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1、ACOMPRESSIVEPHASE-LOCKEDLOOPStephenR.Schnelle,1J.P.Slavinsky,1PetrosT.Boufounos,2MarkA.Davenport,3RichardG.Baraniuk11DepartmentofElectricalandComputerEngineering,RiceUniversity,Houston,TX770052MistubishiElectricResearchLaboratories,Cambridge,MA021393DepartmentofStatistics,Stanfor
2、dUniversity,Stanford,CA94305ABSTRACTPhaseLoopFilter/WedevelopanewmethodfortrackingnarrowbandsignalsacquiredDetectorPhaseUpdateviacompressivesensing.Thecompressivesensingphase-lockedloop(CS-PLL)enablesonetotrackoscillatingsignalsinverylargebandwidthsusingsub-Nyquistsampling.Akeyfe
3、atureoftheap-Oscillatorproachisthefactthatweperformthefrequencytrackingdirectlyonthecompressivemeasurementswithouteverrecoveringthesignal.Fig.1.BasicdiscretetimePLLdesign.TheCS-PLLhasawidevarietyofpotentialapplications,includingcommunications,phasetracking,androbustcontrol.as[2],
4、thatwouldrequiretheuseofaconventionalPLLonthere-IndexTerms—Compressivesensing,phase-lockedloop,FMcoveredsignal.Thankstotheimplementationofothersignalpro-demodulationcessingoperationsinthecompressivedomain,suchasfilteringanddetectionsystems[3],theCS-PLLcanbeintegratedsmoothlyinto1.
5、INTRODUCTIONdevicessuchaswidebandcompressiveradioreceivers,whichcantrackandmonitorawiderangeofradiofrequenciesinreal-time.Compressivesensing(CS)isarecentlydevelopedfieldwithinsignalAspecialcaseoftheCS-PLLincludesPLLsthatuserandomprocessingthatenablestheacquisitionandrecoveryofspar
6、sesignalssampling,whichhavebeenexploredinpreviousworks.Forin-withoutlossofinformationatasamplingratesignificantlybelowstance,asimpleFPGAimplementationofaphase-lockedloopfortheNyquistrate.CSusesarandomizedmeasurementsystem,andquantizedadditiverandomsampling(ARS)wassupportedwithnu-t
7、ypicallyrecoversthesignalviaconvexoptimizationoroneofafleetmericalsimulationsforvaryingloopfilterparametersinarandomofgreedyrecoveryalgorithms.SeveralhardwarearchitectureshavesamplingPLLforsynchronizationapplicationsin[4].Thispaperappliedthistheorytowidebandanalogsignals.generalize
8、sthisapproachtomoregenericCSsamplingsche
