3.23.kishore.ps

是multiuser detection 这本书的习题解答, 很有用的书.

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1 0 bop 257 262 a Fj(Solution)13 b(to)i(3.23)h(b)o(y)f(Shalinee)e
(Kishore)40 b Fi(\(a\))14 b(Pro)q(of)g(of)f(b)q(ound)h(\(3.35\))666
358 y Fh(Q)p Fi(\()p Fh(x)p Fi(\))42 b(=)905 330 y(1)p
876 349 81 2 v 876 357 a Fg(p)p 910 357 46 2 v 910 391
a Fi(2)p Fh(\031)968 302 y Ff(Z)1009 312 y Fe(1)991 396
y Fd(x)1052 358 y Fh(e)1071 341 y Fe(\000)p Fd(t)1110
329 y Fc(2)1126 341 y Fd(=)p Fb(2)1168 358 y Fh(dt)431
b Fi(\(1\))797 472 y(=)905 444 y(1)p 876 463 81 2 v 876
471 a Fg(p)p 910 471 46 2 v 910 505 a Fi(2)p Fh(\031)968
416 y Ff(Z)1009 426 y Fe(1)991 510 y Fd(x)1057 444 y
Fi(1)p 1057 463 21 2 v 1060 501 a Fh(t)1092 472 y Fg(\001)8
b Fh(te)1146 455 y Fe(\000)p Fd(t)1185 443 y Fc(2)1201
455 y Fd(=)p Fb(2)1244 472 y Fh(dt)355 b Fi(\(2\))257
579 y(With)18 b Fh(u)h Fi(=)g(1)p Fh(=t)f Fi(and)25 b
Fh(dv)c Fi(=)e Fh(te)778 564 y Fe(\000)p Fd(t)817 552
y Fc(2)833 564 y Fd(=)p Fb(2)875 579 y Fh(dt)p Fi(,)g(w)o(e)g(get)25
b Fh(du)19 b Fi(=)g Fg(\000)p Fh(t)1252 564 y Fe(\000)p
Fb(2)1304 579 y Fh(dt)f Fi(and)g Fh(v)j Fi(=)e Fg(\000)p
Fh(e)1587 564 y Fe(\000)p Fd(t)1626 552 y Fc(2)1642 564
y Fd(=)p Fb(2)1678 579 y Fi(.)257 629 y(In)o(tegration)14
b(b)o(y)g(parts)g(then)h(giv)o(es)e(us)563 687 y Fg(p)p
597 687 46 2 v 597 724 a Fi(2)p Fh(\031)q(Q)p Fi(\()p
Fh(x)p Fi(\))41 b(=)847 667 y Ff(Z)889 677 y Fe(1)870
761 y Fd(x)931 724 y Fh(u)7 b(dv)632 b Fi(\(3\))773 837
y(=)42 b Fh(uv)q Fg(j)904 820 y Fe(1)904 847 y Fd(x)949
837 y Fg(\000)990 780 y Ff(Z)1032 791 y Fe(1)1013 875
y Fd(x)1074 837 y Fh(v)8 b(du)488 b Fi(\(4\))773 966
y(=)857 938 y Fg(\000)p Fh(e)908 923 y Fe(\000)p Fd(t)947
910 y Fc(2)964 923 y Fd(=)p Fb(2)p 857 957 142 2 v 921
995 a Fh(t)1004 893 y Ff(\014)1004 918 y(\014)1004 943
y(\014)1004 968 y(\014)1004 993 y(\014)1018 904 y Fe(1)1018
1020 y Fd(x)1062 966 y Fg(\000)1104 910 y Ff(Z)1145 920
y Fe(1)1127 1004 y Fd(x)1199 938 y Fi(1)p 1192 957 34
2 v 1192 995 a Fh(t)1207 983 y Fb(2)1231 966 y Fh(e)1250
949 y Fe(\000)p Fd(t)1289 936 y Fc(2)1305 949 y Fd(=)p
Fb(2)1348 966 y Fh(dt)251 b Fi(\(5\))773 1106 y(=)852
1078 y Fh(e)871 1063 y Fe(\000)p Fd(x)916 1050 y Fc(2)933
1063 y Fd(=)p Fb(2)p 852 1096 116 2 v 898 1134 a Fh(x)982
1106 y Fg(\000)1024 1049 y Ff(Z)1065 1060 y Fe(1)1047
1144 y Fd(x)1119 1078 y Fi(1)p 1112 1096 34 2 v 1112
1134 a Fh(t)1127 1122 y Fb(2)1151 1106 y Fh(e)1170 1089
y Fe(\000)p Fd(t)1209 1076 y Fc(2)1225 1089 y Fd(=)p
Fb(2)1268 1106 y Fh(dt)331 b Fi(\(6\))257 1212 y(Observ)o(e)16
b(that)e(since)608 1179 y Ff(R)636 1189 y Fe(1)628 1227
y Fd(x)689 1196 y Fb(1)p 683 1203 29 2 v 683 1226 a Fd(t)696
1218 y Fc(2)717 1212 y Fh(e)736 1197 y Fe(\000)p Fd(t)775
1185 y Fc(2)791 1197 y Fd(=)p Fb(2)834 1212 y Fh(dt)d(>)g
Fi(0)j(for)g Fh(x)d(>)h Fi(0,)h(w)o(e)h(get:)798 1287
y Fg(p)p 833 1287 46 2 v 37 x Fi(2)p Fh(\031)q(Q)p Fi(\()p
Fh(x)p Fi(\))d Fh(<)1028 1295 y(e)1047 1280 y Fe(\000)p
Fd(x)1092 1268 y Fc(2)1108 1280 y Fd(=)p Fb(2)p 1028
1314 116 2 v 1074 1352 a Fh(x)1636 1324 y Fi(\(7\))257
1411 y(This)j(then)h(giv)o(es)e(us)i(b)q(ound)f(\(3.35\):)755
1518 y Fh(Q)p Fi(\()p Fh(x)p Fi(\))d Fh(<)904 1490 y(e)923
1475 y Fe(\000)p Fd(x)968 1462 y Fc(2)985 1475 y Fd(=)p
Fb(2)p 904 1508 V 910 1517 a Fg(p)p 945 1517 46 2 v 34
x Fi(2)p Fh(\031)q(x)1039 1518 y Fi(,)41 b Fh(x)11 b(>)h
Fi(0)444 b(\(8\))320 1615 y(Pro)q(of)13 b(of)h(b)q(ound)g(\(3.34\).)j
(Using)c(the)i(result)g(in)e(\(6\),)g(w)o(e)h(can)h(write)f
Fh(Q)p Fi(\()p Fh(x)p Fi(\))f(as)550 1712 y Fh(Q)p Fi(\()p
Fh(x)p Fi(\))e(=)740 1684 y(1)p 699 1702 105 2 v 699
1711 a Fg(p)p 733 1711 46 2 v 733 1745 a Fi(2)p Fh(\031)q(x)808
1712 y(e)827 1695 y Fe(\000)p Fd(x)872 1682 y Fc(2)888
1695 y Fd(=)p Fb(2)933 1712 y Fg(\000)1009 1684 y Fi(1)p
980 1702 81 2 v 980 1711 a Fg(p)p 1014 1711 46 2 v 1014
1745 a Fi(2)p Fh(\031)1072 1655 y Ff(Z)1113 1666 y Fe(1)1095
1750 y Fd(x)1167 1684 y Fi(1)p 1161 1702 34 2 v 1161
1740 a Fh(t)1176 1728 y Fb(3)1208 1712 y Fg(\001)e Fh(te)1263
1695 y Fe(\000)p Fd(t)1302 1682 y Fc(2)1318 1695 y Fd(=)p
Fb(2)1361 1712 y Fh(dt)238 b Fi(\(9\))257 1809 y(Once)16
b(again)d(w)o(e)h(mak)o(e)e(use)j(of)f(in)o(tegration)f(b)o(y)h(parts)h
(to)e(ev)n(aluate)h(the)h(in)o(tegral)e(in)h(\(9\).)257
1865 y(With)i Fh(u)g Fi(=)g(1)p Fh(=t)512 1850 y Fb(3)547
1865 y Fi(and)23 b Fh(dv)18 b Fi(=)e Fh(te)779 1850 y
Fe(\000)p Fd(t)818 1837 y Fc(2)834 1850 y Fd(=)p Fb(2)876
1865 y Fh(dt)p Fi(,)h(w)o(e)g(get)23 b Fh(du)16 b Fi(=)g
Fg(\000)p Fi(3)p Fh(t)1262 1850 y Fe(\000)p Fb(4)1314
1865 y Fh(dt)g Fi(and)g Fh(v)i Fi(=)e Fg(\000)p Fh(e)1587
1850 y Fe(\000)p Fd(t)1626 1837 y Fc(2)1642 1850 y Fd(=)p
Fb(2)1678 1865 y Fi(.)257 1915 y(W)m(e)e(can)g(then)h(write)428
2017 y Fh(Q)p Fi(\()p Fh(x)p Fi(\))41 b(=)679 1989 y(1)p
637 2007 105 2 v 637 2016 a Fg(p)p 671 2016 46 2 v 671
2050 a Fi(2)p Fh(\031)q(x)746 2017 y(e)765 2000 y Fe(\000)p
Fd(x)810 1987 y Fc(2)826 2000 y Fd(=)p Fb(2)871 2017
y Fi(+)925 1989 y Fh(e)944 1974 y Fe(\000)p Fd(t)983
1961 y Fc(2)999 1974 y Fd(=)p Fb(2)p 923 2007 115 2 v
923 2016 a Fg(p)p 957 2016 46 2 v 957 2050 a Fi(2)p Fh(\031)q(t)1018
2038 y Fb(3)1042 1944 y Ff(\014)1042 1969 y(\014)1042
1994 y(\014)1042 2019 y(\014)1042 2044 y(\014)1056 1955
y Fe(1)1056 2071 y Fd(x)1100 2017 y Fi(+)1176 1989 y(1)p
1146 2007 81 2 v 1146 2016 a Fg(p)p 1181 2016 46 2 v
34 x Fi(2)p Fh(\031)1239 1961 y Ff(Z)1280 1971 y Fe(1)1262
2055 y Fd(x)1334 1989 y Fi(3)p 1327 2007 34 2 v 1327
2045 a Fh(t)1342 2033 y Fb(4)1366 2017 y Fh(e)1385 2000
y Fe(\000)p Fd(t)1424 1987 y Fc(2)1440 2000 y Fd(=)p
Fb(2)1483 2017 y Fh(dt)96 b Fi(\(10\))558 2157 y(=)679
2129 y(1)p 637 2147 105 2 v 637 2155 a Fg(p)p 671 2155
46 2 v 671 2190 a Fi(2)p Fh(\031)q(x)746 2157 y(e)765
2139 y Fe(\000)p Fd(x)810 2127 y Fc(2)826 2139 y Fd(=)p
Fb(2)871 2157 y Fg(\000)921 2129 y Fh(e)940 2113 y Fe(\000)p
Fd(x)985 2101 y Fc(2)1001 2113 y Fd(=)p Fb(2)p 918 2147
123 2 v 918 2155 a Fg(p)p 952 2155 46 2 v 952 2190 a
Fi(2)p Fh(\031)q(x)1022 2178 y Fb(3)1055 2157 y Fi(+)1131
2129 y(1)p 1101 2147 81 2 v 1101 2155 a Fg(p)p 1136 2155
46 2 v 35 x Fi(2)p Fh(\031)1194 2100 y Ff(Z)1235 2110
y Fe(1)1217 2194 y Fd(x)1289 2129 y Fi(3)p 1282 2147
34 2 v 1282 2185 a Fh(t)1297 2173 y Fb(4)1321 2157 y
Fh(e)1340 2139 y Fe(\000)p Fd(t)1379 2127 y Fc(2)1395
2139 y Fd(=)p Fb(2)1437 2157 y Fh(dt)142 b Fi(\(11\))257
2264 y(Since)366 2230 y Ff(R)393 2241 y Fe(1)385 2279
y Fd(x)447 2247 y Fb(3)p 441 2254 29 2 v 441 2278 a Fd(t)454
2270 y Fc(4)474 2264 y Fh(e)493 2249 y Fe(\000)p Fd(t)532
2236 y Fc(2)548 2249 y Fd(=)p Fb(2)591 2264 y Fh(dt)11
b(>)h Fi(0)h(for)h Fh(x)d(>)h Fi(0)i(\(and)f(thereb)o(y)i
Fh(x)d(>)f Fi(1\),)j(w)o(e)g(note:)595 2375 y Fh(Q)p
Fi(\()p Fh(x)p Fi(\))41 b Fh(>)846 2347 y Fi(1)p 804
2366 105 2 v 804 2374 a Fg(p)p 839 2374 46 2 v 34 x Fi(2)p
Fh(\031)q(x)913 2375 y(e)932 2358 y Fe(\000)p Fd(x)977
2346 y Fc(2)994 2358 y Fd(=)p Fb(2)1038 2375 y Fg(\000)1087
2347 y Fh(e)1106 2332 y Fe(\000)p Fd(x)1151 2320 y Fc(2)1167
2332 y Fd(=x)p 1085 2366 123 2 v 1085 2374 a Fg(p)p 1119