6.12.kishore.ps

是multiuser detection 这本书的习题解答, 很有用的书.

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bop 262 307 a Fi(Solutio)o(n)17 b(to)j(6.12)g(b)o(y)g(Shalinee)d(Kishore)h
(4/16/99)41 b Fh(\(a\))18 b(W)m(e)f(kno)o(w)g(from)f(the)262
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(basis)h(of)262 907 y Fe(L)p Fh(-dimensional)11 b(orthonormal)h(signals,)g(w)
o(e)i(see)h(that)f Fi(J)f Fh(is)h(an)f Fe(L)c Fb(\002)h Fe(L)j
Fh(matrix.)k(No)o(w,)c(let)262 957 y Fi(x)h Fh(b)q(e)i(an)o(y)e(v)o(ector)i
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1128 y Fh(\(3\))262 1254 y(with)h Fe(c)374 1260 y Ff(i)399
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2077 y Ff(T)884 2103 y(i)910 2092 y Fh(.)25 b(Th)o(us,)17 b
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b Fe(A)941 2273 y Ff(k)987 2215 y(L)968 2228 y Fd(X)971 2316
y Ff(i)p Fc(=1)1049 2239 y Fh(1)p 1040 2257 39 2 v 1040 2295
a Fe(\025)1064 2301 y Ff(i)1083 2267 y Fi(e)1105 2273 y Ff(i)1119
2267 y Fi(e)1141 2250 y Ff(T)1141 2277 y(i)1167 2267 y Fi(s)1186
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2574 y(1)p eop
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bop 836 342 a Fh(=)42 b Fe(A)941 348 y Ff(k)987 290 y(L)968
302 y Fd(X)971 391 y Ff(i)p Fc(=1)1035 342 y Fe(\013)1062 348
y Ff(k)q(i)1094 342 y Fi(e)1116 348 y Ff(i)1620 342 y Fh(\(11\))262
475 y(Note)14 b(that)g(the)g(p)q(ositiv)o(e)g(factor)g Fe(A)827
481 y Ff(k)861 475 y Fh(do)q(es)h(not)f(e\013ect)h(the)g(metric)e(sgn\()p
Fi(v)1441 460 y Ff(T)1467 475 y Fi(y)q Fh(\).)324 525 y(\(b\))h(F)m(ollo)o
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616 y Fe(;)7 b(\025)1065 622 y Fc(2)1083 616 y Fe(;)g(:)g(:)g(:)e(\025)1181
622 y Ff(L)1206 616 y Fb(g)p Fi(E)1258 599 y Ff(T)1284 616
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Fh(1)p 1011 689 V 1011 727 a Fe(\025)1035 733 y Fc(2)1059 698
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727 a Fe(\025)1161 733 y Ff(L)1191 698 y Fb(g)p Fi(E)1243 681
y Ff(T)1270 698 y Fi(s)1289 704 y Ff(k)1620 698 y Fh(\(13\))719
825 y(=)811 774 y Ff(L)792 786 y Fd(X)796 874 y Ff(i)p Fc(=1)873
797 y Fh(1)p 864 816 39 2 v 864 854 a Fe(\025)888 860 y Ff(i)907
825 y Fi(e)929 831 y Ff(i)943 825 y Fi(e)965 808 y Ff(T)965
836 y(i)991 825 y Fi(s)1010 831 y Ff(k)1620 825 y Fh(\(14\))719
971 y(=)811 919 y Ff(L)792 932 y Fd(X)796 1020 y Ff(i)p Fc(=1)859
971 y Fi(J)884 954 y Fg(\000)p Fc(1)929 971 y Fi(e)951 977
y Ff(i)964 971 y Fi(e)986 954 y Ff(T)986 981 y(i)1012 971 y
Fi(s)1031 977 y Ff(k)1620 971 y Fh(\(15\))719 1117 y(=)41 b
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y Fe(c)989 1123 y Ff(i;k)1620 1117 y Fh(\(16\))719 1222 y(=)g
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1222 y Fh(\(17\))719 1334 y(=)792 1263 y Fd(")817 1334 y Fe(\033)842
1316 y Fc(2)861 1334 y Fi(I)9 b Fh(+)945 1282 y Ff(K)930 1294
y Fd(X)929 1384 y Ff(k)q Fc(=1)997 1334 y Fe(A)1028 1316 y
Fc(2)1028 1344 y Ff(k)1048 1334 y Fi(s)1067 1340 y Ff(k)1087
1334 y Fi(s)1106 1316 y Ff(T)1106 1344 y(k)1132 1263 y Fd(#)1157
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1512 y(eigen)o(v)o(ectors)g(of)e Fi(J)g Fh(allo)o(ws)g(us)h(to)g(write)g
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Ff(T)1493 1523 y(i)1519 1512 y Fi(s)1538 1518 y Ff(k)1558 1512
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1612 y(eigen)o(v)o(ectors)h(iden)o(tical)f(to)h Fb(f)p Fi(s)766
1618 y Fc(1)784 1612 y Fe(;)7 b Fi(s)822 1618 y Fc(2)840 1612
y Fe(;)g(:)g(:)g(:)e Fi(s)933 1618 y Ff(K)965 1612 y Fb(g)18
b Fh(with)g(asso)q(ciated)i(eigen)o(v)o(ectors)f(equal)g(to)262
1661 y Fb(f)p Fe(\033)308 1646 y Fc(2)336 1661 y Fh(+)10 b
Fe(A)409 1646 y Fc(2)409 1672 y(1)428 1661 y Fe(;)d(\033)472
1646 y Fc(2)500 1661 y Fh(+)j Fe(A)573 1646 y Fc(2)573 1672
y(2)591 1661 y Fe(;)d(:)g(:)g(:)e(\033)690 1646 y Fc(2)719
1661 y Fh(+)10 b Fe(A)792 1646 y Fc(2)792 1673 y Ff(K)824 1661
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(subsitution)g(and)262 1711 y(the)i(fact)g(that)g(the)h(signals)e(are)i(unit)
f(energy)m(.)28 b(F)m(urthermore,)17 b(w)o(e)g(see)i(that)e(there)h(are)262
1761 y Fe(L)5 b Fb(\000)g Fe(K)16 b Fh(eigen)o(v)o(ectors)d(orthogonal)e(to)h
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(alues)h Fe(\033)1456 1746 y Fc(2)1475 1761 y Fh(.)17 b(The)c(eigen-)262
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