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1、TMOProgressReport42-141May15,2000ImprovedCarrierTrackingforLow-ThresholdTelemetryUsingaSmootherW.J.Hurd1andA.Mileant2Thisworkestablishesthethresholdperformanceofnoncausalsmoothing¯ltersusedfortrackingresidualcarriersignalswhenperformanceislimitedbybothphaseprocessnoiseandadditiver
2、eceivernoise.Previouswork[1]basedentirelyonlineartheorypredictssigni¯cantimprovementsinphaseestimationbyusingsmoothing¯ltersascomparedwithusingcausalphase-lockedloops(PLLs).Forphaseprocessnoisehavinga1=f3spectraldensity,whichistypicalofmanyoscillators,lineartheorypredictsareductio
3、ninphaseestimationerrorof5dBforthesamephase-noiseandreceiver-noisemagnitudes.Alternatively,lineartheorypredictstheabilityofasmoothertotracka7.5-dBweakersignalwiththesamemean-squarephaseerror,underthesameconditionsofphaseprocessnoise.Simulationsshowthatthesmoothersachieveane®ective
4、loopsignal-to-noiseratio(SNR)within0.5dBoflineartheorywhenthelineartheorypredictsane®ectiveloopSNRaslowas11.4dB.Underthesameconditions,anoptimumPLLwouldhavealinear-modele®ectiveloopSNRofonly6.4dBandwouldperformmorethan1-dBworsethatthis,withmanycycleslips.I.IntroductionThegeneralpr
5、oblemofestimatingthephaseofacarriersignalinnoise,whenthecarrierphaseisarandomprocess,ishighlynonlinear.Whentheconditionsaresuchthattheestimationerrorisfairlysmall,theperformancecanbewellpredictedbyalinearmodel.Forexample,linearmodelsforphase-lockedloops(PLLs)arereasonablyaccuratew
6、henthemean-squarephaseerrorislessthanapproximately0.1rad2.Thelinearmodelisnotadequateinthethresholdregionwhencycleslippingoccurs.Toobtainasimplemodeltopredicttheperformanceofnoncausal¯ltersandto¯ndoptimum¯lters,previouswork[1]hastreatedtheproblemaslinear.Thecurrentworkdeterminesth
7、evalidrangeofthelinearmodelandtheusefulrangeofthesmoothing¯lters,i.e.,therangeabovethreshold.Thelinearanalysismodelsthereceivedcarriersignalasarandomphaseprocessplusadditivewhitereceivernoise.FromWiener¯lteringtheory,theoptimumlinearestimatorofthephaseprocessisthenoncausal¯lter,or
8、smoother,withtransferfunction1TMO
