全球导航卫星系统（GNSS）软件定义无线电：历史、当前发展和标准化工作

Received<day>March2023

Revised<day><month><year>

Accepted<day><month><year>

DOI:xxx/xxxx

ARTICLETYPE

GNSSSoftwareDefinedRadio:History,CurrentDevelopments,

andStandardizationEfforts

ThomasPany1|DennisAkos2|JavierArribas3|M.ZahidulH.Bhuiyan4|PauClosas5|Fabio

Dovis6|IgnacioFernandez-Hernandez7|CarlesFernández–Prades3|SanjeevGunawardena8|ToddHumphreys9|ZaherM.Kassas10|JoséA.LópezSalcedo11|MarioNicola12|MarkL.

Psiaki13|AlexanderRügamer14|Young-JinSong15|Jong-HoonWon15

1UniversityoftheBundeswehrMunich,Neubiberg,Germany

2UniversityofColorado,Boulder,USA

3CentreTecnològicdeTelecomunicacionsdeCatalunya,Barcelona,Spain

4FinnishGeospatialResearchInstitute,Kirkkonummi,Finland

5NortheasternUniversity,Boston,USA

6PolitecnicodiTorino,Turin,Italy

7EuropeanCommission,Brussels,Belgium

8AirForceInstituteofTechnology,Wright-PattersonAFB,USA

9TheUniversityofTexasatAustin,Austin,USA

10TheOhioStateUniversity,Columbus,USA

11UniversitatAutònomadeBarcelona,CerdanyoladelVallès,Spain

12LINKSFoundation,Turin,Italy

13VirginiaTech,Blacksburg,USA

14FraunhoferInstituteforIntegratedCircuitsIIS,Erlangen,Germany

15InhaUniversity,Incheon,SouthKorea

Summary

Takingtheworkconductedbytheglobalnavigationsatellitesystem(GNSS)software-definedradio(SDR)workinggroupduringthelastdecadeasaseed,thiscontributionsummarizesforthefirsttimethehistoryofGNSSSDRdevelopment.IthighlightsselectedSDRimplementationsandachievementsthatareavailabletothepublicorthatinfluencedthegeneralSDRdevelopment.Therelationtothestandard-izationprocessofintermediatefrequency(IF)sampledataandmetadataisdiscussed,andanupdateoftheInstituteofNavigation(ION)SDRStandardisproposed.TheworkfocusesonGNSSSDRimplementationsongeneralpurposeprocessorsandleavesasidedevelopmentsconductedonfieldprogrammablegatearray(FPGA)andapplication-specificintegratedcircuits(ASICs)platforms.Datacollectionsystems(i.e.,front-ends)havealwaysbeenofparamountimportanceforGNSSSDRs,andarethuspartlycoveredinthiswork.TheworkrepresentstheknowledgeoftheauthorsbutisnotmeantasacompletedescriptionofSDRhistory.

KEYWORDS

GNSS,software-definedradio

1IINTRODUCTION

Receiverdevelopmenthasalwaysbeenanintegralpartofsatellitenavigation,eversincetheearlystudiesconductedfortheU.S.GlobalPositioningSystem(GPS).Theveryfirstreceiverswerehugedevices,realizingthecorrelationofthereceived

satellitesignalwithinternallygeneratedcodeandcarrierreplicasbyamixtureofdigitalandanalogelectronics(Eissfeller

&Won,

2017)

.Advancesinsemiconductortechnologysoonenabledsignalprocessingondedicatedchips.ThistechnologywasofcoursecomplextohandleandmostlylocatedwithintheU.S.industry.DespitethesuccessofGPSanditsRussiancounterpartGlobalnayaNavigazionnayaSputnikovayaSistema(GLONASS),receiverinternaltechnologywasbarelyaccessibletothebroaderresearchcommunityforalongtime,asitseemedtobeimpossibletorealizeGNSSsignalprocessingonlow-costcomputers.Evenintheyear1996akeyreceiverdesignpioneerexpressedskepticismthatgeneralpurposemicroprocessors

were,orwouldeverbe,asuitableplatformforimplementingaGNSSreceiver(Kaplan,

1996)

.

