对称三角线性调频连续波雷达信号多周期模糊函数分析

33120092()JournalofNanjingUniversityofScienceandTechnology(NaturalScience)Vo.l33No.1Feb.2009:2007-09-11:2008-11-26:(1981-),,,:,Emai:[e-mail];:(1966-),,,,:,Emai:[e-mail]吴礼,彭树生,肖泽龙,是湘全(,210094):针对大时带宽积对称三角形线性调频连续波信号模糊函数须考虑多普勒效应对复包络函数的影响,该文利用信号复包络求解法,导出了大时带宽积对称三角线性调频连续波信号的单周期与多周期模糊函数,研究了它们的对称性模糊度图及沿主轴切割性质等特性通过分析模糊函数表达式,得到了单多周期信号的理论多普勒分辨率与时延分辨率结果表明:单周期和多周期信号的时延分辨率相同,而N周期信号的多普勒分辨率提高到单周期信号的1/N:线性调频;连续波信号;对称三角多周期模糊函数;多普勒分辨率;时延分辨率:TN958.94:1005-9830(2009)01-0074-05MultiperiodAmbiguityFunctionAnalysisofSymmetricalTriangleLinearFrequencyModulationContinuousWaveSignalsWUL,iPENGShusheng,XIAOZelong,SHIXiangquan(SchoolofElectronicEngineeringandOptoelectronicTechnology,NUST,Nanjing210094,China)Abstract:FortheproblemtotakeintoaccountofDopplereffectonthecomplexenvelopeinlargetimebandwidthproductsymmetricaltrianglelinearfrequencymodulationcontinuouswave(LFMCW)signalambiguityfunction,thispaperadoptsacomplexenvelopesolutiontodeducesingleperiodandmultiperiodambiguityfunctionsofthelargetimebandwidthproductsymmetricaltriangleLFMCWsignals.Theirsymmetry,ambiguitymapandambiguityfunctioncutalongtheirprincipalaxisarestudied.Byanalyzingambiguityfunctionexpressions,thispaperresolvestheoreticDopplersignalresolutionsanddelayresolutionsofsingleperiodandmultiperiodsymmetricaltriangleLFMCWsignals.TheresultsshowthatthesingleperiodandmultiperiodLFMCWsignalshaveasamedelayresolution,andthemultiperiodLFMCWsignalDopplerresolutionis1/Nofsingleperiodsignals.Keywords:linearfrequencymodulation;continuouswavesignals;symmetricaltrianglemultiperiodambiguityfunctions;Dopplerresolutions;delayresolutions164,(LFMCW)[1-3]LFMCW,,LFMCW,[4],[5]LFMCW,[6]LFMCWLFMCW,Levanon,Nsin(NT)/Nsin(T)(T,)[7,8]Freedman[8,9]LFMCW[10],,LFMCW;[10],LFMCW,LFMCW,LFMCW1(TBc/2v),[5](,t!)=-u(t)u*(t+t)ej2!tdt(1):t!,u(t),:(,t!)=-u(t)u*(1+!f0)(t+t)ej2!tdt(2)1.1LFMCWLFMCW[-T,0],[0,T],u(t)=ejkt2/2T-Tt!0e-jkt2/2T0t!T0(3)(,t!)=12TT-Tu(t)u*(1+!f0)(t+t)ej2!tdt(4)(3)(4),!∀0(,t!)(,t!)=ejf0(kt-!)22k!#14Tf0k|!|{C(x1)+C(x2)-j[S(x1)+S(x2)]}+ejf0(kt+!)22k!#14Tf0k|!|#{C(x3)+C(x4)+j[S(x3)+S(x4)]}(5):x1=f0t!-f0kk|!|f0x2=2T-f0t2!-t+f02kk|!|f0x3=-2f0t2!+f02k+tk|!|f0x4=T+f0t2!+f02kk|!|f0C(x)=0xcos2t2dtS(x)=0xsin2t2dt:C(x)S(x)!=0:(,t0)=eiktTsin(kt(T-t))ktT(6)t=t/(1/B),;!=!/(1/T),T;∀=B/f0[6],(5)!∀0:75()331(,t!)=ej(,t!)22∀!#14∀|!|{C(x1)+C(x2)-sgn(!)#j[S(x1)+S(x2)]}+e-j(,t!)22∀!#14∀|!|#{C(x3)+C(x4)+sgn(!)#j[S(x3)+S(x4)]}(7):x1=|!|∀(-1+t!),x2=|!|∀(1-t!+2∀),x3=|!|∀(-1-t!),x4=|!|∀(1+t!+2∀),sgn(!)=1!0-1!0(,t!)|(,t!)|=14∀|!|ejt2+!22∀!{C(x1)+C(x2)-sgn(!)#j[S(x1)+S(x2)]}+e-jt2+!22∀!{C(x3)+C(x4)+sgn(!)#j[S(x3)+S(x4)]}(8)!=0,T:t(,t0)∃ejtsinc(t),|(,t0)|=|sinc(t)|(9)∀=0.0143,11STLFMCW1.2LFMCWLFMCWN,uN(t)uN(t)=1N%N-1i=0u1(t-2iT)(10)NN(,t!)=-uN(t)u*N[(1+!f0)(t+t)]ej2!tdt=-1N%N-1i=0u1(t-2iT)1N%N-1j=0u*1[(1+!f0)#(t-2jT+t)]ej2!tdt=1N%N-1i=0%N-1j=0-u1(t-2iT)u*1[(1+!f0)(t-2jT+t)]ej2!tdt(11)x=t-2iT,N(,t!)=1N%N-1i=0ej4!iT%N-1j=01(t+2(i-j)T),!)(12):1(t+2(i-j)T),!),p=(i-j),N(,t!)=1N%N-1p=-(N-1)ej2!(N-1+p)T#sin2!(N-|p|)Tsin2!T1(t+2pT,!)(13):|t+2pT|T,|t|T,|N(,t!)|=1N%N-1p=-(N-1)sin2!(N-|p|)Tsin2!T#|1(t+2pT,!)|(14),p=0,:|N(,t!)|p=0=sin2!NTNsin2!T|1(,t!)|(15)|N(,t!)|p=0=sin2N!Nsin2!|1(,t!)|(16)2N=8,∀=0.0143LFMCW2STLFMCW22.1(8)(16),LFMCW|(,t!)|=|(-,t-!)|,|(,t!)|=|(,t-!)|,|(,t!)|=|(-,t!)|,t!76164LFMCW,t!t=(1+∀)!t=-(1+∀)!,tt=&(1+∀)!,,,,/t=&!∀0(),,[4]LFMCW,(14),tp1(t+2pT,!)sin2!(N-|p|)Tsin2!T,t!2,LFMCW,(&(1+∀)K2BT,K2BT)(K)2.22.2.1t=0,t=0(8),LFMCW:|1(0,!)|=sin(2!)2!(17)LFMCW1/2,#!=1/2T(18)t=0(16),LFMCW|N(0,!)|p=0=sin2N!2N!(19)LFMCW1/2N,#!=1/2NT(20)(18)(20),LFMCWN(N),33t=0,/STLFMCW2.2.2!=0,|T(,t0)|=|sinc(t)|(21),#t=1,#R=c/(2B)4,4!=0,/STLFMCW2.3LFMCW(N=8)3dB56,,,,,,5STLFMCW3dB77()3316STLFMCW3dB3,LFMCW,,,,,LFMCW:[1]StoveAG.LinearFMCWradartechniques[J].RadarandSignalProcessing,IEEProceedingsF.1992,139(5):343-350.[2]WidzykCapehartE,BrookerG,SchedingS,eta.lApplicationofmillimeterwaveradarsensortoenvironmentmappinginsurfacemining[A].9thInternationalConferenceonContro,lAutomationRoboticsandVision,ICARCV2006[C].Singapore:IEEEControlSystemsSociety,2006.[3],,.3mm[J].(),2005,29(2):166-168.[4],,.LFMCW[J].,2004,26(2):169-173.[5],.[M].:,1984.[6],,,.[J].,2004,32(3):353-356.[7]LevanonN,FreedmanA.PeriodicambiguityfunctionofCWsignalswithperfectperiodicautocorrelation[J].IEEETransactionsonAerospaceandElectronicSystems,1992,28(2):387-395.[8]LevanonN,MozesonE.Radarsignals[M].Hoboken,NewJersey:JohnWileyandSons,Inc,2004.[9]FreedmanA,LevanonN.Propertiesoftheperiodicambiguityfunction[J].IEEETransactionsonAerospaceandElectronicSystems,1994,30(3):938-941.[10],.LFMCW[J].,2004,33(5):543-546.78