宽带线性调频信号Stretch处理误差获取与补偿

20051271SystemsEngineeringandElectronicsJan.2005Vol127No11:2004-03-01;:2004-11-02:(1971-),,,,:1001-506X(2005)01-0036-04Stretch文树梁1,2,袁起1,秦忠宇2(1.北京理工大学电子工程系,北京100081;2.中国航天科工集团二院二十三所,北京100854):宽带线性调频信号是宽带高分辨率雷达的一种信号形式,在实际应用中可采用Stretch处理来降低A/D采样速率的要求先推导了系统有误差时线性调频信号Stretch处理的雷达接收回波数学模型,提出误差估计的方法,并针对Stretch处理的时变特性提出了线性调频信号Stretch处理的误差补偿方法仿真实验表明该方法对宽带线性调频信号误差的估计与补偿是有效的:宽带雷达;CHIRP信号;Stretch处理;误差:TN957:AErroracquisitionandcompensationforwidebandlinearfrequencymodulatedsignalStretchprocessingWENShu-liang1,2,YUANQi1,QINZhong-yu2(1.DepartmentofElectronicsEngineering,BeijingInstituteofTechnology,Beijing100081,China;2.No.23InstituteoftheSecondAcademy,ChinaAerospaceScienceandIndustryCorporation,Beijing100854,China)Abstract:Widebandlinearfrequencymodulatedsignalisasignalformofwidebandhighresolutionradar.ItcanbeprocessedbyusingStretchmethod,whichcandecreasetheA/Dsamplingrateinengineeringapplications.Amath-ematicalmodelforStretchprocessingwhenthesystemisimperfectisobtained,themethodoferrorestimationispro-posed,andthecompensationmethodbasedontime-variantpropertyofStretchprocessingisalsoestablished.Simulationresultsdemonstratetheproposederrorestimationandcompensationmethodiseffective.Keywords:widebandradar;CHIRPsignal;Stretchprocessing;error1,,,,Stretch[1],,FFTCAlcorISAR,THAAD,,,,,,Stretch,,Stretch,,2Stretch,s(t)=recttTej2Pf0t+12ut2+U0,tI-T2T2(1):f0))),u))),T))),U0))),B=uT,rectrect(x)=1,|x|[120,,U(t)=2Pf0t+12ut2+U0Tr(Tr),„t=t-lTr,sx(„t,l)=rect„tTexpj2Pf0t+u2„t2+U0=rect„t3expj2Pf0lTr+f0„t+u2„t2+U0(2),,[2],W1(t)=A1(t)exp[j1(t)],A1(t),1(t),ss(„t,l)=sx(„t,l)W1(t)=rect„tTA1(t)#expj2Pf0lTr+f0„t+u2„t2+U0+1(t)(3),H(f),,,s(t)[2]sout(t)=s(t)H12PUc(t)(4)H1(f)(),(4),1(t),sT(„t,l)=ss(„t,l)H1(f0+u„t)=rect(„tT)A1(t)H1(f0+u„t)#expj2Pf0lTr+f0„t+u2„t2+U0+1(t)(5)vi,lisiRT(„t,l)=RisTAi„t-Sli,l=RirectAi„t-SliT#A1Ai„t-SliH1f0+uAi„t-Sliexpj2Pf0lTr+f0Ai„t-Sli+u2A2i„t-Sli2+U0+1Ai„t-Sli(6):Sli)))li,Ai=1-Di,Di)))i,[3]Ai=1-Di=1-vic1+vicU1-2vic(7)(7)Di2vic,c,vi,fd=-2viKH2(f),(6)f=f0Ai+uA2i„t-Sli,siR(„t,l)=siRT(„t,l)H2(f)=RirectAi(„t-Sli)T#A1Ai(„t-Sli)H1f0+uAi„t-SliH2f0Ai+uA2i„t-Sli#expj2Pf0lTr+f0Ai„t-Sli+u2A2i„t-Sli2+U0+1Ai„t-Sli(8),,,sref(„t,l)=ss(„t-Sl,l)=rect„t-SlTref#expj2Pf0lTr+f0(„t-Sl)+u2(„t-Sl)2+jU0+1„t-Sl(9):Sl)))l,Tref))),T,sio(„t,l)=siR„t,ls*ref„t,l=RirectAi(„t-Sli)TA1Ai(„t-Sli)H1f0+uAi„t-SliH2f0Ai+uA2i„t-Sli#exp1Ai„t-Sli-1„t-Slexp-j2Pu21-A2i„t-Sl2#exp-j2P[(1-Ai)f0]„t-Sl)exp-j2PuA2iSli-Sl„t-Sl+f0AiSli-Sl-u2A2iSli-Sl2(10)^t=„t-Sl,$Sli=Sli-Sl=2$Rlic,(10)sio(^t,l)=RirectAi^t-$SliTA1Ai^t-$SliH1f0+uAi^t-$SliH2f0Ai+uA2i^t-$Sli#expj1Ai^t-$Sli-j1(^t)exp-j2Pu21-A2i^t2#exp-j2P[(1-Ai)f0]^texp-j2PuA2i$Sli^t+f0Ai$Sli-u2A2i$Sli2(11)#37#271Stretch(11)Stretch,,,(11),,3H1(f)H2(f)[4],,,0,sioJ(^t,l)=Rirect^t-$SliTA1^t-$Sli#H1f0+u^t-$SliH2f0+u^t-$Sli#expj1^t-$Sli-1(^t)#exp-j2Pu$Sli^t+f0$Sli-u2$Sli2(12),,[5],s1(^t,l)=rect^tTA1^tH1f0+u^tH2f0+u^t(13)s2i(^t,l)=rect^tTexpj1^t-1^t+$Sli(14)s1(^t,l),(12),$Sli=0,s1(^t,l),$Sli=0,sioJ(^t,l)=Ris1(^t,l)(15)s1(^t,l),,s1(^t,l),$Sli,s1(^t-$Sli,l)sioJB(^t,l)=Ris2i^t-$Sli#exp-j2Pu$Sli^t+f0$Sli-u2$Sli2(16)(16)sioJB(f,l),s2i(^t-$Sli,l)=1Riexpj2Pf0$Sli-u2$Sli2#QsioJBf-u$Sli,lexp(j2Pft)df(17)sioJB(f,l)-u$Sli,s2i(^t-$Sli,l),y(^t)=arctan(s2i(^t-$Sli,l))=1(^t-$Sli)-1(^t)(18)1(f)=y(f)e-j2Pf$Sli-1(19)1(^t),,0,:(1),,1(^t)A1(^t);(2),,H2(f);(3),H1(f)4(11),,(,),sio(^t,l)=RiE(^t-$Sli)#exp-j2PuA2i$Sli^t+f0Ai$Sli-u2A2i$Sli2(20)E(^t,Ai)=rectAi(^t)TA1(Ai(^t))H1(f0+uAi^t)#H2(f0Ai+uA2i^t)expj1[Ai^t]-j1(^t+$Sli)(21)-uA2i$Sli,,,4vic,30m,5000m/s,0.002m,,h(^t,Ai)[6]h(^t,Ai)=1E(^t,Ai)(22)BI,$Slimax=BIT2B,E(^t-$Slimax,Ai)E(^t,Ai)(km),,(),fi=-u$SliA2i,hm=h(^t-$SBlm,Ai)(m=-M,,,0,,,M,$SBlm=m$SlimaxM+0.5)#38#2005,fZm=-u$SBlmA2i,fW=u$SlimaxM+0.5,,12,,,[2]2M+1FFT,,,2M+3FFTfs,MMmax=BITfsB,M12,,,(20),12siBO(^t,l)=Riexp-j2Pf0Ai$Sli-u2A2i$Sli2#EMm=-ME(^t-$Sli,Ai)E(^t-$SBlm,Ai)exp[-j2PuA2i$Sli^t]áhm(^t)(23)á,E(^t-$Sli,Ai)E(^t-$SBlm,Ai)hm(^t)Eim(f)hm(f),fi=-uA2i$Sli,siBO(f,l)=Riexp-j2Pf0Ai$Sli-u2A2i$Sli2#EMm=-MEim(f-fi)hm(f)(24)Eim(f)0Ai(^t)T,Eim(f-fi)fiAi(^t)T,fZmi=-u$SBlmiA2i,mi|$Sli-$SBlmi|m,siBO(f,l)=Riexp-j2Pf0Ai$Sli-u2A2i$Sli2#Eimi(f-fi)(25a)siBO(^t,l)=Riexp-j2Pf0Ai$Sli-u2A2i$Sli2#E(^t-$Sli,Ai)E(^t-$SBlmi,Ai)exp(-j2PuA2i$Sli^t)(25b)Emax(^t-$Sli,Ai)=E(^t-$Sli,Ai)E^t-$Sli?$Slimax2M+1,Ai=1ºEc^t-$Sli?$Slimax2M+1,Ai$Slimax2M+1+(26)Ec(.)E(.),ME(.)1$Slimax,1,5,5.5GHz,500MHz,300us,302us,50dB3;,0.2us,4,,,,34,3,-100m,-99m,-101m,(184)#39#271Stretch9(K=31,SNR=3)6MMSEDFD,MMSEDFDEGCMMSEDFDMRC,MMSEDFDEGCMMSEDFDMRCLMMSE,MMSEDFDMRC,MMSEDFDEGCMMSEDFDMRCMMSEDFDEGCMMSEDFDMRC:[1]LiuH.SignalprocessingapplicationsinCDMAcommunications[M].USA:ArtechHouse,2000.[2]KondoS,MilsteinLB.PerformanceofmulticarrierDS-CDMAststems[J].IEEETrans.onCommun.,1996,44(2):238-246.[3]WangY,WuJ,DuZM,etal.PerformanceofMMSEmultiuserdetec-tionfordownlinkCDMA[A].IEEEInternationalconferenceonCom-mun.,NewOrlean:IEEE.2000.919-923.[4]GraemeWoodware,RapeepatRatasuk,elal.Minimummean-spuarederrormultiuserdecision-feedbackdetectorsforDS-CDMA[J].IEEETrans.onCommun.,2002,50(12):2104-2112.[5]Rapaji