2

ThesituationradicallychangedwhenthealgorithmsofaGPSreceiverwerefirstimplementedasMatlabsoftwareonadesktoppersonalcomputer(PC)andestimatesofdigitalsignalprocessor(DSP)resourcesrequiredtorunthealgorithmsinreal-time

wereencouraging(D.Akos&Braasch,

1996;

D.M.Akos,

1997)

.Soonafter,real-timeprocessingwasdemonstratedevenonconventionalPCsandthewidespreaduseofsoftwareradiotechnologytookoffwithexponentialgrowth.Interestingly,softwareradiotechnologydidnotreplaceexistinghardwarereceiversusuallyrealizedasoneormoreASICs,butcomplementedthese,allowingresearcherstoeasilyimplementandtestnewalgorithmsortodevelophighlyspecializedreceiverswithreasonableeffort.Today,thisisawell-establishedapproachformilitary,scientific,andevencommercialapplicationsasdescribedby

Curran

etal.

(2018)

.

Asdifferentresearchgroupsdevelopedtheirownsoftwareradios,theyuseddifferentdatacollectionsystemstosampletheGNSSsignals.WhereasthedataformatofthedigitalGNSSsignalstreamsiscomparablyeasytodescribe,thewidespreaduseofsoftwareradiotechnologymadeitnecessarytointroduceacertainlevelofstandardization,whichwasfinallyachievedbyagroupofresearchersasdocumentedby

Gunawardenaetal.

(2021)

.Theresultwastheso-

calledIONSDRStandard(IONSDR

WorkingGroup,

2020)

.

Astechnologyfurtherevolved,newGNSSsoftwareradiosemergedandsomedeficienciesoftheIONSDRStandardbecame

apparent(Clementsetal.,

2021)

.Theseconditionspromptedthepresentpaper,whosecontributionsarefour-fold.First,itpresentsthefirsthistoryofGNSSSDRdevelopment(Section

2)

.Second,itoffersadetaileddescriptionofselectGNSSSDRs(Section

3)

.Third,itoverviewsrecentfront-enddevelopments(Section

4)

.Finally,itsummarizesthehistoryoftheIONSDRStandardandproposesanupdatethereto(Section

5)

.

2GNSSSOFTWAREDEFINEDRADIOHISTORY

ThehistoryofGNSSSDRrequiresmorethanabitofrecollection,whichcanbefraughtwithinaccuracies,noneofwhichareintentionalinthepresentwork.Correctionswouldalwaysbewelcome.

GNSSSDRtracesitsrootstoOhioUniversity’sAvionicsEngineeringCenteraround1994.ProfessorMichaelBraasch,anewly-mintedfacultymemberoftheElectricalandComputerEngineeringDepartmentandalreadyrecognizedasanexpertinGNSSmultipath,wasinterestedincreatingahigh-fidelitysimulationoftheinternalsignalprocessingwithinGPSandGLONASSreceivers.DennisAkos,aPh.D.studentintheDepartment,wasintriguedbytheidea.Alreadyharboringakeeninterestincomputerscienceandprogramming,AkostookonthesimulationprojectatBraasch’srequestundertheFAA/NASAJointUniversityProgram.Meanwhile,publicationof“TheSoftwareRadioArchitecture”inthe1995IEEECommunication

Magazine(Mitola,

1995)fueledAkos’sandBraasch’sthinkingthatthis“simulation”couldinsteadbetargetedtowardanactual

softwareradioimplementation.TheresultwasthefirstpublicationonGNSSSDR,whichappearedintheproceedingsofthe

1996IONAnnualMeeting(D.Akos&Braasch,

1996)

.

Developmentofthisinitialsimulation/implementationwassignificantlyfurtheredthroughcooperationwithDr.JamesB.Y.TsuiofWrightPattersonAirForceBase.Well-recognizedasanexpertindigitalreceivers,Tsuihadrecentlytakenaninterestinsatellitenavigation.In1995,twosummerinterns,DennisAkosfromOhioUniversityandMichaelStockmasterfromTheOhioStateUniversity,workedunderTsui’sguidancetodevelopaMatlabimplementationofthesignalprocessingrequiredforbasicGPSreceiveroperation.AdigitaloscilloscopewasusedtocapturetheinitialIFdatathatwerecriticaltodevelopinganddebuggingthoseearlyalgorithms.Akoswasresponsibleforthelower-levelsignalprocessing(acquisitionaswellascode/carriertracking),whileStockmasterimplementedthenavigationsolution.ThecumulativeresultwasthefirsteverGPSSDRimplemen-tation.Althoughfullyoperational,itwas“slowasmolasses”:processing30secondsofIFdatarequiredhoursofcomputationtime.

TsuipublishedthefirsttextbookonGPSSDRin2000(Tsui,

2000)

.Aparallelcontributionofthisinitialeffortwasthedirectradiofrequency(RF)samplingfront-end,whichgarneredsignificantinterestandpushedadvancesinanalog-to-digital

converterdevelopment(D.Akosetal.,

1999)

.

AfterreceivinghisPh.D.in1997,AkosstartedhisacademiccareerasanAssistantProfessorintheSystemteknikDepartmentofLuleåUniversityofTechnologyinSweden,wherehetaughtacourseoncomputerarchitecture.ItwasherethatGPSSDRfirstachievedrealtimeoperation.Foraclassproject,AkosprovidedaMatlab-basedGPSSDRandchallengedagroupofstudentsto“getittorunasfastaspossible”subjecttotherequirementthatthecomplexaccumulationproductsforeachchannelwerewithin10%ofthoseproducedbytheoriginalMatlab-basedGPSSDR.Itwasin1999thatthefirst“realtime”operationwaspossible,processing60secondsofIFdatain55seconds.ThiswasanotableachievementatthetimegiventhatrenownedGPSexpertPhilipWard,whowasresponsibleforsomeofthefirstGPSreceivers,hadrecentlyexpressedskepticismabouttheprospectofa

3

fullysoftware-definedreal-timeGPSSDR,writing“Theintegrate-and-dumpaccumulatorsprovidefilteringandresamplingattheprocessorbasebandinputrate,whichisaround200Hz[...and]wellwithintheinterruptservicingrateofmodernhigh-speedmicroprocessors.Butthe5-

to50-MHzrates[ofintermediatefrequencysamples]wouldnotbemanageable”(Kaplan,

1996)

.ThisrealtimeimplementationeffortwasledbystudentPer-LudvigNormarkandledtotheresultspublishedby

D.M.Akoset

al.

(2001)

.

Inthemeantime,KaiBorre,ageodesyprofessorfromAalborgUniversity,hadalsodevelopedinthemid-late1990sMatlabcodeforGPSreceivers.Borre’scodefocusedonthenavigationblockandincludingfunctionsforconversionofcoordinatesandtimereferences,satellitepositiondetermination,andatmosphericcorrections.ThejointeffortsofAkos,Borre,andothers

wouldlaterleadtothewell-knownbook(Borreetal.,

2007),aprimaryreferenceforGNSSSDRoverthenextyears,andthe

relatedSoftGPSMatlabreceiver.

Upongraduation,NormarkcontinuedhisGNSSreceiverdevelopmentwiththeGPSLaboratoryatStanfordUniversityandthenreturnedhometoSwedenwhereheco-foundedNordNavTechnologies,whichdevelopedthefirstGalileoSDR,andhelpedestablishthearchitecture,togetherwithCambridgeSiliconRadio(CSR),topushGNSStoapricepointacceptabletothemobilephoneadoption.CSR,atthetimeadominantsupplierofBluetoothhardwaretothemobilephonemarket,acquiredNordNavin2006andtheyjointlyredesignedtheCSR2.4GHzradiotomultiplextothe1575.42MHzGPSL1band,exploitingthefactthatmostBluetoothapplicationshavearelativelylowdutycycle.Thisapproach,coupledwiththereal-timesoftwareGPSimplementation,providedanear-zero-added-costGPSreceiver.

TherehavebeennumerouscontributionstoGNSSSDRdevelopmentsincetheseearlyyears,manyofwhicharefromtheco-authorsofthispaper.SelecteddevelopmentsbytheauthorsareoutlinedinSection

3

includingasurveyofachievementsbyotherresearchersinSection

3.11.

Theauthorsareawarethatmanyotherimportantcontributionsaremissing,andmakenoclaimsofestablishingacomprehensivedescription.Inordertogivethereaderabetterorientationaboutthechronologicalorderofalldevelopments,wepresentTab.

1,reiteratingthattheselectionofreferencesispartlysubjectiveandoftensimilardevelopments

havebeencarriedoutbyseveralresearchgroups.ThetimelinedemonstratestheflexibilityofSDRtechnology,i.e.,thesamecodebaseisusedforGPSL1C/Acodesignalsandforsignalsofopportunity(SOP)fromcellularterrestrialtransmittersorfromcommunicationsatellitesinlowEarthorbit(LEO).

3CURRENTSTATUSOFGNSSSOFTWAREDEFINEDRADIOS

InJune2023,aquickinternetsearchdidnotrevealanycomprehensivelistingofallGNSSSDRsand

Wikipedia

(2023)lists

sevenentries,whichisfarbelowthenumberofreceiversknownbytheauthors,evenifthefollowingcriterionisappliedtolimitthescope:aGNSSSDR(orsoftwarereceiver)isdefinedasapieceofsoftwarerunningonageneralpurposecomputerconvertingsamplesofareceivedGNSSsignalintoapositionvelocityandtime(PVT)estimate.Itisclearlyunderstoodthatafront-endincludinganalog-to-digitalconversion(ADC)isrequiredtosamplethereceivedsignal,butotherthanthatnofurtherfunctionalityisallowedtoberealizedviahardware.Withthisdefinition,threecategoriesofsoftwarereceiverscanbeintroduced:

real-timereceivers:monolithicormodularsoftwarepackageswritteninanefficientlow-levelprogramminglanguage(likeCorC++)typicallyoptimizedforrun-timeefficiencyandstability

teaching/researchtools:softwarepackageswritteninahighlevelprogramminglanguagelikePythonorMatlaboptimizedforcodereadabilityandflexibility

snapshotreceivers:receiversoptimizedforveryshortbatchesofsignalsamples

Furthermore,thesoftwarepackageshallallowsomeconfigurationflexibilityand(atleasttheoretically)supporttheIONSDRStandard.Thefollowingsubsectionsintroduceafewselecteddevelopments,emphasizingtherationalebehinddesignchoicesandcurrentstatus.Eachsub-sectionisrepresentedbyoneentryinTab.

2

togivethereaderaquickoverviewofthemaincharacteristicsofeachdevelopment.Section

3.1

describestheworkofPsiaki,Ledvina,andHumphreysandtheireffortsinreal-timeprocessingonDSPswiththebit-wise-parallelapproachprovingtobehighlysuccessfulevenforspaceapplications.Section

3.2

coversworkofPany/othersintheireffortswithmulticonstellation/multifrequencyGNSS.Section

3.3

andSection

3.4

covertheeffortsofBorreandothersinareadableopensourceMatlabGPSSDRstartedin(Borreetal.,

2007),withthemost

recentGNSSupdatereportedin

Borreetal.

(2022)

.Akoshasalsocontinuedthisacademicdevelopmentofasuiteofopen

sourceGNSSSDRs(Bernabeuetal.,

2021)

.Thewidelyusedopen-sourcereceiverGNSS-SDRisdescribedinSection

3.5.

4

TABLE1TimelineofGNSSSDRdevelopments

Year

Milestonewithcomment

Reference

1995

Emergenceofsoftwareradioapproach

(Mitola,

1995)

1996

FirstpublicationofaGPSSDRdevelopment

(D.Akos&Braasch,

1996)

1999

Firstreal-timesoftwarereceiverwithGPSL1C/Acode

(D.M.Akosetal.,

2001)

2000

FirsttextbookonGPSSDRpublished

(Tsui,

2000)

2002+

Useofbit-wisecorrelationandSIMDinstructions

(Ledvinaetal.,

2003;

Panyetal.,

2003)

2002+

GNSSSDRsascommercialproducts

NordNav,IFEN,Trimble,LocusLock,...

2004

Firstmulti-GNSS/multi-frequencyGNSSSDRs

(Ledvina,Psiaki,Sheinfeld,etal.,

2004;

Pany,

Eissfeller,etal.,

2004)

2004

Firstreal-timeGNSS/INSintegrationwithSDR

(Gunawardenaetal.,

2004)

2005

GNSSSDRconsolidationatPolitecnicodiTorinoandLINKSFoundation

Section

3.9

2005

DemonstrationofvectortrackingwithaGNSSSDR

(Panyetal.,

2005)

2006

Firstreal-timeall-in-viewembeddableGNSSSDR

(T.Humphreysetal.,

2006)

2006

FirstuseofSDRtechnologyforAMsignalsofopportu-nity

(McEllroy,

2006;

McEllroyetal.,

2006)

2007

Startofwide-spreadadoptionofSDRtechnologyinGNSSresearch

(Borreetal.,

2007)

2007

Firstdevelopmentofasnapshotreceiver

Section

3.8

2009

Firstmulti-coreGNSSSDR

(T.E.Humphreysetal.,

2009)

2010

Adoptionofacomputersciencebestpracticecollabora-tiveframework

Section

3.5

2010

FirstuseofGPUsforcorrelation

(Hobigeretal.,

2010)

2011+

UseofGNSSSDRforionosphericresearch

(O’Hanlonetal.,

2011;

Peng&Morton,

2011)

2012+

SDRdevelopmentsattheFinnishGeospatialResearchInstitute

(Borreetal.,

2022;

Söderholmetal.,

2016)

2012

UseofaDVB-Tultra-low-costfront-endforGNSSSDR

Section.

3.5

2012+

UseofSDRtechnologyforLTEsignalsofopportunity

(delPeral-Rosadoetal.,

2013;

Driussoetal.,

2017;

Shamaeietal.,

2018)

2014+

UseofGNSSSDRsinspace

(Lightseyetal.,

2014;

Murrianetal.,

2021)

2014

UseofSDRsformixedcellular3GGSM/CDMAandDTVSOP

(Yangetal.,

2014)

2015+

AbundanceofprocessingpowerforGNSSSDRavailable

(Dampfetal.,

2015;

Nicholsetal.,

2022)

2017+

UseofSDRsfor3GCDMAand4GLTESOP

(Kassasetal.,

2017)

2018

FirstuseofPythonfordedicatedteachingofGNSSSDR

Section

3.7

2018

FirstSDRenablingsub-meter-levelcarrier-phase-basedUAVnavigationwith3GCDMAand4GLTESOP

(Khalife&Kassas,

2018

2022)

2020

FormaladoptionofIONSDRStandard

Section

5

2020

UseofSDRforstationarypositioningwithmulti-constellationOrbcommandIridiumLEOSOP

(Farhangian&Landry,

2020;

Orabietal.,

2021)

2021

FirstSDRfor5GSOP

(Shamaei&Kassas,

2021b)

2021+

UseofGNSSSDRtosupportdevelopmentofnewnavi-gationsatellitesystems

(Milleretal.,

2023;

Songetal.,

2021)

2021

FirstSDRenablingvehiclenavigationwithmulti-constellationLEOSOP

(Kassasetal.,

2023

2021)

2022

FirstSDRenablingaircraftnavigationwithcellularSOP

(Kassas,Abdallah,etal.,

2022;

Kassas,Khalife,

Abdallah,Lee,Jurado,etal.,

2022)

5

TABLE2OverviewofGNSSSDRsdiscussedinSection

3

Name

Mainlan-guage

Opensource

Mainfocus

GRID

C++

No

Real-timeoperationofadvancedalgorithmsonembeddeddevices

MuSNAT

C++

No

Analysisofnavigationsignalprocessingandalgorithmprototyping

SoftGPS

MATLAB

Yes

SuiteofGNSSSDRswithwidespreaduseandaccompanyingbook

FGI-GSRx

MATLAB

Yes

Multi-GNSSSDRwithaccompanyingbook

GNSS-SDR

C++

Yes

Real-timeSDRwithmodularstructureandwidespreaduse

AutoNav-SDR

MATLAB

No

SupportforKPS-development,API,andGPU

PyChips

Python

No

Multi-GNSSandoptimizedforuseinteachingclasses

UABSnapshotGNSSReceiver

MATLAB

No

Snapshotreceiverthatcanbeoperatedinthecloud

NGene

ANSIC

No

EfficientGNSSSDRusedinnumerousGalileo-relatedprojects

MATRIX

MATLAB,C++

No

CombinedprocessingofGNSSwithcellular3G/4G/5GandLEO(Starlink,OneWeb,Orbcomm,Iridium,andGlobalstar)signals

TheAUTONAVreceiverusedtosupportthedevelopmentofKoreanPositioningSystem(KPS)isdiscussedinSection

3.6

andPyChips(cf.Section

3.7)isthebasisfortutorialclassesoftheION

.TheUABsnapshotGNSSsoftwarereceiverisdescribedinSection

3.8,whileSection

3.9

discussesaSDRusede.g.totheauthenticationschemes,reflectometryortoassesstheinfluenceofnon-standardGNSStransmissions.Section

3.10

extendsthescopeofSDRtonon-GNSSsignals.

