Joint Adaptation Framework in Mobile Ad Hoc Networks: A Control Theory Perspective

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Neurocomputing

journalhomepage:www.elsevier.com/locate/neucom

Joint adaptation framework in mobile ad hoc networks: A control theory perspective

Linghe Kong

^a,∗

, Bowen Wang

^a

, Xi Chen

^b

, Xue Liu

^b

, Xiao-Yang Liu

^a

, Jiadi Yu

^a

, Guangtao Xue

^a

, Guihai Chen

^a

a Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China

b McGill University, 845 Sherbrooke Street West, Montreal, Quebec H3A 0G4, Canada

a rt i c l e i nf o

Article history:

Received 30 May 2016 Revised 5 November 2016 Accepted 13 December 2016 Available online 15 June 2017 Keywords:

Mobile ad hoc networks Joint adaptation Wireless communication Control theory

a b s t ra c t

Toenhancetheperformanceofwirelesscommunicationsinmobileadhocnetworks,existingmethodsfo- cusontuningonecertainwirelessvariablesuchasrateadaptation,ortwovariablestogethersuchasjoint power-rateadaptation.However,fieldtestsrevealthatnotonlythesinglecontrollablevariablebutalso theircorrelationaffecttheperformance.Tuningthemone-by-oneand ignoringtheircorrelationcannot achievetheoptima.Inthispaper,westudytheadaptationproblemfromadistributedcontrolperspec- tiveandpresentageneraljointadaptationframework(JAF).Leveragingthemultiple-input-multiple-out controlmodel,JAFisscalable,whichembracesallcontrollablevariablesas itsinputsandtargetperfor- mancemetricsasitsoutputs.Moreover,basedontheclosed-loopcontroltheory,JAFadaptstheoptimal combinationofvariablesthroughthefeedbackofthereal-timemeasurements.Extensivesimulationsare conductedtoevaluatethedistributedJAF.Asanexample,everynodeusingJAFjointlyadaptsitsdatarate andtransmissionpowerinoursimulations.ThesimulationresultsdemonstratethatJAFoutperformsthe existingmethodsbyimprovingthethroughputupto13%andthepacketdeliveryratioupto15%simul- taneously.

© 2017ElsevierB.V.Allrightsreserved.

1. Introduction

A Mobile Ad hoc NETwork (MANET) [25] consists of multi- plemobilenodes.Throughequippedwirelessdevices,thesenodes formadynamicadhocnetworkandsharetheirdata.MANETsare promising and have been widely adopted in various real world applications such as vehicular networks [11] and robotic net- works[17].WiththesupportofMANETs,vehicles canavoidsome crashesbysafetymessageandindustrialrobotscancollaboratively playthesoccer.

Lots ofwireless protocolscan be used inMANETs. For exam- ple,vehicularnetworksutilizeIEEE802.11pbasedDSRC[1],robotic networks utilize 802.11g based WiFi, and wearable sensor net- works utilize 802.15.4 based ZigBee. Although the protocols are different, these applications have the same need including high throughputandpacketdeliveryratio(PDR),toguaranteethequal- ityofdatasharing.Inaddition,thegeneralwireless devices,even

∗ Corresponding author.

E-mail addresses: [email protected] (L. Kong), [email protected] (B. Wang), [email protected] (X. Chen), [email protected] (X. Liu), [email protected] (X.-Y. Liu), [email protected] (J. Yu), [email protected] (G.

Xue), [email protected] (G. Chen).

adoptdifferentprotocols,provideseveralcontrollablevariablesin- cludingtransmissionpower,datarate,andetc.

Inordertoenhancethewirelessperformanceindynamicenvi- ronment,manyefforts havecontributedon theadaptation meth- ods.Mostexisting methods focusontuning asinglevariable.For example, transmission power control [10], and data rate adapta- tion[21].Someothermethodsconsiderthejointadaptationoftwo variables.Forexample,jointpower-rateadaptation[14].Neverthe- less, field tests [1] reveal that every variable affects the perfor- mance.Hence,optimizinganyoneortwovariablescannotachieve the optimal performance. In addition, existing adaptation meth- odscannotdirectlyextendtomultivariateadaptationwell,because multiple variables have complex correlation and this correlation isdynamicinMANETs.The studyonjointlyadapting all wireless variablesisstillblankintheliterature.

In this paper, we promote to study a general framework for multivariate adaptation in MANETs using a new perspec- tive:distributed and adaptivecontrol [7,12]. Twousefulconcepts are adopted. First, the multiple-input-multiple-out (MIMO) control model[16]is ableto describe thecomplex correlationamong all wirelessvariablesasinputsandallperformanceofinterestsasout- puts. Second, the closed-loop control system can update the dy- namiccorrelation throughthefeedbackofreal-time performance, http://dx.doi.org/10.1016/j.neucom.2016.12.103

0925-2312/© 2017 Elsevier B.V. All rights reserved.

andthustheoptimalcontrolstrategycanbedecidedaccordingto thecorrelation.Based onthesetwoconcepts,we proposeanovel jointadaptation framework(JAF),whichadaptstheoptimalcombi- nationofmultiplevariablestoenhancetheperformance.Thisgen- eralframeworkisalsoscalableformorecontrollablevariablesand performanceinfutureMANETs.

Although the theoretical basis of JAF is the MIMO control model,thedesignofJAFisnotadirecttransplantofrecentMIMO controllers. In order to enableJAF, it isnecessary to address the particularchallengesinMANETs.(i)Theenvironmentishighlydy- namic.Hence,itisnon-trivialtoquicklycapturethedynamiccor- relation of variables using recent MIMO controllers. (ii) Wireless communications inMANETs could adopteither broadcast oruni- casttransmissionmanners.Inahybridbroadcast/unicastscenario, it isdifficult tomeasure theactual performance because thereis noinformationfeedbackinbroadcastmanner.

