enhancing cellular coverage quality by virtual...

Research ArticleEnhancing Cellular Coverage Quality by Virtual Access Pointand Wireless Power Transfer

Jinsong Gui 1 Lihuan Hui1 and Naixue Xiong 2

1School of Information Science and Engineering Central South University Changsha 410083 China2Department of Mathematics and Computer Science Northeastern State University Tahlequah OK 74133 USA

Correspondence should be addressed to Jinsong Gui jsgui06163com

Received 19 October 2017 Revised 5 March 2018 Accepted 12 March 2018 Published 29 April 2018

Academic Editor Oscar Esparza

Copyright copy 2018 Jinsong Gui 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

The ultradensification deploying for cellular networks is a direct and effective method for the improvement of network capacityHowever the benefit is achieved at the cost of network infrastructure investment and operating overheads especially when thereis big gap between peak-hour Internet traffic and average one Therefore we put forward the concept of virtual cellular coveragearea where wireless terminals with high-end configuration are motivated to enhance cellular coverage quality by both providingRF energy compensation and rewarding free traffic access to InternetThis problem is formulated as the Stackelberg game based onthree-party circular decision where a Macro BS (MBS) acts as the leader to offer a charging power to Energy Transferring Relays(ETRs) and the ETRs and their associating Virtual Access Points (VAPs) act as the followers to make their decisions respectivelyAccording to the feedback from the followers the leader may readjust its strategy The circular decision is repeated until thepowers converge Also the better response algorithm for each game player is proposed to iteratively achieve the Stackelberg-NashEquilibrium (SNE)Theoretical analysis proves the convergence of the proposed game scheme and simulation results demonstrateits effectiveness

1 Introduction

The proliferation of mobile devices machine-to-machine(M2M) communication [1] and data collection for smartcities [2 3] leads to themassive growth of Internet trafficTheliterature [4] forecasts an increase of thousandfold in wirelesstraffic in 2020 as compared to the figures in 2010 which canbe handled by deploying tremendous amount of small cellsresulting in ultradense heterogeneous networks Althoughdense networks with small cells for peak-load scenarioscan meet soaring capacity and coverage demands in futurecellular networks [5 6] these benefits are got at the cost ofnetwork infrastructure investment and operating overheadsfor example more access points and higher backhaul costsmore complex interference management and more powerconsumption

Peak-hour Internet traffic increases more rapidly thanaverage Internet traffic It is reported in [7] that in 2016Internet traffic in the busiest 60-minute period in a dayincreased 51 percent while average traffic had only 32 percent

growth Moreover it is predicted by [7] that busy-hourInternet traffic will increase by a factor of 46 between 2016and 2021 while average Internet traffic will increase by afactor of 32

By reducing transmission range and optimizing trans-mitting power [8 9] network capacity and reliability canbe obviously improved due to effective control of mutualinterference Therefore a simple and easy solution is thatnetwork operators can deploy Small Base Stations (SBSs)enough to support peak traffic However they suffer fromunderutilization of resources at low load conditions In factdue to high costs for deployment and maintenance networkoperators are unwilling to seamlessly deploy dense small cellsto meet the customer needs in peak hour

To address the above problems we put forward the con-cept of virtual cellular coverage area which is an agile cost-effective and energy efficient alternative for small cell deploy-ments and thus helpful for reducing operational expenditureto the network operators due to the large number of smallcell deployments The problem of continuous operation of

HindawiWireless Communications and Mobile ComputingVolume 2018 Article ID 9218239 19 pageshttpsdoiorg10115520189218239

2 Wireless Communications and Mobile Computing

sparsely deployed SBSs can be tackled by providing dataservices by cellular Virtual Access Points (VAPs) during peakhours which can adapt well to the temporal and spatialvariations in traffic load It is more appropriate that wirelessterminals with high-end configuration act as VAPs

VAPs are responsible for receiving data of users far awayfrom a macrostation for example cellular edge users andforward these data to this macrostation which is helpfulfor reducing the transmitting powers of cellular edge usersand thus alleviating interference to the users in the samefrequency bands of adjacent cells Therefore a networkoperator will get more access traffic revenue but VAPs willconsume more energy

In order to compensate for this energy consumptiona network operator may make a Macro BS (MBS) transferpower to VAPs However the power conversion efficiency ofthe Radio Frequency (RF) energy harvesting circuit decreasessharply with the increase of distance In order to improvethe power conversion efficiency a MBS should select a fewnodes to act as Energy Transferring Relays (ETRs) which canforward energy from a MBS to a VAP

In many practical scenarios wireless User Equipment(UE) may be rational such that they only care about theirown interests instead of the overall one Without getting thebenefits from the operator they do not act as either VAPs orETRsTherefore in order tomotivateUE to act as eitherVAPsor ETRs the operator has to provide it with free traffic accessto Internet

To the best of our knowledge few works have studiedhow to enhance cellular coverage quality by VAPs and ETRsThis gap actually motivates us to develop a game-theoreticframework for this problem where any UE is motivated toact as either a VAP or an ETR through providing both RFenergy compensation and free traffic access to Internet Themain contributions of this paper are summarized as follows(1) We propose a game-based constructing method forvirtual cellular coverage area by combining RF energy com-pensation with free traffic access to Internet which can makeup for gaps of small cell coverage(2) We formulate the charging power decision problemand transmission power splitting problem as a Stackelberggame based on three-party circular decision A reverse induc-tion method is used to analyze this proposed Stackelberggame since it can capture the sequential dependence of thedecisions in all the stages of the game(3) The new better response strategy of each playeris proposed and then the Stackelberg-Nash Equilibrium(SNE) can be achieved by running the proposed algorithmsiteratively

The main notations in this work are listed in NotationsUsed in Our Work The rest of the paper is organized asfollows The related works are analyzed and summarizedin Section 2 In Section 3 the game scheme for virtualcellular coverage area construction is discussed in detailincluding networkmodel the time-slotted scheme for energyand information transference the problem formulation andtheoretical analysis and the description for algorithms Thesimulation results are given in Section 4 and the conclusionsare drawn in Section 5

2 Related Work

RF energy harvesting sources are usually divided into twocategories [10] where the first category belongs to ambient orunintended RF energy harvesting sources and the second oneis the type of dedicated or intended RF ones Also there arethe three main RF energy harvesting structures at receiving-ends [11] that is separated structure (ie energy harvestingand information decoding circuitry have their own antennasrespectively) time switching structure (ie energy harvestingand information decoding circuitry share the same antennaat different time slots) and power splitting structure (ieenergy harvesting and information decoding circuitry sharethe same antenna at the same time but split the input power)A time switching structure is usually used more frequentlysince it is comparatively compact in form factor and relativelyeffective in harvesting RF energy

Furthermore the literature [12] summarizes Simulta-neous Wireless Information and Power Transfer (SWIPT)designing schemes which are usually classified as decoupledSWIPT closed-loop SWIPT and integrated SWIPT Thedecoupled SWIPT is characterized by the information andthe power traffic sent from two separate transmitting sourcesIn closed-loop SWIPT scenarios [13ndash18] a base stationusually powers a wireless device in a downlink and receivesthe data from the same wireless device in the uplink Inan integrated SWIPT scheme [19] both the informationand power are carried by the same source over the samesignals

Concurrent multiple RF source transmission reported insome literatures (eg [20 21]) will increase total interferenceA harvest-then-transmit protocol allows a receiver to firstharvest energy from the downlink broadcast signals andthen use the harvested energy to send independent uplinkinformation to theMBS or SBS based on Time DivisionMul-tiple Access (TDMA) In order to mitigate total interferencethe system presented in [22] employs multiple dedicated RFsources with a harvest-then-transmit protocol to improve theharvested energy and data rate The achievable data rate canincrease by up to 87 when energy is harvested from up to5 dedicated RF sources compared to the case when energy isharvested from one source

Some works have focused on energy transfer in multihopmanner for wireless networks for example [23] proposesa method to inject power into the network as flows whereinjected power is carried in multihop manner while [24]explores the optimization of multihop wireless energy trans-fer in wireless networks

Some typical noncooperative game models (eg Stackel-berg game [25] and potential game [26]) are widely used invarious network information systems [27ndash29] A Stackelberggame consists of leaders and followers that compete witheach other for certain resources where the leaders first actby considering behaviors of the followers and the followersact subsequently

An exact potential game can characterize the set of NashEquilibria (NE) where a potential function can track thechanges in the payoff due to the unilateral deviation of aplayer and one or more NE points may exist and coincide

Wireless Communications and Mobile Computing 3

23

4

5 6

1

m

UE

SBS

Reference Point

ETR

VAP Energy Transfer

Information Transfer

s

r

MBS

c

de

a

b

t

i

jkRtℎ

Figure 1 Example for heterogeneous cellular networks

with one point that maximizes the potential function How-ever it cannot support application scenarios with sequentialdependence

In RF energy harvesting communication networks someworks [30ndash35] employ game theory to investigate differentsetups However they hardly have studied the concernedscenario of virtual cellular coverage area construction for amacrocell based on both RF energy compensation and freetraffic access to Internet

In the latest related work [35] the authors consider aradio frequency energy harvesting based Internet of Things(IoT) system which consists of a data access point (DAP)and several energy access points (EAPs) The DAP collectsinformation from its associated sensors EAPs can providewireless charging services to sensors via the RF energytransfer technique

In this paper a MBS firstly offers a charging powerto the ETRs and then asks each ETR to determine itscharging power to its associating VAP where the purpose isto encourage the VAP to relay data from its associating UEto the MBS by compensating it in terms of energy Thereforethe Stackelberg game model is applicable to such applicationscenario with sequential dependence

3 The Game Scheme for VirtualUltra-Network Construction

31 Network Model We consider a macrocell with a MBSlocated at its center as illustrated in Figure 1 Also thereare 119870 UE pieces distributed randomly in Figure 1 whereeach UE may serve as either an ETR or a VAP and alsomay not do so To mitigate interference to UE pieces inneighboring macrocells the maximum transmission powerof MBS is usually limited If the receiving nodes have astrict requirement for the receiving bit error rate UE pieces

far away from a MBS especially cellular edge users hardlymeet the requirement of such low receiving bit error rate Inaddition as stated in the introduction even if the cell-edgeUE pieces send data to the MBS by using their maximumtransmission powers it is generally difficult for the MBS toachieve such low receiving bit error rate

There may also be a few SBSs in Figure 1 Therefore theUE pieces adjacent to the SBSs can access the Internet via theSBSs However for the UE pieces far away from SBSs theymay access the Internet via VAPs Generally since VAPs donot have backhauls they forward the data from the cell-edgeUE pieces to the MBS

The hollow triangles in Figure 1 are the reference pointsused in the election of VAPs which are usually planned andset by the network operator according to the distribution ofthe regions without SBSs Such role as VAP is usually held bythe UE pieces that are closer to the reference points and havemore energy reserve However if theMBS transfers energy toVAPs directly the power conversion efficiency is usually verylowTherefore it is necessary to select a fewUEpieces to act asETRs For example 119894 119896 119903 and 119905 in Figure 1 assume such role

A set of the algorithms for VAP election ETR electionand UE association is listed in Algorithms 1 2 and 3 but thispaper does not discuss it since we focus on the design andanalysis of game scheme for virtual cellular coverage areaconstruction By Algorithm 1 the MBS (eg 119898 in Figure 1)will get its set of VAPs (eg 119878119898 = 119895 119904 in Figure 1 ) Also anyVAP (eg 119895 or 119904 in Figure 1) will get its set of ETRs (eg 119877119895= 119894 119896 in Figure 1 or 119877119904 = 119903 119905 in Figure 1 ) by Algorithm 2while it will get its set of associated UE pieces (eg 119880119895 = 119886 119887in Figure 1 or 119880119904 = 119888 119889 119890 in Figure 1 ) by Algorithm 3

32 Time-Slotted Scheme for Energy and Information Trans-ference In general the MBS adopts OFDMA and com-municates with each UE piece over a few subcarriers in


Run at the macro base station119898Input 119878119898 = Output 119878119898(1) Determine the number of virtual access points (eg 6)(2) Set their reference coordinates (eg the positions of dotted triangle shown in Figure 1)(3) For each reference coordinate point (egV) do(4) Broadcast a request packet at its maximum transmission power(5) Set 119904 and 119889119904V as 0 and a very large value respectively(6) Set the timer 119905Δ as Δ(7) while the timer 119905Δ does not expire do(8) If receive a responding packet from node 119906 then(9) If 119889119904V gt 119889119906V then 119904 = 119906 and 119889119904V = 119889119906V End if(10) End if(11) End while(12) Add 119904 to 119878119898(13) Send a confirmation package to node 119904(14) End forRun at any node 119906Input nullOutput null(1) If receive a requesting packet with a reference point (egV) then(2) If 119889119906V lt 119889th and 119890119906 gt 119890th then(3) Send a response packet to MBS119898(4) End if(5) End if(6) If receive a confirmation with a reference point (egV) then(7) Mark itself as the virtual access point with respect to the reference coordinate point V(8) End if

Algorithm 1 VAP election

Run at any virtual access point (VAP) 119904 isin 119878119898Input 119877119904 = Output 119877119904(1) Broadcast a requesting packet for charging node election at its maximum transmission power(2) Set the timer 119905Δ as Δ(3) while the timer 119905Δ does not expire do(4) If receive a respond packet for charging node election from any node (eg 119903) then(5) If 119889119903119904 lt 119889th then(6) add 119903 to 119877119904(7) Send a confirmation package to node 119903(8) End if(9) End if(10) End whileRun at any node 119903Input nullOutput null(1) If receive a requesting packet for charging node election from any VAP (eg 119904) then(2) If 1198892119903119904 + 1198892119903119898 lt 1198892119904119898 15 lt 119889119903119898119889119903119904 lt 3 and 119890119903 gt 119890th then(3) Send a responding packet to VAP 119904(4) End if(5) End if(6) If receive a confirmation package from any VAP (eg 119904) then(7) Mark itself as the charging node of the VAP 119904(8) End if

Algorithm 2 ETR election for VAP


Run at any virtual access point (VAP) 119904 isin 119878119898Input 119880119904 = Output 119880119904(1) Broadcast a requesting packet for member association at its maximum transmission power(2) Set the timer 119905Δ as Δ(3) while the timer 119905Δ does not expire do(4) If receive a respond packet for member association from any node (eg 119906) then(5) Add 119906 to 119880119904(6) Send a confirmation package to node 119906(7) End if(8) End whileRun at any node 119906Input nullOutput null(1) If receive a requesting packet for member association from any VAP (eg 119904) then(2) 1199041015840 = 119904 and 1198891015840119906119904 = 119889119906119904(3) Set the timer 119905Δ as Δ(4) while the timer 119905Δ does not expire do(5) If receive a requesting packet for member association from any VAP (eg 119904) then(6) If 1198891015840119906119904 gt 119889119906119904 then 1199041015840 = 119904 and 1198891015840119906119904 = 119889119906119904 End if(7) End if(8) End while(9) Send a respond packet for member association to the VAP 1199041015840(10) If receive a confirmation package from the VAP 1199041015840 then(11) mark itself as the member of the VAP 1199041015840(12) End if(13) End if

Algorithm 3 UE association for VAP

Energy transfer from MBS to ETR Energy transfer from ETR to VAP Information transmission

(1 minus ) middot T(1 minus ) middot middot T middot middot T

(1 minus ) middot T middot T

Figure 2 The structure of time frame

the downlink while each UE piece adopts SC-FDMA andcommunicates with the MBS over the same number ofsubcarriers in the uplink Without loss of generality weassume that the fixed number of orthogonal subcarriers isused by the MBS to communicate with each UE piece wherethe total channel frequency band for any UE is denoted as119882Meanwhile it is assumed that theMBS is furnishedwith |119878119898|+1 antennas at least so that it can receive the data from |119878119898|VAPs and broadcast energy to |119878119898| sdot |119877119904| ETRs simultaneouslywhile all UE pieces including ETRs and VAPs are equippedwith one single antenna each In this paper | sdot | denotes thenumber of members in a set (eg |119878119898| is the number of theVAPs in 119878119898 while |119877119904| is the number of the ETRs in 119877119904)

The MBS divides the communication time into timeframes with the same size (eg 119879) For each virtual cellularcoverage area with a VAP (eg 119904 in 119878119898) the MBS specifiesthe structure of each time frame shown in Figure 2 whichincludes two time slots (1) energy transfer time slot in whichETRs harvest the energy from the MBS over frequency band119882 during the 120572 sdot 120573 sdot 119879 time and the VAP (ie 119904) harvests

the energy from the ETRs (ie the members in 119877119904) overfrequency band119882 during the (1minus120572) sdot120573 sdot119879 time with 120573 beingthe fraction of the energy transfer time in T time and 120572 beingthe fraction of the energy transfer time from theMBS to ETRsin 120573 sdot 119879 time 0 lt 120572 lt 1 and 0 lt 120573 lt 1 (2) informationtransmission time slot in which a transmitting node sendsthe information signal to the corresponding receiver by usingthe harvested energy during the 120573 sdot 119879 time together with itsremaining battery energy

During the (1minus120572) sdot120573 sdot119879 time of each time frame the VAP(ie 119904) receives energy from its |119877119904| ETRs in TDMAmode Inother words each ETR will only transmit its energy duringits time slot with length 120591119903 sdot (1 minus 120572) sdot 120573 sdot 119879 where 0 lt 120591119903 lt 1forall119903 isin 1 2 |119877119904| and sum119903isin12|119877119904| 120591119903 = 1 Also during the(1 minus 120573) sdot 119879 time of each time frame the VAP (ie 119904) receivesthe data from its |119880119904| associatedUEpieces in TDMAmode Inother words each UE piece will only transmit its data duringits time slot with length 120576119906 sdot (1 minus120573) sdot 119879 where 0 lt 120576119906 lt 1 forall119906 isin1 2 |119880119904| and sum119906isin12|119880119904| 120576119906 = 1 The timing diagramis shown Figure 3


r middot Tet2 middot Tet1 middot Tet

Tet = (1 minus ) middot middot T

middot middot middot

(a) Energy transfer from ETR to VAP

u middot Tit2 middot Tit1 middot Tit

Tit = (1 minus ) middot T


(b) Information transmission fromUE toVAP

Figure 3 The timing diagram

r middot Tit2 middot Tit1 middot Tit



(a) Information transmission from ETR toMBS

middot middot middot T (1 minus ) middot middot middot T

middot middot T

(b) Information transmission from VAP toMBS

Figure 4 The time slot multiplexing

Although an ETR (eg 119903) receives energy from the MBSduring the 120572 sdot 120573 sdot 119879 time of a time frame and sends energyto the VAP during the (1 minus 120572) sdot 120573 sdot 119879 time of the same timeframe respectively it can send its data to the MBS in thepart of the (1 minus 120573) sdot 119879 time of the same time frame that is120591119903 sdot (1 minus 120573) sdot 119879 time as shown in Figure 4(a) Here since theETR reuses UErsquos transmitting time slot it should employ thedifferent frequency bands

Also for the data received by the VAP in the (1 minus 120573) sdot 119879time of the previous time frame the VAP can send them tothe MBS in the part of the 120572 sdot 120573 sdot 119879 time of the current timeframe that is 120575 sdot 120572 sdot 120573 sdot 119879 time and 0 lt 120575 lt 1 while (1 minus 120575) sdot120572 sdot 120573 sdot 119879 time is used by the VAP to send its own data to theMBS as shown in Figure 4(b) Here since the VAP reuses theMBSrsquos transmitting time slot it should employ the differentfrequency bands

33 Problem Formulation and Theoretical Analysis In thissubsection we first describe wireless energy transfer modeland wireless information transmission model and thendevelop a game-theoretic framework for virtual cellularcoverage area construction

After the MBS (as a leader) offers an initial chargingpower to all the ETRs each ETR (as a follower) determinesits charging power to its associating VAP Once each VAP (asa follower) receives the charging powers from all the ETRsassociated with it it determines its transmission power forrelaying data from its associating UE pieces to theMBS Sincean ETR charging power is subject to the MBS it is moreappropriate that the MBS acts as the leader for the VAPs

We will analyze the proposed Stackelberg game based onthree-party circular decision and obtain its SNE of this gameBased on our analysis we know that each partyrsquos strategyaffects other partiesrsquo strategiesTherefore a reverse inductionmethod can be used to analyze the proposed game because itcan capture the sequential dependence of the decisions in allthe game stages

331 Wireless Signal Propagation Model When a receiver 119895works in the energy harvesting mode the power harvestedfrom source 119894 can be calculated as follows

119901119903119894119895 = 120578119894119895 sdot 119901119905119894119895 sdot 10038161003816100381610038161003816ℎ119894119895100381610038161003816100381610038162 (1)

In (1) 120578119894119895 denotes the power conversion efficiency factorfrom node 119894 to node 119895 119901119905119894119895 is the transmission power at source119894 119901119903119894119895 is the harvested power at receiver 119895 and ℎ119894119895 denotes thechannel power gain between source 119894 and receiver 119895 Herelet 119892119894119895 = |ℎ119894119895|2 which is calculated by using the followingformula [22 36]

119892119894119895 = 10minus(PLref+120595119894119895)10 sdot 119889minus120593119894119895 sdot 120573119894119895 (2)

In (2) 120593 is path loss exponent PLref is the path loss indB at the reference distance 120595119894119895 is the body shadowing lossmargin between source 119894 and receiver 119895 in dB 119889119894119895 is thedistance between source 119894 and receiver 119895 120573119894119895 is the small-scale fading power gain between source 119894 and receiver 119895 Forsimplicity the paper assumes 120578119894119895 = 120578 and 120595119894119895 = 120595

Let 119882 and 1205902 denote the transmission bandwidth andnoise power respectively When the receiver 119895 works in theinformation decoding mode the information decoding rate119887119894119895 from source 119894 to receiver 119895 is as follows

119887119894119895 = 119882 sdot log2(1 + 119901119905119894119895 sdot 1198921198941198951205902 ) (3)

332 Game Formulation and Theoretical Analysis for ETRsIn the subsection we consider a noncooperative scenarioin which the ETRs are all rational and self-interested suchthat they only want to minimize their charging powers andmaximize their transmitting powersTherefore we formulatethe noncooperative game for the ETRs where the gameplayers are the |119877119904| ETRs the game actions are that each


ETR determines the charging power and transmitting powerunder the constraint of itsmaximum transmitting power andthe game utility is the data rate for each ETR

For any ETR (eg 119903) when the MBS (ie 119898) broadcastsenergy at 119901119905119898119903 its harvested power 119901119903119898119903 can be calculatedaccording to formula (1) and specified as 119901119903119898119903 = 120578 sdot 119901119905119898119903 sdot 119892119898119903Also when the maximum transmission power of the ETR 119903 isset as 119901max

119903 the power used in transferring energy from 119903 to119904 isin 119878119898 (ie 119901119905119903119904) and that used in transmitting data from 119903 to119898 (ie 119901119905119903119898) have to meet the following relation

119901max119903 ge 119901119905119903119904 + 119901119905119903119898 (4)

On the one hand the ETR 119903 should employ themore valueof 119901119905119903119904 to transfer energy to the VAP in order to obtain themore free traffic access to Internet on the other hand it hasto use more value of 119901119905119903119898 to transmit its own data such thatthe free traffic share is fully utilizedTherefore the ETR 119903mustdetermine optimal transmission power splitting ratio underthe constraint of 119901max

119903 When the ETR 119903 adopts 119901max

119903 and its battery energystorage and harvested power are 119864119903 and 119901119903119898119903 respectively itscontinuous emission time (ie 119879max

119903 ) can be estimated by thefollowing formula

119879max119903 = 119864119903119901max

119903 minus 119901119903119898119903 (5)

During 119879max119903 the utility of the ETR 119903 is represented as

follows120583119903 (119875119903)= 119879max119903 sdot 120593119903119898 sdot 119882119903 sdot log2(1 + (119901max

119903 minus 119901119905119903119904) sdot 1198921199031198981205902 )

120593119903119898 = log2 (1 + (120578 sdot 119901119905119903119904 sdot 119892119903119904 sdot 119892119904119898) 1205902)0119903 + sum1199031015840isin119877119904 log2 (1 + (120578 sdot 1199011199051199031015840 119904 sdot 1198921199031015840 119904 sdot 119892119904119898) 1205902)

119875119903 = 1199011199051199031015840 119904 | forall1199031015840 isin 119877119904

(6)

In (6) 0119903 is seen as the contribution from a fictitiousselfless node and usually set to a constant (eg 10minus7) wherethe aim is to prevent game participants from colluding tocheat We notice that each playerrsquos strategy (eg 119901119905119903119904 of theETR 119903) only depends on the strategies of the other players(ie 119875minus119903 = 1199011199051199031015840 119904 | forall1199031015840 isin 119877119904 119901119905119903119904) Thus given the strategiesof the other players 119875minus119903 the best response strategy of the ETR119903 is the solution to the following optimization problem Thatis the ETR 119903 needs to find the optimal transmission power119901119905119903119904 to offer to the VAP 119904 to maximize its individual profitwhich can be obtained by solving the following optimizationproblem

max119901119905119903119904119875minus119903

119879max119903 sdot 120593119903119898 sdot 119882119903

sdot log2(1 + (119901max119903 minus 119901119905119903119904) sdot 1198921199031198981205902 )

(7)

We denote by 119901119905lowast119903119904 the optimal solution to optimizationproblem (7) It is straightforward to verify that (7) alwayshas a feasible solution A SNE of the formulated game is afeasible profile119901119905lowast119903119904 that satisfies (7) Now we calculate the bestresponse strategy 119901119905lowast119903119904 for the ETR 119903 by solving optimizationproblem (7) which is described in the following theorem

Theorem 1 Given 119875minus119903 = 1199011199051199031015840 119904 | forall1199031015840 isin 119877119904 119901119905119903119904 the optimalresponse strategy 119901119905lowast119903119904 of the ETR 119903 can be expressed as follows

119901119905lowast119903119904 = 119860119861 (8)

where119860 = 120578 sdot 119892119903119904 sdot 119892119904119898 sdot 1205902 sdot (1 minus 120593119903119898) sdot 119883119903 + 120578 sdot 119892119903119904 sdot 119892119904119898

sdot 119892119903119898 sdot (1 minus 120593119903119898) sdot 119901max119903 sdot 119883119903 minus 119892119903119898 sdot 1205902 sdot 120593119903119898

sdot 119884119903119861 = 120578 sdot 119892119903119904 sdot 119892119904119898 sdot 119892119903119898 sdot 120593119903119898 sdot 119884119903 + 120578 sdot 119892119903119904 sdot 119892119904119898 sdot 119892119903119898

sdot (1 minus 120593119903119898) sdot 119883119903119883119903 = log2(1 + (119901max

119903 minus 119901119905119903119904) sdot 1198921199031198981205902 )

119884119903 = sum1199031015840isin119877119904

log2(1 + 120578 sdot 1199011199051199031015840 119904 sdot 1198921199031015840 119904 sdot 1198921199041198981205902 )

(9)

Proof To maximize its net utility each ETR hopes to deter-mine an optimal transmission power splitting ratio For anarbitrary ETR 119903 its net utility function defined in (6) isa concave function of 119901119905119903119904 since 1205972120583119903(119875119903)120597(119901119905119903119904)2 lt 0Therefore let 120597120583119903(119875119903)120597119901119905119903119904 = 0 the optimal response strategy119901119905lowast119903119904 of the ETR 119903 can be denoted as (8) This completes theproof

In fact this power 119901119905lowast119903119904 cannot be solved directly fromformula (8) since it is included in 119860 and 119861 of formula(8) However due to the concave characteristic stated inTheorem 1 a new approximating algorithm (ie Algorithms4) is proposed in the following text to obtain its approximateoptimal value

333 Game Formulation and Theoretical Analysis for VAPsIn the subsection we consider a noncooperative scenario inwhich the VAPs are all rational and self-interested such thatthey only want to minimize their forwarding powers andmaximize their transmitting powersTherefore we formulatethe noncooperative game for the VAPs where the gameplayers are |119878119898| VAPs the game actions are that each VAPdetermines the forwarding power and transmitting powerunder the constraint of its maximum transmitting powerand the game utility is the data rate for each VAP For anyVAP (eg 119904) its harvesting energy from the |119877119904| ETRs can beestimated by the following formula

119890119904 = sum119903isin119877119904

119879max119903 sdot 120578 sdot 119901119905119903119904 sdot 119892119903119904 (10)


Also when themaximum transmission power of the VAP119904 is set as 119901max119904 the power used in forwarding data from UE

to the MBS 119898 (ie 119901119905119904119898) and that used in transmitting itsown data to the MBS119898 (ie 119901119905119906119898) have to meet the followingrelation

119901max119904 ge 119901119905119904119898 + 119901119905119906119898 (11)

On the one hand the VAP 119904 should employ more value of119901119905119904119898 in forwarding data to the MBS 119898 in order to obtain themore free traffic access to Internet on the other hand it hasto use more value of 119901119905119906119898 to transmit its own data such thatthe free traffic share is fully utilized

Therefore the VAP 119904 must determine optimal transmis-sion power splitting ratio under the constraint of 119901max

119904 Whenthe VAP 119904 adopts 119901max

119904 and its battery energy storage andharvested energy from the ETRs are 119864119904 and 119890119904 respectivelyits continuous emission time (ie 119879max

119904 ) can be estimated bythe following formula

119879max119904 = 119864119904 + 119890119904119901max

119904

(12)

During 119879max119904 the utility of the VAP 119904 is represented as

follows120583119904 (119875119904) = 119879max

119904 sdot 120593119904119898 sdot 119882119904sdot log2(1 + (119901max

119904 minus 119901119905119904119898) sdot 1198921199041198981205902 )

120593119904119898 = log2 (1 + (119901119905119904119898 sdot 119892119904119898) 1205902)0119904 + sum1199041015840isin119878119898 log2 (1 + (1199011199051199041015840 119898 sdot 1198921199041015840 119898) 1205902)

119875119904 = 1199011199051199041015840 119898 | forall1199041015840 isin 119878119898

(13)

In (13) the meaning of 0119904 is similar to 0119903 and also setto a constant (eg 3) We notice that each playerrsquos strategy(eg 119901119905119904119898 of the VAP 119904) only depends on the strategies ofthe other players (ie 119875minus119904 = 1199011199051199041015840 119898 | forall1199041015840 isin 119878119898 119901119905119904119898)Thus given the strategies of the other players 119875minus119904 the bestresponse strategy of the VAP 119904 is the solution to the followingoptimization problem That is the node 119904 needs to findthe optimal forwarding power 119901119905119904119898 to offer data forwardingservice for its associating UE pieces in order to maximizeits individual profit which can be obtained by solving thefollowing optimization problem

max119901119905119904119898119875minus119904

119879max119904 sdot 120593119904119898 sdot 119882119904


(14)

We denote by 119901119905lowast119904119898 the optimal solution to optimizationproblem (14) It is straightforward to verify that (14) alwayshas a feasible solution A SNE of the formulated game is a fea-sible profile 119901119905lowast119904119898 that satisfies (14) Now we calculate the bestresponse strategy 119901119905lowast119904119898 for the VAP 119904 by solving optimizationproblem (14) which is described in the following theorem

Theorem 2 Given 119875minus119904 = 1199011199051199041015840 119898 | forall1199041015840 isin 119878119898 119901119905119904119898 theoptimal response strategy 119901119905lowast119904119898 of the VAP 119904 can be expressedas follows

119901119905lowast119904119898 = 119862119863 (15)

where119862 = 119892119904119898 sdot 1205902 sdot (1 minus 120593119904119898) sdot 119883119904 + 1198922119904119898 sdot (1 minus 120593119904119898)

sdot 119901119898119886119909119904 sdot 119883119904 minus 119892119904119898 sdot 1205902 sdot 120593119904119898 sdot 119884119904119863 = 1198922119904119898 sdot 120593119904119898 sdot 119884119904 + 1198922119904119898 sdot (1 minus 120593119904119898) sdot 119883119904119883119904 = log2(1 + (119901119898119886119909119904 minus 119901119905119904119898) sdot 1198921199041198981205902 )119884119904 = sum1199041015840isin119878119898

log2(1 + 1199011199051199041015840 119898 sdot 1198921199041015840 1198981205902 )

(16)

Proof To maximize its net utility each VAP hopes to deter-mine an optimal transmission power splitting ratio For anarbitrary VAP 119904 its net utility function defined in (13) isa concave function of 119901119905119904119898 since 1205972120583119904(119875119904)120597(119901119905119904119898)2 lt 0Therefore let 120597120583119904(119875119904)120597119901119905119904119898 = 0 the optimal response strategy119901119905lowast119904119898 of the VAP 119904 can be denoted as (15) This completes theproof

Similar to the discussion and solution for 119901119905lowast119903119904 we alsoprovide a new approximate solution (ie Algorithms 5) in thefollowing text to solve 119901119905lowast119904119898334 Game Formulation and Theoretical Analysis for MBSIn the subsection we mainly focus on how the decision inthe MBS is affected by the game results of ETRs and VAPsBased on the conditions described in the previous text theStackelberg game theory including leaders and followerscompeting with each other for certain resources applies tothis scenario

In this paper the MBS acts as the leader and offersan initial charging power to the ETRs with its maximumtransmission power The purpose is to encourage all UEpieces to participate actively Following this the ETRs andtheir associating VAP act as the followers and make theirdecisions according to their utility functions respectivelyAccording to the feedback from the followers the leader mayreadjust its strategy

It is assumed that the MBS broadcasts energy to |119878119898| sdot|119877119904| ETRs with omnidirectional antenna Therefore for anarbitrary ETR (eg 119903) the charging power 119901119905119898119903 is simplifiedas 119901119905119898 The MBS hopes to obtain the maximum forwardingtraffic from the |119878119898|VAPs but just wants to pay the minimumprice of energy Therefore the utility of the MBS 119898 isrepresented as follows

120583119898 (119901119905119898 119875119903 119875119904) = 119888119887 sdot sum119904isin119878119898

119879max119904 sdot 119882

sdot log2 (1 + 119901119905119904119898 sdot 1198921199041198981205902 ) minus 119888119890sdotmax 119879max

119904 | 119904 isin 119878119898 sdot 119901119905119898(17)


In (17) 119888119887 is traffic price per bit while 119888119890 is energy priceper joule According to formulas (1) (5) (10) and (12) 119879max

119904

can be rewritten as follows

119879max119904 = 119891119879119904 (119901119905119898 119875119903 119875119904) = 119864119904 + sum119903isin119877119904 ((119864119903 sdot 120578 sdot (119901max

119903 minus 119901119905119903119898) sdot 119892119903119904) (119901max119903 minus 120578 sdot 119901119905119898 sdot 119892119898119903))119901max

119904

(18)

Thus given 119875119903 and 119875119904 from the ETRs and VAPs respec-tively the best response strategy of the MBS119898 is the solutionto the following optimization problem

max119901119905119898119875119903119875119904

119888119887 sdot sum119904isin119878119898

119879max119904 sdot 119882 sdot log2 (1 + 119901119905119904119898 sdot 1198921199041198981205902 )

minus 119888119890 sdotmax 119879max119904 | 119904 isin 119878119898 sdot 119901119905119898

(19)

Now we calculate the best response strategy 119901119905lowast119898 forthe MBS 119898 by solving optimization problem (19) which isdescribed in the following theorem

Theorem 3 Given 119875119903 and 119875119904 from the ETRs and VAPsrespectively when the following relation is met

119901119905119898 gt [[119888119887 sdot sum119904isin119878119898 (1205972119879119898119886119909119904 120597 (119901119905119898)2) sdot 119882 sdot log2 (1 + (119901119905119904119898 sdot 119892119904119898) 1205902) minus 2119888119890 sdotmax 120597119879119898119886119909119904 120597119901119905119898 | 119904 isin 119878119898

119888119890 sdotmax 1205972119879119898119886119909119904 120597 (119901119905119898)2 | 119904 isin 119878119898]]+

(20)

the optimal response strategy119901119905lowast119898 of theMBS119898 can be expressedas follows

119901119905lowast119898 = [119888119887 sdot sum119904isin119878119898 (120597119879119898119886119909119904 120597119901119905119898) sdot 119882 sdot log2 (1 + (119901119905119904119898 sdot 119892119904119898) 1205902) minus 119888119890 sdotmax 119879119898119886119909119904 | 119904 isin 119878119898119888119890 sdotmax 120597119879119898119886119909119904 120597119901119905119898 | 119904 isin 119878119898 ]+

(21)

where

[sdot]+ ≜ max sdot 0 (22)

120597119879119898119886119909119904120597119901119905119898= 1119901119898119886119909119904 sdot sum

119903isin119877119904

119864119903 sdot 1205782 sdot 119892119898119903 sdot 119892119903119904 sdot (119901119898119886119909119903 minus 119901119905119903119898)(119901119898119886119909119903 minus 120578 sdot 119901119905119898 sdot 119892119898119903)2

(23)

1205972119879119898119886119909119904120597 (119901119905119898)2= 1119901119898119886119909119904 sdot sum

119903isin119877119904


(24)

Proof The optimization problem with respect to (19) alwayshas a feasible solution under the condition that thefirst-order derivative of 120583119898(119901119905119898 119875119903 119875119904) with respect to 119901119905119898that is 1205972120583119898(119901119905119898 119875119903 119875119904)120597(119901119905119904119898)2 is less than 0 Since

1205972120583119898(119901119905119898 119875119903 119875119904)120597(119901119905119904119898)2 can be denoted as 119888119887 sdotsum119904isin119878119898(1205972119879max119904 120597(119901119905119898)2)sdot119882sdotlog2(1+(119901119905119904119898 sdot119892119904119898)1205902)minus119888119890 sdotmax1205972119879max

119904 120597(119901119905119898)2 |119904 isin 119878119898sdot119901119905119898minus2119888119890 sdot max120597119879max119904 120597119901119905119898 | 119904 isin 119878119898 and it will be less

than 0 according to conditions (23) and (24) when expression(20) is met

By solving the first-order derivative of 120583119898(119901119905119898 119875119903 119875119904)withrespect to 119901119905119898 we can obtain the following expression

120597120583119898 (119901119905119898 119875119903 119875119904)120597119901119905119898 = 119888119887 sdot sum119904isin119878119898

1205972119879max119904120597 (119901119905119898)2 sdot 119882


119904120597 (119901119905119898)2 | 119904 isin 119878119898 sdot 119901119905119898minus 2119888119890 sdotmax120597119879max

119904120597119901119905119898 | 119904 isin 119878119898

(25)


Table 1 The game scenarios in our work

Scenario Actor Strategy Payoff

ETR game ETRsEach player hopes to find the optimal

charging power offered to its associatingVAP to maximize its individual profit

The utility of any player is computed byformula (6)

VAP game VAPs

Each player hopes to find the optimalforwarding power to offer data

forwarding service for its associating UEsto maximize its individual profit


Stackelberggame

MBSETRsVAPs

The MBS hopes to obtain the maximumforwarding traffic from the VAPs but just

wants to pay the minimum price ofenergy

The utility of the MBS is computed byformula (17)

Run at any ETR 119903 isin 119877119904Input 120576Output (119901119905119903119904 119901119905119903119898)(1) If receive 119901119905119898119903 (ie 119901119905119898) 120593119903119898 and 120593119904119898 from the MBS119898 then(2) Save 120593119903119898 and 120593119904119898 for use(3) 119901119905119903119904 = 119901119903max2 119901119905119903119898 = 119901119903max minus 119901119905119903119904(4) 120583 = 120583119903(119901119905119903119904 119875119903119901119905119903119904)(5) 119901119903119898119903 = 120578 sdot 119901119905119898119903 sdot 119892119898119903(6) Compute 119879119903max according to formula (5)(7) Send (119901119905119903119904 119901119905119903119898) to the MBS119898(8) While (true) do(9) If receive 120593119903119898 from the MBS119898 then(10) If 120583119903(119901119905119903119904 minus 120576 119875119903 119901119905119903119904 minus 120576) gt 120583 then(11) 120583 = 120583119903(119901119905119903119904 minus 120576 119875119903 119901119905119903119904 minus 120576)(12) 119901119905119903119904 = 119901119905119903119904 minus 120576 119901119905119903119898 = 119901119903max minus 119901119905119903119904(13) Else if 120583119903(119901119905119903119904 + 120576 119875119903 119901119905119903119904 + 120576) gt 120583 then(14) 120583 = 120583119903(119901119905119903119904 + 120576 119875119903 119901119905119903119904 + 120576)(15) 119901119905119903119904 = 119901119905119903119904 + 120576 119901119905119903119898 = 119901119903max minus 119901119905119903119904(16) End if(17) Send (119901119905119903119904 119901119905119903119898) to the MBS119898(18) End if(19) If receive ldquoendrdquo from the MBS119898 then(20) Send (119901119905119903119904 119901119905119903119898) and 120593119904119898 to the VAP 119904 and return(21) End if(22) End while(23) End if

Algorithm 4 ETR-level game

Let expression (25) (ie the first-order derivative of120583119898(119901119905119898 119875119903 119875119904) with respect to 119901119905119898) be equal to 0 we canobtain expression (21) with some algebra manipulationswhich completes the proof

From Theorem 3 we know that expression (19) satisfiesthe concavity under a given condition Therefore if 119901119905119898 thatsatisfies expression (20) is less than MBS maximum power119901max119898 we can design an approximate algorithm to search

the approximate value for 119901119905lowast119898 in the interval from [119901119905119898]+ to119901max119898 To facilitate readersrsquo understanding Table 1 summarizes

the game scenarios actors (or players) strategies (or actions)and payoffs (or utilities) in this paper

34 Distributed Iterative Algorithms for Obtaining SNE Sincewe have derived the optimal transmission power splittinglevels for ETRs and VAPs to achieve their desired data rates(ie from their own to the MBS) as well as allowing theMBS to achieve its maximum utility by adjusting its chargingpower we now propose the three efficient and practicalalgorithms that find the approximately optimal power levelswhich are based on the results of theoretical analysis inSection 33

Based on a reverse induction mode the system interac-tion is as follows Given an initial charging power offeredby the MBS to the ETRs (1) each ETR firstly determinesits charging power to its associating VAP by runningAlgorithm 4 (2) then each VAP determines its transmission


Run at any VAP 119904 isin 119878119898Input 120576Output (119901119905119904119898 119901119905119906119898)(1) If receive (119901119905119903119904 119901119905119903119898) | forall119903 isin 119877119904 and 120593119904119898 from all the ETRs in 119877119904 then(2) 119901119905119904119898 = 119901119904max2 119901119905119906119898 = 119901119904max minus 119901119905119904119898(3) 120583 = 120583119904(119901119905119904119898 119875119904 119901119905119904119898)(4) Compute 119890119904 according to formula (10)(5) Compute 119879119904max according to formula (12)(6) Send (119901119905119904119898 119901119905119906119898) to the MBS119898(7) While (true) do(8) If receive 120593119904119898 from the MBS119898 then(9) If 120583119904(119901119905119904119898 minus 120576 119875119904 119901119905119904119898 minus 120576) gt 120583 then(10) 120583 = 120583119904(119901119905119904119898 minus 120576 119875119904 119901119905119904119898 minus 120576)(11) 119901119905119904119898 = 119901119905119904119898 minus 120576 119901119905119906119898 = 119901119904max minus 119901119905119904119898(12) Else if 120583119904(119901119905119904119898 + 120576 119875119904 119901119905119904119898 + 120576) gt 120583 then(13) 120583 = 120583119904(119901119905119904119898 + 120576 119875119904 119901119905119904119898 + 120576)(14) 119901119905119904119898 = 119901119905119904119898 + 120576 119901119905119906119898 = 119901119904max minus 119901119905119904119898(15) End if(16) Send (119901119905119904119898 119901119905119906119898) to the MBS119898(17) End if(18) If receive ldquoendrdquo from the MBS119898 then return End if(19) End while(20) End if

Algorithm 5 VAP-level game

for relaying data from its associating UE pieces to theMBS according to the results of Algorithm 5 (3) finally theMBS updates its charging power to the ETRs by executingAlgorithm 6 The steps (1) (2) and (3) are repeated until thepowers converge

Parameter 120576 is set to a small value (eg 01sim35) Inany of the three algorithms the better response of any playerin the current round is the better transmission power splittinglevels or charging power offered tomaximize its total revenuegiven those offered by the other players at the previous roundof the iteration process

4 Performance Evaluation

41 Simulation Setting In our simulations the macrocellnetwork consists of one MBS and a set of UE pieces (denotedas) where the number of members in is denoted as ||We assume that || is 1000 For any UE 119894 the initial batterycapacity119864119894 is randomly distributed from 005119883 to 02119883 Joulewhere 119883 can take different values ranging from 20 to 80Therefore the average initial battery capacity 119864av is obtainedby the following formula

119864av = sum119894isin 119864119894|| (26)

We assume that the coverage radius of the MBS is 500mand the UE pieces are randomly located in the macrocellEach ETR or VAP elected from UE pieces has more batteryenergy reserve which can improve the network performanceThe UE pieces associated with each VAP are basically locatednear the edge of the macrocell since such UE pieces need the

23

4

5 6

1

MBS

Rtℎ

(0 0)

(minus05Rtℎ 0866Rtℎ)

(minus05 minus0866Rtℎ) (05Rtℎ minus0866Rtℎ)

(05Rtℎ 0866Rtℎ)

(minusRtℎ

Rtℎ

0) (Rtℎ 0)

Figure 5 The coordinates of reference points

help of VAPsmoreWe set the coordinates of reference pointsas shown in Figure 5 where 119877119905ℎ is valued at 100m

It is assumed that channel noise power 1205902 (at the receiversof all UE pieces including ETRs and VAPs) is valued ata fixed value which is randomly distributed from minus120 tominus60 dBmMHzThe other simulation parameters are listed inTable 2

42 Simulation Schemes and Metrics In this subsection weevaluate the performance of the scheme in this paper viasimulations under a few typical valueswith respect to the time


Run at the MBS119898Input 120576Output 119901119905119898(1) Initialize 119901119905119898 and 120583 as 119901119898max and 0 respectively(2) Initialize 119888119900119906119899119905 119903 and 119888119900119906119899119905 119904 as 0 respectively(3) For each ETR 119903 do 119901119905119903119904 = 0 119901119905119903119898 = 0 119888119900119906119899119905 119903 + + End for(4) For each VAP 119904 do 119901119905119904119898 = 0 119901119905119906119898 = 0 119888119900119906119899119905 119904 + + End for(5) Initialize 120593119903119898 as 119888119900119906119899119905 119904119888119900119906119899119905 119903(6) Initialize 120593119904119898 as 1119888119900119906119899119905 119904(7) Broadcast 119901119905119898 120593119903119898 and 120593119904119898 to all the ETRs(8) While (true)(9) If receive the updated (119901119905119903119904 119901119905119903119898) from any ETR 119903 then(10) Replace the old value of (119901119905119903119904 119901119905119903119898) with its new value(11) Else if receive the old (119901119905119903119904 119901119905119903119898) from any ETR 119903 then(12) Record the cumulative number of ETRs sending old values(13) End if(14) If all the ETRs report (119901119905119903119904 119901119905119903119898) and there is a new value then(15) For each ETR 119903 do compute 120593119903119898 and send it to 119903 End for(16) End if(17) If all the ETRs report the old (119901119905119903119904 119901119905119903119898) then(18) Broadcast the packet including the ldquoendrdquo to all the ETRs(19) End if(20) If receive the updated (119901119905119904119898 119901119905119906119898) from any VAP 119904 then(21) Replace the old value of (119901119905119904119898 119901119905119906119898) with its new value(22) Else if receive the old (119901119905119904119898 119901119905119906119898) from any VAP 119904 then(23) Record the cumulative number of VAPs sending old values(24) End if(25) If all the VAPs report (119901119905119904119898 119901119905119906119898) and there is a new value then(26) For each VAP 119904 do compute 120593119904119898 and send it to 119904 End for(27) End if(28) If all the VAPs report the old (119901119905119904119898 119901119905119906119898) then(29) Broadcast the packet including the ldquoendrdquo to all the VAPs(30) If 120583119898(119901119905119898 119875119903 119875119904) gt 120583 then 120583 = 120583119898(119901119905119898 119875119903 119875119904) 119901119905119898 = 119901119905119898 minus 120576(31) Else break(32) End if(33) go to (2)(34) End if(35) End while(36) Keep energy emission at 119901119905119898

Algorithm 6 MBS-level game

Table 2 Simulation parameters

Symbol Description Value119901max119898 Maximum transmitting power for the MBS 40 dBm119901max119906 Maximum transmitting power for UEs including MTRs and VAPs 26 dBm

PLref Path loss at the reference distance 30 dB120595 Body shadowing loss margin 15 dB120593 Path loss exponent 23120578 Power conversion efficiency factor 08119879 Frame length 100 120583s119888119887 Traffic unit price 45 centsMbit119888119890 Energy unit price 9 centsKWH119882 Transmission bandwidth for each UE 1MHz119882119903 Transmission bandwidth for ETRs 6MHz119882119904 Transmission bandwidth for VAPs 6MHz


slot parameters (ie 120572 120573 120575 120591 and 120576) For any UE 119906 we set atime allocation strategy for 120576119906 as follows

120576119906 = 110038161003816100381610038161198801199041003816100381610038161003816 (27)

For any ETR 119903 the adaptive time allocation for 120591119903 isdetermined by the following formula

120591119903 = 119879max119903sum1199031015840isin12|119877119904| 119879max

1199031015840

(28)

Also the fixed time allocation for 120591119903 is determined by thefollowing formula

120591119903 = 110038161003816100381610038161198771199041003816100381610038161003816 (29)

Our simulation metrics include average data rate forETRs average data rate for VAPs and average data raterelayed by VAPs for associated UE pieces Here the firstmetric is denoted as DRav119903 and estimated by the followingformulas

120583119903 = 119879max119903 sdot 120593119903119898 sdot 119882119903sdot log2(1 + (119901max

119903 minus 119901119905119903119904) sdot1198921199031198981205902 )

119873119903 = lceil 119879max119903120591119903 sdot (1 minus 120573) sdot 119879rceil

DR119903 = 120583119903119873119903 sdot 119879 sdot 120593119903119898 sdot 119882119903DRav119903 = sum119904isin119878119898 sum119903isin119877119904 DR11990310038161003816100381610038161198781198981003816100381610038161003816 sdot 10038161003816100381610038161198771199041003816100381610038161003816

(30)

The second metric is denoted as DRav119904 and estimated bythe following formulas


119904 minus 119901119905119904119898) sdot 1198921199041198981205902 )119873119904 = lceil 119879max

119904(1 minus 120575) sdot 120572 sdot 120573 sdot 119879rceilDR119904 = 120583119904119873119904 sdot 119879 sdot 120593119904119898 sdot 119882119904

DRav119904 = sum119904isin119878119898 DR11990410038161003816100381610038161198781198981003816100381610038161003816

(31)

The third metric is denoted as DRav119906 and estimated bythe following formulas

120574max119906119904 = 119901max

119906 sdot 1198921199061199041205902120574119905ℎ = minus2 ln BER

120583119906 = 120576119906 sdot (1 minus 120573) sdot 119879 sdot 119882sdot log2 (1 +min 120574max

119906119904 120574119905ℎ)1205831015840119904 = 120575 sdot 120572 sdot 120573 sdot 119879 sdot 119882 sdot log2 (1 + 119901119905119904119898 sdot 1198921199041198981205902 )1198731015840119904 = lceil 119879max

119904120575 sdot 120572 sdot 120573 sdot 119879rceil

DR119906 =

sum119906isin119880119904 1205831199061198731015840119904 sdot 119879 sdot 119882 sum119906isin119880119904

120583119906 gt 1205831015840119904log2 (1 + 119901119905119904119898 sdot 1198921199041198981205902 ) otherwise

DRav119906 = sum119904isin119878119898 sum119906isin119880119904 DR11990610038161003816100381610038161198781198981003816100381610038161003816 sdot 10038161003816100381610038161198801199041003816100381610038161003816 (32)

In (32) BER is bit error ratio and takes different values(eg 10minus8) When the set number of UE pieces (ie |119880119904|)must meet the following relational expression the relationalexpressions in (32) are true

sum119906isin119880119904

(1 minus 120573) sdot log2 (1 +min 120574max119906119904 120574119905ℎ)10038161003816100381610038161198801199041003816100381610038161003816

lt lceil119879max119904119879 rceil sdot log2 (1 + 119901119905119904119898 sdot 1198921199041198981205902 )

(33)

In this paper the meaning of lceil119883rceil is the integer that is notless than11988343 Simulation Results and Analysis Firstly we considerthe two groups of simulations which adopt adaptive timeallocation for 120591119903 (ie formula (28)) In the first group ofsimulations the channel noise power 1205902 at all the receiving-ends is fixed as minus90 dBmMHz and the parameter 120576 is setas 01 We evaluate the performance in terms of the threemetrics under the change of average UE battery capacity level(ie the value of119883) as shown in Figure 6

From Figures 6(a) and 6(b) we see that the change ofaverage UE battery capacity has little impact on the averagedata rates of ETRs and VAPs The main reason can befound from formula (30) and formula (31) Without loss ofgenerality we take formula (30) as an example where on theone hand the continuous emission time 119879119903max gets longerwith increase of average UE battery capacity and thus theamount of emitted data is larger during 119879119903max on the otherhand the number of time frames proportionately increaseswith the increase of 119879119903max Therefore according to formula(30) the average data rate for ETRs has been hardly changed

As shown in Figure 6(c) the change of average datarate for associated UE pieces with increase of average UEbattery capacity is different from those of ETRs and VAPsFor the associated UE pieces when the data generated in atime frame is greater than the forwarding amount of theirassociating VAP in the same time frame more time frames


0

20

40

60

80

100

120Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)

03 04 05 06 07 0802Average UE battery capacity ratio

= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

(a) ETR data rate versus UE battery capacity

0

30

60

90

120

150

180

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

(b) VAP data rate versus UE battery capacity

0

4

8

12

16

20

24

28

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

(c) The data rate of associated UE versus UE capacity

Figure 6 Average date rate versus UE battery capacity under adaptive time allocation

are required to complete the forwarding task When averageUE battery capacity is higher the continuous emission time119879119904max gets longer and thus the number of time frames is largerTherefore according to formula (32) the average data rate forassociated UE pieces decreases with increase of average UEbattery capacity since it is limited to the forwarding capacityof the associating VAP

In addition the time slot parameters (ie 120572 120573 and 120575)show the different effects on the three data rates For theaverage data rate of ETRs smaller value for 120573 has morepositive effect on its improvement This is because in a giventime frame any ETR will get more time to transmit its owndata when 120573 takes smaller value (see Figure 4(a)) For theaverage data rate of VAPs when the values for both 120572 and 120573are very large this metric can be significantly improved Eventhough the value for 120573 is very small this metric is relatively

good when the value for 120572 is large enough and the value for 120575is also small enoughThese phenomena can also be explainedby the amount of transmitting time allocated in the same timeframe (see Figure 4(b))

From Figure 6(c) we find that the time slot parametershave little impact on the average data rate for associated UEpieces As explained in the previous text the average data ratefor associated UE pieces is limited to the forwarding capacityof the associating VAP where the forwarding capacity of theassociating VAP is unaffected by the time slot parametersaccording to formula (32)

In the second group of simulations the average UEbattery capacity level for all UE pieces is fixed (eg119883 is fixedas 50) and the parameter 120576 is set as 01 We evaluate theperformance in terms of the three metrics under the changeof channel noise power as shown in Figure 7


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)

minus110 minus100 minus90 minus80 minus70 minus60minus120Channel noise power (dBm)

(a) ETR data rate versus channel noise power

= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

1500

3000

4500

6000

7500

9000

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)

(b) VAP data rate versus channel noise power

= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

200

400

600

800

1000

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)


(c) The data rate of associated UE versus channel noise power

Figure 7 Average date rate versus channel noise power under adaptive time allocation

From Figure 7 we see that with increase of channel noisepower the three data rates show a downward trend Thisis because a larger channel noise power leads to a higherbit error ratio on a receiving end when the correspondingtransmitting power is basically unchanged

Unlike the variation trend in Figures 7(a) and 7(b) thereis a sudden change for the schemes with larger value of 120573in Figure 7(c) when channel noise power is changed fromminus100 to minus90 dBmMHz This can be explained by formula(32)That is when channel noise power is small enough (egless than minus90 dBmMHz) as stated in the previous text theforwarding amount of a VAP in a time frame is greater thanthe data generated by its associating UE pieces in same timeframe Therefore it can complete the forwarding task in a

single time frame and thus obviously improve the averagedata rate for associated UE pieces

However for the schemes with very small value of 120573in Figure 7(c) the change of channel noise power has littleimpact on the average data rate for associatedUE pieces espe-cially when channel noise power is less than minus70 dBmMHzThis is because in this situation the forwarding amountof a VAP in a time frame is usually much lower thanthe data generated by its associating UE pieces in sametime frame and thus almost all the VAPs need more timeframes to complete forwarding task Therefore it is not toounlikely that the change of noise power leads to the suddenchange of data rate In addition with respect to the timeslot parameters of impact on the three data rates the same


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

20

40

60

80

100

120

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)


Figure 8 Average date rate versus UE battery capacity under fixedtime allocation

explanation in Figure 6 can be used to explain the situation inFigure 7

Then our simulations use the fixed time allocation for120591119903 (ie formula (29)) instead of the adaptive time allocationfor 120591119903 (ie formula (28)) where the purpose is to comparethe average data rates of ETRs under the two types of timeallocation schemes since the average data rates of VAPs andassociatedUEpieces are independent of the parameter 120591119903Theother configuration of simulation parameters is the same asthose in the above two groups of simulationsThe simulationresults are shown in Figures 8 and 9

When comparing Figure 8 with Figure 6(a) we observethat the difference between the two time allocation schemesis very small It may be that the advantage of adaptive timeallocation is not obvious due to the adoption of relativelyshort time frame Also when comparing Figure 9 withFigure 7(a) we can find similar result

Finally we evaluate the game convergence rates of ETRVAP andMBSunder the variation of step size (ie the param-eter 120576) through the simulation result shown in Figure 10Also we evaluate the average date rates of ETR VAP andassociated UE pieces under the variation of step size throughthe simulation result shown in Figure 11

From Figure 10 we see that a larger step size leads toa faster convergence The reason behind this phenomenonis straightforward from the description of Algorithm 4ndash6Meanwhile from Figure 11 we find that the variation of stepsize has little impact on the average date rate Thereforethe step size can be appropriately increased to speed up theconvergence of the proposed game scheme

In addition Figure 10 shows the game rounds of a MBSare obviously less than those of ETRs and VAPs From thedescription of Algorithm 6 we can easily find the reasonAlso from Figure 11 we see that a VAP is highly efficient interms of its own data transmission Based on balance betweencontribution and return in terms of data transmission

= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)


Figure 9 Average data rate versus channel noise power under fixedtime allocation

ETRVAPMBS

4 6 8 10 12 142Step size (mW)

0

1000

2000

3000

4000

5000

6000

7000

8000

Con

verg

ence

tim

e (ro

unds

)

Figure 10 Average convergence time versus step size

network operators can consider allocating fewer frequencybands or time slots to VAPs for their Internet access

5 Conclusion

This paper explores a charging power decision and dis-tributed transmission power splitting problembased on gametheory for constructing virtual cellular coverage area inoverlay cellular networks To characterize rational behaviorsof wireless terminal users we formulate a noncooperativegame for the considered system where each terminal user ismodeled as a strategic player that aims to maximize its owndata rate under the constraint for its maximum transmissionpower


ETRVAPUE

0

600

1200

1800

2400

3000

3600

4200

Aver

age d

ata r

ate (

bits

skH

z)

4 6 8 10 12 142Step size (mW)

Figure 11 Average data rate versus step size

Theoretical analysis proves the convergence of the pro-posed game scheme Simulation results indicate that underthe certain conditions the game-theoretic charging powerdecision and transmission power splitting mechanism canspeed up the convergence on the premise of QoS requirementin terms of average date rate However we do not considerthe optimizing problem for time allocation since we focuson the design and analysis of game scheme for virtual cellularcoverage area construction Therefore we plan to address itin our future work

Notations Used in Our Work

119878119898 The set of VAPs119877119904 The set of ETRs associated with a VAP(eg 119904)119880119904 The set of UEs associated with a VAP (eg119904)| sdot | The number of members in a set (eg |119878119898|is the number of the VAPs in 119878119898)119879 The time frame for communication120573 The fraction of energy transfer time in 119879time120572 The fraction of energy transfer time fromthe MBS to ETRs in 120573 sdot 119879 time120575 The fraction of information transmissiontime from a VAP to MBS in 120572 sdot 120573 sdot 119879 timefor the data received by the VAP from itsassociating UEs120591119903 The ratio of time when an ETR transfersenergy to its associating VAP120576119906 The ratio of time when UE transmits itsdata to its associating VAP119901119905119894119895 The transmission power at sender 119894 in link119894 rarr 119895119901119903119894119895 The receiving power at receiver 119895 in link119894 rarr 119895

120578119894119895 The power conversion efficiency factorfrom sender 119894 to receiver 119895ℎ119894119895 The channel power gain from sender 119894 toreceiver 119895120593 Path loss exponent

PLref The path loss in dB at the referencedistance120595119894119895 The body shadowing loss margin betweensender 119894 and receiver 119895 in dB120573119894119895 The small-scale fading power gainbetween sender 119894 and receiver 119895119889119894119895 The distance between sender 119894 and receiver119895119882 Transmission bandwidth for each UE119882119903 Transmission bandwidth for ETRs119882119904 Transmission bandwidth for VAPs1205902 Noise power119887119894119895 The information decoding rate in link119894 rarr 119895119901119903max The maximum transmission power of ETR119903119901119904max The maximum transmission power of VAP119904119864119903 The battery energy storage of ETR 119903119879max

119903 The continuous emission time of ETR 119903119879max119904 The continuous emission time of VAP 119904120583119903(119875119903) The utility of ETR 119903120583119904(119875119904) The utility of VAP 119904120583119898(119901119905119898 119875119903 119875119904) The utility of MBS119898120593119903119898 The fraction of bandwidth for ETR 119903

sending its data to MBS119898120593119904119898 The fraction of bandwidth for VAP 119904sending its data to MBS1198980119903 0119904 The contribution from a fictitious selflessnode119901119905lowast119903119904 The ETR 119903rsquos optimal charging power toVAP 119904119901119905lowast119898 The MBS119898rsquos optimal charging power toETRs119890119904 The harvesting energy of VAP 119904 from the|119877119904| ETRs119888119887 Traffic price per bit119888119890 Energy price per joule120576 The step length for power adjustment119864119894 The initial battery capacity of UE 119894119864av The average initial battery capacity119877119905ℎ The distance from reference points to MBS

DR119903 The data rate for ETR 119903DRav119903 The average data rate for ETRsDR119904 The data rate for VAP 119904DRav119904 The average data rate for VAPsDR119906 The data rate for UE 119906 associated with a

VAPDRav119906 The average data rate relayed by a VAP for

its associated UEs

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article


Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (61272494 61379110)

References

[1] M Wu Y Wu X Liu M Ma A Liu and M Zhao ldquoLearning-based synchronous approach from forwarding nodes to reducethe delay for Industrial Internet of Thingsrdquo EURASIP Journalon Wireless Communications and Networking vol 2018 no 102018

[2] M Huang A Liu T Wang and C Huang ldquoGreen data gather-ing under delay differentiated services constraint for internet ofthingsrdquo Wireless Communications and Mobile Computing vol2018 Article ID 9715428 23 pages 2018

[3] J Tang A Liu M Zhao and T Wang ldquoAn Aggregate SignatureBased Trust Routing for Data Gathering in Sensor NetworksrdquoSecurity and Communication Networks vol 2018 Article ID6328504 30 pages 2018

[4] A Osseiran V Braun T Hidekazu et al ldquoThe foundationof the mobile and wireless communications system for 2020and beyond Challenges Enablers and technology solutionsrdquoin Proceedings of the 2013 IEEE 77th Vehicular TechnologyConference VTC Spring 2013 IEEE Dresden Germany 2013

[5] K Zhou J Gui and N Xiong ldquoImproving cellular downlinkthroughput by multi-hop relay-assisted outband D2D commu-nicationsrdquo EURASIP Journal on Wireless Communications andNetworking vol 2017 no 209 2017

[6] J Gui and J Deng ldquoMulti-hop Relay-Aided Underlay D2DCommunications for Improving Cellular Coverage QualityrdquoIEEE Access vol 6 pp 14318ndash14338 2018

[7] Cisco Visual Networking Index Forecast and Methodology2016ndash2021 CISCOWhite Paper 2017

[8] J Gui and K Zhou ldquoFlexible adjustments between energy andcapacity for topology control in heterogeneous wireless multi-hop networksrdquo Journal of Network and Systems Managementvol 24 no 4 pp 789ndash812 2016

[9] J Gui and J Deng ldquoA topology control approach reducingconstruction cost for lossy wireless sensor networksrdquo WirelessPersonal Communications vol 95 no 3 pp 2173ndash2202 2017

[10] D Mishra De Swades S Jana S Basagni K Chowdhury andWHeinzelman ldquoSmart RF energy harvesting communicationsChallenges and opportunitiesrdquo IEEE Communications Maga-zine vol 53 no 4 pp 70ndash77 2015

[11] S Bi C K Ho and R Zhang ldquoWireless powered commu-nication opportunities and challengesrdquo IEEE CommunicationsMagazine vol 53 no 4 pp 117ndash125 2015

[12] K Huang and X Zhou ldquoCutting the last wires for mobilecommunications by microwave power transferrdquo IEEE Commu-nications Magazine vol 53 no 6 pp 86ndash93 2015

[13] H Ju and R Zhang ldquoThroughput maximization in wire-less powered communication networksrdquo IEEE Transactions onWireless Communications vol 13 no 1 pp 418ndash428 2014

[14] H Ju and R Zhang ldquoUser cooperation in wireless poweredcommunication networksrdquo in Proceedings of the IEEE GlobalCommunications Conference (GLOBECOM rsquo14) pp 1430ndash1435IEEE Austin Tex USA December 2014

[15] L Liu R Zhang and K C Chua ldquoMulti-antenna wireless pow -ered communicationwith energy beamformingrdquo IEEETransac-tions on Communications vol 62 no 12 pp 4349ndash4361 2014

[16] G Yang C K Ho R Zhang and Y L Guan ldquoThroughputoptimization for massive MIMO systems powered by wirelessenergy transferrdquo IEEE Journal on Selected Areas in Communica-tions vol 33 no 8 pp 1640ndash1650 2015

[17] X Kang C K Ho and S Sun ldquoFull-duplex wireless-poweredcommunication network with energy causalityrdquo IEEE Transac-tions onWireless Communications vol 14 no 10 pp 5539ndash55512015

[18] H Ju and R Zhang ldquoOptimal resource allocation in full-duplexwireless-powered communication networkrdquo IEEE Transactionson Communications vol 62 no 10 pp 3528ndash3540 2014

[19] D W K Ng E S Lo and R Schober ldquoWireless informationand power transfer energy efficiency optimization in OFDMAsystemsrdquo IEEE Transactions on Wireless Communications vol12 no 12 pp 6352ndash6370 2013

[20] K Yamazaki Y Sugiyama Y Kawahara S Saruwatari andT Watanabe ldquoPreliminary evaluation of simultaneous dataand power transmission in the same frequency channelrdquo inProceedings of the 2015 IEEE Wireless Communications andNetworking Conference (WCNC) pp 1237ndash1242 New OrleansLA USA 2015

[21] D Altinel and G Karabulut Kurt ldquoEnergy Harvesting fromMultiple RF Sources inWireless Fading Channelsrdquo IEEE Trans-actions on Vehicular Technology vol 65 no 11 pp 8854ndash88642016

[22] J C Kwan and A O Fapojuwo ldquoRadio Frequency Energy Har-vesting and Data Rate Optimization in Wireless Informationand Power Transfer Sensor Networksrdquo IEEE Sensors Journalvol 17 no 15 pp 4862ndash4874 2017

[23] L Xiang J Luo K Han and G Shi ldquoFueling wireless networksperpetually A case of multi-hop wireless power distributionrdquoin Proceedings of the IEEE 24th Annual International Sympo-sium on Personal Indoor and Mobile Radio Communications(PIMRC) pp 1994ndash1999 UK 2013

[24] T Rault A Bouabdallah and Y Challal ldquoMulti-hop wirelesscharging optimization in low-power networksrdquo in Proceedingsof the IEEEGlobal Communications Conference (GLOBECOM)pp 462ndash467 IEEE Atlanta GA USA 2013

[25] D Fudenberg and J Tirole Game Theory MIT Press Cam-bridge Mass USA 1993

[26] D Monderer and L S Shapley ldquoPotential gamesrdquo Games andEconomic Behavior vol 14 no 1 pp 124ndash143 1996

[27] F Ma X Liu A Liu M Zhao C Huang and T Wang ldquoATime andLocationCorrelation Incentive Scheme forDeepDataGathering in Crowdsourcing Networksrdquo Wireless Communica-tions and Mobile Computing vol 2018 Article ID 8052620 22pages 2018

[28] J Gui Y Lu X Deng and A Liu ldquoFlexible resource allocationadaptive to communication strategy selection for cellular clientsusing Stackelberg gamerdquo Ad Hoc Networks vol 66 pp 64ndash842017

[29] J Gui L Hui and N Xiong ldquoA game-based localized multi-objective topology control scheme in heterogeneous wirelessnetworksrdquo IEEE Access vol 5 no 1 pp 2396ndash2416 2017

[30] H Chen Y Li Y Jiang Y Ma and B Vucetic ldquoDistributedpower splitting for SWIPT in relay interference channels usinggame theoryrdquo IEEE Transactions on Wireless Communicationsvol 14 no 1 pp 410ndash420 2015

[31] Y Ma H H Chen Z Lin B Vucetic and X Li ldquoSpectrumsharing in RF-powered cognitive radio networks using gametheoryrdquo in Proceedings of the 26th IEEE Annual International


Symposium on Personal Indoor and Mobile Radio Communi-cations PIMRC pp 992ndash996 IEEE Hong Kong China 2015

[32] H H Chen Y Li Z Han and B Vucetic ldquoA stackelberg game-based energy trading scheme for power beacon-assisted wire-less-powered communicationrdquo in Proceedings of the 40th IEEEInternational Conference on Acoustics Speech and Signal Pro-cessing (ICASSPrsquo15) pp 3177ndash3181 IEEE Brisbane Australia2014

[33] Y Ma H Chen Z Lin Y Li and B Vucetic ldquoDistributed andoptimal resource allocation for power beacon-assisted wireless-powered communicationsrdquo IEEE Transactions on Communica-tions vol 63 no 10 pp 3569ndash3583 2015

[34] H Chen Y Ma Z Lin Y Li and B Vucetic ldquoDistributedPower Control in Interference Channels with QoS Constraintsand RF EnergyHarvesting AGame-Theoretic Approachrdquo IEEETransactions on Vehicular Technology vol 65 no 12 pp 10063ndash10069 2016

[35] Z Hou H Chen Y Li and B Vucetic ldquoIncentive Mecha-nism Design for Wireless Energy Harvesting-Based Internet ofThingsrdquo IEEE Internet of Things Journal 2017

[36] E Dahlman S Parkvall and J Skold ldquoPropagation model andchannel characterizationrdquo inCommunications Engineering DeskReference pp 247ndash256 Academic Press Oxford UK 2009

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sparsely deployed SBSs can be tackled by providing dataservices by cellular Virtual Access Points (VAPs) during peakhours which can adapt well to the temporal and spatialvariations in traffic load It is more appropriate that wirelessterminals with high-end configuration act as VAPs

VAPs are responsible for receiving data of users far awayfrom a macrostation for example cellular edge users andforward these data to this macrostation which is helpfulfor reducing the transmitting powers of cellular edge usersand thus alleviating interference to the users in the samefrequency bands of adjacent cells Therefore a networkoperator will get more access traffic revenue but VAPs willconsume more energy

In order to compensate for this energy consumptiona network operator may make a Macro BS (MBS) transferpower to VAPs However the power conversion efficiency ofthe Radio Frequency (RF) energy harvesting circuit decreasessharply with the increase of distance In order to improvethe power conversion efficiency a MBS should select a fewnodes to act as Energy Transferring Relays (ETRs) which canforward energy from a MBS to a VAP

In many practical scenarios wireless User Equipment(UE) may be rational such that they only care about theirown interests instead of the overall one Without getting thebenefits from the operator they do not act as either VAPs orETRsTherefore in order tomotivateUE to act as eitherVAPsor ETRs the operator has to provide it with free traffic accessto Internet

To the best of our knowledge few works have studiedhow to enhance cellular coverage quality by VAPs and ETRsThis gap actually motivates us to develop a game-theoreticframework for this problem where any UE is motivated toact as either a VAP or an ETR through providing both RFenergy compensation and free traffic access to Internet Themain contributions of this paper are summarized as follows(1) We propose a game-based constructing method forvirtual cellular coverage area by combining RF energy com-pensation with free traffic access to Internet which can makeup for gaps of small cell coverage(2) We formulate the charging power decision problemand transmission power splitting problem as a Stackelberggame based on three-party circular decision A reverse induc-tion method is used to analyze this proposed Stackelberggame since it can capture the sequential dependence of thedecisions in all the stages of the game(3) The new better response strategy of each playeris proposed and then the Stackelberg-Nash Equilibrium(SNE) can be achieved by running the proposed algorithmsiteratively

The main notations in this work are listed in NotationsUsed in Our Work The rest of the paper is organized asfollows The related works are analyzed and summarizedin Section 2 In Section 3 the game scheme for virtualcellular coverage area construction is discussed in detailincluding networkmodel the time-slotted scheme for energyand information transference the problem formulation andtheoretical analysis and the description for algorithms Thesimulation results are given in Section 4 and the conclusionsare drawn in Section 5

2 Related Work

RF energy harvesting sources are usually divided into twocategories [10] where the first category belongs to ambient orunintended RF energy harvesting sources and the second oneis the type of dedicated or intended RF ones Also there arethe three main RF energy harvesting structures at receiving-ends [11] that is separated structure (ie energy harvestingand information decoding circuitry have their own antennasrespectively) time switching structure (ie energy harvestingand information decoding circuitry share the same antennaat different time slots) and power splitting structure (ieenergy harvesting and information decoding circuitry sharethe same antenna at the same time but split the input power)A time switching structure is usually used more frequentlysince it is comparatively compact in form factor and relativelyeffective in harvesting RF energy

Furthermore the literature [12] summarizes Simulta-neous Wireless Information and Power Transfer (SWIPT)designing schemes which are usually classified as decoupledSWIPT closed-loop SWIPT and integrated SWIPT Thedecoupled SWIPT is characterized by the information andthe power traffic sent from two separate transmitting sourcesIn closed-loop SWIPT scenarios [13ndash18] a base stationusually powers a wireless device in a downlink and receivesthe data from the same wireless device in the uplink Inan integrated SWIPT scheme [19] both the informationand power are carried by the same source over the samesignals

Concurrent multiple RF source transmission reported insome literatures (eg [20 21]) will increase total interferenceA harvest-then-transmit protocol allows a receiver to firstharvest energy from the downlink broadcast signals andthen use the harvested energy to send independent uplinkinformation to theMBS or SBS based on Time DivisionMul-tiple Access (TDMA) In order to mitigate total interferencethe system presented in [22] employs multiple dedicated RFsources with a harvest-then-transmit protocol to improve theharvested energy and data rate The achievable data rate canincrease by up to 87 when energy is harvested from up to5 dedicated RF sources compared to the case when energy isharvested from one source

Some works have focused on energy transfer in multihopmanner for wireless networks for example [23] proposesa method to inject power into the network as flows whereinjected power is carried in multihop manner while [24]explores the optimization of multihop wireless energy trans-fer in wireless networks

Some typical noncooperative game models (eg Stackel-berg game [25] and potential game [26]) are widely used invarious network information systems [27ndash29] A Stackelberggame consists of leaders and followers that compete witheach other for certain resources where the leaders first actby considering behaviors of the followers and the followersact subsequently

An exact potential game can characterize the set of NashEquilibria (NE) where a potential function can track thechanges in the payoff due to the unilateral deviation of aplayer and one or more NE points may exist and coincide


23

4

5 6

1

m

UE

SBS

Reference Point

ETR

VAP Energy Transfer


s

r

MBS

c

de

a

b

t

i

jkRtℎ












































middot middot T









119901119903119894119895 = 120578119894119895 sdot 119901119905119894119895 sdot 10038161003816100381610038161003816ℎ119894119895100381610038161003816100381610038162 (1)





119887119894119895 = 119882 sdot log2(1 + 119901119905119894119895 sdot 1198921198941198951205902 ) (3)






119901max119903 ge 119901119905119903119904 + 119901119905119903119898 (4)





119879max119903 = 119864119903119901max

119903 minus 119901119903119898119903 (5)



119903 minus 119901119905119903119904) sdot 1198921199031198981205902 )


119875119903 = 1199011199051199031015840 119904 | forall1199031015840 isin 119877119904

(6)


max119901119905119903119904119875minus119903

119879max119903 sdot 120593119903119898 sdot 119882119903


(7)



119901119905lowast119903119904 = 119860119861 (8)





119903 minus 119901119905119903119904) sdot 1198921199031198981205902 )

119884119903 = sum1199031015840isin119877119904


(9)




119890119904 = sum119903isin119877119904





119901max119904 ge 119901119905119904119898 + 119901119905119906119898 (11)






119879max119904 = 119864119904 + 119890119904119901max

119904

(12)


follows120583119904 (119875119904) = 119879max


119904 minus 119901119905119904119898) sdot 1198921199041198981205902 )


119875119904 = 1199011199051199041015840 119898 | forall1199041015840 isin 119878119898

(13)


max119901119905119904119898119875minus119904

119879max119904 sdot 120593119904119898 sdot 119882119904


(14)



119901119905lowast119904119898 = 119862119863 (15)



log2(1 + 1199011199051199041015840 119898 sdot 1198921199041015840 1198981205902 )

(16)





120583119898 (119901119905119898 119875119903 119875119904) = 119888119887 sdot sum119904isin119878119898

119879max119904 sdot 119882


119904 | 119904 isin 119878119898 sdot 119901119905119898(17)



119904




119904

(18)


max119901119905119898119875119903119875119904

119888119887 sdot sum119904isin119878119898



(19)




119888119890 sdotmax 1205972119879119898119886119909119904 120597 (119901119905119898)2 | 119904 isin 119878119898]]+

(20)



(21)

where


120597119879119898119886119909119904120597119901119905119898= 1119901119898119886119909119904 sdot sum

119903isin119877119904


(23)

1205972119879119898119886119909119904120597 (119901119905119898)2= 1119901119898119886119909119904 sdot sum

119903isin119877119904


(24)






120597120583119898 (119901119905119898 119875119903 119875119904)120597119901119905119898 = 119888119887 sdot sum119904isin119878119898

1205972119879max119904120597 (119901119905119898)2 sdot 119882



119904120597119901119905119898 | 119904 isin 119878119898

(25)







VAP game VAPs




Stackelberggame

MBSETRsVAPs



















119864av = sum119894isin 119864119894|| (26)


23

4

5 6

1

MBS

Rtℎ

(0 0)



(05Rtℎ 0866Rtℎ)

(minusRtℎ

Rtℎ

0) (Rtℎ 0)













120576119906 = 110038161003816100381610038161198801199041003816100381610038161003816 (27)


120591119903 = 119879max119903sum1199031015840isin12|119877119904| 119879max

1199031015840

(28)


120591119903 = 110038161003816100381610038161198771199041003816100381610038161003816 (29)



119903 minus 119901119905119903119904) sdot1198921199031198981205902 )



(30)





DRav119904 = sum119904isin119878119898 DR11990410038161003816100381610038161198781198981003816100381610038161003816

(31)


120574max119906119904 = 119901max





DR119906 =





sum119906isin119880119904



(33)





0

20

40

60

80

100

120Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

30

60

90

120

150

180

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

4

8

12

16

20

24

28

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)



= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

1500

3000

4500

6000

7500

9000

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

200

400

600

800

1000

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

20

40

60

80

100

120

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)



ETRVAPMBS

4 6 8 10 12 142Step size (mW)

0

1000

2000

3000

4000

5000

6000

7000

8000

Con

verg

ence

tim

e (ro

unds

)



5 Conclusion



ETRVAPUE

0

600

1200

1800

2400

3000

3600

4200

Aver

age d

ata r

ate (

bits

skH

z)

4 6 8 10 12 142Step size (mW)











its associated UEs




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



23

4

5 6

1

m

UE

SBS

Reference Point

ETR

VAP Energy Transfer


s

r

MBS

c

de

a

b

t

i

jkRtℎ












































middot middot T









119901119903119894119895 = 120578119894119895 sdot 119901119905119894119895 sdot 10038161003816100381610038161003816ℎ119894119895100381610038161003816100381610038162 (1)





119887119894119895 = 119882 sdot log2(1 + 119901119905119894119895 sdot 1198921198941198951205902 ) (3)






119901max119903 ge 119901119905119903119904 + 119901119905119903119898 (4)





119879max119903 = 119864119903119901max

119903 minus 119901119903119898119903 (5)



119903 minus 119901119905119903119904) sdot 1198921199031198981205902 )


119875119903 = 1199011199051199031015840 119904 | forall1199031015840 isin 119877119904

(6)


max119901119905119903119904119875minus119903

119879max119903 sdot 120593119903119898 sdot 119882119903


(7)



119901119905lowast119903119904 = 119860119861 (8)





119903 minus 119901119905119903119904) sdot 1198921199031198981205902 )

119884119903 = sum1199031015840isin119877119904


(9)




119890119904 = sum119903isin119877119904





119901max119904 ge 119901119905119904119898 + 119901119905119906119898 (11)






119879max119904 = 119864119904 + 119890119904119901max

119904

(12)


follows120583119904 (119875119904) = 119879max


119904 minus 119901119905119904119898) sdot 1198921199041198981205902 )


119875119904 = 1199011199051199041015840 119898 | forall1199041015840 isin 119878119898

(13)


max119901119905119904119898119875minus119904

119879max119904 sdot 120593119904119898 sdot 119882119904


(14)



119901119905lowast119904119898 = 119862119863 (15)



log2(1 + 1199011199051199041015840 119898 sdot 1198921199041015840 1198981205902 )

(16)





120583119898 (119901119905119898 119875119903 119875119904) = 119888119887 sdot sum119904isin119878119898

119879max119904 sdot 119882


119904 | 119904 isin 119878119898 sdot 119901119905119898(17)



119904




119904

(18)


max119901119905119898119875119903119875119904

119888119887 sdot sum119904isin119878119898



(19)




119888119890 sdotmax 1205972119879119898119886119909119904 120597 (119901119905119898)2 | 119904 isin 119878119898]]+

(20)



(21)

where


120597119879119898119886119909119904120597119901119905119898= 1119901119898119886119909119904 sdot sum

119903isin119877119904


(23)

1205972119879119898119886119909119904120597 (119901119905119898)2= 1119901119898119886119909119904 sdot sum

119903isin119877119904


(24)






120597120583119898 (119901119905119898 119875119903 119875119904)120597119901119905119898 = 119888119887 sdot sum119904isin119878119898

1205972119879max119904120597 (119901119905119898)2 sdot 119882



119904120597119901119905119898 | 119904 isin 119878119898

(25)







VAP game VAPs




Stackelberggame

MBSETRsVAPs



















119864av = sum119894isin 119864119894|| (26)


23

4

5 6

1

MBS

Rtℎ

(0 0)



(05Rtℎ 0866Rtℎ)

(minusRtℎ

Rtℎ

0) (Rtℎ 0)













120576119906 = 110038161003816100381610038161198801199041003816100381610038161003816 (27)


120591119903 = 119879max119903sum1199031015840isin12|119877119904| 119879max

1199031015840

(28)


120591119903 = 110038161003816100381610038161198771199041003816100381610038161003816 (29)



119903 minus 119901119905119903119904) sdot1198921199031198981205902 )



(30)





DRav119904 = sum119904isin119878119898 DR11990410038161003816100381610038161198781198981003816100381610038161003816

(31)


120574max119906119904 = 119901max





DR119906 =





sum119906isin119880119904



(33)





0

20

40

60

80

100

120Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

30

60

90

120

150

180

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

4

8

12

16

20

24

28

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)



= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

1500

3000

4500

6000

7500

9000

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

200

400

600

800

1000

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

20

40

60

80

100

120

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)



ETRVAPMBS

4 6 8 10 12 142Step size (mW)

0

1000

2000

3000

4000

5000

6000

7000

8000

Con

verg

ence

tim

e (ro

unds

)



5 Conclusion



ETRVAPUE

0

600

1200

1800

2400

3000

3600

4200

Aver

age d

ata r

ate (

bits

skH

z)

4 6 8 10 12 142Step size (mW)











its associated UEs




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia

































middot middot T









119901119903119894119895 = 120578119894119895 sdot 119901119905119894119895 sdot 10038161003816100381610038161003816ℎ119894119895100381610038161003816100381610038162 (1)





119887119894119895 = 119882 sdot log2(1 + 119901119905119894119895 sdot 1198921198941198951205902 ) (3)






119901max119903 ge 119901119905119903119904 + 119901119905119903119898 (4)





119879max119903 = 119864119903119901max

119903 minus 119901119903119898119903 (5)



119903 minus 119901119905119903119904) sdot 1198921199031198981205902 )


119875119903 = 1199011199051199031015840 119904 | forall1199031015840 isin 119877119904

(6)


max119901119905119903119904119875minus119903

119879max119903 sdot 120593119903119898 sdot 119882119903


(7)



119901119905lowast119903119904 = 119860119861 (8)





119903 minus 119901119905119903119904) sdot 1198921199031198981205902 )

119884119903 = sum1199031015840isin119877119904


(9)




119890119904 = sum119903isin119877119904





119901max119904 ge 119901119905119904119898 + 119901119905119906119898 (11)






119879max119904 = 119864119904 + 119890119904119901max

119904

(12)


follows120583119904 (119875119904) = 119879max


119904 minus 119901119905119904119898) sdot 1198921199041198981205902 )


119875119904 = 1199011199051199041015840 119898 | forall1199041015840 isin 119878119898

(13)


max119901119905119904119898119875minus119904

119879max119904 sdot 120593119904119898 sdot 119882119904


(14)



119901119905lowast119904119898 = 119862119863 (15)



log2(1 + 1199011199051199041015840 119898 sdot 1198921199041015840 1198981205902 )

(16)





120583119898 (119901119905119898 119875119903 119875119904) = 119888119887 sdot sum119904isin119878119898

119879max119904 sdot 119882


119904 | 119904 isin 119878119898 sdot 119901119905119898(17)



119904




119904

(18)


max119901119905119898119875119903119875119904

119888119887 sdot sum119904isin119878119898



(19)




119888119890 sdotmax 1205972119879119898119886119909119904 120597 (119901119905119898)2 | 119904 isin 119878119898]]+

(20)



(21)

where


120597119879119898119886119909119904120597119901119905119898= 1119901119898119886119909119904 sdot sum

119903isin119877119904


(23)

1205972119879119898119886119909119904120597 (119901119905119898)2= 1119901119898119886119909119904 sdot sum

119903isin119877119904


(24)






120597120583119898 (119901119905119898 119875119903 119875119904)120597119901119905119898 = 119888119887 sdot sum119904isin119878119898

1205972119879max119904120597 (119901119905119898)2 sdot 119882



119904120597119901119905119898 | 119904 isin 119878119898

(25)







VAP game VAPs




Stackelberggame

MBSETRsVAPs



















119864av = sum119894isin 119864119894|| (26)


23

4

5 6

1

MBS

Rtℎ

(0 0)



(05Rtℎ 0866Rtℎ)

(minusRtℎ

Rtℎ

0) (Rtℎ 0)













120576119906 = 110038161003816100381610038161198801199041003816100381610038161003816 (27)


120591119903 = 119879max119903sum1199031015840isin12|119877119904| 119879max

1199031015840

(28)


120591119903 = 110038161003816100381610038161198771199041003816100381610038161003816 (29)



119903 minus 119901119905119903119904) sdot1198921199031198981205902 )



(30)





DRav119904 = sum119904isin119878119898 DR11990410038161003816100381610038161198781198981003816100381610038161003816

(31)


120574max119906119904 = 119901max





DR119906 =





sum119906isin119880119904



(33)





0

20

40

60

80

100

120Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

30

60

90

120

150

180

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

4

8

12

16

20

24

28

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)



= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

1500

3000

4500

6000

7500

9000

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

200

400

600

800

1000

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

20

40

60

80

100

120

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)



ETRVAPMBS

4 6 8 10 12 142Step size (mW)

0

1000

2000

3000

4000

5000

6000

7000

8000

Con

verg

ence

tim

e (ro

unds

)



5 Conclusion



ETRVAPUE

0

600

1200

1800

2400

3000

3600

4200

Aver

age d

ata r

ate (

bits

skH

z)

4 6 8 10 12 142Step size (mW)











its associated UEs




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






119901max119903 ge 119901119905119903119904 + 119901119905119903119898 (4)





119879max119903 = 119864119903119901max

119903 minus 119901119903119898119903 (5)



119903 minus 119901119905119903119904) sdot 1198921199031198981205902 )


119875119903 = 1199011199051199031015840 119904 | forall1199031015840 isin 119877119904

(6)


max119901119905119903119904119875minus119903

119879max119903 sdot 120593119903119898 sdot 119882119903


(7)



119901119905lowast119903119904 = 119860119861 (8)





119903 minus 119901119905119903119904) sdot 1198921199031198981205902 )

119884119903 = sum1199031015840isin119877119904


(9)




119890119904 = sum119903isin119877119904





119901max119904 ge 119901119905119904119898 + 119901119905119906119898 (11)






119879max119904 = 119864119904 + 119890119904119901max

119904

(12)


follows120583119904 (119875119904) = 119879max


119904 minus 119901119905119904119898) sdot 1198921199041198981205902 )


119875119904 = 1199011199051199041015840 119898 | forall1199041015840 isin 119878119898

(13)


max119901119905119904119898119875minus119904

119879max119904 sdot 120593119904119898 sdot 119882119904


(14)



119901119905lowast119904119898 = 119862119863 (15)



log2(1 + 1199011199051199041015840 119898 sdot 1198921199041015840 1198981205902 )

(16)





120583119898 (119901119905119898 119875119903 119875119904) = 119888119887 sdot sum119904isin119878119898

119879max119904 sdot 119882


119904 | 119904 isin 119878119898 sdot 119901119905119898(17)



119904




119904

(18)


max119901119905119898119875119903119875119904

119888119887 sdot sum119904isin119878119898



(19)




119888119890 sdotmax 1205972119879119898119886119909119904 120597 (119901119905119898)2 | 119904 isin 119878119898]]+

(20)



(21)

where


120597119879119898119886119909119904120597119901119905119898= 1119901119898119886119909119904 sdot sum

119903isin119877119904


(23)

1205972119879119898119886119909119904120597 (119901119905119898)2= 1119901119898119886119909119904 sdot sum

119903isin119877119904


(24)






120597120583119898 (119901119905119898 119875119903 119875119904)120597119901119905119898 = 119888119887 sdot sum119904isin119878119898

1205972119879max119904120597 (119901119905119898)2 sdot 119882



119904120597119901119905119898 | 119904 isin 119878119898

(25)







VAP game VAPs




Stackelberggame

MBSETRsVAPs



















119864av = sum119894isin 119864119894|| (26)


23

4

5 6

1

MBS

Rtℎ

(0 0)



(05Rtℎ 0866Rtℎ)

(minusRtℎ

Rtℎ

0) (Rtℎ 0)













120576119906 = 110038161003816100381610038161198801199041003816100381610038161003816 (27)


120591119903 = 119879max119903sum1199031015840isin12|119877119904| 119879max

1199031015840

(28)


120591119903 = 110038161003816100381610038161198771199041003816100381610038161003816 (29)



119903 minus 119901119905119903119904) sdot1198921199031198981205902 )



(30)





DRav119904 = sum119904isin119878119898 DR11990410038161003816100381610038161198781198981003816100381610038161003816

(31)


120574max119906119904 = 119901max





DR119906 =





sum119906isin119880119904



(33)





0

20

40

60

80

100

120Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

30

60

90

120

150

180

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

4

8

12

16

20

24

28

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)



= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

1500

3000

4500

6000

7500

9000

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

200

400

600

800

1000

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

20

40

60

80

100

120

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)



ETRVAPMBS

4 6 8 10 12 142Step size (mW)

0

1000

2000

3000

4000

5000

6000

7000

8000

Con

verg

ence

tim

e (ro

unds

)



5 Conclusion



ETRVAPUE

0

600

1200

1800

2400

3000

3600

4200

Aver

age d

ata r

ate (

bits

skH

z)

4 6 8 10 12 142Step size (mW)











its associated UEs




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





119901max119904 ge 119901119905119904119898 + 119901119905119906119898 (11)






119879max119904 = 119864119904 + 119890119904119901max

119904

(12)


follows120583119904 (119875119904) = 119879max


119904 minus 119901119905119904119898) sdot 1198921199041198981205902 )


119875119904 = 1199011199051199041015840 119898 | forall1199041015840 isin 119878119898

(13)


max119901119905119904119898119875minus119904

119879max119904 sdot 120593119904119898 sdot 119882119904


(14)



119901119905lowast119904119898 = 119862119863 (15)



log2(1 + 1199011199051199041015840 119898 sdot 1198921199041015840 1198981205902 )

(16)





120583119898 (119901119905119898 119875119903 119875119904) = 119888119887 sdot sum119904isin119878119898

119879max119904 sdot 119882


119904 | 119904 isin 119878119898 sdot 119901119905119898(17)



119904




119904

(18)


max119901119905119898119875119903119875119904

119888119887 sdot sum119904isin119878119898



(19)




119888119890 sdotmax 1205972119879119898119886119909119904 120597 (119901119905119898)2 | 119904 isin 119878119898]]+

(20)



(21)

where


120597119879119898119886119909119904120597119901119905119898= 1119901119898119886119909119904 sdot sum

119903isin119877119904


(23)

1205972119879119898119886119909119904120597 (119901119905119898)2= 1119901119898119886119909119904 sdot sum

119903isin119877119904


(24)






120597120583119898 (119901119905119898 119875119903 119875119904)120597119901119905119898 = 119888119887 sdot sum119904isin119878119898

1205972119879max119904120597 (119901119905119898)2 sdot 119882



119904120597119901119905119898 | 119904 isin 119878119898

(25)







VAP game VAPs




Stackelberggame

MBSETRsVAPs



















119864av = sum119894isin 119864119894|| (26)


23

4

5 6

1

MBS

Rtℎ

(0 0)



(05Rtℎ 0866Rtℎ)

(minusRtℎ

Rtℎ

0) (Rtℎ 0)













120576119906 = 110038161003816100381610038161198801199041003816100381610038161003816 (27)


120591119903 = 119879max119903sum1199031015840isin12|119877119904| 119879max

1199031015840

(28)


120591119903 = 110038161003816100381610038161198771199041003816100381610038161003816 (29)



119903 minus 119901119905119903119904) sdot1198921199031198981205902 )



(30)





DRav119904 = sum119904isin119878119898 DR11990410038161003816100381610038161198781198981003816100381610038161003816

(31)


120574max119906119904 = 119901max





DR119906 =





sum119906isin119880119904



(33)





0

20

40

60

80

100

120Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

30

60

90

120

150

180

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

4

8

12

16

20

24

28

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)



= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

1500

3000

4500

6000

7500

9000

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

200

400

600

800

1000

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

20

40

60

80

100

120

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)



ETRVAPMBS

4 6 8 10 12 142Step size (mW)

0

1000

2000

3000

4000

5000

6000

7000

8000

Con

verg

ence

tim

e (ro

unds

)



5 Conclusion



ETRVAPUE

0

600

1200

1800

2400

3000

3600

4200

Aver

age d

ata r

ate (

bits

skH

z)

4 6 8 10 12 142Step size (mW)











its associated UEs




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




119904




119904

(18)


max119901119905119898119875119903119875119904

119888119887 sdot sum119904isin119878119898



(19)




119888119890 sdotmax 1205972119879119898119886119909119904 120597 (119901119905119898)2 | 119904 isin 119878119898]]+

(20)



(21)

where


120597119879119898119886119909119904120597119901119905119898= 1119901119898119886119909119904 sdot sum

119903isin119877119904


(23)

1205972119879119898119886119909119904120597 (119901119905119898)2= 1119901119898119886119909119904 sdot sum

119903isin119877119904


(24)






120597120583119898 (119901119905119898 119875119903 119875119904)120597119901119905119898 = 119888119887 sdot sum119904isin119878119898

1205972119879max119904120597 (119901119905119898)2 sdot 119882



119904120597119901119905119898 | 119904 isin 119878119898

(25)







VAP game VAPs




Stackelberggame

MBSETRsVAPs



















119864av = sum119894isin 119864119894|| (26)


23

4

5 6

1

MBS

Rtℎ

(0 0)



(05Rtℎ 0866Rtℎ)

(minusRtℎ

Rtℎ

0) (Rtℎ 0)













120576119906 = 110038161003816100381610038161198801199041003816100381610038161003816 (27)


120591119903 = 119879max119903sum1199031015840isin12|119877119904| 119879max

1199031015840

(28)


120591119903 = 110038161003816100381610038161198771199041003816100381610038161003816 (29)



119903 minus 119901119905119903119904) sdot1198921199031198981205902 )



(30)





DRav119904 = sum119904isin119878119898 DR11990410038161003816100381610038161198781198981003816100381610038161003816

(31)


120574max119906119904 = 119901max





DR119906 =





sum119906isin119880119904



(33)





0

20

40

60

80

100

120Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

30

60

90

120

150

180

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

4

8

12

16

20

24

28

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)



= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

1500

3000

4500

6000

7500

9000

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

200

400

600

800

1000

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

20

40

60

80

100

120

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)



ETRVAPMBS

4 6 8 10 12 142Step size (mW)

0

1000

2000

3000

4000

5000

6000

7000

8000

Con

verg

ence

tim

e (ro

unds

)



5 Conclusion



ETRVAPUE

0

600

1200

1800

2400

3000

3600

4200

Aver

age d

ata r

ate (

bits

skH

z)

4 6 8 10 12 142Step size (mW)











its associated UEs




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








VAP game VAPs




Stackelberggame

MBSETRsVAPs



















119864av = sum119894isin 119864119894|| (26)


23

4

5 6

1

MBS

Rtℎ

(0 0)



(05Rtℎ 0866Rtℎ)

(minusRtℎ

Rtℎ

0) (Rtℎ 0)













120576119906 = 110038161003816100381610038161198801199041003816100381610038161003816 (27)


120591119903 = 119879max119903sum1199031015840isin12|119877119904| 119879max

1199031015840

(28)


120591119903 = 110038161003816100381610038161198771199041003816100381610038161003816 (29)



119903 minus 119901119905119903119904) sdot1198921199031198981205902 )



(30)





DRav119904 = sum119904isin119878119898 DR11990410038161003816100381610038161198781198981003816100381610038161003816

(31)


120574max119906119904 = 119901max





DR119906 =





sum119906isin119880119904



(33)





0

20

40

60

80

100

120Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

30

60

90

120

150

180

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

4

8

12

16

20

24

28

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)



= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

1500

3000

4500

6000

7500

9000

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

200

400

600

800

1000

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

20

40

60

80

100

120

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)



ETRVAPMBS

4 6 8 10 12 142Step size (mW)

0

1000

2000

3000

4000

5000

6000

7000

8000

Con

verg

ence

tim

e (ro

unds

)



5 Conclusion



ETRVAPUE

0

600

1200

1800

2400

3000

3600

4200

Aver

age d

ata r

ate (

bits

skH

z)

4 6 8 10 12 142Step size (mW)











its associated UEs




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









119864av = sum119894isin 119864119894|| (26)


23

4

5 6

1

MBS

Rtℎ

(0 0)



(05Rtℎ 0866Rtℎ)

(minusRtℎ

Rtℎ

0) (Rtℎ 0)













120576119906 = 110038161003816100381610038161198801199041003816100381610038161003816 (27)


120591119903 = 119879max119903sum1199031015840isin12|119877119904| 119879max

1199031015840

(28)


120591119903 = 110038161003816100381610038161198771199041003816100381610038161003816 (29)



119903 minus 119901119905119903119904) sdot1198921199031198981205902 )



(30)





DRav119904 = sum119904isin119878119898 DR11990410038161003816100381610038161198781198981003816100381610038161003816

(31)


120574max119906119904 = 119901max





DR119906 =





sum119906isin119880119904



(33)





0

20

40

60

80

100

120Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

30

60

90

120

150

180

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

4

8

12

16

20

24

28

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)



= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

1500

3000

4500

6000

7500

9000

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

200

400

600

800

1000

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

20

40

60

80

100

120

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)



ETRVAPMBS

4 6 8 10 12 142Step size (mW)

0

1000

2000

3000

4000

5000

6000

7000

8000

Con

verg

ence

tim

e (ro

unds

)



5 Conclusion



ETRVAPUE

0

600

1200

1800

2400

3000

3600

4200

Aver

age d

ata r

ate (

bits

skH

z)

4 6 8 10 12 142Step size (mW)











its associated UEs




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










120576119906 = 110038161003816100381610038161198801199041003816100381610038161003816 (27)


120591119903 = 119879max119903sum1199031015840isin12|119877119904| 119879max

1199031015840

(28)


120591119903 = 110038161003816100381610038161198771199041003816100381610038161003816 (29)



119903 minus 119901119905119903119904) sdot1198921199031198981205902 )



(30)





DRav119904 = sum119904isin119878119898 DR11990410038161003816100381610038161198781198981003816100381610038161003816

(31)


120574max119906119904 = 119901max





DR119906 =





sum119906isin119880119904



(33)





0

20

40

60

80

100

120Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

30

60

90

120

150

180

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

4

8

12

16

20

24

28

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)



= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

1500

3000

4500

6000

7500

9000

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

200

400

600

800

1000

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

20

40

60

80

100

120

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)



ETRVAPMBS

4 6 8 10 12 142Step size (mW)

0

1000

2000

3000

4000

5000

6000

7000

8000

Con

verg

ence

tim

e (ro

unds

)



5 Conclusion



ETRVAPUE

0

600

1200

1800

2400

3000

3600

4200

Aver

age d

ata r

ate (

bits

skH

z)

4 6 8 10 12 142Step size (mW)











its associated UEs




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0

20

40

60

80

100

120Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

30

60

90

120

150

180

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

4

8

12

16

20

24

28

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)



= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

1500

3000

4500

6000

7500

9000

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

200

400

600

800

1000

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

20

40

60

80

100

120

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)



ETRVAPMBS

4 6 8 10 12 142Step size (mW)

0

1000

2000

3000

4000

5000

6000

7000

8000

Con

verg

ence

tim

e (ro

unds

)



5 Conclusion



ETRVAPUE

0

600

1200

1800

2400

3000

3600

4200

Aver

age d

ata r

ate (

bits

skH

z)

4 6 8 10 12 142Step size (mW)











its associated UEs




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500Av

erag

e dat

a rat

e for

ETR

s (bi

tss

kHz)



= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02


0

1500

3000

4500

6000

7500

9000

Aver

age d

ata r

ate f

or V

APs

(bits

sk

Hz)


= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

200

400

600

800

1000

Aver

age d

ata r

ate f

or as

soci

ated

UEs

(bits

sk

Hz)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

20

40

60

80

100

120

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)



ETRVAPMBS

4 6 8 10 12 142Step size (mW)

0

1000

2000

3000

4000

5000

6000

7000

8000

Con

verg

ence

tim

e (ro

unds

)



5 Conclusion



ETRVAPUE

0

600

1200

1800

2400

3000

3600

4200

Aver

age d

ata r

ate (

bits

skH

z)

4 6 8 10 12 142Step size (mW)











its associated UEs




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

20

40

60

80

100

120

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)









= 02 = 02 = 08

= 08 = 02 = 02

= 02 = 08 = 08

= 08 = 08 = 02

0

500

1000

1500

2000

2500

3000

3500

Aver

age d

ata r

ate f

or E

TRs (

bits

skH

z)



ETRVAPMBS

4 6 8 10 12 142Step size (mW)

0

1000

2000

3000

4000

5000

6000

7000

8000

Con

verg

ence

tim

e (ro

unds

)



5 Conclusion



ETRVAPUE

0

600

1200

1800

2400

3000

3600

4200

Aver

age d

ata r

ate (

bits

skH

z)

4 6 8 10 12 142Step size (mW)











its associated UEs




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



ETRVAPUE

0

600

1200

1800

2400

3000

3600

4200

Aver

age d

ata r

ate (

bits

skH

z)

4 6 8 10 12 142Step size (mW)











its associated UEs




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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