7.28.yingyao.ps

是multiuser detection 这本书的习题解答, 很有用的书.

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%%EndProlog
%%BeginSetup
%%Feature: *Resolution 300
TeXDict begin @letter
%%EndSetup
%%Page: 1 1
bop 618 482 a Fj(Solution)21 b(to)h(Problem)f(7.28)843 602
y Fi(Yingw)o(ei)15 b(Y)l(ao)847 699 y(Ma)o(y)h(3,)g(1999)683
854 y Fh(E)r Fg([\()p Fh(Y)i Ff(\000)9 b Fh(Ab)p Fg(\))892
837 y Fe(2)911 854 y Fg(])i(=)h Fh(E)r Fg([)p Fh(N)1061 837
y Fe(2)1079 854 y Fg(])f(=)h Fh(\033)1171 837 y Fe(2)262 966
y Fh(E)r Fg([\()p Fh(Asg)q(n)p Fg(\()p Fh(Y)d Fg(\))h Ff(\000)f
Fh(A)p Fg(\))582 949 y Fe(2)601 966 y Fg(])41 b(=)733 938 y(1)p
733 956 21 2 v 733 994 a(2)759 966 y(4)p Fh(A)811 949 y Fe(2)829
966 y Fh(P)6 b Fg(\()p Fh(sg)q(n)p Fg(\()p Fh(Y)k Fg(\))i Fh(<)g
Fg(0)p Ff(j)p Fh(b)e Fg(=)i(1\))d(+)1263 938 y(1)p 1263 956
V 1263 994 a(2)1288 966 y(4)p Fh(A)1340 949 y Fe(2)1359 966
y Fh(P)d Fg(\()p Fh(sg)q(n)p Fg(\()p Fh(Y)k Fg(\))h Fh(>)h
Fg(0)p Ff(j)p Fh(b)f Fg(=)g Ff(\000)p Fg(1\))654 1067 y(=)42
b(4)p Fh(A)780 1050 y Fe(2)799 1067 y Fh(Q)p Fg(\()853 1039
y Fh(A)p 853 1058 32 2 v 856 1096 a(\033)889 1067 y Fg(\))262
1150 y(In)13 b(order)i(to)f(sho)o(w)637 1210 y(3)p 637 1228
21 2 v 637 1266 a(2)674 1238 y Ff(\024)778 1210 y Fh(E)r Fg([\()p
Fh(Y)19 b Ff(\000)9 b Fh(Ab)p Fg(\))988 1194 y Fe(2)1007 1210
y Fg(])p 723 1228 352 2 v 723 1266 a Fh(E)r Fg([\()p Fh(Asg)q(n)p
Fg(\()p Fh(Y)h Fg(\))f Ff(\000)h Fh(A)p Fg(\))1044 1254 y Fe(2)1062
1266 y Fg(])1090 1238 y(=)1213 1210 y(1)p 1139 1228 168 2 v
1144 1255 a Fe(4)p Fd(A)1186 1246 y Fc(2)p 1144 1262 58 2 v
1155 1285 a Fd(\033)1175 1277 y Fc(2)1207 1271 y Fh(Q)p Fg(\()1261
1255 y Fd(A)p 1261 1262 25 2 v 1263 1285 a(\033)1291 1271 y
Fg(\))1312 1238 y Fh(;)262 1340 y Fg(w)o(e)k(only)f(need)i(to)e(sho)o(w)h
(that)g(for)g Fh(x)d Ff(\025)h Fg(0,)869 1428 y Fh(Q)p Fg(\()p
Fh(x)p Fg(\))f Ff(\024)1039 1400 y Fg(1)p 1018 1419 64 2 v
1018 1457 a(6)p Fh(x)1063 1445 y Fe(2)262 1516 y Fg(Consider)j(the)g
(function)g Fh(f)t Fg(\()p Fh(x)p Fg(\))e(=)g(6)p Fh(x)850
1501 y Fe(2)868 1516 y Fh(Q)p Fg(\()p Fh(x)p Fg(\),)589 1581
y Fh(d)p 577 1599 46 2 v 577 1637 a(dx)628 1609 y(f)t Fg(\()p
Fh(x)p Fg(\))42 b(=)g(6\(2)p Fh(xQ)p Fg(\()p Fh(x)p Fg(\))8
b Ff(\000)i Fh(x)1069 1592 y Fe(2)1122 1581 y Fg(1)p 1092 1599
81 2 v 1092 1607 a Ff(p)p 1127 1607 46 2 v 35 x Fg(2)p Fh(\031)1178
1609 y(e)1197 1592 y Fb(\000)p Fd(x)1242 1579 y Fc(2)1258 1592
y Fd(=)p Fe(2)1294 1609 y Fg(\))750 1719 y Fh(<)42 b Fg(6\()896
1691 y(2)p 866 1709 81 2 v 866 1717 a Ff(p)p 900 1717 46 2
v 900 1752 a Fg(2)p Fh(\031)951 1719 y(e)970 1702 y Fb(\000)p
Fd(x)1015 1689 y Fc(2)1031 1702 y Fd(=)p Fe(2)1076 1719 y Ff(\000)10
b Fh(x)1142 1702 y Fe(2)1195 1691 y Fg(1)p 1165 1709 81 2 v
1165 1717 a Ff(p)p 1200 1717 46 2 v 35 x Fg(2)p Fh(\031)1251
1719 y(e)1270 1702 y Fb(\000)p Fd(x)1315 1689 y Fc(2)1331 1702
y Fd(=)p Fe(2)1367 1719 y Fg(\))262 1820 y(So)j(the)i(v)n(alue)f(of)f
Fh(f)t Fg(\()p Fh(x)p Fg(\))g(=)f(6)p Fh(x)728 1805 y Fe(2)746
1820 y Fh(Q)p Fg(\()p Fh(x)p Fg(\))i(monotonically)d(decreases)17
b(for)c Fh(x)f(>)1442 1786 y Ff(p)p 1477 1786 21 2 v 34 x Fg(2.)18
b(If)c(w)o(e)g(can)262 1870 y(sho)o(w)d Fh(Q)p Fg(\()p Fh(x)p
Fg(\))h Ff(\024)529 1854 y Fe(1)p 511 1861 52 2 v 511 1885
a(6)p Fd(x)547 1876 y Fc(2)580 1870 y Fg(for)f(0)g Ff(\024)h
Fh(x)f Ff(\024)796 1836 y(p)p 831 1836 21 2 v 34 x Fg(2)o(,)h(then)g(it)g
(holds)f(for)h(all)e Fh(x)h Ff(\025)h Fg(0.)17 b(Since)12 b(for)g(all)e
Fh(x)i Ff(\025)f Fg(0,)262 1920 y Fh(Q)p Fg(\()p Fh(x)p Fg(\))g
Ff(\024)411 1904 y Fe(1)p 411 1911 17 2 v 411 1934 a(2)432
1920 y Fg(,)j(w)o(e)g(ha)o(v)o(e)f(for)h(0)d Ff(\024)h Fh(x)f
Ff(\024)852 1904 y Fe(1)p 838 1911 44 2 v 838 1915 a Fb(p)p
865 1915 17 2 v 24 x Fe(3)887 1920 y Fg(,)846 1995 y(1)p 825
2013 64 2 v 825 2051 a(6)p Fh(x)870 2039 y Fe(2)905 2023 y
Ff(\025)954 1995 y Fg(1)p 954 2013 21 2 v 954 2051 a(2)991
2023 y Ff(\025)h Fh(Q)p Fg(\()p Fh(x)p Fg(\))p Fh(:)262 2112
y Fg(Since)g Fh(Q)p Fg(\()p Fh(x)p Fg(\))g(is)f(a)h(monotonic)e(decreasing)j
(function,)f(if)f Fh(Q)p Fg(\()p Fh(x)p Fg(\))g Ff(\024)1316
2096 y Fe(1)p 1299 2103 52 2 v 1299 2126 a(6)p Fd(x)1335 2118
y Fc(2)1367 2112 y Fg(for)h(all)f(0)g Ff(\024)h Fh(x)f Ff(\024)h
Fh(x)1664 2118 y Fe(0)1682 2112 y Fg(,)262 2178 y(then)k(this)f(also)g(holds)
g(for)h(0)e Ff(\024)g Fh(x)g Ff(\024)867 2134 y Fa(q)p 908
2134 114 2 v 957 2162 a Fe(1)p 913 2169 104 2 v 913 2192 a(6)p
Fd(Q)p Fe(\()p Fd(x)988 2196 y Fc(0)1004 2192 y Fe(\))1036
2178 y Fh(<)h Fg(0)p Fh(:)p Fg(76.)22 b(Using)15 b(similar)e(reasoning,)i(w)o
(e)262 2246 y(can)c(get)h(after)f(sev)o(eral)h(iterations)f(that)h
Fh(Q)p Fg(\()p Fh(x)p Fg(\))f Ff(\024)1067 2230 y Fe(1)p 1050
2237 52 2 v 1050 2260 a(6)p Fd(x)1086 2252 y Fc(2)1118 2246
y Fg(holds)g(for)g(all)f(0)h Ff(\024)h Fh(x)f Ff(\024)h Fg(1)p
Fh(:)p Fg(45,)e(hence)262 2296 y(it)j(holds)h(for)f(all)g Fh(x)e
Ff(\025)h Fg(0)i(and)815 2361 y Fh(E)r Fg([\()p Fh(Y)k Ff(\000)9
b Fh(Ab)p Fg(\))1024 2346 y Fe(2)1043 2361 y Fg(])p 759 2379
352 2 v 759 2417 a Fh(E)r Fg([\()p Fh(Asg)q(n)p Fg(\()p Fh(Y)h
Fg(\))f Ff(\000)h Fh(A)p Fg(\))1080 2405 y Fe(2)1099 2417 y
Fg(])1127 2389 y Ff(\024)1176 2361 y Fg(3)p 1176 2379 21 2
v 1176 2417 a(2)967 2574 y(1)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF