Coalition Game Based Full-duplex Popular Content Distribution in mmWave Vehicular Networks
Yibing Wang, Hao Wu, Yong Niu, Zhu Han, Bo Ai, Zhangdui Zhong
11 Coalition Game Based Full-duplex Popular ContentDistribution in mmWave Vehicular Networks
Yibing Wang, Hao Wu, Yong Niu,
Member, IEEE,
Zhu Han,
Fellow, IEEE , Bo Ai,
SeniorMember, IEEE , andZhangdui Zhong,
SeniorMember, IEEE
Abstract —The millimeter wave (mmWave) communication hasdrawn intensive attention with abundant band resources. Inthis paper, we consider the popular content distribution (PCD)problem in the mmWave vehicular network. In order to offloadthe communication burden of base stations (BSs), vehicle-to-vehicle (V2V) communication is introduced into the PCD prob-lem to transmit contents between on-board units (OBUs) andimprove the transmission efficiency. We propose a full-duplex(FD) cooperative scheme based on coalition formation game,and the utility function is provided based on the maximizationof the number of received contents. The contribution of eachmember in the coalition can be transferable to its individualprofit. While maximizing the number of received contents in thefixed time, the cooperative scheme also ensures the individualprofit of each OBU in the coalition. We evaluate the proposedscheme by extensive simulations in mmWave vehicular networks.Compared with other existing schemes, the proposed schemehas superior performances on the number of possessed contentsand system fairness. Besides, the low complexity of the proposedalgorithm is demonstrated by the switch operation number andCPU time.
Index Terms —millimeter wave, vehicular network, vehicle-to-vehicle, cooperative scheme, coalition formation game.
I. I
NTRODUCTION
In recent years, millimeter wave (mmWave) has been widelyused in many fields, among which the mmWave vehicularnetwork is one of them. In this paper, we consider the pop-ular content distribution (PCD) service in mmWave vehicularnetworks. Contents distributed by the PCD service may be thehigh definition map of city, video on demands, real-time trafficinformation, etc. [1]. Due to the emergence of a large numberof multimedia applications, the massive data growth adds theburden on the network capacity and latency. The conventional
Copyright (c) 2015 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected]. Wang, H. Wu, Y. Niu, B. Ai and Z. Zhong are with the State KeyLaboratory of Rail Traffic Control and Safety, Beijing Jiaotong University,Beijing 100044, China (E-mails: [email protected], [email protected]).Z. Han is with the Department of Electrical and Computer Engineeringin the University of Houston, Houston, TX 77004 USA, and also with theDepartment of Computer Science and Engineering, Kyung Hee University,Seoul, South Korea, 446-701 (E-mail: [email protected]).This study was supported by the National Natural Science Foundationof China Grants 61801016, 61725101, and U1834210; and by the Na-tional Key R&D Program of China under Grants 2016YFE0200900 and2018YFE0207600; in part by the State Key Lab of Rail Traffic Control andSafety, Beijing Jiaotong University, under Grant RCS2019ZZ005; in part bythe funding under Grant 2017RC031; in part by the Fundamental ResearchFunds for the Central Universities, China, under grant number I20JB0200030;in part by NSF EARS-1839818, CNS1717454, CNS-1731424, and CNS-1702850. cellular model which only relies on stationary base stations(BSs) to send the data cannot satisfy the user demands now. Inthis case, vehicle-to-vehicle (V2V) communications can helpto achieve dependable transmissions and take over the businessburden of BSs.In order to further improve the network capacity and makeon-board units (OBUs) of vehicles obtain more contents, full-duplex (FD) communications are utilized in the PCD service.The spectral efficiency of the FD communication can be the-oretically doubled due to simultaneous data transmitting andreceiving [2]–[4]. In the transmissions with FD communica-tions, the interference of transmission links is caused not onlyby spectrum reusing but the transmit power of each receiver,that is self interference (SI). For the vehicular network, thehigh-speed mobility of each vehicle in the network results inthe fast-varying channel environment and network topology.Against such a backdrop, it is difficult to determine distribu-tion OBUs and their distribution contents of the PCD basedon V2V communications. Besides, the OBU that holds thedistribution content may have multiple neighboring OBUs, andwhich of these neighboring OBUs can receive the distributioncontent successfully needs to be cautiously determined.Therefore, we consider a scenario of V2V communicationsin the mmWave vehicular network. In this paper, all OBUshave a certain amount of initial contents, and they will obtainother required contents by other OBUs broadcast. For the time-varying PCD problem with the high complexity, the coalitionformation game can obtain a tractable solution efficientlyand directly, and achieve superior performances. Hence, weformulate the problem of how to form broadcasting OBUgroups as a coalition formation game. Thus, there are somecontributions of this paper, which are mainly summarized asfollows • We utilize the advantages of mmWave and FD commu-nications for the PCD problem in vehicular networks.And the implementation of V2V communications in thePCD service reduces the pressure of the network. Forthe proposed cooperation scheme of the mmWave band,OBUs broadcast contents based on the mmWave channelmodel and directional antenna model. Compared withother schemes, the mmWave and FD communicationscan obtain higher transmission rates and improve thetransmission efficiency significantly. • We propose a coalition formation game-based algorithm,which aims at maximizing the number of received con-tents of all OBUs in the fixed time. The utility function isdeveloped based on the maximization of received content a r X i v : . [ c s . I T ] J a n L t h e b r o a d c a s t i n g c o a li t i o n BS BS …… ……
Fig. 1. System model of popular content distribution in vehicular ad hoc networks. number. Because transmission times of different contenttransmissions are various, lifetimes of different coalitionsare different. The contribution of each coalition membercan be transferable to its individual profit, that is the num-ber of neighbors that received contents from the coalitionmember. The proposed scheme not only maximizes theutility function, but also guarantees the individual profitof each coalition member. Coalitions merge and splitaccording to a series of iterative operations based on thepreference relation, and finally self-organize a Nash stablepartition. In addition, we analyse the stability and proofthe convergence in theory. • We propose a broadcasting content selection algorithm todetermine contents for OBUs to broadcast, which is basedon maximizing the utility function of the coalition forma-tion game-based algorithm. Simulation results show thatthe proposed scheme makes OBUs receive more contentscompared with other schemes. Besides, our scheme hasbetter performance on the fairness of individual profits ofbroadcasting OBUs. Moreover, we demonstrate that theproposed scheme has the low complexity.The rest of this paper is organized as follows. Section IIintroduces the related work. In Section III, we provide thesystem model, including the traffic model, antenna model andchannel model. In Section IV, we formulate the PCD problemwith the objective of maximizing the number of possessedcontents. In Section V, a broadcasting content selection algo-rithm is presented. Section VI proposes the coalition formationgame-based algorithm, and gives some related definitions andnecessary proofs. In Section VII, extensive simulations aredone to evaluate the proposed scheme. Section VIII concludesthe entire paper. II. R
ELATED W ORK
There are many relevant literatures on V2R or V2V commu-nications. In [5], a scheme with low complexity is proposed toschedule packets of downlink and uplink transmissions fromone RSU to multiple OBUs. In [6], the authors proposeda V2V communication protocol to improve the safety ofvehicular networks in the ad hoc network. In [7], a V2V-based scheme which jointly optimize the power allocationand modulation/coding is proposed to satisfy requirements oflatency and reliability. In [8], a dependable lattice-based datadissemination scheme for vehicle social internet is presented. There are also some work on the PCD problem and coalitionformation game-based schemes of vehicular networks. In [9],a content centric data dissemination approach based on deeplearning is proposed, which considers the vehicle mobility andcontent type. In [10], a cooperative approach is proposed toachieve dependable content distribution in vehicular networks,which is based on the coalition formation game and big datavehicle trajectory prediction. In [11], a content popularity-based adaptive caching mechanism is presented to minimizethe total operational cost. In [12], a transmission schemebased on V2V-aided and the coalitional game is proposed tocomplete the PCD in VANETs. In [13], the authors proposed acooperation scheme based coalition formation game for RSUsto improve the diversity of the transmission data. In [14],the dynamic PCD of vehicular networks is addressed by aproposed cooperation half-duplex (HD) approach based oncoalition formation game. The proposed schemes in [13] and[14] aim at minimizing the cost and delay. In our paper, theobjective and the utility function of the coalition formationgame are both different. We propose a coalition formationgame-based algorithm, which aims at maximizing the num-ber of received contents of all OBUs in the fixed time. Inaddition, [13] and [14] does not consider the performance onfairness of their proposed scheme or evaluate the CPU timeof the coalition formation game-based algorithm. In [15], theauthors took advantage of coalition formation game to addressbandwidth sharing in V2R communications.In addition, the research on the problem of the mmWavenetworks is also a hot spot. In [16], a multihop path selectionalgorithm and an efficient scheduling scheme for popularcontent downloading in mmWave small cells are proposed toimprove network transmission efficiency. In [17], the authorscharacterize the interference from the side lanes in mmWaveand low terahertz bands. Both multipath interference and directinterference from the transmitting vehicles on the side lanesare considered in [17]. In [18], a broadcast scheduling schemewith utilizing exclusive region is proposed for improving theconcurrency of mmWave links. In [19], the authors proposeda mmWave vehicular framework based on the information-centric network (ICN) to decrease the latency of contentdissemination.However, these existing studies do not combine themmWave and V2V communications to solve the PCD prob-
TABLE IS
UMMARY OF N OTATION AND D ESCRIPTION
Notation Description M , N , C , L number of TSs, number ofOBUs, number of contents,length of the highway c , D c content c , size of content ca ci binary variable of initial pos-sessed content state of OBU i ( a ci = 1 indicates OBU i hasreceived the content c beforeV2V cooperative transmissionsor a ci = 0 indicates OBU i doesn’t have content c beforeV2V cooperative transmissions) v i (0) the initial speed of OBU i inV2V transmission phase ( i, j ) the link from OBU i to OBU jP r ( i, j ) received power at OBU j fromOBU iP t transmit power of links G ts i , G rr i directional antenna gain attransmitter s i , directionalantenna gain at receiver r i P L ( d ) path loss for the link of distance dD l , α l path loss of unit length distance,path loss exponent of link lG , G j,l k,r maximum directivity antennagain, antenna gain at OBU j from link ( k, j ) β j SI cancelation level at OBU jI i,j sum interference of other con-current links to link ( i, j )Λ i,j , c i,j SINR at the receiver of link ( i, j ) , channel capacity of link ( i, j ) th min SINR threshold of V2V links v min , v max , d min , d max lower bound of velocity, upperbound of velocity, lower boundof distance, upper bound of dis-tance θ ( ij,k ) , θ dB , A m angle between beam directionof link ( i, j ) and the directionof OBU k , 3dB beamwidth indegrees, maximum attenuation δ ci binary variable of the contentstate of OBU i ( δ ci = 1 indi-cates OBU i has received thecontent c or δ ci = 0 indicatesOBU i doesn’t have the content c ) ϕ ti,j,c binary variable of the content c ( ϕ ti,j,c = 1 indicates thecontent c is transmitted fromOBU i to j in slot t or ϕ ti,j,c =0 indicates the content c isn’ttransmitted from OBU i to j inslot t ) B t number of transmitting anten-nas of each OBU Γ i , N i , N ∗ i possessed content set of OBU i , neighbor set of OBU i , setof the neighbors that is sureto receive broadcasting contentfrom OBU iγ pi , γ i fin possessed content of OBU i ,selected broadcasting content ofOBU i N γ pi i ∗ set of the neighbors of OBU i that need content γ pi ∆ t , α , µ time duration of one slot, utilitycalculation factor, pricing factor lem in vehicular networks. And they don’t consider how tomaximize the number of received contents of all OBUs inthe fixed time. In the pursuit of utility function maximization,there is no guarantee for individual profits of OBUs in theexisting literature. Hence, we consider the PCD problem inmmWave vehicular networks in this paper. Besides, our currentwork supports FD communications to improve transmissionefficiency. And we propose the new coalition formation game-based scheme which is aimed at maximizing the number ofreceived contents of OBUs in the fixed time. The proposedscheme considers the channel capacity, content request, peerlocation, and potential interference to determine the transmis-sion scheduling and obtain superior performances.III. S YSTEM M ODEL
The system model of the mmWave vehicular network isshown in Fig. 1, which contains two lanes with oppositedriving directions. There are BSs on both the left and rightsides in Fig. 1, and different colored arrows represent differ-ent transmission contents. OBUs possess some contents thatreceived from BSs at the time of beginning, and then coopera-tions with other OBUs based on V2V communications provideopportunities for them to obtain other required contents. Thereis a straight highway of length L in the middle of the Fig.1, and directions of dotted arrows on its left indicate drivingdirections of vehicles in different lanes. In this paper, we onlyconsider related issues of vehicles sharing content throughV2V communications in this highway of length L .On this part of the road, N OBUs are randomly distributedin two lanes, and the set of OBUs is denoted by N . OBUsexchange their possessed contents with other OBUs to obtainas many required files as possible. All OBUs operate inthe FD mode, and are equipped with electronically steerabledirectional antennas to transmit in narrow beams towards otherOBUs. Besides, there are C contents in the vehicular network.We assume that OBUs need to acquire these contents, and theset of contents is C . The sizes of different required contentsare different. For the required content c ∈ C , its size is denotedby D c . At the beginning of the cooperative transmission, eachOBU has a random number of contents, which are receivedfrom BSs.For clarity of illustration, the transmission time is dividedinto a series of non-overlapping time slots (TSs). There are M equal TSs in all for content transmissions. In the followingcontent, the number of TSs is used to measure the length ofthe transmission time.Next, the channel model and traffic model of the proposedscheme will be presented in detail. A. Channel Model
In the vehicular network, channel model has a signif-icant impact on transmission performances. According tothe dynamic channel environments and fast-varying networktopologies, we assume the V2V links exist only betweenneighbor vehicles with line-of-sight (LOS) links, the path lossexpressions are given as [20]
P L ( d ) = D l d − α l , (1) where D l = ( λ/ π ) α l is constant that represents the path lossof unit length distance of LOS links, and λ is the wavelength. α l is the path loss exponent of LOS which is affected by theenvironmental scenario. P L ( d ) represents the path loss for thelink of distance d .From a certain recent tractable models [21], [22], we adoptan independent Nakagami-m distributed channel model foranalyzing mmWave channel fading characteristics, where m is the fading depth parameter. The Nakagami-m distributedchannel model does not assume the existence of LOS, but usesthe gamma function to fit the experimental data. Therefore,the Nakagami-m distributed channel model is more generalin mmWave communication. The probability density function(pdf) of the channel envelope A in Nakagami-m distributed isgiven as [23], [24] f A ( a ; m, ω ) = 2Γ( m ) (cid:16) mω (cid:17) m a m − exp (cid:16) − mω a (cid:17) , (2)where ω is the average power of the signal, and Γ( m ) is thegamma function which is defined by Γ( z ) = (cid:82) ∞ x z − e − x dx for any real number z>
0. In the Nakagami-m distributedchannel model, the channel power gain is gamma-distributed.The pdf of the channel power gain H in gamma-distributed isgiven as [25] f H ( h ; (cid:37), ς ) = ς − (cid:37) h (cid:37) − e − h/ς Γ( (cid:37) ) , (3)where (cid:37) ( (cid:37) = m ) is the shape parameter, ς ( ς = 1 /m ) isthe scale parameter, and Γ( (cid:37) ) is the gamma function withparameter (cid:37) .For desired link ( i, j ) , the received signal power at OBU j from OBU i can be calculated as P r ( i, j ) = P t G h i,j D l d − α l i,j , (4)where P t is the transmit power of the link, G is the maximumdirectivity antenna gain, and h i,j is the channel power gain oflink ( i, j ) in gamma-distributed (3).For interfering link ( k, j ) , the received signal power at OBU j caused by desired link ( k, r ) can be calculated as P r ( k, j ) = P t G j,l k,r h k,j D l d − α l k,j , (5)where G j,l k,r is the antenna gain at OBU j from link ( k, j ) which is calculated as (11), and h k,j is the channel power gainof link ( k, j ) in gamma-distributed channel.Due to FD communication, self interference (SI) needs tobe considered in the V2V phase. For the problem from SI, somany cancellation schemes have been proposed so far, but theexisting SI cancellation schemes cannot completely eliminateSI. In fact, SI cancellation is a very complex research focus, sowe will not introduce related techniques in the paper. In orderto be realistic, we assume that appropriate SI cancellationtechnology is employed, then the amount of remaining selfinterference (RSI) can be represented by the transmit powerof the link receiver in the calculation. If OBU j are the receiverof link ( i, j ) and the transmitter of link ( j, f ) at the same time,the RSI must exist at OBU j and can be denoted by β j P t j,f ( f ∈ N ), where β j represents the SI cancelation level at OBU j and is a non-negative parameter. Multiple antennas can send messages simultaneously, so the RSI can come from multiplelinks at the OBU.According to equation (4), (5) and the expression of RSI,the SINR at the receiver of link ( i, j ) is given as follows Λ i,j = P t G h i,j D l d − α l i,j N W + I i,j + (cid:80) β j P t , (6)where N is the onesided power spectral density of whiteGaussian noise, W is the channel bandwidth, and I i,j is thesum interference of other concurrent links. I i,j = (cid:88) k ∈N \{ i } ,r ∈N \{ j } P t G j,l k,r h k,j D l d − α l k,j . (7)Therefore, the channel capacity of link ( i, j ) between OBU i and j is given by c i,j = W log (1 + Λ i,j ) . (8)In order to guarantee transmission qualities of links, QoSrequirements of V2V links are given, that is, the actual SINRof the link must be larger than the given SINR threshold.For all V2V links, th min is defined as the SINR threshold.Therefore, the condition that the V2V link from OBU i to j can be successfully transmitted can be expressed as Λ i,j ≥ th min . (9) B. Traffic Model
