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Free Space Optical Communication 1st Edition Hemani Kaushal

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Optical Networks

Series Editor: Biswanath Mukherjee

Hemani Kaushal

V.K. Jain

Subrat Kar

Free Space Optical Communication

OpticalNetworks

Serieseditor

BiswanathMukherjee,Davis,California,USA

Moreinformationaboutthisseriesat http://www.springer.com/series/6976

HemaniKaushal•V.K.Jain•SubratKar

FreeSpaceOptical Communication

HemaniKaushal

ElectronicsandCommunication

TheNorthCapUniversity Gurgaon,Haryana,India

SubratKar

ElectricalEngineering IndianInstituteofTechnologyDelhi NewDelhi,India

ElectricalEngineering IndianInstituteofTechnologyDelhi NewDelhi,India

ISSN1935-3839ISSN1935-3847(electronic)

OpticalNetworks

ISBN978-81-322-3689-4ISBN978-81-322-3691-7(eBook) DOI10.1007/978-81-322-3691-7

LibraryofCongressControlNumber:2016963412

©Springer(India)Pvt.Ltd.2017

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Preface

Inrecentyears,thetechnologyofopticalcommunicationhasgainedimportance duetohighbandwidthanddataraterequirements.Thisbookfocusesonfree-space optical(FSO)communicationthatiscapableofprovidingcable-freecommunicationatveryhighdatarates(uptoGbps).Unlikeradiofrequencycommunication thathasrestrictedbandwidthduetoitslimitedspectrumavailabilityandinterference,FSOcommunicationhaslicense-freespectrumasofnow.Thistechnology findsitsapplicationinterrestriallinks,deepspace/inter-satellitelinks,unmanned aerialvehicles(UAVs),high-altitudeplatforms(HAPs),anduplinkanddownlink betweenspaceplatform,aircrafts,andotherground-basedfixed/mobileterminals. Itprovidesgoodprivacywithflexibleinterconnectionthroughadistributedor centralizedcommunicationsystem.Itisagrowingareaofresearchthesedaysdueto itslowpowerandmassrequirement,bandwidthscalability,unregulatedspectrum, rapidspeedofdeployment/redeployment,andcost-effectiveness.However,despite manyadvantages,theperformanceofFSOcommunicationsystemisinfluenced byunpredictableatmosphericconditions,andthisundoubtedlyposesagreat challengetoFSOsystemdesigners.TheprimaryfactorsthatdeterioratetheFSO linkperformanceareabsorption,scattering,andturbulence.Outofthese,the atmosphericturbulenceisamajorchallengethatmayleadtoseriousdegradation inthelinkperformanceandmakethecommunicationlinkinfeasible.Thisbook givesthebasicunderstandingofFSOcommunicationsystemandlaysemphasison improvingtheperformanceofFSOlinkinturbulentatmosphere.

ThepurposeofthisbookistocoverthebasicconceptsofFSOcommunication systemandprovidethereaderswithsufficientin-depthknowledgetodesign awirelessopticallink.Theintendedreadersforthisbookincludeengineers, designers,orresearcheswhoareinterestedinunderstandingthephenomenaoflaser beampropagationthroughtheatmosphere.Thisbookprimarilyfocusesonoutdoor wirelesscommunication,thoughalittlebriefingonindoorwirelesscommunication isgivenintheintroductorychapter.Althoughthisbookisbasedonthedoctoral workofthefirstauthor,ithasbeencompletelyrewrittenandexpandedtocover basicconceptsofFSOcommunicationsystemfromreaders’pointofview.

Thisbookhasbeenorganizedintosevenchapters.Chapter 1 providesan overviewofFSOtechnologywithhistoricalbackgroundanditsvariousapplications.

Chapter 2 givesacomprehensivecoverageofFSOchannelmodelsandvarious atmosphericlossesencounteredduringbeampropagationthroughtheatmosphere includingfree-spaceloss,pointingloss,absorption,andscatteringloss.Thisis followedbythedescriptionofatmosphericturbulenceanditseffectsonthelaser communication,i.e.,beamwander,beamspreading,beamscintillation,spatial coherencedegradation,andimagedancing.Variousmodelsfortheatmospheric turbulentchannelarepresented.Chapter 3 discussesvariouscomponentsofFSO communicationsystem.Itprovidesdescriptionofopticaltransmitter,amplifiers, andreceiver.Thedesignofopticalreceiverthattakesintoaccountdifferenttypes ofdetectors,noisesources,andreceiverperformanceintermsofsignal-to-noise ratioispresented.Finally,variousissuesinvolvedinthelinkdesignlikechoice ofoperatingwavelength,aperturediameter,andreceiverbandwidtharediscussed.

Chapter 4 dealswiththemostchallengingaspectofFSOcommunicationsystem, i.e.,acquisition,tracking,andpointing.Theinitiallinkuporacquisitiontimeputs alimitontheoverallperformanceofthesystem,andhence,itisanessential systemdesignconstraint.Varioussubsystemsinvolvedintheaccuratepointing ofnarrowlaserbeamtowardthetargetarepresentedinthischapter.Chapter 5 presentsbiterrorrate(BER)performanceofFSOlinkforcoherentandnoncoherent modulationschemes.Chapter 6 discussesvarioustechniquesforimprovinglink performance,i.e.,apertureaveraging,spatialdiversity,coding,adaptiveoptics, relay-assistedFSO,etc.Finally,thelastchapterdescribesindetailhowtheoptical systemdesignerscancalculatelinkbudgets.

Gurgaon,IndiaHemaniKaushal NewDelhi,IndiaV.K.Jain NewDelhi,IndiaSubratKar

1OverviewofWirelessOpticalCommunicationSystems

1.1Introduction

1.1.1History

1.1.2IndoorWirelessOpticalCommunication

1.1.2.1TypesofLinkConfigurations

1.1.3Outdoor/Free-SpaceOpticalCommunication

1.2ComparisonofFSOandRadio-Frequency CommunicationSystems ...............................................12

1.3ChoiceofWavelengthinFSOCommunicationSystem

1.4RangeEquationforFSOLink

1.5TechnologiesUsedinFSO

1.5.1DirectDetectionSystem ........................................21

1.5.1.1BasebandModulation

1.5.1.2StatisticalModelforDirectDetection

1.5.1.3SubcarrierModulation

1.5.2CoherentDetection

1.5.3OpticalOrthogonalFrequency-DivisionMultiplexing

1.6EyeSafetyandRegulations

2.1AtmosphericChannel

2.1.1AtmosphericLosses

2.1.1.1AbsorptionandScatteringLosses

2.1.1.2Free-SpaceLoss

2.1.1.3BeamDivergenceLoss

2.1.1.4LossduetoWeatherConditions

2.1.1.5PointingLoss .........................................52

2.1.2AtmosphericTurbulence

2.1.2.1TheEffectofBeamWander

2.1.2.2TheScintillationEffect ..............................59

2.1.3EffectofAtmosphericTurbulenceonGaussian Beam ............................................................63

2.1.3.1ConventionalRytovApproximation

2.1.3.2ModifiedRytovApproximation

2.2AtmosphericTurbulentChannelModel

2.3TechniquesforTurbulenceMitigation

2.3.1ApertureAveraging

2.3.2SpatialDiversity ................................................80

2.3.3AdaptiveOptics .................................................82

2.3.4Coding ..........................................................83

2.3.5HybridRF/FSO .................................................84

2.4Summary ................................................................85 Bibliography

3FSOSystemModulesandDesignIssues

3.1OpticalTransmitter

3.1.1ChoiceofLaser

3.1.2Modulators

3.1.2.1ModulationSchemes .................................98

3.2OpticalReceiver .........................................................99

3.2.1TypesofDetectors ..............................................103

3.2.2ReceiverConfiguration .........................................105

3.2.2.1CoherentPSKHomodyneReceiver .................106

3.2.2.2CoherentFSKHeterodyneReceiver ................108

3.2.2.3DirectDetection(PIN+OA)Receiver forOOK ...............................................108

3.2.2.4DirectDetection(APD)Receiverfor OOK ..................................................110

3.2.2.5DirectDetection(APD)for M-PPM ................112

3.3OpticalPostandPreamplifiers .........................................113

3.4LinkDesignTrade-Off ..................................................115

3.4.1OperatingWavelength ..........................................115

3.4.2ApertureDiameter ..............................................116

3.4.3ReceiverOpticalBandwidth ...................................116

3.5Summary ................................................................117 Bibliography ...................................................................118

4Acquisition,Tracking,andPointing .......................................119

4.1AcquisitionLinkConfiguration ........................................119

4.1.1AcquisitionUncertaintyArea ..................................122

4.1.1.1ProbabilityDistributionFunctionof SatellitePosition ......................................123

4.1.2ScanningTechniques ...........................................124

4.1.3AcquisitionApproach ..........................................127

4.1.4BeamDivergenceandPowerCriteriafor Acquisition

4.2TrackingandPointingRequirements ..................................130

4.3IntegrationofCompleteATPSystem ..................................133

4.4ATPLinkBudget ........................................................134

4.5Summary

5BERPerformanceofFSOSystem

5.1SystemModel

5.2BEREvaluation

5.2.1CoherentSubcarrierModulationSchemes

5.2.2NoncoherentModulationSchemes ............................145

5.2.2.1OnOffKeying ........................................145

5.2.2.2 M-aryPulse-PositionModulation

5.2.2.3DifferentialPPM .....................................150

5.2.2.4DifferentialAmplitudePulse-PositionModulation .153

5.2.2.5DigitalPulseIntervalModulation ...................154

5.2.2.6DualHeader-PulseIntervalModulation

5.3Summary ................................................................159

6.1ApertureAveraging

6.1.1ApertureAveragingFactor

6.1.1.1PlaneWavewithSmall

6.1.1.2PlaneWavewithLarge lo

6.1.1.3SphericalWavewithSmall lo ........................164

6.1.1.4SphericalWavewithLarge

6.2ApertureAveragingExperiment

6.3Diversity .................................................................168

6.3.1TypesofDiversityTechniques .................................170

6.3.2DiversityCombiningTechniques ..............................171

6.3.3Alamouti’sTransmitDiversityScheme ........................175

6.3.4TwoTransmitterandOneReceiverScheme ...................176

6.3.5BERPerformancewithandWithoutSpatialDiversity .......178

6.4Coding ...................................................................181

6.5ChannelCapacity .......................................................182

6.5.1ChannelCodinginFSOSystem ...............................183

6.5.1.1ConvolutionalCodes .................................184

6.5.1.2LowDensityParityCheckCodes ...................187

6.6AdaptiveOptics .........................................................189

6.7Relay-AssistedFSOTransmission .....................................192

6.8Summary ................................................................193 Bibliography ...................................................................194

7.1LinkRequirementsandBasicParameters

7.1.1TransmitterParameters .........................................198

7.1.2AtmosphericTransmissionLossParameter ...................200

7.1.3ReceiverParameters ............................................200

7.2LinkPowerBudget .....................................................201

7.3Summary

ListofFigures

Fig.1.1Classificationofwirelessopticalcommunicationsystems .........2

Fig.1.2ApplicationsofWOCs:(a)chip-to-chip communication,(b)wirelessbodyareanetwork, (c)indoorIRorvisiblelightcommunication,(d) inter-buildingcommunication,and(e)deepspacemissions .......3

Fig.1.3FSOterrestriallink ...................................................5

Fig.1.4DirectedLOSlink ....................................................7

Fig.1.5Multi-beamnon-directedLOSlink ..................................8

Fig.1.6Diffusedlink ..........................................................8

Fig.1.7Multi-beamquasidiffusedlinks.(a)Receiverwith multiplelensarrangement.(b)Receiverwithsingle lensarrangement .....................................................9

Fig.1.8ApplicationsofFSOcommunicationlinks ..........................11

Fig.1.9BlockdiagramofFSOcommunicationlink .........................11

Fig.1.10ComparisonofopticalandRFbeamdivergencefrom MarstowardEarth ....................................................13

Fig.1.11Demonstrationofopticalemissionfromlightsource. (a)LightemissionfromLambertiansource.(b)Light emissionusingbeamformingoptics .................................18

Fig.1.12Opticalmodulators.(a)Internalmodulator.(b)Externalmodulator 21

Fig.1.13Blockdiagramofdirectdetectionreceiver ..........................22

Fig.1.14OOKmodulationschemeforthetransmissionof message110010 ......................................................23

Fig.1.158-PPMschemewitheightslotsforthetransmissionof message110010 ......................................................23

Fig.1.16BlockdiagramofSIMforFSOlink .................................26

Fig.1.17ModulationschemesinFSOsystem .................................27

Fig.1.18Blockdiagramofcoherentopticalcommunicationsystem .........27

Fig.1.19BlockdiagramofOFDMbasedFSOsystem ........................30

Fig.1.20Pictorialrepresentationoflightabsorptionintheeye fordifferentwavelengths .............................................32

Fig.1.21Absorptionoflightvs.wavelength ..................................33

Fig.2.1Broadclassificationofatmosphericlayers ..........................42

Fig.2.2Variousatmosphericlayerswithcorrespondingtemperatures ......42

Fig.2.3Atmospherictransmittance(attenuation)vs.wavelength ...........43

Fig.2.4Averageparticlesizeandcorrespondingparticle densityinatmosphere .................................................43

Fig.2.5Skyradianceduetoscatteringmechanism ..........................46

Fig.2.6Lossduetobeamdivergence .........................................47

Fig.2.7Beamexpandertoincreasediffractionaperture .....................48

Fig.2.8Attenuationvs.visibility.(a)Forheavyfogandcloud. (b)Forlightfogandhaze ............................................51

Fig.2.9Attenuationforfog,snowandrain ...................................52

Fig.2.10Kolmogorovmodelwhere L0 and l0 aretheouterand innerscaleofturbulenteddies,respectively .........................54

Fig.2.11Beamwandereffectdescribedby(a)Movementof the“hotspot”withinthebeamand(b)Beamwander variance ˝r 2 c ˛1=2 D qW 2 LT W 2 ST ,where W ST isthe short-termbeamradiusand W LT thelong-termbeam radiusatthereceiver(the shadedcircles depictrandom motionoftheshort-termbeaminthereceiverplane) ...............57

Fig.2.12Thermsangularbeamwandervarianceasafunctionof transmitterbeamradiusforground-to-satelliteFSOlink ...........58

Fig.2.13Flattenedbeamprofileasafunctionofradial displacementthatleadstoeffectivepointingerror pe ..............59

Fig.2.14Variousdistributionsforintensitystatistics .........................63

Fig.2.15Representationof(a)convergentbeam,(b)collimated beam,and(c)divergentbeam,respectively .........................64

Fig.2.16Gaussianbeamprofileparametersforuplink propagationpath ......................................................65

Fig.2.17Effectivebeamradiusatthereceiver(inm)asa functionoftransmitterbeamradius(incm)forvarious zenithangles ..........................................................69

Fig.2.18Variationsofatmosphericstructureconstantwith altitudefortheFriedmodel ..........................................72

Fig.2.19ComparisonofHVB,HS,CLEAR1,andSLCmodels foratmosphericstructureparameterconstant .......................74

Fig.2.20 C 2 n .h/ profileasafunctionofaltitude ...............................76

Fig.2.21Log-irradiancevarianceasafunctionofrmswind velocity V forzenithangle D 0ı ;30ı ;40ı and 60ı ..............77

Fig.2.22Powerfluctuationsforsmalldetectorplaced145km fromthetransmitter ...................................................77

Fig.2.23Scatteredopticalsignalfromturbulentcellswithin acceptancecone(a)geometricalopticsholdgoodif conewidthislessthanthecelldimensionand(b) diffractioneffectbecomesimportantifconewidth includemanyturbulentcells .........................................78

Fig.2.24Specklespotformationonthereceiverplane .......................79

Fig.2.25Variationsofapertureaveragingfactorwithzenith angle forvariousvaluesofreceiveraperturediameter DR D 15;20 and 30 cmusingHVB5/7model ......................80

Fig.2.26Conceptof(a)receivediversity,(b)transmitdiversity and(c)multipleinputmultipleoutput(MIMO)techniques ........81

Fig.2.27Blockdiagramofanadaptiveopticssystem ........................83

Fig.2.28Channelcapacityvs.peak-to-averagepowerratiofor variousratiosofsignalandbackgroundphotonarrivalrates .......84

Fig.3.1Schematicrepresentationofvariouscomponentsfor ground-to-satelliteopticallink .......................................92

Fig.3.2Schematicdiagramofphasemodulator .............................97

Fig.3.3IntegratedopticLiNbO3 phasemodulator ...........................97

Fig.3.4Mach-Zehnderamplitudemodulator .................................98

Fig.3.5Geometryof(a)extendedsourcewhen FOV < S and(b)stellarorpointsourcewhen FOV > S ...................101

Fig.3.6QuadrantAPDshowingstandarddeadzoneandshared transition ..............................................................105

Fig.3.7Ageneralopticalcommunicationreceivervalidforall configurations .........................................................106

Fig.3.8Variationof Pe withaverage PR forcoherentreceivers ............108

Fig.3.9Variationof Pe withaverage PR fordirectdetection receivers ..............................................................111

Fig.4.1Conceptofacquisitionlinkestablishmentbetween initiatingandtargetparties ..........................................120

Fig.4.2Conceptofpointaheadangle ........................................121

Fig.4.3IllustrationofpointaheadangleinFSOcommunication system .................................................................121

Fig.4.4Variouscontributorstotheacquisitioninitial uncertaintyareabudgetforground-to-satelliteFSOlink ...........122

