7.3.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 Fk(Solution)13 b(to)i(7.3)h(b)o(y)f(Shalinee)e
(Kishore)i(4/22/99:)40 b Fj(Let)15 b(us)f(represen)o(t)i
Fi(S)1567 268 y Fh(i)1595 262 y Fj(as)835 378 y Fi(S)860
384 y Fh(i)886 378 y Fj(=)944 350 y(1)p 935 368 38 2
v 935 406 a Fi(N)1009 326 y Fh(i)985 338 y Fg(X)986 427
y Fh(j)r Ff(=1)1057 345 y Fi(A)1088 330 y Ff(2)1088 356
y Fh(j)p 1057 368 50 2 v 1060 406 a Fi(\033)1085 394
y Ff(2)1636 378 y Fj(\(1\))257 498 y(W)m(e)e(can)g(then)h(write)f(the)g
(signal-to-noise)f(ration)g(in)h(\(7.35\))e(as)738 601
y Fi(\015)759 607 y Fh(k)821 601 y Fj(=)1026 573 y Fi(A)1057
558 y Ff(2)1057 584 y Fh(k)p 900 591 305 2 v 900 637
a Fi(\033)925 625 y Ff(2)953 637 y Fj(+)1006 621 y Ff(1)p
999 628 30 2 v 999 652 a Fh(N)1041 606 y Fg(P)1085 616
y Fh(k)q Fe(\000)p Ff(1)1085 650 y Fh(j)r Ff(=1)1154
637 y Fi(A)1185 623 y Ff(2)1185 649 y Fh(j)1636 601 y
Fj(\(2\))821 750 y(=)1020 698 y Fh(A)1045 685 y Fd(2)1045
706 y Fc(k)p 1020 710 44 2 v 1023 734 a Fh(\033)1043
725 y Fd(2)p 900 740 283 2 v 900 796 a Fj(1)d(+)983 780
y Ff(1)p 976 787 30 2 v 976 810 a Fh(N)1018 765 y Fg(P)1062
775 y Fh(k)q Fe(\000)p Ff(1)1062 808 y Fh(j)r Ff(=1)1136
769 y Fh(A)1161 759 y Fd(2)1161 779 y Fc(j)p 1136 786
42 2 v 1147 810 a Fh(\033)1636 750 y Fj(\(3\))821 890
y(=)900 862 y Fi(N)c Fj(\()p Fi(S)979 868 y Fh(k)1009
862 y Fb(\000)10 b Fi(S)1076 868 y Fh(k)q Fe(\000)p Ff(1)1139
862 y Fj(\))p 900 880 256 2 v 948 918 a(1)f(+)g Fi(S)1044
924 y Fh(k)q Fe(\000)p Ff(1)1636 890 y Fj(\(4\))257 1002
y(No)o(w)j(since)450 968 y Fg(R)477 979 y Fh(b)469 1017
y(a)501 1002 y Fi(C)d(du)i Fj(=)h Fi(C)s Fj(\()p Fi(b)5
b Fb(\000)g Fi(a)p Fj(\))12 b(\(where)i Fi(a)p Fj(,)d
Fi(b)p Fj(,)h(and)g Fi(C)i Fj(are)e(constan)o(ts\),)h(w)o(e)f(can)g
(observ)o(e)257 1052 y(the)j(follo)o(wing)691 1102 y
Fi(S)716 1108 y Fh(k)746 1102 y Fb(\000)9 b Fi(S)812
1108 y Fh(k)q Fe(\000)p Ff(1)p 691 1120 185 2 v 703 1158
a Fj(1)g(+)h Fi(S)800 1164 y Fh(k)q Fe(\000)p Ff(1)892
1130 y Fj(=)936 1073 y Fg(Z)978 1084 y Fh(S)998 1088
y Fc(k)959 1168 y Fh(S)979 1172 y Fc(k)p Fa(\000)p Fd(1)1118
1102 y Fj(1)p 1048 1120 160 2 v 1048 1158 a(1)f(+)h Fi(S)1145
1164 y Fh(k)q Fe(\000)p Ff(1)1220 1130 y Fi(ds)375 b
Fj(\(5\))257 1224 y(Since)18 b Fi(S)394 1230 y Fh(k)432
1224 y Fj(is)f(the)g(summation)d(of)j(non-negativ)o(e)f(n)o(um)o(b)q
(ers,)h(w)o(e)h(see)g(that)f Fi(S)1503 1230 y Fh(k)1541
1224 y Fb(\025)g Fi(S)1615 1230 y Fh(k)q Fe(\000)p Ff(1)1678
1224 y Fj(.)257 1274 y(F)m(rom)12 b(this)i(w)o(e)h(then)f(see)h(that)
573 1343 y Fi(S)598 1349 y Fh(k)629 1343 y Fb(\000)9
b Fi(S)695 1349 y Fh(k)q Fe(\000)p Ff(1)p 573 1361 185
2 v 586 1399 a Fj(1)g(+)g Fi(S)682 1405 y Fh(k)q Fe(\000)p