Toaddress thesetwochallenges, we designtwo tailoredtech- niques forJAF.First,foracquiringthecorrelationofmultiplevari- ables, a combined design of one offline trainer and one online trainer isproposed. The offlinetrainer provides an initialestima- tion of the coarse correlation and the online trainer accurately tracksthesubtlechangeofdynamiccorrelationwithinanegligible duration. Second, to cope with the lack ofcoordination between mobilenodes,JAFutilizesthelocalmeasurementsforapproximat- ing the performance ofthroughput andPDR. Based onthe chan- nel reciprocity,the coreidea of localmeasurements isto exploit thereceiver-sideperformancetoestimatethetransmissionperfor- mance.Thereceiver-sideperformancecanbelocallymeasuredand requirenoacknowledgements fromneighboringnodes.Thistech- niquealsoallowsJAFtooperateinafullydistributedfashion.

Extensive simulations are conducted to evaluate JAF. A large amountofdistributednodesaremoving,computing,andtransmit- tinginaMANET.Asan example,every nodeoperatingJAFjointly adapts its datarate andthe transmission power. Compared with existing methods, JAF significantly improves the wireless perfor- mance,whichincreasesthethroughputupto13%andthePDRup to15%simultaneously.

Themaincontributionofthispaperistwo-fold.

• Tothebestofourknowledge,thisisthefirstworktostatethe multivariateadaptationprobleminMANETs.Inaddition,were- sorttothecontroltheoryconcepttostudythisproblem.

• Toenhancethewirelessperformance, weproposea noveland general JAF.Leveraging the modern control theory,JAF is not only scalableto all variables but alsoadaptive to the optimal performance.ThedesignofJAFtakesthehighlydynamicnature andthehybridcommunicationmannerintoconsideration.

The remainder of this paper is organized as follows. In Section 2,we state theproblem. In Section3, webuild the basic model.WedescribethedesignofJAFinSection4,andanalyzeits featuresinSection5.InSection6,weevaluateJAFusingextensive simulations.InSection7,wereviewtherelatedwork.Weconclude thispaperinSection8.

2. Problemstatement

Inthissection,wepresentthesystemdescriptionandtheprob- lemstatement.

2.1. Systemdescription

Wedescribe thesystemusingthemodelasdepictedinFig.1. Thewirelesssystemisthebasiccomponentofthismodel,includ- ing the wireless radiodevice equipped oneach mobile node and the wireless channel for data transmission. All the other factors

Fig. 1. The wireless system in MANETs has multiple inputs and outputs. As an ex- ample, we consider the inputs including the transmission power and the data rate, meanwhile the outputs including the throughput and the PDR.

connectingwiththewireless systemsareclassifiedintothreecat- egories:outputs,inputs,andnoises.

•Outputs: Theoutputs are theperformance ofinterests. Since thefeasibility of mostMANET applications relieson the efficient andreliablecommunications,weareinterestedintheperformance on efficiency and reliability, which is characterized by two ex- tendedmetrics,throughputandpacketdeliveryratio(PDR).Some otheroutputsmayincludedeliverydelay.

• Inputs: The inputs are the controllable variables in wire- lessdevices.The transmission powerand thedata rateare com- moncontrollablevariablesofferedbymostwirelesssystems.Some other variablesmayincludeCWsizeandpacket rate.It hasbeen demonstrated that every variable significantly affects the perfor- mance[1,14,20].Inthiswork,wetakethemostcommontwovari- ablesintoconsideration.

First, the transmission power decides the transmission range, whichindirectlyimpacts the throughputandthe PDR.Forexam- ple,thetransmissionpowerofDSRCis0–30dBm.

Second,thedatarateisthenumberofbitstransmittedpertime unit.Whenthe linkqualityisgood,ahighdataratecanimprove thethroughput.When thelink quality ispoor,a low datarateis neededtoguaranteethePDR.Awirelessprotocolprovidesseveral data rates. Forexample, there are eight alternative data rates in 802.11pbasedDSRC,whichare{3,4.5,6,9,12,18,24,27}Mbps.

•Noises:ThenoisesaretheuncontrolledvariablesinMANETs.

Thesevariables alsoaffectthe wireless performance, butthey do notundercontrol,suchasSINR,velocity,andelectricalcharacters of hardware. Furthermore, some noises cannot be directly mea- sured,forexample,themulti-pathchannel.

2.2.Multivariateadaptationproblem

Weproposethemultivariateadaptation(m-Ada)problem,which aimstoenhancetheefficiencyandthereliabilityofwirelesscom- municationsinMANETsthroughjointlyadapting allpossiblevari- ables.

Toaddressthem-Ada problem,thebasic ideaisto modelthe correlationbetweenmultipleinputsandoutputs andthen design thecontrolstrategy basedonthecorrelation.Thereare twochal- lengingissuesinmodelingthecorrelation:

(i)Thecorrelation iscomplex.InMANETs,therelationshipbe- tweeninputsandoutputsisnotasimpleone-to-onemapping.The correlationalso existsamongmultiple inputs. Forexample,when thepower isincreased, the resultof throughputis uncertain.On onehand,ahigherpoweroffers abetterlink qualityforahigher rate, which may increase the throughput. On the other hand, a higherpoweralsoleadstoalongertransmissionrange,whichin- creases the receiving probability of messages from irrelevant ve- hicles, and thus the throughput may be decreased. In existing jointadaptationmethods,thecorrelationbetweentwoinputshas beenexplored.Butthesespecificmethodscannot extendtomore (>2)inputs.Inaddition,thetheoreticalcommunicationmodelcan

formulatethecorrelationifallvariablesareknown.However,some variablescannotbeobtainedinpracticalMANETs.

(ii) The correlation is dynamic. The dynamic environment contains a number of uncertainties. For example, field tests in [1] show the highly variable fading phenomenon when vehi- clesequippedwithwireless devicesmovenearI-75,I-275,andI- 696freeway.The reasonliesinthecomplex freewayjunctionar- chitecturessuch as a large number ofoverhead bridges, tunnels, andsudden heavy vehicletraffic.This dynamicenvironment with uncertaintiesseverely affects the correlation betweeninputs and outputs asnoises. Hence, a conventional staticcorrelation model cannotsatisfythedynamiccorrelation.

3. Problemmodel:acontroltheoryperspective

BeforeintroducingthedesignofJAF,weformulatethewireless systeminMANETsasaMulti-InputMulti-Output(MIMO)model.

In the wireless system, thereare totally i differentinputs. For example, i=2 inputs include transmission power u₁ and data rateu₂. They are collectively denoted by an input vector u(^k)= [u₁(^k)^u2(^k)^{]T.Inthisvector,u(k)indicatestheinputvaluesatthe} kthtimeslot.Similarly, theoutput vectory(^k)=[y₁(^k)^y2(^k)^{]T is} used to describe the o=2 outputs, where y₁ is the throughput andy₂ is thePDR. Notethat moreinputsor outputscan be eas- ilyaddedbyappendingu_i(k)oryo(k)intovectors.

The mapping relationshipfromthree inputsto twooutputs is describedbyageneralMIMOmodelaccordingtotheadaptivecon- troltheory[9]:

y

(

^k

)

=A1

(

^k

)

^y

(

^k− 1

)

+· · · +An

(

^k

)

^y

(

^k− n

)

+B0

(

^k

)

^u

(

^k− 1

)

+· · · +Bn−1

(

^k

)

^u

(

^k− n

)

+e

(

^k

)

,

(1)

whereA_j(k)andB_i(k)arematricesofmodelparameters(A_j∈R^o×o, B_j∈R^o×i,and0< j<n), nistheorderofthemodel,ande(k)is anidenticallydistributedvectorwithzeromeans(e∈R^o×1).More- over,eisassumedto be independentwithy, u,AandB.We use e(k)torepresentthenoises.

For simplicity of notation, we rewrite the MIMO model Eq.

(1)as:

y

(

^k+1

)

^=X

(

^k

) φ (

^k

)

^+e

(

^k+1

)

^{, (2)}

where

X

(

^k

)

=[B0,..., Bn−1A1 ,..., An], (3)

φ (

^k

)

=[u^T

(

^k

)

,..., u^T

(

^k− n+1

)

y^T

(

^k

)

,..., y^T

(

^k− n+1

)

^]T. (4) InEq.(3),thematrixX(k)capturesthecorrelationbetweeninputs aswellastheirimpactonoutputs.LeveragingtheMIMOmodelin Eq.(2),weareabletocaptureboththecorrelationbetweenthree inputsandtwo performance metrics.Aswe willshow inthefol- lowingsections,thisMIMOmodelenablesajointcontrol.

4. Designofjointadaptationframework

Inthissection,wepresentthedesignofjointadaptationframe- work (JAF), which jointly controls multiple inputs by exploiting their dynamiccorrelation inorder toachieve the optimalperfor- mance.

4.1.Designoverview

Thearchitecture ofJAFdesignisdepictedinFig.2.Thisdesign consistsoffourprincipalmodules:

The offline estimator determines the basic structure including the order n and the initial correlation matrix Xˆ_Init. Since every wireless device may have different electrical characteristics, it is necessary to estimate the order tailored to every device instead ofadoptingaunifiedvalue.Inaddition,an accurateestimationof n and Xˆ_Init requires plentiful measurements and long computing time.Hence,wedesignthisofflinemodule.

Theonlineestimatorlearnstherealtimeinput-outputfeedback andupdatestheestimatedcorrelationXˆ(^k)^{inthemobileenviron-} ment.Comparedwiththerandominitialvalues,theinitialXˆ_Initob- tainedfromtheofflineestimatorcanhelptoapproximatetheac- tualcorrelationX(k)morequickly.

Theadaptivecontrollerprovidestheoptimalcombinationofin- puts. Using thedynamic correlation, thecontroller computes the maximal throughput subject to the PDR requirement as an con- strainedmultivariate optimizationproblem.Furthermore,weplug a smooth mechanismintheadaptive controllerinorder toavoid thelargechangeofinputs.

Thelocalmeasurementisusedtomeasurethereal-timeoutputs andfeedthemback tothe othermodules. Withthismodule,the JAFformsaclosedloopsystem.

TheJAFdesignhasthreeadvantages:(i)itexplorestheimplicit correlationbetweeninputsandoutputsbenefitingfromtheMIMO model;(ii)itkeepspacewiththedynamicenvironmentwithun- certaintiesleveraging theclosed-loop controlandtheonlineesti- mator;(iii)thisgeneralframeworkisabletoextendtomoreinputs oroutputs.Next,wepresentthefourmodulesindetails.

4.2. Offlineestimatordesign

In order to determine the order n of a MIMO control model, this offline estimatoroperates as the following steps. Firstly, use the least squares(LS) methodto estimate the correlation matrix whensettingtheordern=1,2,...,respectively.Secondly,compute theaveragesquareerrorZ|nforeveryordern.Thirdly,determinen fromZ|naccordingtoF-criterionorAICcriterion[9].Theofflinees- timatorcanbeoperatedbythemanufacturerusinghistoricaldata.

DenoteX|ntobethecorrelationXwhentheorderofthemodel isn.AssumethatwehaveLsetsofmeasuredinputsu(k)andcor- respondingoutputs y(k),wherek=1,2,...,LandL>>n.Accord- ingtotheformationinEq.(4),theseLmeasuredresultscanform (^L− n+1) ^different

φ

^{(k), wherek}=n,n+1,...,L.Then, Xˆ

|

^{n can}

beestimatedusingLStoapproximatetheactualXateverynby

Xˆ

|

n=Y^T

(

^T

)

⁻¹, (5)

where

Y =[y

(

ⁿ

)

^y

(

ⁿ+1

)

... y

(

^L

)

^]T, (6)



=[

φ (

ⁿ

) φ (

ⁿ+1

)

...

φ (

^L

)

^]T. (7) Theestimation error

ε

^{betweeneach pairofmeasured output}

andtheestimatedoutputis

ε (

^k

) |

^n=y

(

^k

)

− ˆy

(

^k

) |

^n=y

(

^k

)

− ˆX

|

ⁿ

φ (

^k− 1

)

. (8) Then,theaveragesquareerroris

Z

|

^n=Lk=n

⁽ ε (

^k

) |

ⁿ

)

²

L− n+1 . (9)

TheorderncanbeobtainedfromZ|naccordingtothestandard F-criterion or AIC criterion, which can be coarsely considered to select the minimal n satisfying Z^

|

ⁿ=0. The order of a wireless systemisusuallylow.Theempiricalorderis2obtainedfromour simulations.

Afternisdetermined,theinitialvaluesofcorrelationXˆarealso determinedbyXˆ_Init=Xˆ

|

^ninEq.(5).

Fig. 2. Architecture of JAF.

4.3. Onlineestimatordesign

In a highly mobile environment, the online estimator is re- quiredtoquicklyupdatethe dynamicX(k) atthetime slotk.The traditional LSmethod cannot satisfy the online requirement be- causeit takesa long time to compute thelarge amountof mea- surements

φ

^{.Therecursive leastsquares(RLS)method[3]ismore}

suitable,becauseitisabletoupdateXˆ(^k+1)^{withonlyonemea-} surement

φ

^{(k)andtheestimated}correlationXˆ(^k)^{atlasttimeslot.}

Therefore,we adoptthe RLSmethodtoupdate thecorrelation matrix in thismodule. Since RLS method hasbeen well studied, we do not repeat the derivation process. Leveragingthe method in [3], thedynamiccorrelation Xˆ(^k+1)^{can be estimatedby the} followingequations:

Xˆ

(

^k+1

)

=Xˆ

(

^k

)

+

ε (

^k+1

) φ

^T

(

^k

)

^P

(

^k− 1

)

λ

+

φ

^T

(

^k

)

^P

(

^k− 1

) φ (

^k

)

^{, (10)}

ε (

^k+1

)

^=y

(

^k+1

)

^{− ˆX}

(

^k

) φ (

^k

)

^{, (11)}

P

(

^k

)

= P

(

^k− 1

)

λ

^−P

⁽

^{k− 1}

⁾ φ (

^k

) φ

^T

(

^k

)

^P

(

^k− 1

) λ (

¹+

φ

^T

(

^k

)

^P

(

^k− 1

) φ (

^k

))

^,

(12) whereXˆ(^k)^{istheestimateofX(k),}

ε

^{(k)istheestimationerrorvec-}

tor,P(k)isthecovariancematrix,and

λ

^{istheforgettingfactor(0}<

λ

≤ 1).Asmall

λ

^givesexponentiallylessweighttooldermeasure- mentsandmoreweighttocurrentmeasurement,whichishelpful inahighlydynamicscenario.Theempiricalvalueofthisforgetting factoris

λ

=0.9proposedby[16].

ThestabilityofRLShasbeentheoreticallyprovedin[3].Wewill showtheconvergenceofthisdesignintheevaluation(Section6).

4.4. Adaptivecontrollerdesign

Theadaptivecontrolleraimstomaximize thethroughputwith the PDR requirement, where the PDRrequirement is denoted by Rreq.Hence,theobjectivefunctioncanbeformulatedas

Maximize: E

{

^y1

(

^k+1

) }

, Subjectto:E

{

^y2

(

^k+1

) }

^Rreq,

u1

(

^k

)

∈U1,

u2

(

^k

)

^{∈U2, (13)}

whereE{.}istheexpectation operator,U₁ isthesetofalternative powerlevelsandU₂isthesetofalternativedatarates.Thedesign goalofEq.(13)canbedescribedasthattheexpectedy₁issteered tothemaximalthroughputwhilesubjecttoseveralconstraints.In particular,theexpectedPDRmustbe greaterthanorequaltothe requirement;thetransmissionpoweru1(k)anddatarateu2(k)are limitedintheirrange.Forexample,u₁(k)isfrom0dBmto30dBm inIEEE802.11pbasedDSRC.

InaccordancewithEq.(11),wehave E

{

^y

(

^k+1

) }

=E

{

^Xˆ

(

^k

) φ (

^k

)

+

ε (

^k+1

) }

=E

{

^yˆ

(

^k+1

) }

+E

{ ε (

^k+1

) }

=yˆ

(

^k+1

)

,

(14)

where yˆ(^k+1)=Xˆ(^k)

φ

(^k) ^{is the estimate of y}(^k+1) ^{and the} expectation of estimation error is E

{ ε

(^k+1)

}

=0 by RLS the- ory.Hence, E

{

^y1(^k+1)

}

=yˆ₁(^k+1) ^andE

{

^y2(^k+1)

}

=yˆ₂(^k+1)^. Then,Eq.(13)canbetransformedto

Maximize: yˆ1

(

^k+1

)

, Subjectto:yˆ2

(

^k+1

)

Rreq,

u1

(

^k

)

∈U1, u₂

(

^k

)

^∈U2,

ˆ

y

(

^k+1

)

=Xˆ

(

^k

) φ (

^k

)

. (15) WefindthatEq.(15)isaconstrainedmultivariateoptimization problem.Inaddition,eachvariableu₁(k)oru₂(k)hasonlyfiniteal- ternativevalues,sothisfunction isconvex. Thistypicaloptimiza- tionproblemcanbeeasilysolvedbyexistingmethodssuchasdi- rectsearch, gradient-basedsearch,orquadraticprogramming. For simplicity,we adopt thedirect search method to solve thisopti- mizationproblemEq.(15)inourdesign.Then,we obtaintheop- timaloutputy_opt(^k+1)^anditscorrespondingoptimalcontrollaw uopt(k).

Ifuopt(k)andu(^k− 1)^{are close(e.g.,thechangeofpowerless} than 2 levels), which means the change of input is not large, we setthe final control law(i.e., final settingofpower andrate) u^∗(^k)=uopt(^k)^{.Otherwise,thesmooth controlmechanismistrig-} gered,because the severe input oscillationwill lead to uncertain impact on other nodes. And the smooth control mechanismcan reducesuchimpact.

