4.51.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 678 307 a Fi(Solution)20 b(to)f(Problem)f(4.51)852 357
y Fh(Yingw)o(ei)13 b(Y)m(ao)262 457 y(\(a\))c(F)m(or)g(an)o(y)f(t)o(w)o(o)h
(signature)h(w)o(a)o(v)o(eforms)d Fg(c)935 463 y Ff(k)967 457
y Fh(=)k([c)1040 463 y Ff(k1)1077 457 y Fe(;)c Fh(c)1114 463
y Ff(k2)1149 457 y Fe(;)g Fd(\001)g(\001)g(\001)e Fe(;)i Fh(c)1260
463 y Ff(kN)1304 457 y Fh(])i(and)g Fg(c)1422 463 y Ff(l)1445
457 y Fh(=)j([c)1519 463 y Ff(l1)1547 457 y Fe(;)7 b Fh(c)1584
463 y Ff(l2)1612 457 y Fe(;)g Fd(\001)g(\001)g(\001)e Fe(;)i
Fh(c)1723 463 y Ff(lN)1759 457 y Fh(],)262 506 y(their)14 b(crosscorrelation)
h(is)620 620 y Fe(\032)641 626 y Fc(k)q(l)684 620 y Fh(=)741
592 y(1)p 733 611 38 2 v 733 649 a Fe(N)799 569 y Fc(N)784
581 y Fb(X)782 669 y Fc(n)p Ff(=0)852 620 y Fe(c)870 626 y
Fc(k)q(n)911 620 y Fe(c)929 626 y Fc(ln)974 620 y Fh(=)c(1)e
Fd(\000)1102 592 y Fh(2)p 1094 611 V 1094 649 a Fe(N)1137 620
y(w)q Fh(\()p Fg(c)1205 626 y Ff(k)1234 620 y Fd(\000)g Fg(c)1296
626 y Ff(l)1308 620 y Fh(\))p Fe(;)262 742 y Fh(where)15 b
Fe(w)q Fh(\()p Fg(c)p Fh(\))f(is)f(the)i(w)o(eigh)o(t)e(of)h(v)o(ector)g
Fg(c)p Fh(.)19 b(So)13 b(the)i(distribution)e(of)g Fe(\032)1371
748 y Fc(k)q(l)1417 742 y Fh(is)560 851 y Fe(P)6 b Fh([)p Fe(\032)626
857 y Fc(k)q(l)668 851 y Fh(=)12 b(1)d Fd(\000)789 823 y Fh(2)p
Fe(i)p 788 841 V 788 879 a(N)831 851 y Fh(])i(=)898 792 y Fb(\022)928
818 y Fc(N)936 854 y Fe(i)958 792 y Fb(\023)995 851 y Fh(2)1016
834 y Fa(\000)p Fc(N)1073 851 y Fe(;)41 b(i)12 b Fh(=)g(0)p
Fe(;)7 b Fh(1)p Fe(;)g Fd(\001)g(\001)g(\001)t Fe(;)g(N)r(:)570
1004 y(E)r Fh([)p Fe(\032)636 987 y Ff(4)636 1014 y Fc(k)q(l)667
1004 y Fh(])k(=)749 952 y Fc(N)734 965 y Fb(X)737 1053 y Fc(i)p
Ff(=0)801 946 y Fb(\022)831 972 y Fc(N)839 1007 y Fe(i)861
946 y Fb(\023)898 1004 y Fh(2)919 987 y Fa(\000)p Fc(N)976
1004 y Fh(\(1)e Fd(\000)1070 976 y Fh(2)p Fe(i)p 1069 995 V
1069 1033 a(N)1112 1004 y Fh(\))1128 987 y Ff(4)1158 1004 y
Fh(=)1225 976 y(3)p 1207 995 57 2 v 1207 1033 a Fe(N)1245 1021
y Ff(2)1277 1004 y Fd(\000)1342 976 y Fh(2)p 1324 995 V 1324
1033 a Fe(N)1362 1021 y Ff(3)262 1113 y Fh(\(b\))14 b(Giv)o(en)f
Fg(c)472 1119 y Ff(k)492 1113 y Fh(,)g(the)i(probabilit)o(y)d(mass)h
(function)g(of)h Fe(\032)1134 1119 y Fc(k)q(j)1184 1113 y Fh(is)503
