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FMICW信号模糊函数分析
Introduction
FrequencyModulatedContinuousWave(FMCW)radarisacommonlyusedradartechnologythatexploitsthefrequencymodulationoftheemittedsignal.FMCWradarsystemsarewidelyusedinapplicationssuchasautomotiveradar,weathermonitoring,andnavigation.OneofthekeyparametersofanFMCWradarsystemistheambiguityfunction,whichcharacterizesthesystem’sabilitytodistinguishbetweentargetsatdifferentrangesandvelocities.
AmbiguityFunction
TheambiguityfunctionofanFMCWradarsystemisamathematicalrepresentationofthesystem’stimeandfrequencyresolution.TheambiguityfunctionisdefinedastheFouriertransformofthetimeandfrequencyresponseoftheradarsystem.Theambiguityfunctionisacomplex-valuedfunctionoftwovariables,delayandDopplerfrequency,whichcanbeexpressedas:
A(τ,Δf)=∫s(t)s(t-τ)exp(-j2πΔft)dt
Inthisequation,s(t)isthetransmittedsignal,τisthedelay,andΔfistheDopplerfrequency.Theambiguityfunctionrepresentstheautocorrelationfunctionofthereceivedsignal,whichisameasureofthesystem’ssignalprocessingcapabilities.
FMCWSignalProcessing
FMCWradarsystemsuseatechniquecalledfrequencymodulationtoprovidehigh-resolutionrangeandvelocitymeasurements.Thetransmittedsignalisacontinuouswavethatismodulatedinfrequencybyasinusoidalwaveform.Themodulationwaveformisusuallyalinearramp,whichresultsinachirpwaveform.Thefrequencymodulationofthetransmittedpulsecausesthepulsetospreadoutintimeasittravelsawayfromtheradarsystem.
Thereceivedsignalisanechoofthetransmittedpulse,whichisreflectedoffofatarget.ThedelayandDopplershiftofthereceivedpulseareproportionaltothetimeandfrequencydifferencebetweenthetransmittedandreceivedpulses.Thetimedelayisproportionaltotherangeofthetarget,whiletheDopplershiftisproportionaltothevelocityofthetarget.
FMCWAmbiguityFunction
TheambiguityfunctionofanFMCWradarsystemisafunctionofbothdelayandfrequency.Thedelayaxisrepresentstherangeofthetarget,whilethefrequencyaxisrepresentstheDopplershiftofthereceivedsignal.Theambiguityfunctiondescribesthesystem’sabilitytodistinguishbetweentargetsatdifferentrangesandvelocities.T