Thesmoothcontrolmechanismaimsatminimizingthefollow- ingquadraticcostfunction

J=E

{||

^W

(

^y

(

^k+1

)

− yopt

(

^k+1

)) ||

²

+

||

^Q

(

^u

(

^k

)

− u

(

^k− 1

)) ||

²

}

, (16) whereyopt(k)istheoptimaloutputs obtainedfromEq.(15),||.||is the2-normoperation,Wisapositive-semidefiniteweightingma- trixontheoutputerrorsandQisapositive-definiteweightingma- trixonthechangeofinputsettings.TheweightingmatricesWand Qarecommonlychosenasdiagonalmatrices.Theirrelativemagni- tudeprovidesawaytotradeoff the optimaloutputforbettersta- bilityoftheinput control. Interestedreadersmayrefer to[9]for detailsonWandQsettings.

The design goalof Eq. (16)can be describedas that the sys- temoutputsapproachtothetheoreticaloptimumwhilepenalizing largechangesofinputs.

In the following, we derive the smooth control law. First, we define

φ

˜

(

^k

)

=[0u^T

(

^k− 1

)

,..., u^T

(

^k− n+1

)

y^T

(

^k

)

^{,..., yT}

(

^{k− n+1}

)

^{]. (17)}

SubstitutingXˆ(^k)^{andEq.(17)intoEq.(16),wehave} J=E

{||

^W

(

^Xˆ

(

^k

) φ

^˜

(

^k

)

+Bˆ0u

(

^k

)

+

ε (

^k+1

))

−yopt

(

^k+1

)) ||

²

}

+

||

^Q

(

^u

(

^k

)

− u

(

^k− 1

)) ||

²

=

||

^W

(

^Xˆ

(

^k

) φ

^˜

(

^k

)

^{− yopt}

(

^k+1

)) ||

²⁺

||

^WBˆ0u

(

^k

) ||

²

+2u^T

(

^k

)

^BˆT0W^TW

(

^Xˆ

(

^k

) φ

^˜

(

^k

)

− yopt

(

^k+1

))

+

||

^Qu

(

^k

) ||

²⁺

||

^Qu

(

^k− 1

) ||

²

−2u^T

(

^k− 1

)

^QTQu

(

^k

)

+E

||

^W

ε (

^k+1

) ||

^{2. (18)}

ThecostfunctionJisatits minimumwherethefollowingderiva- tiveiszero.

∂

^J

∂

^u

(

^k

)

⁼²

(

^WBˆ0

)

^TW

(

^Xˆ

(

^k

) φ

^˜

(

^k

)

− yopt

(

^k+1

))

+2

(

^WBˆ0

)

^TWBˆ0u

(

^k

)

+2Q^TQu

(

^k

)

− 2Q^TQu

(

^k− 1

)

=0. (19)

SolvingEq.(19),weobtainthesmoothcontrollawusmo(k) usmo

(

^k

)

=



(

^WBˆ0

)

^TWBˆ0+Q^TQ



−1

·



Q^TQu

(

^k− 1

)

+

(

^WBˆ0

)

^TW

(

^yopt

(

^k+1

)

− ˆX

(

^k

) φ

^˜

(

^k

)) 

(20) asthefinalcontrollawu^∗(^k)=usmo(^k)^{.Notethatthesmoothcon-} trolmechanism doesnot violate the convergence to the optimal output, butconsume a longer convergence duration in exchange foramoresmoothchangeofinputs.

4.5.Localmeasurementdesign

Itisnon-trivialtoacquireothernodes’throughputandPDRbe- causeof the hybrid communication manner. In thismodule, the measurementsare definedforunicastandbroadcast,respectively.

Fortheunicastmanner,thevaluesofboththroughputandPDRcan beattached inthe acknowledgement(ACK). Hence, a node could acquireits neighbors’performance directly fromtheACK. Onthe contrary, forthe broadcast manner, there is no ACK mechanism.

Thismodulemeasurey(k)bytheaverageperformanceofallneigh- bors.Basedonthechannelreciprocity,neighborscanhavesimilar transmissionperformance because every node operates thesame JAF.Thus,thecoreideaoflocalmeasurementistoutilizeanode’s ownperformanceyˆ(^k)^toapproximatetheaverageperformanceof itsneighborsy(k). Notethat anode canmeasure itsperformance includingthroughputandPDRlocally.

5. JAFanalysis

In thissection, we analyze the compatibility, complexity, and stabilityofJAFdesign.

5.1.Compatibilityanalysis

The operation ofJAFneeds thethroughputandPDRmeasure- ments,which are computedusingthe physicallayer information.

Moreover, the transmission power and data rate are also physi- cal orMAC layer variables. Hence, JAF should be placed closeto thephysicallayer.Meanwhile,thepositionofJAFshouldbehigher thanlower MAClayer becausethe dataratemustbe determined before adding it into the header of MAC frame. Using 802.11p basedDSRCasanexample,wesetJAFasamiddleMAClayerbe- tween the upper MAC layer of IEEE 1609.4 and the lower MAC layer, which can merge into the existing DSRC protocol stack as shownin Fig.3. In thisway, the function ofJAF can be enabled anddisabled ondemand.And itdoesnot conflictwithanyother layers.Inaddition,JAFdoesnotrequireanychangeofexistingpro- tocolstack,whichshowsitstrongcompatibility.

Fig. 3. JAF is designed as a middle MAC merged into current existing wireless pro- tocol stack. For example, in DSRC.

5.2. Timecostanalysis

InJAF,therearetwoonlinemodules,theonlineestimatorand the adaptivecontroller, involvein thecomputingtasks. Forprac- tice, the time cost of these two modules are desired to be low.

Otherwise,alargetimecostwilldecreasethethroughput.

Withrespect to the online estimator,the main task ofRLS is to solve Xˆ(^k+1) ^{in Eq. (10), whose complexity is owing to the} matrix multiplication. According to [8],the complexity of P(k) is determinedbyP(^k− 1)

φ

(^k)

φ

^T(^k)^P(^k− 1),wherethesizeofP(^k− 1)^is(ⁱ+o)ⁿ×(ⁱ+o)^nand

φ

^{(k) is}(ⁱ+o)ⁿ× 1.Thus,P(k) isO((ⁱ+ o)⁴ⁿ⁴)^{;Similarly,thecomplexityof}

ε

(^k+1)^isO(^o(ⁱ+o)²ⁿ²)^;And thefinalcomplexityoftheonlineestimatorforXˆ(^k+1)^isO(^o(ⁱ+ o)⁷ⁿ⁷)^{determined by}

ε

(^k+1)

φ

^T(^k)^P(^k− 1)^{.Sinceall parameters} o=2,i=2,andn=2areverysmall,thetimecost oftheonline estimatorislow.

In regard to the adaptive controller, the main task is to ob- tain the control law u^∗ accordingto Eq. (15).Even using thein- efficient direct search method, the computational complexity is O(



1



2



3o(ⁱ+o)²ⁿ²),whereϱ1,ϱ2,andϱ3 arethenumberofal- ternative power levels and data rates, respectively. In detail, the search spaceisϱ1ϱ2ϱ3 includingall combinationsofthree inputs.

And foreachcombination, yˆ(^k+1)=Xˆ(^k)

φ

(^k) ^{needs tobe com-} puted,whosecomplexityisO(^o(ⁱ+o)²ⁿ²)^{.e.g.,inDSRC,}



1=32,



2=8and



3=9,thetimecostofadaptivecontrollerisalsolow.

5.3. Stabilityanalysis

The main components involved in stabilityof JAFinclude the MIMOmodelandtheadaptivecontroller. (i)Inthiswork,we ap- proximatethewirelesssysteminMANETasalinearMIMOmodel.

(ii)Theadaptivecontrollerisa constrainedmultivariateoptimiza- tion function, in which one output y₁ is set asthe optimization objectiveandanotheroutputy₂issetastheconstraint.Sotheop- timaloutputscanalwaysbederived.Hence,JAFisastablecontrol strategy.Inaddition,weevaluatethestabilityinsimulations.

6. Performanceevaluation

ToevaluateJAFinMANETs,weimplementitonthe ns-2sim- ulationplatformandperformextensivesimulations inavehicular network,whichisatypicalMANETapplication.

6.1. Simulationsettings

Thesimulationsettingsareasfollows:

HighwayScenario.We conduct oursimulations ina typical bi- directionalhighwayscenario.Thebi-directionalhighwayisof2000 meters long and 30 meters wide with four lanes in each direc- tion. Inaddition, thereare two entries along each direction. One entrance is atthe beginning of the highway, andthe other isat the1-kilometerspotonthehighway. Vehiclesrandomlyenterthe

20 40 100 200 300 0

1 2 3 4

Number of Nodes

Throughput (Mbps)

FPC CARS FPC+CARS JAF

Fig. 4. Average throughput under different traffic densities.

highway through all fourentries anddrive witha speed limitof 100 kmsper h. Upon arrivingatthe endofone direction, vehi- clesgooff thehighwayandenterthehighwayagainattheother direction.Thetotalnumberofvehiclesvariesfrom20to300.The traffic tracesaregeneratedby SUMO,whichprovides microscopic movementlogsofvehicles.

VehicleSettings.Eachvehicleisconsideredasamobilenodeand is equippedwitha DSRC radio. Foreach node, thedefaulttrans- mission datarateissetas3Mbpsformaximizingthepacketde- livery ratio.The other optionsofdata ratesare6Mbps, 12 Mbps and 24 Mbps. The default transmission power is set to 20 dBm.

Each vehicle can adjust its transmission power from 0 dBm to 30dBmwitha2dBmstep.

CommunicationSettings.Eachnodecaneitherunicastorbroad- castitsmessages.Thegenerationperiodsofunicastmessagesand broadcast messages are 0.1 s and1 s, respectively. If a unicast messageisgenerated,anode willrandomlyselectsaneighboring nodetotransmitthismessage.Thepacketsizeissetto500 bytes, whichisatypicalpacketsizeusedinindustrialprojects(e.g.,Cali- forniaDepartmentofTransportation/AirResourcesBoardModeling Program).

Propagation Model. We employ the V2V channel model [6]in our ns-2 simulation platform. This model is established through fieldtests.Itusesatwo-slopefunctiontocapturethepropagation featuresofavehicularscenario.

MethodsStudied.Wecomparativelystudythefollowingadapta- tionmethodsinoursimulations:

• JAF:thejointadaptationframeworkweproposeinthispaper.It jointlycontrolsthetransmissionpoweranddatarateaccording tothelocalmeasurementsofthethroughput,PDRandenviron- mentparameters.

• CARS[21]: a state-of-the-artdata rateadaptation methodtai- loredfor vehicularnetworks. Inour evaluation, CARS exploits environmentmeasurements includingthe SINRvalue, velocity, anddensitytoselecttheoptimaldatarate.

• FPC[10]:afeedback-basedtransmissionpowercontrolmethod.

FPCaimstocontrolthetransmissionrangeofeachvehicleata propervalue.Toachievethis,FPCutilizesthefeedbackbeacons inbroadcastpacketsastransmissionpowercontrolreferences.

• FPC+CARS: a sequential combination ofFPC and CARS. It first adjuststhetransmissionpowerbasedonFPC,thenchoosesthe datarateusingCARS.

6.2. PerformanceresultsofthroughputandPDR

Fig.4showshowthethroughputchangeswiththetrafficden- sity. As we can observe fromthe figure, the throughput firstin- creaseswiththetrafficdensityandthenreachesasaturatedvalue.

This is because asmore andmore nodes appear in thecommu- nicationrangeof anode, theamountofreceived packets startto

0 0.2 0.4 0.6 0.8 1

0 0.2 0.4 0.6 0.8 1

Packet Delivery Ratio

CDF

FPC CARS FPC+CARS JAF

Fig. 5. The CDF of average PDR when the node number is 100.

increase.However,thereisanupperlimitofthroughputduetothe wirelesscollision.TheresultsshowthatJAFcanadapttoachang- ingenvironmentmuchbetterthanexistingsolutions.Comparedto CARSandFPC,JAFcansignificantlyincreasethethroughputviaap- plyingjointcontrolofallvariables.InFig.4,itisalsoworthnoting that FPC+CARS yields a lower throughput than CARS. This result indicatesthat apoordesign ofsequentialcontrol forseveralvari- ablesone-by-onewouldobtainaworseperformancethanjustone variableadaptation.Thisresultfurtherdemonstratesthatmultiple variablesarenotindependentfromeachother.Therefore,thereex- istsatradeoff betweenmultiplevariable.FPC+CARSignoressucha tradeoff,andevendecreasesthewirelessperformance withanin- appropriate combinationof transmission powerand data rate. In contrast,JAFutilizesaMIMOmodel,whichimplicitlycorrelatesall variables.Hence,JAFisabletoprovidea bettercombinationthan thatofFPC+CARSandCARS.

Fig.5showsthecumulativedistributionfunction(CDF)ofeach node’s average PDR, when the number of nodes is 100. In this case, the wireless channel is approaching the saturation point.It is shown in Fig.5 that JAF achieves the highest PDR.Compared with the second best method, JAF increases the worst-case PDR byup to15.2%(Thecorresponding improvementinthroughputis 13.1%.). Considering the congested and nearly saturated channel, thisimprovementis considerable.In Fig.5 we canalso findthat FPC(whichfixesitsdatarateas3Mbps)yieldsthelowestPDR.This suggeststhatthe3Mbpsdatarateisnotalwaysthemostreliable datarate.Onthecontrary,JAFandCARSadjustthedataratesonce thechannelbecomestoocongestedforthedatarateof3Mbps.As aresult,JAFandCARSoutperformsFPCwhenthetrafficdensityis large.

6.3.Selectionoftransmissionpoweranddatarate

Then, we illustrate the insights of JAF by comparing the se- lections of data rate and transmission power of different meth- ods.Withoutlossofgenerality,werandomlychooseascenario,in whichthenumberofnodesis100.

Fig.6presentstheoccurrenceprobabilityofeachdatarate,and Fig.7summarizestheoccurrenceprobabilityofeachtransmission power.Inthiscase, thechannel isapproachinga congestedstate.

Todealwiththiscongestedchannelandreducethecollisionprob- ability,bothJAFandCARSintendtousethedatarateof12Mbps asshowninFig.6.CARSuses12Mbpsin77.0%ofthecases.How- ever,itcannotfurtherimprovetheperformance,astheSINRvalue cannot be further increasedwithout transmission power control.

DuetothelimitedSINR,CARSfallsbackto3Mbpsand6Mbpsin 23% ofthecases. Combiningthe finding thatFPC+CARS performs evenworse than CARSasshownin Figs.4 and5,theseobserva- tionsfurther verifythatan inappropriate jointcontrolsometimes harmstheperformance.Inordertobettersupportthedatarateof

3Mbps 6Mbps 12Mbps 24Mbps 0

0.2 0.4 0.6 0.8 1

Data Rate

Occurrence Probability

FPC CARS FPC+CARS JAF

Fig. 6. The occurrence probability of each data rate.

20 22 24 26 28 30

0 0.2 0.4 0.6 0.8 1

TX Power (dBm)

Occurrence Probability

FPC CARS FPC+CARS JAF

Fig. 7. The occurrence probability of each transmission power.

0 4 8 12 16 20 24 28 32 0

0.5 1 1.5 2 2.5 3

Simulation time (s)

Throughput (Mbps)

Estimated value True value

Fig. 8. The convergence of the estimated throughput.

12Mbps, JAF employs hightransmissionpowers more frequently than other methods as shown in Fig. 7. It applies the highest transmissionpower30dBmin51.4%ofallthecases.Highertrans- mission powers allow JAF to increase the SINR of the receivers.

Consequently,JAFisabletousethedatarateof12Mbpsin94.4%

ofthecasesandfullyexploittheadvantageofthisdatarate. This resultsuggeststhatagoodcombinationenablesJAFtofurtherim- provethewirelessperformanceinMANETs.

6.4.Convergenceoftheonlineestimator

WealsoevaluatetheconvergenceoftheonlineestimatorofJAF.

Trafficconditionsofindividual nodesinthesameMANET aredif- ferent.Foreachone, its trafficconditionalso variesfromtimeto time.Werandomlypickanode,andinvestigatetheconvergenceof itsonlineestimator.Fig.8presentstheestimatedandactualvalues ofthroughput.Itshowsthattheestimationprovidedbytheonline estimatorcan quicklyconverge tothe actual value in only 2up- dateperiods.Afterthat,theestimatedvaluefollowsthechangeof theactualvalueclosely.Wealsohavesimilarobservationsonthe

0 4 8 12 16 20 24 28 32

0 0.2 0.4 0.6 0.8 1

Simulation time (s)

Packet Delivery Ratio

Estimated value True value

Fig. 9. The convergence of the estimated PDR.

Fig. 10. The stability of JAF.

estimationofPDRasshowninFig.9.Therefore,weconcludethat theonlineestimatorofJAFconvergesquickly.

6.5. StabilityofJAF

Stabilityisanimportantmetricincontrolsystems.Toverifythe stability,weconductasimulationthatallnodesarerandomlydis- tributed andstationary inthe area. In mobile scenario, since in- putskeepchangingaccordingtothedynamics,thestabilitycannot berecognized clearly.Thus,we simulateinsuch astationarysce- nario,whichisageneralsnapshotofmobilescenario.Thechange of throughput of one certain node is plotted in Fig. 10. We can summarizethatJAFisstable, whichreachesaconstant outputaf- ter10sandisoverlappedwiththetheoreticalresult.

7. Relatedwork

Adaptationmethods havebeenextensively studiedinwireless communications.Inthissection,weonlydiscussthework thatis mostpertinenttoours.

In stationary wireless networks, the classical power control methodPCMAP[18]samplesseveralsuccessiveSNRvaluesforop- timalpowerestimation.Similarly,theclassicalrateselectionmeth- odsARF [15],SampleRate[2],andRRAA[24] decidetheiroptimal data rates ina given time window by measuring the numberof successive packet losses, the average of per-packet transmission times, and the packet loss ratio, respectively. All these methods operatebasedonalongwindowtosamplemeasurements.There- fore,theycanworkwellinrelativestationarynetworks,butcannot keeppacewiththequickchangesinhighlydynamicMANETs.

In mobile networks, most adaptation methods take the mo- bility intoaccount. For example,LINT [19] adjusts the powerfor topologycontrolinmobilenetworksusingthedynamicnumberof neighbors.RBAR[13]selectstheoptimalratebythereceiver-based SNR measurements. Then, RAM [5] extends the receiver-based

rateadaptation design withchannel asymmetry inconsideration.

SoftRate [23] determines the best rate using the channel bit er- ror rate, which is estimated by the physical layer information.

D-FPAV[22] focusesonthetransmissionfairnessofsafety-critical informationbyadistributedpowercontrolmethod.FPC [10]uti- lizesfeedbackbeaconstoadaptthepowerleveltoapropertrans- missionrange.CARS[21]isacustomizedrateselectionmethodfor VANETs,whichleveragescontextinformationsuchasvelocity and distance to perform fast rate adaptation. DORA [4] works under thenoisyVANETchannelsforoptimalrateselection.Nevertheless, thesemethodsonlyfocusonsinglevariable’sadaptation,whichto- tally ignore the impact of multiple inputs and multiple outputs.

Thus,theycannotattaintheoptimuminourproblem.

OnlyafewVANETworkspayattentiontojointcontrol.Forex- ample,Huangetal.[14]proposesthejointtransmissionprobability andpowercontrol foraccurate tracking.Rawatetal.[20] studies the joint power andcontention window size control for dissem- ination performance. The joint control methods in these papers are sequential combinations of multiple individual control meth- ods. Therefore, they fail to capture the correlation betweenvari- ables,andcanonlyachievesuboptimalperformanceandreliability.

8. Conclusion

InMANETs, notonly singlevariables butalsotheir correlation significantlyaffecttheperformanceofwirelesscommunications.To enhancetheperformance,wepresentageneraladaptationframe- workJAF,whichconsidersthewirelesssystemasanMIMOcontrol model.Basedon theMIMOmodel,JAFcapturesthedynamiccor- relationbetweenmultipleinputsandoutputs usingan onlinees- timator. Leveragingthe estimatedcorrelation,JAFthenjointlyad- justs the inputs to achieve the optimal outputs. Extensive simu- lation results demonstrate that JAF significantly outperforms the state-of-the-artadaptationmethodsandtheircombination.

Acknowledgment

ThisresearchwassupportedinpartbyNationalNaturalScience FoundationofChinagrants61672349and61303202.

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Linghe Kong is currently an associate professor at Shang- hai Jiao Tong University. From 2014 to 2015, he was a Postdoctoral Fellow in the School of Computer Science of McGill University. He received his Ph.D. degree in Com- puter Science from Shanghai Jiao Tong University 2012, Dipl. Ing. degree in Telecommunication from TELECOM SudParis 2007, and B. E. degree in Automation from Xi- dian University 2005. His research interests include wire- less sensor networks, mobile computing, and RFID.

Bowen Wang is currently Master student at Shanghai Jiao Tong University. He re- ceived his B.E. degree from Shanghai Jiao Tong University 2015. His research inter- ests include mobile computing and Crowdsensing.

Xi Chen is currently a Ph.D. student and a research assistant at Cyber-Physical Sys- tems Laboratory, School of Computer Science, McGill University. He received both of his M.Eng. and B.S. degrees from Department of Electronic Engineering, Shanghai Jiao Tong University. His research interests include Vehicle-to-Vehicle (V2V) com- munications and vehicular networks, optimization of electric vehicles, energy and cost management of cloud computing, green and energy-aware computing.

Xue Liu received the B.S. degree in mathematics and the MS degree in automatic control both from Tsinghua University, China, and the PhD degree in computer sci- ence from the University of Illinois at Urbana-Champaign in 2006. He is an associate professor in the School of Computer Science at McGill University. His research in- terests include computer networks and communications, smart grid, real-time and embedded systems, cyber-physical systems, data centers, and software reliability.

Xiao-Yang Liu received his B.Eng Degree in computer science and technology from the Huazhong University of Science and Technology, Wuhan, China, in 2010. He is now a PhD candidate in the Department of Computer at the Shanghai Jiao Tong University. His research interests include Internet of Things, Wireless Networks and Cybersecurity.

Jiadi Yu received the Ph.D. degree in Computer Science from Shanghai Jiao Tong University, Shanghai, China, in 2007. He is currently an Associate Professor in De- partment of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China. Prior to joining Shanghai Jiao Tong University, he was a postdoc- toral fellow in the Data Analysis and Information Security (DAISY) Laboratory at Stevens Institute of Technology from 2009 to 2011. His research interests include cyber security and privacy, mobile and pervasive computing, cloud computing and wireless sensor networks.

Guangtao Xue is currently a Professor in Department of Computer Science and En- gineering, Shanghai Jiao Tong University, Shanghai, China. He received the Ph.D.

degree in Computer Science from Shanghai Jiao Tong University, Shanghai, China.

His research interests include Mobile and Wireless Computing, Big data, Social Net- works, Distributed Computing, and Wireless Sensor Networks.

Guihai Chen earned his B.S. degree from Nanjing University in 1984, M.E. degree from Southeast University in 1987, and Ph.D. degree from the University of Hong Kong in 1997. He is a distinguished professor of Shanghai Jiaotong University, China.

He had been invited as a visiting professor by many universities including Kyushu Institute of Technology, Japan in 1998, University of Queensland, Australia in 20 0 0, and Wayne State University, USA during September 2001 to August 2003. He has a wide range of research interests with focus on sensor network, peer-to-peer com- puting, high performance computer architecture and combinatorics.