiencein software defined multi-tier LTE-A networksrdquo IEEE Networkvol 29 no 4 pp 46ndash52 2015

[10] C Xu L Song Z Han et al ldquoEfficiency resource allocation fordevice-to-device underlay communication systems a reverseiterative combinatorial auction based approachrdquo IEEE Journalon Selected Areas in Communications vol 31 no 9 pp 348ndash3582013

[11] L Ferdouse W Ejaz K Raahemifar A Anpalagan and MMarkandaier ldquoInterference and throughput aware resourceallocation for multi-class D2D in 5G networksrdquo IET Commu-nications vol 11 no 8 pp 1241ndash1250 2017

[12] T D Hoang L B Le and T Le-Ngoc ldquoCooperative device-to-device communications in cellular networksrdquo IEEE Transac-tions onWireless Communications vol 15 no 10 pp 7099ndash71132016

[13] M Andrews K Kumaran K Ramanan A Stolyar P Whitingand R Vijayakumar ldquoProviding quality of service over a sharedwireless linkrdquo IEEE Communications Magazine vol 39 no 2pp 150ndash154 2001

[14] L Wang L Liu X Cao X Tian and Y Cheng ldquoSociality-aware resource allocation for device-to-device communicationsin cellular networksrdquo IET Communications vol 9 no 3 pp342ndash349 2015

[15] V Shah andA O Fapojuwo ldquoSocially aware resource allocationfor device-to-device communication in downlinkOFDMAnet-worksrdquo in Proceedings of the 2014 IEEE Wireless Communica-tions and Networking Conference WCNC 2014 pp 1673ndash1678Istanbul Turkey April 2014

[16] Y Li T Wu P Hui D Jin and S Chen ldquoSocial-aware D2Dcommunications qualitative insights and quantitative analysisrdquoIEEE Communications Magazine vol 52 no 6 pp 150ndash1582014

[17] FWang L Song Z Han Q Zhao and XWang ldquoJoint schedul-ing and resource allocation for device-to-device underlay com-municationrdquo in Proceedings of the IEEE Wireless Communi-cations and Networking Conference (WCNC rsquo13) pp 134ndash139IEEE Shanghai China April 2013

[18] F Tang Z M Fadlullah N Kato F One and R MiuraldquoAC-POCA anti-coordination game based partially overlap-ping channels assignment in combined UAV and D2D based

12 Wireless Communications and Mobile Computing

networksrdquo IEEE Transactions on Vehicular Technology vol PPno 99 pp 1-1

[19] S M Azimi M H Manshaei and F Hendessi ldquoHybrid cellularand device-to-device communication power control Nashbargaining gamerdquo in Proceedings of the 2014 7th InternationalSymposium on Telecommunications IST 2014 pp 1077ndash1081Tehran Iran September 2014

[20] Z Zhou K Ota M Dong and C Xu ldquoEnergy-efficient match-ing for resource allocation in D2D enabled cellular networksrdquoIEEE Transactions on Vehicular Technology vol 66 no 6 pp5256ndash5268 2017

[21] C Xu C Gao Z Zhou Z Chang and Y Jia ldquoSocial network-based content delivery in device-to-device underlay cellularnetworks using matching theoryrdquo IEEE Access vol 5 pp 924ndash937 2017

[22] X Feng G Sun X Gan et al ldquoCooperative spectrum sharingin cognitive radio networks a distributed matching approachrdquoIEEE Transactions on Communications vol 62 no 8 pp 2651ndash2664 2014

[23] J Zhang ldquoThe interdisciplinary research of big data andwireless channel a cluster-nuclei based channel modelrdquo ChinaCommunications vol 13 no supplement 2 Article ID 7833457pp 14ndash26 2016

[24] S Mumtaz K M Saidul Huq J Rodriguez and V FrascollaldquoEnergy-efficient interference management in LTE-D2D com-municationrdquo IET Signal Processing vol 10 no 3 pp 197ndash2022016

[25] N Kayastha D Niyato P Wang and E Hossain ldquoApplicationsarchitectures and protocol design issues for mobile socialnetworks a surveyrdquo Proceedings of the IEEE vol 99 no 12 pp2130ndash2158 2011

[26] J Zhang L Tian Y Wang and M Liu ldquoSelection transmit-tingmaximum ratio combining for timing synchronization ofMIMO-OFDM systemsrdquo IEEE Transactions on Broadcastingvol 60 no 4 pp 626ndash636 2014

[27] M Zhou Y Wei Z Tian X Yang and L Li ldquoAchieving cost-efficient indoor fingerprint localization on wlan platform ahypothetical test approachrdquo IEEEAccess vol 5 pp 15865ndash158742017

[28] ldquoZacharyrsquoskarateclubrdquohttpsenwikipediaorgwikiZachary27skarate club

[29] D Wu L Zhou and Y Cai ldquoSocial-aware rate based contentsharing mode selection for D2D content sharing scenariosrdquoIEEE Transactions on Multimedia vol 19 no 11 pp 2571ndash25822017

[30] J Huang Y Yin Y Sun Y Zhao C-C Xing and Q DuanldquoGame theoretic resource allocation for multicell D2D commu-nications with incomplete informationrdquo in Proceedings of theIEEE International Conference on Communications ICC 2015pp 3039ndash3044 London UK June 2015

[31] Y Xiao K-C Chen C Yuen and L A DaSilva ldquoSpectrumsharing for device-to-device communications in cellular net-works a game theoretic approachrdquo in Proceedings of the IEEEInternational SymposiumonDynamic SpectrumAccessNetworks(DYSPAN rsquo14) pp 60ndash71 IEEE McLean Va USA April 2014

[32] D Niyato and E Hossain ldquoA game-theoretic approach tocompetitive spectrum sharing in cognitive radio networksrdquo inProceedings of the IEEEWireless Communications and Network-ing Conference (WCNC rsquo07) pp 16ndash20 Kowloon China March2007

[33] D Monderer and L S Shapley ldquoPotential gamesrdquo Games andEconomic Behavior vol 14 no 1 pp 124ndash143 1996

[34] N Nie and C Comaniciu ldquoAdaptive channel allocation spec-trum etiquette for cognitive radio networksrdquo in Proceedingsof the 1st IEEE International Symposium on New Frontiers inDynamic SpectrumAccess Networks (DySPAN rsquo05) pp 269ndash278Baltimore Md USA November 2005

[35] Y Xing C N Mathur M A Haleem R Chandramouli andK P Subbalakshmi ldquoDynamic spectrum access with QoS andinterference temperature constraintsrdquo IEEE Transactions onMobile Computing vol 6 no 4 pp 423ndash433 2007

[36] T Heikkinen ldquoA potential game approach to distributed powercontrol and schedulingrdquo Computer Networks vol 50 no 13 pp2295ndash2311 2006

[37] Y Li D Jin J Yuan and ZHan ldquoCoalitional games for resourceallocation in the device-to-device uplink underlaying cellularnetworksrdquo IEEE Transactions on Wireless Communications vol13 no 7 pp 3965ndash3977 2014

[38] H Ryu and S-H Park ldquoPerformance comparison of resourceallocation schemes for D2D communicationsrdquo in Proceedingsof the 2014 IEEE Wireless Communications and NetworkingConference Workshops WCNCW 2014 pp 266ndash270 IstanbulTurkey April 2014

[39] Y Li S Su and S Chen ldquoSocial-aware resource allocationfor device-to-device communications underlaying cellular net-worksrdquo IEEE Wireless Communications Letters vol 4 no 3 pp293ndash296 2015

[40] D I Laurenson D G M Cruickshank and G J R PoveyldquoComputationally efficient multipath channel simulator for theCOST 207 modelsrdquo in Proceedings of the IEE Colloquium onComputer Modelling of Communication Systems pp 81ndash86London UK May 1994

Wireless Communications and Mobile Computing 7

Based on the potential game theory we can demonstratethe existence of the Nash Equilibrium of our proposed UFMgame For Γ for every 119889 isin D and for every 119886minus119889 isin 119860minus119889

119875 (119889) = Γ119889 (119886minus119889 119886119889) minus Γ119889 (119886minus119889 1198861015840119889) (20)

Theorem 1 In certain history point 119905 function 119875(119889) derivedfrom UFM game is subgame perfect

Proof We suppose strategy 119886119889 denotes occupying the spec-trum resource of cellular user 119888 which is taken by D2D pairs119889 initially Therefore the initial indicator is 119909119888119889 Once D2Dpair119889 change its strategy andmake a request for the spectrumresource of cellular user 1198881015840 the indicator changes to1199091015840119888119889Thenwe can obtain

Γ119889 minus Γ1015840119889 = 120572 sdot 119877 + 120573 sdot 119880119889 (119883) minus 120576 sdot 119868119889rarr119888 minus 120572 sdot 1198771015840 minus 120573sdot 119880119889 (119883) minus 120576 sdot 1198681015840119889rarr119888

= 120572 sdot (119877 minus 1198771015840) minus 120576 sdot (119868119889rarr119888 minus 1198681015840119889rarr119888) (21)

We denote Δ 1 = 119877 minus 1198771015840 and Δ 2 = 119868119889rarr119888 minus 1198681015840119889rarr119888 As we cansee Δ 1 ≫ Δ 2 Finally we conclude that

Γ119889 minus Γ1015840119889 gt 0 (22)

It means that no D2D pair can acquire performanceenhancement by changing its strategy so we prove that ourproposed game is subgame perfect As subgame is the restric-tion from the perspective of history circumstances it canlead to the Nash Equilibrium of the game directly

4 Resource Allocation Scheme forUFM Game Theory

41 Priority Searching Based Solution The value of the utilityfunction Γ119889 varies when D2D pair chooses to reuse spectrumresource from different cellular user and the final aim of theUFM game is to determine the order of the utility function bythe size of value According to analysis in Sections 32 and 33the resource allocation strategy 119886lowast has a Nash EquilibriumIt means that we can finally achieve an optimal strategy bysubstituting the other strategies one by one in finite times Itis similar to the establishment of preference list and iteratesuntil acquiring the best selection among different alternatives[10] Inspired by the one-to-one matching theory we willshow the main idea of the proposed resource allocationalgorithm in detail

Definition 2 For anyD2D pairs we define the binary priorityrelation set≻119894 to represent the entire set of resource allocationstrategies that each D2D pair 119894 would possibly take In ourUFM game D2D pairs can choose to reuse the resourceoccupied by the associated cellular users or not according tothe priority set For any D2D pairs 119886119894 ≻119894 1198861015840119894 means D2D pairs119894 prefer choosing 119888 as the target resource source instead of 1198881015840

Since the priority set is determined by the utility function wecan define the priority as follows

1198861015840119894 ≻119894 119886119894 lArrrArrΓ119894 (1198861015840119894 ) gt Γ119894 (119886119894)

forall119894 isin D(23)

This definition demonstrates that D2D users 119894 are likelyto reuse the spectrum resource of cellular users 119888 as no moreoptions can bring additional performance gains We can setthe highest priority for cellular user 119888 in the set belonging toD2D user 119894 By this a complete priority set can be obtainedby repeating searching operation For every D2D pair wecan also design an optimization resource allocation schemebased on the priority set In this scheme everyD2Dpair urgesfinding its own highest priority and reusing the spectrumresource shared by the corresponding cellular users

Let us present Algorithm 1Based on the definitions and priority searching operation

we can obtain a final Nash-stable resource scheme 119886fin forD2D users to solve the utility maximization problem whichis given in Algorithm 1 From the whole knowledge givenabove we can see that D2D users make switching iterationfollowing a logically standard based on an arbitrarily choseninitial resource allocation strategy 119886ini At the beginning ofeach iteration D2D user 119894 isin D is randomly chosen by thesystem in step (13) And then the selectedD2D user replacesits resource allocation strategy with 119886ini by random choosinga occupied cellular users and determine its strategies 119886119894 anduniformly selects another social-trust cellular user 1198881015840 isin CThen the D2D pair will request the base station for the chan-nel state information once establishing communication linkwith these two cellular users 119888 and 1198881015840 After acquiring specifiedinformation the BS will computes the utility function of theresource allocation strategies of 119886 and 1198861015840 and broadcast tothe participant of the game model Meanwhile making thedecision that whether to carried out the switch operationfor D2D link If 119886119894 ≻119894 1198861015840119894 the switch operation will not beexecuted Otherwise the switch operation will be executedThe iteration will continue until all of the priority searchingoperations for each D2D pair are traversed and reach a finalNash Equilibrium scheme 119886fin

Different from those conventional D2D resource allo-cation schemes our proposed scheme needs to select suit-able community detection dataset and analyze the social-community information inside And a priority based poten-tial game theory is applied in our scheme This importantinformation is taken into consideration in our proposedscheme fully

42 Uniqueness and Boundedness According to Theorem 1for a given history point 119905 the combination of strategy 119886119894 119886119894 isin119860 119894 can reach a status of being subgame perfect as reactionto the combination of strategy 119886minus119894 To prove the uniquenessand boundedness of our proposed game it is necessary toconfirm that if there exist any participant forall1006704119894 isin D and its

