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Context-Aware Small Cell Networks: How Social MetricsImprove Wireless Resource Allocation

Omid Semiari1, Walid Saad1, Stefan Valentin2, Mehdi Bennis3, and H. Vincent Poor41Wireless@VT, Bradley Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, VA, USA,

Email: osemiari@vt.edu,walids@vt.edu2Huawei Technologies, Paris, France, Email: stefanv@ieee.org

3Center for Wireless Communications-CWC, University of Oulu, Finland, Email: bennis@ee.oulu.fi4Electrical Engineering Department, Princeton University, Princeton, NJ, USA, Email: poor@princeton.edu

Abstract—In this paper, a novel approach for optimizing andmanaging resource allocation in wireless small cell networks(SCNs) with device-to-device (D2D) communication is proposed.The proposed approach allows to jointly exploit both the wirelessand social context of wireless users for optimizing the overallallocation of resources and improving traffic offload in SCNs.This context-aware resource allocation problem is formulated asa matching game in which user equipments (UEs) and resourceblocks (RBs) rank one another, based on utility functions thatcapture both wireless and social metrics. Due to social inter-relations, this game is shown to belong to a class of matchinggames with peer effects. To solve this game, a novel, self-organizing algorithm is proposed, using which UEs and RBscan interact to decide on their desired allocation. The proposedalgorithm is then proven to converge to a two-sided stablematching between UEs and RBs. The properties of the resultingstable outcome are then studied and assessed. Simulation resultsusing real social data show that clustering of socially connectedusers allows to offload a substantially larger amount of trafficthan the conventional context-unaware approach. These resultsshow that exploiting social context has high practical relevancein saving resources on the wireless links and on the backhaul.

Index Terms— wireless small cell networks; matching games;heterogeneous networks; game theory.

I. I NTRODUCTION

The introduction of smartphones and tablets has led to theproliferation of bandwidth-intensive wireless services,suchas multimedia streaming and social networking, that havestrained the capacity of present-day wireless communicationnetworks [1]. This increasing trend led to the emergence ofwireless small cell networks (SCNs) as a promising solutionto meet the quality-of-service (QoS) requirements of suchemerging wireless services [2]–[5]. In SCNs, the main ideais to massively deploy small cell base stations (SCBSs) withrelatively low transmit power, overlaid on existing cellularinfrastructure. Small cells allow to increase the capacityandcoverage of a wireless network by bringing the user equip-ments (UEs) closer to their serving base stations. Nonetheless,

This research was supported by the U.S. National Science Foundation underGrants CNS-1460316 and CNS-1513697.

the deployment of small cells introduces new challenges interms of interference management, resource allocation, andnetwork modeling. These challenges stem from many keyfeatures of SCNs such as the unplanned SCBS distribution,limited coverage, dense SCBS deployment, and limited back-haul capacities, among others [2]–[9].

The authors in [6] proposed a control-based scheduler fortraffic management at small cells. In [7], an optimizationproblem is solved at each cell to perform resource allo-cation while taking into account cell range expansion andoffloading metrics. Most of these existing approaches mainlyadopt centralized methods for resource allocation [6], [7].Although interesting, such centralized approaches have severaldrawbacks since they assume the presence of a centralizedcontroller for the small cells, depend on SCBSs cooperation,and require macro base station (MBS) coordination. However,resource allocation in SCNs needs to be decentralized, self-organizing, and computationally efficient; specifically whenthe number of small cells increases. In this regard, game theoryhas emerged as a popular tool to realize distributed approachesfor wireless networks [8]–[13]. In [8], the authors proposeda distributed resource allocation in the uplink of a two tiernetwork, by posing the problem as a matching game. Theysolved the game using the Hungarian algorithm. In [9], theresource allocation in SCNs is formulated as an evolutionarygame. In [10], the theory of one-to-one and many-to-onematching markets is extended for the resource allocation inwireless networks. In [11], the authors used matching theoryto perform distributed scheduling at the downlink of a MIMO-OFDMA system. Other works that apply matching in somelimited wireless settings are found in [12] and [13]. In fact,prior works do not handle the challenges of SCNs that areunderlaid with device-to-device (D2D) connections and inwhich there is a need not only to manage interference, butto also account for redundant transmissions by exploiting theability of D2D to provide popular content caching. The bodyof work in [8]–[13] focuses on resource allocation while onlyaccounting for classical physical layer metrics such as the

SINR and is restricted to networks without D2D. In addition,itis based on the classical deferred acceptance algorithm whichcannot be applied for scenarios with peer effects such as inour case. Context-aware resource allocation, as done in ourpaper, is a new design paradigm that can help to boost theperformance of small cell networks and to exploit D2D forpopular content distribution.

Along with the use of SCNs for improving network per-formance, D2D communications has recently emerged as aninteresting approach to provide proximity services to usersof an SCN, thus assisting in further offload of the cellularsystem’s traffic [14]–[18]. Indeed, due to the evolution of nu-merous data centric applications, it is very likely that devicesin proximity of one another tend to interact directly overthe wireless spectrum. Communication of such neighboringdevices via the infrastructure of the SCN (i.e., via SCBSs) isneither spectrum nor power efficient [14]. In addition, SCNsare envisioned to have a capacity-limited backhaul [4] and,thus, the use of underlaid D2D can help offload traffic fromthe SCNs’ backhaul. In this respect, D2D communication overthe cellular spectrum is viewed as an attractive candidate tohandle these scenarios [17]–[19]. D2D over cellular networksis significantly different from D2D over unlicensed bandssuch as WiFi or traditional short-range D2D via Zigbee andBluetooth. Indeed, D2D over cellular allows longer rangesand higher QoS, while also requiring to properly manageinterference with cellular transmissions [15], [16], and [19].Some of the main challenges associated with deploying theD2D technology include introducing proximity services thatleverage D2D, managing the wireless resources in D2D de-ployments, and protecting such low power and vulnerablecommunication links from interference [14]–[17].

In addition to the conventional physical layer metrics tooptimize the SCN’s performance, modern UEs can offer aversatile range of information from higher network layers thatcould help to reap the prospective gains of D2D deploymentsin SCNs. Such additional information, referred to ascontextinformation, may include the data extracted from online socialnetworks [20]–[23], the history of a user’s throughput [24],prediction of a user’s location [25], or the delay-throughputtolerance of the applications [26]. The work in [20] developsan analytical model for the epidemic information spreadingamong mobile users of an ad hoc network. In [21], the resourceallocation in wireless LAN is defined as an optimizationproblem, taking the notion of social distance into account.The authors in [22] and [23] extend the work in [21] byintroducing new utility functions which again account forthe social distance of users, extracted from the social graph.Existing context-aware works [20]–[26] are mostly tailoredto macrocell networks, are based on centralized approaches,and do not address the SCN or D2D over SCN challenges.In addition, although the use of social networks has been

demonstrated to be useful to improve wireless systems, mostexisting works such as [20]–[23] are based solely on the phys-ical aspects of the social network, e.g., centrality measures.Such notion of social context is insufficient to capture commoninterests. For example, the large number of friends of a userin a social network does not necessarily mean that such a useris influential enough to require more bandwidth. In contrast,there is a need to adopt a more holistic view for the socialcontext by basing it on other social dimensions such as theactual interactions between users. Here, we note that, althoughanother body of works such as [27]–[30] has further exploredthe use of social metrics in networking applications, suchworks are not adequate for deployment in wireless cellularsystems such as SCNs with D2D as they do not deal withissues such as interference and network offload.

The main contribution of this paper is to propose a novel,self-organizing, context-aware framework for optimizingre-source allocation in D2D-enabled SCNs. We formulate theproblem as a two-sided one-to-one matching game in whicheach UE is assigned to one resource block (RB). In this game,the UEs and SCBS-controlled RBs rank one another basedon utilities that capture the social context of the users aswell as the wireless physical layer metrics. The social contextincludes the information inferred from the social networkprofiles of the wireless users. This information is mainly basedon the similarities between users’ interests, activities,and theirinteractions such as tagging or wall posting. The proposedscheme allows to exploit the fact that users who are stronglyconnected in a social network are likely to request similartype of data over the physical wireless network. We show thatthe proposed game is a matching game withpeer effectsinwhich the strategy of each player is affected by the decisionsof its peers. This is in contrast to most existing works onmatching theory for wireless networks [8]–[13] that deal withconventional matching games in which there is no peer effect.To solve this context-aware resource management game, wepropose a novel, self-organizing algorithm that allows to finda stable matching between users and RBs. We show that ourproposed algorithm allows the SCBSs and UEs to interact andconverge to a stable matching with manageable complexity.Simulation results using real traces are used to analyze theperformance of the proposed approach.

The rest of the paper is organized as follows. SectionII describes the system model. Section III introduces themodeling of social context in wireless D2D-enabled SCNs.Section IV defines the problem as the matching game andSection V presents the proposed algorithm. Simulation resultsare analyzed in Section VI and conclusions are drawn inSection VII.

Fig. 1. Physical model for interference management in a D2D enabled SCN.

II. SYSTEM MODEL

Consider the downlink of an OFDMA small cell networkwith a setL of L SCBSs randomly distributed within thenetwork. The total bandwidthB is divided intoN RBs in thesetN and there are a total ofM active users withM being theset of all users. We consider a co-channel network deploymentin which the total bandwidth is shared between all smallcells. In this network, we assume that users can communicatedirectly via D2D communication links within the cellular band.Such D2D communications enhance the indoor coverage andhelps to offload the small cell traffic. In our model, some usersare chosen as a serving user equipment (SUE) that are allowedto serve other UEs via D2D communication. LetMs be theset ofMs SUEs andMu be the set ofMu non-serving UEs.Thus,M = Ms ∪Mu andMs ∩Mu = ∅. The criterion forSUE selection is discussed further in Section III-A. Moreover,let K = Ms ∪L be the joint set of all SCBSs and SUEs with|K| = Ms + L. Hereinafter, we use the term “serving node(SN)” to refer to either an SCBS or an SUE. Moreover, werefer to cellular links and D2D links, respectively, as SCBSsto UEs and SUEs to UEs links.

For resource allocation in D2D-enabled SCNs, one simpleapproach is to allow the SCBSs to share all the RBs with theSUEs. However, in such a scheme, the D2D communicationlinks will be dominated by the interference from the SCBSs.To overcome this problem, we propose to divide the spectrumin such a way that no mutual interference occurs betweenSCBSs and SUEs. Consequently, the sources of interferenceand the SINR relations will differ at each RBn ∈ N ,depending on whether RBn is reused by an SCBS or an SUE.In this model, D2D links, SCBS to SUE links, and cellularlinks are separated in the frequency domain. Hence, the setof resource blocksN , is divided into non-overlapping sets,namely,N1, N2, and N3 as shown in Fig. 1.N1 and N2

represent the set ofN1 andN2 RBs dedicated to the direct

links from SCBSs to UEs and SCBSs to SUEs, respectively. Inaddition,N3 is the set ofN3 dedicated RBs that are shared byall SUEs for D2D transmission. We lethknm be the channelstate of subcarriern ∈ N in the transmission from SNk touserm. In this model, SCBSs may interfere with one another,since they share subbandsN1 andN2. However, SCBSs willnot interfere with D2D links as SUEs and SCBSs transmiton two different orthogonal bands. This encourages UEs tobe served via D2D links which can improve the offloadingcapabilities of the network.

The achievable rate for the transmission between an SNk ∈ K and a userm ∈ M over RBn ∈ Ni is

Φknm(γ(i)knm) = wn log(1 + γ

(i)knm), (1)

wherewn is the bandwidth of RBn andγ(i)knm is the instan-

taneous SINR for userm from SN k when using RBn. Thesuperscripti ∈ 1, 2, 3 indicates the set of RBs to which RBn belongs. Fori ∈ 1, 2 we have

γ(i)lnm =

plnhlnm∑

l′∈L,l′ 6=l pl′nhl′nm + σ2, (2)

where pln denotes the transmit power of SCBSl over RBn. Moreover,m corresponds to an arbitrary UE and SUE,respectively, fori = 1 and i = 2. For the transmissions overN3, the SINR is given by:

γ(3)msnm

=pmsnhmsnm

∑

m′

s∈Ms,m′

s 6=mspm′

snhm′

snm+ σ2

, (3)

wherepmsn denotes the transmit power of SUEms over RBn andσ2 is the variance of the receiver’s Gaussian noise.

Given this model, one important problem is how to allocatethe bandwidth resources to the wireless users. As discussedinSection I, beyond power allocation and interference manage-ment techniques, we can boost the capacity of wireless net-works by making the network better informed of its environ-ment. Recent studies [27], [29], [30] have shown that friends insocial networks, e.g. Facebook, have many common interestsand activities that define their so-calledsocial tie. Such socialties’ strength could properly show how frequently people inter-act with their friends, share popular videos or pictures, orinviteone another to activities of common interest. Therefore, suchinterrelationships can explain how often socially connectedpeople request common contents [17], [20]–[23]. Observingsuch behavior is interesting for SCN resource allocation, sinceit motivates the possibility of serving a user directly by otherusers with shared interests over D2D communication, insteadof requesting the content from SCBSs. Therefore, such schemeallows the network to decrease redundant transmissions andoffload this traffic from the backhaul network. In fact, weare investigating acontent distributionmodel that allows thenetwork to use certain devices as SUEs, to serve as “cachingpoints” whose storage can be used to cache popular contentvia overlay D2D. Therefore, our model is not a classicalcooperative communication or relaying system.

Fig. 2. A schematic of a D2D enabled SCN which exploits the contextinformation underneath the social network. The network in the right handside shows the Facebook friendship graph of user 4.

For example, consider the scenario shown in Fig. 2, wherea group of friends, e.g. students in a dorm or coworkers ofa company spend a significant amount of time each day inneighboring rooms. Beyond this physical closeness, there is asocial relationship between users at a higher layer that canunderline their common interests in various topics such assports or media. Since these users might have mutual interests,they are likely to be interested in common contents. Hence,although the formation of social ties is an application orientedmetric, however, it strongly impacts how they access theirwireless services, thus, directly impacting resource allocation.One illustrative example is the case in which one user, sayuser1, shares a certain video on the social network, which,in turn, will be viewed by some of its friends, due to themutual interests. Hence, those users could be served usingdata that may be cached at UE1, directly through the D2Dlink. Clearly, by knowing the social ties between the users,the network will, on the one hand, be able to avoid multipletransmission of the same data and, on the other hand, will beable to allocate additional resources to the users outside thesocial group. In this work, we use the termtraffic offload torefer to the reduction of redundant transmissions from SCBSsto UEs that can be obtained by exploiting D2D links betweenSUEs and UEs. Such traffic offload will alleviate the traffic onthe backhaul-constrained SCBSs while also allowing to serviceadditional users over the SCBSs’ RBs [18].

With this in mind, we propose to exploit, jointly withconventional channel information, the users’ social interrela-tionships in order to optimize resource allocation in D2D-enabled SCNs. The resource allocation can be posed as anoptimization problem in which RBs are assigned to UEs(ξ⋆ : N → M) such that the overall sum utility of the networkis maximized. Taking the social context into account, we canformulate the problem as

maximizeξ⋆

∑

k∈K

∑

n∈N

∑

m∈M

ξknmΩm(Φknm(γknm),Z), (4)

subject to∑

k∈K

∑

m∈M

ξknm ≤ 1, ∀n ∈ N , (5)

∑

k∈K

∑

n∈N

ξknm ≤ 1, ∀m ∈ M, (6)

ξknm ∈ 0, 1, (7)

where Z is a matrix that captures the social tie strengthbetween every user pair and will be formally defined in SectionIII. Moreover, Ωm(.) is the utility of userm which is afunction of achievable rates and social ties. If userm isconnected to an SCBS,Ωm(.) simply represents the achievablerate of the link. If userm is connected to an SUE,Ωm(.) is thesum of the link’s achievable rate, plus a term that determineshow much userm is socially connected to the cluster. Theoptimization problem in (4) aims to maximize the sum utilityof all users. The constraint in (5) ensures that each RB isassigned to only one user, and the constraint in (6) ensuresthat each user is assigned to one RB.

Due to the unplanned deployment of backhaul-constrainedSCBSs and the limited possibilities for SCBS coordination [4],our goal is to develop aself-organizing, decentralizedresourceallocation solution. This decentralized solution for the problemin (4)-(7) will be addressed in depth in Section IV. Beforedoing so, we formally define the social tie strength in the nextSection and explain how such context information could beextracted from the social networks.

III. M ODELING RELATIONSHIP STRENGTH IN SOCIAL

NETWORKS

A. Social Context in the Proposed SCN Model and SUEChoice

Let zij denote the social tie strength between two UEsiand j. We define the social tie as a metric that determineshow strong the relationship of two users is as inferred fromthe social network. This metric should then be incorporatedinto a proper utility function to be used in the context-awareresource allocation problem in (4). In order to benefit fromcaching at the edge, popular contents must be cached at UEsthat are chosen to serve as SUEs. Here, we assume that auser is chosen as SUEms if its total social influenceIms

=∑

m∈M,m 6=mszmsm is larger than other users1. Ims

can beinterpreted as a weighted degree ofms in a social networkgraph where the edge weights are determined by thez term.We note that network operators need to provide some form ofreward and incentive mechanisms to their users so that theyact as SUEs. We can now define the notion of asocial cluster

1Without loss of generality, other approaches for selectingSUE can alsobe accommodated.

Definition 1. A social cluster (SC)is defined as a set,Cms,

composed of an SUEms and all the UEs which are connectedto ms via D2D links.

We use the termsocial here to emphasize that the socialrelationships of the users affect the formation of the cluster, aswill be elaborated in Section IV. Due to the social effects, wecan make the following observations: 1) a UEm is encouragedby its friends to join the same SC in order to form sociallystronger clusters, 2) SUEs with larger clusters (more assignedUEs) must get higher quality links from theN2 set, since thequality of the link from SCBS to SUE indirectly affects thequality of the direct D2D links, and 3) to improve offloading,SCBSs have an incentive to encourage UEs, with at least onefriend as SUE, to use D2D links.

Suchpeer effectsmotivate the need for an advanced modelthat can accurately define the strength of ties,zij . In [31], agraphical model is proposed to learn the strength of ties amonga set of Facebook users which is suitable for our model. Inparticular, based on the homophily property, it is observedthatthe stronger the tie, the higher the similarity [30]. Therefore,if two users have more attribute similarities in their profiles,e.g., the common groups that two UEs are members of, orthe geographical locations, then their relationship is stronger.The relationship strength can be modeled as ahidden effectofprofile similarities and inferred via statistical learningconcepts[29], [30]. In the following, we review a learning model basedon [31] that allows to understand how we can find the strengthof ties, z from a given social network dataset.

B. Learning Model

We note that the strength of the social relationship betweentwo user impacts the nature and frequency of online inter-actions between a pair of users. Moreover, users naturallyinvest more of their resources (e.g., time) to build and maintainthe relationships that they deem more important [31]. Hence,as the relationship becomes stronger, it is more likely thatacertain type of interaction will take place between the pairofusers. In this way, we can model the relationship strength asthe hidden cause of user interactions.

Formally, letxi andxj be, respectively, the attribute vectorsof two UEs i and j. An attribute vector is a vector thatincludes some of a user’s social profile information, such astheuser’s age, political view, major, or the level of education. Therelationship strength betweeni andj can be defined as a latentvariablezij which will be inferred for every pair of users. Inaddition, letyij be the vector of interactions whose elementsyij,f , f = 1, ..., F are theF different interactions consideredbetween i and j. Essentially, the interactions include theactivities of UEi that involves UEj, e.g., tagging one anotheror posting on each others’ walls. This variable is assumedto be binary such thatyij,f = 1 if this interaction hasoccurred between UEi and UE j and yij,f = 0, otherwise.

Fig. 3. The graphical representation of the social tie strength model [31].

Furthermore, the vectoreij,f = [e1ij,f , ..., eϑij,f ]

T is definedfor each interactionf occurred between usersi and j. Thisvector can show how much userj is important for userito interact. For instance, if useri has tagged userj andassumingϑ = 1, then e1ij,f can be the overall number ofusers that useri usually tags. Thus, smallere1ij,f impliesstronger tie between usersi and j. This social model canbe represented by a directed graphical model as shown inFig. 3. In this model,zij summarizes the profile similaritiesand interactions between usersi and j. However, it is notobservable from users’ profiles. Hence, we need to estimatezij so as to maximize the overall observed data likelihood. Tothis end, the joint distribution ofz andy can be representedusing general factorization:

P (zij ,yij |xi,xj) = P (zij |xi,xj)F∏

f=1

P (yij,f |zij). (8)

In order to infer the latent variables, we need to adopt theconditional probability of the relationship strength given theattribute similarities, i.e.,P (zij |xi,xj). In this regard, weconsider the widely used Gaussian distribution [31]

P (zij |xi,xj) = N (wT ζ(xi,xj), υ), (9)

where the similarity vectorζ(xi,xj) is the set of similaritymeasures taken on the pair of users(i, j) andw denotes thevector of parameters of the model in (9).

Now, in order to completely describe the joint distributionin (8), the conditional probability ofyij,f given zij andeij,f ,can be modeled by using the logistic function:

P (yij,f = 1|uij,f ) =1

1 + e−(Tfuij,f )

, (10)

where uij,f = [eij,f , zij ]T . Moreover, f =

[f,1, f,2, ..., f,ϑ+1]T are the parameters of the model

in (10) that must be estimated. From Fig. 3 and given latentvariablezij , all elements ofyij become independent of each

other. LetD = (i1, j1), (i2, j2), ..., (iD, jD) be the set ofuser sample pairs observed from the network. The variablesxi, xj , yij and eij,f could all be extracted from the socialnetwork. Hence, conditioned to the attribute similaritiesandmodel parameters, we can write (8) as:

P (zij ,yij |xi,xj ,w,) = (11)

∏

(i,j)∈D

P (zij |xi,xj ,w)

F∏

f=1

P (yij,f |zij ,f )

.

Here, by substituting (9) and (10) in (11), the joint distributioncan be written as:

P (zij ,yij |xi,xj ,w,) ∝ (12)

∏

(i,j)∈D

e−1

2υ (wT ζij−zij)

2F∏

f=1

e−(Tf uij,f )(1−yij,f )

1 + e−(Tfuij,f )

.