Fig.4.5Probabilityofacquisitionasafunctionoftheratioof half-widthofuncertaintyarea, U ,tothedeviationof satelliteposition, ...................................................124

Fig.4.6Spiralscanpattern(a),continuousspiralscan,and(b) stepspiralscan ........................................................125

Fig.4.7Single-scanmeanacquisitiontimevs.fieldof uncertainty ............................................................126

Fig.4.8Segmentedandrasterscan,(a)segmentedscan,and(b) rasterscan ............................................................127

Fig.4.9Stare/scanacquisitiontechniquewhereoneterminal (TerminalA)slowlyscansitstransmittingsignalwhile otherterminal(TerminalB)scansthroughitsentire uncertainregion .......................................................128

Fig.4.10Totalpointingerror ...................................................130

Fig.4.11Quadrantdetector .....................................................131

Fig.4.12BlockdiagramofATPsystembetweengroundstation andonboardsatellite ..................................................134

Fig.5.1Thereceivedirradiancepdfforvariousvaluesof receiverantennae(M D 1;3;7; and 10)inweak atmosphericturbulencelevelof 2 I D 0:25 .........................140

Fig.5.2Biterrorprobabilityvs.SNRforSC-BPSKand SC-QPSKmodulationschemesforweakatmospheric turbulence .............................................................144

Fig.5.3TheBERvs.receiversensitivityfordifferentnoise sourcesinweakturbulencelevelof 2 I D 0:3 .......................144

Fig.5.4BERvs.SNRforOOKmodulationschemeinweak atmosphericturbulence ...............................................147

Fig.5.5VariationinthresholdlevelofOOKvs.logintensity standarddeviationforvariousnoiselevels ..........................147

Fig.5.6Waveformfor4-PPMscheme ........................................148

Fig.5.7Biterrorprobabilityvs.SNRfor4-PPMschemein weakatmosphericturbulence ........................................149

Fig.5.8BERasafunctionofscintillationindexfor Kb D 10, T =300K, D 0:028, Rb D 155 Mbps,and M D 150 ...............151

Fig.5.98-DPPMschemeforthetransmissionofmessage110010 .........151

Fig.5.10Waveformsfor(a)4-PPMand(b)4-DPPMusing rectangularpulse. Pt istheaveragetransmittedpower and Tc isthechipduration ............................................152

Fig.5.11Thesymbolstructurefor(a)DPPM(M D 4)and(b) DAPPM(A D 2, M D 2) .............................................153

Fig.5.12ComparisonofsymbolstructureforPPMandDPIM forsametransmittedsourcebitcombination,i.e.,01and10 .......155

Fig.5.13ComparisonofpacketerrorrateperformanceofPPM andPIMschemesformodulationlevels2,4,and8 withsameaveragepowerpersymbol ................................156

Fig.5.14ComparativepacketerrorrateperformanceforDPIM, PPM,andOOKschemesvs.averagereceivedirradiance ..........156

Fig.5.15SymbolstructureofDHPIMschemewith(a) H0 and (b) H1 headers ........................................................157

Fig.5.16PlotofvariantsofPPMfor(a)capacityofvariantsof PPMnormalizedtocapacityofOOKand(b)average opticalpowerrequirementtoachievepackererror rate= 10 6 overdispersivechannel ..................................158

Fig.6.1Variationofapertureaveragingfactor, Af with normalizedreceiverlensradius, d forvarious atmosphericturbulenceconditions ...................................162

Fig.6.2Variationofapertureaveragingfactor, Af fordifferent aperturediameters, DR with(a)horizontallink propagationand(b)slantlinkpropagation .........................164

Fig.6.3Apertureaveragingfactor, Af fordifferentpropagation models(i.e.,plane,sphericalandGaussian)in(a) moderateand(b)strongatmosphericturbulence ....................165

Fig.6.4Apertureaveragingexperiment.(a)Three-dimensional viewofOTGchamberand(b)experimentalsetup ..................166

Fig.6.5Theoreticalandexperimentalresultsofaperture averaging .............................................................168

Fig.6.6Representationof(a)frequencydiversityand(b)time diversity ...............................................................170

Fig.6.7Representationof(a)receiveand(b)transmitspatial diversity ...............................................................171

Fig.6.8Selectioncombining .................................................172

Fig.6.9Maximumratiocombining ..........................................173

Fig.6.10Equalgaincombining ................................................175

Fig.6.11Alamouti’stransmitdiversityschemewithtwotransmit andonereceiveantennae .............................................177

Fig.6.12Biterrorprobabilityvs.SNRwithspatialdiversityin weakturbulence . l D 0:1 and 0:3/ forsubcarrier(a) BPSKand(b)QPSKmodulationschemeswhenthere isnocorrelationamongtransmittedantennabeams . D 0:0/ .............................................................180

Fig.6.13Biterrorprobabilityvs.SNRwithspatialdiversityin weakturbulence . l D 0:1 and 0:3/ forSC-BPSK(a)

D 0:3 and(b) D 0:7 .............................................180

Fig.6.14Biterrorprobabilityvs.SNRwithspatialdiversityin weakturbulence . l D 0:1 and 0:3/ forSC-QPSK(a)

D 0:3 and(b) D 0:7 .............................................181

Fig.6.15BlockdiagramofFSOcommunicationsystemwith encoderanddecoder ..................................................183

Fig.6.16Convolutionalencoderwithtwomemoryelementsand coderate=1/2 .........................................................185

Fig.6.17BiterrorprobabilityforSC-BPSKwithconvolutional code(L D 3 and7)andcoderate=1/2 ..............................186

Fig.6.18BiterrorprobabilityforSC-QPSKwithconvolutional code(L D 3 and7)andcoderate=1/2 ..............................187

Fig.6.19BiterrorprobabilitywithLDPCcodeat l D 0:25 for (a)SC-BPSKand(b)SC-QPSK ....................................188

Fig.6.20Conventionaladaptiveopticssystemusingwavefront sensorandreconstructor ..............................................190

Fig.6.21Modelfreeadaptiveopticssystem ...................................191

Fig.6.22RMSwavefronttiltasafunctionofzenithanglefor differenttelescopeapertures .........................................191

Fig.6.23Relayconfigurations:(a)seriesrelayand(b)parallel relay ...................................................................192

Fig.7.1Variationsoflinkmarginwithzenithanglefor SC-BPSKmodulationschemewithandwithout diversityatwavelengths(a) D 1064 nmand(b) D 1550 nm,respectively ...........................................203

ListofTables

Table1.1Chronologyofindooropticalwirelessresearch ....................10

Table1.2ComparisonofindoorWOCandWi-Fisystems ....................10

Table1.3WavelengthsusedinpracticalFSOcommunicationsystem .......16

Table1.4ComparisonofRFandopticalOFDMsystems .....................31

Table1.5LaserclassificationaccordingtoIECandANSI standards .............................................................35

Table1.6Accessibleemissionlimitsfor850and1550nm accordingtoIECstandard ...........................................36

Table1.7VariousrequirementsofClass1and1Mlasersfor850 and1550nm ..........................................................36

Table2.1Molecularabsorptionattypicalwavelengths .......................45

Table2.2Sizeofvariousatmosphericparticlespresentinthe opticalchannelandtypeofscatteringprocess ......................46

Table2.3Visibilityrangevaluescorrespondingtoweatherconditions .......50

Table2.4Rainfallratesandtheirvisibilityranges .............................52

Table2.5Turbulenceprofilemodelsfor C 2 n ....................................75

Table3.1AttributesforlasersusedinFSO ....................................95

Table3.2Typicalvaluesofdarkcurrentforvariousmaterials ................102

Table3.3CommunicationandbeacondetectorsinFSOlink .................103

Table3.4Comparisonbetweencoherentandnoncoherent receiverconfigurations ..............................................105

Table3.5ParametersforFSOlinkdesign ......................................117

Table4.1Acquisition,tracking,andcommunicationlinkmargin (2.5Gbps,DPSKmodulation,BERof 10 9 with5dB codinggainat1550nmwavelength) ................................135

Table5.1Valuesof Ka and Kb fordifferentnoise-limitingconditions ........143

Table5.2Systemparameters ...................................................145

Table5.3Mappingbetweensourcebitsandtransmittedchipsof 4-PPMand4-DPPMschemes .......................................152

Table5.4Mappingbetween4-PPMand4-DPIMchips ......................155

Table5.5Mappingof3-bitOOKwordsintoPPM,DPPM, DHPIM,andDAPPMsymbols ......................................158

Table5.6ComparisonofvariantsofPPM .....................................159

Table6.1Parametersusedinlaboratoryexperimentation

Table6.2 C 2 n R valuesfordifferenttemperaturedifference

Table6.3Alamouti’sspacetimeencodingschemefor two-branchtransmitdiversityscheme ..............................177

Table6.4Comparisonofcodinggainswithconvolutionaland LDPCcodesforSC-BPSKandSC-QPSKmodulation schemesinweakatmosphericturbulence . l D 0:25/ atBER D 10 6 and 10 4 ,respectively ..............................189

Table7.1Linkdesignrequirements ...........................................198

Table7.2Commonlyusedparametersandtheirabbreviationsin linkpowerbudget ....................................................198

Table7.3Valuesofseriescoefficientsforpointinglossfactorcalculation ...200

Table7.4Variouscommunicationlinkcomponents/parameters andtheirvaluesforlinkpowerbudgetcalculations ................201

Table7.5LinkpowerbudgetofSC-BPSKmodulationscheme usingLDPCcodeforground-to-satelliteuplinkatzero zenithangle ...........................................................202

ListofSymbols

s Planaremissionangle

˛a Aerosolabsorptioncoefficient

˛m Molecularabsorptioncoefficient

˛r Angularpointingerror

˛T Transmittertruncationratio

ˇ Modulationindex

ˇa Aerosolscatteringcoefficient

ˇfog . / Specificattenuationoffog

ˇm Molecularscatteringcoefficient

filter

Bandwidthofopticalbandpassfilter

T Rootsumsquareoftwo-axispointingbiaserror Quantumefficiencyofthedetector

Narrow-bandfiltertransmissionfactor

R Receiveropticsefficiency

TP Transmitterpointinglossfactor

T Transmitteropticsefficiency

Atmosphericattenuationcoefficient

2 Mutualcoherencefunctionofsecondorder

code Codinggain

i InstantaneousSNR

R Receiverobscurationratio

s Scatteringangle

T Transmitterobscurationratio

Scalarspatialfrequency

ƒ Receiverbeamparameter(amplitudechangeduetodiffraction)

Operatingwavelength

0 Transmitterbeamparameter(amplitudechangeduetodiffraction)

B Rateofarrivalofbackgroundphotons

s Rateofarrivalofsignalphotons

˝r 2

c ˛ Beamwanderdisplacementvariance

L Constraintlengthofcode

P Peak-to-averagepowerratioofthesignal

R Rainfallrate

V Characteristicvelocity

F Fresnellength

M Avalanchemultiplicationfactor

r Radiusofatmosphericparticles

h Planck’sconstant

Operatingfrequency

k Kinematicviscosity

b Beamsolidangle

FOV Solidanglereceiverfieldofview

!IF Intermediatefrequency

!L Frequencyoflocaloscillator

S Stellarorpointsourcefieldofview

s Emissionangle

!

s Frequencyofincomingsignal Phaseoftransmittedsignal

ˆn Powerspectraldensityofrefractiveindexfluctuations

‰ Complexphasefluctuations

Correlationamongbeams

2 b Backgroundnoisecurrentvariance

2 d Detectordarkcurrentnoisevariance

2 I Scintillationindex

2 l Varianceoflog-irradiance

pe Effectivepointingerrordisplacement

2 R Rytovvariance

2 s Signalshotnoisevariance

2 Th Thermalnoisevariance

tilt RMSturbulence-inducedwavefronttip/tilt

T Rootsumsquareoftwo-axisjitter

2 x Varianceoflarge-scaleirradiancefluctuations

2 y Varianceofsmall-scaleirradiancefluctuations

2 lnx Varianceoflarge-scalelog-irradiance

2 lny Varianceofsmall-scalelog-irradiance

Opticaldepth

‚ Receiverbeamparameter(amplitudechangeduetorefraction)

‚0

Zenithangle

Transmitterbeamparameter(amplitudechangeduetorefraction)

0 Isoplanaticangle

div Beamdivergence

FOV Angularfieldofviewofreceiver

H Azimuthpointingerrorangle

jitter Beamjitterangle

unc Areaofuncertaintyinsolidangle

V Elevationpointingerrorangle

4fc Coherencebandwidth

4tc Coherencetime

" Overlapfactor

Normalizeddistancevariable

t Safetymarginagainsthigh-frequencyfluctuations

A Photodiodearea

A0 AmplitudeofGaussianbeam

Af Apertureaveragingfactor

AR Effectiveareaofthereceiver

As Surfacearea

B Signalbandwidth

Bd Dopplerspread

Bo Opticalfilterbandwidth

C Channelcapacity

c Velocityoflight

C 2 n Refractiveindexstructureconstant

C 2 t Temperaturestructureconstant

Cv Velocitystructureconstant

D OFDMbiascomponent

DR Receiveraperturediameter

Dt Structurefunctionfortemperature

Dn Structurefunctionforrefractiveindex

Dv Structurefunctionforwindvelocity

ELO Localoscillatorsignalvoltage

ER Receivedsignalvoltage

eL Electricfieldoflocaloscillator

es Electricfieldofincomingsignal

F Excessnoisefactor

f Signalfrequency

F 0 Phasefrontradiusofcurvatureofthebeamatthereceiverplane

F0 Phasefrontradiusofcurvatureofthebeamatthetransmitterplane

Fn Noisefigure

GR Receivergain

GT Transmittergain

H Altitudeofthesatellite

h Plank’sconstant

h0 Altitudeofthetransmitter

HB Backgroundradianceofextendedsources

I Irradiance/intensity

I0 Irradiancewithoutturbulence

I Exo-atmosphericsolarconstant

IBG Backgroundnoisecurrent

Idb Bulkdarkcurrent

Ids Surfacedarkcurrent

Id Darkcurrent

I p Photodetectorcurrent

k Wavenumber

KB Boltzmann’sconstant

Kb Averagenumberofnoisephotons

kb Numberofinformationordatabits

keff Ionizationratio

Ks Averagenumberofsignalphotons

L0 Turbulenteddyouterscalesize

l0 Turbulenteddyinnerscalesize

lf Dimensionofturbulentflow

LG Beamdivergenceloss

Lp Pointingloss

LR Transmissionlossofreceiveroptics

Ls Spacelossfactor

m Numberofmemoryregisters

N Numberofreceivers

n Indexofrefraction

n0 Meanvalueofindexofrefraction

NB Irradianceenergydensitiesofpointsources

nc Lengthofcode

Nr Numberoftotalreceiverscanarearepeats

nsp Spontaneousemissionfactor

Nt Numberoftotaltransmitterscanarearepeats

P 0 Atmosphericpressure

Pacq Probabilityofacquisition

PB Backgroundnoisepower

Pce Probabilityofchiperror

Pdetection Probabilityofdetection

Pew Probabilityofworderror

Pe Probabilityoferror

PL Poweroflocaloscillator

PR Receivedpower

Psp Amplifierspontaneousoutputnoisepower

Ps Powerofincomingsignal

PT Transmittedpower

q Electroniccharge

R Linkrange

r Spatialseparationoftwopointsinspace

r0 Atmosphericcoherencelength

Rb Bitrate

Rdwell Receiverdwelltime

RL Loadresistance

Re Reynoldsnumber

Sn Noisepowerspectraldensity

T AbsolutetemperatureinKelvin

T 0 Atmospherictemperature

T Transmittancefactor

Ta Atmospherictransmittance

Tb Bitduration

Tdwell Transmitterdwelltime

Tm Multipathspread

TSS Singlescanacquisitiontime

Tss Beamspreadduetoatmosphericturbulence

Ts Slotwidth

U Electricfield

W Effectivebeamradiusatthereceiver

W0 Transmitterbeamsize

wc Numberof1sineachcolumninsparsematrix

We Effectivespotsizeinturbulence

WLT Long-termspotsize

wr Numberof1sineachrowinsparsematrix

p Sizedistributioncoefficientofscattering

V Visibilityrange

ListofAbbreviations

AFAmplify-and-Forward

AMAmplitudeModulation

AOAdaptiveOptics

APDAvalanchePhotodetector

ASEAmplifiedSpontaneousEmission

ATPAcquisition,Tracking,andPointing

AWGNAdditiveWhiteGaussianNoise

BERBitErrorRate

BPSKBinaryPhaseShiftKeying

BSTSBoostSurveillanceandTrackingSystem

CALIPSOCloud-AerosolLidarandIRPathfinderSatelliteObservation

CCDCharge-CoupledDevices

CDFCumulativeDistributionFunction

CFCompress-and-Forward

DAPIMDifferentialAmplitudePulseIntervalModulation

DAPPMDifferentialAmplitudePulsePositionModulation

DEFDetect-and-Forward

DHPIMDualHeaderPulseIntervalModulation

DOLCEDeepSpaceOpticalLinkCommunicationsExperiment

DPIMDifferentialPulseIntervalModulation

DPPMDifferentialPulsePositionModulation

EGCEqual-GainCombining

ESAEuropeanSpaceAgency

ETSEngineeringTestSatellite

FDMFrequencyDivisionMultiplexing

FIRFar-Infrared

FMFrequencyModulation

FOUFieldofUncertainty

FOVFieldofView

FPAFocalPixelArray

FSOFree-SpaceOptical

FSOIFSOInterconnect

GOLDGround/OrbiterLasercommDemonstration

GOPEXGalileoOpticalExperiment

HAPHigh-AltitudePlatform

IFIntermediateFrequency

IM/DDIntensityModulated/DirectDetection

IRInfrared

ISROIndianSpaceResearchOrganisation

JPLJetPropulsionLaboratory

KIODOKIrari’sOpticalDownlinktoOberpfaffenhofen

LCSLaserCross-LinkSubsystem

LDLaserDiode

LDPCLow-DensityParityCheck

LEDLight-EmittingDiode

LIRLong-Infrared

LOLocalOscillator

LOLAAirborneLaserOpticalLink

LOSLine-of-Sight

LPFLow-PassFilter

MEMSMicroelectromechanicalSystem

MIRMid-infrared

MISOMultipleInputSingleOutput

MLCDMarsLaserCommunicationDemonstration

MLSDMaximumLikelihoodSequenceDetection

MOLAMarsOrbiterLaserAltimeter

MRCMaximum-RatioCombining

NASANationalAeronauticsandSpaceAdministration

NBFNarrow-BandFilter

NEANoiseEquivalentAngle

NIRNear-Infrared

NRZNon-returntoZero

NSDANationalSpaceDevelopmentAgency

OICETSOpticalInter-orbitCommunicationsEngineeringTestSatellite

OOKOn-OffKeying

OTGOpticalTurbulenceGenerator

PAAPointAheadAngle

PAMPulseAmplitudeModulation

PAPMPulseAmplitudeandPulsePositionModulation

PAPRPeak-to-AveragePowerRatio

PCBPrintedCircuitBoard

PDFProbabilityDensityFunction

PERPacketErrorRate

PPMPulsePositionModulation

QAMQuadratureAmplitudeModulation

QAPDQuadrantAvalanchePhotodetector

QPINQuadrantP-Intrinsic

QPSKQuadraturePhaseShiftKeying

RFRadioFrequency

ROSARFOpticalSystemStudyforAurora

RSSRootSumSquare

RZReturntoZero

SCSelectionCombining

SFTSSpaceFlightTestSystem

SILEXSpaceIntersatelliteLinkExperiment

SIRShort-Infrared

SISOSingleInputSingleOutput

SNRSignal-to-NoiseRatio

SOLACOSSolidStateLaserCommunicationsinSpace

SROILShort-RangeOpticalIntersatelliteLink

TESTroposphericEmissionSpectrometer

TPPMTruncatedPPM

UAVUnmannedAerialVehicle

VLCVisibleLightCommunication

VLSIVery-Large-ScaleIntegration

WBANWirelessBodyAreaNetwork

WLANWirelessLocalAreaNetwork

WOCWirelessOpticalCommunication

WPANWirelessPersonalAreaNetwork

Chapter1

OverviewofWirelessOpticalCommunication Systems

1.1Introduction

WOCcommunicationisconsideredasthenextfrontierforhigh-speedbroadband connectionduetoitsuniquefeatures:extremelyhighbandwidth,easeofdeployment,tariff-freebandwidthallocation,lowpower( 1/2ofradio-frequency(RF) systems),lessmass( 1/2ofRFsystems),smallsize( 1/10thediameterof RFantenna),andimprovedchannelsecurity.Ithasemergedagoodcommercial alternativetoexistingradio-frequencycommunicationasitsupportslargerdata ratesandprovideshighgainduetoitsnarrowbeamdivergence.Itiscapable oftransmittingdataupto10Gbpsandvoiceandvideocommunicationthrough theatmosphere/freespace.WOChavetwobroadcategories,namely,indoorand outdoorwirelessopticalcommunications.IndoorWOCisclassifiedintofour genericsystemconfigurations,i.e.,directedline-of-sight(LOS),non-directedLOS, diffused,andquasidiffused.Outdoorwirelessopticalcommunicationisalsotermed asfree-spaceoptical(FSO)communication.TheFSOcommunicationsystemsare alsoclassifiedintoterrestrialandspacesystems.Figure 1.1 showstheclassification ofWOCsystems.

Overthelastfewyears,massiveexpansioninWOCtechnologyhasbeen observedduetohugeadvancesinoptoelectroniccomponentsandtremendous growthinthemarketofferingwirelessopticaldevices.Itseemstobeoneofthe promisingtechnologiesforaddressingtheproblemofhugebandwidthrequirements and“lastmilebottleneck.”TherearemanycommercialapplicationsofWOC technologywhichincludesground-to-LEO,LEO-to-GEO/LEO-to-ground,GEOto-ground,LEO/GEO-to-aircraft,deepspaceprobes,groundstations,unmanned aerialvehicles(UAVs),high-altitudeplatforms(HAPs),etc.[1–4].Italsofinds applicationsintheareaofremotesensing,radioastronomy,spaceradiocommunication,military,etc.WhenWOCtechnologyisusedoververyshortdistances, itistermedasFSOinterconnects(FSOI),anditfindsapplicationsinchip-tochiporboard-to-boardinterconnections.FSOIhasgainedpopularitythesedays

©Springer(India)Pvt.Ltd.2017

H.Kaushaletal., FreeSpaceOpticalCommunication,OpticalNetworks, DOI10.1007/978-81-322-3691-7_1

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"To complete the purchase of the yacht for Gwendolen. I wanted to give it to her absolutely unencumbered. Mr. Tracy was selling some capital for me and said I must wait till the following settling day for the cash, and I asked Melville to lend me the hundred I needed until the matter was completed. But he didn't send it. He never even answered my letter."

"He tells me he sent you a hundred pounds in notes," Sir Geoffrey said distinctly. "Isn't that true?"

"No," said Ralph indignantly; "it's an absolute lie." He paced the room in angry impatience. It seemed incredible that his own brother could be capable of such an utterly unworthy trick. Sir Geoffrey closed his book with a snap and pressed his lips together.

"I ought to have known you both better," he said; "but Melville's story was so circumstantial, and there was the evidence of your letter, too. I was completely taken in. But now I know what to do."

Ralph stopped abruptly.

"What are you going to do?" he asked.

"Instruct Tracy to take proceedings against Melville for getting money under false pretences."

"But that's punishable with imprisonment," said Ralph aghast.

"Certainly it is," said Sir Geoffrey grimly.

"But you can't make a convict of my brother, and your nephew!"

"Our relationship to him is our misfortune," said Sir Geoffrey, "not our fault. I shall do what I say."

"Look here, Uncle Geoffrey," said Ralph excitedly, "after all, this is largely my affair. I will give you back the hundred pounds—I've got the money now—and I will go to town at once and square accounts with Melville. Did he tell you where he was staying?"

"No," said his uncle; "I did not enquire."

"Well, I'm sure to get news of him at Jermyn Street, if he isn't actually there. Promise to abandon all idea of prosecution, and leave this in my hands. Promise?"

Sir Geoffrey looked with pleasure at his nephew as he stood erect before him, glowing with just indignation, but with chivalrous desire to spare his brother this crowning shame.

"How you two fellows are brothers passes my comprehension," he said. "Well, Ralph, I tell you what I will do. I'll give you a week—you need not go up to town again to-day, for that would be hard on Gwen. I'll give you a week, and if you can make Melville disgorge the money I'll take it back with uncommon satisfaction. If you fail, I reserve liberty of action."

"That's fair, I suppose," said Ralph reluctantly; then he added more hopefully, "but it will be all right; of course, it will be all right."

Sir Geoffrey shook his head doubtfully, but the mellow roar of the gong reverberated through the house announcing luncheon, and he welcomed the interruption.

"Shake hands, my boy," he said. "I'm sorry I misjudged you, even for a moment. And now come along, or Gwen will think I've frightened away your appetite."

He linked his arm within his nephew's, and went into the dining-room with all his wonted cheerfulness restored.

CHAPTER V.

AND AFFINITY.

Possession of money has an invigorating effect upon the majority of people, and Melville, who like most gamblers lived only in the present, awoke in the morning feeling a new man because of the open cheque for £100 which he had secured the night before. No qualms of conscience disturbed his equanimity because of the device he had adopted to obtain it. As soon as his toilette and breakfast were completed he could get the money from the bank, and the future, with its difficulties and complications, might be left to take care of itself. The solid satisfaction derived from the possession of money was enough for the moment.

Moreover, to-day contained an element of surprise in the shape of his pending visit to his unknown relative, and next to money there is probably nothing that has so much charm for the average gambler as the element of surprise, had any kindred spirit been with him at the time Melville would have made wagers upon the age and appearance of this Lady Holt, of whose existence he had never heard before. She was old, of course, and most likely intensely disagreeable; incompatibility of temper was doubtless the reason of her separation from Sir Geoffrey, and desire to avoid scandal the explanation of her complete seclusion from the world. The phrasing of her letter showed that she was precise, and upon that fragmentary piece of evidence Melville erected in imagination a complete living personality, in much the same way as scientists "restore" an entire prehistoric mammoth from a single tooth.

He dressed with particular care, and after an early breakfast went cheerfully downstairs and drove to his uncle's bank. Then, with eighteen five-pound notes in his pocket book and ten pounds in cash in his waistcoat, he was in a position to spend in a sufficiently agreeable manner the hours that intervened before he was due at South Kensington.

A refresher, in the shape of a sherry and bitters at the club, was followed by a delicate but entirely adequate luncheon at the Dieu-donnée, and Melville's enjoyment of it was not diminished by the fact that, happening to meet a casual acquaintance there, he lunched at the same table, and suggested that they should toss to decide which of the twain should pay the joint account, with the result that the casual acquaintance lost. Evidently the fickle jade was smiling on Melville; a couple of games of billiards followed

the luncheon, and another refresher the billiards, and in high good humour Melville sauntered down the Ladies' Mile, preparatory to driving from Albert Gate to The Vale.

Opposite the French Embassy he parted from his friend.

"Sorry I can't ask you to come with me, old man," he said genially, "but I'm obliged to pay a duty visit to an aged aunt."

The friend expressed his sincere commiseration, but Melville only laughed.

"It's a very little flaw in an otherwise perfect day. You must lunch with me next time, and I will give you your revenge at billiards," and carefully choosing a well-appointed hansom he drove away.

The Vale, South Kensington, is a little-known cul-de-sac lying just off the Fulham Road. It contains but half-a-dozen houses, with trim lawns in front and quite large gardens in the rear; great elms shade the houses, and the remoteness from the main road makes them very quiet; in all of them are French windows and small verandahs, and there is an air of quietude and refinement about the place that makes it very attractive.

"The old lady does herself pretty well," thought Melville to himself as he walked up the gravelled path and noticed the close-cropped lawn and the blaze of geraniums and petunias. "I wonder what she knows about me, and what line I'd better take! The interesting musician might be diplomatic perhaps."

He thought that the maid who opened the door looked curiously at him as he enquired whether Lady Holt was at home, but, after all, that was a trifling matter, capable of bearing many interpretations. His interest was, however, more fully aroused by the drawing-room into which he was shown to await his aunt's coming, for it was not at all the sort of environment in which he had imagined he would find Sir Geoffrey's wife. It was essentially the drawing-room of a worldly woman of the world, furnished with taste, but evidently at great cost; photographs and silver boxes, enamels and

ivories were scattered in profusion over the many tables, water colours by rising artists covered the walls, cushions and flowers were everywhere.

"I shall have to readjust my preconceived notions of my elderly relative," he said to himself as he took a rapid survey of the pretty room; "this is a veritable canary's cage."

Then the door opened, and at the rustle of silk petticoats he turned to make a formal bow to his aunt. But as he turned, an exclamation of surprise escaped his lips and his single eye-glass dropped upon the floor, for the woman who entered was no precise and ringletted old lady, but the one who had asked him for his card at Monte Carlo, and who had expressed such sympathy with him when he was reduced to the necessity of applying for the viaticum. It was indeed no other than the charming Mrs. Sinclair.

She came forward with perfect self-possession, but a gleam of amusement lurked in her eyes.

"This is really a most astonishing experience," Melville said, as he bowed over her hand. "You are quite the last person I expected to see."

"Not the last you wanted to see, I hope," she replied, "but I confess delight is not the predominant expression upon your face at the moment. Won't you sit down?"

Melville picked up his monocle and polished it carefully before readjusting it in his eye.

"But tell me," he persisted, "what are you doing here?"

"Living here," Mrs. Sinclair answered. "What else do you suppose?"

"I can't quite sort things," Melville said apologetically. "To begin with, you see, I had never heard until last night that there was a Lady Holt, and when I got her note asking me to call here to-day I tried to picture what she would be like."

"What was the result of your efforts?" Mrs. Sinclair enquired.

Melville laughed slightly.

"Well, I'm bound to admit that I imagined my uncle's choice in women would be early Victorian, so to speak, and I don't think it's anything but a compliment to say that the early Victorian brand isn't very likely to agree with you. If you like Lady Holt, there is hope for me."

"I like her very much," Mrs. Sinclair said. "Mr. Melville, it isn't quite fair, perhaps, to lay snares for young men, and you evidently don't grasp the situation. You remember your last night at Monte Carlo?"

"It was not the sort of night to forget readily," Melville replied grimly. "I never had such monstrous bad luck at the tables before."

"You gave me one of your cards and I promised to write to you."

"You did," said Melville.

"I have kept my promise," said Mrs. Sinclair. "I wrote to you yesterday and asked you to come to see me. I am Lady Holt."

The astonishment depicted on Melville's face was ludicrous, and Mrs. Sinclair rippled over with mirth.

"I never thought to see you so taken aback," she said. "What I like so much about English gentlemen is that they are so imperturbable, and now you are gazing at me as if I were a freak."

"Really, I beg your pardon," Melville said. "but to think how grossly I have misjudged Sir Geoffrey!"

"Come, that's much better," Mrs. Sinclair replied. "Yes, Mr. Ashley, the confession has to be made; I am your aunt."

"I'm uncommonly delighted to hear it," Melville said heartily, "and I've only one regret in learning the fact."

"And that is——?" his new-found relative enquired.

"That I did not know it long ago," Melville replied. His wonted composure returned, and with it his wonted desire to stand well in the opinion of those in whose company he happened to be—a desire, it may be said, characteristic of many men who drift into bad lives from weakness rather than from natural vice. "Tell me, have you refrained from claiming relationship with me all this time because you heard I was a bad lot?"

"I perceive you are not expert in drawing inferences," Mrs. Sinclair said; "one does not associate the particularly goody-goody type of young man with Monte Carlo, and that is where I saw you first."

"That is true," Melville admitted. "I must plead guilty to not being goody-goody. By the way, am I to call you 'aunt'?"

Mrs. Sinclair shuddered.

"Certainly not," she said emphatically; "there is no necessity to draw public attention to the question of my age."

"What am I to call you?" he persisted.

"Call me Mrs. Sinclair," she said. "How old are you?"

"Thirty-five," Melville answered. "Why?"

"Then you are old enough to call me Lavender when we are alone," she said. "Out of doors it had better be Mrs. Sinclair, I suppose. It is a censorious world."

She leaned back in her chair and surveyed her nephew critically; the scrutiny was satisfactory, and she was glad of the impulse that had prompted her to disclose her identity to him. Yet, shrewd and clever woman as she was, she had taken a step which, while it could never be retraced, was the first towards the undoing of them both. There were other things in her life which in her hours of reflection she regretted, not least among them being her separation from a husband whose good qualities she fully recognised, but nothing in the past had been so fraught with peril to herself

as this alliance with her husband's nephew, which she owed to a single moment of caprice.

"Confess now," she said presently, "you are burning with curiosity to know all about everything?"

"That is a comprehensive way of putting it," he laughed, "but it is true. Tell me everything that is necessary, and as much more as you think fit."

"The only thing that is necessary," Mrs. Sinclair replied, "is that I actually am Sir Geoffrey Holt's wife. I married him years ago, when I was too young to realise all that marriage means, especially marriage to a man many years older than oneself. And—it didn't answer. That is really all." She had no intention of telling Melville very much about herself, and, of course, he could not cross-examine her. "He had not come into the title then," she went on, "and indeed there was no reason for supposing he ever would, for his brother was quite young enough to have married and had sons. Perhaps——" She paused, and Melville took advantage of the pause to give expression to the thought that was uppermost in his mind.

"I wonder that his marriage has been so completely forgotten. I never heard of it, and I'm quite sure my brother never has, yet he has been like a son to Sir Geoffrey, and knows a lot about his affairs."

Mrs. Sinclair flushed a little.

"Sir Geoffrey is a very proud man. He always was; indeed, that had a great deal to do with our mutual incompatibility, and proud men are apt to hold their tongues about their failures. Oh, yes!" she said, laughing, though there was no mirth in her laughter, "it was a dismal failure, and so we agreed to separate and never trouble each other again."

"And you never have?" said Melville.

"We never have."

"Sir Geoffrey is a very rich man," Melville remarked, following the line of his own thoughts.

"I believe he is," said Mrs. Sinclair indifferently. "All the money in the world doesn't make some things worth while."

"But I suppose he is very generous to you?"

"I wouldn't touch a penny of his money," said Mrs. Sinclair vehemently. Melville, of course, dropped the subject, but noted her reply for future use. What he wanted to ascertain most at the moment was Lady Holt's feeling for her husband, but she gave him no opportunity.

"What's your brother like?" she enquired. "Anything like you?"

"Nothing," said Melville shortly. "Ralph is a paragon of all the virtues and I'm—not."

"And he's like a son to Sir Geoffrey?" said Mrs. Sinclair. "Is he to be his heir?"

"I don't know," Melville answered moodily. "I suppose so; but, as a matter of fact, Sir Geoffrey hasn't made his will, so I don't know what he will do with his money."

Mrs. Sinclair yawned. The conversation really did not interest her much, and she had her own reasons for not wishing to let it get too intimate. She had taken a fancy to Melville when she first saw him in the Riviera; he belonged to the type of man in whose company she was most at home, and she foresaw a certain amount of pleasurable excitement in which she could participate with him without being worried by demonstrations of a more affectionate interest, which men not related to her were apt to make. A nephew is safer than a cousin.

"You must ask me to dine with you," she said, "and we will develop our acquaintance gradually. I hate finding out all about people at once and having nothing left to learn."

"Dine with me to-night," said Melville promptly. The hundred pounds were burning a hole in his pocket, and he felt convinced that more would be

forthcoming now from the same source. "Where shall it be?"

"Wherever you like," Mrs. Sinclair replied. "I'm always interested in people's varying ideas of hospitality. Come here for me at half-past seven and take me to the appointed place. Only don't tell me now where it is to be."

"All right," said Melville with alacrity. He liked her point of view and felt amazingly sympathetic already. Moreover, he recognised as clearly as she did the value of their relationship as a preventative of mutual misunderstandings. "I will go and fix it up. 'Pon my honour, I'm awfully delighted about this."

"Respect my confidence," she said gravely. "I may rely on that?"

"Absolutely," he answered. "I never interfere with other people's private business. It's not my form; and, besides, I'm so grateful to you for recognising me that I'm not going to forfeit a good thing."

Mrs. Sinclair was satisfied. She rang the bell for the maid to open the door, and smiled graciously upon her nephew.

"I hope you're going to be a great success," she said, as he rose to go. "There is an element of romance in the way fate has brought us together that is fascinating, and really you are a very creditable nephew."

Melville smiled sardonically. His aunt's husband held such a different opinion!

"I am a particularly fortunate one, I think," was all he said, and as he went out into the Fulham Road he thought the sun had never shone so brightly. Fortune had turned her wheel again, and his gambler's soul exulted.

CHAPTER VI. BRAVADO.

It was, indeed, with a very similar sense of satisfaction to that enjoyed by a man who, when playing cut-throat euchre, finds the joker in his hand, that Melville contemplated the advent of Mrs. Sinclair into his life. In many respects she was a charming woman; vigorous and resourceful in consequence of her somewhat adventurous career, but womanly and free from affectation. Moreover, if she could not claim entire exoneration from the charge of being an adventuress, she was entitled to several important limitations in the term; she gambled, it is true, and led an extravagant life, but she did both out of her own resources, and did not prey upon society as do most of the evening-gowned frequenters of the Casino. What other skeletons might be hidden in the secret cupboard of her life, Melville did not yet trouble to surmise; he assumed that among them was the grisly relic of her marriage with his uncle. The marriage had been a failure; the couple had separated and agreed to let the story be forgotten; "Sinclair" was merely a nom-de-guerre, and everything was capable of a perfectly satisfactory explanation, with the exception of her financial independence. Melville could not understand the feeling which prompted her to refuse assistance from her husband, more especially in such a case as this, where she might dictate her own terms for consenting to suppress the fact of her existence. What her motive was in so doing was one of the first things Melville intended to ascertain; there might be money in the knowledge. But the first thing he intended to do was to tell Sir Geoffrey that he knew this amazing secret of the marriage, for he felt convinced that he could make money by holding his tongue on that subject to the world at large.

Such were the thoughts that passed through Melville's mind as he walked from the station to The Grange at Fairbridge, where the Austens lived. With him to decide was to act, and the previous night he had resolved to adopt a bold policy and face Sir Geoffrey and Ralph at once; they had had time to compare notes about the hundred pounds, and a stormy interview with them both was inevitable, but it possessed no terrors for Melville now. He guessed correctly that for the credit of the family neither

of them would detail the facts to the Austens, with whom he was particularly anxious to stand well. Too selfish a man to be capable of real love for any woman, he yet liked Gwendolen better than any other woman he had ever seen, and he was quite willing to "range himself" if she would be his wife. That she was engaged to his brother troubled him very little. Engagements had been broken off before now, and the idea of cutting Ralph out had a certain piquancy that rendered the attempt worth making.

Looking delightfully cool and well-bred in his grey flannel suit and straw hat, with a turn-down collar that seemed to suggest an innocent simplicity of character, Melville walked slowly down the hill from the station and presented himself at the Austens' door. The ladies were in the garden, the servant informed him, and there Melville sought them, confident of a friendly greeting from them both.

Mrs. Austen was unaffectedly glad to see him. She had a tolerant feeling for nearly all young men, and Melville's marvellous gift as a musician had an especial charm for her. To Gwendolen he was Ralph's brother, and hitherto Ralph had championed Melville's cause, with the result that the girl was disposed to regard him as a somewhat maligned young man. So to-day they made much of him, and, under the influence of their warm welcome and gentle refinement, Melville was at his best.

"I've been sowing wild oats at Monte Carlo," he said gently, "and I found it vanity. So I've come home. No, I had no adventures and met nobody I knew. I lost all my money, and I'm very sorry for myself."

He congratulated Gwendolen on her engagement to Ralph, and there was a touch of pathos in his voice that proved him to be a consummate actor. Altogether, he enjoyed himself hugely, and awaited the critical moment of meeting his brother with actual pleasure. Ralph was expected early in the afternoon, and Melville lunched at the Grange and occupied the centre of its little stage with much complacency.

After luncheon Gwendolen remained indoors to watch for Ralph, and Melville sat in the verandah with Mrs. Austen and waxed confidential. She liked to be regarded as the recipient of the confidences of young men, and

Melville played upon her amiable weakness, being careful to invent such peccadilloes only as would not strain her charity unduly.

"Heaven divides its gifts very unequally," he remarked presently.

"Why that platitude?" asked Mrs. Austen.

"I was thinking of Ralph and myself," he said. "Of course, Sir Geoffrey has been equally generous to us both, but I notice that Ralph gets all the affection. He was always Uncle Geoffrey's favourite, and now he is engaged to Gwen." He sighed pathetically, and Mrs. Austen considered.

"I think your uncle is just as fond of you as he is of Ralph," she said, "but you're not a home bird and your brother is. Really, I don't think Sir Geoffrey could have been kinder to you if you had been his own son."

"Not kinder," Melville said, "but fonder, more affectionate. You have known him a long time, Mrs. Austen. Why do you suppose he never married?"

"I have often wondered," Mrs. Austen said, "but I never met him until he came into the title and estates, and he was not a young man then. He may never have wanted to marry, or he may have had some disappointment. At all events, it's an excellent thing for you boys that he never did."

"Excellent," Melville assented heartily. Mrs. Austen evidently had no suspicion of the facts; that meant that Sir Geoffrey did not want her to know them, and that, too, was excellent. "Ah! here comes Ralph, dancing on air."

Judging by the expression on Ralph's face, dancing on air was a disagreeable mode of progression. He was, indeed, furious at finding Melville thus established in the heart of the citadel; he was conscious, too, of a disadvantage in being thus taken by surprise. Confident in the justice of his indignation, he could have invaded Melville's chambers and demanded explanations and apologies for the fraud; here all the force of his attack would be wasted in the interval before he could deliver it.

He made no offer to shake hands, and, flushed with anger, he compared unfavourably with Melville, sitting so imperturbable, and prepared for all contingencies.

Melville employed every little artifice of which he was capable to heighten the contrast between his brother and himself, of which he saw Mrs. Austen was conscious. He made room for Ralph upon the verandah, and chatted gaily of a hundred trifles, but to all his flippancies Ralph returned only monosyllabic answers, appearing awkward and ill-mannered even in Gwendolen's biassed judgment.

At last Melville rose to go, and with alacrity Ralph rose too.

Melville protested politely.

"Don't let me take you away, old man," he said.

"But I want to have a talk with you," Ralph answered.

"Thought you weren't particularly pleased to see me," Melville returned placidly, "but I'm glad I was wrong. Good-bye, Mrs. Austen, and thanks awfully for a jolly time. May I come again soon?"

"Do," she answered, "there's always cold luncheon and a warm welcome here for you." She made the remark pointedly, for she was a little vexed with Ralph. She even went so far as to restrain Gwendolen from accompanying the brothers to the gate, and as they disappeared at the end of the drive Ralph was conscious of almost being in disgrace with his future mother-in-law.

Outside, however, on the main road his embarrassment vanished.

"What the deuce do you mean by coming here like this?" he said angrily.

"My dear Ralph," said Melville coolly, "The Grange doesn't belong to you, nor does the Manor House—yet. I've been to The Grange because I

wanted to see the Austens, and now I'm going to the Manor House because I want to see Sir Geoffrey."

Ralph was unfeignedly astonished.

"You want to see Sir Geoffrey?" he gasped.

"I do," said Melville. "Why not?"

"I wonder you have the audacity to look him in the face again," said Ralph hotly. "You are a liar and a thief."

"Go slow, Ralph," said Melville, "go slow. It seems to me you're off your chump. If your engagement hasn't turned your brain, tell me what all this pother is about, and leave mud-slinging till afterwards. What do you mean?"

Ralph was almost deceived by his brother's calmness; at any rate, it had the effect of making him struggle to regain command of his own temper.

"I wrote to you when you were at Monte Carlo," he said more quietly, "and asked you to lend me a hundred pounds."

"That's so," said Melville. "Sorry I couldn't oblige you, but I didn't even read your letter till I was on my way home, and then I was broke myself."

"But you got a hundred pounds out of Sir Geoffrey," spluttered Ralph.

"I did," said Melville. "I hope you did the same."

"Good heavens, man!" cried Ralph, as angrily as before; "don't try your vile swindles on me too. You told Sir Geoffrey you lent me that hundred pounds and got him to hand you over an open cheque for the amount in repayment of what you said was my debt, leaving him to get explanations from me afterwards."

"I hope the old man wasn't very crusty," said Melville sweetly.

"But your whole story was an infernal lie," roared Ralph, "and you got that money by a vulgar, low-down swindle. You are a liar, Melville, and a thief. I wish to heaven Sir Geoffrey had kicked you out of the house before he parted with the cheque."

"I daresay you do," Melville replied, unmoved; "but really, Ralph, you've had your whack out of the old buck, and now you're going to marry the Austen money you needn't grudge me a bit, need you? It's not exactly brotherly."

The sneering affront goaded Ralph almost to madness.

"You can thank me that you've not been arrested already for getting that money under false pretences," he said, livid with passion. "If Sir Geoffrey had had his own way you would have been, and 'pon my word, I'm beginning to be sorry I begged you off."

"Perhaps it isn't too late even yet," said Melville, no less calmly than before, "but I fancy you are exaggerating. Sir Geoffrey is always intemperate in his language, but I can't believe he would adopt such extremely unpleasant measures as the prosecution of his own nephew. However, I'll talk to him about it. I came down with the intention of doing so after I left The Grange."

Ralph was nonplussed. Such unlimited assurance as that displayed by Melville was outside his experience, and it even began to have some effect upon him.

"I think it was a mean and dirty trick," he said, "to make out that I owed you anything when I didn't, but that part of the business you can settle with your own conscience. What are you going to do now about the money?"

"How do you mean?" Melville enquired innocently.

"Well," said Ralph, "I persuaded Sir Geoffrey to drop the idea of legal proceedings by saying that as you had used my name the matter ought to be left in my hands. I've been to town to get the money, and I repaid him this morning."

"That's really awfully good of you," Melville said effusively. "I am infinitely obliged to you, but I'm afraid I shall have to owe it to you for a little while."

"It's simple waste of time to talk to you," said Ralph with scorn, "but there's one more remark I have to make, and you may as well remember it, for I mean what I say. I can't undo the fact that you are my brother, but I can do a good deal to prevent it from being forced on my attention, and one way is to avoid seeing you. Now, in future I'll trouble you to keep away from The Grange."

Melville coloured. This was a contingency he had not foreseen, and for a moment he lost his judgment.

"Jealous, eh?" he enquired, with ill-affected sarcasm. He was no coward physically, but he almost quailed before the blaze in his brother's eyes. Ralph did not trouble to fling back the taunt. With suppressed passion he spoke rapidly and distinctly, and each word flicked Melville on the raw.

"You are a contemptible swindler, and if you only have rope enough you'll hang yourself in the end. I'm quits with Sir Geoffrey over your last fraud, and it's worth every penny of the money to have learnt to know you as you are; but now I do know you I'll take jolly good care that you don't hang about my friends. Sir Geoffrey has ordered you out of the Manor House, and I order you out of The Grange. Go there again, and I'll tell Mrs. Austen all about this business and twist your neck into the bargain."

Melville forced a laugh.

"It will be time enough for you to order me out of houses when you possess any. When you are master of The Grange I shall keep clear of the place, you may be sure. Until then I shall call upon Mrs. Austen whenever I choose."

"If you go to The Grange I shall tell Mrs. Austen what has happened," Ralph repeated, "and she will order you out then herself."

"I dare you to do it," said Melville. In reality the idea filled him with uneasiness, but he was too shrewd to show it. Instead, he remarked reflectively, as if considering Ralph's interests only, "Mrs. Austen might begin to think she was allowing her daughter to marry into a queer family, supposing for the moment that she took everything you said for gospel."

Ralph drove his hands deep into his pockets. Honesty such as his often seems very stupid when confronted with the cleverness of a knave, and he felt unequal to a discussion with his brother. But he wished he had been less loyal to him in the past, less sturdy an advocate for his defence when Sir Geoffrey arraigned him. It was humiliating to think how completely Melville had taken him in. They walked in silence to the Manor House, and Ralph paused by the gate.

"I'm not going to argue with you, and I have nothing to add to what I said about The Grange. Go there and you'll see. Here is the Manor House. If you take my advice you will leave me here and get back to town by the next train."

"When I ask your advice I'll consider about taking it," Melville answered gently; he saw how his own coolness angered and flurried Ralph. "As for The Grange, Mrs. Austen has kindly invited me to dine there and bring my violin, and I need scarcely say I have accepted. And as for Sir Geoffrey, I have come down to see him, and if he's at home I will see him now; if he is out I shall wait."

"You are beyond me," Ralph said hopelessly. "Well, I don't want to keep you away from Sir Geoffrey if you are anxious to see him, but if I were in your shoes, which, thank heaven, I am not, I would blow out my brains rather than face him. I don't believe you have any shame left."

He opened the gate and, with Melville, walked up the drive. As they came in sight of the house, however, his mind shrank from the prospect of having to be present at so painful an interview between his uncle and brother as he felt sure this one must be. He stopped abruptly.

"You will probably find Sir Geoffrey in the library," he said. "I am going down to the houseboat."

"All right," said Melville unconcernedly. "I dare say I shall see you again later. If Sir Geoffrey asks me to stay, I will. By-bye," and noting with amusement the incredulous surprise written on Ralph's countenance he nodded cheerfully to him and walked in through the open doorway of the Manor House.

CHAPTER VII.

MELVILLE LEADS TRUMPS.

Melville possessed in an eminent degree the gift of winning the affection of his inferiors. Where no conflict of interest was possible he gave full play to the sympathetic part of his nature, which was his as it is the nature of all musicians. It was part of his policy, too, to stand well in the favour of those upon whom his comfort depended, and thus, although he was indifferent to the appeals of those who were inconvenienced by his indebtedness to them, and would resort to any subterfuge rather than pay his tradesmen's bills, yet he was a lenient and considerate master to his valet in Jermyn Street, was regarded with admiration by the hall porters of his club, and was held in affection by the old retainers at the Manor House, who had known him for so many years.

With Martin Somers, Sir Geoffrey's butler, Melville was an especial favourite. The old man had taught him all he knew of outdoor sports, and had often stood his friend when in earlier days the boy was in disgrace with his uncle.

Melville turned from the hall into the dining-room and rang the bell. It was cool and shady in this room, and Melville was conscious of a pang of regret at the knowledge that the place would never be his. His life had been full of variety and excitement, but it had cost him all chance of ever being master of the Manor House. Already he was an unwelcome visitor, and

when in course of time it passed into Ralph's possession, its doors would very probably be closed to him altogether.

"Ralph is a stupid clown," he muttered, "but I'm not sure that he hasn't done better for himself than I have. To own this place and be Gwen's husband should be good enough for anyone."

The sigh that escaped him was born of sincerity, but he turned briskly to face his immediate task as the butler came in answer to the ring. Melville shook hands with him, making no reference to his previous evening visit to his uncle.

"Here I am again, Martin," he said cheerfully, "'Pon my word, it's good to see you."

"You've been abroad, Master Melville?" Martin asked.

"Yes," said Melville; "same old racket, same old place, same old luck."

Martin shook his head.

"I've no faith in Monte Carlo," he remarked austerely; "never heard of any good coming from there."

"That's rude," said Melville, "seeing that I've just come from there. How is Sir Geoffrey?"

"Pretty well, sir," the butler replied; "I may say very well."

"He's a wonderful old chap," said Melville. "He'll be marrying soon and having a family of his own; see if he doesn't."

"Sir Geoffrey never took any account of the ladies," Martin remarked. "It's a pity, in some ways; but, bless you, sir, he's got all the family a man needs in Master Ralph and yourself."

"Too much, perhaps," said Melville. "Go and tell him I'm here, Martin, will you."

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