8 Wireless Communications and Mobile Computing

(01) Input Number of mobile users119873 and random resource allocation strategy 119886ini(02)Output A priority based resource allocation scheme 119886fin(03) Utilize the dataset of Karate Club network(04) Calculate the transmission rate of the D2D links and cellular links(05) Obtain 119880119889(119883) and 119868119889rarr119888(06) if 119880119889(119883) le 119868119889rarr119888 remove the D2D links(07) else keep the D2D links(08) Define the matrix of indicator 119909119888119889 isin [0 1](09) 119868 = find 119909119888119889 = 0 ampamp 119868 = 1(10)There is just one 119888 cellular users qualified to shareresources to D2D user 119903 = 119903119888119889(11) else if uniformly randomly choose one cellular users 119888 and 119886possible cellular users 1198881015840 and denote its associate resourcesharing as 119886119894 isin 119886ini(12) Calculate Γ(1198861015840119894 ) and Γ(119886119894) priority = 0(13) if 1198861015840119894 ≻119894 119886119894 then Priority = 1(14) else repeat (15)sim(16)(15) if Priority == 1 then(16) D2D pairs quit current resource occupying strategy of 119888 andturn to adapt the new resource allocation strategy of 1198881015840(17) substitute the current resource occupying strategy 119886 forstrategy 1198861015840 and add it to 119886cur(18)Until all of the D2D pairs complete the priority searching operation resourceoccupying strategy switching operation and reach Nash Equilibrium 119886fin

Algorithm 1 The utility function maximization D2D links redistribution algorithm

corresponding strategy 1006704119886119894 can give better reaction to thestrategy combination 119886minus119894 than 119886119894 and make 1006704119886119894 ≻119894 119886119894 availableSo we provide the following proof relative to the uniquenessand boundedness of our proposed UFM game

Theorem 3 For all of the D2D pairs whose 119909119888119889 = 1 theproposed priority searching based scheme can only obtain aunique resource allocation scheme 119886finProof Based on the description in Algorithm 1 we supposereversely that the combination of strategy 119886119894 is not subgameperfect And then there must exist certain participant 119894 thathas strategy forall1006704119894 isin D and outperforms 119886119894 Now we investigateanother strategy 119886119894 and when 119905 lt 1006704119905 1006704119886119894 is equal to 119886119894 but after1006704119905 it is equal to 119886119894Then in any subgame after the history point1006704119905 strategy forall1006704119894 isin D is at least as well as 119886119894 for the reason thatforall1006704119894 isin D has deviated from 119886119894 once We can also conclude thatstrategy forall1006704119894 isin D is at least as well as 119886119894 after the history point119905 which is contrary to the assumption that strategy forall1006704119894 isin Dimproves the strategy 119886119894 And so on we can investigate other119886119894 to prove its equal benefit with forall1006704119894 isin D until reaching theunique resource allocation scheme 119886fin

Through the above analysis we prove the uniqueness ofthe UFM game by Reduction to Absurdity In each iterationin Algorithm 1 it may lead to a new resource allocationstrategy As there is only C in the physical domain andlimitedD D2D pairs due to the limited social relationship inthe social domain each of the D2D pairs is correspondingto C types of resource allocation scheme So the prioritysearching operation will eventually end in limited steps Thisfact assures the boundedness of our proposed UFM gamebased scheme

5 Simulation Results and Discussions

In this section we implement the simulation results from dif-ferent perspective to verify the performance of our proposedUFM algorithm and elaborate some necessary explanationfor the results Main simulation parameters have been givenin Table 1 Simulations are executed in a single cell whichare within an isolated community circumstance Path lossmodels are considered for cellular and D2D links along withshadow fadingmodel According to the dataset of Karate clubwe conduct the simulation within a 500m times 500m area toguarantee most of the club memberrsquos activities are within thisarea and 34 members of the club are randomly distributedwithin the BS coverage area Meanwhile the bandwidth ofallocated resource is assigned arbitrarily within the rangelimitation We compare our proposed UFM algorithm withthe following resource allocation schemes (a) distributedresource allocation (DRA) which allocates the D2D com-munication resource by thinking in a distributed way [37]and (b) optimal social-community aware resource allocation(OSRA) which allocates the D2D communication resourceto reduce the total transmission time [38] All the results areaveraged over 10 timesrsquo trial

Without loss of generality on one hand we prescribethe pathloss model between the base station and all themobile users as COST (EuropeanCooperation in Science andTechnology) 231 Hata model [39]

PLCU = 367 + 35 times lg (119889) (24)

Meanwhile we prescribe the pathloss model betweendifferent cellular users and D2D users as Xia model [40]given as follows

Wireless Communications and Mobile Computing 9

Table 1 System simulated parameters in the performance evalua-tion

Parameter ValueCoverage radius of BS 500mDistance of D2D 20msim50mNoise figure 9 dB at deviceTransmission power BS 46 dBm device 23 dBmMaximum D2D transmitter power 23 dBmRange of bandwidth 10MHzsim20MHzCommunication demand 50WInterference threshold 56 times 10minus6W119899 119904 119911 120591 1120572 120573 20

PL = 665 + 40 times log (119889) 119889 gt 501007 + 20 times lg (119889) 119889 lt 50 (25)

Since we assume the inner distance of D2D pair remainsin close standards and relatively close the free space modelcan be given by

PL = 384 + 20 times lg (119889) (26)

Moreover we consider the case of fast fading model forRayleigh fading In different situation we adopt a differentfading model to investigate In this way the evaluation of theaverage performance is objective We also set a great numberof criterions for our simulation the maximum power state ofD2D users is set at 23 dBm and the maximum interferencewhich mobile users can tolerate is assumed to be 50 times 10minus6Before investigating the system performance based on ourproposed UFM game we tend to show the joint influenceof the power interference caused by spectrum sharing andsocial characteristics in each social community illustrated inFigure 4

In this section we analyze the sum power interferenceand sum social utility respectively as the number of cellularusers varies The case of 10 cellular users means the situationof system whose spectrum resource is in short supply Inthis situation D2D users possibly have to share the spectrumresource of the same users while the case of 30 cellular usersmeans D2D pairs have many resource-occupying choicesThe results indicate that the sumpower interference decreaseswith the trend of the number of cellular users increasing asthe sum social utility stay in quite a stable level And whenthe number of cellular users in the system exceeds 18 theinfluence from social utility will surpass the influence frompower interference And thenwe evaluate the system sum rateand sum time with different number of cellular users usingthe proposed UFM algorithm and the other two advancedschemes which is illustrated in Figures 5 and 6

Figure 5 compares the sum rate of the three algorithmsunder the isolated scenarios in which we set the number ofcellular users varied in the range of [10 30] From Figure 5we observe that by removing some interference-intolerableD2D links significant performance enhancement can be

Social utilityPower interference

0

20

40

60

80

100

120

140

(Bits

(slowast

Hz)

)

12 14 16 18 20 22 24 26 2810Number of cellular users

Figure 4 Comparison of the joint interference

Comparison of sum rate of the system times104

12 14 16 18 20 22 24 26 302810Number of cellular users

1

2

3

4

5

6

7

8

UFMOSRADRA

(Bits

(slowast

Hz)

)

Figure 5 Transmission rate comparison of different resource alloca-tion algorithms with different number of cellular users

achieved when the cellular users are relatively sufficientBut in the situation that cellular users are not sufficientperformances of the two are roughly equalThe reason is thatthe excessive reuse relationships of frequency with the samecellular user will cause unbearable interference to the cellularusers According to our algorithm the D2D link will beremoved automatically in both schemes

Figure 6 compares the sum transmission time of the threealgorithms under the isolated scenarios From Figure 6 wecan observe that in the case that someunnecessaryD2D linkshas been removed the UFM algorithm still provides quite aconsiderable reduction of transmission timeThat is because

10 Wireless Communications and Mobile Computing

Comparison of sum time of the system

UFMOSRADRA

times10minus3

05

1

15

2

25

3

35

4

45

5

55

Sum

tim

e (s

)

12 14 16 18 20 22 24 26 28 3010Number of cellular users

Figure 6 Transmission time comparison of different resource allo-cation algorithms with different number of cellular users

we allowD2Dusers to continue to acquire content via cellularcommunication when D2D communication comes acrosslink interruption So the sum transmission time will not beaffected greatly

For the purpose of evaluating the system performancewhile the number of D2D users varies within a certainrange we set geographical scope as 300m times 300m aroundthe BS and suppose the number of cellular users is 10 Asillustrated in Figures 7 and 8 the variation range of numberof D2D pairs is [5 30] the result demonstrates that ourproposed UFM game always attains the best performancewith the increase of D2D users compared to the OSRAand DRA This is because in the algorithm of DRA orOSRA there exist little coordination measures to restrictD2D pairs to select their resource and it is inevitable toestablish some high-interference links between D2D pairsand cellular users In our proposed algorithm UFM gameeffectively coordinates both social relationship and powerinterference and then decides whether to access the spectrumresource of certain cellular users not in a random way Inthese circumstances we can avoid many high-risk links andattain a better system performance in terms of the evaluationof the sum transmission rate At this point we can summarizethat our proposed scheme precedes the other two schemes ina relatively comprehensive scale

6 Conclusion and Future Work

This paper studies game-theory based social-aware resourceallocation in the D2D communication underlaying cellularnetwork based on the realistic social network By consideringthe power interference and social utility in the physical andsocial domain respectively a game-theoretic based utilityfunction maximization scheme has been proposed Also to

Comparison of sum rate of the system

UFMOSRADRA

times104

0

1

2

3

4

5

6

7

8

10 15 20 25 305Number of D2D pairs

(Bits

(slowast

Hz)

)Figure 7 Transmission rate comparison of different resource alloca-tion algorithms with different number of D2D pairs

Comparison of sum time of the system

UFMOSRADRA

times10minus3

0

1

2

3

4

5

6

7

8

9

Sum

tim

e (s

)

10 15 20 25 305Number of D2D pairs

Figure 8 Transmission time comparison of different resource allo-cation algorithms with different number of D2D pairs

demonstrate the optimality of our proposed scheme thispaper provides evidence for the existence of Nash Equilib-rium theoretically Meanwhile a priority searching operationbased resource allocation scheme is designed to implementthe Nash Equilibrium of the proposed UFM game The pro-posed UFM scheme is numerically shown having superiorityover traditional DRA and OSRA scheme the performancesof sum rate and total transmission time are better thanthe OSRA and DRA algorithm through massive simulation

Wireless Communications and Mobile Computing 11

result suggesting that the proposed scheme is more ideal forjoint social-aware resource scenarios considering the socialcharacteristics Nevertheless some issues related to furthersystem optimization remain to be addressed such as powerallocation of mobile nodes and cluster formation of socialcommunity

Notations

N Set of mobile usersC Set of cellular usersD Set of D2D pairsΦ The UFM game≻119894 Set of utility priority119868119889rarr119888 Interference from 119889th D2D to 119888th cellular signal119868119888rarr119889 Interference from 119888th cellular signal to 119889th D2D119880119889(119883) Social utility of 119889th D2D pairsΓ119889(119883) Utility function of 119889th D2D pairs119909119888119889 Indicator of resource reusing relations119909lowast119889 The Nash Equilibrium of 119889th D2D pair119883119889 Set of all feasible strategies in UFM game

Conflicts of Interest

The authors declare no conflicts of interest related to thepublication of this paper

Acknowledgments

This work is partly supported by the National NaturalScience Foundation of China (61571240 61671253) the Pri-ority Academic Program Development of Jiangsu HigherEducation Institutions the Major Projects of the NaturalScience Foundation of the Jiangsu Higher Education Insti-tutions (16KJA510004) the Open Research Fund of Nationaland Local Joint Engineering Laboratory of RF Integrationand Micro-Assembly Technology Nanjing University ofPosts and Telecommunications (KFJJ20170305) the OpenResearch Fund ofThe State Key Laboratory of Integrated Ser-vices Networks Xidian University (ISN17-04) Jiangsu Spe-cially Appointed Professor Grant (RK002STP16001) Inno-vation and Entrepreneurship of Jiangsu High-Level TalentGrant (CZ0010617002) High-Level Talent Startup Grantof Nanjing University of Posts and Telecommunications(XK0010915026) and ldquo1311 Talent Planrdquo ofNanjingUniversityof Posts and Telecommunications

References

[1] Y Cao T Jiang and C Wang ldquoCooperative device-to-devicecommunications in cellular networksrdquo IEEE Wireless Commu-nications Magazine vol 22 no 3 pp 124ndash129 2015

[2] J Liu N Kato J Ma and N Kadowaki ldquoDevice-to-devicecommunication in LTE-advanced networks a surveyrdquo IEEECommunications Surveys amp Tutorials vol 17 no 4 pp 1923ndash1940 Fourthquarter 2015

[3] A Asadi Q Wang and V Mancuso ldquoA survey on device-to-device communication in cellular networksrdquo IEEE Communi-cations Surveys amp Tutorials vol 16 no 4 pp 1801ndash1819 2014

[4] H Nishiyama M Ito and N Kato ldquoRelay-by-smartphonerealizing multihop device-to-device communicationsrdquo IEEECommunications Magazine vol 52 no 4 pp 56ndash65 2014

[5] M Zhou Y Tang Z Tian L Xie and W Nie ldquoRobust neigh-borhood graphing for semi-supervised indoor localization withlight-loaded location fingerprintingrdquo IEEE Internet of ThingsJournal vol PP no 99 pp 1-1

[6] K Doppler M Rinne C Wijting C B Ribeiro and K HugldquoDevice-to-device communication as an underlay to LTE-advanced networksrdquo IEEE Communications Magazine vol 47no 12 pp 42ndash49 2009

[7] J Liu H Nishiyama N Kato and J Guo ldquoOn the outageprobability of device-to-device-communication-enabled mul-tichannel cellular networks an RSS-threshold-based perspec-tiverdquo IEEE Journal on Selected Areas in Communications vol34 no 1 pp 163ndash175 2016

[8] M Zhou Y Tang W Nie L Xie and X Yang ldquoGrassMAgraph-based semi-supervised manifold alignment for indoorWLAN localizationrdquo IEEE Sensors Journal vol 17 no 21 pp7086ndash7095 2017

[9] J Liu S Zhang N Kato H Ujikawa and K Suzuki ldquoDevice-to-device communications for enhancing quality of experiencein software defined multi-tier LTE-A networksrdquo IEEE Networkvol 29 no 4 pp 46ndash52 2015

[10] C Xu L Song Z Han et al ldquoEfficiency resource allocation fordevice-to-device underlay communication systems a reverseiterative combinatorial auction based approachrdquo IEEE Journalon Selected Areas in Communications vol 31 no 9 pp 348ndash3582013

[11] L Ferdouse W Ejaz K Raahemifar A Anpalagan and MMarkandaier ldquoInterference and throughput aware resourceallocation for multi-class D2D in 5G networksrdquo IET Commu-nications vol 11 no 8 pp 1241ndash1250 2017

[12] T D Hoang L B Le and T Le-Ngoc ldquoCooperative device-to-device communications in cellular networksrdquo IEEE Transac-tions onWireless Communications vol 15 no 10 pp 7099ndash71132016

[13] M Andrews K Kumaran K Ramanan A Stolyar P Whitingand R Vijayakumar ldquoProviding quality of service over a sharedwireless linkrdquo IEEE Communications Magazine vol 39 no 2pp 150ndash154 2001

[14] L Wang L Liu X Cao X Tian and Y Cheng ldquoSociality-aware resource allocation for device-to-device communicationsin cellular networksrdquo IET Communications vol 9 no 3 pp342ndash349 2015

[15] V Shah andA O Fapojuwo ldquoSocially aware resource allocationfor device-to-device communication in downlinkOFDMAnet-worksrdquo in Proceedings of the 2014 IEEE Wireless Communica-tions and Networking Conference WCNC 2014 pp 1673ndash1678Istanbul Turkey April 2014

[16] Y Li T Wu P Hui D Jin and S Chen ldquoSocial-aware D2Dcommunications qualitative insights and quantitative analysisrdquoIEEE Communications Magazine vol 52 no 6 pp 150ndash1582014

[17] FWang L Song Z Han Q Zhao and XWang ldquoJoint schedul-ing and resource allocation for device-to-device underlay com-municationrdquo in Proceedings of the IEEE Wireless Communi-cations and Networking Conference (WCNC rsquo13) pp 134ndash139IEEE Shanghai China April 2013

[18] F Tang Z M Fadlullah N Kato F One and R MiuraldquoAC-POCA anti-coordination game based partially overlap-ping channels assignment in combined UAV and D2D based

12 Wireless Communications and Mobile Computing

networksrdquo IEEE Transactions on Vehicular Technology vol PPno 99 pp 1-1

[19] S M Azimi M H Manshaei and F Hendessi ldquoHybrid cellularand device-to-device communication power control Nashbargaining gamerdquo in Proceedings of the 2014 7th InternationalSymposium on Telecommunications IST 2014 pp 1077ndash1081Tehran Iran September 2014

[20] Z Zhou K Ota M Dong and C Xu ldquoEnergy-efficient match-ing for resource allocation in D2D enabled cellular networksrdquoIEEE Transactions on Vehicular Technology vol 66 no 6 pp5256ndash5268 2017

[21] C Xu C Gao Z Zhou Z Chang and Y Jia ldquoSocial network-based content delivery in device-to-device underlay cellularnetworks using matching theoryrdquo IEEE Access vol 5 pp 924ndash937 2017

[22] X Feng G Sun X Gan et al ldquoCooperative spectrum sharingin cognitive radio networks a distributed matching approachrdquoIEEE Transactions on Communications vol 62 no 8 pp 2651ndash2664 2014

[23] J Zhang ldquoThe interdisciplinary research of big data andwireless channel a cluster-nuclei based channel modelrdquo ChinaCommunications vol 13 no supplement 2 Article ID 7833457pp 14ndash26 2016

[24] S Mumtaz K M Saidul Huq J Rodriguez and V FrascollaldquoEnergy-efficient interference management in LTE-D2D com-municationrdquo IET Signal Processing vol 10 no 3 pp 197ndash2022016

[25] N Kayastha D Niyato P Wang and E Hossain ldquoApplicationsarchitectures and protocol design issues for mobile socialnetworks a surveyrdquo Proceedings of the IEEE vol 99 no 12 pp2130ndash2158 2011

[26] J Zhang L Tian Y Wang and M Liu ldquoSelection transmit-tingmaximum ratio combining for timing synchronization ofMIMO-OFDM systemsrdquo IEEE Transactions on Broadcastingvol 60 no 4 pp 626ndash636 2014

[27] M Zhou Y Wei Z Tian X Yang and L Li ldquoAchieving cost-efficient indoor fingerprint localization on wlan platform ahypothetical test approachrdquo IEEEAccess vol 5 pp 15865ndash158742017

[28] ldquoZacharyrsquoskarateclubrdquohttpsenwikipediaorgwikiZachary27skarate club

[29] D Wu L Zhou and Y Cai ldquoSocial-aware rate based contentsharing mode selection for D2D content sharing scenariosrdquoIEEE Transactions on Multimedia vol 19 no 11 pp 2571ndash25822017

[30] J Huang Y Yin Y Sun Y Zhao C-C Xing and Q DuanldquoGame theoretic resource allocation for multicell D2D commu-nications with incomplete informationrdquo in Proceedings of theIEEE International Conference on Communications ICC 2015pp 3039ndash3044 London UK June 2015

[31] Y Xiao K-C Chen C Yuen and L A DaSilva ldquoSpectrumsharing for device-to-device communications in cellular net-works a game theoretic approachrdquo in Proceedings of the IEEEInternational SymposiumonDynamic SpectrumAccessNetworks(DYSPAN rsquo14) pp 60ndash71 IEEE McLean Va USA April 2014

[32] D Niyato and E Hossain ldquoA game-theoretic approach tocompetitive spectrum sharing in cognitive radio networksrdquo inProceedings of the IEEEWireless Communications and Network-ing Conference (WCNC rsquo07) pp 16ndash20 Kowloon China March2007

[33] D Monderer and L S Shapley ldquoPotential gamesrdquo Games andEconomic Behavior vol 14 no 1 pp 124ndash143 1996

[34] N Nie and C Comaniciu ldquoAdaptive channel allocation spec-trum etiquette for cognitive radio networksrdquo in Proceedingsof the 1st IEEE International Symposium on New Frontiers inDynamic SpectrumAccess Networks (DySPAN rsquo05) pp 269ndash278Baltimore Md USA November 2005

[35] Y Xing C N Mathur M A Haleem R Chandramouli andK P Subbalakshmi ldquoDynamic spectrum access with QoS andinterference temperature constraintsrdquo IEEE Transactions onMobile Computing vol 6 no 4 pp 423ndash433 2007

[36] T Heikkinen ldquoA potential game approach to distributed powercontrol and schedulingrdquo Computer Networks vol 50 no 13 pp2295ndash2311 2006

[37] Y Li D Jin J Yuan and ZHan ldquoCoalitional games for resourceallocation in the device-to-device uplink underlaying cellularnetworksrdquo IEEE Transactions on Wireless Communications vol13 no 7 pp 3965ndash3977 2014

[38] H Ryu and S-H Park ldquoPerformance comparison of resourceallocation schemes for D2D communicationsrdquo in Proceedingsof the 2014 IEEE Wireless Communications and NetworkingConference Workshops WCNCW 2014 pp 266ndash270 IstanbulTurkey April 2014

[39] Y Li S Su and S Chen ldquoSocial-aware resource allocationfor device-to-device communications underlaying cellular net-worksrdquo IEEE Wireless Communications Letters vol 4 no 3 pp293ndash296 2015

[40] D I Laurenson D G M Cruickshank and G J R PoveyldquoComputationally efficient multipath channel simulator for theCOST 207 modelsrdquo in Proceedings of the IEE Colloquium onComputer Modelling of Communication Systems pp 81ndash86London UK May 1994

8 Wireless Communications and Mobile Computing

(01) Input Number of mobile users119873 and random resource allocation strategy 119886ini(02)Output A priority based resource allocation scheme 119886fin(03) Utilize the dataset of Karate Club network(04) Calculate the transmission rate of the D2D links and cellular links(05) Obtain 119880119889(119883) and 119868119889rarr119888(06) if 119880119889(119883) le 119868119889rarr119888 remove the D2D links(07) else keep the D2D links(08) Define the matrix of indicator 119909119888119889 isin [0 1](09) 119868 = find 119909119888119889 = 0 ampamp 119868 = 1(10)There is just one 119888 cellular users qualified to shareresources to D2D user 119903 = 119903119888119889(11) else if uniformly randomly choose one cellular users 119888 and 119886possible cellular users 1198881015840 and denote its associate resourcesharing as 119886119894 isin 119886ini(12) Calculate Γ(1198861015840119894 ) and Γ(119886119894) priority = 0(13) if 1198861015840119894 ≻119894 119886119894 then Priority = 1(14) else repeat (15)sim(16)(15) if Priority == 1 then(16) D2D pairs quit current resource occupying strategy of 119888 andturn to adapt the new resource allocation strategy of 1198881015840(17) substitute the current resource occupying strategy 119886 forstrategy 1198861015840 and add it to 119886cur(18)Until all of the D2D pairs complete the priority searching operation resourceoccupying strategy switching operation and reach Nash Equilibrium 119886fin

Algorithm 1 The utility function maximization D2D links redistribution algorithm

corresponding strategy 1006704119886119894 can give better reaction to thestrategy combination 119886minus119894 than 119886119894 and make 1006704119886119894 ≻119894 119886119894 availableSo we provide the following proof relative to the uniquenessand boundedness of our proposed UFM game

Theorem 3 For all of the D2D pairs whose 119909119888119889 = 1 theproposed priority searching based scheme can only obtain aunique resource allocation scheme 119886finProof Based on the description in Algorithm 1 we supposereversely that the combination of strategy 119886119894 is not subgameperfect And then there must exist certain participant 119894 thathas strategy forall1006704119894 isin D and outperforms 119886119894 Now we investigateanother strategy 119886119894 and when 119905 lt 1006704119905 1006704119886119894 is equal to 119886119894 but after1006704119905 it is equal to 119886119894Then in any subgame after the history point1006704119905 strategy forall1006704119894 isin D is at least as well as 119886119894 for the reason thatforall1006704119894 isin D has deviated from 119886119894 once We can also conclude thatstrategy forall1006704119894 isin D is at least as well as 119886119894 after the history point119905 which is contrary to the assumption that strategy forall1006704119894 isin Dimproves the strategy 119886119894 And so on we can investigate other119886119894 to prove its equal benefit with forall1006704119894 isin D until reaching theunique resource allocation scheme 119886fin

Through the above analysis we prove the uniqueness ofthe UFM game by Reduction to Absurdity In each iterationin Algorithm 1 it may lead to a new resource allocationstrategy As there is only C in the physical domain andlimitedD D2D pairs due to the limited social relationship inthe social domain each of the D2D pairs is correspondingto C types of resource allocation scheme So the prioritysearching operation will eventually end in limited steps Thisfact assures the boundedness of our proposed UFM gamebased scheme

5 Simulation Results and Discussions

In this section we implement the simulation results from dif-ferent perspective to verify the performance of our proposedUFM algorithm and elaborate some necessary explanationfor the results Main simulation parameters have been givenin Table 1 Simulations are executed in a single cell whichare within an isolated community circumstance Path lossmodels are considered for cellular and D2D links along withshadow fadingmodel According to the dataset of Karate clubwe conduct the simulation within a 500m times 500m area toguarantee most of the club memberrsquos activities are within thisarea and 34 members of the club are randomly distributedwithin the BS coverage area Meanwhile the bandwidth ofallocated resource is assigned arbitrarily within the rangelimitation We compare our proposed UFM algorithm withthe following resource allocation schemes (a) distributedresource allocation (DRA) which allocates the D2D com-munication resource by thinking in a distributed way [37]and (b) optimal social-community aware resource allocation(OSRA) which allocates the D2D communication resourceto reduce the total transmission time [38] All the results areaveraged over 10 timesrsquo trial

Without loss of generality on one hand we prescribethe pathloss model between the base station and all themobile users as COST (EuropeanCooperation in Science andTechnology) 231 Hata model [39]

PLCU = 367 + 35 times lg (119889) (24)

Meanwhile we prescribe the pathloss model betweendifferent cellular users and D2D users as Xia model [40]given as follows

Wireless Communications and Mobile Computing 9

Table 1 System simulated parameters in the performance evalua-tion

Parameter ValueCoverage radius of BS 500mDistance of D2D 20msim50mNoise figure 9 dB at deviceTransmission power BS 46 dBm device 23 dBmMaximum D2D transmitter power 23 dBmRange of bandwidth 10MHzsim20MHzCommunication demand 50WInterference threshold 56 times 10minus6W119899 119904 119911 120591 1120572 120573 20

PL = 665 + 40 times log (119889) 119889 gt 501007 + 20 times lg (119889) 119889 lt 50 (25)

Since we assume the inner distance of D2D pair remainsin close standards and relatively close the free space modelcan be given by

PL = 384 + 20 times lg (119889) (26)

Moreover we consider the case of fast fading model forRayleigh fading In different situation we adopt a differentfading model to investigate In this way the evaluation of theaverage performance is objective We also set a great numberof criterions for our simulation the maximum power state ofD2D users is set at 23 dBm and the maximum interferencewhich mobile users can tolerate is assumed to be 50 times 10minus6Before investigating the system performance based on ourproposed UFM game we tend to show the joint influenceof the power interference caused by spectrum sharing andsocial characteristics in each social community illustrated inFigure 4

In this section we analyze the sum power interferenceand sum social utility respectively as the number of cellularusers varies The case of 10 cellular users means the situationof system whose spectrum resource is in short supply Inthis situation D2D users possibly have to share the spectrumresource of the same users while the case of 30 cellular usersmeans D2D pairs have many resource-occupying choicesThe results indicate that the sumpower interference decreaseswith the trend of the number of cellular users increasing asthe sum social utility stay in quite a stable level And whenthe number of cellular users in the system exceeds 18 theinfluence from social utility will surpass the influence frompower interference And thenwe evaluate the system sum rateand sum time with different number of cellular users usingthe proposed UFM algorithm and the other two advancedschemes which is illustrated in Figures 5 and 6

Figure 5 compares the sum rate of the three algorithmsunder the isolated scenarios in which we set the number ofcellular users varied in the range of [10 30] From Figure 5we observe that by removing some interference-intolerableD2D links significant performance enhancement can be

Social utilityPower interference

0

20

40

60

80

100

120

140

(Bits

(slowast

Hz)

)

12 14 16 18 20 22 24 26 2810Number of cellular users

Figure 4 Comparison of the joint interference

Comparison of sum rate of the system times104

12 14 16 18 20 22 24 26 302810Number of cellular users

1

2

3

4

5

6

7

8

UFMOSRADRA

(Bits

(slowast

Hz)

)

Figure 5 Transmission rate comparison of different resource alloca-tion algorithms with different number of cellular users

achieved when the cellular users are relatively sufficientBut in the situation that cellular users are not sufficientperformances of the two are roughly equalThe reason is thatthe excessive reuse relationships of frequency with the samecellular user will cause unbearable interference to the cellularusers According to our algorithm the D2D link will beremoved automatically in both schemes

Figure 6 compares the sum transmission time of the threealgorithms under the isolated scenarios From Figure 6 wecan observe that in the case that someunnecessaryD2D linkshas been removed the UFM algorithm still provides quite aconsiderable reduction of transmission timeThat is because

10 Wireless Communications and Mobile Computing

Comparison of sum time of the system

UFMOSRADRA

times10minus3

05

1

15

2

25

3

35

4

45

5

55

Sum

tim

e (s

)

12 14 16 18 20 22 24 26 28 3010Number of cellular users

Figure 6 Transmission time comparison of different resource allo-cation algorithms with different number of cellular users

we allowD2Dusers to continue to acquire content via cellularcommunication when D2D communication comes acrosslink interruption So the sum transmission time will not beaffected greatly

For the purpose of evaluating the system performancewhile the number of D2D users varies within a certainrange we set geographical scope as 300m times 300m aroundthe BS and suppose the number of cellular users is 10 Asillustrated in Figures 7 and 8 the variation range of numberof D2D pairs is [5 30] the result demonstrates that ourproposed UFM game always attains the best performancewith the increase of D2D users compared to the OSRAand DRA This is because in the algorithm of DRA orOSRA there exist little coordination measures to restrictD2D pairs to select their resource and it is inevitable toestablish some high-interference links between D2D pairsand cellular users In our proposed algorithm UFM gameeffectively coordinates both social relationship and powerinterference and then decides whether to access the spectrumresource of certain cellular users not in a random way Inthese circumstances we can avoid many high-risk links andattain a better system performance in terms of the evaluationof the sum transmission rate At this point we can summarizethat our proposed scheme precedes the other two schemes ina relatively comprehensive scale

6 Conclusion and Future Work

This paper studies game-theory based social-aware resourceallocation in the D2D communication underlaying cellularnetwork based on the realistic social network By consideringthe power interference and social utility in the physical andsocial domain respectively a game-theoretic based utilityfunction maximization scheme has been proposed Also to

Comparison of sum rate of the system

UFMOSRADRA

times104

0

1

2

3

4

5

6

7

8

10 15 20 25 305Number of D2D pairs

(Bits

(slowast

Hz)

)Figure 7 Transmission rate comparison of different resource alloca-tion algorithms with different number of D2D pairs

Comparison of sum time of the system

UFMOSRADRA

times10minus3

0

1

2

3

4

5

6

7

8

9

Sum

tim

e (s

)

10 15 20 25 305Number of D2D pairs

Figure 8 Transmission time comparison of different resource allo-cation algorithms with different number of D2D pairs

demonstrate the optimality of our proposed scheme thispaper provides evidence for the existence of Nash Equilib-rium theoretically Meanwhile a priority searching operationbased resource allocation scheme is designed to implementthe Nash Equilibrium of the proposed UFM game The pro-posed UFM scheme is numerically shown having superiorityover traditional DRA and OSRA scheme the performancesof sum rate and total transmission time are better thanthe OSRA and DRA algorithm through massive simulation

Wireless Communications and Mobile Computing 11

result suggesting that the proposed scheme is more ideal forjoint social-aware resource scenarios considering the socialcharacteristics Nevertheless some issues related to furthersystem optimization remain to be addressed such as powerallocation of mobile nodes and cluster formation of socialcommunity

Notations

N Set of mobile usersC Set of cellular usersD Set of D2D pairsΦ The UFM game≻119894 Set of utility priority119868119889rarr119888 Interference from 119889th D2D to 119888th cellular signal119868119888rarr119889 Interference from 119888th cellular signal to 119889th D2D119880119889(119883) Social utility of 119889th D2D pairsΓ119889(119883) Utility function of 119889th D2D pairs119909119888119889 Indicator of resource reusing relations119909lowast119889 The Nash Equilibrium of 119889th D2D pair119883119889 Set of all feasible strategies in UFM game

Conflicts of Interest

The authors declare no conflicts of interest related to thepublication of this paper

Acknowledgments

This work is partly supported by the National NaturalScience Foundation of China (61571240 61671253) the Pri-ority Academic Program Development of Jiangsu HigherEducation Institutions the Major Projects of the NaturalScience Foundation of the Jiangsu Higher Education Insti-tutions (16KJA510004) the Open Research Fund of Nationaland Local Joint Engineering Laboratory of RF Integrationand Micro-Assembly Technology Nanjing University ofPosts and Telecommunications (KFJJ20170305) the OpenResearch Fund ofThe State Key Laboratory of Integrated Ser-vices Networks Xidian University (ISN17-04) Jiangsu Spe-cially Appointed Professor Grant (RK002STP16001) Inno-vation and Entrepreneurship of Jiangsu High-Level TalentGrant (CZ0010617002) High-Level Talent Startup Grantof Nanjing University of Posts and Telecommunications(XK0010915026) and ldquo1311 Talent Planrdquo ofNanjingUniversityof Posts and Telecommunications

References

[1] Y Cao T Jiang and C Wang ldquoCooperative device-to-devicecommunications in cellular networksrdquo IEEE Wireless Commu-nications Magazine vol 22 no 3 pp 124ndash129 2015

[2] J Liu N Kato J Ma and N Kadowaki ldquoDevice-to-devicecommunication in LTE-advanced networks a surveyrdquo IEEECommunications Surveys amp Tutorials vol 17 no 4 pp 1923ndash1940 Fourthquarter 2015

[3] A Asadi Q Wang and V Mancuso ldquoA survey on device-to-device communication in cellular networksrdquo IEEE Communi-cations Surveys amp Tutorials vol 16 no 4 pp 1801ndash1819 2014

[4] H Nishiyama M Ito and N Kato ldquoRelay-by-smartphonerealizing multihop device-to-device communicationsrdquo IEEECommunications Magazine vol 52 no 4 pp 56ndash65 2014

[5] M Zhou Y Tang Z Tian L Xie and W Nie ldquoRobust neigh-borhood graphing for semi-supervised indoor localization withlight-loaded location fingerprintingrdquo IEEE Internet of ThingsJournal vol PP no 99 pp 1-1

[6] K Doppler M Rinne C Wijting C B Ribeiro and K HugldquoDevice-to-device communication as an underlay to LTE-advanced networksrdquo IEEE Communications Magazine vol 47no 12 pp 42ndash49 2009

[7] J Liu H Nishiyama N Kato and J Guo ldquoOn the outageprobability of device-to-device-communication-enabled mul-tichannel cellular networks an RSS-threshold-based perspec-tiverdquo IEEE Journal on Selected Areas in Communications vol34 no 1 pp 163ndash175 2016

[8] M Zhou Y Tang W Nie L Xie and X Yang ldquoGrassMAgraph-based semi-supervised manifold alignment for indoorWLAN localizationrdquo IEEE Sensors Journal vol 17 no 21 pp7086ndash7095 2017

[9] J Liu S Zhang N Kato H Ujikawa and K Suzuki ldquoDevice-to-device communications for enhancing quality of experiencein software defined multi-tier LTE-A networksrdquo IEEE Networkvol 29 no 4 pp 46ndash52 2015

[10] C Xu L Song Z Han et al ldquoEfficiency resource allocation fordevice-to-device underlay communication systems a reverseiterative combinatorial auction based approachrdquo IEEE Journalon Selected Areas in Communications vol 31 no 9 pp 348ndash3582013

[11] L Ferdouse W Ejaz K Raahemifar A Anpalagan and MMarkandaier ldquoInterference and throughput aware resourceallocation for multi-class D2D in 5G networksrdquo IET Commu-nications vol 11 no 8 pp 1241ndash1250 2017

[12] T D Hoang L B Le and T Le-Ngoc ldquoCooperative device-to-device communications in cellular networksrdquo IEEE Transac-tions onWireless Communications vol 15 no 10 pp 7099ndash71132016

[13] M Andrews K Kumaran K Ramanan A Stolyar P Whitingand R Vijayakumar ldquoProviding quality of service over a sharedwireless linkrdquo IEEE Communications Magazine vol 39 no 2pp 150ndash154 2001

[14] L Wang L Liu X Cao X Tian and Y Cheng ldquoSociality-aware resource allocation for device-to-device communicationsin cellular networksrdquo IET Communications vol 9 no 3 pp342ndash349 2015

[15] V Shah andA O Fapojuwo ldquoSocially aware resource allocationfor device-to-device communication in downlinkOFDMAnet-worksrdquo in Proceedings of the 2014 IEEE Wireless Communica-tions and Networking Conference WCNC 2014 pp 1673ndash1678Istanbul Turkey April 2014

[16] Y Li T Wu P Hui D Jin and S Chen ldquoSocial-aware D2Dcommunications qualitative insights and quantitative analysisrdquoIEEE Communications Magazine vol 52 no 6 pp 150ndash1582014

[17] FWang L Song Z Han Q Zhao and XWang ldquoJoint schedul-ing and resource allocation for device-to-device underlay com-municationrdquo in Proceedings of the IEEE Wireless Communi-cations and Networking Conference (WCNC rsquo13) pp 134ndash139IEEE Shanghai China April 2013

[18] F Tang Z M Fadlullah N Kato F One and R MiuraldquoAC-POCA anti-coordination game based partially overlap-ping channels assignment in combined UAV and D2D based

12 Wireless Communications and Mobile Computing

networksrdquo IEEE Transactions on Vehicular Technology vol PPno 99 pp 1-1

[19] S M Azimi M H Manshaei and F Hendessi ldquoHybrid cellularand device-to-device communication power control Nashbargaining gamerdquo in Proceedings of the 2014 7th InternationalSymposium on Telecommunications IST 2014 pp 1077ndash1081Tehran Iran September 2014

[20] Z Zhou K Ota M Dong and C Xu ldquoEnergy-efficient match-ing for resource allocation in D2D enabled cellular networksrdquoIEEE Transactions on Vehicular Technology vol 66 no 6 pp5256ndash5268 2017

[21] C Xu C Gao Z Zhou Z Chang and Y Jia ldquoSocial network-based content delivery in device-to-device underlay cellularnetworks using matching theoryrdquo IEEE Access vol 5 pp 924ndash937 2017

[22] X Feng G Sun X Gan et al ldquoCooperative spectrum sharingin cognitive radio networks a distributed matching approachrdquoIEEE Transactions on Communications vol 62 no 8 pp 2651ndash2664 2014

[23] J Zhang ldquoThe interdisciplinary research of big data andwireless channel a cluster-nuclei based channel modelrdquo ChinaCommunications vol 13 no supplement 2 Article ID 7833457pp 14ndash26 2016

[24] S Mumtaz K M Saidul Huq J Rodriguez and V FrascollaldquoEnergy-efficient interference management in LTE-D2D com-municationrdquo IET Signal Processing vol 10 no 3 pp 197ndash2022016

[25] N Kayastha D Niyato P Wang and E Hossain ldquoApplicationsarchitectures and protocol design issues for mobile socialnetworks a surveyrdquo Proceedings of the IEEE vol 99 no 12 pp2130ndash2158 2011

[26] J Zhang L Tian Y Wang and M Liu ldquoSelection transmit-tingmaximum ratio combining for timing synchronization ofMIMO-OFDM systemsrdquo IEEE Transactions on Broadcastingvol 60 no 4 pp 626ndash636 2014

[27] M Zhou Y Wei Z Tian X Yang and L Li ldquoAchieving cost-efficient indoor fingerprint localization on wlan platform ahypothetical test approachrdquo IEEEAccess vol 5 pp 15865ndash158742017

[28] ldquoZacharyrsquoskarateclubrdquohttpsenwikipediaorgwikiZachary27skarate club

[29] D Wu L Zhou and Y Cai ldquoSocial-aware rate based contentsharing mode selection for D2D content sharing scenariosrdquoIEEE Transactions on Multimedia vol 19 no 11 pp 2571ndash25822017

[30] J Huang Y Yin Y Sun Y Zhao C-C Xing and Q DuanldquoGame theoretic resource allocation for multicell D2D commu-nications with incomplete informationrdquo in Proceedings of theIEEE International Conference on Communications ICC 2015pp 3039ndash3044 London UK June 2015

[31] Y Xiao K-C Chen C Yuen and L A DaSilva ldquoSpectrumsharing for device-to-device communications in cellular net-works a game theoretic approachrdquo in Proceedings of the IEEEInternational SymposiumonDynamic SpectrumAccessNetworks(DYSPAN rsquo14) pp 60ndash71 IEEE McLean Va USA April 2014

[32] D Niyato and E Hossain ldquoA game-theoretic approach tocompetitive spectrum sharing in cognitive radio networksrdquo inProceedings of the IEEEWireless Communications and Network-ing Conference (WCNC rsquo07) pp 16ndash20 Kowloon China March2007

[33] D Monderer and L S Shapley ldquoPotential gamesrdquo Games andEconomic Behavior vol 14 no 1 pp 124ndash143 1996

[34] N Nie and C Comaniciu ldquoAdaptive channel allocation spec-trum etiquette for cognitive radio networksrdquo in Proceedingsof the 1st IEEE International Symposium on New Frontiers inDynamic SpectrumAccess Networks (DySPAN rsquo05) pp 269ndash278Baltimore Md USA November 2005

[35] Y Xing C N Mathur M A Haleem R Chandramouli andK P Subbalakshmi ldquoDynamic spectrum access with QoS andinterference temperature constraintsrdquo IEEE Transactions onMobile Computing vol 6 no 4 pp 423ndash433 2007

[36] T Heikkinen ldquoA potential game approach to distributed powercontrol and schedulingrdquo Computer Networks vol 50 no 13 pp2295ndash2311 2006

[37] Y Li D Jin J Yuan and ZHan ldquoCoalitional games for resourceallocation in the device-to-device uplink underlaying cellularnetworksrdquo IEEE Transactions on Wireless Communications vol13 no 7 pp 3965ndash3977 2014

[38] H Ryu and S-H Park ldquoPerformance comparison of resourceallocation schemes for D2D communicationsrdquo in Proceedingsof the 2014 IEEE Wireless Communications and NetworkingConference Workshops WCNCW 2014 pp 266ndash270 IstanbulTurkey April 2014

[39] Y Li S Su and S Chen ldquoSocial-aware resource allocationfor device-to-device communications underlaying cellular net-worksrdquo IEEE Wireless Communications Letters vol 4 no 3 pp293ndash296 2015

[40] D I Laurenson D G M Cruickshank and G J R PoveyldquoComputationally efficient multipath channel simulator for theCOST 207 modelsrdquo in Proceedings of the IEE Colloquium onComputer Modelling of Communication Systems pp 81ndash86London UK May 1994

Wireless Communications and Mobile Computing 9

Table 1 System simulated parameters in the performance evalua-tion

Parameter ValueCoverage radius of BS 500mDistance of D2D 20msim50mNoise figure 9 dB at deviceTransmission power BS 46 dBm device 23 dBmMaximum D2D transmitter power 23 dBmRange of bandwidth 10MHzsim20MHzCommunication demand 50WInterference threshold 56 times 10minus6W119899 119904 119911 120591 1120572 120573 20

PL = 665 + 40 times log (119889) 119889 gt 501007 + 20 times lg (119889) 119889 lt 50 (25)

Since we assume the inner distance of D2D pair remainsin close standards and relatively close the free space modelcan be given by

PL = 384 + 20 times lg (119889) (26)

Moreover we consider the case of fast fading model forRayleigh fading In different situation we adopt a differentfading model to investigate In this way the evaluation of theaverage performance is objective We also set a great numberof criterions for our simulation the maximum power state ofD2D users is set at 23 dBm and the maximum interferencewhich mobile users can tolerate is assumed to be 50 times 10minus6Before investigating the system performance based on ourproposed UFM game we tend to show the joint influenceof the power interference caused by spectrum sharing andsocial characteristics in each social community illustrated inFigure 4

In this section we analyze the sum power interferenceand sum social utility respectively as the number of cellularusers varies The case of 10 cellular users means the situationof system whose spectrum resource is in short supply Inthis situation D2D users possibly have to share the spectrumresource of the same users while the case of 30 cellular usersmeans D2D pairs have many resource-occupying choicesThe results indicate that the sumpower interference decreaseswith the trend of the number of cellular users increasing asthe sum social utility stay in quite a stable level And whenthe number of cellular users in the system exceeds 18 theinfluence from social utility will surpass the influence frompower interference And thenwe evaluate the system sum rateand sum time with different number of cellular users usingthe proposed UFM algorithm and the other two advancedschemes which is illustrated in Figures 5 and 6

Figure 5 compares the sum rate of the three algorithmsunder the isolated scenarios in which we set the number ofcellular users varied in the range of [10 30] From Figure 5we observe that by removing some interference-intolerableD2D links significant performance enhancement can be

Social utilityPower interference

0

20

40

60

80

100

120

140

(Bits

(slowast

Hz)

)

12 14 16 18 20 22 24 26 2810Number of cellular users

Figure 4 Comparison of the joint interference

Comparison of sum rate of the system times104

12 14 16 18 20 22 24 26 302810Number of cellular users

1

2

3

4

5

6

7

8

UFMOSRADRA

(Bits

(slowast

Hz)

)

Figure 5 Transmission rate comparison of different resource alloca-tion algorithms with different number of cellular users

achieved when the cellular users are relatively sufficientBut in the situation that cellular users are not sufficientperformances of the two are roughly equalThe reason is thatthe excessive reuse relationships of frequency with the samecellular user will cause unbearable interference to the cellularusers According to our algorithm the D2D link will beremoved automatically in both schemes

Figure 6 compares the sum transmission time of the threealgorithms under the isolated scenarios From Figure 6 wecan observe that in the case that someunnecessaryD2D linkshas been removed the UFM algorithm still provides quite aconsiderable reduction of transmission timeThat is because

10 Wireless Communications and Mobile Computing

Comparison of sum time of the system

UFMOSRADRA

times10minus3

05

1

15

2

25

3

35

4

45

5

55

Sum

tim

e (s

)

12 14 16 18 20 22 24 26 28 3010Number of cellular users

Figure 6 Transmission time comparison of different resource allo-cation algorithms with different number of cellular users

we allowD2Dusers to continue to acquire content via cellularcommunication when D2D communication comes acrosslink interruption So the sum transmission time will not beaffected greatly

For the purpose of evaluating the system performancewhile the number of D2D users varies within a certainrange we set geographical scope as 300m times 300m aroundthe BS and suppose the number of cellular users is 10 Asillustrated in Figures 7 and 8 the variation range of numberof D2D pairs is [5 30] the result demonstrates that ourproposed UFM game always attains the best performancewith the increase of D2D users compared to the OSRAand DRA This is because in the algorithm of DRA orOSRA there exist little coordination measures to restrictD2D pairs to select their resource and it is inevitable toestablish some high-interference links between D2D pairsand cellular users In our proposed algorithm UFM gameeffectively coordinates both social relationship and powerinterference and then decides whether to access the spectrumresource of certain cellular users not in a random way Inthese circumstances we can avoid many high-risk links andattain a better system performance in terms of the evaluationof the sum transmission rate At this point we can summarizethat our proposed scheme precedes the other two schemes ina relatively comprehensive scale

6 Conclusion and Future Work

This paper studies game-theory based social-aware resourceallocation in the D2D communication underlaying cellularnetwork based on the realistic social network By consideringthe power interference and social utility in the physical andsocial domain respectively a game-theoretic based utilityfunction maximization scheme has been proposed Also to

Comparison of sum rate of the system

UFMOSRADRA

times104

0

1

2

3

4

5

6

7

8

10 15 20 25 305Number of D2D pairs

(Bits

(slowast

Hz)

)Figure 7 Transmission rate comparison of different resource alloca-tion algorithms with different number of D2D pairs

Comparison of sum time of the system

UFMOSRADRA

times10minus3

0

1

2

3

4

5

6

7

8

9

Sum

tim

e (s

)

10 15 20 25 305Number of D2D pairs

Figure 8 Transmission time comparison of different resource allo-cation algorithms with different number of D2D pairs

demonstrate the optimality of our proposed scheme thispaper provides evidence for the existence of Nash Equilib-rium theoretically Meanwhile a priority searching operationbased resource allocation scheme is designed to implementthe Nash Equilibrium of the proposed UFM game The pro-posed UFM scheme is numerically shown having superiorityover traditional DRA and OSRA scheme the performancesof sum rate and total transmission time are better thanthe OSRA and DRA algorithm through massive simulation

Wireless Communications and Mobile Computing 11

result suggesting that the proposed scheme is more ideal forjoint social-aware resource scenarios considering the socialcharacteristics Nevertheless some issues related to furthersystem optimization remain to be addressed such as powerallocation of mobile nodes and cluster formation of socialcommunity

Notations

N Set of mobile usersC Set of cellular usersD Set of D2D pairsΦ The UFM game≻119894 Set of utility priority119868119889rarr119888 Interference from 119889th D2D to 119888th cellular signal119868119888rarr119889 Interference from 119888th cellular signal to 119889th D2D119880119889(119883) Social utility of 119889th D2D pairsΓ119889(119883) Utility function of 119889th D2D pairs119909119888119889 Indicator of resource reusing relations119909lowast119889 The Nash Equilibrium of 119889th D2D pair119883119889 Set of all feasible strategies in UFM game

Conflicts of Interest

The authors declare no conflicts of interest related to thepublication of this paper

Acknowledgments

This work is partly supported by the National NaturalScience Foundation of China (61571240 61671253) the Pri-ority Academic Program Development of Jiangsu HigherEducation Institutions the Major Projects of the NaturalScience Foundation of the Jiangsu Higher Education Insti-tutions (16KJA510004) the Open Research Fund of Nationaland Local Joint Engineering Laboratory of RF Integrationand Micro-Assembly Technology Nanjing University ofPosts and Telecommunications (KFJJ20170305) the OpenResearch Fund ofThe State Key Laboratory of Integrated Ser-vices Networks Xidian University (ISN17-04) Jiangsu Spe-cially Appointed Professor Grant (RK002STP16001) Inno-vation and Entrepreneurship of Jiangsu High-Level TalentGrant (CZ0010617002) High-Level Talent Startup Grantof Nanjing University of Posts and Telecommunications(XK0010915026) and ldquo1311 Talent Planrdquo ofNanjingUniversityof Posts and Telecommunications

References

[1] Y Cao T Jiang and C Wang ldquoCooperative device-to-devicecommunications in cellular networksrdquo IEEE Wireless Commu-nications Magazine vol 22 no 3 pp 124ndash129 2015

[2] J Liu N Kato J Ma and N Kadowaki ldquoDevice-to-devicecommunication in LTE-advanced networks a surveyrdquo IEEECommunications Surveys amp Tutorials vol 17 no 4 pp 1923ndash1940 Fourthquarter 2015

[3] A Asadi Q Wang and V Mancuso ldquoA survey on device-to-device communication in cellular networksrdquo IEEE Communi-cations Surveys amp Tutorials vol 16 no 4 pp 1801ndash1819 2014

[4] H Nishiyama M Ito and N Kato ldquoRelay-by-smartphonerealizing multihop device-to-device communicationsrdquo IEEECommunications Magazine vol 52 no 4 pp 56ndash65 2014

[5] M Zhou Y Tang Z Tian L Xie and W Nie ldquoRobust neigh-borhood graphing for semi-supervised indoor localization withlight-loaded location fingerprintingrdquo IEEE Internet of ThingsJournal vol PP no 99 pp 1-1

[6] K Doppler M Rinne C Wijting C B Ribeiro and K HugldquoDevice-to-device communication as an underlay to LTE-advanced networksrdquo IEEE Communications Magazine vol 47no 12 pp 42ndash49 2009

[7] J Liu H Nishiyama N Kato and J Guo ldquoOn the outageprobability of device-to-device-communication-enabled mul-tichannel cellular networks an RSS-threshold-based perspec-tiverdquo IEEE Journal on Selected Areas in Communications vol34 no 1 pp 163ndash175 2016

[8] M Zhou Y Tang W Nie L Xie and X Yang ldquoGrassMAgraph-based semi-supervised manifold alignment for indoorWLAN localizationrdquo IEEE Sensors Journal vol 17 no 21 pp7086ndash7095 2017

[9] J Liu S Zhang N Kato H Ujikawa and K Suzuki ldquoDevice-to-device communications for enhancing quality of experiencein software defined multi-tier LTE-A networksrdquo IEEE Networkvol 29 no 4 pp 46ndash52 2015

[10] C Xu L Song Z Han et al ldquoEfficiency resource allocation fordevice-to-device underlay communication systems a reverseiterative combinatorial auction based approachrdquo IEEE Journalon Selected Areas in Communications vol 31 no 9 pp 348ndash3582013

[11] L Ferdouse W Ejaz K Raahemifar A Anpalagan and MMarkandaier ldquoInterference and throughput aware resourceallocation for multi-class D2D in 5G networksrdquo IET Commu-nications vol 11 no 8 pp 1241ndash1250 2017

[12] T D Hoang L B Le and T Le-Ngoc ldquoCooperative device-to-device communications in cellular networksrdquo IEEE Transac-tions onWireless Communications vol 15 no 10 pp 7099ndash71132016

[13] M Andrews K Kumaran K Ramanan A Stolyar P Whitingand R Vijayakumar ldquoProviding quality of service over a sharedwireless linkrdquo IEEE Communications Magazine vol 39 no 2pp 150ndash154 2001

[14] L Wang L Liu X Cao X Tian and Y Cheng ldquoSociality-aware resource allocation for device-to-device communicationsin cellular networksrdquo IET Communications vol 9 no 3 pp342ndash349 2015

[15] V Shah andA O Fapojuwo ldquoSocially aware resource allocationfor device-to-device communication in downlinkOFDMAnet-worksrdquo in Proceedings of the 2014 IEEE Wireless Communica-tions and Networking Conference WCNC 2014 pp 1673ndash1678Istanbul Turkey April 2014

[16] Y Li T Wu P Hui D Jin and S Chen ldquoSocial-aware D2Dcommunications qualitative insights and quantitative analysisrdquoIEEE Communications Magazine vol 52 no 6 pp 150ndash1582014

[17] FWang L Song Z Han Q Zhao and XWang ldquoJoint schedul-ing and resource allocation for device-to-device underlay com-municationrdquo in Proceedings of the IEEE Wireless Communi-cations and Networking Conference (WCNC rsquo13) pp 134ndash139IEEE Shanghai China April 2013

[18] F Tang Z M Fadlullah N Kato F One and R MiuraldquoAC-POCA anti-coordination game based partially overlap-ping channels assignment in combined UAV and D2D based

12 Wireless Communications and Mobile Computing

networksrdquo IEEE Transactions on Vehicular Technology vol PPno 99 pp 1-1

[19] S M Azimi M H Manshaei and F Hendessi ldquoHybrid cellularand device-to-device communication power control Nashbargaining gamerdquo in Proceedings of the 2014 7th InternationalSymposium on Telecommunications IST 2014 pp 1077ndash1081Tehran Iran September 2014

[20] Z Zhou K Ota M Dong and C Xu ldquoEnergy-efficient match-ing for resource allocation in D2D enabled cellular networksrdquoIEEE Transactions on Vehicular Technology vol 66 no 6 pp5256ndash5268 2017

[21] C Xu C Gao Z Zhou Z Chang and Y Jia ldquoSocial network-based content delivery in device-to-device underlay cellularnetworks using matching theoryrdquo IEEE Access vol 5 pp 924ndash937 2017

[22] X Feng G Sun X Gan et al ldquoCooperative spectrum sharingin cognitive radio networks a distributed matching approachrdquoIEEE Transactions on Communications vol 62 no 8 pp 2651ndash2664 2014

[23] J Zhang ldquoThe interdisciplinary research of big data andwireless channel a cluster-nuclei based channel modelrdquo ChinaCommunications vol 13 no supplement 2 Article ID 7833457pp 14ndash26 2016

[24] S Mumtaz K M Saidul Huq J Rodriguez and V FrascollaldquoEnergy-efficient interference management in LTE-D2D com-municationrdquo IET Signal Processing vol 10 no 3 pp 197ndash2022016

[25] N Kayastha D Niyato P Wang and E Hossain ldquoApplicationsarchitectures and protocol design issues for mobile socialnetworks a surveyrdquo Proceedings of the IEEE vol 99 no 12 pp2130ndash2158 2011

[26] J Zhang L Tian Y Wang and M Liu ldquoSelection transmit-tingmaximum ratio combining for timing synchronization ofMIMO-OFDM systemsrdquo IEEE Transactions on Broadcastingvol 60 no 4 pp 626ndash636 2014

[27] M Zhou Y Wei Z Tian X Yang and L Li ldquoAchieving cost-efficient indoor fingerprint localization on wlan platform ahypothetical test approachrdquo IEEEAccess vol 5 pp 15865ndash158742017

[28] ldquoZacharyrsquoskarateclubrdquohttpsenwikipediaorgwikiZachary27skarate club

[29] D Wu L Zhou and Y Cai ldquoSocial-aware rate based contentsharing mode selection for D2D content sharing scenariosrdquoIEEE Transactions on Multimedia vol 19 no 11 pp 2571ndash25822017

[30] J Huang Y Yin Y Sun Y Zhao C-C Xing and Q DuanldquoGame theoretic resource allocation for multicell D2D commu-nications with incomplete informationrdquo in Proceedings of theIEEE International Conference on Communications ICC 2015pp 3039ndash3044 London UK June 2015

[31] Y Xiao K-C Chen C Yuen and L A DaSilva ldquoSpectrumsharing for device-to-device communications in cellular net-works a game theoretic approachrdquo in Proceedings of the IEEEInternational SymposiumonDynamic SpectrumAccessNetworks(DYSPAN rsquo14) pp 60ndash71 IEEE McLean Va USA April 2014

[32] D Niyato and E Hossain ldquoA game-theoretic approach tocompetitive spectrum sharing in cognitive radio networksrdquo inProceedings of the IEEEWireless Communications and Network-ing Conference (WCNC rsquo07) pp 16ndash20 Kowloon China March2007

[33] D Monderer and L S Shapley ldquoPotential gamesrdquo Games andEconomic Behavior vol 14 no 1 pp 124ndash143 1996

[34] N Nie and C Comaniciu ldquoAdaptive channel allocation spec-trum etiquette for cognitive radio networksrdquo in Proceedingsof the 1st IEEE International Symposium on New Frontiers inDynamic SpectrumAccess Networks (DySPAN rsquo05) pp 269ndash278Baltimore Md USA November 2005

[35] Y Xing C N Mathur M A Haleem R Chandramouli andK P Subbalakshmi ldquoDynamic spectrum access with QoS andinterference temperature constraintsrdquo IEEE Transactions onMobile Computing vol 6 no 4 pp 423ndash433 2007

[36] T Heikkinen ldquoA potential game approach to distributed powercontrol and schedulingrdquo Computer Networks vol 50 no 13 pp2295ndash2311 2006

[37] Y Li D Jin J Yuan and ZHan ldquoCoalitional games for resourceallocation in the device-to-device uplink underlaying cellularnetworksrdquo IEEE Transactions on Wireless Communications vol13 no 7 pp 3965ndash3977 2014

[38] H Ryu and S-H Park ldquoPerformance comparison of resourceallocation schemes for D2D communicationsrdquo in Proceedingsof the 2014 IEEE Wireless Communications and NetworkingConference Workshops WCNCW 2014 pp 266ndash270 IstanbulTurkey April 2014

[39] Y Li S Su and S Chen ldquoSocial-aware resource allocationfor device-to-device communications underlaying cellular net-worksrdquo IEEE Wireless Communications Letters vol 4 no 3 pp293ndash296 2015

[40] D I Laurenson D G M Cruickshank and G J R PoveyldquoComputationally efficient multipath channel simulator for theCOST 207 modelsrdquo in Proceedings of the IEE Colloquium onComputer Modelling of Communication Systems pp 81ndash86London UK May 1994

10 Wireless Communications and Mobile Computing

Comparison of sum time of the system

UFMOSRADRA

times10minus3

05

1

15

2

25

3

35

4

45

5

55

Sum

tim

e (s

)

12 14 16 18 20 22 24 26 28 3010Number of cellular users

Figure 6 Transmission time comparison of different resource allo-cation algorithms with different number of cellular users

we allowD2Dusers to continue to acquire content via cellularcommunication when D2D communication comes acrosslink interruption So the sum transmission time will not beaffected greatly

For the purpose of evaluating the system performancewhile the number of D2D users varies within a certainrange we set geographical scope as 300m times 300m aroundthe BS and suppose the number of cellular users is 10 Asillustrated in Figures 7 and 8 the variation range of numberof D2D pairs is [5 30] the result demonstrates that ourproposed UFM game always attains the best performancewith the increase of D2D users compared to the OSRAand DRA This is because in the algorithm of DRA orOSRA there exist little coordination measures to restrictD2D pairs to select their resource and it is inevitable toestablish some high-interference links between D2D pairsand cellular users In our proposed algorithm UFM gameeffectively coordinates both social relationship and powerinterference and then decides whether to access the spectrumresource of certain cellular users not in a random way Inthese circumstances we can avoid many high-risk links andattain a better system performance in terms of the evaluationof the sum transmission rate At this point we can summarizethat our proposed scheme precedes the other two schemes ina relatively comprehensive scale

6 Conclusion and Future Work

This paper studies game-theory based social-aware resourceallocation in the D2D communication underlaying cellularnetwork based on the realistic social network By consideringthe power interference and social utility in the physical andsocial domain respectively a game-theoretic based utilityfunction maximization scheme has been proposed Also to

Comparison of sum rate of the system

UFMOSRADRA

times104

0

1

2

3

4

5

6

7

8

10 15 20 25 305Number of D2D pairs

(Bits

(slowast

Hz)

)Figure 7 Transmission rate comparison of different resource alloca-tion algorithms with different number of D2D pairs

Comparison of sum time of the system

UFMOSRADRA

times10minus3

0

1

2

3

4

5

6

7

8

9

Sum

tim

e (s

)

10 15 20 25 305Number of D2D pairs

Figure 8 Transmission time comparison of different resource allo-cation algorithms with different number of D2D pairs

demonstrate the optimality of our proposed scheme thispaper provides evidence for the existence of Nash Equilib-rium theoretically Meanwhile a priority searching operationbased resource allocation scheme is designed to implementthe Nash Equilibrium of the proposed UFM game The pro-posed UFM scheme is numerically shown having superiorityover traditional DRA and OSRA scheme the performancesof sum rate and total transmission time are better thanthe OSRA and DRA algorithm through massive simulation

Wireless Communications and Mobile Computing 11

result suggesting that the proposed scheme is more ideal forjoint social-aware resource scenarios considering the socialcharacteristics Nevertheless some issues related to furthersystem optimization remain to be addressed such as powerallocation of mobile nodes and cluster formation of socialcommunity

Notations

N Set of mobile usersC Set of cellular usersD Set of D2D pairsΦ The UFM game≻119894 Set of utility priority119868119889rarr119888 Interference from 119889th D2D to 119888th cellular signal119868119888rarr119889 Interference from 119888th cellular signal to 119889th D2D119880119889(119883) Social utility of 119889th D2D pairsΓ119889(119883) Utility function of 119889th D2D pairs119909119888119889 Indicator of resource reusing relations119909lowast119889 The Nash Equilibrium of 119889th D2D pair119883119889 Set of all feasible strategies in UFM game

Conflicts of Interest

The authors declare no conflicts of interest related to thepublication of this paper

Acknowledgments

This work is partly supported by the National NaturalScience Foundation of China (61571240 61671253) the Pri-ority Academic Program Development of Jiangsu HigherEducation Institutions the Major Projects of the NaturalScience Foundation of the Jiangsu Higher Education Insti-tutions (16KJA510004) the Open Research Fund of Nationaland Local Joint Engineering Laboratory of RF Integrationand Micro-Assembly Technology Nanjing University ofPosts and Telecommunications (KFJJ20170305) the OpenResearch Fund ofThe State Key Laboratory of Integrated Ser-vices Networks Xidian University (ISN17-04) Jiangsu Spe-cially Appointed Professor Grant (RK002STP16001) Inno-vation and Entrepreneurship of Jiangsu High-Level TalentGrant (CZ0010617002) High-Level Talent Startup Grantof Nanjing University of Posts and Telecommunications(XK0010915026) and ldquo1311 Talent Planrdquo ofNanjingUniversityof Posts and Telecommunications

References

[1] Y Cao T Jiang and C Wang ldquoCooperative device-to-devicecommunications in cellular networksrdquo IEEE Wireless Commu-nications Magazine vol 22 no 3 pp 124ndash129 2015

[2] J Liu N Kato J Ma and N Kadowaki ldquoDevice-to-devicecommunication in LTE-advanced networks a surveyrdquo IEEECommunications Surveys amp Tutorials vol 17 no 4 pp 1923ndash1940 Fourthquarter 2015

[3] A Asadi Q Wang and V Mancuso ldquoA survey on device-to-device communication in cellular networksrdquo IEEE Communi-cations Surveys amp Tutorials vol 16 no 4 pp 1801ndash1819 2014

[4] H Nishiyama M Ito and N Kato ldquoRelay-by-smartphonerealizing multihop device-to-device communicationsrdquo IEEECommunications Magazine vol 52 no 4 pp 56ndash65 2014

[5] M Zhou Y Tang Z Tian L Xie and W Nie ldquoRobust neigh-borhood graphing for semi-supervised indoor localization withlight-loaded location fingerprintingrdquo IEEE Internet of ThingsJournal vol PP no 99 pp 1-1

[6] K Doppler M Rinne C Wijting C B Ribeiro and K HugldquoDevice-to-device communication as an underlay to LTE-advanced networksrdquo IEEE Communications Magazine vol 47no 12 pp 42ndash49 2009

[7] J Liu H Nishiyama N Kato and J Guo ldquoOn the outageprobability of device-to-device-communication-enabled mul-tichannel cellular networks an RSS-threshold-based perspec-tiverdquo IEEE Journal on Selected Areas in Communications vol34 no 1 pp 163ndash175 2016

[8] M Zhou Y Tang W Nie L Xie and X Yang ldquoGrassMAgraph-based semi-supervised manifold alignment for indoorWLAN localizationrdquo IEEE Sensors Journal vol 17 no 21 pp7086ndash7095 2017

[9] J Liu S Zhang N Kato H Ujikawa and K Suzuki ldquoDevice-to-device communications for enhancing quality of experiencein software defined multi-tier LTE-A networksrdquo IEEE Networkvol 29 no 4 pp 46ndash52 2015

[10] C Xu L Song Z Han et al ldquoEfficiency resource allocation fordevice-to-device underlay communication systems a reverseiterative combinatorial auction based approachrdquo IEEE Journalon Selected Areas in Communications vol 31 no 9 pp 348ndash3582013

[11] L Ferdouse W Ejaz K Raahemifar A Anpalagan and MMarkandaier ldquoInterference and throughput aware resourceallocation for multi-class D2D in 5G networksrdquo IET Commu-nications vol 11 no 8 pp 1241ndash1250 2017

[12] T D Hoang L B Le and T Le-Ngoc ldquoCooperative device-to-device communications in cellular networksrdquo IEEE Transac-tions onWireless Communications vol 15 no 10 pp 7099ndash71132016

[13] M Andrews K Kumaran K Ramanan A Stolyar P Whitingand R Vijayakumar ldquoProviding quality of service over a sharedwireless linkrdquo IEEE Communications Magazine vol 39 no 2pp 150ndash154 2001

[14] L Wang L Liu X Cao X Tian and Y Cheng ldquoSociality-aware resource allocation for device-to-device communicationsin cellular networksrdquo IET Communications vol 9 no 3 pp342ndash349 2015

[15] V Shah andA O Fapojuwo ldquoSocially aware resource allocationfor device-to-device communication in downlinkOFDMAnet-worksrdquo in Proceedings of the 2014 IEEE Wireless Communica-tions and Networking Conference WCNC 2014 pp 1673ndash1678Istanbul Turkey April 2014

[16] Y Li T Wu P Hui D Jin and S Chen ldquoSocial-aware D2Dcommunications qualitative insights and quantitative analysisrdquoIEEE Communications Magazine vol 52 no 6 pp 150ndash1582014

[17] FWang L Song Z Han Q Zhao and XWang ldquoJoint schedul-ing and resource allocation for device-to-device underlay com-municationrdquo in Proceedings of the IEEE Wireless Communi-cations and Networking Conference (WCNC rsquo13) pp 134ndash139IEEE Shanghai China April 2013

[18] F Tang Z M Fadlullah N Kato F One and R MiuraldquoAC-POCA anti-coordination game based partially overlap-ping channels assignment in combined UAV and D2D based

12 Wireless Communications and Mobile Computing

networksrdquo IEEE Transactions on Vehicular Technology vol PPno 99 pp 1-1

[19] S M Azimi M H Manshaei and F Hendessi ldquoHybrid cellularand device-to-device communication power control Nashbargaining gamerdquo in Proceedings of the 2014 7th InternationalSymposium on Telecommunications IST 2014 pp 1077ndash1081Tehran Iran September 2014

[20] Z Zhou K Ota M Dong and C Xu ldquoEnergy-efficient match-ing for resource allocation in D2D enabled cellular networksrdquoIEEE Transactions on Vehicular Technology vol 66 no 6 pp5256ndash5268 2017

[21] C Xu C Gao Z Zhou Z Chang and Y Jia ldquoSocial network-based content delivery in device-to-device underlay cellularnetworks using matching theoryrdquo IEEE Access vol 5 pp 924ndash937 2017

[22] X Feng G Sun X Gan et al ldquoCooperative spectrum sharingin cognitive radio networks a distributed matching approachrdquoIEEE Transactions on Communications vol 62 no 8 pp 2651ndash2664 2014

[23] J Zhang ldquoThe interdisciplinary research of big data andwireless channel a cluster-nuclei based channel modelrdquo ChinaCommunications vol 13 no supplement 2 Article ID 7833457pp 14ndash26 2016

[24] S Mumtaz K M Saidul Huq J Rodriguez and V FrascollaldquoEnergy-efficient interference management in LTE-D2D com-municationrdquo IET Signal Processing vol 10 no 3 pp 197ndash2022016

[25] N Kayastha D Niyato P Wang and E Hossain ldquoApplicationsarchitectures and protocol design issues for mobile socialnetworks a surveyrdquo Proceedings of the IEEE vol 99 no 12 pp2130ndash2158 2011

[26] J Zhang L Tian Y Wang and M Liu ldquoSelection transmit-tingmaximum ratio combining for timing synchronization ofMIMO-OFDM systemsrdquo IEEE Transactions on Broadcastingvol 60 no 4 pp 626ndash636 2014

[27] M Zhou Y Wei Z Tian X Yang and L Li ldquoAchieving cost-efficient indoor fingerprint localization on wlan platform ahypothetical test approachrdquo IEEEAccess vol 5 pp 15865ndash158742017

[28] ldquoZacharyrsquoskarateclubrdquohttpsenwikipediaorgwikiZachary27skarate club

[29] D Wu L Zhou and Y Cai ldquoSocial-aware rate based contentsharing mode selection for D2D content sharing scenariosrdquoIEEE Transactions on Multimedia vol 19 no 11 pp 2571ndash25822017

[30] J Huang Y Yin Y Sun Y Zhao C-C Xing and Q DuanldquoGame theoretic resource allocation for multicell D2D commu-nications with incomplete informationrdquo in Proceedings of theIEEE International Conference on Communications ICC 2015pp 3039ndash3044 London UK June 2015

[31] Y Xiao K-C Chen C Yuen and L A DaSilva ldquoSpectrumsharing for device-to-device communications in cellular net-works a game theoretic approachrdquo in Proceedings of the IEEEInternational SymposiumonDynamic SpectrumAccessNetworks(DYSPAN rsquo14) pp 60ndash71 IEEE McLean Va USA April 2014

[32] D Niyato and E Hossain ldquoA game-theoretic approach tocompetitive spectrum sharing in cognitive radio networksrdquo inProceedings of the IEEEWireless Communications and Network-ing Conference (WCNC rsquo07) pp 16ndash20 Kowloon China March2007

[33] D Monderer and L S Shapley ldquoPotential gamesrdquo Games andEconomic Behavior vol 14 no 1 pp 124ndash143 1996

[34] N Nie and C Comaniciu ldquoAdaptive channel allocation spec-trum etiquette for cognitive radio networksrdquo in Proceedingsof the 1st IEEE International Symposium on New Frontiers inDynamic SpectrumAccess Networks (DySPAN rsquo05) pp 269ndash278Baltimore Md USA November 2005

[35] Y Xing C N Mathur M A Haleem R Chandramouli andK P Subbalakshmi ldquoDynamic spectrum access with QoS andinterference temperature constraintsrdquo IEEE Transactions onMobile Computing vol 6 no 4 pp 423ndash433 2007

[36] T Heikkinen ldquoA potential game approach to distributed powercontrol and schedulingrdquo Computer Networks vol 50 no 13 pp2295ndash2311 2006

[37] Y Li D Jin J Yuan and ZHan ldquoCoalitional games for resourceallocation in the device-to-device uplink underlaying cellularnetworksrdquo IEEE Transactions on Wireless Communications vol13 no 7 pp 3965ndash3977 2014

[38] H Ryu and S-H Park ldquoPerformance comparison of resourceallocation schemes for D2D communicationsrdquo in Proceedingsof the 2014 IEEE Wireless Communications and NetworkingConference Workshops WCNCW 2014 pp 266ndash270 IstanbulTurkey April 2014

[39] Y Li S Su and S Chen ldquoSocial-aware resource allocationfor device-to-device communications underlaying cellular net-worksrdquo IEEE Wireless Communications Letters vol 4 no 3 pp293ndash296 2015

[40] D I Laurenson D G M Cruickshank and G J R PoveyldquoComputationally efficient multipath channel simulator for theCOST 207 modelsrdquo in Proceedings of the IEE Colloquium onComputer Modelling of Communication Systems pp 81ndash86London UK May 1994

Wireless Communications and Mobile Computing 11

result suggesting that the proposed scheme is more ideal forjoint social-aware resource scenarios considering the socialcharacteristics Nevertheless some issues related to furthersystem optimization remain to be addressed such as powerallocation of mobile nodes and cluster formation of socialcommunity

Notations

N Set of mobile usersC Set of cellular usersD Set of D2D pairsΦ The UFM game≻119894 Set of utility priority119868119889rarr119888 Interference from 119889th D2D to 119888th cellular signal119868119888rarr119889 Interference from 119888th cellular signal to 119889th D2D119880119889(119883) Social utility of 119889th D2D pairsΓ119889(119883) Utility function of 119889th D2D pairs119909119888119889 Indicator of resource reusing relations119909lowast119889 The Nash Equilibrium of 119889th D2D pair119883119889 Set of all feasible strategies in UFM game

Conflicts of Interest

The authors declare no conflicts of interest related to thepublication of this paper

Acknowledgments

This work is partly supported by the National NaturalScience Foundation of China (61571240 61671253) the Pri-ority Academic Program Development of Jiangsu HigherEducation Institutions the Major Projects of the NaturalScience Foundation of the Jiangsu Higher Education Insti-tutions (16KJA510004) the Open Research Fund of Nationaland Local Joint Engineering Laboratory of RF Integrationand Micro-Assembly Technology Nanjing University ofPosts and Telecommunications (KFJJ20170305) the OpenResearch Fund ofThe State Key Laboratory of Integrated Ser-vices Networks Xidian University (ISN17-04) Jiangsu Spe-cially Appointed Professor Grant (RK002STP16001) Inno-vation and Entrepreneurship of Jiangsu High-Level TalentGrant (CZ0010617002) High-Level Talent Startup Grantof Nanjing University of Posts and Telecommunications(XK0010915026) and ldquo1311 Talent Planrdquo ofNanjingUniversityof Posts and Telecommunications

References

[1] Y Cao T Jiang and C Wang ldquoCooperative device-to-devicecommunications in cellular networksrdquo IEEE Wireless Commu-nications Magazine vol 22 no 3 pp 124ndash129 2015

[2] J Liu N Kato J Ma and N Kadowaki ldquoDevice-to-devicecommunication in LTE-advanced networks a surveyrdquo IEEECommunications Surveys amp Tutorials vol 17 no 4 pp 1923ndash1940 Fourthquarter 2015

[3] A Asadi Q Wang and V Mancuso ldquoA survey on device-to-device communication in cellular networksrdquo IEEE Communi-cations Surveys amp Tutorials vol 16 no 4 pp 1801ndash1819 2014

[4] H Nishiyama M Ito and N Kato ldquoRelay-by-smartphonerealizing multihop device-to-device communicationsrdquo IEEECommunications Magazine vol 52 no 4 pp 56ndash65 2014

[5] M Zhou Y Tang Z Tian L Xie and W Nie ldquoRobust neigh-borhood graphing for semi-supervised indoor localization withlight-loaded location fingerprintingrdquo IEEE Internet of ThingsJournal vol PP no 99 pp 1-1

[6] K Doppler M Rinne C Wijting C B Ribeiro and K HugldquoDevice-to-device communication as an underlay to LTE-advanced networksrdquo IEEE Communications Magazine vol 47no 12 pp 42ndash49 2009

[7] J Liu H Nishiyama N Kato and J Guo ldquoOn the outageprobability of device-to-device-communication-enabled mul-tichannel cellular networks an RSS-threshold-based perspec-tiverdquo IEEE Journal on Selected Areas in Communications vol34 no 1 pp 163ndash175 2016

[8] M Zhou Y Tang W Nie L Xie and X Yang ldquoGrassMAgraph-based semi-supervised manifold alignment for indoorWLAN localizationrdquo IEEE Sensors Journal vol 17 no 21 pp7086ndash7095 2017

[9] J Liu S Zhang N Kato H Ujikawa and K Suzuki ldquoDevice-to-device communications for enhancing quality of experiencein software defined multi-tier LTE-A networksrdquo IEEE Networkvol 29 no 4 pp 46ndash52 2015

[10] C Xu L Song Z Han et al ldquoEfficiency resource allocation fordevice-to-device underlay communication systems a reverseiterative combinatorial auction based approachrdquo IEEE Journalon Selected Areas in Communications vol 31 no 9 pp 348ndash3582013

[11] L Ferdouse W Ejaz K Raahemifar A Anpalagan and MMarkandaier ldquoInterference and throughput aware resourceallocation for multi-class D2D in 5G networksrdquo IET Commu-nications vol 11 no 8 pp 1241ndash1250 2017

[12] T D Hoang L B Le and T Le-Ngoc ldquoCooperative device-to-device communications in cellular networksrdquo IEEE Transac-tions onWireless Communications vol 15 no 10 pp 7099ndash71132016

[13] M Andrews K Kumaran K Ramanan A Stolyar P Whitingand R Vijayakumar ldquoProviding quality of service over a sharedwireless linkrdquo IEEE Communications Magazine vol 39 no 2pp 150ndash154 2001

[14] L Wang L Liu X Cao X Tian and Y Cheng ldquoSociality-aware resource allocation for device-to-device communicationsin cellular networksrdquo IET Communications vol 9 no 3 pp342ndash349 2015

[15] V Shah andA O Fapojuwo ldquoSocially aware resource allocationfor device-to-device communication in downlinkOFDMAnet-worksrdquo in Proceedings of the 2014 IEEE Wireless Communica-tions and Networking Conference WCNC 2014 pp 1673ndash1678Istanbul Turkey April 2014

[16] Y Li T Wu P Hui D Jin and S Chen ldquoSocial-aware D2Dcommunications qualitative insights and quantitative analysisrdquoIEEE Communications Magazine vol 52 no 6 pp 150ndash1582014

[17] FWang L Song Z Han Q Zhao and XWang ldquoJoint schedul-ing and resource allocation for device-to-device underlay com-municationrdquo in Proceedings of the IEEE Wireless Communi-cations and Networking Conference (WCNC rsquo13) pp 134ndash139IEEE Shanghai China April 2013

[18] F Tang Z M Fadlullah N Kato F One and R MiuraldquoAC-POCA anti-coordination game based partially overlap-ping channels assignment in combined UAV and D2D based

12 Wireless Communications and Mobile Computing

networksrdquo IEEE Transactions on Vehicular Technology vol PPno 99 pp 1-1

[19] S M Azimi M H Manshaei and F Hendessi ldquoHybrid cellularand device-to-device communication power control Nashbargaining gamerdquo in Proceedings of the 2014 7th InternationalSymposium on Telecommunications IST 2014 pp 1077ndash1081Tehran Iran September 2014

[20] Z Zhou K Ota M Dong and C Xu ldquoEnergy-efficient match-ing for resource allocation in D2D enabled cellular networksrdquoIEEE Transactions on Vehicular Technology vol 66 no 6 pp5256ndash5268 2017

[21] C Xu C Gao Z Zhou Z Chang and Y Jia ldquoSocial network-based content delivery in device-to-device underlay cellularnetworks using matching theoryrdquo IEEE Access vol 5 pp 924ndash937 2017

[22] X Feng G Sun X Gan et al ldquoCooperative spectrum sharingin cognitive radio networks a distributed matching approachrdquoIEEE Transactions on Communications vol 62 no 8 pp 2651ndash2664 2014

[23] J Zhang ldquoThe interdisciplinary research of big data andwireless channel a cluster-nuclei based channel modelrdquo ChinaCommunications vol 13 no supplement 2 Article ID 7833457pp 14ndash26 2016

[24] S Mumtaz K M Saidul Huq J Rodriguez and V FrascollaldquoEnergy-efficient interference management in LTE-D2D com-municationrdquo IET Signal Processing vol 10 no 3 pp 197ndash2022016

[25] N Kayastha D Niyato P Wang and E Hossain ldquoApplicationsarchitectures and protocol design issues for mobile socialnetworks a surveyrdquo Proceedings of the IEEE vol 99 no 12 pp2130ndash2158 2011

[26] J Zhang L Tian Y Wang and M Liu ldquoSelection transmit-tingmaximum ratio combining for timing synchronization ofMIMO-OFDM systemsrdquo IEEE Transactions on Broadcastingvol 60 no 4 pp 626ndash636 2014

[27] M Zhou Y Wei Z Tian X Yang and L Li ldquoAchieving cost-efficient indoor fingerprint localization on wlan platform ahypothetical test approachrdquo IEEEAccess vol 5 pp 15865ndash158742017

[28] ldquoZacharyrsquoskarateclubrdquohttpsenwikipediaorgwikiZachary27skarate club

[29] D Wu L Zhou and Y Cai ldquoSocial-aware rate based contentsharing mode selection for D2D content sharing scenariosrdquoIEEE Transactions on Multimedia vol 19 no 11 pp 2571ndash25822017

[30] J Huang Y Yin Y Sun Y Zhao C-C Xing and Q DuanldquoGame theoretic resource allocation for multicell D2D commu-nications with incomplete informationrdquo in Proceedings of theIEEE International Conference on Communications ICC 2015pp 3039ndash3044 London UK June 2015

[31] Y Xiao K-C Chen C Yuen and L A DaSilva ldquoSpectrumsharing for device-to-device communications in cellular net-works a game theoretic approachrdquo in Proceedings of the IEEEInternational SymposiumonDynamic SpectrumAccessNetworks(DYSPAN rsquo14) pp 60ndash71 IEEE McLean Va USA April 2014

[32] D Niyato and E Hossain ldquoA game-theoretic approach tocompetitive spectrum sharing in cognitive radio networksrdquo inProceedings of the IEEEWireless Communications and Network-ing Conference (WCNC rsquo07) pp 16ndash20 Kowloon China March2007

[33] D Monderer and L S Shapley ldquoPotential gamesrdquo Games andEconomic Behavior vol 14 no 1 pp 124ndash143 1996

[34] N Nie and C Comaniciu ldquoAdaptive channel allocation spec-trum etiquette for cognitive radio networksrdquo in Proceedingsof the 1st IEEE International Symposium on New Frontiers inDynamic SpectrumAccess Networks (DySPAN rsquo05) pp 269ndash278Baltimore Md USA November 2005

[35] Y Xing C N Mathur M A Haleem R Chandramouli andK P Subbalakshmi ldquoDynamic spectrum access with QoS andinterference temperature constraintsrdquo IEEE Transactions onMobile Computing vol 6 no 4 pp 423ndash433 2007

[36] T Heikkinen ldquoA potential game approach to distributed powercontrol and schedulingrdquo Computer Networks vol 50 no 13 pp2295ndash2311 2006

[37] Y Li D Jin J Yuan and ZHan ldquoCoalitional games for resourceallocation in the device-to-device uplink underlaying cellularnetworksrdquo IEEE Transactions on Wireless Communications vol13 no 7 pp 3965ndash3977 2014

[38] H Ryu and S-H Park ldquoPerformance comparison of resourceallocation schemes for D2D communicationsrdquo in Proceedingsof the 2014 IEEE Wireless Communications and NetworkingConference Workshops WCNCW 2014 pp 266ndash270 IstanbulTurkey April 2014

[39] Y Li S Su and S Chen ldquoSocial-aware resource allocationfor device-to-device communications underlaying cellular net-worksrdquo IEEE Wireless Communications Letters vol 4 no 3 pp293ndash296 2015

[40] D I Laurenson D G M Cruickshank and G J R PoveyldquoComputationally efficient multipath channel simulator for theCOST 207 modelsrdquo in Proceedings of the IEE Colloquium onComputer Modelling of Communication Systems pp 81ndash86London UK May 1994

12 Wireless Communications and Mobile Computing

networksrdquo IEEE Transactions on Vehicular Technology vol PPno 99 pp 1-1

[19] S M Azimi M H Manshaei and F Hendessi ldquoHybrid cellularand device-to-device communication power control Nashbargaining gamerdquo in Proceedings of the 2014 7th InternationalSymposium on Telecommunications IST 2014 pp 1077ndash1081Tehran Iran September 2014

[20] Z Zhou K Ota M Dong and C Xu ldquoEnergy-efficient match-ing for resource allocation in D2D enabled cellular networksrdquoIEEE Transactions on Vehicular Technology vol 66 no 6 pp5256ndash5268 2017

[21] C Xu C Gao Z Zhou Z Chang and Y Jia ldquoSocial network-based content delivery in device-to-device underlay cellularnetworks using matching theoryrdquo IEEE Access vol 5 pp 924ndash937 2017

[22] X Feng G Sun X Gan et al ldquoCooperative spectrum sharingin cognitive radio networks a distributed matching approachrdquoIEEE Transactions on Communications vol 62 no 8 pp 2651ndash2664 2014

[23] J Zhang ldquoThe interdisciplinary research of big data andwireless channel a cluster-nuclei based channel modelrdquo ChinaCommunications vol 13 no supplement 2 Article ID 7833457pp 14ndash26 2016

[24] S Mumtaz K M Saidul Huq J Rodriguez and V FrascollaldquoEnergy-efficient interference management in LTE-D2D com-municationrdquo IET Signal Processing vol 10 no 3 pp 197ndash2022016

[25] N Kayastha D Niyato P Wang and E Hossain ldquoApplicationsarchitectures and protocol design issues for mobile socialnetworks a surveyrdquo Proceedings of the IEEE vol 99 no 12 pp2130ndash2158 2011

[26] J Zhang L Tian Y Wang and M Liu ldquoSelection transmit-tingmaximum ratio combining for timing synchronization ofMIMO-OFDM systemsrdquo IEEE Transactions on Broadcastingvol 60 no 4 pp 626ndash636 2014

[27] M Zhou Y Wei Z Tian X Yang and L Li ldquoAchieving cost-efficient indoor fingerprint localization on wlan platform ahypothetical test approachrdquo IEEEAccess vol 5 pp 15865ndash158742017

[28] ldquoZacharyrsquoskarateclubrdquohttpsenwikipediaorgwikiZachary27skarate club

[29] D Wu L Zhou and Y Cai ldquoSocial-aware rate based contentsharing mode selection for D2D content sharing scenariosrdquoIEEE Transactions on Multimedia vol 19 no 11 pp 2571ndash25822017

[30] J Huang Y Yin Y Sun Y Zhao C-C Xing and Q DuanldquoGame theoretic resource allocation for multicell D2D commu-nications with incomplete informationrdquo in Proceedings of theIEEE International Conference on Communications ICC 2015pp 3039ndash3044 London UK June 2015

[31] Y Xiao K-C Chen C Yuen and L A DaSilva ldquoSpectrumsharing for device-to-device communications in cellular net-works a game theoretic approachrdquo in Proceedings of the IEEEInternational SymposiumonDynamic SpectrumAccessNetworks(DYSPAN rsquo14) pp 60ndash71 IEEE McLean Va USA April 2014

[32] D Niyato and E Hossain ldquoA game-theoretic approach tocompetitive spectrum sharing in cognitive radio networksrdquo inProceedings of the IEEEWireless Communications and Network-ing Conference (WCNC rsquo07) pp 16ndash20 Kowloon China March2007

[33] D Monderer and L S Shapley ldquoPotential gamesrdquo Games andEconomic Behavior vol 14 no 1 pp 124ndash143 1996

[34] N Nie and C Comaniciu ldquoAdaptive channel allocation spec-trum etiquette for cognitive radio networksrdquo in Proceedingsof the 1st IEEE International Symposium on New Frontiers inDynamic SpectrumAccess Networks (DySPAN rsquo05) pp 269ndash278Baltimore Md USA November 2005

[35] Y Xing C N Mathur M A Haleem R Chandramouli andK P Subbalakshmi ldquoDynamic spectrum access with QoS andinterference temperature constraintsrdquo IEEE Transactions onMobile Computing vol 6 no 4 pp 423ndash433 2007

[36] T Heikkinen ldquoA potential game approach to distributed powercontrol and schedulingrdquo Computer Networks vol 50 no 13 pp2295ndash2311 2006

[37] Y Li D Jin J Yuan and ZHan ldquoCoalitional games for resourceallocation in the device-to-device uplink underlaying cellularnetworksrdquo IEEE Transactions on Wireless Communications vol13 no 7 pp 3965ndash3977 2014

[38] H Ryu and S-H Park ldquoPerformance comparison of resourceallocation schemes for D2D communicationsrdquo in Proceedingsof the 2014 IEEE Wireless Communications and NetworkingConference Workshops WCNCW 2014 pp 266ndash270 IstanbulTurkey April 2014

[39] Y Li S Su and S Chen ldquoSocial-aware resource allocationfor device-to-device communications underlaying cellular net-worksrdquo IEEE Wireless Communications Letters vol 4 no 3 pp293ndash296 2015

[40] D I Laurenson D G M Cruickshank and G J R PoveyldquoComputationally efficient multipath channel simulator for theCOST 207 modelsrdquo in Proceedings of the IEE Colloquium onComputer Modelling of Communication Systems pp 81ndash86London UK May 1994

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