C. Inference

Given the defined learning model, we can now infer thesocial tie strength between each arbitrary pair of users(i, j).One way to estimatezij is to adopt the approach of [31]in which zij is treated as a parameter. Essentially, we canfind the point estimatesw, ˆ, z that maximize the likelihoodP (y, z, w, ˆ|x). To avoid overfitting the training dataset forthe model in (9) and (10), regularizersλw and λ will beused respectively for the parametersw and with Gaussianpriors. Overfitting can occur if the size of thew vector is toolarge for the observed data from the attribute vectorx. Using(12), we have:

P (zij ,yij ,w,|xi,xj) = (13)

P (zij ,yij |xi,xj ,w,)P (w,|xi,xj),

and since the model parametersω and are independent ofone another, as well as of the attributes of the users, we canwrite the joint conditional distribution in (13) as

P (zij ,yij ,w,|xi,xj) = P (zij ,yij |xi,xj ,w,)P (w)P ().(14)

and hence,

logP (zij ,yij ,w,|xi,xj) =∑

(i,j)∈D

(

−1

2υ

(

wT ζij − zij)2)

+

∑

(i,j)∈D

F∑

f=1

(

−(1− yij,f )(Tf uij,f )−log

(

1 + e−(Tf uij,f )

))

−λw

2wTw −

F∑

f=1

λ

2Tf f + C, (15)

whereC is a constant. (15) is a concave function and, thus,the latent variable and parameters can be derived by usinggradients of this function. Using the iterative Newton-Raphsonalgorithm, we can maximize the function in (15) and find the

optimum values forzij , f , andw. We denoteZ as aM×Mmatrix, wherezij is the element ofi-th row andj-th column.

Given the proposed wireless model of Section II along withthe inferred social tie metricZ, we are now able to account forthe social interconnections among users in conjunction withthe physical layer constrains of the D2D-enabled SCN. Wenext develop a matching-based approach to allocate resourcesin a social context aware SCN.

IV. CONTEXT-AWARE RESOURCEALLOCATION AS A

MATCHING GAME

Having defined the social context, our next goal is to solvethe resource allocation problem in (4). The problem given by(4), subject to (5)-(7), is a 0-1 integer programming, whichisa satisfiability problem as such one of Karp’s 21 NP-completeproblems [32]. Hence, it is difficult to solve this problem viaclassical optimization approaches. Moreover, for a large-scaleSCN network with D2D communication, it is desirable tosolve the context-aware resource allocation problem in (4)-(7)using a decentralized, self-organizing approach in which theSCBSs and devices can interact and make resource allocationdecisions based on their local information without relyingona centralized entity for coordination. In addition, owing to theneed for exploiting context information, it is of interest todefine individual SN or UE utilities that capture the locallyavailable context at each node.

To this end, matching theory is a promising approach to per-form decentralized resource management in wireless networks[8], [10], [11], [13], [33]. The main benefit of matching theoryis its ability to define individual utilities per UE and SNs aswell as the available algorithmic implementations that allowto provide a largely decentralized and self-organizing solutionto the resource allocation problem in (4)-(7) while accountingfor all the nodes’ information. In essence, a matching game isa situation in which two sets of players must be assigned toone another, depending on their preferences. In a matchinggame, each player must rank the players in the opposingset using apreference relationwhich captures this player’sevaluation of the players in the other set. In the studiedcontext-aware model, the preference relation can be based ona variety of metrics related to the social and wireless realms.In this regard, we formulate the proposed resource allocationproblem in SCNs as a two-sided one-to-one matching gamein which each SN-controlled RBn ∈ N will be assigned toat most one userm ∈ M and vice versa. Therefore, we canformulate the problem as a one-to-one matching game givenby the tuple(M,N ,≻M,≻N ). Here,≻M= ≻mm∈M and≻N= ≻nn∈N denote, respectively, the set of the preferencerelation of users and RBs. We formally define the notion of amatching:

Definition 2. A matchingµ is defined as a function from thesetM∪N into the set ofM∪N such thatm = µ(n) if and

only if µ(m) = n.

LetVm(.) andUn(.) denote, respectively, the utility functionof UEm and RBn. Given these utilities, we can say that a userm prefers RBn1 to n2, if Vm(n1) > Vm(n2). This preferenceis denoted byn1 ≻m n2. Similarly, an RBn prefers UEm1 tom2, if Un(m1) > Un(m2) and this is denoted bym1 ≻n m2.

A. Users’ Preferences

Depending on whether an RBn is offered by an SUE or anSCBS, the UEs will have different utility functions. Moreover,the utility of one player may depend on the matching of otherplayers, due to the peer effects described in Section III-A.Inthis regard, letamms;µ = amms

|µ be a variable used todetermine the existence of a D2D link between UEm andSUE ms, conditioned on the current matchingµ. Similarly,we useamms;µµ′ = amms

|µ, µ′, to indicate whether acertain UEm is a member ofCms

in both matchingsµ andµ′. The motivation for this definition will be explained inSection V-B. Before computing the utilities, UEs first obtainthe corresponding channel response of each RB, from all SNsand form aK×N channel coefficient matrixHm. UsingHm,each userm ∈ M shapes its achievable data rate matrix, i.e.Φm, whose elements are given by (1)-(3). From (1) and (2), theutilities of a UE and an SUE, respectively, for RBsn1 ∈ N1

andn2 ∈ N2, are given by:

Vmni,l(γ(i)lnm) = wni

log(

1 + γ(i)lnm

)

, (16)

wherem corresponds to a UE (i = 1) or an SUE (i = 2).From (3), the utility of a userm using an RBn ∈ N3 is givenby:

Vmn,ms(Z, γ(3)

msnm, µ) = (17)

wn log(

1 + γ(3)msnm

)

+ αm

zmms+

∑

j∈Mu\m

ajms;µµ′zmj

,

whereαm is a weighting parameter that allows to control theimpact of the social ties on the overall decision of the user.Theutilities given by (16) state that UEs and SUEs, respectively,rank RBsn1 ∈ N1 andn2 ∈ N2 based only on the achievablerates. However, (17) captures the peer effects on the UEs’preferences for RBsn ∈ N3. A UE can benefit more from themutual interests among the SC members, if the SC membersare more socially connected with one another and with theUE. The second term in (17) implies that the UE prefers tojoin an SC that has stronger ties with it.

B. SN-based RBs’ Preferences

The proposed matching game can be fully represented oncethe preference of each RB is defined. The decision of an RBn ∈ N is mainly controlled by the SCBS or SUE that isusing it. Hence, in the proposed game, SCBSs and SUEs makedecisions on behalf of their RBs. In the considered model,there are three groups of RBs, each of which has a different

preference over the UEs. Similar to Section IV-A, we definea novel scheme at the RB side of the game, which is basedon the information extracted from the corresponding socialnetwork. For the transmission between SCBSl ∈ L and UEm ∈ Mu, over RBn ∈ N1, the utility of RB n ∈ N1 whenchoosing UEm is given by:

Unm,l(Z, γ(1)lnm) = wn log

(

1 + γ(1)lnm

)

− βn(∑

j∈Ms

zmj).

(18)Hence,m1 ≻n m2 if and only if Unm1,l > Unm2,l. βn isa weighting parameter that controls the impact of the socialcontext. The second term in the right hand side of (18) impliesthat RBsn ∈ N1 give less utility to UEs who can be servedby an SUE.

In addition, the utility achieved by RBn ∈ N2 whenselecting SUEms, Unms,l is given by

Unms,l(Z, γ(2)lnms

, µ) = wn log(

1 + γ(2)lnms

)

+ νn ·Xms,

(19)whereXms

=∑

m∈Muamms;µzmms

is the total cumulativesocial tie strength of a particular SUEms and νn is aweighting parameter that controls the importance of the SCthat the SUE has formed in RBn’s utility. The utility functionin (19) promotes SUEs with higher social ties since they arelikely to form larger SCs. Finally, the utility of RBn ∈ N3

for userm via D2D link from SUEms is given by

Unm,ms(γ(3)

msnm) = wn log

(

1 + γ(3)msnm

)

+ κnzmms. (20)

The utility function in (20) implies that UEs must be acceptedbased on both quality of the D2D link and social context.κn

is a weighting parameter and implies that how important therole of social tie is for RBn ∈ N3 of an SUEms ∈ Ms inaccepting a UEm ∈ Mu.

V. PROPOSEDCONTEXT-AWARE RESOURCEALLOCATION

ALGORITHM

Given the formulated context-aware matching game, ourgoal is to find astable matching, which is one of the keysolution concepts in matching theory [33]. LetA(M,N )denote the set of all possible matchings, andµ(m,n) denotea subset ofA(M,N ), wherem andn are matched together.Then, we define a stable matching as follows:

Definition 3. A pair (m,n) /∈ µ, wherem ∈ M, n ∈ Nis said to be ablocking pair for the matchingµ, if there isanother matchingµ′ ∈ µ(m,n), whereµ′ ≻m µ and µ′ ≻n

µ. A matchingµ∗ is stableif and only if there is no blockingpair.

A stable matching solution for resource allocation problemin (4)-(7) ensures that after allocating resources to the users, noRB-UE or RB-SUE pair in SCN would benefit from replacingtheir current association with a new link. That is, no usercan benefit by changing its assigned frequency resource and

vice versa. For the proposed context-aware resource allocationgame, we can make the following observation:

Remark 1. The proposed SCN matching game haspeereffects.

The RBs and users in a context-aware resource allocationgame may change their preferences as the game evolves. Thatis, the preference of one player may depend on the preferencesof the other players. For instance, the peer effects introducedin Section III-A make the preferences of RBs and usersinterdependent, due to the social interrelationships amongusers. This type of game is known as thematching game withpeer effects, in which players have preference ordering overthe set of all possible matchingsA(M,N ) [34]. This is incontrast with the traditional matching games in which playershave fixed preference ordering [10]–[13], [33].

For traditional matching games such as in [10]–[13], [33],one can use the deferred acceptance algorithm, originallyintroduced in [35], to find a stable matching. However, suchan algorithm may not be able to converge to a stable matchingwhen the game has peer effects [33], such as in the proposedcontext-aware resource allocation model. Therefore, there is aneed to develop new algorithms, that significantly differ fromexisting applications of matching theory in wireless such as[10]–[13], so as to find the solution of the studied matchinggame.

A. Proposed Socially-Aware Resource Allocation Algorithm

To solve the formulated matching game, we propose anovel algorithm for resource allocation in D2D-enabled SCNs.Table I shows the various stages of this proposed socially-aware resource allocation (SARA) algorithm that allows tosolve the SCNs’ matching game.

The proposed algorithm is composed of four main stages:Stage 1 includes the matching of SUEs with RBsn ∈ N2,Stage 2 focuses on the matching of UEs with RBsn ∈N1 ∪N3, Stage 3 focuses on updating the SC information, andStage 4 during which the actual downlink transmission occurs.Initially, the SCBSs use the knowledge of social ties amongusers to choose the SUEs as discussed in III-A. Each SCBSsends a proposal to its neighboring users that are deemedinfluential enough to be an SUE. UEs accept or reject theproposals and the SCBSs broadcast the set of SNs,K, and thesets of RBs,Ni, i = 1, 2, 3.

After initialization, each SUE applies forn ∈ N2 based on(16) and each RB accepts the most preferred UE and rejectsother proposals based on the utilities defined in (19). Stage1terminates once each SUE is accepted by an RB or rejected byall its preferred RBs. This matching remains unchanged untilSUEs update the clusterCms

, ∀ms ∈ Ms, sets. However, thenew context information changes the preferences of the RBsfor SUEs based on (19). That is due to the fact thatXms

=

TABLE IPROPOSEDSOCIAL CONTEXT-AWARE RESOURCEALLOCATION

ALGORITHM

Inputs: L,M,N ,H,Z

Initialize: SCBSs send proposal to high influential UEs to act as SUE.SCBSs broadcast the setK and announce the set of available RBs inN1, N2, andN3. Initialize the set ofCms for each SUE as an emptyset.Stage 1:

(a) SUEs determine their preference ordering for RBsn ∈ N2,using (16).(b) RBsn ∈ N2 calculate utility of each SUE applicant using(19) for the current state of the matching.(c) SUEs apply for RBsn ∈ N2 and get accepted or rejectedvia the deferred acceptance algorithm.

Stage 2:(a) UEs apply for RBsn ∈ N1 andn ∈ N3, using (16) and(17), respectively.(b) RBs n ∈ N1 and n ∈ N3 calculate utility of each UEapplicant using (18) and (20), respectively.(c) UEs get accepted or rejected by RBsn ∈ N1 ∪ N3 throughdeferred acceptance algorithm.

Stage 3:(a) Update SC information,Cms for ∀ms ∈ Ms.(b) SUEs broadcast SC information of the current matching, i.e.,amms;µ coefficients to their nearby UEs.

while Cms ,∀ms ∈ Ms remain unchanged for two consecutivematchingsrepeat Stage 1 to Stage 3Stage 4:

(a) For any cluster member, SUE determines if the currentrequested data exists in its directory.(b) Actual downlink transmission of data occurs from each RBto its matched SUE or UE.

Output: Stable matchingµ∗

∑

m∈Muamms;µzmms

determines how much the members ofan SUE’s cluster are socially connected. A largerXms

impliesthat the members can benefit more from D2D due to commoninterests in their requested data. Therefore, RBsn ∈ N2 preferto be matched to an SUE with largerXms

. Due to the changein their preference ordering, SUEs and RBsn ∈ N2 need torepeat this stage once the context information is updated.

Following the first stage, UEs apply forn ∈ N1 or n ∈ N3,based on the utilities defined in (16) and (17), respectively.The SCBSs and SUEs controlling RBsn ∈ N1 andn ∈ N3,accept the UE that gives the higher utility based, respectively,on (18) and (20), and reject the rest of the applicants. As longasCms

, ∀ms ∈ Ms, do not change, UEs have strict preferenceover RBsn ∈ N1 ∪ N3 and vice versa. Stage2 ends onceeach UE is accepted by one RB or rejected by all RBs of itspreference list.

All clusters are subject to change due to the peer effectsin the matching game. Thus, players need to update theirpreferences based on the newCms

, ∀ms ∈ Ms, informationresulted from Stage2. In Stage 3, each SUEms updates theSC information, i.e.Cms

,ms ∈ Ms, based on the results of thecurrent matching and broadcastsCms

set to its nearby UEs andthe corresponding SCBS. According to this information, play-

ers sort their preferences conditioned on the current matching.The algorithm terminates, once theCms

,ms ∈ Ms sets do notchange for two consecutive matchings. In the final stage, oncethe matching is complete, the downlink transmission of theUEs occurs, using the allocated resource blocks. This stageisessentially the actual communication stage in the D2D-enabledSCN.

B. Convergence and Stability of the Proposed Algorithm

In this subsection, we prove the stability of the algorithmproposed in Table I. Prior to doing so, we make the followingdefinition:

Definition 4. Given the social interrelationship between UEs,an SCCms

is said to beS-stable, if both of the followingconditions are satisfied:1) No UEm outside the clusterCms

can join it. That is, foranym /∈ Cms

andn ∈ N3 belonging toms, there is no pair(m,n) /∈ µ wherem ≻n µ(n) andn ≻m µ(m).2) No UEm inside theCms

can leave the cluster. That is, foranym ∈ Cms

andn ∈ N1 ∪ N3 that does not belong toms,there is no pair(m,n) /∈ µ wherem ≻n µ(n) andn ≻m

µ(m).A matching is S-stable, if and only if all the clusters are S-stable.

This notion of stability guarantees that the peer effectscannot make a UE outside the SCs join a cluster. In addition,the UEs inside SCs will not leave or change their clusters.However, it is not sufficient to ensure the required two-sidedstability of the matching. Next, we discuss a property of theproposed game and show why the S-stability of SCs is non-trivial.

Proposition 1. Given the information on the social clusters,once a UEm is accepted by an RB of a particular SC,µ(m)will not rejectm in favor of any new applicant. However, thisdoes not imply UEm has no incentive to leave the cluster.

Proof: First, consider the game at its initial state whereno UE has been assigned to any SUE (no SC is formed).That is,

∑

j∈Mu\majms;µµ′zmj = 0 and Vmn,ms

=

wn log(

1 + γ(3)msnm

)

+ αmzmmsfor ∀m ∈ Mu. Thus, from

(17), a UEm that applies for RBn ∈ N3 during the firstmatching will do so only due to the higher achievable ratesplus social tie with the corresponding SUE. Without loss ofgenerality, the preference ordering of UEm is identified withtwo setsU andW , where

U = ∀n′ ∈ N1|Vmn′,l > Vmn,ms

∪ ∀n′ ∈ N3|Vmn′,ms> Vmn,ms

;

W = ∀n′ ∈ N1|Vmn′,l < Vmn,ms

∪ ∀n′ ∈ N3|Vmn′,ms< Vmn,ms

. (21)

In (21), U and W , represent the set of all RBs that are,respectively, more preferred and less preferred to UEm thanRB n. Thus, the preference ordering of UEm can be denotedby U ≻m n ≻m W . In Stage 2, the process of acceptance orrejection of applicants is done in a manner analogous to theconventional deferred acceptance algorithm [10]. Thus, wecanensure that, for a given SC setting, eachn ∈ N3 has accepted,out of the applicants, the UE thatµ(n) = maximize

mUnm,ms

(γ(3)msnm

)

= maximizem

wn log(

1 + γ(3)msnm

)

+ κn · zmms. (22)

Therefore, if another UEm′ applies for the RBn during thenext matchingµ′, then necessarilyn′ = µ(m′) ∈ W , if UE m′

is not unmatched. This is due to the fact that, ifn′ = µ(m′) ∈U , then it means that UEm′ already satisfies (22) for RBn′,and hence, it will be accepted byn′, before applying ton.

Now, sinceµ(m′) ∈ W , we can conclude thatUnm′,ms<

Unm,ms; since otherwise,µ(m′) = n which contradicts (22).

In other words, the UEs who are accepted in the first iterationwill not be rejected by their match as the game proceeds.We can hold the same argument for the next iterations.Nevertheless, this does not imply that UEm necessarily staysin its cluster forever. To show this, we give an example.Example: With this example, we show that UEs may alter theS-stability of the clusters. Given two UEsm andm′, two RBsn ∈ N1 andn′ ∈ N3, and two SUEsms1 andms2, assumethatVmn;ms1

> Vmn′;ms2before any SC is formed and let the

current matching beCms1= ms1,m with µ(m) = n and

Cms2= ms2,m

′ with µ(m′) = n′. Once the SC informationis updated for UEs, the utility of UEm for RBsn andn′ mightchange toVmn;ms1

< Vmn′;ms2, due to its social tie withm′.

Therefore,m will leave its current clusterCms1and will join

Cms2. Due to this move, both clusters are not considered S-

stable.Based on the Proposition 1, we can show the S-stability

of the proposed context-aware resource allocation game asfollows:

Theorem 1. Each SC becomes S-stable after a finite numberof iterations and, thus, the proposed algorithm in TableI isguaranteed to converge.

Proof: From Proposition 1, eachn ∈ N3 will not reject itscurrent matchµ(n), in favor of other applicants. Thus, a newUE m can join an SC, only if it applies for an unmatchedn ∈ N3. After each matching is done, more UEs will joinSCs, due to the non-negative social effect they impose on oneanother. Eventually, there is a stage where no more UEs preferto join clusters.

There can be only two possibilities if a UEm withµ(m) ∈ N3 can leave its cluster, and thus, alter the S-stability condition:Case 1: there is an unmatchedn ∈ N1

such thatn ≻m µ(m), and Case 2: there is an unmatched

n ∈ N3 corresponding to another cluster where, again, wehaven ≻m µ(m). Next, we show that even when either Case1 or Case 2 occurs, the current SC will converge to an S-stableSC.

For the first case, we can check that UEm has surely beenrejected in previous matchings by an RBn ∈ N1 such thatn ≻m µ(m). Here, sinceµ(n) is matched to another playerand RBn is unmatched now,m will be accepted by RBn.If µ(n) never applies again for RBn, then we can ensurethat UEm will not be rejected byn, since it satisfiesµ(n) =maximizem Unm,l(γ

(1)lnm). Thus, UEm will not get back to its

SC again. Ifµ(n) applies again to RBn, then RBn will rejectm. However,µ(n) cannot cycle between RBn and another RBn′ for unlimited number of iterations. This is due to the factthat, ifµ(n) oscillates betweenn and another RBn′ ∈ N3, thereason is due to the peer effect by a current SC memberm′′

who also oscillates betweenn′ and another RB. However,µ(n)will set aµ(n)m′′;µµ′ = 0, if m′′ does not stay in SC for twoconsecutive matchings. Therefore,µ(n) has to finally decidebetweenn andn′ after finite iterations. Moreover, if an RBn′ ∈ N1 is the reason due to whichµ(n) cycles, then similarlywe can show thatµ(n′) will have to stop the oscillation aftera finite number of iterations. Consequently,µ(n) will stoposcillation.

Case 2 implies that some of the friends of UEm hasencouragedm to join their cluster. Here, if UEm joins thenew SC, it will never prefer the previous SC to new one,unless some of its friends, saym′, leave the cluster. Then,UE m ignores the peer effect ofm′ by settingamm′;µµ′ = 0and reorganizes its preference ordering. After a finite numberof iterations, the friends’ list who stay in the cluster willnotchange and, thus, UEm stays in the new cluster or comes backto the previous cluster and will never cycle between those two.In addition, if the incentive for UEm to join RBn′ of the newcluster does not stem from the friendship relationship, then,this implies thatn′ ≻m µ(m) and UEm has been rejectedby n′ in previous matchings. Thus, similar to the previouscase, we can observe that after finite iterations, theµ(n′) stopsoscillating, and, hence, UEm will decide whether to stay withµ(m) or leave it.

Given the results in Proposition 1 and Theorem 1, we cannow state the main result with regard to the two-sided stabilityof the matching.

Theorem 2. The proposed algorithm in TableI is guaranteedto reach a two-sided stable matching between users and RBs.

Proof: In order to prove the two-sided stability, we needto show that there is no blocking pair(m,n) or (ms, n) thatmeets either of the following:

(m,n) /∈ µ | µ(m) ∈ N3 , n ∈ N1 ∪N3; (23)

(ms, n) /∈ µ | ms ∈ Ms , n ∈ N2; (24)

(m,n) /∈ µ | µ(m) ∈ N1 , n ∈ N1 ∪N3. (25)

All SCs are S-stable once the algorithm terminates since,otherwise, the SC sets will be different from those in previousmatching which contradicts the termination condition.

From Theorem 1, we can see that no UEm havingµ(m) ∈N3 would make a blocking pair with any RBn1 ∈ N1 orn3 ∈ N3 from another cluster, due to the S-stability of allclusters. In addition, the matching of RBsn ∈ N3 belongingto SUE ms and UEs inCms

is done through the deferredacceptance algorithm. Therefore, these players will not forma blocking pair. Consequently, there is no blocking pair thatsatisfies (23).

In addition, the preferences of RBsn ∈ N2 become strictlyfixed, once the S-stability is satisfied at all clusters. Then,followed by the deferred acceptance algorithm, we ensure thatthe given matching between SUEs and RBsn ∈ N2 is stableand there is no blocking pair that satisfies (24).

Finally, no RB n ∈ N3 makes a blocking pair with anym whereµ(m) ∈ N1, due to the S-stability of all clusters.Moreover, the matching of RBsn ∈ N1 and UEsm whereµ(m) ∈ N1 is followed by the deferred acceptance algorithm.Therefore, these players will not form a blocking pair and thereis no blocking pair that satisfies (28). Hence, the proposedSARA algorithm is guaranteed to reach a two-sided stablematching for all D2D and cellular links.

C. Complexity Analysis of the Proposed Algorithm

In order to analyze the computational complexity of theproposed algorithm, we can start by investigating the simplecase in which the matching game has no peer effect, i.e., usersand RBs have strict preference ordering. Here, we considertwo cases: 1) when the number of UEs is less than the totalnumber of RBs, i.e.,Mu ≤ NT , whereNT = N1×L+N3×Ms and 2) when the number of UEs is greater than the totalnumber of RBs, i.e.,Mu > NT . Our goal is to analyze theworst case scenario, i.e., the maximum number of iterationsand the maximum number of matching proposals sent fromUEs to either SCBSs or SUEs (which relate to the messagingoverhead). In each iteration, UEs send a proposal to their mostpreferred RB, and RBs receive the proposals, accept the mostpreferred one and reject the other UEs. Therefore, it is clearthat the number of unmatched UEs at each iteration is equal orless than the number of unmatched UEs at previous iterations.

For the first case, once the algorithm converges, all the UEsare matched, since RBs prefer any UE to being unallocated.We can easily observe that the worst case happens, if all UEshave the same preference ordering. Hence, at the end of eachiteration t, there areMu − t unmatched UEs. Therefore, themaximum number of iterations,tmax, is obtained when all theusers are matched, i.e.,Mu−tmax = 0. Hence, the complexityis of the orderO(Mu). Furthermore, at each iterationt, Mu−t+1 proposals are sent. Hence, the messaging overhead,Smax,is equal to:

Smax =

tmax∑

t=1

(Mu − t+ 1) =Mu(Mu + 1)

2. (26)

Similarly for the second case, we know that once thealgorithm converges, there are exactlyMu − NT unmatchedusers. Again, the worst case happens, if all UEs have the samepreference ordering. Hence, at each iteration, only one UE getsaccepted. Therefore, the maximum number of iterations,tmax,is obtained when there areMu−NT unmatched users, i.e., thecomplexity is of the orderO(NT ). The messaging overheadis equal to:

Smax =

tmax∑

t=1

(Mu − t+ 1) = (27)

NT∑

t=1

(Mu − t+ 1) = (Mu + 1)NT −NT (NT + 1)

2.

As we see from the above equations, forMu < NT , thecomplexity of the matching algorithm increases linearly withthe number of users. In addition, the messaging overheadexhibits quadratic increase with respect to the number of users.Moreover, forMu > NT , the upperbound for complexity isindependent of the number of users.

The complexity of the proposed context-aware algorithmwill further depend on the social matrixZ. However, for agiven SCs, the complexity of our algorithm follows the aboveanalysis. From Theorem 1, we know that SCs change onlyfor a finite number of iterations. Hence, we can anticipatethat the overall complexity of the context-aware approach belinearly proportional to the complexity of the context-unawareapproach.

VI. SIMULATION RESULTS AND ANALYSIS

A. Social Context Dataset and Simulation Parameters

For the evaluation of our results, we first use the learningmodel introduced in Section III. We have computed the socialtie matrixZ, for a set of 80 users from the Facebook network.We have used the real dataset released by Stanford University[36], which is generated by surveying a number of volunteerFacebook users, known as ego nodes. For the selected egonode, the dataset contains 224 anonymized attributes for eachuser, including education, gender, location, language, andwork, among others. In addition, the dataset specifies 32anonymized circles and determines which subset of users arein which circle. Each circle is a group, composed of a subsetof users, which can be thought as a high school institution ora company. For our simulations, we assume that if two usersiandj are within at least one common circle, then they interactwith each other on Facebook. Finally, in order to determine thetendency of useri to interact with another userj, we considerthe degree of useri in the ego network, i.e., the number offriends of useri. The motivation behind this assumption canbe explained as follows: if useri picks userj to interact with

from a larger number of friends, this implies that userj ismore important to useri than other users.

In order to select the SUEs, we choose the four users withthe highest weighted degree from the ego network. Thus,in our simulations, we haveMs = 4 and the weights aredetermined by the social tie strengthz for each pair of users.We considerL = 7 SCBSs distributed randomly within asquare area of2 km × 2 km. The number of active RBs forSCBS to UE link, SCBS to SUE link, and SUE to UE link,respectively, areN1 = 5, N2 = 3, andN3 = 5, unless statedotherwise. Here, we would like to note that depending on thechannel state information and social ties among users, spec-trum partitioning can be done dynamically and the proposedmodel is not limited to any specific resource partitioning. Inthis work, however, we assume that throughout the resourceallocation, neither the social tie matrixZ, nor the channelstate information are changing and therefore, the partitionsare static. Each RB is composed of12 consecutive subcarriers,each of which having a15 KHz bandwidth, according to 3GPPRel-12 Standard [37]. The transmit power of SCBSs and SUEsare set to2 W and10 mW, respectively. The wireless channelexperiences Rayleigh fading, with the propagation loss setto 3.The receivers’ noise is assumed Gaussian with zero mean andwith variance equals to−90 dBm. The weighting parameters,αm, βn, νn and κn are set to half of the RB bandwidth.Throughout the simulations, the unmatched users are assigneda zero utility. All statistical results are averaged over a largenumber of independent runs for different locations and channelgains.

For comparison purposes, we compare our proposed ap-proach with two centralized approaches: 1) the context-awarecentralized solution which aims to maximize the overall util-ities of all UEs and RBs, 2) the context-unaware centralizedapproach, that maximizes the throughput of the users. Insimulation results, the centralized solutions refer to thelinearprogramming relaxation of the original 0-1 integer program-ming problem in (4)-(7) by letting0 ≤ ξ ≤ 1. To obtaincentralized solutions in our simulations, we used the YALMIPtoolbox of MATLAB. In addition, we compare our results withthe context-unaware distributed algorithm that is based ontheone-to-one matching game similar to our proposed algorithm,however, no social context is incorporated. That is, UEs andRBs rank one another only based on the maximum SINRvalues. This benchmark algorithm is in line with some existingworks such as [11] and [10].

In addition, we show the effect of context-awareness bycomparing the offloaded traffic of both approaches as one ofthe main performance metrics in our results. We define theoffloaded traffic as the number of users who will be serveddirectly by data that is cached in a directory or folder atthe level of the SUE. The users obtain this offloaded trafficvia D2D communications without having to use the SCN’s

10 20 30 40 50 60 70 800

1

2

3

4

5

6

7

Number of users (Mu)

Ave

rage

soc

ial t

ie o

f eac

h cl

uste

r

Proposed SARA algorithmContext−unaware approachContext−aware centralized solutionContext−unaware centralized solution

Fig. 4. Comparison of the average social tie of SCs for proposed SARAalgorithm with other three approaches.

infrastructure, due to the correlation in their requests forcontent as discussed in Section III. To compute this offloadedtraffic, we must find the probabilityPm(yd = 1) of requestingcontent that already exists in the directory of SUEms by eachUE m ∈ Cms

:

Pm(yd = 1) =∑

d∈Dms

Pm(yd = 1|d ∈ Dms)P (d ∈ Dms

),

(28)where d and Dms

denote, respectively, the requested fileand the set of files of the SUEms’s directory. The Priorinformation,P (d ∈ Dms

) in (28), depends on both the historyof requested files in previous time slots and on the mutualsocial tie between all members of the SC. Finding a closed-form solution for (28) to model the correlation between usersin the time domain is difficult. Thus, for simplicity, we assumethat requesting a file from the directory of an SUE can bemodeled as an interactionyd between the user and its SC set.Motivated by (10), we modelPm(yd = 1) as a function ofcluster’s average social tiezms

= 1|Cms |−1

∑

m∈Cmszmms

, asfollows

Pm(yd = 1) =1

1 + e(−ρzms ); ∀m ∈ Cms

, (29)

whereρ is a constant normalizing parameter. Equation (29)allows to relax the dependencies between users by consideringaverage social tie of the cluster.

B. Simulation Results and Discussions

In Fig. 4, we show the average social tie in the finalclusters resulting from the proposed approach and the otherthree algorithms. Clearly, from this figure, we can observethat the members of the clusters in average are much moresocially connected in SARA compared to the context-unawareapproach. Fig. 4 shows that the average cluster social tie isup

10 20 30 40 50 60 70 805

10

15

20

25

30

35

40

45

50

Number of users (Mu)

Ave

rage

sum

rat

e [M

bit/s

]

Proposed SARA algorithmContext−unaware approachContext−aware centralized solutionContext−unaware centralized solution

Fig. 5. Comparison of the average sum rate of the proposed SARA algorithmand other three approaches.

to 77% higher for the proposed SARA algorithm relative to thecontext-unaware scenario forMu = 70 UEs. As the number ofusers increases and the SCBS resources become more scarce,UEs have no choice but to join the D2D clusters. However,Fig. 4 shows that by using the proposed SARA algorithm,the UEs will be more socially connected within their clustersand can benefit more from the social interconnections of oneanother.

In Fig. 5, the average sum rate of all users is comparedfor the SARA algorithm with the distributed context-unawareapproach and centralized approaches. It is not surprising to seethat the average sum rate of our proposed approach is slightlybelow that of an algorithm that is focused on optimizing onlythe data rate. Fig. 5 shows that the gap between the twoalgorithms does not exceed3% for all network sizes. However,as will be shown in Fig. 6, this small loss in average ratewill be compensated by having more offloaded traffic in thedownlink of the SCN. Interestingly, the rate performance ofthe proposed approach is very close to the centralized solutionand the gape between the two algorithms does not exceed4%for all network sizes.

Fig. 6 compares the average offloaded traffic at each timeslot for the proposed algorithm and other three approachesas the number of users varies. We note that for the context-unaware approaches, the contents stored in the SUE’s direc-tory do not depend on the average social tie of the socialcluster. Consideringρ = 0 in (29) allows us to model thisindependence. The average offloaded traffic determines howmany of UEs in average could be served directly by datathat is cached in the SUEs’ directories. The offloaded trafficincreases with the number of users, since more UEs will moveto the D2D tier. However, this metric will saturate for the

10 20 30 40 50 60 70 802

4

6

8

10

12

14

16

18

20

Number of users (Mu)

Ave

rage

offl

oade

d tr

affic

at e

ach

time

slot

Proposed SARA algorithmContext−unaware approachContext−aware centralized solutionContext−unaware centralized solution

Fig. 6. Comparison of the average offloaded traffic between the proposedSARA algorithm and other three approaches. Theρ = 0.5 and ρ = 0

is assumed, respectively, for context-aware algorithms and context-unawareapproaches.

large network sizes, since the number of RBsn ∈ N3 islimited. We can see that the proposed approach achieves a veryclose performance to the context-aware centralized solution, interms of traffic offloads, for the network size with more thanMu = 40 UEs. Moreover, we observe that the performanceof the context-unaware approach coincides with the centralsolution. This is primarily due to the fact that context-unawareapproach follows the deferred acceptance algorithm which isknown to achieve optimal solution for the proposing players(i.e. users) [10], [35]. In Fig. 6, we can see that the proposedSARA algorithm outperforms the context-unaware approachby increasing the offloaded traffic for different network sizes.Fig. 6 shows that the proposed SARA algorithm can offloadup to 84% more traffic from the SCN’s infrastructure whencompared to the context-unaware approach for a network withMu = 70 UEs.

In Fig. 7, we show the average offloaded traffic for differentvalues of theρ parameter in (29) and different number ofusers. One interesting observation from Fig. 7 is that theproposed SARA algorithm offloads more traffic as the networksize grows and eventually saturates, since the number of RBsis fixed. In fact, Fig. 7 implies that, at the cost of a slightreduction in the average rate of the matched users (see Fig.5), the proposed SARA algorithm allows to admit more usersinto the network. Hence, the proposed approach can be usedto optimize the tradeoff between serving more users in acongested network and the average rate of current users. Byproperly setting the control parameters in the utility functions,this tradeoff can be balanced according to the traffic of thenetwork.

In Fig. 8, we show the average offloaded traffic resulting

00.2

0.40.6

0.81

020

4060

80100

0

5

10

15

20

Parameter ρNumber of users Mu

Ave

rage

offl

oade

d tr

affic

at e

ach

time

slot

Fig. 7. The average offloaded traffic resulted by proposed SARA algorithm,versus differentMu and different values ofρ.

2 3 4 5 6 7 8 9 102

4

6

8

10

12

14

16

18

Number of RBs for SUE to UEs links (N3)

Ave

rage

offl

oade

d tr

affic

at e

ach

time

slot

Proposed SARA algorithmContext−unaware approachContext−aware centralized solutionContext−unaware centralized solution

Fig. 8. Comparison of the average offloaded traffic for the proposed SARAalgorithm with other three approaches, versus different number of RBsn ∈

N3. The valuesMu = 30 andN1 = 5 is assumed and the parameterρ isset to0.1.

from the proposed SARA algorithm and other approaches asthe number of RBsn ∈ N3 varies for a network withMu = 30UEs. This figure shows that, as the number of SUE resourcesincreases, the context-aware approach achieves better offloadperformance. That is due to the fact that more users withshared interests can join the same cluster which results toform stronger social clusters. In Fig. 8, we can see that the gapbetween the offloaded traffic of the proposed SARA algorithmand the context-unaware approach consistently increases as thenetwork sizes grows. Fig. 8 shows that the proposed SARAalgorithm can offload up to78% more traffic from the SCN’sinfrastructure when compared to the context-unaware approachfor a network withN3 = 8 RBs.

Fig. 9 shows the average number of iterations resulting from

10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

Number of users Mu

Ave

rage

num

ber

of it

erat

ions

N

1=3, N

2=3, N

3=3

N1=5, N

2=3, N

3=5

Fig. 9. Average number iterations of the proposed SARA algorithm vsnetwork size, for different number of RBs. The error bars indicate the95%confidence.

the proposed SARA algorithm versus the network sizeMu, fortwo different RB numbers. In this figure, we can see that, asthe number of UEs increases, the average number of iterationsincreases due to the increase in the number of players. Fig.9 demonstrates that the proposed matching approach has areasonable convergence time that does not exceed an averageof 72 iterations for all network sizes and withN1 = 5, N2 = 3,andN3 = 5 number of RBs. The maximum of the averagenumber of iterations reduces to40, when there areN1 = 3,N2 = 3, andN3 = 3 RBs.

VII. C ONCLUSION

In this paper, we have presented a novel approach forcontext-aware resource allocation in D2D-enabled small cellnetworks. We have formulated the context-aware resourceallocation problem as a one-to-one matching game and wehave shown that the game exhibits peer effects. To solve thegame, we have proposed a distributed social-aware resourceallocation algorithm that exploits the physical layer metricsof the wireless network along with the users’ social ties fromthe underlaid social network. Then, we have shown that theproposed algorithm is guaranteed to converge to a two-sidedstable matching between the users and the network’s resourceblocks. Simulation results have shown that the proposedmatching-based algorithm yields socially well-connectedclus-ter between D2D links, thus, allowing to offload significantlymore traffic than conventional context-unaware approach. Theresults provide novel insights into the gains that future wirelessnetworks can achieve from exploiting social context. Theresults show that with manageable complexity, the proposedcontext-aware approach can substantially improve the wirelessresource utilization by offloading a large amount of trafficfrom the backhaul-constrained small cell network. This workcan be extended to dynamic resource allocation in which the

spectrum partitioning may vary, depending on the social tiestrength among users.

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