Considering a mobility model in highway scenarios, whichis similar to the Freeway Mobility Model (FMM) in [26]. Atthe beginning, all vehicles are randomly distributed in lanesand drive at their initial speeds. To cope with the high-speedmovement of the vehicle, we need to obtain state parametersof each vehicle every time slot. Vehicles randomly choose toaccelerate or decelerate in every slot.In order to simplify the network structure, we assume thatthere is a two-lane freeway without intersections as shownin Fig. 1. For two subsequent vehicles in the same lane, thedistance between them is limited to [ d min , d max ] . d min is asecurity distance and d max is an upper bound of distance. Inaddition to the distance, the velocity of each vehicle is limitedto [ v min , v max ] . Thus, the initial speed of OBU i is limited by v min ≤ v i (0) ≤ v max , and vehicles speed up or slow downby probability p . The choice of each vehicle is independent,and the acceleration is a > . We assume that vehicles in eachlane will not change the direction of travel on this highway.Limitations of velocity and distance are to make the networkmodel more in line with the actual vehicle network.According to the above constraints, the speed of OBU i ∈ N in slot t satisfies ( < p < / ): v i ( t + 1) = min [ v i ( t ) + a, v max ] p,max [ v i ( t ) − a, v min ] p,v i ( t ) , − p. (10)On account of different speeds of different vehicles andlimited distances between subsequent vehicles, some vehicleshave overtaking behavior in the actual situation. However,there is only single lane of one direction in the setting highway vehicle ivehicle jvehicle k (ij,k) Fig. 2. Interference model between V2V communications model. In order to ensure the safety of vehicle traveling, wedon’t consider the situation of the vehicles overtaking in thispaper. For any OBU i ∈ N with OBU j ahead in the samelane, the constraints of OBU’s behavior change are given asfollows1) If d i,j ≤ d min , OBU i decelerates to v i ( t + 1) = v min .2) If d i,j ≥ d max , OBU i accelerates to v i ( t + 1) = v max . C. Antenna Pattern
Considering mmWave communications in the vehicular net-work, directional antenna is necessary to ensure transmissionquality [27]. Thus, what follows is a specific analysis of theantenna model for V2V communications.We have assumed that all OBUs communicate in the FDmode, which means each vehicle can send and receive mes-sages simultaneously. To simplify the problem, we assume thateach vehicle can send messages to multiple vehicles at thesame time, but can receive message from only one vehicle.So we adopt multiple antennas to form multiple directionalbeams at each vehicle for transmitting multiple data linkssimultaneously [28]. The maximum number of beams formedsimultaneously at each vehicle is denoted by B t .The interference model between V2V communications inthe smart antenna is shown as Fig. 2. We assume vehicleshave perfect channel state information (CSI) and can steertheir antenna orientations for the maximum directivity gain[21], [29]. The perfect beam alignment for the desired link hasthe maximum directivity antenna gain of G , i.e., the antennagain of the link between OBU i and j is G . We denote theangle between the beam direction and the direction of an OBUby θ , i.e., the angle between beam direction of link ( i, j ) andthe direction of OBU k is θ ( ij,k ) . Thus, the antenna gain ofthe interfering link ( i, j ) at OBU k is specified as [30], [31] G k,l ij = − min (cid:34) (cid:18) θ ( ij,k ) θ dB (cid:19) , A m (cid:35) + G , − π ≤ θ ≤ π, (11)where θ dB is the 3dB beam-width in degrees, and A m is themaximum attenuation. When θ = 0 , G i = G is the antennagain of the desired link.IV. P ROBLEM F ORMULATION
In this section, we propose the formulation of the co-operative transmission in the vehicular network. This workaims at maximizing the amount of received contents in thefixed time. Moreover, the main challenge is how to jointlydetermine the broadcasting content of each broadcasting OBU, and how to group broadcasting OBUs from a content numbermaximization perspective. We define a binary variable δ ci to indicate whether the OBU i has received the content c successfully. If that is the case, we have δ ci = 1 ; otherwise, δ ci = 0 . Hence, the objective function of the proposed schemeis given by max |N | (cid:88) i ∈N (cid:88) c ∈C δ ci . (12)For the OBU i , we define a binary variable ϕ ti,j,c to indicatewhether the content c is transmitted from OBU i to OBU j in slot t . If it is the case, we have ϕ ti,j,c = 1 ; otherwise, ϕ ti,j,c = 0 . Due to the transmission characteristic of theFD mode, each OBU can be the transmitter and receiver atthe same time. However, one OBU cannot be the receiversof multiple concurrent links owing to the setting of singlereceiving antenna of each OBU. Then, we can obtain therelated constraint as follows. (cid:88) i ∈N (cid:88) c ∈C ϕ ti,j,c ≤ , ∀ j ∈ N . (13)In any slot, the broadcast contents of one OBU to otherOBUs should be the same. Therefore, we can obtain thefollowing constraint. ϕ ti,j,c + ϕ ti,j (cid:48) ,c (cid:48) ≤ , ∀ i ∈ N , ∀ j, j (cid:48) ∈ N , ∀ c, c (cid:48) ∈ C . (14)According to the setting of B t receiving antennas of eachOBU, the constraint of OBU i can be given by (cid:88) j ∈N ϕ ti,j,c ≤ B t , ∀ i ∈ N , ∀ c ∈ C . (15)In summary, the problem of optimal selection and schedul-ing can be formulated as follows.max |N | (cid:88) i ∈N (cid:88) c ∈C δ ci . s.t. (13) − (15) . This optimal problem is a nonlinear integer programmingproblem, and is NP-hard [32]. We propose the selectionapproach to maximize the number of received contents in nextsection. Besides, we will also propose a game theory modeland define the utility function of the coalitional game.V. B
ROADCASTING C ONTENT S ELECTION A LGORITHM
Focusing on the V2V cooperative transmission, we firstdetermine the broadcasting content of each OBU. The numbersof slots for different content transmissions are unequal, butthe broadcasting content selections of OBUs are all simulta-neously executed before the transmissions. In a certain slot t ,we select the broadcasting contents of OBUs. Due to the shortduration of the slot, we assume vehicles are stationary in a timeslot. The possessed content set of OBU i ∈ N is denoted by Γ i . The neighbor set of OBU i is denoted by N i , and OBUs in N i satisfy (9). The set of the neighbors that is sure to receivebroadcasting content from OBU i is denoted by N ∗ i ⊆ N i .We have assumed the number of transmitting antennas of eachOBU is B t , so we have |N ∗ i | ≤ B t . Moreover, the selectedbroadcasting content of OBU i is denoted by γ i fin . For any OBU in the system, it can be the neighbor of severalOBUs, but it only can receive the content from one OBU ineach slot. If there are LOS links between OBU i and bothOBU m and OBU n , we can obtain the constraint as follows. i ∈ N m & i ∈ N n , If i ∈ N ∗ m , i (cid:54)∈ N ∗ n , If i ∈ N ∗ n , i (cid:54)∈ N ∗ m . (16)OBUs broadcasting different contents has a significant im-pact on transmission performances. Therefore, we proposea broadcasting content selection algorithm. The goal of theselection algorithm is to successfully transmit broadcastingcontents from broadcasting OBUs to as many neighbor OBUsas possible.First, each broadcasting OBU must select its broadcastingcontent from its possessed contents. We denote one of thepossessed contents of OBU i by γ pi ∈ Γ i . And then theset of the neighbors that need content γ pi can be denoted by N γ pi i ∗ . When | N γ pi i ∗ | isn’t larger than the number of transmittingantennas of broadcasting OBU, we only compare the value of | N γ pi i ∗ | to select the broadcasting content. For maximizing thenumber of OBUs that receive the broadcasting content, γ pi isselected to be broadcasted by OBU i , if and only if |N γ pi i ∗ | ≥ |N γ qi i ∗ | , ∀ γ qi ∈ Γ i , |N γ pi i ∗ | ≤ B t , |N γ qi i ∗ | ≤ B t . (17)However, there may be more than B t neighbors of broad-casting OBUs. According to different content sizes and dif-ferent transmission rates, we define a parameter to estimatethe TS number of content γ pi transmission from broadcastingOBU i to its neighbor jT γ pi i,j = D γ pi c i,j · ∆ t , (18)where c i,j is the transmission rate calculated by (8), and ∆ t is the time duration of one slot. D γ pi is the size of content γ pi .Since concurrent links are not determined, we do not considerinterferences of other links here.For any possessed content γ pi of OBU i , we select B t neighbor OBUs j , j , ..., j | B t | ∈ N γ pi i ∗ with relatively small T γ pi i,j , T γ pi i,j , ..., T γ pi i,j | Bt | to receive it. In this case, γ pi is selectedto be broadcasted by OBU i , if and only ifmax { T γ pi i,j , T γ pi i,j , ..., T γ pi i,j | Bt | } ≤ max { T γ qi i,j (cid:48) , T γ qi i,j (cid:48) , ..., T γ qi i,j (cid:48)| Bt | } , ∀ γ qi ∈ Γ i , j (cid:48) , j (cid:48) , ..., j (cid:48)| B t | ∈ N γ qi i ∗ . (19)Transmitting contents that need less slots preferentially cancomplete their transmissions quickly and leave slots for othercontents. Therefore, OBUs can obtain more contents. If thenumber of neighbors that need different broadcasting contentsare the same, this selection method is equally applicable. Thebroadcasting content selection algorithm is summarized inAlgorithm 1. In Lines 5-13, selecting the broadcasting contentfor the broadcasting OBU with more than B t neighbors ac-cording to (19). In Lines 17-24, the algorithm does the contentselection under the condition of equal number of neighborOBUs. Finally, we obtain the selected broadcasting content of Algorithm 1
Broadcasting Content Selection Algorithm
Initialization:
Obtain the location of each OBU; obtain theneighbor set and possessed content set of each OBU; setNum = 0 ; set T = ∞ ; set γ i fin = 0 and N ∗ i = ∅ of eachOBU; for OBU i ( ≤ i ≤ N ) do for possessed content γ pi ( γ pi ∈ Γ i ) do num = |N γ pi i ∗ | ; if num > Num then if num > B t then for OBU j ( j ∈ N i ) do calculate T γ pi i,j ; end for select B t neighbor OBUs j , j , ..., j | B t | ∈ N γ pi i ∗ with relatively small T γ pi i,j , T γ pi i,j , ..., T γ pi i,j | Bt | ; if max { T γ pi i,j , T γ pi i,j , ..., T γ pi i,j | Bt | } < T then γ i fin = γ pi ; end if else γ i fin = γ pi ; end if else if num = Num then for
OBU j ( j ∈ N i ) do calculate T γ pi i,j ; end for if max { T γ pi i,j , T γ pi i,j , ..., T γ pi i,j |N γpii ∗ | } < T then γ i fin = γ pi ; end if end if end if end for Output γ i fin and N ∗ i ; end for each OBU and the neighbors that receive this selected contentin Line 27.For the complexity of the selection algorithm, the outer for loop has O ( N ) iterations. The number of the iterations of the for loop in Line 2 is | Γ i | , where | Γ i | in the worst case is O ( C ) . The for loop in Line 6 has |N i | iterations, and |N i | inthe worst case is O ( N − .So the computational complexityof this algorithm is O ( CN ( N − .Broadcasting contents of different OBUs are decided bythis broadcasting content selection algorithm, and then we willconstruct the coalition formation game.VI. F ULL - DUPLEX C OALITION F ORMATION A LGORITHM
In this section, we propose a FD coalition formationalgorithm, and provide some related definitions and somenecessary proofs.
A. Coalition Formation Concepts
Since the proposed solution is based on the cooperation ofplayers, we model the PCD problem as a coalition formation game [13], [33], [34]. After determining the broadcastingcontent of each OBU by Algorithm 1, we need to select OBUsthat can broadcast their selected broadcasting contents at thesame time. The set of simultaneous broadcasting OBUs isdefined by S . The limitations of simultaneous transmissionsof OBUs have been detailed in Section IV. In addition toconstrains of simultaneous broadcasting, selecting OBUs intothe simultaneous broadcasting group to acquire more contentsis the key. This problem is modeled as a coalitional game witha transferable utility, and the definition of the coalitional gameis as follows. Definition 1:
A coalitional game is defined by a pair ( N , V ) , where N is the set of game players and V is afunction over the real line, V ( S ) is a real number describingthe value that coalition S ⊆ N can receive, the members of S can be distributed in arbitrary manner, and the coalitionalgame is with transferable utility.For any coalition S , the value V ( S ) comes from coopera-tions among OBUs in coalition S . In order to get the accuratevalue of V ( S ) , we need to calculate the total revenue generatedby coalition S first. The total revenue of S is calculated byutility function U ( S ) .According to the contribution of content transmissions be-tween OBUs, we define the utility function U ( S ) is propor-tional to the number of network’s received contents which arefrom broadcasting OBUs in S . A certain number of contentscan be received from broadcasting OBUs in S , and the setof these contents is denoted by C t . Thus, the utility function U ( S ) is given by U ( S ) = α ( (cid:88) i ∈N (cid:88) c ∈ C t δ ci ) . (20)where α > is a utility calculation factor.The player cooperations can increase the number of receivedcontents of OBUs, but these gains are limited by inherent coststhat need to be paid by OBUs for broadcasting and receiving.These costs can be captured by a cost function C ( S ) whichlimits the total revenue. Since broadcast durations of OBUs ineach coalition are short, we hold that the amount of neighborsof each OBU is approximately stable. Thus, the cost function C ( S ) is considered as follows C ( S ) = (cid:40) µ | S | , if | S | > , , otherwise , (21)where µ > is the pricing factor. OBUs in a coalition needto determine broadcast contents, synchronize and transmitcontents to other OBUs. Thus, for each coalition S ∈ N ,OBUs need to pay a cost for coordination, which is anincreasing function of the coalition size such as in (21).Consequently, the value V ( S ) of any coalition S can beexpressed by the utility function in (20) and the cost functionin (21), which is given by V ( S ) = U ( S ) − C ( S ) . (22)This value function quantifies the effective revenue of OBUcooperations in a coalition S . In the next section, a coalitionformation algorithm will be devised to obtain the coalitionwith the utility function. In fact, coalition formation is a very noticeable topic ingame theory [35]–[37]. Choosing the players to join or leave acoalition based on well-defined preferences is one of the majorapproaches for forming coalitions. This approach for coalitionformation is based on many existing coalition formation con-cepts, such as the hedonic games or merge-and-split algorithm[36]–[38]. For the proposed coalition formation of the PCD,we introduce some related definitions.First, the proposed cooperation model entails the formationof disjoint coalitions, which is given as follows Definition 2:
A coalitional structure or partition is definedas the coalition set
Π = { S , ..., S l } , Π partitions the OBUset N , coalitions in Π are disjoint, i.e., ∀ k , S k ⊆ N , (cid:83) lk =1 S k = N (the OBUs in the same coalition can broadcastsimultaneously).In order to make explanations more convenient, a relateddefinition is given by Definition 3:
For any OBU i ∈ N , given a partition Π , thecoalition S k ∈ Π , i ∈ S k , the coalition of i in Π is denotedas S Π ( i ) .Based on the relation of preferences in the coalition forma-tion game, each OBU must compare and order its potentialcoalitions. To be specific, each player must select a coalitionwhich it prefers to be a member of. For evaluating thesepreferences over the coalitions, the definition of preferencerelation is introduced. Definition 4:
For any OBU i ∈ N , a preference relation (cid:23) i is defined as a binary relation over the partition of all coalitionsthat OBU i can possibly form, it is complete, reflexive, andtransitive, i.e., the set { S k ⊆ N : i ∈ S k } .Hence, given any two coalitions S , S ⊆ N , S (cid:23) i S implies that OBU i prefers being a member of coalition S with i ∈ S over coalition S with i ∈ S , or at least,OBU i prefers both coalitions equally. On the basis of thispreference relation (cid:23) i , a asymmetric counterpart is denotedby (cid:31) i , S (cid:31) i S implies that OBU i strictly prefers beinga member of coalition S over coalition S . In order tospecifically compare or sort the coalitions, we concrete thepreference relation into a function which is used to comparethe profit of received contents of different coalitions. To bespecific, the profit of the coalition can be calculated with theamount of contents which are successfully received. Therefore,we utilize the value V ( S ) in 22 to compare the profit broughtby OBU i joining any coalition. In addition, the individualprofits of other members in any coalition cannot be damagedby the joining of OBU i . The individual profit of OBU j in coalition S can be calculated with the amount of neighborsthat can receive broadcasting content γ j fin from OBU j . Due tocollisions of simultaneous broadcasting OBUs, the neighborsthat can receive broadcasting content from any OBU in thecoalition may change when members of this coalition change.The individual profit of OBU j in coalition S can be expressedas ψ jS .Based on the value V ( S ) , we propose the following pref-erence relation ( S , S ⊆ N ) S (cid:31) i S ⇔ V ( S ∪ { i } ) > V ( S ∪ { i } )& ψ jS ∪{ i } ≥ ψ jS , ∀ j ∈ S . (23) Algorithm 2
The Full-duplex Coalition Formation Algorithm
Initialization:
The OBUs in the network are randomly di-vided into an initial partition Π ini ; Set the history col-lections h ( i ) = ∅ , ∀ i ∈ N ; Set the current partition Π cur = Π ini ; Set the final Nash-stable partition Π fin =Π ini ; repeat Randomly choose an OBU i ∈ N with current partition Π cur , and denote its current coalition by S k = S Π ( i ) ; Search for a coalition S m ∈ Π cur ∪∅ , where S m ∪{ i } (cid:31) i S k , S m (cid:54) = S Π ( i ) , S m ∪ { i } (cid:54)∈ h ( i ) ; Perform the broadcasting packet selection algorithm asper V, and re-calculate the individual profit ψ jS of anyOBU j . if the switch operation from S k to coalition S m ∈ Π cur ∪∅ exists then Add the current coalition S Π cur ( i ) to the historycollection h ( i ) ; OBU i leaves the current coalition S Π cur ( i ) and joinsthe new coalition S Π new ( i ) ; Update the current partition Π cur to the new partition Π (cid:48) cur ; Π cur = Π (cid:48) cur ; Since OBU i joins the new coalition S Π new ( i ) andimproves its payoff, update the cost of all the coali-tions in new partition; end if until the partition converges to a final Nash-stable parti-tion Π fin These coalition formation concepts have been defined inthis section, and then we will propose the coalition formationalgorithm over these definitions.
B. Full-duplex Coalition Formation Algorithm
In order to choose the most appropriate coalition for eachOBU, we propose an algorithm that allows the OBU to takedistributed decisions for selecting which coalitions to join. TheOBUs form disjoint coalitions by switching operations, whichis defined as following.
Definition 5:
Given a partition
Π = { S , ..., S l } of theOBUs set N , if any OBU i ∈ N decides to leave its currentcoalition S Π ( i ) = S k and join another coalition S m ∈ Π ∪{∅} ,perform a switch operation from S k to S m . The partition Π ( Π ⊆ N ) is modified into a new partition Π (cid:48) such that Π (cid:48) = (Π \ { S k , S m } ) ∪ { S k \ { i } , S m ∪ { i }} .The basic rule for performing the switch operations is givenas follow Switch Rule 1 : Given a partition
Π = { S , ..., S l } of the OBUsset N , for any OBU ∀ i ∈ N , if and only if S m ∪ { i } (cid:31) i S k and S m ∪ { i } (cid:54)∈ h ( i ) ( S k ∈ Π , S m ∈ Π ∪ {∅} ), a switchoperation from S k to S m is allowed.Here h ( i ) is a history set of coalitions that OBU i has visitedin the past and then left. In this rule, any OBU i ∈ N canleave its current coalition S Π ( i ) , and join another coalition.The new coalition is strictly preferred over last coalitionthrough the preference relation defined in (23). The coalition formation game is specifically summarized in Algorithm 2.In this algorithm, every OBU try to select its top preferredcoalition by performing switch operations. We assume thatthe order in which the OBUs make their switch operations israndom. As each time a switch operation as (5) is performed,the algorithm needs to re-determine the neighbors of eachbroadcasting OBU and re-perform the broadcasting contentselection algorithm as per V. With the partition changing,the best broadcasting contents selected by the broadcastingOBUs may also change. The proposed algorithm needs toadopt the dynamic broadcasting content selection, thereby amore realistic result of utility function comparison can beobtained. Finally, we will get the optimal OBU coalition. Theconvergence of the proposed coalition formation algorithm isguaranteed as follows Theorem 1:
Whatever the initial partition Π ini is, theproposed coalition formation-based algorithm can map to aseries of switch operations, and the algorithm will alwaysconverge to the final partition Π fin which is composed ofmany disjoint coalitions. Proof:
For the proof of this theorem, we denote thepartition which is formed during turn k of any OBU i ∈ N by Π kn k , where n k is the number of switch operations of theturn k . As the OBU is randomly selected of each turn, thepartition may or may not change, details are as follows Π kn k = Π k +1 n k +1 , n k = n k +1 , (24)where the number of switch operations is n k and is unchanged,the meaning of (24) is that there is no possible switch operationof the turn k + 1 and the partition does not change. Π tn t → Π t +1 n t +1 , n t (cid:54) = n t +1 , (25)(27) means that a switch operation is performed in the turn t + 1 and the new partition is yielded.From the preference relation defined in (23), it can be foundthat a single switch operation of any OBU i ∈ N may leadto yield an unvisited partition or a previously visited partitionwith a non-cooperative OBU i (OBU i is a singleton coalitionof the new partition). If there is a non-cooperative OBU i in partition, it need decide to join a new coalition or remainnoncooperative. If OBU i remains non-cooperative, the currentpartition cannot be changed to any visited partitions in thenext turn, as shown in (24). If OBU i decides to join a newcoalition, the switch operation made by OBU i will form anunvisited partition without non-cooperative OBUs, as shownin (27). No matter how to do it, an unvisited partition will beformed. Besides that, as the well known fact is the numberof partitions of a set is given by the Bell number [35], thereare finite different partitions in total. So the entire convergingprocess is given by Π → Π = Π → ... → Π sn s . (26)Because the different partitions of the fixed OBUs is finiteand each switch operation yields an unvisited partition, thenumber of transformations in (26) is finite, and the sequencein (26) will always terminate and converge to a final partition Π fin = Π sn s after s turns. Thus, the coalition formation of the proposed algorithm will converge to a final network partition Π fin composed of a number of disjoint OBU coalitions, whichcompletes the proof.The proposed algorithm finally converges to the partition Π inf and stays in a stable state. The stability of Π inf is definedby the following stability concept [36] Definition 6:
For any partition
Π = { S , ..., S l } , if ∀ i ∈ N , S Π ( i ) (cid:23) i S k ∪ { i } for all S k ∈ Π ∪ {∅} , it is Nash-stable.The definition 6 implies that, if there is no OBU hasan incentive to perform a switch operation from its currentcoalition to another coalition, the current partition must bea Nash-stable partition. The Nash-stable partition implies thatany OBU i does not prefer to be the part of any other coalition S k over being the part of its current coalition S Π ( i ) , as per(24). Besides, OBU i cannot hurt the profits of other OBUsin Nash-stable partition. Proposition 1:
The final partition Π fin of our proposedcoalition formation algorithm is Nash-stable. Proof:
We make a hypothesis that the final partition Π fin resulting from the proposed coalition formation algorithm isnot Nash-stable. Consequently, there must be an OBU i ∈N and a coalition S k in partition Π fin , which can satisfy theconditions S k ∪{ i } (cid:31) i S Π fin ( i ) , and hence, OBU i can performa switch operation. So this situation contradicts with the factthat Π fin is the result of the convergence of the Algorithm2. The hypothesis cannot be established. Thus, any partition Π fin resulting from the coalition formation algorithm is Nash-stable.For V2V communications, vehicles exchange their pos-sessed contents to get different popular contents by the pro-posed coalition formation algorithm, but the coalition forma-tion algorithm is limited by the network scale. If the networkscale is large with too many OBUs in the network, contentscannot be shared in time and the delay for receiving morecontents is long. In addition, in the lanes where vehicles aresparsely distributed, there may be some vehicles that cannotcommunicate with other vehicles due to distance and areseparated from other vehicles. Thus, the splitting of OBUs isneeded to catch up the changes of environment and adapt to thedynamic number of OBUs. Once the number of OBUs exceedsthe threshold or some OBUs split into the disconnected parts,all the OBUs in the network automatically split into multiplesubnetworks without any overlap. There have been manyalgorithms of network splitting in the existing literature [14],we will not repeat it in this paper. So we can conclude that thenumber of OBUs involved in our scheme is not large, or OBUswill split into multiple subnetworks and execute the algorithmin each subnetwork.VII. S IMULATION R ESULTS
A. Simulation Setup
In this section, we simulate performances of the proposedscheme and other existing schemes. We consider a straight 2-lane highway which has been introduced in Section III. V2Vcommunications are in the 28GHz mmWave vehicle network.To ensure that contents can be transmitted normally whenvehicles are moving fast, we update positions of vehicles
TABLE II S IMULATION P ARAMETERS
Parameter Symbol ValueLength of the simulation area L m Number of time slots M Number of OBUs in the network N ∼ Slot duration ∆ t ms Transmit power P t
30 dBmSystem bandwidth W N -134dbm/MHzSI cancelation level β − SINR threshold of the V2V link th min dB Number of contents C Content size D Mb ∼ Mb Acceleration a m/s Probability of changing speed p . Minimal speed v min m/s Maximal speed v max m/s Minimal distance d min m Maximal distance d max m Pricing factors α, µ , Path loss exponent α l Fading factor of channel model m Maximum number of V2V beams B t Maximum antenna gain G dBi Maximum attenuation of antenna model A m dB θ dB . ◦ and calculate new transmission rates of links every 10 slots,and then transmission scheme continues to be executed. Thesimulation parameters of the highway scenario are listed inTable II. And we set parameters of mobility model, antennamodel, and channel model with reference to [14], [31], and[24].In the simulations, we compare the following performancemetrics of each scheme respectively.1) Possessed contents : The number of contents possessedby all OBUs.2)
Fairness : Fairness performance is denoted by the jainsfairness measure. The Jains fairness measure in [39] can beused to determine whether the individual profit of each OBUin coalition are fairly achieved. The number of neighbors thatcan receive the broadcasting content from OBU i ( i ∈ S ) is ψ iS . Thus, the Jains fairness measure is J ( ψ S , ψ S , ..., ψ | S | S ) = ( (cid:80) i ∈ S ψ iS ) | S | · (cid:80) i ∈ S ( ψ iS ) . (27)3) Number of switch operations : The number of switchoperations that are performed until the partition achieves aNash-stable partition.4)
CPU time : CPU time is the actual duration for the entirescheme executing once.Existing schemes compared with the proposed scheme (
FDcooperative scheme ) are as follows1) coalition game scheme [10]: It uses V2V communicationsto transmit and relay contents in the vehicular network, and isalso based on the coalition formation game. The utility func-tion is given based on the minimization of average networkdelay.2) non-cooperative scheme : Broadcasting content of eachOBU is selected randomly, and there is no coordination Number of OBUs P o ss e ss ed c on t en t s FD cooperative schemeNon-cooperative schemeCoalition game scheme
Fig. 3. Number of possessed contents versus the number of OBUs. between OBUs. Broadcasting OBUs transmit contents to alltheir neighbors without considering collisions.In order to obtain more reliable average results, all simula-tions in this paper perform 200 times.
B. Simulation Results
In Fig. 3, we plot the number of possessed contents underdifferent OBU amounts. We can see that possessed contentamounts of three schemes are all increasing with the increasednumber of OBUs. The more OBUs in vehicle networks,the more OBUs can simultaneously broadcast and the moreneighbors can receive contents from broadcasting OBUs. Forthe non-cooperative scheme, possessed contents are much lessthat of the proposed cooperative scheme. Besides, the risingtrend of the non-cooperative scheme is also more slowly.The non-cooperative scheme randomly selects broadcastingcontents of OBUs, and there are so many collisions amongbroadcasting OBUs. Therefore, the non-cooperative schemehas the relatively worst performance on possessed contentsamong three schemes. For the coalition game scheme, thegrowth trend is similar to that of the proposed scheme. Pos-sessed contents of the coalition game scheme are fewer thanthat of the proposed scheme, since this scheme is proposed tominimize the network transmission delay. When the number ofOBUs is 14, the proposed FD cooperative scheme promotesthe number of possessed contents by 12.5% compared withthe coalition game scheme, and by 136.8% compared withthe non-cooperative scheme.In Fig. 4, we plot the fairness under different numbers ofOBUs. Along with the increase of OBUs, trends of the pro-posed scheme and the coalition game scheme are both falling,but the trend of the non-cooperative scheme is rising. Forthe non-cooperative scheme, collisions from no coordinationamong OBUs leads to few OBUs in coalitions. Few OBUsof each coalition can improve the fairness. With the increasednumber of OBUs, collisions among OBUs are becoming more,and the number of OBUs that can simultaneously broadcastare decreasing. Thus, the non-cooperative scheme has a risingtrend of the fairness. For other two cooperative scheme,
Number of OBUs F a i r ne ss FD cooperative schemeNon-cooperative schemeCoalition game scheme
Fig. 4. Fairness under versus the number of OBUs.
Number of OBUs N u m be r o f s w i t c h ope r a t i on s FD cooperative schemeCoalition game scheme
Fig. 5. Number of switch versus the number of OBUs. coordinations make more OBUs simultaneously broadcast withthe increase of OBUs. And then their trends of the fairnessboth fall due to more broadcasting OBUs. Compare with thecoalition game scheme, our proposed scheme protects theindividual profit of each OBU in coalition. Therefore, theperformance of the proposed scheme on fairness is better thanthat of the coalition game scheme.In Fig. 5, we plot the number of switch operations underdifferent numbers of OBUs. The non-cooperative scheme hasno switch operations, so there are only two result curves. Thenumber of switch operations can reflect the complexity of eachalgorithm. We can see that switch operations of two schemesare both becoming more with the increased number of OBUs.Besides, switch operations of the proposed FD cooperativescheme are less than that of the coalition game scheme. Thecoalition game scheme seeks to the minimization of averagenetwork delay, so it needs to execute coalition game algorithmmore times in the fixed time compared with the proposedalgorithm. However, Fig. 5 can illustrate that the complexityof the proposed algorithm is lower.In Fig. 6, we plot the CPU time with the different numbers Number of OBUs C P U t i m e ( s ) FD cooperative schemeCoalition game scheme
Fig. 6. CPU time versus the number of OBUs.
16 17 18 19 20 21 22 23 24
SINR threshold (dB) P o ss e ss ed c on t en t s FD cooperative schemeNon-cooperative schemeCoalition game scheme
Fig. 7. Number of possessed contents versus the SINR threshold. of OBUs. In order to verify the complexity of the entirescheme (including the broadcasting content selection algo-rithm in Section V), the CPU times of different schemesare calculated. The result is similar to the result in Fig.5, our proposed algorithm has shorter CPU time and lowercomplexity. And we can also see that the CPU time forexecuting the entire proposed scheme once is less than asecond when the number of OBUs is less than 10.In Fig. 7, we plot the number of possessed contents underdifferent SINR thresholds. The number of OBUs is set to10. For these three schemes, overall trends of their resultcurves are the same. With the increase of SINR threshold,the possessed content numbers of schemes all increase firstand then decrease. Properly increasing of SINR threshold canavoid some transmissions with very small rates. And thenrates of other transmissions can be increased, which willlead to shorter transmit time and more possessed contents.When the SINR threshold is increased to a certain value(i.e., th min = 20 dB in Fig. 7), the numbers of possessedcontents of all schemes start to decrease. This is becausethat too small SINR thresholds weaken the advantage of SI level/-lg( ) P o ss e ss ed c on t en t s FD cooperative schemeNon-cooperative schemeCoalition game scheme
Fig. 8. Number of possessed contents versus the SI level. spatial reuse and reduce possessed contents of the network.So an appropriate actual SINR threshold is important fortransmission performances. In other simulations of this paper,we set the value of the SINR threshold to be 20dB.In Fig. 8, we plot the number of possessed contents underdifferent SI cancelation levels. The number of OBUs is set to10. The abscissa x is − lg ( β ) , i.e., the SI cancelation level β = 10 − x . The small value of β represents the high SIcancelation level. With the improvement of SI cancelationlevel, the numbers of possessed contents of three schemesall increase first and then keep stable. Properly increasingof the SI cancelation level can improve transmission rates ofbroadcasting contents. To some extent, high rates lead to morepossessed contents. When the SI cancelation level achievesa certain value (i.e., β = 10 − in Fig. 8), the numbers ofpossessed contents of three schemes start to be unchanged. Inthis case, the performance of these schemes mainly dependson different algorithms, and FD communications can no longerbring more promotion.VIII. C ONCLUSION
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