Game Based Energy Cost Optimization for …downloads.hindawi.com/journals/mpe/2018/9315954.pdfMathematicalProblemsinEngineering [] Y. Saleem, M. H. Rehmani, and S. Zeadally, “Integration

Research ArticleGame Based Energy Cost Optimization for Unmanned AerialVehicle Communication Networks

Changhua Yao Lei Zhu Lei Wang and Junye Meng

The Army Engineering University of PLA Nanjing China

Correspondence should be addressed to Lei Zhu LeiZhuxueshuj163com

Received 26 November 2017 Revised 29 January 2018 Accepted 26 February 2018 Published 10 April 2018

Academic Editor Eduardo Rodriguez-Tello

Copyright copy 2018 Changhua Yao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Due to the limited transmission power the data transmission between the unmanned aerial vehicle and the ground station oftenneeds the synergetic forwardingThe optimization of the synergetic forwarding organization is important to the performance of theunmanned aerial vehicle communication networks This paper aims to optimize the energy cost using the synergetic forwardingmode in the unmanned aerial vehicle communication networks To reduce the expensive information exchange and improve therobust of the network we put forward an energy cost orient forwarding allocation approach using game based intelligent algorithmThe theoretic analysis and simulation results verify that the put forwardmethod could achieve optimal energy cost communicationorganization

1 Introduction

The unmanned aerial vehicle (UAV) is the hot researchpoint recently [1] With its flexibility and low cost the UAVcould complete many kinds of work which are hard to thehuman such as dangerous detection long-time monitoringand remote rescuing Limited by singleUAVrsquos ability theUAVswarm consisting of multiple UAVs draws more and moreattention [2] Besides many key issues the communicationorganization for the UAVs is a basic problem

There are some researches on the UAV communicationnetworks In [3] Rosati et al proposed a speed-aware routingalgorithm that is applied in the context of high-speed UAVsIn [4] Zhu et al studied the design and evaluation of airbornecommunication networks In [5] Ortiz et al studied thedesign and development of a robust ATP subsystem for thealtair UAV-to-ground lasercomm 25Gbps demonstrationLuo et al proposed a distributed gateway selection algorithmfor UAV networks in [6] Yin et al put forward queuingmodels for deciding the optimal choice of UAVs to forwardpackets in [7] In [8] Saleem et al stated the integration ofcognitive radio technology with unmanned aerial vehiclesincluding the important issues and research challenges In [9]Choi et al paid attention to the energy-efficient maneuveringand communication of a single UAV-based relay Author Puri

made a survey of unmanned aerial vehicles (UAV) for trafficsurveillance in [10] In [11] Bekmezci et al made a surveyon the flying ad hoc networks In [12] Wang et al studiedthe position unmanned aerial vehicles in the mobile ad hocnetwork In [13] Ono et al studied the relay network basedon unmanned aircraft network

With the ground station system supported [5] the UAVcommunication network could solve the fast informationtransmission problem well However common UAV usuallywould be limited by energy the long-distance data transmis-sion is not a good way since the pow cost increases with thedistance fast In addition the data transmission would notbe done when the UAV is out of the range As a result thesynergetic forwarding in the UAV communication networkis necessary to pay attention to [14] Another important issuein the UAV communication network is the pow cost whichis very sensitive to the UAV especially for the ones supportedby the battery How to optimize the synergetic forwardingcommunication organization considering the energy cost isimportant to the whole system In [9] Choi et al studied theenergy-efficient maneuvering and communication of a singleUAV-based relay in depth In [14] Wu et al made importantresearch on the movement design by considering the energycost A mobile forwarding approach was proposed for themonitored data transmission However this work focused

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 9315954 7 pageshttpsdoiorg10115520189315954

2 Mathematical Problems in Engineering

on a single base stationrsquos movement optimization it is nota multiuser network In [15] a power consumption optimalsynergetic forwarding scheme was put forward to improvethe systemrsquos lifetime by Li et al nevertheless the research in[14]mainly focuses on singleUAVrsquosmovement design not forthe UAV communication network The approach proposedin [15] is a centralized one not the focused point in ourwork Due to the UAVrsquos high dynamism the centralizedoptimization approach would not be capable of dealing withthe topology change and information exchange problems Tothe best of our knowledge the energy cost improvement issuein the UAV communication network has not been well solvedin existing works

In this paper we aim to study the energy cost improve-ment issue in the UAV communication network We putforward an energy cost orient forwarding allocation approachto achieve the optimal solution to the UAV communicationnetworks energy optimization issue The theoretic analysisis presented by modeling this problem as a game [16] Theexperiments are carried out to verify the theoretic result andthe performance of proposed intelligent learning algorithm

2 Network Model and Problem Formulation

A scenario where UAV communication networks are sup-ported by the ground communication station system [5]is shown in Figure 1 The UAV communication networksconsist of 119872 common UAVs (CUAVs) and 119873 forwardingUAVs (FUAVs) Usually the CUAVsrsquo communication wouldbe limited by their energy it is hard for CUAVs to com-municate with the grand stations directly The FUAVs areusually the ones supported by fuel which have the abilityto communicate with the ground stations directly In theUAV communication networks the FUAVs would work asthe forwarding node for the CUAVs With different groundstations and different FUAVsrsquo communication devices thelink bandwidths would also be different As shown in thescenario in Figure 1 the bandwidths of FUAVs might be6MHz 15MHz 20MHz and so on

Note that the topology of the UAV communicationnetwork is varying all the time As shown in Figure 1 theCUAVs FUAVs and the mobile ground stations are allmoving The dynamic topology is the character of the UAVcommunication networks and the distances between CUAVsand FUAVs vary As a result the transmission powers cost forthe communication would also change to meet the requireddata transmission quality The selection of FUAV to forwardthe data would be critical for the CUAVsrsquo energy cost Thefollowing attributes have important effect on the energy costthe distance to FUAV the transmission channel quality andthe bandwidth As shown in Figure 1 CUAV1 could select oneof the four FUAVs as the communication forwarding nodeto the ground station system The selection would be deter-mined by the expected energy cost DefineΠ119865 = 1 2 119873and Π119862 = 1 2 119872 as the set of FUAVs and CUAVsDefine 119861119865 = 1198611 1198612 119861119873 as the bandwidths vector Thebandwidth allocation between CUAVs could be designed bydifferent scheme it is assumed that the bandwidth would beequally allocated by the connected CUAVs in this paper for

the simplification The CUAVsrsquo selection of forwarding nodewould be decided by the CUAVsrsquo traffic requirement and thedistance to the FUAVs

Based on the Shannon theory assuming that119862119898 selects119865119899as the forwarding node the achieved data transmission ratewould be

119877119898119899 = 119861119898119899 log(1 + 119864119898119899120575119898119899minus1205741198981198991205881198981198991198611198981198991198730 ) (1)

where 1198730 is the noise power spectrum density 120575119898119899 is thedistance between 119862119898 and 119865119899 120574119898119899 is the path-loss exponentbetween 119862119898 and 119865119899 and 120588119898119899 is the instantaneous randomcomponent of the path lossThen the energy cost (EC) of119862119898would be

119864119898119899 = 1198611198991198730 (exp(|Ω119899|119877119898119899119861119899) minus 1)1003816100381610038161003816Ω1198991003816100381610038161003816 120575119898119899minus120574119898119899120588119898119899 (2)

where |Ω119899| is the number of CUAVs selected 119865119899 as theforwarding node

It should be noted that in the UAV communicationnetworks the best forwarding node selection would be notonly affected by some CUAV itself but also determined byother UAVsrsquo selection With the whole UAV communicationnetworks the goal is that the sum of the energy cost isminimized

Problem min 119864net = 119872sum119898=1

119864119898 (3)

that is

Problem max minus 119864net = minus 119872sum119898=1

119864119898 (4)

The main challenges of this problem are as follows firstthe optimization for the forwarding node allocation in UAVcommunication networks is the combinational optimizationissue The searching approach could achieve the best combi-nation but the computing complex would increase fast whenthe UAV network increasesThe possible combination wouldbe 735 = 379 times 1029 in relatively small 35 common UAVand 7 forwarding UAV communication networks With thegenetic algorithm ant colony algorithm and the like theperformance of the optimization could not be guaranteedSecond the information exchange required by the centralizedoptimization approach would not be practical for the limitedcommunication capability and the limited time Third thedynamism of the UAV communication network brings seri-ous problem to the centralized optimization including thedynamism of topology and the dynamism of environmentIn the following sections we solve this problem based on thegame theory which could achieve the optimal state of thenetwork without the centralized optimization

3 The Energy Cost Orient ForwardingAllocation Approach

In this section we put forward an energy cost orientforwarding allocation approach (ECOFAA) to optimize the

Mathematical Problems in Engineering 3

Link 1

Link 3Link 4

Link 2

CommonUAV1

Ground station 1

Ground station 2

Ground station 3

CommonUAV1

Move

Move

ForwardingUAV

ForwardingUAV

Move

15－（Ｔ6－（Ｔ

20－（Ｔ

30－（Ｔ

Ground Ground

Move

Figure 1 Ground system supported UAV communication network

energy cost optimization of UAV communication networkThe allocation approach is shown in Figure 2

In the approach in Figure 2 the parameter 120573 gt 0 plays therole of adjusting with the change of environment Note thatthe probabilistic selection scheme [17] is adopted to avoid thesuboptimal trap problem in best-response algorithm [18] andthe like

Remark 1 The put forward energy cost orient forwardingallocation approach is a distributed method rather than acentralized one All the UAVs make their action decisionby themselves rather than by some control center This isimportant to the practicability of the approach in the dynamicenvironment that the UAV communication network faces

Theorem 2 The put forward energy cost orient forwardingallocation approachwould achieve theminimal energy cost andstable network state

Proof With the UAV communication network shown inFigure 1 when the UAVs adopt the action updating strategiesas the put forward approach the system could be seen as agame model as follows and each CUAV could be seen as aplayer in the game Define the energy cost orient forwardingallocation (ECOFA) game as follows

119866 = Π119862 Π119865 Ψ 119860 (5)

whereΨ is the topology relationship of the UAV communica-tion networks among which119873119898119899 sub Ψ is the communicationdistance between 119865119899 and 119862119898 119862119898 could communicate with119865119899 if 119873119898119899 = 1 otherwise 119873119898119899 = 0 119860 = 1198601 otimes 1198602 otimessdot sdot sdot otimes 119860119872 is the action profiles of all the nodes where otimes isthe Cartesian product and 119860119898 is the possible actions of 119862119898Define 119862119898rsquos action as 119886119898 isin 119860119898 119906119898 is the utility function of119862119898 119906119898(119886119898 119886minus119898)would be 119862119898rsquos utility when 119862119898rsquos action is 119886119898and other playersrsquo action is 119886minus119898119873119890119894119898 is the set of CUAVs

119873119890119894119898 = 119894 isin Π119862 if 119873119898119895 = 1 119873119894119895 = 1 forall119895 isin Π119865 (6)

In the put forward ECOFA game inspired by the synergydesign in networks [18ndash20] 119862119898rsquos utility function would be asfollows

119906119898 (119886119898 119886minus119898) = minus119864119898 minus sum119894isin119873119890119894119898

119864119894 (7)

According to potential game theory [19] define thepotential function of the ECOFA game as follows

Γ (119886119898 119886minus119898) = minus119864net = minus 119872sum119898=1

119864119898= minus119864119898 minus sum

119894isin119873119890119894119898

119864119894 minus sum119894isinΠ119862119873119890119894119898

119864119894(8)


Initialization CUAVs stochasticallychoose an forwarding UAV

Reward Computing Compute the energy costaccording to the current network state

Updating Selection In the communication range ofspecial FUAV the one whose random timer firstlycounts to zero can change its strategy OthersCUAVs would keep the old strategies

Strategy Updating Stochastically adopt anaction from its possible strategies according tothe following

Network State Collection The topologyenvironment ground stations

UAVsrsquo strategies are stable

All the UAVsrsquo strategies updated

Yes

No

No

Yes

approach ０Ｌ(am(i + 1) = aandm)

= ＲＪum(aandm aminusm)sumaisinA

ＲＪum(am

aminusm)

Figure 2 The energy cost orient forwarding allocation approach

Assume that 119862119898 updates its action from 119886119898 to 119886and119898 andother UAVs hold their actions based on the definitionof 119873119890119894119898 the change of the potential function would becomputed as follows

ΔΓ = Γ (119886119898 119886minus119898) minus Γ (119886and119898 119886minus119898) = minus119864net + 119864andnet= minus119864119898 minus sum

119894isin119873119890119894119898

119864119894 minus sum119894isin119878119862119873119890119894119898

119864119894minus (minus119864and119898 minus sum

119894isin119873119890119894119898

119864and119894 minus sum119894isin119878119862119873119890119894119898

119864and119894 )= 119864and119898 minus 119864119898 + sum

119894isin119873119890119894119898


119864119894 + sum119894isinΠ119862119873119890119894119898

119864and119894minus sum119894isinΠ119862119873119890119894119898

119864119894 = 119864and119898 minus 119864119898 + sum119894isin119873119890119894119898


119864119894= 119906119898 (119886119898 119886minus119898) minus 119906119898 (1198861015840119898 119886minus119898) = Δ119906

(9)

According to analysis [19] the put forward ECOFAgame is an exact potential game Then it has at least one

pure strategy NE point and the optimal state of potentialfunction in the ECOFA game would be a Nash equilibriumpoint According to the design of the potential function theoptimal energy cost network state would also be a Nashequilibrium point of the ECOFA game With the networkstate transmission in the put forward approach suppose 119886119898 =119865119898(119894) as the 119862119898rsquos action in the 119894th iteration in the put forwardapproach Define Ω(119894) = (1198651(119894) 1198652(119894) 119865119898(119894) 119865119872(119894)) asthe network state which is a discrete time Markov processwith a unique stationary distribution [20] Define the uniquestationary distribution of CUAVsrsquo strategy profile as a =1198861 1198862 119886119872 which would be given by the following

120587 (a) = exp 120573Γ (a)sumaisin119860 exp 120573Γ (a) (10)

where Γ(a) is the potential function of the game 119860 = 1198601 otimes1198602 otimes sdot sdot sdot otimes 119860119872 is the set of strategies of all the UAVsDefine Ω(119894 + 1) = a2 Ω(119894) = a1 Define the transi-

tion probability from state a1 to a2 as 119875a1a2 the transitionprobability from state a2 to a1 as 119875a2a1 Supposing a CUAVupdating the FUAV chosen from 119886119898(119894) = 119865119898(119894) to 119886and119898(119894 +1) = 119865and119898(119894 + 1) then the UAV communication network


state would be changed from a1 to a2 that is from Ω(119894) =(1198651(119894) 1198652(119894) 119865119898(119894) 119865119872(119894)) toΩ(119894+1) = (1198651(119894+1) 1198652(119894+1) 119865and119898(119894 + 1) 119865119872(119894 + 1))With the UAV communication network consisting of 119872

CUAVs the probability of 119862119898 updating its forwarding FUAVwould be 1119872 Then

120587 (a1) 119875a1 a2= [ exp 120573Γ (a1)sumaisin119860 exp 120573Γ (a)]

times [( 1119872)( exp 120573119906and119898 (119886and119898 119886minus119898)sum119886119898isin119860119898 exp 120573119906119898 (119886119898 119886minus119898))]= exp 120573 (Γ (a1) + 119906and119898 (119886and119898 119886minus119898))119872 times sumaisin119860 exp 120573Γ (a) times sum119886119898isin119860119898 exp 120573119906119898 (119886119898 119886minus119898)

(11)

Similarly


times [( 1119872)( exp 120573119906119898 (119886119898 119886minus119898)sum119886119898isin119860119898 exp 120573119906119898 (119886119898 119886minus119898))]= exp 120573 (Γ (a2) + 119906119898 (119886119898 119886minus119898))119872 times sumaisin119860 exp 120573Γ (a) times sum119886119898isin119860119898 exp 120573119906119898 (119886119898 119886minus119898)

(12)

According to the character of the exactly potential gamewe have

Γ (a1) minus Γ (a2) = 119906119898 (119886119898 119886minus119898) minus 119906and119898 (119886and119898 119886minus119898) (13)

Then we have

exp 120573 (Γ (a1) + 119906and119898 (119886and119898 119886minus119898))= exp 120573 (Γ (a2) + 119906119898 (119886119898 119886minus119898)) (14)

Thus

120587 (a1) 119875a1 a2 = 120587 (a2) 119875a2a1 (15)

As a result

suma1isin119860

120587 (a1) 119875a1 a2 = suma1isin119860

120587 (a2) 119875a2 a1 = 120587 (a2) suma1isin119860

119875a2a1= 120587 (a2)

(16)

Based on the analysis in [20] the put forward approachhas the stationary distribution Define that a is the CSUVsrsquoforwarding choosing selection in the optimal energy costnetwork state then

a = argaisin119860

min119864net = argaisin119860

min Γ (a) (17)

According to the analysis above the put forwardapproach would converge to a unique stationary distribution

Table 1 The simulation parameters

Number of CUAVs 25Number of FUAVs 6The communication data rate [6 10 15 20 25 32]MHzThe bandwidths of FUAVs 1 MbitsThe noise power minus130 dBThe path-loss exponent 2

120587(a) = exp120573Γ(a)sumaisin119860 exp120573Γ(a) When 120573 rarr infinexp120573Γ(a) ≫ exp120573Γ(a) foralla isin 119860 a

The probability of achieving best energy cost networkstate a will be

lim120573rarrinfin

120587 (a) = exp 120573Γ (a)sumaisin119860 exp 120573Γ (a) = 1 (18)

The above result shows that the put forward intelligentlearning approach would converge to the optimal energy coststate of the UAV communication network In addition thestate would be stable since it is a Nash equilibrium pointwhere none of the players would like to change its strategyHence the theorem is proved

The above analysis proves that the put forward approachwould converge to the optimal network state Importantlythe proposed approach is an online method which couldadjust the UAVsrsquo strategies according to the change of theenvironment the change of the topology and so on In all theproposed approach is a distributed and online optimizationmethod which is suitable to the dynamic UAV communica-tion network

4 Numeric Results and Discussion

To verify the performance of put forward energy cost orientforwarding allocation approach (ECOFAA) the comparisonbetween the ECOFAA and some existing algorithms havebeen carried out The simulation is done by Matlab Thesimulation parameters are depicted in Table 1 and Figure 3

The parameter setting in the simulation is not specializedThe parameters such as number of CUAVs number ofFUAVs the communication data rate the bandwidths ofFUAVs the noise power and the path-loss exponent couldall be changed The parameter setting is not sensitive to theproposed approach

The simulation results on the energy cost have beenshown in Figure 4 To show the details of the course in theput forward ECOFAA approach the energy cost of threerandomly chosen CUAVs are observed As shown in Figure 4all of the three CUAVsrsquo energy costs converge to a stable valueat last which proves that the CUAVsrsquo forwarding selectionactions would not vary again after the proposed ECOFAAconverges It should be noted that other CUAVs forwardingselection could directly or indirectly affect some CUAVrsquos ECin theUAVcommunication network so the energy cost of theobserved CUAVs would not be stable during the updatingTo verify the proposed approach in an average aspect 1500


CommonUAV1

ForwardingUAV

Figure 3 The topology of the simulation network consists of 6FUAVs and 25 CUAVs

50 100 150 200 250 300 3500Updating Iteration

The EC of CUAV1The EC of CUAV2The EC of networkBR algorithm [18]

The EC of CUAV3The EC of networkproposed ECOFAA

100

101

Ener

gy co

st (E

C) (m

W)

Figure 4 The energy cost of CUAVs in the updating procedure ofproposed ECOFAA

independent simulating experiments have been carried outand the average numeric result has been shown It couldbe seen that the put forward ECOFAA outperformed thebest-response learning algorithm [18] when the learning con-verges The proposed ECOFAA achieves lower energy costThe best-response learning algorithm would converge fasterthan the proposed ECOFAA but the total energy cost wouldbe higher That means the best-response learning algorithmcould not achieve the best FUAV forwarding allocation statefor the UAV communication network At the beginningthe forwarding UAVs are randomly allocated and the totalenergy cost of the whole UAV communication networkwould be relatively high After the forwarding UAV selectionupdating by the proposed ECOFAA the total energy cost of

the network would be reduced obviously Importantly thetotal energy cost would not vary after the proposed methodconverges The simulation result of energy cost convergingverifies that proposed FUAV allocation approach would bestable

5 Conclusion

In this paper we studied on the UAV communication net-works energy optimization issuewhich is critical to thewholeUAVnetworkWe put forward an energy cost orient forward-ing allocation approach to achieve the optimal solution to theUAV communication networks energy optimization issueThe theoretic analysis and simulation results show that theUAV communication networkrsquos forwarding allocation wouldbe stable and energy cost would be optimal after the proposedintelligent learning course

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The work is supported by the National Natural ScienceFoundation of China (nos 61702543 61271254 71501186 and71401176)

References

[1] S Hayat E Yanmaz and R Muzaffar ldquoSurvey on UnmannedAerial Vehicle Networks for Civil Applications A Communi-cations Viewpointrdquo IEEE Communications Surveys amp Tutorialsvol 18 no 4 pp 2624ndash2661 2016

[2] S Hyo-Sang and P Segui-Gasco UAV CommunicationNetworkss Selection-Making Paradigms Encyclopedia ofAerospace Engineering 2014

[3] S Rosati K Kruzelecki L Traynard and B Rimoldi ldquoSpeed-aware routing for UAV ad-hoc networksrdquo in Proceedings of the2013 IEEE Globecom Workshops GC Wkshps 2013 pp 1367ndash1373 USA December 2013

[4] Y Zhu Q Huang J Li and D Wu ldquoDesign and evaluation ofairborne communication networksrdquo in Proceedings of the 7thInternational Conference on Ubiquitous and Future NetworksICUFN 2015 pp 277ndash282 Japan July 2015

[5] G G Ortiz S Lee S Monacos M Wright and A BiswasldquoDesign and development of a robust ATP subsystem for thealtair UAV-to-ground lasercomm 25-Gbps demonstrationrdquo inProceedings of the SPIE - The International Society of Photo-Optical Instrumentation Engineers Free-Space Laser Communi-cation Technologies XV High-Power Lasers and Applicationspp 103ndash114 San Jose CA USA January 2003

[6] F Luo C Jiang J Du et al ldquoA distributed gateway selectionalgorithm for UAV networksrdquo IEEE Transactions on EmergingTopics in Computing vol 3 no 1 pp 22ndash33 2015

[7] C Yin Z Xiao X Cao X Xi P Yang and D Wu ldquoEnhancedrouting protocol for fast flying UAV networkrdquo in Proceedingsof the 2016 IEEE International Conference on CommunicationSystems ICCS 2016 pp 1ndash6 China December 2016


[8] Y Saleem M H Rehmani and S Zeadally ldquoIntegration ofCognitive Radio Technology with unmanned aerial vehiclesIssues opportunities and future research challengesrdquo Journalof Network and Computer Applications vol 50 pp 15ndash31 2015

[9] D H Choi S H Kim and D K Sung ldquoEnergy-efficientmaneuvering and communication of a single UAV-based relayrdquoIEEE Transactions on Aerospace and Electronic Systems vol 50no 3 pp 2320ndash2327 2014

[10] A Puri A Survey of Unmanned Aerial Vehicles (UAV) forTraffic Surveillance Department of Computer Science andEngineering University of South Florida 2005

[11] I Bekmezci O K Sahingoz and S Temel ldquoFlying Ad-HocNetworks (FANETs) a surveyrdquo Ad Hoc Networks vol 11 no 3pp 1254ndash1270 2013

[12] H Wang D Huo and B Alidaee ldquoPosition unmanned aerialvehicles in the mobile Ad hoc networkrdquo Journal of Intelligent ampRobotic Systems vol 74 no 1-2 pp 455ndash464 2014

[13] F Ono H Ochiai and R Miura ldquoA Wireless Relay NetworkBased on Unmanned Aircraft System with Rate OptimizationrdquoIEEE Transactions on Wireless Communications vol 15 no 11pp 7699ndash7708 2016

[14] Y Wu B Zhang S Yang X Yi and X Yang ldquoEnergy-efficientjoint communication-motion planning for relay-assisted wire-less robot surveillancerdquo in Proceedings of the IEEE INFOCOM2017 - IEEE Conference on Computer Communications pp 1ndash9Atlanta GA USA May 2017

[15] K Li W Ni X Wang R P Liu S S Kanhere and S JhaldquoEnergy-efficient cooperative relaying for unmanned aerialvehiclesrdquo IEEE Transactions on Mobile Computing vol 15 no6 pp 1377ndash1386 2016

[16] D Fudenberg and D LevineTheTheory o f Learning in GamesMIT Press 1998

[17] P J M van Laarhoven and E H L Aarts Simulated AnnealingTheory and Applications Reidel Holland 1987

[18] W Zhong Y Xu and H Tianfield ldquoGame-theoretic oppor-tunistic spectrum sharing strategy selection for cognitiveMIMO multiple access channelsrdquo IEEE Transactions on SignalProcessing vol 59 no 6 pp 2745ndash2759 2011

[19] J RMarden G Arslan and J S Shamma ldquoCooperative controland potential gamesrdquo IEEE Transactions on Systems Man andCybernetics Part B Cybernetics vol 39 no 6 pp 1393ndash14072009

[20] H P Young Individual Strategy and Social Structure PrincetonUniversity Press Princeton NJ USA 1998

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on a single base stationrsquos movement optimization it is nota multiuser network In [15] a power consumption optimalsynergetic forwarding scheme was put forward to improvethe systemrsquos lifetime by Li et al nevertheless the research in[14]mainly focuses on singleUAVrsquosmovement design not forthe UAV communication network The approach proposedin [15] is a centralized one not the focused point in ourwork Due to the UAVrsquos high dynamism the centralizedoptimization approach would not be capable of dealing withthe topology change and information exchange problems Tothe best of our knowledge the energy cost improvement issuein the UAV communication network has not been well solvedin existing works

In this paper we aim to study the energy cost improve-ment issue in the UAV communication network We putforward an energy cost orient forwarding allocation approachto achieve the optimal solution to the UAV communicationnetworks energy optimization issue The theoretic analysisis presented by modeling this problem as a game [16] Theexperiments are carried out to verify the theoretic result andthe performance of proposed intelligent learning algorithm

2 Network Model and Problem Formulation

A scenario where UAV communication networks are sup-ported by the ground communication station system [5]is shown in Figure 1 The UAV communication networksconsist of 119872 common UAVs (CUAVs) and 119873 forwardingUAVs (FUAVs) Usually the CUAVsrsquo communication wouldbe limited by their energy it is hard for CUAVs to com-municate with the grand stations directly The FUAVs areusually the ones supported by fuel which have the abilityto communicate with the ground stations directly In theUAV communication networks the FUAVs would work asthe forwarding node for the CUAVs With different groundstations and different FUAVsrsquo communication devices thelink bandwidths would also be different As shown in thescenario in Figure 1 the bandwidths of FUAVs might be6MHz 15MHz 20MHz and so on

Note that the topology of the UAV communicationnetwork is varying all the time As shown in Figure 1 theCUAVs FUAVs and the mobile ground stations are allmoving The dynamic topology is the character of the UAVcommunication networks and the distances between CUAVsand FUAVs vary As a result the transmission powers cost forthe communication would also change to meet the requireddata transmission quality The selection of FUAV to forwardthe data would be critical for the CUAVsrsquo energy cost Thefollowing attributes have important effect on the energy costthe distance to FUAV the transmission channel quality andthe bandwidth As shown in Figure 1 CUAV1 could select oneof the four FUAVs as the communication forwarding nodeto the ground station system The selection would be deter-mined by the expected energy cost DefineΠ119865 = 1 2 119873and Π119862 = 1 2 119872 as the set of FUAVs and CUAVsDefine 119861119865 = 1198611 1198612 119861119873 as the bandwidths vector Thebandwidth allocation between CUAVs could be designed bydifferent scheme it is assumed that the bandwidth would beequally allocated by the connected CUAVs in this paper for

the simplification The CUAVsrsquo selection of forwarding nodewould be decided by the CUAVsrsquo traffic requirement and thedistance to the FUAVs

Based on the Shannon theory assuming that119862119898 selects119865119899as the forwarding node the achieved data transmission ratewould be

119877119898119899 = 119861119898119899 log(1 + 119864119898119899120575119898119899minus1205741198981198991205881198981198991198611198981198991198730 ) (1)

where 1198730 is the noise power spectrum density 120575119898119899 is thedistance between 119862119898 and 119865119899 120574119898119899 is the path-loss exponentbetween 119862119898 and 119865119899 and 120588119898119899 is the instantaneous randomcomponent of the path lossThen the energy cost (EC) of119862119898would be

119864119898119899 = 1198611198991198730 (exp(|Ω119899|119877119898119899119861119899) minus 1)1003816100381610038161003816Ω1198991003816100381610038161003816 120575119898119899minus120574119898119899120588119898119899 (2)

where |Ω119899| is the number of CUAVs selected 119865119899 as theforwarding node

It should be noted that in the UAV communicationnetworks the best forwarding node selection would be notonly affected by some CUAV itself but also determined byother UAVsrsquo selection With the whole UAV communicationnetworks the goal is that the sum of the energy cost isminimized

Problem min 119864net = 119872sum119898=1

119864119898 (3)

that is

Problem max minus 119864net = minus 119872sum119898=1

119864119898 (4)

The main challenges of this problem are as follows firstthe optimization for the forwarding node allocation in UAVcommunication networks is the combinational optimizationissue The searching approach could achieve the best combi-nation but the computing complex would increase fast whenthe UAV network increasesThe possible combination wouldbe 735 = 379 times 1029 in relatively small 35 common UAVand 7 forwarding UAV communication networks With thegenetic algorithm ant colony algorithm and the like theperformance of the optimization could not be guaranteedSecond the information exchange required by the centralizedoptimization approach would not be practical for the limitedcommunication capability and the limited time Third thedynamism of the UAV communication network brings seri-ous problem to the centralized optimization including thedynamism of topology and the dynamism of environmentIn the following sections we solve this problem based on thegame theory which could achieve the optimal state of thenetwork without the centralized optimization

3 The Energy Cost Orient ForwardingAllocation Approach

In this section we put forward an energy cost orientforwarding allocation approach (ECOFAA) to optimize the


Link 1

Link 3Link 4

Link 2

CommonUAV1

Ground station 1

Ground station 2

Ground station 3

CommonUAV1

Move

Move

ForwardingUAV

ForwardingUAV

Move

15－（Ｔ6－（Ｔ

20－（Ｔ

30－（Ｔ

Ground Ground

Move







119866 = Π119862 Π119865 Ψ 119860 (5)





119864119894 (7)



119864119898= minus119864119898 minus sum

119894isin119873119890119894119898

119864119894 minus sum119894isinΠ119862119873119890119894119898

119864119894(8)









Yes

No

No

Yes



ＲＪum(am

aminusm)




119894isin119873119890119894119898

119864119894 minus sum119894isin119878119862119873119890119894119898


119894isin119873119890119894119898


119864and119894 )= 119864and119898 minus 119864119898 + sum

119894isin119873119890119894119898


119864119894 + sum119894isinΠ119862119873119890119894119898





(9)











(11)

Similarly



(12)



Then we have


Thus

120587 (a1) 119875a1 a2 = 120587 (a2) 119875a2a1 (15)

As a result

suma1isin119860

120587 (a1) 119875a1 a2 = suma1isin119860

120587 (a2) 119875a2 a1 = 120587 (a2) suma1isin119860

119875a2a1= 120587 (a2)

(16)


a = argaisin119860


min Γ (a) (17)






lim120573rarrinfin









CommonUAV1

ForwardingUAV





100

101

Ener

gy co

st (E

C) (m

W)




5 Conclusion




Acknowledgments


References





























Journal of












Journal of







Volume 2018






Volume 2018









Link 1

Link 3Link 4

Link 2

CommonUAV1

Ground station 1

Ground station 2

Ground station 3

CommonUAV1

Move

Move

ForwardingUAV

ForwardingUAV

Move

15－（Ｔ6－（Ｔ

20－（Ｔ

30－（Ｔ

Ground Ground

Move







119866 = Π119862 Π119865 Ψ 119860 (5)





119864119894 (7)



119864119898= minus119864119898 minus sum

119894isin119873119890119894119898

119864119894 minus sum119894isinΠ119862119873119890119894119898

119864119894(8)









Yes

No

No

Yes



ＲＪum(am

aminusm)




119894isin119873119890119894119898

119864119894 minus sum119894isin119878119862119873119890119894119898


119894isin119873119890119894119898


119864and119894 )= 119864and119898 minus 119864119898 + sum

119894isin119873119890119894119898


119864119894 + sum119894isinΠ119862119873119890119894119898





(9)











(11)

Similarly



(12)



Then we have


Thus

120587 (a1) 119875a1 a2 = 120587 (a2) 119875a2a1 (15)

As a result

suma1isin119860

120587 (a1) 119875a1 a2 = suma1isin119860

120587 (a2) 119875a2 a1 = 120587 (a2) suma1isin119860

119875a2a1= 120587 (a2)

(16)


a = argaisin119860


min Γ (a) (17)






lim120573rarrinfin









CommonUAV1

ForwardingUAV





100

101

Ener

gy co

st (E

C) (m

W)




5 Conclusion




Acknowledgments


References





























Journal of












Journal of







Volume 2018






Volume 2018
















Yes

No

No

Yes



ＲＪum(am

aminusm)




119894isin119873119890119894119898

119864119894 minus sum119894isin119878119862119873119890119894119898


119894isin119873119890119894119898


119864and119894 )= 119864and119898 minus 119864119898 + sum

119894isin119873119890119894119898


119864119894 + sum119894isinΠ119862119873119890119894119898





(9)











(11)

Similarly



(12)



Then we have


Thus

120587 (a1) 119875a1 a2 = 120587 (a2) 119875a2a1 (15)

As a result

suma1isin119860

120587 (a1) 119875a1 a2 = suma1isin119860

120587 (a2) 119875a2 a1 = 120587 (a2) suma1isin119860

119875a2a1= 120587 (a2)

(16)


a = argaisin119860


min Γ (a) (17)






lim120573rarrinfin









CommonUAV1

ForwardingUAV





100

101

Ener

gy co

st (E

C) (m

W)




5 Conclusion




Acknowledgments


References





























Journal of












Journal of







Volume 2018






Volume 2018













(11)

Similarly



(12)



Then we have


Thus

120587 (a1) 119875a1 a2 = 120587 (a2) 119875a2a1 (15)

As a result

suma1isin119860

120587 (a1) 119875a1 a2 = suma1isin119860

120587 (a2) 119875a2 a1 = 120587 (a2) suma1isin119860

119875a2a1= 120587 (a2)

(16)


a = argaisin119860


min Γ (a) (17)






lim120573rarrinfin









CommonUAV1

ForwardingUAV





100

101

Ener

gy co

st (E

C) (m

W)




5 Conclusion




Acknowledgments


References





























Journal of












Journal of







Volume 2018






Volume 2018









CommonUAV1

ForwardingUAV





100

101

Ener

gy co

st (E

C) (m

W)




5 Conclusion




Acknowledgments


References





























Journal of












Journal of







Volume 2018






Volume 2018





























Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








Documents

Game Based Energy Cost Optimization for …downloads.hindawi.com/journals/mpe/2018/9315954.pdfMathematicalProblemsinEngineering [] Y. Saleem, M. H. Rehmani, and S. Zeadally, “Integration