1218 y Fe(P)6 b Fh([)p Fe(\032)569 1224 y Fc(k)q(j)616 1218
y Fh(=)12 b(1)d Fd(\000)737 1190 y Fh(2)p Fe(i)p 736 1209 38
2 v 736 1247 a(N)779 1218 y Fh(])i(=)h Fe(P)6 b Fh([)p Fe(w)q
Fh(\()p Fg(c)959 1224 y Ff(k)987 1218 y Fd(\000)j Fg(c)1049
1224 y Ff(j)1062 1218 y Fh(\))i(=)h(i])f(=)h(P[)p Fg(c)1273
1224 y Ff(j)1297 1218 y Fd(2)f Fh(C)1366 1224 y Ff(k)1385 1218
y Fh(\(i\)])p Fe(;)262 1320 y Fh(where)k Fe(C)412 1326 y Fc(k)432
1320 y Fh(\()p Fe(i)p Fh(\))e(=)g Fd(f)p Fg(c)f Fd(2)g(f\000)p
Fh(1)p Fe(;)7 b Fh(+1)p Fd(g)797 1305 y Ff(N)823 1320 y Fd(j)p
Fh(w\()p Fg(c)j Fd(\000)f Fg(c)974 1326 y Ff(k)994 1320 y Fh(\))k(=)f(i)p
Fd(g)p Fh(.)19 b(Since)c(for)f(an)o(y)g Fe(l)i Fh(and)e Fe(m)h
Fh(\()p Fe(l)f Fd(6)p Fh(=)f Fe(m)p Fh(\),)262 1370 y Fg(c)283
1376 y Ff(l)309 1370 y Fh(and)h Fg(c)411 1376 y Ff(m)455 1370
y Fh(are)h(indep)q(enden)o(t,)g(the)g(crosscorrelations)h Fe(\032)1178
1376 y Fc(k)q(l)1224 1370 y Fh(and)e Fe(\032)1326 1376 y Fc(k)q(m)1391
1370 y Fh(are)h(indep)q(enden)o(t.)262 1419 y(So,)553 1487
y Fe(E)r Fh([)p Fe(\032)619 1470 y Ff(2)619 1497 y Fc(k)q(l)650
1487 y Fe(\032)671 1470 y Ff(2)671 1497 y Fc(k)q(m)721 1487
y Fh(])c(=)h(\()p Fe(E)r Fh([)p Fe(\032)870 1470 y Ff(2)870
1497 y Fc(k)q(l)902 1487 y Fh(]\))930 1470 y Ff(2)959 1487
y Fh(=)g(\()p Fe(E)r Fh([\(1)d Fd(\000)1158 1459 y Fh(2)p Fe(i)p
1157 1478 V 1157 1516 a(N)1199 1487 y Fh(\))1215 1470 y Ff(2)1234
1487 y Fh(]\))1262 1470 y Ff(2)1292 1487 y Fh(=)1359 1459 y(1)p
1341 1478 57 2 v 1341 1516 a Fe(N)1379 1504 y Ff(2)262 1571
y Fh(\(c\))362 1675 y Fe(E)r Fh([)p Fe(\032)428 1681 y Fc(k)q(m)478
1675 y Fe(\032)499 1681 y Fc(lm)542 1675 y Fe(\032)563 1681
y Fc(k)q(n)604 1675 y Fe(\032)625 1681 y Fc(ln)659 1675 y Fh(])i(=)749
1646 y(1)p 731 1665 V 731 1703 a Fe(N)769 1691 y Ff(4)792 1675
y Fe(E)r Fh([)837 1635 y Fb(X)856 1722 y Fc(\013)904 1635 y
Fb(X)924 1724 y Fc(\014)971 1635 y Fb(X)991 1722 y Fc(\015)1038
1635 y Fb(X)1058 1722 y Fc(\021)1104 1675 y Fe(c)1122 1681
y Fc(k)q(\013)1164 1675 y Fe(c)1182 1681 y Fc(m\013)1236 1675
y Fe(c)1254 1681 y Fc(l\014)1287 1675 y Fe(c)1305 1681 y Fc(m\014)1356
1675 y Fe(c)1374 1681 y Fc(k)q(\015)1414 1675 y Fe(c)1432 1681
y Fc(n\015)1474 1675 y Fe(c)1492 1681 y Fc(l\021)1523 1675
y Fe(c)1541 1681 y Fc(n\021)1581 1675 y Fh(])262 1803 y(Since)j
Fe(k)q(;)7 b(l)q(;)g(m;)g(n)12 b Fh(are)i(di\013eren)o(t,)h
Fe(E)r Fh([)p Fe(c)844 1809 y Fc(k)q(\013)885 1803 y Fe(c)903
1809 y Fc(m\013)956 1803 y Fe(c)974 1809 y Fc(l\014)1007 1803
y Fe(c)1025 1809 y Fc(m\014)1077 1803 y Fe(c)1095 1809 y Fc(k)q(\015)1135
1803 y Fe(c)1153 1809 y Fc(n\015)1195 1803 y Fe(c)1213 1809
y Fc(l\021)1243 1803 y Fe(c)1261 1809 y Fc(n\021)1302 1803
y Fh(])e(will)g(only)g(b)q(e)h(nonzero)262 1853 y(when)g Fe(\013)d
Fh(=)h Fe(\014)i Fh(=)e Fe(\015)i Fh(=)e Fe(\021)q Fh(.)18
b(So,)654 1954 y Fe(E)r Fh([)p Fe(\032)720 1960 y Fc(k)q(m)770
1954 y Fe(\032)791 1960 y Fc(lm)834 1954 y Fe(\032)855 1960
y Fc(k)q(n)896 1954 y Fe(\032)917 1960 y Fc(ln)951 1954 y Fh(])11
b(=)1041 1926 y(1)p 1023 1945 V 1023 1983 a Fe(N)1061 1971
y Ff(4)1091 1915 y Fb(X)1111 2002 y Fc(\013)1158 1954 y Fh(1)h(=)1257
1926 y(1)p 1239 1945 V 1239 1983 a Fe(N)1277 1971 y Ff(3)262
2075 y Fh(\(d\))515 2145 y Fe(E)r Fh([)p Fe(\032)581 2151 y
Fc(k)q(j)617 2145 y Fe(\032)638 2151 y Fc(j)r(l)666 2145 y
Fe(\032)687 2151 y Fc(lk)719 2145 y Fh(])f(=)809 2117 y(1)p
791 2135 V 791 2173 a Fe(N)829 2161 y Ff(3)852 2145 y Fe(E)r
Fh([)897 2105 y Fb(X)916 2192 y Fc(\013)964 2105 y Fb(X)984
2195 y Fc(\014)1031 2105 y Fb(X)1051 2192 y Fc(\015)1097 2145
y Fe(c)1115 2151 y Fc(k)q(\013)1157 2145 y Fe(c)1175 2151 y
Fc(j)r(\013)1214 2145 y Fe(c)1232 2151 y Fc(j)r(\014)1270 2145
y Fe(c)1288 2151 y Fc(l\014)1321 2145 y Fe(c)1339 2151 y Fc(l\015)1371
2145 y Fe(c)1389 2151 y Fc(k)q(\015)1429 2145 y Fh(])262 2260
y(Since)k Fe(k)q(;)7 b(j;)g(l)15 b Fh(are)h(di\013eren)o(t,)g
Fe(E)r Fh([)p Fe(c)787 2266 y Fc(k)q(\013)828 2260 y Fe(c)846
2266 y Fc(j)r(\013)885 2260 y Fe(c)903 2266 y Fc(j)r(\014)941
2260 y Fe(c)959 2266 y Fc(l\014)992 2260 y Fe(c)1010 2266 y
Fc(l\015)1042 2260 y Fe(c)1060 2266 y Fc(k)q(\015)1100 2260
y Fh(])e(will)g(only)g(b)q(e)i(nonzero)g(when)f Fe(\013)e Fh(=)262
2310 y Fe(\014)h Fh(=)e Fe(\015)r Fh(.)18 b(So,)701 2377 y
Fe(E)r Fh([)p Fe(\032)767 2383 y Fc(k)q(j)803 2377 y Fe(\032)824
2383 y Fc(j)r(l)852 2377 y Fe(\032)873 2383 y Fc(lk)905 2377
y Fh(])11 b(=)994 2349 y(1)p 977 2367 V 977 2405 a Fe(N)1015
2393 y Ff(3)1045 2337 y Fb(X)1064 2425 y Fc(\013)1112 2377
y Fh(1)g(=)1211 2349 y(1)p 1193 2367 V 1193 2405 a Fe(N)1231
2393 y Ff(2)967 2574 y Fh(1)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF