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193©Vol.19No.320072JournalofSystemSimulationFeb.,2007593SAR1,211.,1000802.,100080(SyntheticApertureRADARSAR)SARSARSARTP273A1004-731X(2007)03-0593-04NovelAzimuthPre-filterDesignMethodUsingExtend-LagrangeFunctionforReal-timeAirborneSARImagingSystemGUOMeng1,2,WANGZhen-song1(1.InstituteofComputingTechnology,ChineseAcadmicofScience,Beijing100080,China;2.GruduateSchoolofChineseAcademicofScience,Beijing100080,China)AbstractAsoneofkeyprocessingofthereal-timeairbornesyntheticapertureRADAR(SAR)imagingsystem,theperformanceofAzimuthPre-filterfordatareductiondeterminesthequalityofSARimages.AnewAzimuthPre-filterdesignmethodwasproposed.TheoptimizecriterionofMinimumoftheMean-SquareErrorinpass-bandandMinimumoftheMaximumErrorinstop-bandwasproposed,andanovelcomputingmethodusingextend-LagrangefunctionforAzimuthPre-filterinreal-timeairborneSARImagingSystemwasalsoproposed.Theanalysisresultsofcomputersimulationshowthat,withthisnewmethod,atsamecomputationalcost,memorysize,andpowercost,thebetterperformanceoffiltercanbeachieved.Thus,thismethodismoresuitableforreal-timeairborneapplications.KeywordsReal-timeairborneSARimagingsystem;azimuthPre-filter;optimizecriterion;extend-Lagrangefunction1(SyntheticApertureRADARSAR)SAR(RD)ChirpScaling(CS)SARSAR[1,2]SARPRFPRFPRF2005-11-212006-03-13(60303017);863(2003AA135093)(1981-),,,,(1945-),,,,,SAR1NNSAR[4]2NKNKP=P1193Vol.19No.320072Feb.,2007594∑I∑Q'I)(nhI)(nhI)(nhQ∑'Q∑MUXCCUIQPRFCLK2NSARSARSARSAR[4-6][1]P4P[5][5]FIR1M()SARFIR[7]HammingKaiserBlackman[7]GibbsSAR234451()dHw()dhn,()0,jwdeHw-⎧=⎨⎩a,ccccwwwwwww--≤-≤pp1()()2ccwjwnddwhnHwedw-=∫p)(nh)(wH101/21()20()()1()cos()2NjwnnNNjwnHwhneNehnnw--=---==-⎡⎤=-⎢⎥⎣⎦∑∑FIRNN201()()2cwpdDHwHwdw=-∫p220()()ccwwHwdwPSRHwdw=∫∫p201()()2cwdMinHwHwdw⎧⎫⎪⎪-⎨⎬⎪⎪⎩⎭∫pIQ193Vol.19No.320072,SARFeb.,2007595{}{}[,)()()cdwwMinMaxHwHw∈-p)(nh-15dB()0.032,Hw≤cww≤p11/21()200201()()()cos()21()()2()0.032,cNNNjwjwnnnwdcNHwhneehnnwMinHwHwdwHwww-----==-⎡⎤==-⎢⎥⎣⎦⎧⎫⎪⎪-⎨⎬⎪⎪⎩⎭≤≤∑∑∫pp(1))(nh-15dB[3]2(1)202/21001()()()2111()cos()22ccwdwNnfhHwHwdwNhnnwdw-==--⎡⎤=--⎢⎥⎣⎦∫∑∫rpp[(0),(1)(1)]ThhhhN=-rL(1)/210()0.032()10.032()cos(),2kkNknghHwNhnnw-==--⎡⎤=--⎢⎥⎣⎦∑r[1,],[,)kckKww∈∈pKK(1){()}()0,(1,2,)kMinfhghkK⎧⎪⎨≥=⎪⎩rrL(2)(2)[3]12[,,,]TkKYyyyy=rLL2()0kkghy-=r2{()}()0,(1,2,)kkMinfhghykK⎧⎪⎨-==⎪⎩rrL222112221ˆ(,,,)()(())(())21()(())22KKkkkkkkkKkkkkkMhYMfhghyghyMfhyMghMM====--+-⎧⎫⎪⎪⎡⎤=+---⎨⎬⎢⎥⎣⎦⎪⎪⎩⎭∑∑∑rrrrrrrrjllllM12[,,,,,]TkK=rLLlllll,22211(())(())2KKkkkkkkkMghyghy==-+-∑∑rrl,221(())2KkkkMghy=-∑rˆ{(,,,)}MinhYMrrrjl(3)(3