A Two-stage Game Framework to Secure Transmission in Two-Tier UAV Networks
11 A Two-stage Game Framework to SecureTransmission in Two-Tier UAV Networks
Mengnian Xu, Yanjiao Chen,
Member, IEEE , Wei Wang,
Senior Member, IEEE
Abstract —The multi-UAV network is promising to extendconventional networks by providing broader coverage and betterreliability. Nevertheless, the broadcast nature of wireless signalsand the broader coverage expose multi-UAV communications tothe threats of passive eavesdroppers. Recent studies mainly focuson securing a single legitimate link, or communications between aUAV and multiple ground users in one / two-UAV-aided networks,while the physical layer secrecy analysis for hierarchical multi-UAV networks is underexplored. In this paper, we investigatea general two-tier UAV network consisting of multiple UAVtransmitters (UTs) and multiple UAV receivers (URs) in thepresence of multiple UAV eavesdroppers (UEs). To protect alllegitimate UT-UR links against UEs at the physical layer, wedesign a two-stage framework consisting of a UT-UR associationstage and a cooperative transmission stage. Specifically, weformulate the secure transmission problem into a many-to-onematching game followed by an overlapping coalition formation(OCF) game, taking into account the limited capabilities andthe throughput requirements of URs, as well as the transmissionpower constraints of UTs. A matching algorithm and an OCFalgorithm are proposed to solve these two sequential gameswhose convergences and stabilities are guaranteed theoretically.Simulation results show the superiority of our algorithms andthe e ff ectiveness of our two-stage game framework in the termsof secrecy performance. Index Terms —Multi-UAV network, physical layer security,matching, overlapping coalition formation.
I. I ntroduction
Unmanned aerial vehicles (UAVs) have been rapidly de-veloped over the last decades based on their widely knownadvantages such as low cost and on-demand deployment.Since a multi-UAV network can cooperatively complete themission more e ffi ciently with larger coverage and resilienceto node failure, the use of multi-UAV networks to performvarious sensing tasks has recently drawn much attention, suchas precision agriculture, city tra ffi c monitoring, and disastermanagement [1]–[3]. In a multi-tier UAV architecture [4],di ff erent types of UAVs that have unique features such asmaximum flight altitude, communication coverage, computingability and durability, can take di ff erent roles, which enablesmore functional diversity for next-generation wireless commu-nications. This work was supported in part by the National Natural Science Foundationof China under Grants 62071194, 91738202, 61972296 and 61702380, YoungElite Scientists Sponsorship Program by CAST under Grant 2018QNRC001,National Key R&D Program of China under Grant 2017YFE0121500, andWuhan Advanced Application Project under Grant 2019010701011419.M. Xu and W. Wang are with the School of Electronic Information andCommunications, Huazhong University of Science and Technology, Wuhan430074, China (e-mail: { mengnian, weiwangw } @hust.edu.cn).Y. Chen is with the School of Computer Science, Wuhan University, Wuhan430072, China (e-mail: [email protected]). Although the broadcast nature of wireless signals andthe broad coverage provide e ffi cient collaboration in a UAVnetwork, they also expose UAV-to-UAV communications tomalicious eavesdroppers, especially the more flexible UAVeavesdroppers. A multi-UAV network usually collects vital orconfidential messages, such as the information for monitoringan airport or a nuclear station, which may be interceptedby criminals or terrorists to commit crimes. Therefore it isincreasingly urgent and necessary to ensure secure communi-cations against eavesdroppers in multi-UAV networks.In contrast to traditional cryptographic-based methods tosecure transmission, which are computationally costly andunsuitable for resource-constrained UAVs, physical layer se-curity (PLS) has been an e ff ective alternative. Nevertheless,although PLS in wireless communications has received muchattention, there have been few studies on protecting multi-UAVcommunications against eavesdropping. Most existing PLSschemes in UAV-aided networks focus on securing a singlelegitimate source-destination communication link, leaving thesecure transmission issue in hierarchical multi-UAV commu-nications underexplored. Specifically, they either protect asingle UAV-ground link from terrestrial eavesdropping [5], [6],or secure a single traditional terrestrial link against groundeavesdroppers [7] or UAV eavesdroppers [8], in which onlyone UAV acts as a mobile BS / relay / jammer to improve PLS.Furthermore, secure communications between a UAV-BS andmultiple ground users in the presence of ground eavesdroppershave been studied in [9], where an additional UAV-jammer isused to disturb the eavesdroppers, and PLS is improved byjointly optimizing the trajectories and transmit power of UAV-BS and UAV-jammer. However, these two UAVs are assumedto fly at a fixed altitude, which simplifies the analysis but limitsthe applicability in practice. In addition, it is di ffi cult to applyUAV trajectory and transmit power control method directlyinto multi-UAV networks since then the collision avoidancebecomes non-negligible and more complex.In this paper, we take the first step to investigate a two-tierUAV network consisting of multiple UAV transmitters (UTs)and multiple UAV receivers (URs), where each UT collectssensing data from its coverage of interest and then delivers thedata to a UR for further processing. In this case, multiple UAVeavesdroppers (UEs) intend to wiretap on the legitimate links.Our goal is to secure all legitimate UT-UR links against UEsin this network by jointly considering the UT-UR associationand the cooperative transmission scheduling. On one hand, byproperly associating UTs and URs, short-distance LoS linksfor data transmission can be proactively established whichbenefit both secrecy performance and the UR throughput a r X i v : . [ c s . G T ] S e p requirements. On the other hand, by performing cooperativebeamforming in which case a UT-source and some otherUT-relays transmit together towards the intended UR [10],the achievable secrecy rate can be significantly improved.Thereby we design a two-stage framework consisting of aUT-UR association stage and a cooperative transmission stage.To achieve this two-stage framework, we need to tackle thefollowing challenges.In the first UT-UR association stage, the limited processingcapability of each UR should be considered, thus the num-ber of UTs that a UR can serve is limited. Moreover, thethroughput requirements of URs should also be addressed inthe association process, which may conflict with the need forhigh network secrecy performance. The second cooperativetransmission stage aims to find an e ff ective relay selectionstrategy for each UT under a transmission power constraint,to maximize the total secrecy utility of the whole network.However, such a UT-UR association problem and a relayselection problem are non-trivial to solve because both of themare NP-hard problems.To tackle the above challenges, we formulate the UT-URassociation problem as a many-to-one matching game, inwhich UTs and URs make their matching decisions basedon their individual preferences. Then, to model the complexcooperative behaviors among the UTs in the cooperativetransmission stage, we formulate the relay selection problemas an overlapping coalition formation (OCF) game, in whicha UT can join multiple coalitions to assist multiple UTs’transmission in di ff erent time slots. In this way, by solvingthese two sequential games, the network can achieve a sta-ble association structure and a stable overlapping coalitionstructure to perform secure cooperative transmission. In ourproposed multi-UAV network, UTs and URs are viewed asselfish and rational agents aiming to improve their own utilitiesthrough interaction and cooperation. This scenario fits thefuture heterogeneous UAV network paradigm where di ff erentcompanies with potential conflict interests launch their UAVs.As game players, UTs and URs make their own decisionsin a distributed manner, which provides the network withself-organizing capability and adaptability to diverse circum-stances, thus benefiting the management and control of multi-UAV networks.A comprehensive survey of the application of game theoryto UAV networks is presented in [11]. Compared with cen-tralized optimization methods that usually require frequent in-formation exchange between UAVs and the central controller,game-based methods enable individual UAVs to make theirown decisions, thus reducing the communication overhead.Our main contributions can be summarized as follows. • We design a two-stage framework to protect all legitimatecommunication links against UAV eavesdroppers in ahierarchical multi-UAV network from a physical layerperspective. • We formulate the UT-UR association problem into amany-to-one matching game. Based on the characteristicsof our matching problem, we design a matching algorithmto achieve a pairwise stable matching result with highersocial welfare of UTs and URs. • We formulate the relay selection problem as an OCFgame. We also propose an OCF algorithm that maximizesthe collaboration between UTs and fully seeks the opti-mal structure, to achieve a stable coalition structure forperforming cooperative transmission. • Extensive simulations under various system parametersprove the superiority of our algorithms, and the e ff ective-ness of our two-stage game framework in the terms ofsecrecy performance.II. R elated W ork In this section, we show that our technical work di ff ers fromsome existing works related to matching theory and coalitionformation game theory in recent years, and we summarize thedi ff erences as follows. Matching Theory.
Our matching algorithm di ff ers fromthe existing works. First, we have distinctly di ff erent flowdesign. Quite a few works [12]–[14] on matching theory areextensions of the classical deferred acceptance (DA) algorithm,whose convergence and stability are easily guaranteed. Incomparison, our proposed algorithm consists of two phases,i.e., a preliminary interaction and a swapping operation. Notethat the DA algorithm is used as a baseline for comparisonwith our algorithm in our paper. Second, we have distinctmatching rules. The proposed algorithms in [15]–[18] di ff erfrom the conventional DA algorithm. However, none of thesealgorithms are applicable to our problem since our preferencefunctions have di ff erent characteristics. The matching rulesin [15]–[18] include that one cannot propose to the same objecttwice and one can remove current matched objects. Di ff erentfrom these rules, our matching rules are specifically designedfor our particular preference functions, aiming to yield highersocial welfare. Coalition Formation Game Theory.
Our coalition for-mation algorithm di ff ers from the existing works. Someworks [19], [20] focused on the non-overlapping coalitionformation game model, in which the players can only formdisjoint coalitions. In our paper, we model the relay selectionproblem as an OCF game that allows a player to participatein multiple coalitions to cooperate with more UTs, henceimproving the performance gain via a more complex coalitionstructure. Apart from the di ff erences in game formulation, ouralgorithm design is also di ff erent. For example, the solutionin [19] is based on split-and-merge strategies, which are onlysuitable for the disjoint coalition formation games. And thealgorithm in [20] is only based on a switching rule, whichgreatly limits the search for the potential optimal coalitionstructure. In comparison, our proposed algorithm can reach astable overlapping coalition formation. It is worth mentioningthat we have used the disjoint coalition game model andthe commonly-used merge-and-split strategies as one of ourbaseline schemes for comparison.Our algorithm design is also di ff erent from the related workson OCF games [21], [22]. First, we have di ff erent initial states,which are important for the evolution of coalition formation.In [21], [22], the initial overlapping coalition structure (OCS)is given as a set of singleton coalition. Unlike the simple Mission area
Data s UE i UR k UT Fig. 1. A two-tier UAV network consisting of multiple UTs and URs in thepresence of multiple UEs. The UTs and URs are deployed to execute varioussensing tasks, e.g. precision agriculture, city tra ffi c monitoring. singleton coalitions, we identify all potential partners of a UTand put them into a coalition. Besides, we add a correctiveaction to obtain a preliminary structure, which takes intoaccount the constraints of the limited communication rangeand the necessary number of coalition members. In this way,our initialization can maximize collaboration between players.Second, we have di ff erent operation rules for each player toupdate OCS. Specifically, in [21], only the joining operationand the singleton coalition formation operation are allowed,and in [22], only the switching operation and the singletoncoalition formation operation are allowed, which may hinderthe formation of desirable coalition structures in the iterationprocess. In comparison with the limited operation, we provideeach player with more options to search for a better structure.III. S ystem M odel A. Scenario Description
We investigate a two-tier UAV network consisting of M URs, N UTs, and S UEs in the air, which are defined as M (cid:44) { , , ..., M } , N (cid:44) { , , ..., N } , and S (cid:44) { , , ..., S } respectively. We denote by UT k the UT k , by UR i the UR i ,and by UE s the UE s in this paper. As illustrate in Fig. 1, thereare N UTs collecting data from their areas of coverage, and M URs flying at a higher altitude to receive and process data fromthe UTs. A UR can serve multiple UTs while a UT can onlychoose one UR as its receiver. We assume that this networkadopts a time division multiple access (TDMA) protocol whichis a typical transmission protocol, and our proposed algorithmcan be readily extended to the case of other protocols suchas frequency division multiple access (FDMA). Each UT k isallocated with a fixed time slot T S k for its data transmission, ∀ k = , , · · · , N . Without loss of generality, we consider thatall UTs and URs operate over a common frequency band W . Thus, when this network is well timed and synchronized,the transmission is collision-free, since there is only one UTtransmitting data in each time slot and each UR will onlyreceive data from its matched UTs.All the UTs, URs and UEs are assumed to work in ahalf-duplex mode, be equipped with a single omni-directionalantenna. Let h ki , h ks represent the channel gain of UT-URlink and UT-UE link respectively, where k ∈ { , , ..., N } , i ∈ { , , ..., M } , and s ∈ { , , ..., S } . We also assume that theglobal location information, including the UEs, is completely known as the locations of eavesdroppers can be estimated viaan optical camera or synthetic aperture radar (SAR) equippedon the UAV [6], [9]. UTs can further estimate the channelgain based on the obtained location information since the LoSchannel gains only depend on the distance. Unlike the air-to-ground propagation model which needs to calculate both LoSand NLoS pathloss, UAV-to-UAV communications are indeedair-to-air propagations, thus there is no need to consider NLoSchannel due to few obstacles in the air and the dominance ofLoS link [23]. For simplicity, we model the LoS channel as h mn = d − α/ mn e j θ , mn ∈ { ki , ks } , ∀ k , i , s , where d ki and d ks arethe distances from UT k to UR i and UE s respectively. α is thepath loss exponent, and θ is a random phase distributed within[0 , π ).Note that we focus on a static scenario where UAVs staystatic or quasi-static performing various sensing tasks. Thedramatical fluctuation of channels caused by the dynamic flightstates of the UAV [24], [25] is beyond the scope of our study.The impact of mobility and flight states of the UAV on physicallayer security is an interesting research topic and it may beour future work. B. Cooperative Data Transmission
We consider a common cooperative relaying protocol re-ferred to as decode-and-forward (DF). The complete datatransmission can be divided into two phases. In the first phase,the UT source broadcasts its message to some UT relays,which is referred to as the broadcast phase. In the secondphase, all the relays together with the UT source cooperativelytransmit a weighted version of the re-encoded message to theintended UR receiver, which is referred to as the transmissionphase (note that the intended UR receiver refers to the desiredUR receiver of the UT source). For each UT k ’s messagetransmission, T S k is evenly divided into two sub-slots for thebroadcast phase and the transmission phase, respectively.We consider there is an overall power budget P for each UT k ’s transmission, which constrains UT k and all its UTrelays. We denote P b as the transmit power in the broadcastphase, and P t as the total transmit power of the source andall the relays in the transmission phase. Obviously, we have0 ≤ P b , P t ≤ P . Suppose there are n − UT k to transmit towards UR i , the beamforming weights aredenoted by a n × w ( n − n UTs to UR i and UE s are denoted by h TR i = (cid:2) h T R i , h T R i , · · · , h T n R i (cid:3) (cid:62) , h TE s = (cid:2) h T E s , h T E s , · · · , h T n E s (cid:3) (cid:62) , respectively, where ( · ) (cid:62) means transpose. We define a n × S channel matrix H TE , whichrepresents the channels between n UTs and S UEs. Thus, when UT k together with its relays transmit a weighted version of itsmessage, the received signal at UR i and UE s are given by y R i = h † TR i w ˆ x + n R i (1) y E s = h † TE s w ˆ x + n E s , (2)where ( · ) † represents conjugate transpose, ˆ x is the re-encodedsymbol which is normalized, i.e., E {| ˆ x | } =
1, and n R i and n E s represent white complex Gaussian noise with zero-mean andvariance σ at the UR i and UE s , respectively. Then in the presence of multiple UEs, the achievable secrecyrate in the transmission phase can be expressed as C k = (cid:20) log(1 + γ R i ) − max s ∈S log(1 + γ E s ) (cid:21) + = log(1 + (cid:12)(cid:12)(cid:12) w † h TR i (cid:12)(cid:12)(cid:12) σ i ) − max s ∈S log(1 + (cid:12)(cid:12)(cid:12) w † h TE s (cid:12)(cid:12)(cid:12) σ s ) + , (3)where [ a ] + represents max( a , γ R i and γ E s representthe signal-to-noise-ratio (SNR) at UR i and UE s , respectively.For simplicity, we consider an extreme case in which wecompletely null out signals at all UEs, i.e., w † H TE = × S ,which is referred to as null-steering beamforming [10]. Then,the second item in (3) is zero. We aim to maximize theachievable secrecy rate with the constraints of transmit powerbudget and nulling out signals at UEs. To get the optimalweight vector, we formulate this problem as w ∗ = arg max w (cid:12)(cid:12)(cid:12) w † h TR i (cid:12)(cid:12)(cid:12) s . t . w † w ≤ P w † H TE = × S . (4)There is a closed-form solution for the above optimizationproblem, which is given by [10] w ∗ = √ P (cid:13)(cid:13)(cid:13) ( I n − U TE ) h TR i (cid:13)(cid:13)(cid:13) ( I n − U TE ) h TR i , (5)where I n is the n × n identity matrix, (cid:107) a (cid:107) is the 2-norm of vector a , and U TE (cid:44) H TE (cid:16) H † TE H TE (cid:17) − H † TE . Note that in order tosuccessfully null the signal at all S UEs and obtain the optimalweight vector, we need n > S here, which means that a UTneeds at least additional S UT relays to execute cooperativebeamforming together.IV. A M any - to - one M atching G ame for UT-UR A ssociation
A. Many-to-one Matching Game Formulation
In the first stage, we need to optimally match multiple UTs(no more than the UR’s quota, i.e., the maximum number ofUTs the UR can serve) with one UR considering their di ff erentcharacteristics and requirements. Specifically, for each UT, weview its secrecy rate performance as its benefit, and for eachUR, we regard its average throughput as its benefit. We aimto maximize the social welfare of both URs and UTs in aself-organized manner. Before showing the proposed matchingalgorithm, we introduce several basic definitions [26]. Definition 1
In our scenario, a many-to-one matching is afunction Φ : M ∪ N → M ∪ N , such that Φ ( UR i ) ⊆ N , and | Φ ( UR i ) | ≤ Q i , ∀ i ∈ M Φ ( UT k ) ∈ M , and | Φ ( UT k ) | = , ∀ k ∈ N Φ ( UR i ) = UT k ⇔ Φ ( UT k ) = UR i , ∀ i ∈ M , ∀ k ∈ N , where Q i represents the quota of UR i . These three conditionsimply that each UR can be matched with multiple UTs whileeach UT can match only one UR. Definition 2
Given two disjoint and finite sets of players,
Θ = { θ p } | Θ | p = and Ω = { ω q } | Ω | q = , a preference relation (cid:31) is a complete and transitive binary relation between these two sets.The expression ω q (cid:31) θ p ω q (cid:48) imply that player θ p prefer ω q over ω q (cid:48) , similarly, θ p (cid:31) ω q θ p (cid:48) imply player ω q prefer θ p to θ p (cid:48) . To quantify the degree of preference, we employ preferencefunctions. As mentioned before, each UT aims to secure thecommunication between itself and a UR as much as possible,thus it prefers the UR who could bring it better secrecyperformance. Hence, we design the preference of UT k over UR i as the secrecy rate under direct transmission U ik = log(1 + P | h ki | σ i ) − max s ∈S log(1 + P | h ks | σ s ) + , (6)and if there is U ik > U i (cid:48) k , which is equal to UR i (cid:31) UT k UR i (cid:48) ,then UT k prefers UR i to UR i (cid:48) in the matching process.Next, we design the preference function of UR i . We viewthe average throughput of a UR as the average receiving ratewithin the time for receiving data. The set of UTs matchedwith UR i is denoted by T i . Then the preference of UR i overthe set T i is given as U T i i = W | T i | (cid:88) j ∈ T i log(1 + γ ji ) , T i ⊆ N , | T i | ≤ Q i , (7)where W is the shared bandwidth, γ ji represents the SNR of UT j - UR i link. This preference function implies that, duringthe matching process, each UR prefers those UTs who couldbring higher SNR under the constraint of quota Q i .To better define an important definition a stable matching ,we first explain the notion of a blocking individual and ablocking pair. A blocking individual means that there exists aplayer who prefers to be unmatched over matching the currentplayer under Φ , in which case we say this matching is blockedby an individual. A blocking pair ( θ p , ω q ) means that both θ p and ω q can get higher utility if they match with eachother, compared to their current match, in which case we saythis matching is blocked by a pair ( θ p , ω q ). The conventionalstability of a matching can be defined as stable if it is notblocked by any individual or pair. B. Solution for the Matching Game
Based on the preferences design, we can see that each UT’spreference is fixed and only dependent on the matched UR.However, the profit a UR can obtain is dependent on the setof matched UTs. The preferences of each UR is variable asthe matching structure changes in each iteration and acceptingmore UTs does not necessarily bring greater benefits to a UR,which makes the classical DA algorithm unsuitable and thismatching problem becomes challenging.Obviously, for a rational UR in each iteration, it intendsto accept only the most preferred UT among the combinedpool of old partners and new applicants, rejecting all the rest.However, this will lead to N − M UTs unmatched eventually,which is not allowed in our work. To avoid this and achievehigher social welfare, we set up a few constraints in thematching process. The first one is that each UR can’t kickout the existing matched partners. Second, a UT has a secondchance to propose to the UR who has rejected it before. Three,
Algorithm 1
UT-UR Many-to-one Matching Algorithm.
Data: Q i , h ki , h ks , P , W , σ Result: Φ Initialization: T unmatch = N ; e i = Q i , ∀ i ∈ M Calculate preference lists: PT k = { U k , U k , · · · , U Mk } , ∀ k ∈ N ;Calculate RP lists: PR i = { ˜ U i , ˜ U i , · · · , ˜ U Ni } , ∀ i ∈ M ;2. Phase I:
Obtain a preliminary matching ˜ Φ . repeatfor all UT k ∈ T unmatch do propose to the current most preferred UR based on PT k . end forfor ∀ UR i that receive proposal doif e i = then reject all applicants. else divide the applicants into two categories: first-time applicants A i ,and second-time (or more) applicants B i . If | B i | > = e i , UR i accept e i preferred applicants in B i , and reject others. If | B i | < e i , UR i accept all members in B i and some applicants in A i according to A i , which is determined by Algorithm 2, and reject others. end ifend forUpdate Φ , e i and T unmatch Record rejection: for each rejected UT k , record the number of times UR i rejects it and update PT k : U ik = U ik − δ . until T unmatch = ∅ Phase II:
Swapping-matching operation. Φ ← ˜ Φ repeat Search for approved swapping pairs: { UT s , UT t , UR h , UR g } swap them: Φ ← Φ ts until (cid:64) any approved swapping Φ ts each UR should accept the UTs applying to it for the secondtime or more as much as possible, of course, under a conditionof not exceeding its quota.Before delving into our proposed algorithm, we first re-define a new preference of UR i over UT k as ˜ U ki = W log(1 + γ ji ) , i ∈ N , which is only dependent on the specific UT k ,nothing to do with other UTs. We refer to it as the referencepreference (RP) of UR i over UT k in the following. Moreover,we refer to the open positions to accommodate new applicantsas seat , and denote the current capacity for new UTs of UR i by e i .Our proposed matching algorithm is summarized in Algo-rithm 1, which consists of a preliminary interaction and aswapping operation. As for which UTs in A i to accept whenthere are available seats for A i , we summarize the rules inAlgorithm 2 briefly.When Phase I is over, we get a preliminary matching result˜ Φ . If there is a blocking pair, i.e., a UT and a UR prefer eachother to their current partner, then the UT is free to moveto the UR and the UR is free to kick out another UT (ifnecessary) to make space for the UT. Considering that wedo not allow any UT or UR to go outside the system, norcan any UT remain unmatched, we sort to a weaker notionof stability, namely pairwise stability . First, we define a swapmatching , denoted by Φ ts = { Φ \ { ( UT s , UR h ) , ( UT t , UR g ) }} ∪{ ( UT s , UR g ) , ( UT t , UR h ) } , where Φ ( UT s ) = UR h , Φ ( UT t ) = UR g , in which UT s and UT t switch places while other UTsremain unchanged. Note that one of these two UTs involvedin this swap can be a “seat”. Then we give the definition ofpairwise stable as follows [27] Definition 3
A matching Φ is pairwise stable (PS) if and Algorithm 2
Selecting Algorithm (from List A i ) Data: h ki , P k , W , σ , e i , A i Result: A i Initialization: A i = ∅ Sort UTs in A i in descending order according to the RP value in PR i : L i = { th . UT , th . UT , · · · , | A i | th . UT } ;2. Selection in order:for nth . UT = UT k ∈ L i , n = min ( e i , | A i | ) doif ˜ U ki > = U currenti then Add UT k into A i . else Break; end ifend for A i is the list of applicants in A i to be accepted. only if there exists no pair of UTs ( UT s , UT t ) , Φ ( UT s ) = UR h , Φ ( UT t ) = UR g such that ∀ m ∈ { UT s , UT t , UR h , UR g } , U m ( Φ ts ) ≥ U m ( Φ ) and2) ∃ m ∈ { UT s , UT t , UR h , UR g } , U m ( Φ ts ) > U m ( Φ ) . In fact, a swap operation can only occur when all agents of { UT s , UT t , UR h , UR g } “approve” it, i.e., the swap must strictlyincrease at least one agent’s utility without decreasing thebenefits of all others. In Phase II, we repeat searching forapproved swapping pairs and swap the UTs involved untilthere no longer exist such pairs.The convergence of Phase I is ensured by our proposed threeconstraints in the matching process, because that as long as thetotal number of “seats” (cid:80) Mi = Q i > = N , all UTs can get matchedwith a UR finally even if the preliminary matching ˜ Φ maybe unstable. And the convergence of Phase II is guaranteeddue to that the number of “approved” swaps is finite. Thus,matching Φ will converge to a pairwise stable matching inwhich no agent has the incentive to swap from its currentmatching partner to another.V. A n O verlapping C oalition F ormation G ame for C ooperative T ransmission A. Overlapping Coalition Formation Game Formulation
After the UT-UR association is completed, all UTs havedetermined their intended data receivers. In the second stage,each UT needs to carefully select its relay UT according to thepotential benefits and the required costs. UT k and all its relayUTs will form a group to perform cooperative beamformingtowards the intended UR in the time slot T S k . Due to thateach UT can act as the relay of multiple UTs in di ff erenttime slots, and there is not any utility transfer between UTs,we use a nontransferable utility (NTU) OCF game to figureout an e ff ective overlapping coalition structure, in which eachUT can participate in multiple coalitions to achieve higherutility. To better understand the proposed OCF algorithm, weintroduce some related definitions in OCF game [28]. Definition 4
A NTU overlapping coalition formation game isdefined as G = ( N , v ) , where N is the set of players in thisgame, and v is the utility function. Note that v ( ∅ ) = . Definition 5
An overlapping coalition structure Π over ( N , v ) is defined as a set list: Π = { C , C , · · · , C u } , where u is the Time slot
Transmitters Broadcast Phase Transmission Phase
C C
C C UT UT UT UT UT UT UT C C C C (TS k )(F k ) TS TS TS TS TS TS TS C C C C C Fig. 2. Illustration of an overlapping coalition structure. number of coalitions, ∀ ≤ x ≤ u , C x ⊆ N , ∪ ux = C x = N , andas the coalitions can be overlapped, ∃ x (cid:44) x (cid:48) , C x (cid:84) C x (cid:48) (cid:44) ∅ . Corresponding to our investigated scenario, the OCF gameplayers are N UTs. For each UT k , it may have some allies whocan act as its relays during time slot T S k , and we denote thegroup of all its allies plus itself by a set F k . In time slot T S k ,all members in F k will perform the cooperative beamformingtogether. Given an overlapping coalition structure, each UTcan assist the data transmission of some specific UTs in thecorresponding time slots. For example, as illustrated in Fig. 2,there are seven UT players and they form a four-coalitionoverlapping coalition structure. UT and UT have a samegroup, i.e., F = F = C = { UT , UT , UT , UT } . UT and UT have a same group, i.e., F = F = C ∪ C = { UT , UT , UT , UT , UT } , and similarly, there are F = C = { UT } , F = C = { UT , UT , UT } , F = C = { UT } .Next, we analyze the payo ff and costs of UTs duringthe cooperative beamforming transmission. For UT k matchedwith UR i , in its broadcast phase, there exist a secrecy rateloss due to the fact that UE s may overhear the informationtransmission. We define the cost function as the maximumloss value among all UEs, i.e., c k =
12 max s ∈S log(1 + P b | h ks | σ s ) , (8)where 1 / UT k and its alliessend a weighted version of the message with the optimalweight vector w ∗ , the achievable secrecy rate C k , i.e., thepayo ff of UT k , is given by C k =
12 log( α + | ( w ∗ ) † h TR i | σ i ) , (9)where α = + P b | h ki | /σ i . Note that P b | h ki | /σ i is the receivedSNR at the destination UR i in the broadcast phase.Furthermore, we suppose there exists a minimum SNRthreshold above which the relays can e ff ectively decode sig-nals, denoted by ˆ γ . Thus, given a coalition structure, in orderthat all the members of F k can successfully decode the signalof UT k and the secrecy loss in this phase can be minimized, thebroadcast power P b should be P b = ˆ γ σ / | h k ˜ k | , where h k ˜ k isthe channel gain between UT k and UT ˜ k who is the furthest allyof UT k in set F k . If the required P b exceeds the transmit power Algorithm 3
The Overlapping Coalition Formation Algorithm
Initialization:
Π = { C , C , · · · , C N } , C m = ∅ , for m = N .1. For k = N , identify all potential partners of UT k and put them intocoalition C k .2. Correct the coalitions:If ∃ k , | C k | < S +
1, then C k = { UT k } , and kick out UT k from C p (if UT k exists in C p ), ∀ p (cid:44) k , p ∈ N If ∃ m , n , C m = C n , m < n , remove C n from structure Π .A preliminary structure Π = { C , C , · · · , C u } is obtained, where u is thenumber of coalitions after correcting. repeatfor UT k , k = N do it randomly select C a ∈ { C j | k ∈ C j , C j ∈ Π } and C b ∈ { C j | k (cid:60) C j , C j ∈ Π } ∪ ∅ . Π Quit (cid:44) { Π \ C a } ∪ { C a \ { i }} if v k ( Π Quit ) ≥ v k ( Π )and u ( Π Quit ) ≥ u ( Π ) then Π k = Π Quit else Π Join (cid:44) { Π \ C b } ∪ { C b ∪ { i }} if v k ( Π Join ) > v k ( Π )and u ( Π Join ) ≥ u ( Π ) then Π k = Π Join else Π Switch (cid:44) { Π \ { C a , C b }} ∪ { C b ∪ { i }} ∪ { C a \ { i }} if v k ( Π Switch ) > v k ( Π )and u ( Π Switch ) ≥ u ( Π ) then Π k = Π Switch else Π k = Π end ifend ifend ifend for Select a structure with the highest total utility from a set Ω (cid:44) { Π , Π , · · · , Π N } and set it as the new structure: Π = arg max Π k ∈ Ω { u ( Π k ) } until ∀ k ∈ N , Π k = Π budget P , this F k can not perform cooperative beamformingsuccessfully and we define the utility in such case as minusinfinity. Moreover, in another case where 1 < | F k | < S + w ∗ can be found in (4). Therefore, when a UTis very far from all other UTs, or its neighbors are not enoughto form a coalition, it probably chooses to transmit alone, inwhich case the utility expression is the same as the preferencefunction of UT k in the matching stage.In a nutshell, given an overlapping coalition structure, wedefine the utility function v of UT k as v k = [ C k − c k ] + , P b ≤ P , | F k | ≥ ( S + U ik , | F k | = −∞ , otherwise . (10)In addition, we define the total utility u ( Π ) under anoverlapping coalition structure Π as the sum of all individualutilities, i.e., u ( Π ) = (cid:80) k ∈N v k . B. Solution for the Overlapping Coalition Formation Game
To update the overlapping coalition structure, we definethree basic operations for a UT, which are
Join, Quit, Switch . Join is joining a coalition it doesn’t belong to.
Quit is quittingfrom a coalition it belongs to.
Switch is switching from acurrent coalition to another new one. Since a UT’s join orleave may influence some related UTs’ utilities, we takeboth individual and the total utility into account when weconduct these operations in our algorithm. Before describing the proposed OCF algorithm, the concept of stability in anOCF game is introduced.
Definition 6
An overlapping coalition structure is stable if for ∀ k ∈ N , UT k can not make any feasible operations, includingQuit, Join or Switch move. To achieve a stable overlapping coalition structure, weproposed the OCF algorithm, which is summarized in Algo-rithm 3. After a specially designed initialization, UT k makes adecision whether to quit from a coalition, or join a coalition, orswitch from a coalition to another one, or make no change. Thestructure with the highest total utility is set as the new coalitionstructure. All UTs repeat this process until any UT wouldstay in the current coalitions and make no change, becausemaking any move while others remain the same won’t bringany benefits.Next, we prove that the proposed algorithm can achieve astable overlapping coalition structure, after a finite number ofiterations. Theorem 1
Our proposed OCF algorithm converges to astable overlapping coalition structure with probability 1.Proof: (Convergence) Given the number of players isfinite, the total number of possible overlapping coalitionstructures is finite. In Algorithm 3, we use a sequence { Π (1) → Π (2) → Π (3) → · · · } describe the evolution ofcoalition structure. Since each structure with the same high-est total utility has an equal chance of being set as thenew coalition structure, the evolution process won’t keeprepeating the previous structure all the time. In addition,every time a UT makes a move ( Quit / Join / Switch ), a newcoalition structure di ff erent from the last one will form. Sowe can describe the evolution of coalition structure such as { Π a → Π b → Π b → Π c → · · · } , where Π a (cid:44) Π b , Π a (cid:44) Π c , Π b (cid:44) Π c . Then we explain why the case { Π a → Π b → Π b → Π a → · · · } , in which a ”circle” appears, won’thappen. Supposing a evolution process with a ”circle” just like { Π a → Π b → Π b → Π a → · · · } , we denote the moves from Π a to Π b and from Π b to Π a as Move and Move , respec-tively. Then all possible combinations of the ( Move , Move )are ( Quit , Join ) , ( Join , Quit ) , ( S witch , S witch ) (note that thesetwo moves must be of a same UT). If the moves is(
Quit , Join ), according to the move rules, there must be u ( Π b ) ≥ u ( Π a ) , v ( Π b ) ≥ v ( Π a ); u ( Π a ) ≥ u ( Π b ) , v ( Π a ) > v ( Π b ),which is a contradiction obviously. Similar proof can be madefor another two combinations. Therefore, a “circle” won’tappear in the evolution of coalition structure. In conclusion,during the iteration process, the coalition structure may stayunaltered but it won’t turn back among a finite structure set.Therefore, our proposed algorithm will converge to a finalcoalition structure.(Stability) Once the algorithm converges to a final structure Π f inal , it must be stable, because if Π f inal is unstable and UT k intends to make a move, there is Π k (cid:44) Π , which contradictsthe fact that the algorithm terminated. Ground Air Area Area for URs
Area for UTs
Area for UEs
Fig. 3. Illustration for the distribu-tion settings of UTs, URs and UEs. Fig. 4. A snapshot of the finalstructure with N =
12 UTs, M = = = imulation parameters .Parameter Symbol ValueNumber of UTs N M R Q W σ -60dBmUT transmission power budget P α γ VI. P erformance E valuation A. Simulation Setup
As illustrated in Fig. 3, the UTs are randomly distributed ina rectangular area of 2 km × km × m in the air, the URs arerandomly distributed in a higher area of 2 km × km × m ,and the UEs are randomly located in the 2 km × km × km area which involves the areas of UTs and URs. The simulationparameters are given in Table I unless otherwise specified. TheURs and UEs are assumed to have the same noise power, andall URs are assumed to have the same quota. In order to obtainmore reliable simulation results, for a fixed number of UTs,URs and UEs, we repeat generating random location layoutsby 100 times and average the simulation results.Fig. 4 shows a snapshot of a pairwise-stable matching andoverlapping coalition structure resulting from our proposed al-gorithms. The UTs, URs, and UEs are represented by crosses,circles, and red squares respectively. We use the same color de-note the matching relationship, i.e., the UTs are matched witha UR with the same color. The gray dotted circles representthe overlapping coalition structure that UTs eventually formed.It shows that the UTs form a complex overlapping coalitionstructure under this position layout. Some UTs such as UT and UT participate in multiple coalitions, which means theyown lots of allies when performing cooperative beamforming,of course, they also need to assist their allies in turn duringthese allies’ time slots. Therefore, it’s a mutually beneficialway to work in coalitions. In addition, there may exist UTsthat prefer to work alone, just like UT , this is because it istoo far away from other UTs to benefit from the cooperation. B. Performance Analysis
To evaluate the e ff ectiveness of our proposed matchingalgorithm and OCF algorithm, which are labeled as PMAand OCFA respectively, we compare them with other practical schemes. First, we fix the matching scheme in stage 1 to bePMA, and compare the OCFA with the other three practicalschemes under various system parameters in terms of the totalutility of all UTs, which represents the secrecy performance ofthe whole network when transmitting data. Then, we focus onvalidating the performance of PMA compared to other typicalmatching schemes in terms of the social welfare of all UTsand URs. In addition, we give some necessary analyses for allsimulation results.Now we compare the proposed OCFA with the followingthree transmission schemes, note that the same transmit powerbudget P is applied to the individual or the whole coalition:a) Alone Scheme (AS), where each UT transmits its databy itself without any other cooperating relay in the cooperativetransmission stage, which is a non-cooperative approach.b)
Full Group Scheme (FGS), where each UT transmitsits data with all the UTs within its e ff ective communicationcircle being its relays in the cooperative transmission stage.c) Disjoint Coalition Scheme (DCS), where the UTs formdisjoint coalitions in the cooperative transmission stage. Weemploy the q-merge and 2-split scheme proposed in [29]. Theparameter q is the maximum number of coalitions that mergeinto a larger coalition and is set from 2 to 6. We choose themaximum performance value in this scheme for comparisonin our evaluation.In Fig. 5, we plot the average utility per UT of four schemesunder varying N . When N is from 10 to 30, we can see theaverage utility per UT of OCFA, FGS, and DCS increase as N becomes larger, while that of AS is almost maintained ata relatively low level. It is because that for the cooperativeschemes including OCFA, FGS, and DCS, there are morepotential allies within each UT’s communication range as thenumber of UTs increases, which probably results in biggercoalitions and more complex overlapping coalition structure.However, for the AS, in which each UT transmits its dataalone during its whole time slot, the increase of neighbors ofa UT will not benefit it and may even bring in a competitionfor the same desired UR in stage 1. Therefore, the cooperativeapproaches including OCFA, FGS, and DCS are superior toAS, which is a non-cooperative approach.From Fig. 6, it is noticed that the total utilities of fourschemes have a very slight increase as the quota for eachUR increases. It is because that with more provided ”seat”in stage 1, a UT has more chance to match the preferredUR, who can establish better channel state with itself ingeneral, resulting in an improvement in the total utility whenperforming cooperative beamforming in stage 2. However,when a UR can serve more UTs, although there are more“hole”, a UT can only switch to this “hole” when all involvedagents approve this operation, which limits big changes in thematching results. Therefore, the impact of quota on the totalutility is very slight.In Fig. 7, we vary the number of URs to be 2 to 7. As allUTs need to match a UR finally, there must be a constraintof M × Q > = N , thus we adapt Q correspondingly as thenumber of URs changes ( Q is set 6, 4, 3, 3, 3, 2 as the numberof URs to be 2 ∼ M . When the number of URs is 7, the total utility of OCFA is largerthan that of FGS, DCS and AS about 9%, 10% and 54%,respectively. In addition, the total utilities of four schemesincrease as the number of URs increases. This is due to thatwith more URs in the network, UTs are more likely to matcha UR with better channel conditions, thereby improving theutility when performing cooperative beamforming. Besides,the AS still gets the worst performance compared to the otherthree cooperative approaches. In Fig. 8, we vary the numberof UEs from 1 to 6. We can observe that with more UEsdistributed in the network, the total utilities of four schemeswill decrease, which is in accordance with our forecasts. Withmore UEs randomly distributed in this area, a UT is morelikely to be close to a UE, which leads to a higher secrecyloss for this UT no matter it works alone or in a team, i.e., ina cooperative or non-cooperative way.We also investigate the impact of transmit power P vari-ation on the total utilities of four schemes. From Fig. 9, wecan notice that the total utilities of OCFA, FGS and DCSincrease obviously as the transmit power increases, while theAS curve grows very slightly. The reason is that with largertransmit power, UTs work in a cooperative way have a widercommunication circle, which means they could own morepotential allies to combat against eavesdropping. Despite a partof power loss and secrecy loss resulting from the informationbroadcast phase, the gains from cooperation outweigh thelosses, which leads to an obvious improvement in the totalutility. For AS, the increase of transmit power would onlyresult in a slight improvement in the secrecy performance.Furthermore, we can see that when the transmit power is18dBm, the curves of OCFA and FGS begin to meet. Inessence, when the transmit power increases to 18dBm, thee ff ective communication circle radius becomes about 2.5km,which implies a UT can cover nearly all others within itscommunication range in this network, and all UTs probablyform a grand coalition to perform cooperative beamforming.Therefore, when the transmit power is large enough, OCFAand FGS obtain the same total utility in which cases a grandcoalition of all UTs will form.In Fig. 10 and Fig. 11, we vary the SNR threshold andthe noise power to investigate their impacts on the totalutility, respectively. As shown in Fig. 10, the total utilitiesof OCFA, FGS and DCS decrease as the SNR thresholdincreases, while the total utility of AS has no change. Itis easy to understand that with a larger SNR threshold, aUT can not form a coalition with the UTs far away fromit because they can not successfully decode and forward themessage when performing cooperative beamforming, whichleads to a smaller e ff ective communication circle. As for AS,the change of SNR threshold has no e ff ect on it due to itsnon-cooperative way. Fig. 11 indicates that the total utilitiesof all four schemes decrease as the noise power increases.With higher noise power and fixed SNR threshold, each UT’scommunication circle becomes smaller, which means each UTwill have fewer potential allies. Then we can notice that whenthe noise power is about -70dBm or lower, OCFA and FGSshow the same performance, in which case a grand coalitionof all UTs forms to perform cooperative beamforming. As the A v e r a g e u tilit y p e r U T OCFAASFGSDCS
Fig. 5. Average user utility compari-son of four transmission schemes withdi ff erent number of UTs. T o t a l u tilit y OCFAASFGSDCS
Fig. 6. Total utility comparison withdi ff erent number of Q . T o t a l u tilit y OCFAASFGSDCS
Fig. 7. Total utility comparison withdi ff erent number of M . T o t a l u tilit y OCFAASFGSDCS
Fig. 8. Total utility comparison withdi ff erent number of R.
10 12 14 16 18 20Transmission power (dBm)51015202530 T o t a l u tilit y OCFAASFGSDCS
Fig. 9. Total utility comparison withdi ff erent transmission power. T o t a l u tilit y OCFAASFGSDCS
Fig. 10. Total utility comparison withdi ff erent SNR threshold. -75 -70 -65 -60 -55 -50 -45Noise power (dBm)0510152025303540 T o t a l u tilit y OCFAASFGSDCS
Fig. 11. Total utility comparison withdi ff erent noise power. S o c i a l W e l f a r e o f U T s a nd U R s PMARMSDAMS
Fig. 12. Social welfare comparison ofthree matching schemes with di ff erentnumber of UTs. noise power becomes higher, all UTs will make their rationaldecisions to quit from the grand coalition and self-organizedinto a new complex overlapping coalition structure based ontheir utilities. When the noise power increases to about -50dBm, as shown in this figure, the cooperative approachesof OCFA, FGS and DCS become no di ff erent from AS, inwhich case each UT forms a single-player coalition due to amuch higher broadcast communication cost.Finally, in order to show the e ff ectiveness of the proposedmatching algorithm in the UT-UR association stage, we com-pare PMA with the classical DA matching algorithm [26],labeled as DAMS. In addition, a random matching scheme(RMS) is given as a benchmark.Fig. 12 indicates that PMA outperforms DAMS slightlyin terms of the social welfare of UTs and URs in stage 1.The underlying reason is that in PMA, a UR can chooseto reject some first-time applicants who cannot improve itscurrent benefit even if there are left ”seats” for them, while inDAMS a UR accepts as many applicants as possible (up to thequota). In our considered network, there may be cases wherea UE becomes very close to a UT, and for this UT, which URto match makes no di ff erence to its benefit according to thepreference function, however, it makes a di ff erence to URs.The UT who does not care which UR to match may be morepreferred by another UR rather than the one it is applyingto. Thus in PMA, URs can own more options, and the socialwelfare of UTs and URs can be improved to some extent.In Fig. 13, we show the e ff ectiveness of our proposed two-stage framework. As shown in this figure, when neither stageis applied, i.e., random UT-UR association and alone trans-mission, the total utility is very low. Employing stage 1 canprovide a good matching structure for the subsequent transmis-sion to achieve better total utility, and employing stage 2 canfurther improve the total utility due to the e ff ective overlapping No stage 1 and no stage 2 T o t a l u tilit y (a) Only stage 1 T o t a l u tilit y (b) Only stage 2 T o t a l u tilit y (c) Stage 1 and stage 2 T o t a l u tilit y (d)Fig. 13. (a) Total utility when neither stage is employed (random UT-URassociation and alone transmission), (b) Total utility when only stage 1 isemployed (UT-UR association with the proposed matching game and alonetransmission), (c) Total utility when only stage 2 is employed (random UT-URassociation and cooperative beamforming with the OCF game) and (d) Totalutility when both stage 1 and stage 2 are employed (UT-UR association withthe matching game and cooperative beamforming with the OCF game). coalition based cooperative beamforming. Furthermore, thecombination of these two stages can significantly improvethe total utility, thereby greatly enhancing the transmissionsecurity in the network.VII. C onclusion In this paper, we investigate the secure transmission problemin a two-tier UAV network. To enhance the PLS of this net-work, we utilize cooperative beamforming to combat against the UEs and design a two-stage framework consisting of aUT-UR association stage and a cooperative transmission stage.We formulate the UT-UR association problem and the relayselection problem into a many-to-one game and an OCF game,respectively. Then a many-to-one matching algorithm and anOCF algorithm are proposed to solve these two sequentialgames. The stabilities of these two algorithms are theoreticallyproved, and extensive simulations are shown to demonstratethe superior performance of our proposed schemes and thee ff ectiveness of our proposed two-stage framework.R eferences [1] D. Doering, A. Benenmann, R. Lerm, E. P. de Freitas, I. Muller, J. M.Winter, and C. E. Pereira, “Design and optimization of a heterogeneousplatform for multiple UAV use in precision agriculture applications,” IFAC Proceedings Volumes , vol. 47, no. 3, pp. 12 272–12 277, 2014.[2] M. Elloumi, R. Dhaou, B. Escrig, H. Idoudi, and L. A. Saidane,“Monitoring road tra ffi c with a UAV-based system,” in . IEEE,2018, pp. 1–6.[3] S. Dey, M. N. Kamal, S. Dutta, A. Tiwari, S. Ray, M. J. Moatasimbillah,N. Saha, N. Adhikary, D. Mukherjee, S. Nayak et al. , “Ad-hoc networkedUAVs as aerial mesh network for disaster management application andremote sensing: An approach,” in . IEEE, 2017, pp. 301–304.[4] S. Sekander, H. Tabassum, and E. Hossain, “Multi-tier drone architecturefor 5G / B5G cellular networks: Challenges, trends, and prospects,”
IEEECommunications Magazine , vol. 56, no. 3, pp. 96–103, 2018.[5] M. Cui, G. Zhang, Q. Wu, and D. W. K. Ng, “Robust trajectoryand transmit power design for secure UAV communications,”
IEEETransactions on Vehicular Technology , vol. 67, no. 9, pp. 9042–9046,2018.[6] G. Zhang, Q. Wu, M. Cui, and R. Zhang, “Securing UAV communi-cations via joint trajectory and power control,”
IEEE Transactions onWireless Communications , vol. 18, no. 2, pp. 1376–1389, 2019.[7] Y. Zhou, P. L. Yeoh, H. Chen, Y. Li, R. Schober, L. Zhuo, andB. Vucetic, “Improving physical layer security via a UAV friendlyjammer for unknown eavesdropper location,”
IEEE Transactions onVehicular Technology , vol. 67, no. 11, pp. 11 280–11 284, 2018.[8] J. Tang, G. Chen, and J. P. Coon, “Secrecy performance analysis ofwireless communications in the presence of UAV jammer and randomlylocated UAV eavesdroppers,”
IEEE Transactions on Information Foren-sics and Security , 2019.[9] X. Zhou, Q. Wu, S. Yan, F. Shu, and J. Li, “UAV-enabled securecommunications: Joint trajectory and transmit power optimization,”
IEEE Transactions on Vehicular Technology , vol. 68, no. 4, pp. 4069–4073, 2019.[10] L. Dong, Z. Han, A. P. Petropulu, and H. V. Poor, “Improving wirelessphysical layer security via cooperating relays.”
IEEE Transactions onSignal Processing , vol. 58, no. 3, pp. 1875–1888, 2010.[11] M. E. Mkiramweni, C. Yang, J. Li, and W. Zhang, “A survey of gametheory in unmanned aerial vehicles communications,”
IEEE Communi-cations Surveys & Tutorials , vol. 21, no. 4, pp. 3386–3416, 2019.[12] T. LeAnh, N. H. Tran, W. Saad, L. B. Le, D. Niyato, T. M. Ho,and C. S. Hong, “Matching theory for distributed user association andresource allocation in cognitive femtocell networks,”
IEEE Transactionson Vehicular Technology , vol. 66, no. 9, pp. 8413–8428, 2017.[13] K. Hamidouche, W. Saad, and M. Debbah, “Popular matching gamesfor correlation-aware resource allocation in the internet of things,” in
GLOBECOM 2017-2017 IEEE Global Communications Conference .IEEE, 2017, pp. 1–6.[14] C. Pham, N. H. Tran, S. Ren, W. Saad, and C. S. Hong, “Tra ffi c-awareand energy-e ffi cient vNF placement for service chaining: Joint samplingand matching approach,” IEEE Transactions on Services Computing ,2017.[15] O. Semiari, W. Saad, Z. Daw, and M. Bennis, “Matching theory forbackhaul management in small cell networks with mmWave capabili-ties,” in .IEEE, 2015, pp. 3460–3465. [16] R. El-Bardan, W. Saad, S. Brahma, and P. K. Varshney, “Matching theoryfor cognitive spectrum allocation in wireless networks,” in . IEEE, 2016,pp. 466–471.[17] S. A. Kazmi, N. H. Tran, W. Saad, Z. Han, T. M. Ho, T. Z. Oo, andC. S. Hong, “Mode selection and resource allocation in device-to-devicecommunications: A matching game approach,”
IEEE Transactions onMobile Computing , vol. 16, no. 11, pp. 3126–3141, 2017.[18] S. A. Kazmi, A. Ndikumana, A. Manzoor, W. Saad, C. S. Hong et al. ,“Distributed radio slice allocation in wireless network virtualization:Matching theory meets auctions,”
IEEE Access , vol. 8, pp. 73 494–73 507, 2020.[19] D. Niyato, P. Wang, W. Saad, and A. Hjorungnes, “Controlled coalitionalgames for cooperative mobile social networks,”
IEEE Transactions onVehicular Technology , vol. 60, no. 4, pp. 1812–1824, 2011.[20] W. Saad, Z. Han, R. Zheng, A. Hjorungnes, T. Basar, and H. V. Poor,“Coalitional games in partition form for joint spectrum sensing andaccess in cognitive radio networks,”
IEEE Journal of Selected Topicsin Signal Processing , vol. 6, no. 2, pp. 195–209, 2011.[21] Z. Zhang, L. Song, Z. Han, and W. Saad, “Coalitional games withoverlapping coalitions for interference management in small cell net-works,”
IEEE Transactions on Wireless Communications , vol. 13, no. 5,pp. 2659–2669, 2014.[22] T. Wang, L. Song, Z. Han, and W. Saad, “Overlapping coalitional gamesfor collaborative sensing in cognitive radio networks,” in . IEEE,2013, pp. 4118–4123.[23] N. Goddemeier and C. Wietfeld, “Investigation of air-to-air channelcharacteristics and a UAV specific extension to the rice model,” in . IEEE, 2015, pp. 1–5.[24] X. Xiao, W. Wang, T. Chen, Y. Cao, T. Jiang, and Q. Zhang, “Sensor-augmented neural adaptive bitrate video streaming on UAVs,”
IEEETransactions on Multimedia , vol. 22, no. 6, pp. 1567–1576, 2019.[25] S. He, W. Wang, H. Yang, Y. Cao, T. Jiang, and Q. Zhang, “State-aware rate adaptation for UAVs by incorporating on-board sensors,”
IEEE Transactions on Vehicular Technology , vol. 69, no. 1, pp. 488–496,2019.[26] Y. Gu, W. Saad, M. Bennis, M. Debbah, and Z. Han, “Matching theoryfor future wireless networks: Fundamentals and applications,”
IEEECommunications Magazine , vol. 53, no. 5, pp. 52–59, 2015.[27] E. Bodine-Baron, C. Lee, A. Chong, B. Hassibi, and A. Wierman, “Peere ff ects and stability in matching markets,” in Algorithmic Game Theory .Springer Berlin Heidelberg, 2011, pp. 117–129.[28] R. Zhang, Z. Zhao, X. Cheng, and L. Yang, “Overlapping coalitionformation game based opportunistic cooperative localization scheme forwireless networks,”
IEEE Transactions on Communications , vol. 65,no. 8, pp. 3629–3642, Aug 2017.[29] R. Mochaourab, E. Jorswieck, and M. Bengtsson, “Distributed clusteringfor multiuser networks through coalition formation,” arXiv preprintarXiv:1701.06220arXiv preprintarXiv:1701.06220