www.pudn.com > SolutionsforMultiuserDetection.rar > 4.1.huaidai.ps

%!PS (but not EPSF; comments have been disabled)
%DVIPSCommandLine: dvips -o 4.1.huaidai.ps problem4-1
%DVIPSParameters: dpi=600, compressed, comments removed
%DVIPSSource:  TeX output 1999.03.08:1536
/TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N
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D69
D72 D76 D101 D107 D109
D111 D114 D119
D E end
TeXDict begin

1 0 bop 1146 569 a Fm(ELE533)52 b(Homew)l(ork)f(5)1586
951 y Fl(Huaiyu)40 b(Dai)1590 1269 y Fk(6)e(Mar)h(1999)-186
1700 y Fj(PR)m(OBLEM)d(4.1.)44 b Fi(let)785 1674 y(^)778
1700 y Fj(b)33 b Fi(b)s(e)g(the)g(v)m(ector)g(in)f(the)h(set)g
Fh(f\000)p Fi(1)p Fg(;)17 b Fi(+1)p Fh(g)2295 1664 y
Ff(K)2396 1700 y Fi(that)32 b(maximizes)1347 1894 y(\012\()p
Fj(b)p Fi(\))d(=)e(2)p Fj(b)1798 1853 y Ff(T)1853 1894
y Fj(Ay)d Fh(\000)e Fj(b)2182 1853 y Ff(T)2238 1894 y
Fj(Hb)p Fg(:)-186 2088 y Fi(Sho)m(w)33 b(that)1314 2182
y(^)1317 2209 y Fg(b)1358 2224 y Ff(k)1429 2209 y Fi(=)28
b(sgn\()p Fg(y)1760 2224 y Ff(k)1824 2209 y Fh(\000)1927
2126 y Fe(X)1924 2310 y Ff(j)t Fd(6)p Fc(=)p Ff(k)2063
2182 y Fi(^)2066 2209 y Fg(b)2107 2224 y Ff(j)2144 2209
y Fg(A)2217 2224 y Ff(j)2254 2209 y Fg(\032)2304 2224
y Ff(j)t(k)2379 2209 y Fi(\))p Fg(:)-186 2537 y Fj(Solutions:)-186
2744 y Fi(Let)33 b(us)h(expand)g(the)f(expression)h(for)e(\012\()p
Fj(b)p Fi(\))i(in)m(to)e(scalar)g(form)g(and)h(tak)m(e)g(out)g(those)h
(items)e(that)g(are)h(related)-186 2864 y(to)f Fg(b)-26
2879 y Ff(k)401 3049 y Fi(\012\()p Fj(b)p Fi(\))c(=)g(2)p
Fg(A)863 3064 y Ff(k)905 3049 y Fg(y)953 3064 y Ff(k)996
3049 y Fg(b)1037 3064 y Ff(k)1102 3049 y Fh(\000)23 b
Fi(2)p Fg(b)1292 3064 y Ff(k)1453 2941 y(K)1425 2966
y Fe(X)1351 3150 y Ff(j)t Fc(=1)p Ff(;j)t Fd(6)p Fc(=)p
Ff(k)1636 3049 y Fg(A)1709 3064 y Ff(k)1751 3049 y Fg(A)1824
3064 y Ff(j)1861 3049 y Fg(\032)1911 3064 y Ff(j)t(k)1986
3049 y Fg(b)2027 3064 y Ff(j)2086 3049 y Fi(+)f Fg(C)7
b Fi(\()p Fg(b)2340 3064 y Fc(1)2380 3049 y Fg(;)17 b
Fh(\001)g(\001)g(\001)e Fg(;)i(b)2642 3064 y Ff(k)r Fd(\000)p
Fc(1)2775 3049 y Fg(;)g(b)2860 3064 y Ff(k)r Fc(+1)2993
3049 y Fg(;)g Fh(\001)g(\001)g(\001)d Fg(;)j(b)3254 3064
y Ff(K)3323 3049 y Fi(\))462 b(\(1\))-186 3297 y(Where)34
b Fg(C)7 b Fi(\()p Fg(b)282 3312 y Fc(1)321 3297 y Fg(;)17
b Fh(\001)g(\001)g(\001)e Fg(;)i(b)583 3312 y Ff(k)r
Fd(\000)p Fc(1)716 3297 y Fg(;)g(b)801 3312 y Ff(k)r
Fc(+1)934 3297 y Fg(;)g Fh(\001)g(\001)g(\001)d Fg(;)j(b)1195
3312 y Ff(K)1264 3297 y Fi(\))32 b(is)h(only)f(function)g(of)g
Fg(b)2181 3312 y Ff(j)2218 3297 y Fg(;)17 b(j)33 b Fh(6)p
Fi(=)28 b Fg(k)s Fi(.)-186 3515 y(Since)75 3489 y(^)69
3515 y Fj(b)k Fi(maximizes)f(\(1\),)819 3489 y(^)823
3515 y Fg(b)864 3530 y Ff(k)939 3515 y Fi(should)i(maximize)1017
3783 y(\012)1087 3798 y Ff(k)1130 3783 y Fi(\()p Fg(b)1209
3798 y Ff(k)1252 3783 y Fi(\))28 b(=)f(2)p Fg(A)1543
3798 y Ff(k)1586 3783 y Fg(y)1634 3798 y Ff(k)1676 3783
y Fg(b)1717 3798 y Ff(k)1782 3783 y Fh(\000)c Fi(2)p
Fg(b)1972 3798 y Ff(k)2133 3675 y(K)2106 3700 y Fe(X)2032
3885 y Ff(j)t Fc(=1)p Ff(;j)t Fd(6)p Fc(=)p Ff(k)2316
3783 y Fg(A)2389 3798 y Ff(k)2432 3783 y Fg(A)2505 3798
y Ff(j)2542 3783 y Fg(\032)2592 3798 y Ff(j)t(k)2663
3757 y Fi(^)2667 3783 y Fg(b)2708 3798 y Ff(j)3823 3783
y Fi(\(2\))-186 4084 y(Otherwise)46 b(w)m(e)g(can)g(substitute)1101
4057 y(~)1104 4084 y Fg(b)1145 4099 y Ff(k)1238 4084
y Fi(=)j(arg)17 b(max)1698 4099 y Ff(b)1728 4111 y Fb(k)1787
4084 y Fi(\012)1857 4099 y Ff(k)1900 4084 y Fi(\()p Fg(b)1979
4099 y Ff(k)2022 4084 y Fi(\))45 b(for)2263 4057 y(^)2267
4084 y Fg(b)2308 4099 y Ff(k)2396 4084 y Fi(while)f(k)m(eeping)i(other)
g(comp)s(onen)m(t)f(un-)-186 4214 y(c)m(hanged)34 b(and)e(get)h(a)f
(new)i(v)m(ector)1124 4188 y(~)1117 4214 y Fj(b)f Fi(whic)m(h)g(ac)m
(hiev)m(es)h(larger)e(\012\()p Fj(b)p Fi(\))h(than)2620
4188 y(^)2614 4214 y Fj(b)p Fi(.)-186 4420 y(W)-8 b(e)33
b(can)g(rewrite)f(\(2\))h(as)889 4689 y(\012)959 4704
y Ff(k)1002 4689 y Fi(\()p Fg(b)1081 4704 y Ff(k)1124
4689 y Fi(\))28 b(=)f(2)p Fg(A)1415 4704 y Ff(k)1458
4689 y Fi(\()p Fg(y)1544 4704 y Ff(k)1608 4689 y Fh(\000)1810
4581 y Ff(K)1782 4606 y Fe(X)1708 4790 y Ff(j)t Fc(=1)p
Ff(;j)t Fd(6)p Fc(=)p Ff(k)1989 4662 y Fi(^)1992 4689
y Fg(b)2033 4704 y Ff(j)2070 4689 y Fg(A)2143 4704 y
Ff(j)2180 4689 y Fg(\032)2230 4704 y Ff(j)t(k)2305 4689
y Fi(\))p Fg(b)2384 4704 y Ff(k)2455 4689 y Fi(=)h(2)p
Fg(A)2681 4704 y Ff(k)2723 4689 y Fg(S)6 b(b)2830 4704
y Ff(k)3823 4689 y Fi(\(3\))-186 4963 y(F)-8 b(rom)31
b(whic)m(h)i(it)f(can)h(easily)e(b)s(e)i(seen)h(that)729
5130 y(^)732 5157 y Fg(b)773 5172 y Ff(k)844 5157 y Fi(=)28
b(arg)17 b(max)1158 5217 y Ff(b)1188 5229 y Fb(k)1299
5157 y Fi(\012)1369 5172 y Ff(k)1412 5157 y Fi(\()p Fg(b)1491
5172 y Ff(k)1534 5157 y Fi(\))28 b(=)g(sgn\()p Fg(S)6
b Fi(\))27 b(=)h(sgn\()p Fg(y)2345 5172 y Ff(k)2410 5157
y Fh(\000)2512 5074 y Fe(X)2509 5258 y Ff(j)t Fd(6)p
Fc(=)p Ff(k)2648 5130 y Fi(^)2652 5157 y Fg(b)2693 5172
y Ff(j)2730 5157 y Fg(A)2803 5172 y Ff(j)2839 5157 y
Fg(\032)2889 5172 y Ff(j)t(k)2965 5157 y Fi(\))p Fg(:)793
b Fi(\(4\))3873 5406 y Fa(2)1857 5655 y Fi(1)p eop end
userdict /end-hook known{end-hook}if