Investigation of Rank Distance Properties of Cyclic, Abelian Codes and Study of their Applicability for Error Correction in Wireless Devices

Abstract

The useofmultiple-antennaconfigurationscoupledwithsuitablesignalprocessing techniques isoneofthemostpromisingtechniquetoachievehighdataratesandim- provedqualityofserviceinwirelesscommunicationsystems.Overtheyearsmany Multiple-Input Multiple-Output(MIMO)techniqueshavebeenproposedtoachieve high spectralefficiencies,higherdataratesandimprovedreliabilityofcommunica- tion. MIMOtechniqueshavebeenbroadlydividedintotwobroadcategories;Spatial Multiplexingtechniques(SMX)[Foschini(1996)],whichisemployedtoenhancethe capacity ofsystemandSpaceTimeCodingTechniques(STC)[Tarokhetal.(1998)], which havebeenemployedtoimprovethereliabilityofcommunications.InSMX,in- dependent streamsofinformationareradiatedfrommultipletransmitantennas.SMX achieveshighermultiplexinggain,butthistechniqueisnotsuitableforlargescale MIMO, duetoincreaseddecodingcomplexityatthereceiver.SpaceTimeBlockCodes (STBCs) arechannelcodeswhichmaximizespatialdiversity.STBCsarecapableof providingimprovedcodinggainforsamespectralefficiencycomparedwithequivalent diversityschemes.Thisinturnenhancestheoverallreliabilityofthewirelesscom- munication system.STBCscombatchannelimperfectionsandimprovetheintegrityof data transferbycombiningcodinggainwithdiversitygain[Alamouti(1998)]. Space Time(ST)techniquesemployingmultipleantennassufferfromexcessenergy consumption, duetotheactivationofallantennasandtheirpoweramplifierchains.A energyefficientMIMOtechniquenamely,SpatialModulation(SM)wasproposedby Mesleh etal.in[Meslehetal.(2008)].Thistechniqueachievesincreasedenergyeffi- ciencybyactivatingonlyasingleantennaatatime.Spectralefficiencyisfurtherim- provedbyconveyinginformationthroughthemediumofactiveantennaindices[Mesleh et al.(2008)].ThusSMisanenergyconservingtechniquethatutilizesthespatialdi- mension ofmultipleantennaconfigurationtoconveyadditionalinformation.Thecon- cept ofSMwasfurtherimprovedbyappendingaSTBCwiththeSMscheme.This i arrangement wasintroducedby[Basaretal.(2011)]andisknownasSpaceTimeBlock Coded SpatialModulation(STBC-SM).Mostoftheliteratureonthistopichasbeen devotedtothestudyanddesignofOrthogonalSTBC-SMs.However,ithasbeenob- servedthatseveralNon-orthogonalSTBCsprovideperformance(bothintermsofBit Error Rate(BER)andSpectralefficiency)thanconventionalOrthogonal-STBCs.This has leadustostudytheperformanceofseveralfamiliesofNon-OrthogonalSTBCs when employedoverdifferenttypesofchannelsinthisthesis. The useoferrorcontrolcodeenhancestheintegrityofdatatransfer,especiallywhen the communicationsystemisoperatinginanenvironmentperturbedbychannelinduced distortion andnoise.Thisisdonebyintroducingcontrollednumberofredundantbits into theinformationbitstream.Thedisciplineoferrorcontrolcodeshasevolvedfrom designing binarycodesforbinarysymmetricchannelstodesigningcomplexsymbol oriented codesforvarioustypesofchannelsincludingsemiconductor,opticalandmag- netic memories[Moon(2005)].Acomprehensivestudyoftheliteraturehasinspired us toexploretheuseoffullrankcodesoverSTBCs,STBC-SMsystemsandinother evolvingapplications. In thisthesiswehavedesignedaclassoffullrankNonorthogonalSpaceTime Block Codes(NSTBC)whicharederivedfromfullrankCyclicandAbeliancodes.It is observedthattheseNSTBCsoutperformconventionalSTBCswhenemployedover a varietyofchannelfadingconditions.Thedescriptionofresearchworkconducted commences inChapter3afterabriefdescriptionofthestateofart(literaturesurvey) giveninChapter2.InChapter3,wehaveproposedaclassofSpatiallyModulated Non OrthogonalSpaceTimeBlockCodes(SM-NSTBC)designedfrom n􀀀length non- binary Cycliccodesover GF(qm) where q is aprimeand m is orderoftheextensionfield (m n). TheproposedSM-NSTBCoutperformsconventionalSpatiallyModulated Orthogonal SpaceTimeBlockCodes(SM-OSTBC),STBC-SM,SMschemesandtheir variantsintermsofaveragebiterrorrate(ABER)performance. In chapter4,theconceptofreceivespatialmodulationhasbeenexplored.Thetech- nique ofPrecodedSM-NSTBCisproposedtoattainreceivespatialmodulation.Inthis scheme apartofinformationisconveyedbyreceiveantennaindicesinadditiontothe ii conventionallyradiatedNSTBCsymbols.Thisisachievedbyadoptingsuitableprecod- ing techniqueatthetransmitter.TheperformanceofproposedPrecodedSM-NSTBC scheme issynthesizedforspatiallycorrelatedandspatiallyuncorrelatedRayleighfad- ing environments. The designofacooperativecommunicationsystemwithAmplifyandForwardre- laying forSpatiallyModulatedNon-orthogonalSpaceTimeBlockCode(SM-NSTBC- AF) isdiscussedinChapter5.Asinglerelaywithmultipleantennaelementsisassumed to existbetweensourceanddestination.Theinformationtransmittedbythesourceis receivedbytherelayinfirsttimeslot,inthesecondtimeslotthisinformationisam- plified andforwardedtothedestination.Intheproposedscheme,adirectlinkbetween source anddestinationaswellasthecooperativelink(linkbetweensourceanddesti- nation througharelay)areassumedtoexistandoperateintandem.Itisobservedthat this approachprovidesimprovedABERperformanceoverconventionalschemes.This scheme hasbeencomparedwithequivalentschemesemployingamplifyandforward relaying, namelyCooperativeSTBC-SMschemesandCooperativeSMschemes. In Chapter6,thesystemandchannelmodelofHighAltitudePlatforms(HAPs)has been studied.TheeffectofImperfectChannelStateInformation(Imp-CSI)isinvesti- gatedtoobtaininsightintotheperformanceofHAP-MIMOlinkswhendeployedinreal life situations.TheperformanceoffullrankSM-NSTBC,STBC-SMandSM-OSTBC schemes overaHAP-MIMOenvironmentisanalyzed.ItisobservedthatproposedSM- NSTBC outperformscompetingschemesundertheconditionsofperfect-CSIavailabil- ity aswellasimperfect-CSI. In thelastpartofthisthesiswehaveinvestigatedthedesignofNSTBCsderived from non-binaryAbeliancodes.First,adescriptionofthetransformdomainproper- ties andrank-distancepropertiesofAbeliancodeshasbeenprovided.Thisisfollowed by thedesignandsynthesisofSpatiallyModulatedNon-orthogonalSpaceTimeBlock Codes derivedfrom n-length fullrankAbeliancodesover GF(qm). Itisobservedthat the proposedAbelianSM-NSTBCprovidesaperformanceimprovementwhencom- pared withCyclicSM-NSTBCandotherconventionalSTBCs. In summary,inthisthesiswehaveutilizedtherankdistancecharacterizationof iii Cyclic andAbeliancodes.ThecodewordsderivedfromCyclicandAbeliancodeswhen viewedas (m n) matrices possessfullrank.Byemployingsuitablerankpreserving maps wehavesynthesizedfullrankNon-orthogonalSTBCsfromthesefullrankcodes. SM-NSTBC schemeswhichachievehighreliability,highspectralefficiencywithmod- erate decodingcomplexityhavebeendesigned.Theperformanceofproposedschemes havebeenanalyzedunderRayleighfadingenvironments.Further,wehaveexplored the conceptofreceivespatialmodulationandhavesynthesizedschemeswhichemploy full rankNon-orthogonalSTBCs.Thisisfollowedbythederivationofatechnique which employscooperativeSM-NSTBCwithamplifyandforwardrelayingtoimprove the overalllinkperformance.WehavealsoproposedaMIMOschemewhichcanbe employedonaHighAltitudePlatformcommunicationsystem.Theperformanceofthis scheme overHAP-MIMOenvironmenthasbeendetermined.Thedesignofallsystems has beendonekeepinginviewofthe3GPPcommunicationstandards. It isexpectedthattheresultscontainedinthisthesiswillbeusefulforthedesigns of moderncommunicationsystemssuchas5Gandbeyond-5G.