Distributed Relay Selection for Heterogeneous UAV Communication Networks Using A Many-to-Many Matching Game Without Substitutability
Dianxiong Liu, Yuhua Xu, Yitao Xu, Qihui Wu, Jianjun Jing, Yuanhui Zhang, Alagan Anpalagan
aa r X i v : . [ c s . N I] D ec Distributed Relay Selection for Heterogeneous UAVCommunication Networks Using A Many-to-ManyMatching Game Without Substitutability
Dianxiong Liu ∗† , Yuhua Xu ∗† , Yitao Xu ∗ , Qihui Wu ‡ , Jianjun Jing ∗ , Yuanhui Zhang § and Alagan Anpalagan ¶∗ College of Communications Engineering, PLA Army Engineering University, Nanjing, China. † Science and Technology on Communication Networks Laboratory, Shijiazhuang, China. ‡ College of Electronic and Information Engineer, Nanjing University of Aeronautics and Astronautics, Nanjing,China. § PLA Zhenjiang Watercraft College, China. ¶ Department of Electrical and Computer Engineering, Ryerson University, Toronto, Canada.Emails: [email protected], [email protected], [email protected], [email protected],[email protected], [email protected], [email protected]
Abstract —This paper proposes a distributed multiple relayselection scheme to maximize the satisfaction experiences ofunmanned aerial vehicles (UAV) communication networks. Themulti-radio and multi-channel (MRMC) UAV communicationsystem is considered in this paper. One source UAV can select oneor more relay radios, and each relay radio can be shared by mul-tiple source UAVs equally. Without the center controller, sourceUAVs with heterogeneous requirements compete for channelsdominated by relay radios. In order to optimize the global satis-faction performance, we model the UAV communication networkas a many-to-many matching market without substitutability. Wedesign a potential matching approach to address the optimizationproblem, in which the optimizing of local matching process willlead to the improvement of global matching results. Simulationresults show that the proposed distributed matching approachyields good matching performance of satisfaction, which isclose to the global optimum result. Moreover, the many-to-many potential matching approach outperforms existing schemessufficiently in terms of global satisfaction within a reasonableconvergence time.
Index Terms —UAV communication networks, Distributed mul-tiple relay selection, Satisfaction experiences, Many-to-manymatching market without substitutability, Potential matching.
I. I
NTRODUCTION
UAV communications can improve the breadth and dimen-sion of wireless communication [1]. Large-scale model ofUAVs is the developing trend, and it is an urgent problem tosolve the communication problem among the group of UAVs.There is a cluster head in the UAV group, keeping communi-cation with the ground control center and communicating toother UAVs. Each UAV needs to maintain the communicationconnection with the UAV controller. However, due to thelimitation of transmit power, some UAVs can not communicatedirectly with the controller. Thus, the relay technology isneeded in UAV communication networks [1].In the relay model with a large number of UAVs, onlysuitable relay selections can lead to better performances. Al-though the relay selection of ground communication has been studied [2]–[8], these results are not fully applicable to UAVnetworks. The reason is that one UAV may need to completediverse information transmissions for different tasks at thesame time. Therefore, multiple radio systems equipped to UAVnetworks are available such as [7], [8]. Thus, it is meaningfulto propose selection strategies of multiple nodes. However,previous existing works mainly focus on problems of one-to-one relay selection strategies [2], [3] or many-to-one relayselection strategies [4]–[6]. These selection approaches arenot suitable to many-to-many UAV communication systems,in which strategies of relay selection will be more complex.Moreover, existing literatures [2]–[5] mainly focus on thethroughput performance, ignoring the actual demands of users.It may be inadvisable to overemphasize the throughput per-formance when requirements of users are heterogeneous.Therefore, this paper mainly develops more reasonable relayselections with the heterogeneous requirements of UAVs. Asource UAV (SV) with large capacity requirements can connectto multiple radios of relay UAVs (RVs), while the SV with alow capacity requirement connects to less relay radios.In complex UAV networks, centralized approaches maybring a large amount of information overheads. Therefore, itis necessary to develop distributed approaches. However, it isa difficult problem for decision makers to optimize the per-formance of whole network according to their own selectionstrategy. In this case, the UAV relay network can be modeledas a many-to-many matching market [9]. Matching models arepowerful and promising to address the assignment problemin wireless networks [10]–[12]. However, all the existingmodels above are matching markets with substitutability, inwhich players obtain resources by replacing the other players.These models are not suitable to model relay sharing networkswithout substitutability.To solve this problem, we model the UAV relay networkas a many-to-many matching game without substitutability. Inthe game model, SVs and RVs have their individual utilities,so as to make selection strategies respectively. SVs share the s s s r r s c c c c s r c s s s Fig. 1. A multi-channel and multi-radio UAV relay network. time resource of the access channel equally. According tothe matching performance, RVs determine whether to acceptrequests of SVs or not. Different from the traditional matchinggame, the proposed game is non-substituted. To the best ofour knowledge, it is the first application of matching marketwithout substitutability in wireless networks.Inspired by the potential function in [13], We propose adistributed potential matching algorithm (PMA). The perfor-mance of the global utility will be improved as the optimizingof local matching results. It shows that matching resultscan achieve a global stable matching of satisfaction. Theperformances of the proposed algorithm are evaluated in termsof satisfaction and convergence rate, which show that theproposed algorithm can improve the global satisfaction withina reasonable convergence time.The rest of this paper is organized as follows. In Section II,the system model is provided and the relay selection problemis formulated. In Section III, the application of many-to-many matching game in satisfaction-aware relay assignment isanalyzed. In Section IV, the potential matching approach forthe many-to-many matching market is proposed. In SectionV, the simulation results are shown and the performance ofour distributed algorithm is analyzed. Finally, the conclusionis drawn in Section VI.II. S
YSTEM M ODEL AND P ROBLEM F ORMULATION
A. System Model
We consider a UAV communication network with N SVs, M RVs and one destination (UAV controller), where eachsource-destination pair { s n , d } has an opportunity to be as-sisted by RVs. The sets of SVs and RVs are denoted by S = { s , s , ..., s N } and R = { r , r , ..., r M } , respectively.Each UAV is equipped with one or more radios so that eachSV can connect to different radios of RVs at the same time.Radios of RVs can serve as transmitters at given channels.The set of relay radios is denoted by C = { c , c , ..., c L } .We assume that there is no inter-channel interference becausethe number of orthogonal channels is enough for radios ofRVs [4], [5]. Due to the interference constraint, there is nocapacity benefit if two different radios of one node work in asame channel. Each radio works in a half-duplex mode and the communi-cation is frame-by-frame fashion. Each frame is divided intotwo time slots. The first time slot is used for the link of theSV to the RV, while the second time slot is used for the linkof the RV to the destination by relay modes. There are twomain relay modes, amplify-and-forward (AF) and decode-and-forward (DF) [14]. In this paper, we use the AF mode, andthe proposed scheme can be extended to DF or hybrid modes.Under the AF mode, RVs receive signals from SVs andthen amplify and transmit them to the destination. In orderto represent the performance of relay assignment among SVs,we assume that the direct transmission diversity between SVsand the destination would not exist [2]. The capacity withoutdirect transmission diversity is expressed as, C AF ( s, r ( c ) , d ) = W · log (cid:18) γ sr γ rd γ sr + γ rd (cid:19) , (1)where the transmitting bandwidth is denoted by W . The SV,radio of RV and destination are denoted by s , r ( c ) and d ,respectively. For ease of expression, the signal-to-noise-ratio(SNR) at the RV coming from the SV is denoted by γ sr , γ sr = P s | h s,r | /σ . The transmission power of the SV isdenoted by P s . h s,r captures the path gain between the SVand the RV, and the parameter σ is the variance of whiteGaussian noise (AWGN). Similarly, the SNR from the SVand the RV to the destination are denoted by γ sd and γ rd ,respectively.We assume that each radio of one SV can connect to oneradio of the RV at most, so each SV can be connected to anumber of relay radios that do not exceed the number of radiosit equipped with. That is, X c l ∈C δ nl ≤ α n , (2)where δ nl is the indicator function, which equals to 1 if SV s n connects to relay radio c l successfully, or else equals to 0if failed. The number of radios of s n is denoted by α n .In relay networks, multiple SVs will share time resourcesequally if they connect to a same relay radio [5]. The numberof SVs connecting to one relay radio c l is denoted by A ( c l ) .Therefore, obtained throughput of c l can be denoted by B l .That is, B l = P s n ∈S C AF ( s n , r m ( c l ) , d ) δ nl A ( c l ) , (3)where P s n ∈S δ nl equals to A ( c l ) . Similarly, with the help ofmultiple relay radios, the data rate of s n can be denoted by u n . That is, u n = X c l ∈C C AF ( s n , r m ( c l ) , d ) δ nl A ( c l ) . (4) s . t . X c l ∈C δ nl ≤ α n (5)It should be noted that the performance of one source-relaypair would be influenced by the other SVs which have thesame radio choices.In UAV networks with heterogeneous requirements, eachSV has individual type of service. Therefore, each SV aims tofind the set of relay radios to meet the throughput requirement. Let u ′ n denote the throughput requirement of SV s n , and thedata rate is used for the utility function. Let f n ( ψ n , ψ − n ) denote the satisfaction index of s n , where ψ n = { ψ n | ψ n ∈ C } is the selection strategy of s n and elements of ψ are relayradios. ψ − n represents selection strategies of the other SVs.Without loss of generality, we assume that the form of thesatisfaction function is a universal sigmoid function, which candescribe different communication services of utility functionsof SVs [15], f n ( ψ n , ψ − n ) = 11 + exp (cid:2) − λ (cid:0) u n − u ′ n + νλ (cid:1)(cid:3) , (6)where we set ν > so that f n ( ψ n , ψ − n ) ≥ − exp(7) ≈ when the obtained throughput higher than the requiredthroughput, i.e., u n ≥ u ′ n . The satisfaction function is shownas a slightly S-shaped curve, which is suitable to expressdifferent types of demands. λ denotes the trend-changingspeed which reflects the requirement degree of communicationservices. B. Problem Formulation
The problem of multiple relay selection needs to be solvedto improve the global satisfaction experience. SVs chooseRVs according to their throughput requirements. As shownin Fig. 1, some SVs need to access multiple relay radiossimultaneously to achieve transmission rate requirements. Inthis case, the optimization problem of global satisfaction canbe defined based on the system model, maxmize Λ = X s n ∈S f n ( ψ n , ψ − n ) , (7)where the global satisfaction utility is denoted by Λ . Theproposed problem in (7) aims to maximize the aggregatesatisfaction of all SVs in the network.III. S ATISFACTION - AWARE RELAY ASSIGNMENT AS AMANY - TO - MANY MATCHING GAME
A. Many-to-many matching game model
Matching game theory is a powerful decentralized approachto develop the issue of resource allocation without a centercontroller and global information exchange [10]. The complexresource assignment problem can be modeled as a largedistributed solution by defining individual utilities for two setsof players.In this paper, the problem of relay selection is modeledas a many-to-many matching market, which is a promisingresearch field but it is still rarely developed. In the model,each SV s n ∈ S will be assigned to one or more radios c l ∈ C controlled by RVs, and each relay radio can also be shared bymultiple SVs. The definition of the many-to-many matchinggame is given as follow [9], Definition 1.
A many-to-many matching µ is a mapping bytwo sets of players ( S , C ) and two preference relations ≻ n , ≻ l .Each player s n ∈ S and c l ∈ C constructs preference lists overone another, ranking the players in S and C , respectively. Thematching process is constrained to, • µ ( s ) is contained in C , and µ ( c ) is contained in S ; • | µ ( s ) | ≤ q s for all s n ∈ S ; • s is in µ ( c ) if and only if c is in µ ( s ) where the preference relation ≻ is defined as a complete andreflexive binary relation between players in S and C . µ ( s ) means the subset of relay radios which are connected by SV s , and µ ( c ) is the subset of SVs connecting to relay radio c .The quota is the maximal number of each player can match,denoted by q . The second constraint means that quotas of SVsare fixed while quotas of RVs are dynamic. The third constraintensures that the matching is the mutual consent between twosets of players. Therefore, the matching game can be expressedas a tuple, G ( S , C , ≻ n , ≻ l , q n ) . (8)In classic matching games, quotas of two sets of playersare both fixed. However, quotas of RVs in this network areunfixed, where one RV can serve dynamic number of SVswithout substitutability. The matching problems of dynamicquotas and non-substitution motivate us to develop a newscheme that significantly differs from existing applicationsof matching game in wireless networks such as [9]–[11].Therefore, we propose a suitable solution to solve the problemof satisfaction-aware many-to-many relay assignment in (7). B. Proposed matching game without substitutability model
In this paper, the many-to-many matching game withoutsubstitutability is proposed to optimize the global satisfaction.In the proposed game, SVs and relay radios select elementsin the opposing set according to their own selection criteria.
1) For SVs preferences:
In UAV communication networkswith heterogeneous types of service, each SV s n seeks to findrelay radios with high data rate so as to achieve its data raterequirement. f n ( ψ n , ψ − n ) → ⇒ find µ ( s n ) ∈ { c l | c l ∈ C} , (9) s . t . u n = P c l ∈C C AF ( s n ,r m ( c l ) ,d ) δ nl A ( c l ) ≥ u ′ n P c l ∈C δ nl ≤ α n (10)where f n ( ψ n , ψ − n ) → means that the objective of s n is toobtain the desired transmission rate u ′ n . Therefore, s n willsearch for suitable RVs to avoid the blind pursuit of highthroughput.According to throughput requirements, the preference ofeach SV s n can be expressed as, ( s n , c l ) ≻ n ( s n , c j ) ⇔ u n ( s n , c l ) > u n ( s n , c j ) , (11)where u n ( s n , c l ) and u n ( s n , c j ) represent the obtainedthroughput of s n assisted by c l and c j , respectively. Therefore,relay radios which can provide better services will obtainhigher priorities. It can be noted that subsets of source-relaypairs which can meet the requirement of s n have the samepriority. The available resource of s n is impacted by the otherSVs’ choice dynamically, in which the situation belongs to oneof the “peer effects” [6] in matching game model. Moreover,strategies of the other SVs are uncertain for s n . Therefore, during the matching process, the preference ordering of oneSV is dynamic according to the realistic data rate.
2) Preferences of radios of RVs:
RVs assist the transmis-sion of SVs to improve the global transmission performance.In the matching process, SVs propose matching proposals andthen RVs decide whether to accept them according to thepreference criterion. Because the selection strategy of one SVmay influence the other SVs which have the same strategysets, we define the utility function of relay radios as, U c ( s n , ψ n ) = f n ( ψ n , ψ − n ) + P k ∈J n (cid:2) f k ( ψ k , ψ J k ) − f k (cid:0) ψ k , ψ J k \ n (cid:1)(cid:3) , (12)where k ∈ J n denotes SVs which have the same relaypreference elements in their preference lists, and they may beimpacted by the decision of SV s n . Therefore, f k ( ψ k , ψ J k ) is the satisfaction result of the other SVs s k . f k (cid:0) ψ k , ψ J k \ n (cid:1) is the satisfaction result of s k if s n gives up the competitionfor radios.It should be noted that not all the SVs would choose exactlythe same radios even if the preference lists have overlappingparts. Some SVs that may cause interference to s n can berepresented as I n = {∀ s k | δ kl = 1 } , s . t . c l ∈ (cid:8) ¯ ψ n ∪ ψ n (cid:9) (13)where ¯ ψ n and ψ n mean the prepared selection strategy, and thecurrent selection strategy of s n , respectively. We assume thatthe selection strategy of s n changes from ψ = { ψ | ψ ∈ C } to ¯ ψ = (cid:8) ¯ ψ (cid:12)(cid:12) ¯ ψ ∈ C (cid:9) . Only SVs in I n can influence thetransmission performance of s n . Thus, it can be found that f k ( ψ k , ψ J k ) = f k ( ψ k , ψ I k ) . (14)In this case, the satisfaction of SVs in J n \I n will not beinfluenced no matter which relay radios are chosen by s n .Thus, it can also be found that f k ( ψ k , ψ J k ) = f k (cid:0) ψ k , ψ J k \ n (cid:1) , k ∈ J n \I n (15)Based on (14) and (15), U c ( s n , ψ n ) can be simplified to U c ( s n , ψ n ) = f n ( ψ n , ψ − n ) + P k ∈I n (cid:2) f k ( ψ k , ψ I k ) − f k (cid:0) ψ k , ψ I k \ n (cid:1)(cid:3) . (16)Relay radios controlled by RVs determine whether to acceptstrategies changes of s n . Different from the classic matchingprocess, matching processes in the proposed many-to-manymatching game without substitutability are not substituted.SVs share resources of relay radios rather than replace eachother. Inspired by the potential function in [13], the optimalsolution of the satisfaction maximization problem in (16) willlead to a global stable matching result. Definition 2.
A matching results is a global stable matchingif and only if no player can improve its matching utility bydeviating unilaterally, i.e., ∄ Λ (cid:0) ¯ ψ n , ψ − n (cid:1) > Λ ( ψ n , ψ − n ) , (17) s . t . ∀ s n ∈ N , ψ n ⊆ C , | ψ n | ≤ α n (18) Algorithm1 : Distributed potential matching approach (PMA) for many-to-many relay selection network
Initialization:
Each SV randomly chooses relay radios;
Loop in iteration k ; Stage I:
Relay radios estimate and utilities computationEach SV calculates utility function over its all available relay radio, thenit chooses a set of available relay radios based on the mixed strategy, wherethe component that denotes the probability of radio selection c l in the mixedstrategy is given as ¯ ψ n ( c l ) = u ( s n , c l ) P c l ∈C u ( s n , c l ) . (19) Stage II:
Matching evaluationBased on (16), relative RVs decide if accept or not with a mixed strategy,where the component contains “accept” or “reject”. P = exp (cid:8) β · U c (cid:0) ¯ ψ n (cid:1) , β · U c ( ψ n ) (cid:9) exp (cid:8) β · U c (cid:0) ¯ ψ n (cid:1)(cid:9) + exp { β · U c ( ψ n ) } , (20)for some learning parameter β > . end Loop until µ mi,j can improve the satisfaction results. Output:
Convergence to a stable matching result.
Theorem 1.
Optimizing the local matching process, the globalnetwork will achieve a stable matching result.Proof:
Due to space limitations, this article does not givea specific proof. The specific proof will be given in [16].It is shown that the many-to-many game model withoutsubstitutability has at least one stable matching result. In thisgame model, SVs needn’t exchange information with the otherSVs, and RVs only need to exchange information with aportion of the other RVs in the same strategy sets of SVs.Therefore, the game model reduces the information exchangesof SVs as well as RVs.IV. P
OTENTIAL MATCHING APPROACH FORMANY - TO - MANY MATCHING MARKET
In order to study the relay selection with limited informationexchanges, a distributed potential matching approach (PMA)is proposed in this paper, in which each SV knows the channelstate information (CSI) so as to reorganize preference orderingof relay radios.Here, PMA with limited information exchanges is proposedin Algorithm 1, which consists of two stages: utility computa-tion of relay radio and matching evaluation. In Stage I, basedon the location information in the relay system, each SV formsits own preference list according to the CSI. Although SVsobtain the CSI information in every iteration, they can obtainneither strategies of the other SVs, nor influences of their ownstrategies. Therefore, it randomly chooses a set of relay radiosaccording to the mixed strategy (19), where the number ofconnection is no more than the number of its own radios.SVs ask requests of connection exchange to RVs, and RVswill accept the exchange proposal according to (20). With asufficiently large β , the global satisfaction maximization canbe achieved with an arbitrarily high probability [17].Note that RVs receive proposals from SVs and only needto exchange information with the relative RVs. The approachdecreases the information exchanges and mitigates the costsof SVs and the global network. V. S
IMULATION R ESULTS AND D ISCUSSIONS
In a 2000 × W = 10 MHz bandwidth for each channelof the system, and the noise power density of the systemis -174 dBm/Hz. The maximum transmission powers of SVsare set to 20 dBm and RVs are set to 30 dBm. SVs haveindividual data rate requirements range from 10 Mbps to40 Mbps randomly and the α of each SV also is random( < α ≤ ). All results are obtained by simulating 600topologies independently and taking the expected values. Tobalance the tradeoff between exploration and exploitation, β = k is chosen in our simulation, where k means the theiteration step. A. Convergence performance
We consider a UAV communication network consisting offive RVs and thirteen SVs. Therefore, thirteen SVs share tenrelay radios according to different requirements. It can be seenthat in this scenario, the maximum number of possible strategyselection profiles is (cid:0) C + 10 (cid:1) .The average convergence behavior of five approaches areshown in Fig. 2, in which the global optimum is obtainedby using the exhaustive search method. It is noted from thefigure that the proposed distributed PMA with many-to-manymatching model catches up with the global optimum. Also, theperformance comparison of many-to-one relay selection (eachSV chooses one radio at most) and the best response algorithm[13] with many-to-many matching model is given. Both twoalgorithms can not achieve the optimal performance. It can benoted that the result of many-to-many selection is better thanthat of the many-to-one selection, which means that the many-to-many relay selection can achieve more flexible resourceassignment in the network with heterogeneous requirements.Fig. 3 represents the cumulative distribution function (CDF)for the convergence time of the proposed algorithm. In Fig. 3,we can see that, the average number of iteration increasesdue to the increase of the number of players in the UAVnetwork. With the number of devices increases, the collisionsamong SVs also increase. However, the collisions have a finalupper boundary because the UAV network becomes a saturatedstate. Fig. 3 demonstrates that the proposed matching approachhas a reasonable convergence time that does not exceed 300iterations with 20 SVs and 10 relay radios in the incompleteinformation network. B. Satisfaction performance comparison
The average satisfaction performance of different algorithmswith varying network scales are compared. We consider relaynetworks with five RVs and the number of SVs are varying.
Iteration time G l oba l s a t i s f a c t i on Global optimum (exhaustive search)The proposed PMA with many−to−many matching modelThe proposed PMA with many−to−one matching modelThe best response [13] with many−to−many matching modelRandom selection with many−to−many matching model
Fig. 2. Evolution results of satisfaction performance with 13 SVs and 10relay radios. CD F (cid:54)(cid:57) s15 (cid:54)(cid:57) s (cid:3) (cid:54)(cid:57) s Fig. 3. The performance of convergence with kinds of numbers of SVs inthe network.
Fig. 4 shows the proportion value of the average satisfactionresulting by the proposed PMA with many-to-many model,PMA with many-to-one matching model, the best response al-gorithm [13] with many-to-many matching model and SAMA[6] with many-to-one matching model.It is illustrated in Fig. 4 that, the proposed PMA has asignificant advantage in term of satisfaction at all network sizesand the proportion of satisfaction is higher than 0.95 when thenumber of source-destination pairs is not more than 16. It canbe noted that, the best response algorithm [13] is better thanthe PMA with many-to-one matching model when the numberof SVs is higher than 15, while the contrary result is obtainedwhen the number of SVs less than 15. The SAMA [6] is amatching algorithm with substitutability, and the performanceis worse than that of the PMA. These results mean that 1)many-to-many selection strategies can obtain more flexibleresource allocation in heterogeneous requirement networks;2) unsuitable many-to-many selection strategies may achieveworse results than that of many-to-one relay model; 3) therelay selection network can achieve better performances by
10 15 20 250.650.70.750.80.850.90.951
The source node number (N) G l oba l s a t i s f a c t i on The proposed PMA with many−to−many matching modelThe best response [13] with many−to−many matching modelThe proposed PMA with many−to−one matching modelThe SAMA [6] with many−to−one matching model
Fig. 4. The comparison of average satisfaction among SVs with heterogeneousrequirements. the matching game without substitutability.VI. C
ONCLUSION
In this paper, the selection problem of the multi-channelmulti-radio UAV relay network has been studied. We haveformulated the selection network as a many-to-many matchingmarket. To solve the selection problem, we have proposeda many-to-many matching game without substitutability. Adistributed potential matching algorithm has been designed,in which the local matching processes lead to a global sta-ble matching result. Simulation results have shown that theproposed potential-matching approach yields stable matchingresults, which outperform existing schemes with the ob-jective of satisfaction optimization. In UAV networks withheterogeneous requirements, many-to-many approach achievesmore flexible resource assignments. Based on this work, thetransmission characteristics of dynamic UAV communicationnetworks will be studied in the future.A
CKNOWLEDGEMENT
This work was supported by the National Science Foun-dation of China under Grant No. 61771488, No. 61671473,No. 61631020 and No. 61401508, the in part by Natural Sci-ence Foundation for Distinguished Young Scholars of JiangsuProvince under Grant No. BK20160034, and in part by theOpen Research Foundation of Science and Technology onCommunication Networks Laboratory. The authors would liketo thank Miss Mengyun Tang for her helpful discussions.R
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