3.24.huaidai.ps

来自「是multiuser detection 这本书的习题解答, 很有用的书.」· PS 代码 · 共 930 行 · 第 1/5 页

1F80323574B33C>97 D<EC01E0EC03F0EC07F8140FA315F015E0EC038091C7FCB2EB07C0
EB3FF0EB7FFCEBF87C3801E07E3803C03E3807803F120F495A5A121E123E003C5B5C127C
EA78015CEAF8035C120013075CA2130F5CA2131F5C133F5CA2137F91C7FCA24913785BA2
000114F84913F01203EBF80115E0A2EC03C013F0EC0780140F15000001131EEBF87C6CB4
5AEB7FE0EB1F801D5077CE24>105 D<EB0FC0D93FF0EC03C0D97FFCEC07E0D9F07C140F
3801E07E2603C03E141F2607803F15C0120F495A48163F001E1780123E003C5B4A147F00
7C1700EA78015CD8F8035D4A5C120013074A13015F130F5C1603011F5D5CA21607013F5D
5CA2160F017FEDE00F91C7FCA2161FEFC01F181EA2043F133E047F133C17806D02FF137C
4B14786E4814F8011F903907CFC0F09139C00F8FC1903B0FF03F07E3E0903B03FFFC03FF
C06DD9F0011380903B003FC0007E00383577B33F>117 D<EB0FC0D93FF0EC03C0D97FFC
EC07E0D9F07C140F3801E07E2603C03E141F2607803F15C0120F495A48163F001E178012
3E003C5B4A147F007C1700EA78015CD8F8035D4A5C120013074A13015F130F5C1603011F
5D5CA21607013F5D5CA2160F017F5D91C7FCA2161F5FA3163F4C5AA26D14FF5D6E4890C7
FC011F5B6E5A90380FF03F903903FFFCFE6D13F09038003FC0EC00015EA215035EA2D803
C0495AEA07F0000F4A5A121F4B5A4B5A4991C8FC5D018013FE391E0001FC001F495A6CEB
07E09038801FC03907E07F802603FFFEC9FCC613F8EB3F80334C77B339>121
D E /Fn 12 120 df<ED1FFE4AB512E0020F14FC023F14FF9126FFE00713C0D903FEC713
F0D907F0EC3FF8D91FC06E7E49C8EA07FE017E6F7E017883496F7F48486F7F1203498348
48167F01F88313FE6D6C153F486D82A4805CA37E6C5B6C48C95BD80078167F90CAFCA261
A218FF61A24D5B615F96C7FC4D5A60170F4D5AEF3FE04D5A4D5A4C48C8FCEE07FCEE1FF0
92381FFFC091260FFFFEC9FCA2EEFFE091C7EA07FCEE00FFEF3FC0EF1FF0717EEF07FE71
7E717F717F85727E727EA285727EA2727EA31A80A2841AC0A3EA07E0EA1FF8487E487EB5
FCA51A80605BA26C48180013F001C05E007CCA5B7E4E5A7E6D4C5A6C6C5F000717FF01F0
4B5B6C6C4B5B6C6C5F6CB4030F90C7FC6D6C4A5AD93FF04A5AD90FFCECFFF8902707FFE0
0713E0010190B612806D6C92C8FC020F14F8020314E09126001FFEC9FC42757AF14F>51
D<183CA2187C18FCA217011703A21707170FA2171FA2173F177F177717F7EE01E717C716
031787EE0707160F160E161E163C1638167816F016E0150116C01503ED078016005D151E
151C153C15385D15F05D14014A5A5D14074AC7FC140E141E141C143C5C147014F0495A5C
13035C49C8FC5B130E131E5B1338137813705B12015B1203485A90C9FC5A121E121C123C
12385A12F0BCFCA5CAD80FFCC7FCB3A44D7E4D7E94B512C0030FB712FCA548737DF24F>
I<016017C001781603017E160FD97FC0ED7F8002F8913807FF00DAFFC0EBFFFE92B65A60
6018C0604DC7FC17F817E0017892C8FC020F13F891CBFCB3A8ED07FE92387FFFC00203B5
12F891390FF803FE91391F8000FF027CC7EA3FC04A6E7ED979E06E7ED97BC06E7ED97F80
6E7E91C87F017E6F7E017C6F13801378F07FC0017017E090CAFCF03FF0A219F8181FA219
FCA319FE180FA419FFA7EA1FE0487E487E487EA419FEA2181F5B4917FC5B0070CAFC183F
007818F8A26C18F0187F003E18E0001E17FF001F18C06C4C13806C7E6D4B13006C6C4B5A
6C6C4B5A6D4B5AD800FE4B5A017F4B5AD93FC049485AD91FF001075BD907FFD93FFEC7FC
6D90B55A010015F0023F14C0020749C8FC020013E0407579F14F>I<BD12FEA5D8003F01
F0C96C7F01074916034BEE007F6D190F871B018788A2F43F801C1FA21C0FA21C07A31C03
A21DC0A31C01A6F400E0191CA41D00A5193CA4197CA219FC18011803180F18FF92B7FCA5
03C0C7FC180F180318011800197CA2193CA4191CA41D07A41D0E96C9FCA51D1E1D1CA41D
3CA31D381D78A31DF8A21C01A2F403F0A21C07A21C0F1C1F1C3FF4FFE0631B0749191F6F
4CB5FC013F6D163FBEFC1DC0A4607678F56C>69 D<B80203B712FCA5D8003F01FCCAECF0
00010701E0051F1380A26D497190C7FCB3B3AA92BBFCA503C0CA120FB3B3AF496D4D7FA2
013F01FC94B512F0B80203B712FCA5667678F577>72 D<B812E0A5D8003F49CCFC010713
F05D6D5BB3B3B3AC1C70A51CE0A81B01A31CC01B03A41B07A21B0FA21B1FA2F33F80A21B
7F1BFF62621A0F621A7F494DB5FC6F150F013F6D4AB61200BDFCA5547678F563>76
D<ED1FFC4AB512C0020714F091391FF00FFC91397F8001FFD901FEC7EA7FC049486E7E49
486E7E49486E7E49486E7E49486E7E4948140101FF824890C91380A24848EE7FC0A2485A
000FEF3FE05BA2001F18F0181F485AA3007F18F8A349160FA212FF90B9FCA301E0CBFCAB
127F7FA3123FA36C7EA219386C7E1978000718707F000318F06C6C17E018016C6DED03C0
6D6C1680013F16076D6CED0F006D6C151E6D6C5D6D6C5D6DB44A5A6D6C6C495ADA3FE0EB
1F80DA0FFE01FEC7FC0203B512F8DA007F13E0DB07FEC8FC3D4D7BCB46>101
D<EB01F0EA07FFB5FCA51201EA007F133FA2131FB3B10507B512FEA5050114C07149C7FC
19F019C0614EC8FC60EF01F04D5A604D5A4DC9FC173E5F5F4C5A4C5A4C5A4C5A4CCAFC16
3C5E16FC15014B7E4B7E5D033F7F037C7F5D9139F1F07FE09139F3E03FF0ECF7C09139FF
801FF8ED000F02FC804A6D7E4A13034A80707F8284717E173F84717E170F84717EA2717E
717FA2717F727EA2727E85181F858585496C83D9FFFC037F13F0B600FC0103B612C0A54A
787AF753>107 D<D901F0902601FFC0ED0FFED807FF021F01FC92B512E0B5027F01FF02
0314F8922601FC0101C090390FE00FFE922803E0003FE090391F0001FFDB0F80D91FF801
7C6D13C04BC7000F4A147FC6023C912707FC01E06E7E013F496E6C48486E7E011F0170DA
01FF496E7E03F0160790260FF1E04CC8FCDAF3C06E019E6F7E4B169C02F717BC92C913B8
02FFDC7FF86F7E4A5FA34A5FA44A5FB3B3A8496C4C6C4B7ED97FFF030301F8031F13C0B7
D88007B600FC013FB612E0A57B4B7ACA86>109 D<ED07FE92387FFFE00203B512FC9139
0FFC03FF913A3FC0003FC04AC7EA0FE0D901FEEC07F8D903F8EC01FC49486E7E4948157F
49486F7E49486F7E017F8349C96C7E4916070001844848707EA2000784491601000F84A2
4848701380A2003F19C0A349177F007F19E0A412FF1AF0AD007F19E0A26D17FFA2003F19
C0A46C6C4C1380A2000F1900A26C6C4C5AA26C6C4C5A0001606D160F6C606D6C4B5A6D6C
4B5AA26D6C4B5AD907F003FEC7FCD903FCEC03FC6D6C4A5A6D6C6CEB1FF0DA3FE0EB7FC0
91270FFC03FFC8FC0203B512FCDA007F13E0DB07FEC9FC444D7BCB4F>111
D<D903E0EB1FE0D80FFFECFFFCB501037F923907E01F8092391F807FC092383E00FF4B48
13E000011478D8007F13F090383FE1E015C0EB1FE39126E7800013C0EF7F8092C7EA3F00
02EF91C7FC14EE14FE5CA45CA55CB3B3A480133F90B5FCB712C0A5334B7ACA3D>114
D<B600F0017FB500F849B512FCA5000149C849C8003F13E026007FF8DB3FF8030F13004A
031F705A013F4DED03F8180F011F755A735E6D6C1507667315036D6C63A24E7E6D6C50C7
FC85606D6C031C160E866FEC387F6D63866FEC703F027F62866FDAE01F1578023F1A7086
6F902601C00F15F0021F62866F90260380071401020F62866F9026070003140302076286
6F010E01011407020397C8FC866F496D5C6E190E053C1580DC8038027F131E6E191C0578
15C0DCC070023F133C037F183805F015E07048021F1378033F187004E116F092261FF1C0
020F5BA204F316F892260FFB80913807F9C0A204FF16FD6F90C86CB45AA36F486F90C9FC
A36F486F5AA36F48167CA24C163C047016386E4B7EC973>119 D
E end
TeXDict begin

1 0 bop 1146 569 a Fn(ELE533)52 b(Homew)l(ork)f(4)1586
951 y Fm(Huaiyu)40 b(Dai)1574 1271 y Fl(25)f(F)-10 b(eb)39
b(1999)-186 1714 y Fk(Problem)51 b(3.24.)83 b Fj(Sho)m(w\(3.64\):)70
b(If)45 b Fk(X)g Fj(is)h(a)f(complexed-v)-5 b(alued,)48
b(zero-mean)d(Gaussian)h Fi(L)p Fj(-v)m(ector)g(with)-186
1834 y(indep)s(enden)m(t)38 b(real)d(and)i(imaginary)d(parts)i(and)h
(if)e(the)i(eigen)m(v)-5 b(alues)37 b Fi(\025)2498 1849
y Fh(1)2537 1834 y Fi(;)17 b(:)g(:)g(:)f(;)h(\025)2813
1849 y Fg(L)2901 1834 y Fj(of)36 b(the)h(co)m(v)-5 b(ariance)36
b(matrix)-186 1955 y Fi(E)6 b Fj([)p Fk(XX)89 1918 y
Ff(\003)128 1955 y Fj(])32 b(are)h(distinct,)f(then)1154
2149 y Fi(E)6 b Fj([)p Fi(Q)p Fj(\()p Fe(k)p Fk(X)p Fe(k)p
Fj(\)])28 b(=)1791 2041 y Fg(L)1755 2066 y Fd(X)1758
2249 y Fg(i)p Fh(=1)1902 2082 y Fi(\013)1964 2097 y Fg(i)p
1902 2126 91 4 v 1922 2218 a Fj(2)2002 2149 y(\(1)22
b Fe(\000)2366 2082 y Fj(1)p 2220 2126 340 4 v 2220 2143
a Fd(q)p 2303 2143 257 4 v 94 x Fj(1)g(+)2498 2197 y
Fh(2)p 2482 2213 68 4 v 2482 2271 a Fg(\025)2523 2281
y Fc(i)2570 2149 y Fj(\))-186 2414 y(where)1475 2584
y Fi(\013)1537 2599 y Fg(j)1601 2584 y Fj(=)1803 2476
y Fg(L)1774 2501 y Fd(Y)1705 2685 y Fg(i)p Fh(=1)p Fg(;i)p
Ff(6)p Fh(=)p Fg(j)2080 2516 y Fi(\025)2137 2531 y Fg(j)p
1977 2561 301 4 v 1977 2652 a Fi(\025)2034 2667 y Fg(j)2092
2652 y Fe(\000)h Fi(\025)2249 2667 y Fg(i)-186 2917 y
Fk(Solution:)-186 3124 y Fj(Denote)33 b(the)g(co)m(v)-5
b(ariance)32 b(matrix)f(as)1430 3244 y Fk(\006)d Fj(=)f
Fi(E)6 b Fj([)p Fk(XX)1917 3203 y Ff(\003)1956 3244 y
Fj(])28 b(=)g Fk(CC)2277 3203 y Fg(T)3823 3244 y Fj(\(1\))-186
3412 y(Whic)m(h)d(w)m(e)i(kno)m(w)f(as)f Fb(Cholesky)j(De)-5
b(c)g(omp)g(osition)23 b Fj(with)i Fi(C)32 b Fj(as)25
b(an)g(in)m(v)m(ertible)g(lo)m(w)m(er)g(triangular)e(matrix.)39
b(De\014ne)-186 3532 y(a)32 b(new)i(v)m(ector)f(from)f
Fi(X)40 b Fj(through)33 b(linear)e(transformation)1642
3737 y Fk(Y)f Fj(=)d Fk(C)1941 3696 y Ff(\000)p Fh(1)2036
3737 y Fk(X)1702 b Fj(\(2\))-186 3942 y(The)24 b(new)g(v)m(ector)g
Fk(Y)i Fj(is)c(a)h(Gaussian)f(v)m(ector)i(with)f(indep)s(enden)m(t)h
(real)f(and)g(imaginary)d(parts)j(and)h(indep)s(enden)m(t)-186
4063 y(co)s(e\016cien)m(ts)34 b(with)e(zero-mean)g(and)h(unit)f(v)-5
b(ariance)32 b(due)h(to)1146 4268 y Fi(E)6 b Fj([)p Fk(YY)1424
4227 y Ff(\003)1462 4268 y Fj(])28 b(=)g Fk(C)1702 4227
y Ff(\000)p Fh(1)1796 4268 y Fi(E)6 b Fj([)p Fk(XX)2071
4227 y Ff(\003)2110 4268 y Fj(]\()p Fk(C)2256 4227 y
Ff(\000)p Fh(1)2350 4268 y Fj(\))2388 4227 y Fg(T)2471
4268 y Fj(=)27 b Fk(I)1207 b Fj(\(3\))-186 4473 y(Supp)s(ose)34
b(co)m(v)-5 b(ariance)32 b(matrix)f Fk(\006)i Fj(is)f(symmetric)f(and)i
(p)s(ositiv)m(e)f(de\014nite)h(so)g(it)e(can)i(b)s(e)g(diagonalized)d
(as)1630 4678 y Fk(\006)e Fj(=)f Fk(T\003T)2076 4637
y Fg(T)3823 4678 y Fj(\(4\))-186 4883 y(Then)34 b(w)m(e)f(ha)m(v)m(e)
818 5053 y Fi(U)38 b Fj(=)28 b Fe(k)p Fk(X)p Fe(k)1211
5012 y Fh(2)1277 5053 y Fj(=)f Fk(X)1465 5012 y Ff(\003)1505
5053 y Fk(X)g Fj(=)g Fk(Y)1808 5012 y Ff(\003)1847 5053
y Fk(\006Y)j Fj(=)e Fk(Z)2215 5012 y Ff(\003)2255 5053
y Fk(\003Z)g Fj(=)2569 4945 y Fg(L)2533 4970 y Fd(X)2536
5152 y Fg(i)p Fh(=1)2669 5053 y Fi(\025)2726 5068 y Fg(i)2754
5053 y Fe(j)p Fi(Z)2849 5068 y Fg(i)2877 5053 y Fe(j)2905
5012 y Fh(2)3823 5053 y Fj(\(5\))-186 5285 y(Where)1671
5406 y Fk(Z)g Fj(=)g Fk(T)1949 5365 y Fg(T)2004 5406
y Fk(Y)1734 b Fj(\(6\))1857 5655 y(1)p eop
2 1 bop -186 167 a Fj(is)42 b(an)h(Unitary)f(transformation)e(so)j(v)m
(ector)h Fk(Z)f Fj(is)f(also)g(a)g(Gaussian)g(v)m(ector)i(with)e(indep)
s(enden)m(t)i(real)e(and)-186 287 y(imaginary)34 b(parts)i(and)h(indep)
s(enden)m(t)h(co)s(e\016cien)m(ts)f(with)f(zero-mean)g(and)h(unit)e(v)
-5 b(ariance.)55 b Fi(\025)3365 302 y Fg(i)3393 287 y
Fi(;)17 b(i)34 b Fj(=)g(1)p Fi(;)17 b(:)g(:)g(:)f(;)h(L)-186
408 y Fj(are)33 b(eigen)m(v)-5 b(alues)32 b(of)g(the)h(co)m(v)-5
b(ariance)33 b(matrix.)-186 614 y(Supp)s(ose)40 b(the)g(probabilit)m(y)
e(densit)m(y)i(function)f(and)g(c)m(haracteristic)g(function)g(of)g
Fi(U)50 b Fj(are)40 b Fi(f)3259 629 y Fg(U)3318 614 y
Fj(\()p Fi(u)p Fj(\))p Fi(;)17 b(u)37 b(>)j Fj(0)f(and)-186
734 y(\010\()p Fi(t)p Fj(\))28 b(=)g Fi(E)6 b Fj([)p
Fi(e)277 698 y Fg(itu)372 734 y Fj(],)32 b(then)i(the)f
Fb(L)-5 b(aplacian)33 b(T)-7 b(r)i(ansform)31 b Fj(of)h(the)h
Fb(p)-5 b(df)32 b Fj(is)898 850 y Fd(Z)981 877 y Ff(1)944
1039 y Fh(0)1072 967 y Fi(f)1120 982 y Fg(U)1179 967
y Fj(\()p Fi(u)p Fj(\))p Fi(e)1356 926 y Ff(\000)p Fg(su)1488
967 y Fi(du)27 b Fj(=)g Fi(\036)p Fj(\()p Fi(is)p Fj(\))83
b(=)g Fi(E)6 b Fj([)p Fi(e)2330 926 y Ff(\000)p Fg(su)2463
967 y Fj(])2021 1185 y(=)83 b Fi(E)6 b Fj([)p Fi(e)2330
1144 y Ff(\000)p Fg(s)2430 1086 y Fd(P)2517 1106 y Fc(L)2517
1173 y(i)p Fa(=1)2633 1144 y Fg(\025)2674 1154 y Fc(i)2700
1144 y Ff(j)p Fg(z)2753 1154 y Fc(i)2779 1144 y Ff(j)2799
1120 y Fa(2)2837 1185 y Fj(])2021 1405 y(=)2213 1297
y Fg(L)2184 1322 y Fd(Y)2180 1504 y Fg(i)p Fh(=1)2311
1405 y Fi(E)g Fj([)p Fi(e)2461 1363 y Ff(\000)p Fg(s\025)2590
1373 y Fc(i)2616 1363 y Ff(j)p Fg(z)2669 1373 y Fc(i)2695
1363 y Ff(j)2715 1340 y Fa(2)2754 1405 y Fj(])1042 b(\(7\))-186
1670 y(Where)34 b(the)f(last)e(step)j(is)e(obtained)g(b)m(y)h(indep)s
(endence)i(of)d Fi(Z)2102 1685 y Fg(i)2130 1670 y Fj(.)-186
1876 y(Because)40 b Fi(Z)260 1891 y Fg(i)326 1876 y Fj(is)d(a)h
(complexed-v)-5 b(alued)37 b(Gaussian)h(v)-5 b(ariable)36
b(with)i(unit)f(v)-5 b(ariance,)40 b(the)e(real)f(and)h(imaginary)-186
1997 y(part)43 b(of)h Fi(Z)226 2012 y Fg(i)297 1997 y
Fj(is)f(indep)s(enden)m(t)i(with)f(distribution)d Fe(N)15
b Fj(\(0)p Fi(;)i Fj(1)p Fi(=)p Fj(2\).)75 b(So)44 b
Fi(V)68 b Fj(=)47 b Fe(j)p Fi(Z)2751 2012 y Fg(i)2778
1997 y Fe(j)d Fj(has)g Fb(R)-5 b(ayleigh)44 b(Distribution)-186
2117 y Fi(f)-138 2132 y Fg(V)-77 2117 y Fj(\()p Fi(v)t
Fj(\))27 b(=)h(2)p Fi(v)20 b(e)342 2081 y Ff(\000)p Fg(v)433
2058 y Fa(2)473 2117 y Fi(;)d(v)31 b(>)c Fj(0.)43 b(Then)1118
2350 y Fi(E)6 b Fj([)p Fi(e)1268 2309 y Ff(\000)p Fg(s\025)1397
2319 y Fc(i)1423 2309 y Fg(v)1459 2286 y Fa(2)1499 2350
y Fj(])83 b(=)1768 2233 y F