)(,)hYrrYrYrhrˆ{(,,,)}MinhYMrrrjlYr0Yr21{0,()}kkkyMaxMghM=-rlˆ{(,,,)}MinhYMrrrjl(,,)hMrrl2211(,,)(){[(0,())]}2KkkkkhMfhMaxMghM==+--∑rrrrjlll(,,)hMrrjl[3](1)(0)h→)1(→lM1a(0,1)∈b0e1=t(2))1(-→th(){(,,)}tMinhM→→jl)(th→(3)()()tkgh→→e()th→(4)⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡=→→→→→→)()()()()()()()(2)(1)(tKtktttkhghghghghgMM(4)Mb≥-→→→→)()()1()(tktkhghgMMa=(5)(5)(5)→l(1)(){0,ttkkMax+=-ll()()}tkMgh→→l1+=tt(2)340.25SAR193Vol.19No.320072Feb.,20075964{}[]2/47001()1()cos(7.5)2nMinfhMinhnnwdw=⎧⎫⎪⎪=--⎨⎬⎪⎪⎩⎭∑∫rpp[]70()0.032()0.032()cos(7.5)0,kkknghHwhnnw==-=--≥∑r[1,],[,)kckKww∈∈ph(0)h(15)0h(1)h(14)0.00521317h(2)h(13)0.02875704h(3)h(12)0.05201988h(4)h(11)0.07921504h(5)h(10)0.1147553h(6)h(9)0.1338148h(7)h(8)0.1622188================3FrequencydomainNormalizedFrequency:0.25Magnitude(dB):-25.4500-50-100-150-200Magnitude(dB)NormalizedFrequency(rad/sample)00.20.40.60.8334.950.084FrequencydomainNormalizedFrequency:0.25Magnitude(dB):-25.4Magnitude(dB)-50-60-70-20-30-40100-1000.20.40.60.8NormalizedFrequency(rad/sample)4447.350.10HammingKaiser0.165[5]2010FrequencydomainNormalizedFrequency:0.1Magnitude(dB):11NormalizedFrequency(rad/sample)00.20.40.60.840200-20-40-60Magnitude(dB)56264SARSAR(600)193Vol.19No.320072Feb.,20076001.01.52.02.53.03.54.0-1000100200300400500600700YAxisTitleXAxisTitleSSRED(H=0.90)SSRED(H=0.65)REDTD51.01.52.02.53.03.54.0-0.015-0.010-0.0050.0000.0050.010YAxisTitleXAxisTitleSSRED(H=0.90)SSRED(H=0.65)REDTD6(2)SSREDmaxp(3)SSREDH4InternetH(SSRED)[1]FloydS,JacobsonV.RandomEarlyDetectionGatewaysforCongestionAvoidance[J].IEEE/ACMTransactionsonNetworking(S1063-6692),1993,1(4):397-413.[2]FloydS.RecommendationonUsingtheGentleVariantofREDAlgorithm[EB/OL].[3]FloydS,GummadiR,ShenkerS.AdaptiveRED:AnAlgorithmforIncreasingtheRobustnessofRED’sActiveQueueManagement[R].Technicalreport,ICSI.2001.[4]FengW,KandlurD,SahaD,ShinK.StochasticFairBlue:AQueueManagementAlgorithmforEnforcingFairness[C]//ProceedingsofINFOCOM2001,Anchorage,Alaska,2001,1520-1529.[5]LelandWE,TaqquM,WillingerW.OntheSelf-SimilarNatureofEthernetTraffic(extendedversion)[J].IEEE/ACMTransactionsonNetworking(S1063-6692),1994,2(1):1-15.[6]PaxsonV,FloydS.WideAreaTraffic:theFailureofPoissonModeling[J].IEEE/ACMTransactionsonNetworking(S1063-6692),1995,3(3):226-244.[7]CrovellaME,BestavrosA.Self-SimilarityinWorld-WideWebTraffic:EvidenceandPossibleCauses[J].IEEE/ACMTransactionsonNetworking(S1063-6692),1997,5(6):835-846.[8]ParkK,WillingerW.SelfSimilarNetworkTrafficandPerformanceEvaluation[M].NewYork:Wiley,2000.[9],,.[J].,19