3.26.kishore.ps

是multiuser detection 这本书的习题解答, 很有用的书.

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%%EndProlog
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%%Page: 1 1
1 0 bop 257 262 a Fj(Solution)19 b(to)j(3.26)g(b)o(y)g(Shalinee)d
(Kishore)40 b Fi(Note)20 b(\014rst)g(that)g(for)f Fh(Y)9
b Fi(,)20 b(a)g(normal)257 311 y(random)15 b(v)n(ariable)h(\(zero-mean)
g(and)h(unit)f(v)n(ariance\),)h(E[)p Fh(Y)1229 296 y
Fg(2)p Ff(n)1268 311 y Fi(])f(=)g(1)11 b Fe(\001)g Fi(3)g
Fe(\001)f Fi(5)d Fh(:)g(:)g(:)e Fi(\(2)p Fh(n)11 b Fe(\000)h
Fi(1\))257 361 y(where)j Fh(n)d Fi(=)g(1)p Fh(;)7 b Fi(2)p
Fh(;)g(:)g(:)g(:)m Fi(.)17 b(W)m(e)d(kno)o(w)611 463
y(E[)p Fh(Q)p Fi(\()p Fh(Y)9 b Fi(\)])i(=)851 435 y(1)p
821 453 81 2 v 821 462 a Fe(p)p 856 462 46 2 v 34 x Fi(2)p
Fh(\031)913 406 y Fd(Z)955 417 y Fc(1)937 501 y(\0001)1005
463 y Fh(P)6 b Fi([)p Fh(Y)19 b Fe(\024)12 b Fh(y)q Fi(])p
Fh(e)1189 446 y Fc(\000)p Ff(y)1233 433 y Fb(2)1250 446
y Ff(=)p Fg(2)1292 463 y Fh(dy)302 b Fi(\(1\))257 578
y(No)o(w,)12 b(let)g Fh(Y)21 b Fi(=)11 b Fe(jj)p Fj(X)p
Fe(jj)f Fi(=)646 542 y Fd(p)p 688 542 489 2 v 36 x Fh(X)725
563 y Fg(2)722 589 y(1)p Ff(r)766 578 y Fi(+)g Fh(X)845
563 y Fg(2)842 589 y(1)p Ff(i)882 578 y Fi(+)f Fh(:)e(:)g(:)e(X)1015
563 y Fg(2)1012 590 y Ff(Lr)1063 578 y Fi(+)10 b Fh(X)1142
563 y Fg(2)1139 590 y Ff(Li)1176 578 y Fi(.)17 b(By)12
b(this)g(de\014nition)g(of)f Fh(Y)e Fi(,)j(the)257 628
y(probabilit)o(y)h(of)g(negativ)o(e)h(v)n(alues)f(of)h
Fh(Y)23 b Fi(are)14 b(zero.)19 b(W)m(e)13 b(also)h(kno)o(w)f(that)h
(for)g Fh(y)f Fe(\025)f Fi(0,)564 708 y Fh(P)6 b Fi([)p
Fh(Y)20 b Fe(\024)12 b Fh(y)q Fi(])42 b(=)g(1)9 b Fe(\000)g
Fh(P)d Fi([)p Fh(Y)20 b(>)12 b(y)q Fi(])553 b(\(2\))772
811 y(=)42 b(1)9 b Fe(\000)g Fh(e)936 794 y Fc(\000)p
Ff(y)980 781 y Fb(2)996 794 y Ff(=)p Fg(\(2)p Ff(\015)1062
781 y Fb(2)1078 794 y Fg(\))1100 759 y Ff(L)p Fc(\000)p
Fg(1)1103 771 y Fd(X)1102 859 y Ff(n)p Fg(=0)1185 783
y Fi(1)p 1177 801 37 2 v 1177 839 a Fh(n)p Fi(!)1226
752 y Fd(\022)1273 783 y Fh(y)1294 768 y Fg(2)p 1261
801 64 2 v 1261 839 a Fi(2)p Fh(\015)1305 827 y Fg(2)1329
752 y Fd(\023)1360 759 y Ff(n)1636 811 y Fi(\(3\))257
927 y(Using)14 b(these)h(observ)n(ations,)f(w)o(e)g(can)g(write)363
1046 y(E[)p Fh(Q)p Fi(\()p Fh(Y)9 b Fi(\)])41 b(=)663
1018 y(1)p 633 1036 81 2 v 633 1045 a Fe(p)p 667 1045
46 2 v 667 1079 a Fi(2)p Fh(\031)725 990 y Fd(Z)767 1000
y Fc(1)748 1084 y Fg(0)809 975 y Fd( )842 1046 y Fi(1)9
b Fe(\000)g Fh(e)932 1029 y Fc(\000)p Ff(y)976 1016 y
Fb(2)993 1029 y Ff(=)p Fg(\(2)p Ff(\015)1059 1016 y Fb(2)1075
1029 y Fg(\))1097 994 y Ff(L)p Fc(\000)p Fg(1)1099 1007
y Fd(X)1098 1094 y Ff(n)p Fg(=0)1182 1018 y Fi(1)p 1174
1036 37 2 v 1174 1074 a Fh(n)p Fi(!)1222 987 y Fd(\022)1269
1018 y Fh(y)1290 1003 y Fg(2)p 1258 1036 64 2 v 1258
1074 a Fi(2)p Fh(\015)1302 1062 y Fg(2)1326 987 y Fd(\023)1356
994 y Ff(n)1379 975 y Fd(!)1419 1046 y Fh(e)1438 1029
y Fc(\000)p Ff(y)1482 1016 y Fb(2)1498 1029 y Ff(=)p
Fg(2)1541 1046 y Fh(dy)53 b Fi(\(4\))554 1174 y(=)663
1146 y(1)p 633 1164 81 2 v 633 1173 a Fe(p)p 667 1173
46 2 v 667 1207 a Fi(2)p Fh(\031)725 1117 y Fd(Z)767
1128 y Fc(1)748 1212 y Fg(0)809 1174 y Fh(e)828 1157
y Fc(\000)p Ff(y)872 1144 y Fb(2)888 1157 y Ff(=)p Fg(2)931
1174 y Fh(dy)663 b Fi(\(5\))628 1305 y Fe(\000)667 1253
y Ff(L)p Fc(\000)p Fg(1)670 1266 y Fd(X)668 1354 y Ff(n)p
Fg(=0)752 1277 y Fi(1)p 744 1296 37 2 v 744 1334 a Fh(n)p
Fi(!)821 1277 y(1)p 791 1296 81 2 v 791 1304 a Fe(p)p
825 1304 46 2 v 825 1338 a Fi(2)p Fh(\031)883 1249 y
Fd(Z)925 1259 y Fc(1)906 1343 y Fg(0)967 1305 y Fh(e)986
1282 y Fc(\000)p Ff(y)1030 1269 y Fb(2)1046 1251 y Fd(\000)1087
1271 y Fb(1)p 1070 1276 48 2 v 1070 1297 a(2)p Fa(\015)1101
1291 y Fb(2)1122 1282 y Fg(+)1153 1271 y Fb(1)p 1153
1276 15 2 v 1153 1292 a(2)1172 1251 y Fd(\001)1200 1247
y(\022)1247 1277 y Fh(y)1268 1262 y Fg(2)p 1235 1296
64 2 v 1235 1334 a Fi(2)p Fh(\015)1279 1322 y Fg(2)1304
1247 y Fd(\023)1334 1253 y Ff(n)1371 1305 y Fh(dy)223
b Fi(\(6\))257 1434 y(Since)395 1417 y Fg(1)p 371 1424
65 2 v 371 1428 a Fc(p)p 398 1428 38 2 v 25 x Fg(2)p
Ff(\031)447 1400 y Fd(R)475 1410 y Fc(1)467 1448 y Fg(0)517
1434 y Fh(e)536 1418 y Fc(\000)p Ff(y)580 1406 y Fb(2)596
1418 y Ff(=)p Fg(2)639 1434 y Fh(dy)13 b Fi(=)e(1)p Fh(=)p
Fi(2,)456 1570 y(E[)p Fh(Q)p Fi(\()p Fh(Y)e Fi(\)])41
b(=)726 1542 y(1)p 726 1561 21 2 v 726 1599 a(2)761 1570
y Fe(\000)838 1542 y Fi(1)p 808 1561 81 2 v 808 1569
a Fe(p)p 842 1569 46 2 v 842 1603 a Fi(2)p Fh(\031)900
1514 y Fd(Z)942 1524 y Fc(1)923 1608 y Fg(0)984 1570
y Fh(e)1003 1536 y Fc(\000)p Ff(y)1047 1523 y Fb(2)1063
1493 y Fd(\020)1093 1522 y Fb(1+)p Fa(\015)1145 1513
y Fb(2)p 1093 1529 69 2 v 1103 1550 a(2)p Fa(\015)1134
1544 y Fb(2)1166 1493 y Fd(\021)1200 1570 y Fh(dy)394
b Fi(\(7\))721 1705 y Fe(\000)760 1653 y Ff(L)p Fc(\000)p
Fg(1)763 1665 y Fd(X)762 1753 y Ff(n)p Fg(=1)845 1676
y Fi(1)p 838 1695 37 2 v 838 1733 a Fh(n)p Fi(!)914 1676
y(1)p 884 1695 81 2 v 884 1703 a Fe(p)p 919 1703 46 2
v 35 x Fi(2)p Fh(\031)976 1648 y Fd(Z)1018 1658 y Fc(1)999
1742 y Fg(0)1060 1705 y Fh(e)1079 1670 y Fc(\000)p Ff(y)1123
1657 y Fb(2)1139 1627 y Fd(\020)1169 1656 y Fb(1+)p Fa(\015)1221
1648 y Fb(2)p 1169 1663 69 2 v 1180 1685 a(2)p Fa(\015)1211
1679 y Fb(2)1243 1627 y Fd(\021)1277 1646 y(\022)1323
1676 y Fh(y)1344 1661 y Fg(2)p 1312 1695 64 2 v 1312
1733 a Fi(2)p Fh(\015)1356 1721 y Fg(2)1380 1646 y Fd(\023)1411
1653 y Ff(n)1447 1705 y Fh(dy)147 b Fi(\(8\))257 1843
y(Here)15 b(w)o(e)g(substitute,)f Fh(x)e Fi(=)701 1795
y Fd(q)p 743 1795 88 2 v 748 1824 a Fg(1+)p Ff(\015)809
1816 y Fb(2)p 748 1833 78 2 v 769 1857 a Ff(\015)788
1849 y Fb(2)830 1843 y Fh(y)q Fi(.)19 b(Then,)327 1982
y(E)q([)p Fh(Q)p Fi(\()p Fh(Y)9 b Fi(\)])41 b(=)597 1954
y(1)p 597 1973 21 2 v 597 2011 a(2)632 1982 y Fe(\000)709
1954 y Fi(1)p 679 1973 81 2 v 679 1981 a Fe(p)p 714 1981
46 2 v 34 x Fi(2)p Fh(\031)771 1926 y Fd(Z)813 1936 y
Fc(1)794 2020 y Fg(0)855 1982 y Fh(e)874 1965 y Fc(\000)p
Ff(x)919 1952 y Fb(2)935 1965 y Ff(=)p Fg(2)978 1982
y Fh(dx)1031 1911 y Fd( )1063 1906 y(s)p 1104 1906 124
2 v 1145 1954 a Fh(\015)1168 1942 y Fg(2)p 1109 1973
114 2 v 1109 2011 a Fi(1)9 b(+)h Fh(\015)1204 1999 y
Fg(2)1228 1911 y Fd(!)1636 1982 y Fi(\(9\))593 2130 y
Fe(\000)632 2078 y Ff(L)p Fc(\000)p Fg(1)634 2090 y Fd(X)633
2178 y Ff(n)p Fg(=1)823 2101 y Fi(1)p 709 2120 249 2
v 709 2158 a Fh(n)p Fi(!\(1)e(+)i Fh(\015)856 2146 y
Fg(2)875 2158 y Fi(\))891 2146 y Ff(n)914 2158 y Fi(2)935
2146 y Ff(n)997 2101 y Fi(1)p 967 2120 81 2 v 967 2128
a Fe(p)p 1002 2128 46 2 v 35 x Fi(2)p Fh(\031)1060 2073
y Fd(Z)1101 2083 y Fc(1)1083 2167 y Fg(0)1143 2130 y
Fh(e)1162 2112 y Fc(\000)p Ff(x)1207 2100 y Fb(2)1224
2112 y Ff(=)p Fg(2)1259 2130 y Fh(x)1283 2112 y Fg(2)p
Ff(n)1329 2130 y Fh(dx)1382 2059 y Fd( )1414 2054 y(s)p
1456 2054 124 2 v 1496 2101 a Fh(\015)1519 2089 y Fg(2)p
1461 2120 114 2 v 1461 2158 a Fi(1)f(+)g Fh(\015)1555
2146 y Fg(2)1580 2059 y Fd(!)1616 2130 y Fi(\(10\))519
2275 y(=)597 2247 y(1)p 597 2265 21 2 v 597 2303 a(2)632
2275 y Fe(\000)679 2247 y Fi(1)p 679 2265 V 679 2303
a(2)790 2247 y(1)p 710 2265 182 2 v 710 2273 a Fd(p)p
751 2273 140 2 v 751 2310 a Fi(1)g(+)h Fh(\015)846 2298
y Fc(\000)p Fg(2)905 2275 y Fe(\000)947 2223 y Ff(L)p
Fc(\000)p Fg(1)949 2235 y Fd(X)948 2323 y Ff(n)p Fg(=1)1024
2247 y Fi(1)f Fe(\001)g Fi(3)g Fe(\001)f Fi(5)f Fh(:)g(:)g(:)h
Fe(\001)g Fi(\(2)p Fh(n)h Fe(\000)h Fi(1\))p 1024 2265
358 2 v 1057 2303 a Fh(n)p Fi(!\(1)f(+)g Fh(\015)1204
2291 y Fg(2)1224 2303 y Fi(\))1240 2291 y Ff(n)1262 2303
y Fi(2)1283 2291 y Ff(n)p Fg([phone] y Fi(1)p 1391
2265 182 2 v 1391 2273 a Fd(p)p 1432 2273 140 2 v 1432
2310 a Fi(1)g(+)h Fh(\015)1527 2298 y Fc(\000)p Fg(2)1616
2275 y Fi(\(11\))519 2420 y(=)597 2392 y(1)p 597 2410
21 2 v 597 2448 a(2)632 2420 y Fe(\000)679 2392 y Fi(1)p
679 2410 V 679 2448 a(2)790 2392 y(1)p 710 2410 182 2
v 710 2419 a Fd(p)p 751 2419 140 2 v 751 2455 a Fi(1)f(+)h
Fh(\015)846 2443 y Fc(\000)p Fg(2)903 2349 y Fd( )936
2420 y Fi(1)f(+)1007 2368 y Ff(L)p Fc(\000)p Fg(1)1010
2380 y Fd(X)1009 2468 y Ff(n)p Fg(=1)1084 2392 y Fi(1)g
Fe(\001)g Fi(3)g Fe(\001)g Fi(5)e Fh(:)g(:)g(:)g Fe(\001)i
Fi(\(2)p Fh(n)g Fe(\000)h Fi(1\))p 1084 2410 358 2 v
1139 2448 a Fh(n)p Fi(!\(1)e(+)i Fh(\015)1286 2436 y
Fg(2)1305 2448 y Fi(\))1321 2436 y Ff(n)1344 2448 y Fi(2)1365
2436 y Ff(n)1446 2349 y Fd(!)1616 2420 y Fi(\(12\))963
2628 y(1)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF