7.9.huaidai.ps

是multiuser detection 这本书的习题解答, 很有用的书.

5312 y(1)2061 5254 y Fj(if)2160 5215 y Fe(A)2213 5224
y Fd(2)p 2160 5231 V 2160 5289 a Fe(A)2213 5298 y Fd(1)2285
5254 y Fa(\024)29 b Fj(4)p Fa(j)p Fi(\032)p Fa(j)p Fj(\(1)21
b Fa(\000)h Fi(\032)2803 5218 y Fh(2)2843 5254 y Fj(\);)1137
5396 y(1)875 b(otherwise.)3823 5314 y(\(5\))1857 5655
y(1)p eop
2 1 bop -186 167 a Fj(for)32 b Fa(j)p Fi(\032)p Fa(j)27
b Fi(<)h Fj(1)p Fi(=)p Fj(2,)k(and)764 438 y Fi(\021)816
396 y Fe(s)812 462 y Fh(1)880 438 y Fj(=)984 213 y Fg(8)984
288 y(>)984 313 y(>)984 338 y(<)984 487 y(>)984 512 y(>)984
537 y(:)1099 307 y Fj(1)22 b Fa(\000)h Fj(4)1329 268
y Fe(A)1382 277 y Fd(2)p 1329 284 88 4 v 1329 342 a Fe(A)1382
351 y Fd(1)1426 307 y Fa(j)p Fi(\032)p Fa(j)f Fj(+)1725
268 y Fh(1)p 1662 284 161 4 v 1662 342 a(1)p Ff(\000)p
Fe(\032)1788 323 y Fd(2)1843 256 y Fe(A)1896 232 y Fd(2)1896
278 y(2)p 1843 284 88 4 v 1843 342 a Fe(A)1896 320 y
Fd(2)1896 365 y(1)2023 307 y Fj(if)2122 268 y Fe(A)2175
277 y Fd(2)p 2122 284 V 2122 342 a Fe(A)2175 351 y Fd(1)2247
307 y Fa(\024)29 b Fj(1)p Fi(=)p Fa(j)p Fi(\032)p Fa(j)21
b(\000)i(j)p Fi(\032)p Fa(j)p Fj(;)1099 461 y(\()1147
422 y Fe(A)1200 431 y Fd(2)p 1147 438 V 1147 496 a Fe(A)1200
505 y Fd(1)1267 461 y Fa(\000)f(j)p Fi(\032)p Fa(j)p
Fj(\))1510 425 y Fh(2)2023 461 y Fj(if)2122 415 y Fh(1)p
Fe(=\032)p Ff(\000j)p Fe(\032)p Ff(j\024)p Fe(A)2467
424 y Fd(2)p 2122 438 380 4 v 2268 496 a Fe(A)2321 505
y Fd(1)2539 461 y Fa(\024)28 b Fj(1)22 b(+)g Fa(j)p Fi(\032)p
Fa(j)p Fj(;)1099 589 y(1)875 b(otherwise.)3823 438 y(\(6\))-186
762 y(for)32 b Fa(j)p Fi(\032)p Fa(j)27 b(\025)i Fj(1)p
Fi(=)p Fj(2.)-186 968 y(Let)k(us)g(de\014ne)1406 1112
y Fi(f)11 b Fj(\()1513 1045 y Fi(A)1586 1060 y Fh(2)p
1513 1089 113 4 v 1513 1180 a Fi(A)1586 1195 y Fh(1)1635
1112 y Fj(\))28 b(=)g(\(1)21 b Fa(\000)2023 1045 y Fi(A)2096
1060 y Fh(2)p 2023 1089 V 2023 1180 a Fi(A)2096 1195
y Fh(1)2145 1112 y Fa(j)p Fi(\032)p Fa(j)p Fj(\))2289
1071 y Fh(2)2329 1112 y Fj(;)1467 b(\(7\))1177 1404 y
Fi(g)t Fj(\()1276 1337 y Fi(A)1349 1352 y Fh(2)p 1276
1381 V 1276 1472 a Fi(A)1349 1487 y Fh(1)1398 1404 y
Fj(\))28 b(=)f(1)22 b Fa(\000)h Fj(4)1797 1337 y Fi(A)1870
1352 y Fh(2)p 1797 1381 V 1797 1472 a Fi(A)1870 1487
y Fh(1)1919 1404 y Fa(j)p Fi(\032)p Fa(j)f Fj(+)2260
1337 y(1)p 2155 1381 261 4 v 2155 1472 a(1)g Fa(\000)g
Fi(\032)2375 1444 y Fh(2)2435 1337 y Fi(A)2508 1301 y
Fh(2)2508 1361 y(2)p 2435 1381 113 4 v 2435 1472 a Fi(A)2508
1438 y Fh(2)2508 1494 y(1)2557 1404 y Fj(;)1239 b(\(8\))1432
1692 y Fi(h)p Fj(\()1536 1625 y Fi(A)1609 1640 y Fh(2)p
1536 1669 V 1536 1760 a Fi(A)1609 1775 y Fh(1)1658 1692
y Fj(\))28 b(=)g(\()1876 1625 y Fi(A)1949 1640 y Fh(2)p
1876 1669 V 1876 1760 a Fi(A)1949 1775 y Fh(1)2020 1692
y Fa(\000)23 b(j)p Fi(\032)p Fa(j)p Fj(\))2264 1651 y
Fh(2)2303 1692 y Fi(:)1493 b Fj(\(9\))-186 2020 y(It)41
b(can)g(b)s(e)g(v)m(eri\014ed)g(that)g Fi(g)t Fj(\()924
1980 y Fe(A)977 1989 y Fd(2)p 923 1996 88 4 v 923 2054
a Fe(A)976 2063 y Fd(1)1020 2020 y Fj(\))h Fa(\024)g
Fi(f)11 b Fj(\()1326 1980 y Fe(A)1379 1989 y Fd(2)p 1325
1996 V 1325 2054 a Fe(A)1378 2063 y Fd(1)1423 2020 y
Fj(\))40 b(when)1774 1980 y Fe(A)1827 1989 y Fd(2)p 1774
1996 V 1774 2054 a Fe(A)1827 2063 y Fd(1)1913 2020 y
Fa(\024)2132 1973 y Fh(2)p Ff(j)p Fe(\032)p Ff(j)p 2042
1996 291 4 v 2109 2032 a Fd(1)p 2052 2044 145 4 v 2052
2094 a(1)p Fc(\000)p Fb(\032)2162 2080 y Fd(2)2206 2059
y Ff(\000)p Fe(\032)2297 2040 y Fd(2)2342 2020 y Fj(.)68
b(And)41 b Fi(h)p Fj(\()2763 1980 y Fe(A)2816 1989 y
Fd(2)p 2763 1996 88 4 v 2763 2054 a Fe(A)2816 2063 y
Fd(1)2860 2020 y Fj(\))h Fa(\024)g Fi(f)11 b Fj(\()3166
1980 y Fe(A)3219 1989 y Fd(2)p 3165 1996 V 3165 2054
a Fe(A)3218 2063 y Fd(1)3263 2020 y Fj(\))40 b(when)3614
1980 y Fe(A)3667 1989 y Fd(2)p 3614 1996 V 3614 2054
a Fe(A)3667 2063 y Fd(1)3753 2020 y Fa(\024)i Fj(1.)-186
2181 y(F)-8 b(urther)33 b(more)e(w)m(e)j(alw)m(a)m(ys)f(ha)m(v)m(e)1636
2283 y(2)p Fa(j)p Fi(\032)p Fa(j)p 1518 2327 393 4 v
1590 2380 a Fh(1)p 1528 2396 161 4 v 1528 2454 a(1)p
Ff(\000)p Fe(\032)1654 2435 y Fd(2)1721 2419 y Fa(\000)22
b Fi(\032)1870 2391 y Fh(2)1948 2351 y Fi(<)27 b Fj(1)p
Fi(=)p Fa(j)p Fi(\032)p Fa(j)-186 2699 y Fj(Notice)j(that)h
Fi(\021)380 2663 y Fe(c)376 2724 y Fh(1)446 2699 y Fj(is)f(decreasing)h
(and)f Fi(\021)1251 2663 y Fe(s)1247 2724 y Fh(1)1288
2699 y Fj(\(b)s(oth)g(cases\))i(is)e(con)m(v)m(ex,)j(and)e(they)g(are)g
(equal)f(at)h(the)g(p)s(oin)m(t)3643 2660 y Fe(A)3696
2669 y Fd(2)p 3643 2676 88 4 v 3643 2734 a Fe(A)3696
2743 y Fd(1)3768 2699 y Fj(=)d(0.)-186 2820 y(So)42 b(the)h(in)m(terv)
-5 b(al)42 b(for)g(the)h(con)m(v)m(en)m(tional)f(matc)m(hed)h(\014lter)
f(receiv)m(er)i(ac)m(hiev)m(es)g(higher)e(asymptotic)g(e\016ency)-186
2940 y(than)33 b(the)g(successiv)m(e)i(canceler)e(is)f(b)s(et)m(w)m
(een)j(0)d(and)h(another)f(p)s(oin)m(t)g(where)i Fi(\021)2727
2904 y Fe(c)2723 2965 y Fh(1)2795 2940 y Fj(and)f Fi(\021)3037
2904 y Fe(s)3033 2965 y Fh(1)3106 2940 y Fj(in)m(tersects.)-186
3155 y(If)42 b(0)h Fi(<)g Fa(j)p Fi(\032)p Fa(j)f Fi(<)i
Fj(1)p Fi(=)p Fj(2,)f(w)m(e)g(alw)m(a)m(ys)f(ha)m(v)m(e)1425
3109 y Fh(2)p Ff(j)p Fe(\032)p Ff(j)p 1335 3132 291 4
v 1402 3167 a Fd(1)p 1345 3179 145 4 v 1345 3229 a(1)p
Fc(\000)p Fb(\032)1455 3215 y Fd(2)1500 3194 y Ff(\000)p
Fe(\032)1591 3176 y Fd(2)1678 3155 y Fi(<)h Fj(4)p Fa(j)p
Fi(\032)p Fa(j)p Fj(\(1)28 b Fa(\000)h Fi(\032)2223 3119
y Fh(2)2263 3155 y Fj(\).)70 b(Insp)s(ection)42 b(of)g(\(4\))f(and)h
(\(5\))f(rev)m(eals)h Fi(\021)3912 3119 y Fe(c)3908 3180
y Fh(1)-186 3322 y Fj(in)m(tersects)34 b(with)e Fi(g)t
Fj(\()p Fi(x)p Fj(\).)-186 3537 y(In)h(this)f(situation,)f(when)825
3498 y Fe(A)878 3507 y Fd(2)p 825 3514 88 4 v 825 3572
a Fe(A)878 3581 y Fd(1)950 3537 y Fa(\024)1155 3491 y
Fh(2)p Ff(j)p Fe(\032)p Ff(j)p 1065 3514 291 4 v 1132
3549 a Fd(1)p 1075 3561 145 4 v 1075 3611 a(1)p Fc(\000)p
Fb(\032)1185 3597 y Fd(2)1230 3577 y Ff(\000)p Fe(\032)1321
3558 y Fd(2)1726 3699 y Fi(\021)1778 3658 y Fe(c)1774
3724 y Fh(1)1842 3699 y Fa(\025)d Fi(\021)1999 3658 y
Fe(s)1995 3724 y Fh(1)-186 3987 y Fj(If)33 b Fa(j)p Fi(\032)p
Fa(j)27 b(\025)i Fj(1)p Fi(=)p Fj(2,)j(insp)s(ection)g(of)g(\(4\))g
(and)h(\(6\))g(rev)m(eals)g(when)2112 3940 y Fh(2)p Ff(j)p
Fe(\032)p Ff(j)p 2022 3963 291 4 v 2089 3999 a Fd(1)p
2032 4011 145 4 v 2032 4061 a(1)p Fc(\000)p Fb(\032)2142
4047 y Fd(2)2187 4026 y Ff(\000)p Fe(\032)2278 4007 y
Fd(2)2350 3987 y Fa(\024)c Fj(1)p Fi(=)p Fa(j)p Fi(\032)p
Fa(j)21 b(\000)i(j)p Fi(\032)p Fa(j)p Fj(,)32 b(i.e.)44
b(1)p Fi(=)p Fj(2)27 b Fa(\024)i(j)p Fi(\032)p Fa(j)e(\024)3634
3878 y Fg(q)p 3717 3878 205 4 v 3727 3947 a Fh(3)p Ff(\000)3817
3892 y(p)p 3876 3892 36 3 v 55 x Fh(5)p 3727 3963 185
4 v 3801 4021 a(2)3921 3987 y Fj(,)-186 4153 y Fi(\021)-134
4117 y Fe(c)-138 4178 y Fh(1)-66 4153 y Fj(in)m(tersects)34
b(with)e Fi(g)t Fj(\()p Fi(x)p Fj(\).)-186 4369 y(In)h(this)f
(situation,)f(when)825 4329 y Fe(A)878 4338 y Fd(2)p
825 4345 88 4 v 825 4403 a Fe(A)878 4412 y Fd(1)950 4369
y Fa(\024)1155 4322 y Fh(2)p Ff(j)p Fe(\032)p Ff(j)p
1065 4345 291 4 v 1132 4381 a Fd(1)p 1075 4393 145 4
v 1075 4443 a(1)p Fc(\000)p Fb(\032)1185 4429 y Fd(2)1230
4408 y Ff(\000)p Fe(\032)1321 4389 y Fd(2)1726 4530 y
Fi(\021)1778 4489 y Fe(c)1774 4555 y Fh(1)1842 4530 y
Fa(\025)d Fi(\021)1999 4489 y Fe(s)1995 4555 y Fh(1)-186
4818 y Fj(On)i(the)h(other)g(hand,)g(if)849 4771 y Fh(2)p
Ff(j)p Fe(\032)p Ff(j)p 759 4795 291 4 v 826 4830 a Fd(1)p
769 4842 145 4 v 769 4892 a(1)p Fc(\000)p Fb(\032)879
4878 y Fd(2)924 4857 y Ff(\000)p Fe(\032)1015 4838 y
Fd(2)1087 4818 y Fi(>)d Fj(1)p Fi(=)p Fa(j)p Fi(\032)p
Fa(j)17 b(\000)h(j)p Fi(\032)p Fa(j)p Fj(,)30 b(i.e.)1838
4710 y Fg(q)p 1921 4710 205 4 v 1931 4779 a Fh(3)p Ff(\000)2021
4724 y(p)p 2080 4724 36 3 v 55 x Fh(5)p 1931 4795 185
4 v 2005 4852 a(2)2152 4818 y Fi(<)e Fa(j)p Fi(\032)p
Fa(j)f(\024)h Fj(1,)j(it)e(can)i(b)s(e)g(seen)g(that)g(1)p
Fi(=)p Fa(j)p Fi(\032)p Fa(j)16 b(\000)j(j)p Fi(\032)p
Fa(j)27 b Fi(<)-186 4985 y Fj(1)g Fi(<)h Fj(1)22 b(+)g
Fa(j)p Fi(\032)p Fa(j)p Fj(,)32 b(So)h Fi(\021)516 4949
y Fe(c)512 5009 y Fh(1)584 4985 y Fj(in)m(tersects)h(with)e
Fi(h)p Fj(\()p Fi(x)p Fj(\).)-186 5191 y(In)h(this)f(situation,)f(when)
825 5152 y Fe(A)878 5161 y Fd(2)p 825 5168 88 4 v 825
5225 a Fe(A)878 5234 y Fd(1)950 5191 y Fa(\024)d Fj(1)1726
5311 y Fi(\021)1778 5270 y Fe(c)1774 5336 y Fh(1)1842
5311 y Fa(\025)g Fi(\021)1999 5270 y Fe(s)1995 5336 y
Fh(1)1857 5655 y Fj(2)p eop
3 2 bop -186 167 a Fj(Finally)30 b(when)k Fi(\032)28
b Fj(=)f(0,)33 b Fi(\021)743 131 y Fe(c)739 191 y Fh(1)806
167 y Fj(=)27 b Fi(\021)961 131 y Fe(s)957 191 y Fh(1)1026
167 y Fj(=)g(1.)-186 373 y(\(1\))32 b(is)g(v)m(eri\014ed)i(as)e(ab)s(o)
m(v)m(e.)-186 579 y(\(b\))-186 785 y(The)c(near-far)f(resistence)h(is)f
(just)h(the)f(minim)m(um)d(v)-5 b(alue)27 b(of)g(the)g(a)m(ymptotic)g
(e\016cience)h(as)3180 746 y Fe(A)3233 755 y Fd(2)p 3180
762 88 4 v 3180 820 a Fe(A)3233 829 y Fd(1)3304 785 y
Fj(v)-5 b(aries.)42 b(Accord-)-186 906 y(ing)30 b(to)h(\(a\),)g(this)g
(is)f(just)h(the)h(v)-5 b(alue)30 b(of)h Fi(f)11 b Fj(\()p
Fi(x)p Fj(\))31 b(at)g(the)g(in)m(tersection)g(p)s(oin)m(t,)g(since)g
Fi(f)11 b Fj(\()p Fi(x)p Fj(\))31 b(is)g(decreasing.)43
b(plug)31 b(in)-186 1035 y Fi(x)d Fj(=)11 996 y Fe(A)64
1005 y Fd(2)p 11 1012 V 11 1070 a Fe(A)64 1079 y Fd(1)136
1035 y Fj(=)339 989 y Fh(2)p Ff(j)p Fe(\032)p Ff(j)p
249 1012 291 4 v 316 1047 a Fd(1)p 259 1059 145 4 v 259
1109 a(1)p Fc(\000)p Fb(\032)369 1095 y Fd(2)414 1075
y Ff(\000)p Fe(\032)505 1056 y Fd(2)582 1035 y Fj(and)33
b Fi(x)28 b Fj(=)f(1)33 b(in)m(to)f Fi(f)11 b Fj(\()p
Fi(x)p Fj(\),)32 b(\(2\))g(is)g(v)m(eri\014ed.)-186 1288
y(\(c\))-186 1494 y(W)-8 b(e)40 b(can)g(see)h(that)f
Fi(g)t Fj(\()p Fi(x)p Fj(\))g(ac)m(hiev)m(es)h(its)e(minim)m(um)e(of)i
(\(1)27 b Fa(\000)h Fj(2)p Fi(\032)2188 1458 y Fh(2)2227
1494 y Fj(\))2265 1458 y Fh(2)2345 1494 y Fj(at)39 b
Fi(x)i Fj(=)2693 1455 y Fe(A)2746 1464 y Fd(2)p 2693
1471 88 4 v 2693 1528 a Fe(A)2746 1537 y Fd(1)2830 1494
y Fj(=)f(2)p Fa(j)p Fi(\032)p Fa(j)p Fj(\(1)26 b Fa(\000)i
Fi(\032)3369 1458 y Fh(2)3409 1494 y Fj(\).)65 b(And)40
b Fi(h)p Fj(\()p Fi(x)p Fj(\))-186 1630 y(ac)m(hiev)m(es)34
b(its)e(minim)m(um)d(of)k(0)f(at)g Fi(x)c Fj(=)1272 1591
y Fe(A)1325 1600 y Fd(2)p 1272 1607 V 1272 1665 a Fe(A)1325
1674 y Fd(1)1397 1630 y Fj(=)f Fa(j)p Fi(\032)p Fa(j)p
Fj(.)-186 1847 y(If)33 b Fa(j)p Fi(\032)p Fa(j)27 b Fi(<)g
Fj(1)p Fi(=)p Fj(2,)32 b(w)m(e)i(alw)m(a)m(ys)f(ha)m(v)m(e)h(2)p
Fa(j)p Fi(\032)p Fa(j)p Fj(\(1)21 b Fa(\000)i Fi(\032)1448
1811 y Fh(2)1488 1847 y Fj(\))k Fa(\024)h Fj(4)p Fa(j)p
Fi(\032)p Fa(j)p Fj(\(1)22 b Fa(\000)g Fi(\032)2071 1811
y Fh(2)2111 1847 y Fj(\).)44 b(Insp)s(ection)33 b(of)f(\(5\))g(rev)m
(eals)1552 2067 y(\026)-56 b Fi(\021)1597 2026 y Fe(s)1593
2092 y Fh(1)1662 2067 y Fj(=)27 b(\(1)22 b Fa(\000)h
Fj(2)p Fi(\032)2073 2026 y Fh(2)2112 2067 y Fj(\))2150
2026 y Fh(2)2189 2067 y Fi(:)-186 2373 y Fj(If)32 b Fa(j)p
Fi(\032)p Fa(j)27 b(\025)i Fj(1)p Fi(=)p Fj(2,)i(then)i(similar)c(to)i
(\(b\),)i(when)g Fa(j)p Fi(\032)p Fa(j)27 b Fi(<)h Fj(1)p
Fi(=)1794 2291 y Fa(p)p 1876 2291 49 4 v 1876 2373 a
Fj(2,)k(2)p Fa(j)p Fi(\032)p Fa(j)p Fj(\(1)20 b Fa(\000)i
Fi(\032)2395 2337 y Fh(2)2435 2373 y Fj(\))27 b Fa(\024)i
Fj(1)p Fi(=)p Fa(j)p Fi(\032)p Fa(j)20 b(\000)h(j)p Fi(\032)p
Fa(j)32 b Fj(and)g Fa(j)p Fi(\032)p Fa(j)c Fi(<)f Fj(1)p
Fi(=)p Fa(j)p Fi(\032)p Fa(j)21 b(\000)g(j)p Fi(\032)p
Fa(j)p Fj(.)-186 2493 y(The)34 b(minim)m(um)29 b(is)j(ac)m(hiev)m(ed)i
(within)d([0)p Fi(;)17 b Fj(1)p Fi(=\032)22 b Fa(\000)g(j)p
Fi(\032)p Fa(j)p Fj(].)1552 2713 y(\026)-56 b Fi(\021)1597
2672 y Fe(s)1593 2738 y Fh(1)1662 2713 y Fj(=)27 b(\(1)22
b Fa(\000)h Fj(2)p Fi(\032)2073 2672 y Fh(2)2112 2713
y Fj(\))2150 2672 y Fh(2)2189 2713 y Fi(:)-186 3019 y
Fj(When)33 b Fa(j)p Fi(\032)p Fa(j)28 b(\025)g Fj(1)p
Fi(=)435 2937 y Fa(p)p 518 2937 V 82 x Fj(2)o(,)33 b(the)g(minim)m(um)c
(will)h(b)s(e)j(ac)m(hiev)m(ed)h(with)e([1)p Fi(=\032)22
b Fa(\000)h(j)p Fi(\032)p Fa(j)p Fi(;)17 b Fj(1)k(+)h
Fa(j)p Fi(\032)p Fa(j)p Fj(].)1740 3239 y(\026)-56 b
Fi(\021)1785 3198 y Fe(s)1781 3264 y Fh(1)1849 3239 y
Fj(=)28 b(0)p Fi(:)1857 5655 y Fj(3)p eop end
userdict /end-hook known{end-hook}if