WhereasatthebeginningoftheGNSSSDRdevelopmentthedifferentreceiverswerelinkedtospecificpersonsorresearchinstitutes,todayoftendifferentreceivers,toolsorcodebasesareusedatthesameinstitute.Ontheotherhand,codebasesfirstdevelopedbyasingleinstitutespreadintodifferentinstitutes.Forexample,thedevelopmentsof

Borreetal.

(2007)forkedinto

severalbranches[e.g.

(Bernabeuetal.,

2021;

FGI,

2022;

Zhang,

2022)],asdiscussedinSection

3.3

andSection

3.4.

3.1Bit-WiseParallelismandtheEmergenceofGRID

Theoriginalreal-timeGNSSsoftwareradioworkby

D.M.Akos

(1997)inspiredaneffortwithintheCornellGPSgroup

.Psiakihadbeenworkingwithnon-real-timesoftwareGNSSsignalprocessinginMatlabforabouttwoyearswhenhestartedtowonderwhethertheslowMatlaboperationscouldbetranslatedtoruninreal-timeonageneraldesktopworkstation.ThebottleneckinGNSSdigitalsignalprocessingoccurswhendoingtheoperationsthatinitiallyprocessthehigh-frequencyRFfront-endsamples.RFfront-endstypicallysampleat4MHzorfaster.A12channelreceiverwouldhavetoperformontheorderof400millionoperationspersecondormoreinorderdoalloftheneededsignalprocessing.Psiakiconceivedtheconceptofbit-wiseparallelprocessingasameansofaddressingthischallenge.Herecruitedthen-Ph.D.candidateBrentLedvinatomakeanattemptatimplementingtheseideasintheCprogramminglanguageonaReal-TimeLinuxdesktopworkstation.Ledvinasucceededin

developinga12-channelreal-timeL1C/A-codereceiverafterabout6months’effort(Ledvinaetal.,

2003)

.

Themainconceptofbit-wiseparallelismistoworkefficientlywithRFfront-enddatathathavealownumberofquantizationbits.IfanRFfront-endproducesa1-bitdigitaloutputstream,then32successivesign-bitsamplescanbestoredinasingle32-bitunsignedintegerwordonageneral-purposeprocessor.Thirty-twosuccessiveoutputsamplesofa2-bitRFfront-endcanbestoredintwo32-bitwords,onecontainingthesuccessivesignbitsandtheothercontainingthesuccessivemagnitudebits.Eachchannelofthesoftwarereceivergeneratesa1-bitora2-bitrepresentationof32successivesamplesofitsIFcarrierreplica,bothin-phaseandquadrature,andthesuccessivesamplesarestoredinparallelin32-bitunsignedintegerwords.Similarly,itgeneratesa1-bitrepresentationof32successivesamplesofitspromptpseudo-randomnoise(PRN)codereplicaandstorestheminparallelinasingle32-bitunsignedintegerword.Italsogeneratesanearly-minus-latePRNcodereplicathatrequires1.5bitspersample,whichtakesuptwo32-bitunsignedintegerwordstostore32samples.Thesereplicasignalscanbegeneratedveryefficientlybyusingpre-tabulated32-bitwords.Thesoftwarereceiverthenperformsaseriesofbit-wiseAND,OR,XOR,andsimilaroperationsthathavetheeffectofperformingPRNcodemixingandIF-to-basebandcarriermixing.Theoutputsofthemixingoperationsarecontainedinasmallnumberof32-bitwords,thenumberofwhichdependsonthenumberofbitsineachRFfront-endoutputsampleandthenumberofbitsintheIFcarrierreplicas.

6

Thefinaloperationisaccumulationoftheresultsinthe32-bitwords.Thisinvolvessetsofbit-wiseBooleanoperations,asper

Ledvinaetal.

(2003),followedbysummationofthenumberof1-bitsintheresulting32-bitunsignedintegerwords

.Thebitsummationoperationsprovedtobeachallengeintermsofminimizingexecutiontime.Ledvinasolvedthisproblembyusingapre-computed1-dimensionaldatatablewhoseinputwastheunsignedintegerandwhoseoutputwasthenumberof1-bits.Inordertokeepthetablesizereasonable,itonlycountedthebitsina16-bitunsignedintegerword.Theoriginalreceiver’s32-bitwordsweresplitinhalf,twotablelook-upswereperformed,andtheresultssummedinordertocountallthe1-bits.Theoriginalalgorithmsaredefinedby

Ledvinaetal.

(2003),

Ledvina,Psiaki,Powell,&Kintner

(2004),and

Ledvina,Psiaki,Powell,&

Kintner

(2006)

.

WhenusingverylongPRNcodes,suchastheL2CCLcode,theoriginalmethod’swhole-periodPRNcodetablesoftheproper32-bitwordsatvariouscodephasesbecameimpracticallylarge.Therefore,anewmethodwasdevelopedforlongPRNcodes.Ittabulates32-bitwordsofshortgenericPRNcodechipsequences,withallpossiblecombinationsofashortsequencesofchipsconsideredatvariousPRNcodeoffsetsrelativetothestartofthesamplesofthe32-bitword.Thosemethodsaredescribedby

Psiaki

(2006)andby

Ledvinaetal.

(2007)

.Thistechniqueprovedinvaluablefordealingwithlongcodes.

Aprocessorthatcanoperateonwidersegmentsofdata,upto512bitsforcurrentsingleinstructionmultipledata(SIMD)

instructions,gainssubstantialadditionalsignalprocessingspeedincreases(Nicholsetal.,

2022)

.Note,however,thatthespeedincreasefactorsoverbrute-forceintegercalculationsaretypicallynotashighasthenumberofbitsperword.Thatis,thetechniquesdonotspeeduptheoperationsbyafactorof32whenprocessing32samplesinparallelbyusing32-bitwordstorepresent32samples.Fora2-bitRFfront-endanda32-bitprocessor,thespeed-upfactormightbeonly4becausethebit-wiseparallelapproachrequiresmultipleoperationsdueto,say,asimplemultiplicationofonetimeseriesbyanother.Ifonedoublesthenumberofbitsperword,however,thenthespeedtendstodouble.Aparticularlyhelpfulfeatureofsomerecentprocessordesignsistheirinclusionofahardwiredcommandtocountallthe1bitsinaword.This“popcount”intrinsicobviatesthetablelook-upsthatcounted1-bitsintheoriginalbitwiseparalleldesign.IfthenumberofbitsincreasesintheRFfront-endsamplesand/ortheIFcarrierreplicas,however,thenthebit-wiseparallelmethodofsignalprocessingslowsdown.Signalsrepresentedby3or4bitsmightcausetheprocessingspeedgainsofbit-wiseparallelalgorithmstobelimitedorevennon-existent.

Aftergettingthebasicalgorithmsworkinginreal-timeusing32-bitwords,theCornellgroupshowcasedtheefficacyofreal-timeGNSSsoftwareradiobyusingthetechniquestodevelopadual-

frequencyL1C/AandL2Creceiver(Ledvina,Psiaki,

Sheinfeld,etal.,

2004)andaGPS/GalileoL1civilianreceiver(Ledvina,Psiaki,Humphreys,etal.,

2006)

.Thesereal-timesoftwareGNSSreceiverseachrequiredonlyseveralperson-daystodevelopthemfromtheoriginalL1C/Acodereceiver.Ofcourse,theL1/L2receiverrequiredanewdual-frequencyRFfront-end.TheGPS/GalileoreceiverrequiredknowledgeofthecivilianGalileoE1PRNcodes,whichhadnotbeenpublishedatthattime.ThisrequirementledtoasupportingeffortwhichsuccessfullydeducedtheGalileoGIOVE-AE1PRNcodesbyrecordingtheirrawRFfront-endsamplesandpost-processingthosesamplesusingasuiteofcustom-designedSDRsignalprocessingalgorithmsinordertopullthechipsoutofthenoise

(Psiakietal.,

2006)

.

Thenextdevelopmentwastore-implementthebit-wiseparallelcodeforembedded(low-power,low-cost)processing.Ini-tiallytargetingaTexasInstrumentsDSP,thisworkwasaccomplishedin2006bythen-Ph.D.candidateToddHumphreys

(T.Humphreysetal.,

2006)

.Later,asaprofessoratTheUniversityofTexasatAustin,Humphreysandhisstudents—notablyJahshanBhattiandMatthewMurrian—undertook