Robust Resource Allocation in Future Wireless Networks PDF
Preview Robust Resource Allocation in Future Wireless Networks
Saeedeh Parsaeefard Ahmad Reza Sharafat Nader Mokari Robust Resource Allocation in Future Wireless Networks Robust Resource Allocation in Future Wireless Networks Saeedeh Parsaeefard • Ahmad Reza Sharafat Nader Mokari Robust Resource Allocation in Future Wireless Networks 123 SaeedehParsaeefard AhmadRezaSharafat DepartmentofCommunication FacultyofElectrical Technologies andComputerEngineering ResearchInstituteforCommunications TarbiatModaresUniversity andInformationTechnology Tehran,Iran Tehran,Iran NaderMokari FacultyofElectrical andComputerEngineering TarbiatModaresUniversity Tehran,Iran ISBN978-3-319-50387-5 ISBN978-3-319-50389-9 (eBook) DOI10.1007/978-3-319-50389-9 LibraryofCongressControlNumber:2016960207 ©SpringerInternationalPublishingAG2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Wireless networks and services are vital elements of daily life around the world. Presently,therearecloseto4.8billionmobilesubscribersandmorethan8billion mobileconnections(includingmachine-to-machine)intheworld,andthenumbers are increasing at a very rapid pace. The revenue generated worldwide in 2015 for providingmobileservicesexceededUS$1trillion.Itisexpectedthatby2020,there willbemorethan50billionmobileconnections;hence,thereisaneedtoprovidethe requiredresourcesforthisanticipatedphenomenalgrowth.However,theresources (e.g.,frequencyspectrum,energy)arelimited,whichcallsforinnovativeapproaches to improving efficiencies, managing complexities, providing quality, and ensuring availability and security. It is of the utmost importance to meet the requirements ofnewservicesinacost-effectiveandefficientmanner;theirproliferationdepends onit. The conventional approach is to formulate resource allocation in wireless net- worksasoptimizationproblemsthataimtomaximizethegoodput(e.g.,throughput) of networks or users while minimizing their badput (e.g., energy consumption, interference). Many existing resource allocation schemes assume exact parameter valuesandsideinformationtoachievetheirobjectives.However,theirperformance issensitivetotheaccuracyandavailabilityofparametervaluesandotherancillary information. Such assumptions in many instances are unrealistic due to the ever increasing number of wireless devices in the neighborhood and their mobility, as well as the nonlinear and time-varying nature of propagation of electromagnetic waves, and in some cases result in significant and unacceptable degradation of the quality of service experienced by users. To deal with the undesirable side effects of such simplifying and unrealistic assumptions, there is a need to introduce robustness into resource allocation schemes that would be efficient and fair, with acceptable complexity,cost,andoverhead. The nominal (i.e., no uncertainty) optimization problems in many cases are not easy to solve in a straightforward manner because they are nondeterministic polynomial-time and nonconvex. Introducing robustness in such problems is nor- v vi Preface mallydonebywayofintroducingadditionalconstraintsthatattimesarestochastic and nonlinear, which aggravates the problem even further. It is in this light that developing practical schemes for the robust allocation of resources in wireless networksisaformidablechallenge. Thisbookrepresentsanattempttopresentthestateoftheartincurrentresearch on this topic and to show that, in general, many existing techniques and methods inrobustallocationwillbeusableinfuturewirelessnetworks.Anotherobjectiveof thisbookistodemonstratethatthereisanurgentneedtodevisealternativeschemes toimproveperformanceandavoidsomeoftheveryseriousobstaclesandlimitations pointed out in the literature. The book contains five chapters, which are described brieflyinwhatfollows. InChapter1,weexplainwhyrobustoptimizationtheoryisimportantinwireless networks and how, in general, it can be applied for allocating resources in such networks. We begin the chapter by presenting fundamental notions of wireless communications relevant to the book and describe different types of resource allocation problems,namely, network-centric (cooperative) anduser-centric(com- petitive) approaches. The objective of the cooperative approach is to maximize the total network utility, whereas in the competitive approach, the goal of each user is to maximize its own utility. We also show how to map a nominal (i.e., nonrobust)optimizationproblemintoitsrobustcounterpart.Finally,weexplainthe implementationissuespertainingtorobustoptimizationproblems. InChapter2,wecoverrobustcooperativetransmitpowerallocationinwireless networks, where the uncertain parameters are channel gains between secondary users and primary access points. The objective of secondary users is to use the frequency spectrum that belongs to the primary network subject to keep their interference to the primary network below a given threshold while maximizing their own social utility. We present the system model and formulate the robust resourceallocationproblemusingtheconceptofuncertaintyregionwithinwhichall instancesofuncertainparametervaluesareassumedtobeconfined.Wealsoshow that by properly defining the uncertainty region, the computational complexity of solvingrobustproblemscanbereducedtothelevelofnonrobustproblems,develop algorithmsfortradingoffbetweenthroughputreductionandrobustness,anddevise schemestoreducesignalinginrobustsolutionsfordistributedapproaches. In Chapter 3, we study robust noncooperative resource allocation where each user competes with other users over utilizing the resources to maximize its own utility. In doing so, we present a game-theoretic formulation of the problem and discuss its solution where greedy, noncooperative, and rational users utilize the available but noisy and uncertain side information to achieve their objectives. To tackleuncertaintyandimprovetheutilityofeachuser,weapplyworst-caserobust optimization in noncooperative games and present their analysis for allocating resourcesinwirelessnetworks.Specifically,viavariationalinequalities,wepresent a systematic approach to securing the conditions for the existence and uniqueness ofthegames’equilibria,derivethegapbetweentheutilityvaluesofnonrobustand robustgames,andpresentdistributedalgorithmsforsolvingsuchgames. Preface vii InChapter4,wepresentataxonomyofrelaxationmethodsforsolvingnoncon- vexandintractablerobustoptimizationproblemsforallocatingresourcesinwireless networks and provide several examples of such problems in existing and future wireless networks. We also show how such problems can be solved. In particular, wepresentcasesinwhichuncertaintyinchannelstateinformation(CSI)isassumed tobewithinagivenregion,whenonlystatisticsofuncertaintyinCSIareavailable, orwhennoCSIisavailabletousers,andwediscusstherelevanceofeachcasein futurewirelessnetworks. InChapter5,wepresentabriefoverviewofimportantfeaturesoffuturewireless networks that will affect resource allocation; then we identify important problems inrobustresourceallocationinsuchnetworksthatcanbetackledusingthematerial inChapters1,2,3,and4. We would like to acknowledge the contributions of the coauthors of our joint papersonthetopicsdiscussedinthisbook.OurgratitudegoestoProfessorMihaela vanderSchaar,ProfessorEkramHossain,ProfessorPaeizAzmi,Dr.HamidSaeedi, Dr.MehdiRasti,andDr.MohammadRezaJavanfortheirinvaluablehelp. Wewouldalsoliketoexpressourdeepestappreciationtoourfamilies,fortheir understanding, support, encouragement, and sacrifices while this book was being written.Tothemwededicateourbook. Tehran,Iran SaeedehParsaeefard AhmadRezaSharafat NaderMokari Contents 1 Introduction .................................................................. 1 1.1 Motivation............................................................... 1 1.2 FormulatingResourceAllocationProblems........................... 4 1.3 MathematicalBackground.............................................. 8 1.3.1 StochasticRobustOptimization................................ 8 1.3.2 Worst-CaseRobustOptimization.............................. 9 1.3.3 Hybrid Approach: Bounded Uncertainty andProbabilisticConstraints................................... 11 1.4 GenericSystemModel.................................................. 15 1.4.1 System Model for Wireless Networks with HomogeneousUsers............................................ 17 1.4.2 System Model for Wireless Networks with HeterogeneousUsers ........................................... 18 1.4.3 PhysicalLayerSecurityinWirelessChannels ................ 20 1.5 CostofRobustness...................................................... 25 1.6 OrganizationofThisBook ............................................. 26 References..................................................................... 27 2 RobustCooperativeResourceAllocation ................................. 33 2.1 Introduction ............................................................. 33 2.2 Single-ChannelCellularCognitiveRadioNetworks.................. 35 2.2.1 RobustProblem................................................. 36 2.3 Multi-channelCognitiveRadioNetworks ............................. 49 2.3.1 RobustProblems................................................ 52 2.3.2 Trade-OffAlgorithms .......................................... 60 2.4 Overview of Other Works on Robust Cooperative ResourceAllocation .................................................... 68 2.5 ConcludingRemarks.................................................... 70 Appendices .................................................................... 71 References..................................................................... 77 ix x Contents 3 RobustNoncooperativeResourceAllocation ............................. 81 3.1 Introduction ............................................................. 81 3.2 OverviewofNominalNoncooperativeStrategicGames.............. 83 3.2.1 ExistenceandUniquenessofNE .............................. 85 3.2.2 SocialUtility(SumRate)atNE ............................... 91 3.2.3 DistributedAlgorithms......................................... 93 3.3 Worst-CaseRobustPowerControlinNoncooperativeGames ....... 95 3.3.1 Robust Power Control for Noncooperative HomogeneousUsers............................................ 95 3.3.2 RobustPowerControlinNoncooperativeCRNs.............. 111 3.3.3 Robust Power Control for Noncooperative HeterogeneousUsers ........................................... 114 3.4 ConcludingRemarks.................................................... 122 Appendices .................................................................... 124 References..................................................................... 140 4 NonconvexRobustProblems ............................................... 145 4.1 Introduction ............................................................. 145 4.2 TaxonomyofRelaxationMethods ..................................... 146 4.2.1 DirectRelaxation ............................................... 148 4.2.2 LagrangianRelaxation.......................................... 177 4.3 ApplicationofRelaxationMethodsforRobustResource Allocation ............................................................... 180 4.3.1 PartialCSIFeedback:BoundedUncertainty.................. 181 4.3.2 PartialCSIFeedback:StochasticUncertainty................. 212 4.3.3 NoCSIFeeback................................................. 222 4.4 ConcludingRemarks.................................................... 227 Appendices .................................................................... 228 References..................................................................... 229 5 ConclusionsandFutureResearch.......................................... 233 5.1 FutureWirelessNetworks .............................................. 233 5.2 FutureofResourceAllocation.......................................... 236 5.3 ConcludingRemarks.................................................... 237 References..................................................................... 238 Index............................................................................... 241 NotationsandSymbols xi Notationsand Symbols Table1 NotationsandSymbols Notation Description R Setofrealnumbers RC Setofnonnegativerealnumbers RCC Setofpositiverealnumbers Rn Setofn-dimensionalrealvectors Rm(cid:2)n Setofrealm(cid:2)nmatrices C Setofn-dimensionalcomplexvectors Cn Setofcomplexnumbers Hn Setofn(cid:2)ncomplexHermitianmatrices Sn Setofn(cid:2)nsymmetricmatrices Sn Setofsymmetricpositivesemidefinitematrices C Sn Setofsymmetricpositivedefinitematrices CC .(cid:3)/T Matrixorvectortranspose .(cid:3)/(cid:3) Matrixorvectorconjugate (cid:4) Element-wisegreaterthanorequaltoforvectors (cid:5) Element-wisegreaterthanforvectors (cid:6) Element-wiselessthanorequaltoforvectors (cid:7) Element-wiselessthanforvectors .(cid:3)/H ComplexHermitianconjugate tr.A/ TraceofA (cid:2) .A/ MinimumeigenvalueofA min (cid:2) .A/ MaximumeigenvalueofA max (cid:2)C.A/ maxf(cid:2) .A/;0g max vec.A/ VectorobtainedbystackingthecolumnvectorofA I n(cid:2)nidentitymatrix n diagfa1;(cid:3)(cid:3)(cid:3);ang n(cid:2)ndiagonalmatrixwhoseithdiagonalentryisaz k(cid:3)k2andk(cid:3)k1 Euclideannormandvector1-norm,respectively k(cid:3)k MatrixFrobeniusnorm F Ef(cid:3)g Statisticalexpectationfunction Prfg Probabilityfunction exp.(cid:3)/ Exponentialfunction j(cid:3)j2 Magnitudesquaredforscalarsor element-wisemagnitudesquaredforvectors r Vectordifferentialoperator rank.(cid:3)/ Matrixrank R.(cid:3)/ Rangeofmatrix x(cid:8)CN.y;Z/ CircularlysymmetriccomplexGaussianrandomvector withmeanyandcovariancematrixZ RefAgandImfAg RealandimaginarypartsofcomplexmatrixA det.A/ DeterminantofA ˝ Kroneckerproduct ˇ Element-wiseordotproduct
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