3.25.huaidai.ps

是multiuser detection 这本书的习题解答, 很有用的书.

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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 1681 y Fk(Problem)23 b(3.25.)40 b Fj(Find)21
b Fi(E)6 b Fj([)p Fi(Q)p Fj(\()p Fh(k)p Fk(X)p Fh(k)p
Fj(\)])22 b(if)e Fk(X)h Fj(is)h(a)f(complexed-v)-5 b(alued,)23
b(zero-mean)f(Gaussian)f(three-dimensional)-186 1801
y(v)m(ector)34 b(with)e(indep)s(enden)m(t)i(co)s(e\016cien)m(ts)f(with)
g(indep)s(enden)m(t)g(real)f(and)h(imaginary)d(parts)i(and)h(v)-5
b(ariances)1490 1977 y Fi(E)6 b Fj([)p Fh(j)p Fk(X)1708
1992 y Fg(1)1747 1977 y Fh(j)1775 1936 y Fg(2)1814 1977
y Fj(])84 b(=)e(2)p Fi(\015)2188 1936 y Fg(2)2228 1977
y Fi(;)1490 2123 y(E)6 b Fj([)p Fh(j)p Fk(X)1708 2138
y Fg(2)1747 2123 y Fh(j)1775 2082 y Fg(2)1814 2123 y
Fj(])84 b(=)e(2)p Fi(\015)2188 2082 y Fg(2)2228 2123
y Fi(;)1490 2268 y(E)6 b Fj([)p Fh(j)p Fk(X)1708 2283
y Fg(3)1747 2268 y Fh(j)1775 2227 y Fg(2)1814 2268 y
Fj(])84 b(=)e(4)p Fi(\015)2188 2227 y Fg(2)2228 2268
y Fi(:)-186 2530 y Fk(Solutions:)-186 2736 y Fj(As)33
b(in)f(problem)f(3-24,)h(w)m(e)h(ha)m(v)m(e)1016 2981
y Fi(U)38 b Fj(=)28 b Fh(k)p Fk(X)p Fh(k)1409 2940 y
Fg(2)1475 2981 y Fj(=)g Fk(X)1664 2940 y Ff(\003)1703
2981 y Fk(X)f Fj(=)g Fk(Y)2006 2940 y Ff(\003)2045 2981
y Fk(\006Y)j Fj(=)2381 2873 y Fe(L)2345 2898 y Fd(X)2348
3081 y Fe(i)p Fg(=1)2481 2981 y Fi(\025)2538 2996 y Fe(i)2567
2981 y Fh(j)p Fi(Y)2652 2996 y Fe(i)2679 2981 y Fh(j)2707
2940 y Fg(2)3823 2981 y Fj(\(1\))-186 3232 y(where)44
b Fi(\025)163 3247 y Fg(1)247 3232 y Fj(=)h Fi(\025)425
3247 y Fg(2)509 3232 y Fj(=)g(2)p Fi(\015)735 3196 y
Fg(2)774 3232 y Fi(;)17 b(\025)875 3247 y Fg(3)959 3232
y Fj(=)45 b(4)p Fi(\015)1185 3196 y Fg(2)1266 3232 y
Fj(And)f Fk(Y)h Fj(is)d(a)g(Gaussian)g(v)m(ector)i(obtained)e(from)g
Fk(X)g Fj(through)g(linear)-186 3352 y(transformation.It)28
b(has)i(indep)s(enden)m(t)h(zero-mean)f(and)g(unit)f(v)-5
b(ariance)29 b(co)s(e\016cien)m(ts)i(with)f(indep)s(enden)m(t)h(real)
-186 3473 y(and)i(imaginary)d(parts.)-186 3679 y(With)d(partial)e
(fraction)i(expansion)h(of)f(the)h(c)m(haracteristic)f(function\(with)g
Fc(L)-5 b(aplacian)29 b(T)-7 b(r)i(ansform)p Fj(\))26
b(of)h Fh(k)p Fk(X)p Fh(k)3882 3643 y Fg(2)3921 3679
y Fj(,)-186 3799 y(w)m(e)34 b(get)276 4042 y Fi(E)6 b
Fj([)p Fi(e)426 4001 y Ff(\000)p Fe(s)p Ff(k)p Fb(x)p
Ff(k)627 3977 y Fa(2)666 4042 y Fj(])27 b(=)864 3934
y Fg(3)828 3959 y Fd(Y)824 4141 y Fe(i)p Fg(=1)1090 3974
y Fj(1)p 965 4018 300 4 v 965 4110 a Fi(s\025)1068 4125
y Fe(i)1118 4110 y Fj(+)22 b(1)1302 4042 y(=)1448 3934
y Fg(3)1406 3959 y Fd(X)1409 4141 y Fe(i)p Fg(=1)1657
3974 y Fi(\013)1719 3989 y Fe(i)p 1552 4018 V 1552 4110
a Fi(s\025)1655 4125 y Fe(i)1706 4110 y Fj(+)g(1)1890
4042 y(=)2159 3974 y(4)p 2004 4018 360 4 v 2004 4110
a(1)f(+)h(4)p Fi(\015)2277 4081 y Fg(2)2317 4110 y Fi(s)2395
4042 y Fj(+)2619 3974 y Fh(\000)p Fj(2)p 2503 4018 V
2503 4110 a(1)g(+)g(2)p Fi(\015)2777 4081 y Fg(2)2816
4110 y Fi(s)2894 4042 y Fj(+)3176 3974 y Fh(\000)p Fj(1)p
3002 4018 475 4 v 3002 4110 a(\(1)g(+)g(2)p Fi(\015)3314
4081 y Fg(2)3353 4110 y Fi(s)p Fj(\))3437 4081 y Fg(2)3823
4042 y Fj(\(2\))-186 4378 y(With)32 b(in)m(v)m(erse)i
Fc(L)-5 b(aplacian)34 b(T)-7 b(r)i(ansform)31 b Fj(of)h(Eq.)h(2)f(w)m
(e)i(get)f(the)g Fc(p)-5 b(df)32 b Fj(of)g Fh(k)p Fk(X)p
Fh(k)2607 4342 y Fg(2)774 4599 y Fi(f)822 4614 y Fe(U)881
4599 y Fj(\()p Fi(u)p Fj(\))27 b(=)1177 4531 y(1)p 1153
4576 96 4 v 1153 4667 a Fi(\015)1209 4638 y Fg(2)1259
4599 y Fi(e)1304 4558 y Ff(\000)p Fe(u=)p Fg(4)p Fe(\015)1510
4534 y Fa(2)1571 4599 y Fh(\000)1704 4531 y Fj(1)p 1681
4576 V 1681 4667 a Fi(\015)1737 4638 y Fg(2)1786 4599
y Fi(e)1831 4558 y Ff(\000)p Fe(u=)p Fg(2)p Fe(\015)2037
4534 y Fa(2)2099 4599 y Fh(\000)2256 4531 y Fj(1)p 2209
4576 145 4 v 2209 4667 a(4)p Fi(\015)2314 4638 y Fg(4)2363
4599 y Fi(ue)2464 4558 y Ff(\000)p Fe(u=)p Fg(2)p Fe(\015)2670
4534 y Fa(2)2709 4599 y Fi(;)17 b(u)27 b(>)g Fj(0)835
b(\(3\))-186 4904 y(So)172 5115 y Fi(P)14 b Fj(\()p Fh(k)p
Fk(X)p Fh(k)26 b(\024)i Fi(x)p Fj(\))g(=)g Fi(P)14 b
Fj(\()p Fi(U)38 b Fh(\024)28 b Fi(x)1207 5074 y Fg(2)1247
5115 y Fj(\))83 b(=)1527 4998 y Fd(Z)1610 5024 y Fe(x)1650
5001 y Fa(2)1573 5186 y Fg(0)1705 5115 y Fi(f)1753 5130
y Fe(U)1812 5115 y Fj(\()p Fi(u)p Fj(\))p Fi(du)1368
5351 y Fj(=)g(4\(1)21 b Fh(\000)i Fi(e)1829 5310 y Ff(\000)p
Fe(x)1924 5287 y Fa(2)1958 5310 y Fe(=)p Fg(4)p Fe(\015)2068
5287 y Fa(2)2108 5351 y Fj(\))f Fh(\000)h Fj(3\(1)e Fh(\000)i
Fi(e)2570 5310 y Ff(\000)p Fe(x)2665 5287 y Fa(2)2699
5310 y Fe(=)p Fg(2)p Fe(\015)2809 5287 y Fa(2)2849 5351
y Fj(\))f(+)3065 5284 y(1)p 3017 5328 V 3017 5420 a(2)p
Fi(\015)3122 5391 y Fg(2)3171 5351 y Fi(x)3226 5310 y
Fg(2)3266 5351 y Fi(e)3311 5310 y Ff(\000)p Fe(x)3406
5287 y Fa(2)3440 5310 y Fe(=)p Fg(2)p Fe(\015)3550 5287
y Fa(2)3823 5351 y Fj(\(4\))1857 5655 y(1)p eop
2 1 bop -186 167 a Fj(Finally)360 426 y Fi(E)6 b Fj([)p
Fi(Q)p Fj(\()p Fh(k)p Fk(X)p Fh(k)p Fj(\)])83 b(=)1153
358 y(1)p 1082 402 191 4 v 1082 420 a Fh(p)p 1165 420
108 4 v 82 x Fj(2)p Fi(\031)1299 309 y Fd(Z)1382 335
y Ff(1)1345 497 y Fg(0)1473 426 y Fi(P)14 b Fj(\()p Fh(k)p
Fk(X)p Fh(k)27 b(\024)h Fi(x)p Fj(\))17 b Fi(e)2060 385
y Ff(\000)p Fe(x)2155 361 y Fa(2)2189 385 y Fe(=)p Fg(2)2264
426 y Fi(dx)913 711 y Fj(=)83 b(2\(1)21 b Fh(\000)1329
556 y Fd(s)p 1412 556 334 4 v 1507 644 a Fj(2)p Fi(\015)1612
615 y Fg(2)p 1422 688 314 4 v 1422 780 a Fj(1)h(+)g(2)p
Fi(\015)1696 751 y Fg(2)1745 711 y Fj(\))g Fh(\000)h
Fj(3)p Fi(=)p Fj(2\(1)e Fh(\000)2260 556 y Fd(s)p 2343
556 285 4 v 2437 644 a Fi(\015)2493 615 y Fg(2)p 2353
688 265 4 v 2353 780 a Fj(1)h(+)g Fi(\015)2578 751 y
Fg(2)2627 711 y Fj(\))g(+)g(1)p Fi(=)p Fj(4)3138 644
y Fi(\015)p 2942 688 451 4 v 2942 780 a Fj(\(1)f(+)h
Fi(\015)3204 751 y Fg(2)3244 780 y Fj(\))3282 751 y Fg(3)p
Fe(=)p Fg(2)3823 711 y Fj(\(5\))1857 5655 y(2)p eop end
userdict /end-hook known{end-hook}if