二阶锥规划方法对于时空域滤波器的优化设计与验证ahref=

E2006,36(2):153~171153SCIENCEINCHINASer.EInformationSciences***(,710072).,,,.,FIR.,,.,,...,.,,.,.[1],,.,,.(finite-impulseresponse,FIR),30,FIR,[2]:2004-08-22;:2005-10-17*(:60472073)**E-mail:[e-mail][3][4].,Gibbs,.,().,,,,.FIR,.FIRL1,L2L∞(Chebyshev).,L∞[5,6].,L2[7,8].,,.,[9,10][11]()()[12].,.FIR,:,;,..,..DolphDolph-Chebyshev[13],;,.,.,..,“”.,[14].,.,Olen[15],.,,,.Olen,.[16~21],(L2).2:155∞,.,(),.,.,Capon(MVDR)[22],.,[23].,,,,.MVDR,[24][25].,,[26],.,.,,..,(second-orderconeprogramming,SOCP)[27],,,[28],.[29].,,,.,FIR.1,,156E36SCIENCEINCHINASer.EInformationSciencesiI,(1a)ybyTminsubjectto,T||||iiid++Aybcy1,2,,i=,(1b)gFy=,(1c)1α×∈b^,1α×∈y^,(1)iiαα−×∈A^,(1)1iiα−×∈b^,1iα×∈c^,Ti∈cy\,,id∈\gα×∈F^,1g×∈g^,⋅Euclid,T()⋅,,.(1b)^\,(2)iiiiiiSOCdα∈⎥⎦⎤⎢⎣⎡+⎥⎥⎦⎤⎢⎢⎣⎡byAcTiiSOCαiα^,(1)1,,iiitSOCttααΔ−×⎧⎫⎡⎤⎪⎪=∈∈⎨⎬⎢⎥⎣⎦⎪⎪⎩⎭\^xxx.(3)1(3=iα),..1(1c){}g−∈0gFy,(4){0}g{}1{|,}ggΔ×=∈=0^xxx0.(5)(1),().,(semidefiniteprogramming)[30]2:157(1b)⎥⎥⎦⎤⎢⎢⎣⎡++++iiiiiiiiddycbyAbyAIycTTT)()(;0,(6)I,“;”.,SeDuMi[31].,(1),[27].2,.FIR,,,.2.1FIRFIR,fT)]1(,),1(),0([−=Lhhhh,1j2π/T0()()()sLlfflHfhlef−−===∑ehfF∈,(7),j2π/j(1)2π/T()[1,,,]ssffLfffee−−−=e[0,/2]sFf=,fs.,.,,,.Ffk∈(Kk,,2,1=),.:pKkpkkdkfHfH/11)()(⎟⎟⎠⎞⎜⎜⎝⎛−∑=λ,(8)Hd(fk)fk,λk,.,L1,L2L∞,p=1,2∞.,(9)∑=−KkkkdkffH1T|))()(|(minhehλ,(10)∑=−KkkkdkffH12T|)()(|minhehλ158E36SCIENCEINCHINASer.EInformationSciences.(11)|))()(|(maxminThehkkdkkffH−λ(10)L2,(1).εk(k=1,2,,K),(10),subjectto∑=Kkkk1)(minελhT2|()()|dkkkHffε−eh,1,2,,kK=.(12)(12),T2|()()|dkkkHffε−eh⇔T222|2()2()|1212dkkkkkkHffεεε−++−+ehε+⇔2T22()2()(1)1dkkkkHffεε−+−eh⇔T2()2()11dkkkkHffεε−+−eh.(13),0TT21],,,,[hyKεεε=T121[,,,,]KLλλλ×=0b∑==Kkkk1T)(ελyb1L,(12)L×1,subjecttoybyTminT1T12()2()1()KkdkLfHfk××⎡⎤⎡⎤−⎢⎥⎢⎥−−⎣⎦⎢⎥⎣⎦00eyq,T11[()]Lk×+0qy1,2,,,kK=(14),T21],,,,,[)(Kiqqqqk=q0,,1,.iikqik≠⎧=⎨=⎩(15)L2FIR(10),SeDuMi.:1),(10)(12).→2),,,(12)(14).→3),.,L1L∞.,2:159)|)()(|(minpKkpkkdkFfffHk⎥⎦⎤⎢⎣⎡−∑=∈heλ,subjectto221/T1(|()()|)pMpmdmmmHffλδ=⎡⎤−⎢⎥⎣⎦∑ehBmFf,∈,(16)p1,p2=1,2∞,.δ,Fmin,FB⊂F.Fmin,FB,FminFB,,.FB,.,[5~12],.2.2N,,.θ,(17)wvvw)()()(TTθθθ==pθT21)](,),(),([)(θθθθNvvv=v,.T21],,,[N=w.FIR,,.MVDR,(θ0).,subjectto*TminwRwwnT0()1θ=vw,(18)Rn,(·)*.(1c).RnCholesky,,(19)UURH=n(·)H,.(20)2***T**T||||)()(wUwUwUwRw==n160E36SCIENCEINCHINASer.EInformationSciences,,||U*w||,.,()(ξ).ΘSL,:T|()|θξvw,SLθΘ∀∈.(21),.[24](whitenoisegainconstraint),(γ):||||γw.(22),.,[32]:|)(|maxmin0T0wvwθθθwΔ−,subjectto,||1)(0T=wvθ||γw,(23)Δw.[32]||||min*wUw,subjectto,1)(0T=wvθT|()|θξvw(SLθΘ∀∈),||||γw.(24)(patternsynthesis)[33]⎟⎟⎠⎞⎜⎜⎝⎛−∑mmmdmp2T|)()(|minwvwθθλ,mMLθΘ∈,subjecttoT|()|θξvw,SLθΘ∀∈,||||γv,(25)pd(θm)θm,λm,ΘML.(25)(16)FIR,,SeDuMi.,[13~26](23)~(25).,.,,.[34].,,(),.2:161(frequencyinvariantbeamformer,FIB).FIB,.FIR.FIB:,fk(25)w(fk),.FIR,,FIB.()FP,n(n=1,,N)fkwn(fk),nFIR,()()ndknkHfwf=,kPfF∈.(26)LFIR,(1)/2Lζ=−(Ts).ζ,..ζ,,nς(Ts,),nfk()exp[j2πint()]()exp[j2πint()]nkknsnkknswffTwffTςζςζ=−−⋅−,(27)int(·),int()nnτςζ=−(,,,,),FIR.,FIRn,()()exp(j2π)ndknkknsHfwffTτ=,PkFf∈,Nn,,2,1=.(28)FIR(16).FIR2.,FIR,.,162E36SCIENCEINCHINASer.EInformationSciences2FIRFIB.,exp(j2π)nkknsfTκ=−τ,,(28),()()nkndknkwfHfκ=.(29)nhn,(7)(29)w=[w1,w2,,wN]T.(30)T,T,T,11T])(,,)(,,)([)(kNNkknnkkkkffffκκκhehehew=fk,θ,fT1)],(,),,([),(θθθkNkkfvfvf=vk,θ)(),(),(Tkkkfffpwvθθ=T,T,T,11TT])(,,)(,,)()[,(kNNkknnkkkkffffκκκθhehehev=])(),(,,)(),(,,)(),([,T,T,1T1kNkkNknkknkkkffvffvffvκθκθκθeee=TTTT1],,,,[Nnhhh⋅heκv~)}(]),({[Tkkkff⊗=Dθhu~),(Tθkf=,(31)DHadamard,.⊗Kronecker.,[~T1hh=,TTT,n],,Nhh[]T,,,1,,,,kNknkkκκκ=κ,)(]),([),(kkkkfffeκvu⊗=Dθθ.:,.,,FIR,.Fs,θmpd(θm).FIR2:163[35]|)~),()(|max(minThuhmkmdmfpθθλ−,PkfF∀∈mMLθΘ∈,subjecttoT|(,)|kfθξuh,SkfF∀∈mMLθΘ∈,||||σh,(32)λm,σ,ξ.(32).FIBFIR.2.4,.,,.,,.D(DN)D[]1,,,,dDΘθθθ=,sd(t)(d=1,,D),()()()()tttΘ=+xVsn,(33)1()[(),,()]DΘθθ=VvvND,,n(t).T1)](,),([)(tststD=sNNH,()()()()tttΘ=+HxHVsHn.(34),,.,(),(),,PSθΘθθθΘ∈⎧=⎨∈⎩0vHv(35)ΘP,ΘS.,θp(1,,pP=)θs(Ss,,1=),Minimaxminmax||()()||pPppθΘθθ∈−HHvv,Pp,,1=,subjectto||()||sθβHv,sSθΘ∈,1,,sS=,||||FΔH,(36)164E36SCIENCEINCHINASer.EInformationSciencesβ,||·||FFrobenius,||.||FΔHHN,.],,,[21TNhhhH=.(37)TTT2T1],,,[Nhhhh=(36)Tminmax||(())||pPNNppθΘθ×∈⊗−hIvhv,Tsubjectto||(())||NNsθβ×⊗Ivh,sSθΘ∈,Ss,,1=,||||Δh,(38).,.,.NN×IN2.5,.,,[36].,[37].,,.,,.[38].,,,.,,.,2.4.v(r,z)(r,z.,KRAKEN[39])v(θ),..,2:165(“”)(“”)VSVP.2.4,(r,z):||||maxminppPpvHvVvH−∈,subjectto||||sβHv,SsVv∈∀,||||FΔH.(39)[40].32,.3.112,#1,#2,,#12,0º.1920Hz,fs=6000Hz,FP=[960,1920]Hz.[90º,90º]2.5º,960Hz(),5{}51mmθ=={17.5°,10°,0°,10°,17.5°}(3“*”).SLΘ=[90°2.5°25°][25°2.5°90°],25dB.60Hz[0,f∪s/2],FP=[960601920]Hz17.FS=[060780]∪[2100603000]Hz,FT=[84060900][1980602040]Hz.∪.(25),1,0.7.173.,,25dB.,1750.024.166E36SCIENCEINCHINASer.EInformationSciences3,FIR.L=64,#2,(28)(4“*”).45dB,(16)(p1=2,p2=∞)FIR,4.,45dB.170.008.4#2FIR12,2.,5.175,0.032,0.055.FIR,23dB,2:167σ=0.5,25dB,,(34).,6.175,0.030,0.031.25dB..63.224,,168E36SCIENCEINCHINASer.EInf