Ff(1)805 1371 y Fj(=)879 1314 y Fg(Z)920 1325 y Fh(S)940
1329 y Fc(k)902 1409 y Fh(S)922 1413 y Fc(k)p Fa(\000)p
Fd(1)1060 1343 y Fj(1)p 991 1361 160 2 v 991 1399 a(1)g(+)g
Fi(S)1087 1405 y Fh(k)q Fe(\000)p Ff(1)1163 1371 y Fi(ds)432
b Fj(\(6\))805 1499 y Fb(\025)879 1443 y Fg(Z)920 1453
y Fh(S)940 1457 y Fc(k)902 1537 y Fh(S)922 1541 y Fc(k)p
Fa(\000)p Fd(1)1026 1471 y Fj(1)p 991 1490 91 2 v 991
1528 a(1)9 b(+)g Fi(s)1094 1499 y(ds)501 b Fj(\(7\))805
1593 y(=)42 b(log)o(\(1)9 b(+)h Fi(S)1045 1599 y Fh(k)1066
1593 y Fj(\))f Fb(\000)h Fj(log)o(\(1)f(+)h Fi(S)1299
1599 y Fh(k)q Fe(\000)p Ff(1)1362 1593 y Fj(\))258 b(\(8\))805
1680 y(=)42 b(log)939 1621 y Fg(\022)996 1652 y Fj(1)9
b(+)g Fi(S)1092 1658 y Fh(k)p 975 1670 160 2 v 975 1708
a Fj(1)g(+)g Fi(S)1071 1714 y Fh(k)q Fe(\000)p Ff(1)1140
1621 y Fg(\023)1636 1680 y Fj(\(9\))257 1778 y(F)m(rom)j(this)i
(result,)h(w)o(e)f(see)h(that)f(eac)o(h)g Fi(\015)907
1784 y Fh(k)942 1778 y Fj(is)g(b)q(ounded)g(as)757 1877
y Fi(\015)778 1883 y Fh(k)810 1877 y Fb(\025)e Fi(N)g
Fj(log)959 1819 y Fg(\022)1016 1849 y Fj(1)d(+)h Fi(S)1113
1855 y Fh(k)p 995 1868 V 995 1906 a Fj(1)f(+)g Fi(S)1091
1912 y Fh(k)q Fe(\000)p Ff(1)1160 1819 y Fg(\023)1616
1877 y Fj(\(10\))257 1976 y(Th)o(us)15 b(w)o(e)f(see)h(that)413
2030 y Fh(K)398 2043 y Fg(X)398 2132 y Fh(k)q Ff(=1)465
2082 y Fi(\015)486 2088 y Fh(k)549 2082 y Fb(\025)42
b Fi(N)683 2030 y Fh(K)668 2043 y Fg(X)667 2132 y Fh(k)q
Ff(=1)735 2082 y Fj(log)795 2024 y Fg(\022)852 2054 y
Fj(1)9 b(+)g Fi(S)948 2060 y Fh(k)p 831 2073 V 831 2111
a Fj(1)g(+)g Fi(S)927 2117 y Fh(k)q Fe(\000)p Ff(1)996
2024 y Fg(\023)1616 2082 y Fj(\(11\))549 2213 y(=)42
b Fi(N)11 b Fj(log)728 2155 y Fg(\022)785 2185 y Fj(1)e(+)g
Fi(Y)880 2191 y Fh(K)p 763 2204 171 2 v 763 2242 a Fj(1)g(+)h
Fi(Y)859 2248 y Fh(K)r Fe(\000)p Ff(1)948 2213 y Fb(\001)973
2185 y Fj(1)f(+)h Fi(Y)1069 2191 y Fh(K)r Fe(\000)p Ff(1)p
973 2204 V 973 2242 a Fj(1)f(+)h Fi(Y)1069 2248 y Fh(K)r
Fe(\000)p Ff(2)1155 2213 y Fi(:)d(:)g(:)1216 2185 y Fj(1)i(+)g
Fi(Y)1311 2191 y Ff(2)p 1216 2204 115 2 v 1216 2242 a
Fj(1)g(+)g Fi(Y)1311 2248 y Ff(1)1344 2213 y Fb(\001)g
Fj(\(1)g(+)h Fi(Y)1477 2219 y Ff(1)1495 2213 y Fj(\))1511
2155 y Fg(\023)1616 2213 y Fj(\(12\))549 2300 y(=)42
b Fi(N)11 b Fj(log\(1)e(+)h Fi(Y)833 2306 y Fh(K)865
2300 y Fj(\))735 b(\(13\))549 2412 y(=)42 b Fi(N)11 b
Fj(log)728 2329 y Fg(0)728 2404 y(@)764 2412 y Fj(1)e(+)849
2384 y(1)p 841 2403 38 2 v 841 2441 a Fi(N)905 2361 y
Fh(K)890 2373 y Fg(X)892 2461 y Fh(j)r Ff(=1)962 2380
y Fi(A)993 2365 y Ff(2)993 2391 y Fh(j)p 962 2403 50
2 v 965 2441 a Fi(\033)990 2429 y Ff(2)1017 2329 y Fg(1)1017
2404 y(A)1616 2412 y Fj(\(14\))963 2628 y(1)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF