Robust Resource Allocation in Future Wireless Networks

255 Pages·2017·3.74 MB·English

by  Saeedeh Parsaeefard

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
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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