i,j=1,2,3. xi(t)=s(t-di)+ni(t),i=1,2,3. (1) ~~.x=(f)=2~55(f)+~~~(f), (4) `)~ixj(f)=4~ss(f)exp(-j27rf(di-di)),(5) Tdi~J)=T3-?'i=otan-1Im2 U)](6) ~rfre4)xx3(f)] ~~3yiT3Pi T3-r2(7) ri+r22=2ro2+rodsinsin+d2,(8) rl2-r22=4rodsincos,(9) rig+r22+r32=3ro2+4d2.(10)
22^21r dlilrd2i2 r3bb22 o=1+-r3-4d211) -1JlJ2~ =tan^^^^ rd2b1j1-rd1b2j2 xro+d2-r3,(12) 8=sin-1i13(2+-d2-r3. 4rod3 rd2b1j2- +'rdb2jl^^(13)b 1B2 Ii=B2+4+2/B2+4, Ji=Bit+4+2,i=1,2. (14) rdi(fo)=1rdz(f)df,(15) Bi(fo)=B2(f)df,(16) E[`~xixj(f)]=(f)+0(1/T ),. (17) Var[Re[~xix;(1)]] =C[~xixi(f)~xjxj(f)+Re2[I(1)] COV[~xixi(1)1Re[I(1)]] =C(f)Re[Y(f)]+0(1/T), (22) Cov[&zxi(f),Im[~xixj(1)]] =C~xixi(f)Im[4xixj(1)]+0(1/T), (23) C,_-1/2~t_m=-M 1/2ztM IW(f)12dfof~w2(m) (24)TT rd2:i~ CORe[43i]8Im[43i]-Im[~3i]bRe[~3i] 3iI2 (25) 22 VarrCCO4ii~33-I~3ilX27)dil.2 ~f2ii3ii2 -Im2[4(f)]l2+0(1/T), (18) Var[Im[4xix;(f)]] =C[4xixi(f)I(f)+Im2[4xixj(f)] -Re2[4(f )]/2+0(1/T), (19) Cov[Re[I(f)]~Im[~xixj(f)] =C.Re[I(f)]Im[4(f)]+0(1/T), (20) Cov[3(f)~'xjxj(f)] =CI4xixj(f)I2+0(1/T), (21) ^(~+133-2I~3iI23(-33)2 COv[rdi,rd3]=2 I~3iI223iI2 +(4ii-433)2ii433(28)2I 3iI4 coc 7tf2~3iI2I~3jI2.
Cov[Bj,Bj] {Re[3i]Re[43j](433Re[Iij]-Re[43j~3i]) -Re[3i]II11[3j](33Im[~ji]+Im['3jI3i]) -Im[3i]Re[3j](33Im[ij]+Im[I3jI3i]) +Im[~3i]Im[43j](I33Re[Iij]+Re[43j13i])}, =Ci1()ij I3i3jI2-I~3iI2-I~3jI2+332) 3i11~3j {Re[3j]Re[ij~3iJ1-33I~3jI2} ii-x33{re[~ 3j11~3iI3 +-33)jj-41'33)2I'I 3iI3I'3iI3 3i]Re[~ji~3j]1 +Im[~3i]Im[4jiI3j]-~33I~3iI2} ReRe+Re[3j3i]) +Re[3iJIm[3j](33Im[ij]+Im[I3i43j]) +Im[3i]Re[3j](I33Im[ji]+Im[13j43i]) +Im[I3i]Im[j](Re[4ij]-Re[3jI3i]) ^~0 Cov[rd~,Bj]-c2 ~rf x(re[~3i]im[~ji~3j]i~ 3i121~3j -Im[~gi]Re[~ji~3j]) -~JJ-X33{~33Im[~ij]ReL~3i~3j] (29) (30) ~33Re[~ij](Re[~3i]II11[~3j] -Im[ 13i]Re[43j]) +Im[~3j~3i]Re[~3i~3j] -Re[~3j~3i]Im[~3i~3j]} (31)COV[Bifrdi]=0, (32) VarC2(rig+r32)SNR+ri2r32[rd]=C, Var[B,.]_(i(rig-f-r32) 2ri2r32SNR2 (33) X{(rig+r32)SNR+ri2r32},(34) Cov[rdi,rdj]=C~0r3 (35)2 rf2snr Co=Cri(r32-2)+rj(r-r) rjr32rir32 rirjr31ri(r3-ri) + r32rirj+snrrj+ rj(r3-rj) +rirjr3+(r3-r)(r32-rj2)snr2 Cov[I'dz,Bj]=0.(37) +2rirj x2+1 (36) rirjr32snrrirjj br=2r(oei+arbrd(38) abiard2 aro1rd B23roBi2Bi2+4 arorl(40)(2 rdi3ro2rdi Bi2+4+2)(ri+2r3(39) ri+r3)a Var[r0]=Var[B1]+Var[B2]aB 1aB2 +(Var[rdl]+Var[rd2] arpar +2aBaBCov[B1,B2] aror0 andandcov[rdl,rd2].(41) Var[]=Var[EiJaB+(Var[2] Ba2 Var[d a~ +a ndr+and-)var[rd2] i}~ a~a~bc lab2 ov[bl,b2]ab Cov[rd1,rd2],(42)a rdlard2
ar[]=2a aea8v ivar+2var[e2}ab2 ae2ae2+ arvar[rdi]+andvar{d2] dl aeae abicov[b1,bab2 aet90 +2Cov[rdi,rd2],(43)a rd1ard2 Cov[ro,cb]=Var[Bi] aroaq5+ 22Var[B2]+aroq5Var[rd1]aBaBand1and1 +aroavarrd+cov[bi,b2]a ndand[2]abiab2 aroa ab2abicov[bi,b2] aroa+c ov[rdi,rd2]a rdlard2 aroa(44)+c ov[rdi,rd2]a nd2and1 aroaec ov[ro,8]=ab iabivar[bi] aroaearoae+ ab2ab2var[b2]+andandvar[rd1] aro59aro rdvar[rd2]+cov[bi,b2]ard2ad2abiab2 aro59+c ov[bi,b2]ab 2aBi aroae+c oy[rdi,rd2la rdlard2 aroae ard2ardl Cov[q,8]=a~b59Var[Bi] abiabi a;aev arb2]+a~ae+var[rd1]ab 2aB2[ardlardl +a98var[rd2l+aaecov[bi,b2]a rd2ard2abiab2 +abaecov[bi,b2]ab 2aBi +acae[rd1,rd2la rdlard2 +aaecov[rd1,rd2](46)a rd2ard1 3 a93rdi Iix{risin+3cos abi2rdcos9 ( -2rsin+23dsin92rir3 36ro, r (47) rdi2rdirodcos9ri+cos 2rsin+2sin9q536 2ri+r3 a -3rdiIZx abi2rdsin9 Ti(cosq5-3sin-3, (2ri+r3)cos5 ard ricos3sin r cos (48) (49) (50) Bi2+4+2I i= (51) Bi2Bi2+4
sin9cosqrocos9cos-rosin9sin~b H=sin9sin~brocos9sin~b-rosin9cosc cos9-rosin90 (53) )exp2xeaxe,(54)=(i2i312iai1/2i Var[y]Cov[x,y]Cov[x,z] Ae=Cov[x,y]Var[y]Cov[y,z], (55) Cov[x,z]Cov[y,z]Var[z] -2 1-x2/2d2~-Q/2(57)P 0ex--=e.2~r2~r 1AmaxQ~0.3, (58)2 rn