Random Wireless Networks An Information Theoretic Perspective

247 Pages·2015·1.845 MB·English

by  Rahul Vaze

Random Wireless Networks
An Information Theoretic Perspective
RahulVaze
CambridgeHouse,4381/4AnsariRoad,Daryaganj,Delhi110002,India
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⃝c RahulVaze2015
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Firstpublished2015
PrintedinIndia
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Vaze,Rahul.
Randomwirelessnetworks:aninformationtheoreticperspective/RahulVaze.
pagescm
Includesbibliographicalreferencesandindex.
Summary:“Providesdetaileddiscussiononsinglehopandmultihopmodel,
feedbackconstraintsandmoderncommunicationtechniquessuchas
multipleantennanodesandcognitiveradios”–Providedbypublisher.
ISBN978-1-107-10232-3(hardback)
1.Wirelesscommunicationsystems.I.Title.
TK5103.2.V392015
621.382’1–dc23
2014044738
ISBN978-1-107-10232-3Hardback
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Contents
ListofFigures vii
Preface xi
Acknowledgments xiv
Notation xv
1 Introduction 1
1.1 Introduction 1
1.2 Point-to-PointWirelessSignalPropagationModel 3
1.3 ShannonCapacity 5
1.4 OutageCapacity 6
1.5 WirelessNetworkSignalModel 7
1.6 ConnectivityinWirelessNetworks 10
Bibliography 11
2 TransmissionCapacityofadhocNetworks 12
2.1 Introduction 12
2.2 TransmissionCapacityFormulation 13
2.3 BasicsofStochasticGeometry 16
2.4 RayleighFadingModel 19
2.5 Path-LossModel 22
2.6 OptimalALOHATransmissionProbability 26
2.7 CorrelationswithALOHAProtocol 27
2.8 TransmissionCapacitywithSchedulinginWirelessNetworks 31
2.9 ReferenceNotes 41
Bibliography 42
3 MultipleAntennas 43
3.1 Introduction 43
3.2 RoleofMultipleAntennasinadhocNetworks 44
3.3 ChannelStateInformationOnlyatReceiver 44
3.4 ChannelStateInformationatBothTransmitterandReceiver 58
3.5 Spectrum-Sharing/CognitiveRadios 66
3.6 ReferenceNotes 77
Bibliography 77
v
vi Contents
4 Two-WayNetworks 80
4.1 Introduction 80
4.2 Two-WayCommunication 80
4.3 EffectofLimitedFeedbackonTwo-WayTransmissionCapacitywithBeamforming 90
4.4 ReferenceNotes 94
Bibliography 94
5 PerformanceAnalysisofCellularNetworks 95
5.1 Introduction 95
5.2 RandomCellularNetwork 96
5.3 Distance-DependentShadowingModel 103
5.4 ReferenceNotes 113
Bibliography 114
6 DelayNormalizedTransmissionCapacity 116
6.1 Introduction 116
6.2 DelayNormalizedTransmissionCapacity 117
6.3 FixedDistanceDedicatedRelaysMulti-HopModelwithARQ 127
6.4 SharedRelaysMulti-HopCommunicationModel 137
6.5 ReferenceNotes 144
Bibliography 144
7 PercolationTheory 146
7.1 Introduction 146
7.2 DiscretePercolation 147
7.3 ContinuumPercolation 154
7.4 ReferenceNotes 175
Bibliography 175
8 PercolationandConnectivityinWirelessNetworks 176
8.1 Introduction 176
8.2 SINRGraph 177
8.3 PercolationonthePSG 177
8.4 ConnectivityontheSINRGraph 185
8.5 InformationTheoreticSecureSINRGraph 192
8.6 ReferenceNotes 200
Bibliography 200
9 ThroughputCapacity 202
9.1 Introduction 202
9.2 ThroughtputCapacityFormulation 203
9.3 InformationTheoreticUpperBoundontheThroughputCapacity 214
9.4 ExtendedNetworks 221
9.5 ReferenceNotes 223
9.A HierarchicalCooperation 223
9.B MutualInformationofMultipleAntennaChannelwithQuantization 224
Bibliography 228
Index 229
List of Figures
2.1 Transmission capacity with Rayleigh fading and path-loss model with ALOHA
protocol. 26
2.2 Network goodput G with Rayleigh fading as a function of ALOHA access
probabilityp. 27
2.3 Dotsrepresenttransmittersandsquaresrepresentreceivers.Onlythosetransmitters
(squares)areallowedtotransmitthatlieoutsidethediscsofradiusd centeredat
gz
allthereceivers. 32
2.4 TransmissioncapacitywithRayleighfadingasafunctionofguardzonedistanced . 34
gz
2.5 A pictorial description of PPP Φ in comparison to original process Φ, where the
h
densityincreaseswithincreasingdistancefromtheorigin. 36
2.6 NetworkgoodputwithRayleighfadingasafunctionofCSMAtransmitterchannel
accessthresholdofτ forneighbourhoodcontentionthresholdofτ =1. 37
h c
2.7 Network goodput with Rayleigh fading as a function of CSMA neighbourhood
contentionthresholdτ withchannelaccessthresholdofτ =1. 38
c h
2.8 SpatialmodelforCSMAwithpacketarrivals. 39
2.9 OutageprobabilitycomparisonofALOHAandSINR-basedCSMAwithRayleigh
fading. 41
3.1 Transmit-receivestrategywithnoCSIatthetransmitter. 45
3.2 Squares represent the N nearest canceled interferers with dashed lines, solid
canc
circles represent the r nearest uncanceled interferers whose interference
contribution will be used to derive the lower bound on the outage probability, and
unfilledcirclesarealltheotheruncanceledinterferers. 51
3.3 Transmission capacity versus N with CSIR while canceling the nearest interferers
fork =1,d=1m,β =1bits,α=3,ϵ=0.1. 56
3.4 Transmit-receivestrategywithbeamformingatthetransmitter. 60
3.5 EmpiricalexpectedvalueofthereciprocalofthelargesteigenvalueofH00H†00. 63
3.6 Transmission capacity versus the number of antennas N with multimode
beamforming and canceling the nearest interferers with single stream data
transmissionk =1,d=5m,β =1(B =1bits/sec/Hz),α=4,ϵ=0.1. 64
3.7 Transmission capacity versus the number of transmitted data streams k with
multimode beamforming and canceling the nearest interferers with d = 5 m,
β =1,α=4,ϵ=0.1,totalnumberofantennasN =8. 65
vii
viii ListofFigures
3.8 Transmit-receivestrategyofsecondarytransmittersandreceivers(dots)andprimary
transmittersandreceivers(squares),whereeachsecondarytransmittersuppressesits
interferencetowarditsN 1nearestprimaryreceivers. 68
t
−
3.9 Each dot (secondary transmitter) suppresses its interference toward its 3 nearest
squares (primary receivers) denoted by dashed lines, but still a square can receive
interferencefromoneofits3nearestdots. 69
3.10 Density of the secondary network with respect to number of transmit and receive
antennasN ,N atthesecondarynodes. 72
t r
4.1 Schematic for wireless network with two-way communication, where black dots
representnodesofΦ andgraydotsrepresentnodesofΦ . 81
T R
4.2 Schematicoftwo-waycommunicationwithtwopairsofnodes. 85
4.3 Comparisonofone-wayandtwo-waytransmissioncapacitywithd = 5m,α = 4,
B =1Mbits,B =0.03Mbits,F =1.1MHz,andF =1MHz. 87
TR RT TR
4.4 Two-waytransmissioncapacityasafunctionofbandwidthallocation. 88
4.5 Comparisonoftransmissioncapacityperformanceofbeamformingwithgenie-aided
andpracticalfeedbackasafunctionofnumberoftransmitantennasN. 93
5.1 (a) Multi-tier wireless network with macro (dots), femto (circles), and pico
basestations (squares) versus (b) the random cellular network deployment with
identical density. Fig. (a) shows the Voronoi regions of macro basestations, while
(b)showsthetheVoronoiregionsofallbasestationscombined. 96
5.2 ConnectionprobabilityP (β)asafunctionofthebasestationdensityλ.Fortheno
c
noisecase,P (β)isinvarianttoλ.Withadditivenoise,P (β)doesdependonλ,but
c c
thedependenceisveryminimal,andnonoiseassumptionisfairlyaccurate. 100
5.3 Connection probability P (β) as a function of SINR threshold β for λ = 1 and
c
path-lossexponentα=4. 101
5.4 ComparingtheconnectionprobabilityP (β)asafunctionofSINRthresholdβ for
c
λ= 1andpath-lossexponentα = 4fortherandomwirelessnetworkandasquare
gridnetwork. 103
5.5 Circle nodes are basestations and the square node is the receiver. The blockage
processisdescribedbyrandomlyorientedrectangles,andthethicknessoftheline
between basestations and receiver indicates the relative signal strength at the
receiverthatisinverselyproportionaltothenumberofblockagescrossingthelink. 105
5.6 Link of length d between basestation T and mobile user at o. Any rectangle of
L
Σ(C ,ℓ,w,θ)intersects onlyifitscenterliesintheregiondefinedbyvertices
k n
L
ABCDEF, where each vertex is the center of the six rectangles of length ℓ and
widthw. 107
5.7 ConnectionprobabilityasafunctionofthebasestationdensityforE[L]=E[W]=
15m,µ =4.5 10 4/m2,λ =3.5 10 5/m2,α=4,andP =1. 112
0 − 0 −
× ×
6.1 Retransmission strategywhere in anyslot, retransmission (shadedsquare) is made
if1 =1andnoattemptismade(emptysquare)otherwise. 119
Ts(t)
6.2 SuccessprobabilityasafunctionofDforN =1. 126
h
6.3 Schematicofthesystemmodelwhereconnectedlinesdepictapathbetweenasource
anditsdestination. 128
ListofFigures ix
6.4 Success probability as a function of number of retransmissions D for a two-hop
network N = 2 with d = d = 1m and equally dividing the retransmissions
h 1 2
constraintovertwohops,D =D =D/2. 132
1 2
6.5 Delay normalized transmission capacity as a function of retransmissions used on
firsthopD withtotalretransmissionsD = 4,forequidistantandnon-equidistant
1
twohopsN =2. 135
h
6.6 Delay normalized transmission capacity as a function of number of hops N for
h
λ=0.1andλ=0.5. 138
6.7 Transmissionmodelformulti-hopcommunication,wheredotsaretransmittersand
squares are receivers, and the spatial progress for T is the largest projection of
0
squaresonthex-axisforwhiche =1. 143
0j
7.1 SquarelatticeZ2 withopenandclosededges. 148
7.2 Dual latticeD2 of the square lattice Z2 is represented with dashed lines, where an
edgeisopen/closedinD2 iftheedgeofZ2intersectingitisopen/closed. 149
7.3 DepictionofaclosedcircuitofduallatticeD2 surroundingtheorigin. 150
7.4 Countingthemaximumnumberofclosedcircuitsoflengthnsurroundingtheorigin. 151
7.5 Left-rightcrossingsofboxB byconnectedpathsofsquarelatticeZ2. 153
n/2
7.6 HexagonaltiltingofR2 witheachfaceopen(shaded)/closedindependently. 154
7.7 Gilbert’sdiscmodelwhereeachnodehasaradioranger/2andanytwonodesare
connectedthatareatadistanceoflessthanr. 155
7.8 InvariancepropertyoftheGilbert’sdiscmodelunderfixedλr2,wherescalingradio
rangeby1/randscalingdistancebetweenanytwonodesalsoby 1 hasnoeffecton
r
theconnectionmodel,wherethetwo-sidedarrowdepictsanedge. 156
7.9 MappingGilbert’sdiscmodelonahexagonaltilingofR2,whereafaceisopenifit
containsatleastonenodeofΦ. 157
7.10 Thelargestregionforfindingnewneighborsofx thatarenotneighborsoftheorigin.158
1
7.11 ArealizationoftheGilbert’srandomdiscmodel,whereeachnodex hasradiusr
i i
andtwonodesaredefinedtobeconnectediftheircorrespondingdiscsoverlap. 166
7.12 DepictionofscenarioconsideredforobtainingProposition7.3.20,wherethefarthest
nodeliesoutsideofB andeventG(r). 168
10r
7.13 Covering of B B by discrete points (black dots) lying on the boundary of B
10 9 10
\
usingboxesB . 169
1
7.14 Depiction of scenario when both events E(o,10r) and A (r) occur
B100r
simultaneously,givingrisetotwosmallereventsthatarei.i.d.withE(o,r)around
B andB . 171
10r 80r
8.1 DefinitionofeventA foranyedgeeinS. 179
e
8.2 TwoadjacentopenedgesofSimplyaconnectedcomponentofG (λ,r)crossing
P
rectangle R ’s corresponding to the open edges of S. Solid lines are for rectangle
e
R anddashedlinesforR . 181
e1 e2
8.3 Squaregridformedbycenters(representedasdots)ofedgesofSwithside s . 184
√2
8.4 Square tiling of the unit square, and pictorial definition of square s (m) for each
t
nodex . 186
t
8.5 Coloringthesquaretilingoftheunitsquarewithfoursetsofcolors. 188