www.pudn.com > SolutionsforMultiuserDetection.rar > 3.3.kishore.ps
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b(to)f(obtain)672 1376 y Fg(P)6 b Fh([)p Fg(Z)14 b Fh(=)e
Fg(z)r Fd(j)p Fg(H)871 1382 y Fe(i)884 1376 y Fh(])p
Fg(P)6 b Fh([)p Fg(H)976 1382 y Fe(i)988 1376 y Fh(])p
669 1395 335 2 v 669 1433 a Fg(P)g Fh([)p Fg(Z)13 b Fh(=)f
Fg(z)r Fd(j)p Fg(H)867 1439 y Fe(j)884 1433 y Fh(])p
Fg(P)6 b Fh([)p Fg(H)976 1439 y Fe(j)991 1433 y Fh(])1019
1404 y Fd(\025)1070 1376 y Fg(P)g Fh([)p Fg(H)1150 1382
y Fe(i)1162 1376 y Fh(])p 1068 1395 108 2 v 1068 1433
a Fg(P)g Fh([)p Fg(H)1148 1439 y Fe(j)1164 1433 y Fh(])1192
1404 y(=)12 b Fg(\034)1254 1410 y Fe(ij)1636 1404 y Fh(\(3\))257
1512 y(W)m(e)k(can)g(divide)g(the)h(n)o(umerator)e(and)h(denominator)e
(of)h(the)i(left-hand)f(side)g(of)g(\(3\))g(b)o(y)257
1536 y Fc(P)301 1546 y Fe(M)301 1579 y(k)q Ff(=1)371
1567 y Fg(P)6 b Fh([)p Fg(Z)13 b Fh(=)f Fg(z)r Fd(j)p
Fg(H)569 1573 y Fe(k)589 1567 y Fh(])p Fg(P)6 b Fh([)p
Fg(H)681 1573 y Fe(k)699 1567 y Fh(])14 b(to)f(get:)410
1656 y Fg(P)6 b Fh([)p Fg(Z)14 b Fh(=)e Fg(z)r Fd(j)p
Fg(H)609 1662 y Fe(i)622 1656 y Fh(])p Fg(P)6 b Fh([)p
Fg(H)714 1662 y Fe(i)726 1656 y Fh(])p Fg(=)766 1625
y Fc(P)809 1635 y Fe(M)809 1668 y(k)q Ff(=1)878 1656
y Fg(P)g Fh([)p Fg(Z)14 b Fh(=)e Fg(z)r Fd(j)p Fg(H)1077
1662 y Fe(k)1096 1656 y Fh(])p Fg(P)6 b Fh([)p Fg(H)1188
1662 y Fe(k)1207 1656 y Fh(])p 407 1675 816 2 v 407 1721
a Fg(P)g Fh([)p Fg(Z)13 b Fh(=)f Fg(z)r Fd(j)p Fg(H)605
1727 y Fe(j)622 1721 y Fh(])p Fg(P)6 b Fh([)p Fg(H)714
1727 y Fe(j)729 1721 y Fh(])p Fg(=)769 1689 y Fc(P)812
1700 y Fe(M)812 1733 y(k)q Ff(=1)882 1721 y Fg(P)g Fh([)p
Fg(Z)14 b Fh(=)d Fg(z)r Fd(j)p Fg(H)1080 1727 y Fe(k)1100
1721 y Fh(])p Fg(P)6 b Fh([)p Fg(H)1192 1727 y Fe(k)1210
1721 y Fh(])1238 1684 y(=)1289 1656 y Fg(P)g Fh([)p Fg(H)1369
1662 y Fe(i)1381 1656 y Fd(j)p Fg(Z)s Fh(])p 1287 1675
151 2 v 1287 1713 a Fg(P)g Fh([)p Fg(H)1367 1719 y Fe(j)1383
1713 y Fd(j)p Fg(Z)s Fh(])1454 1684 y Fd(\025)12 b Fg(\034)1516
1690 y Fe(ij)1636 1684 y Fh(\(4\))257 1798 y(T)m(o)i(c)o(ho)q(ose)h(a)e
(particular)h(h)o(yp)q(othesis)h Fg(H)917 1804 y Fe(i)930
1798 y Fh(,)f(w)o(e)g(can)h(therefore)g(equiv)n(alen)o(tly)e(compare)g
(if)257 1847 y(the)d(ratio)f(of)g(the)h Fb(a)h(p)n(osteriori)d
Fh(probabilit)o(y)g(of)h(h)o(yp)q(othesis)h Fg(H)1228
1853 y Fe(i)1251 1847 y Fh(\()p Fg(P)c Fh([)p Fg(H)1347
1853 y Fe(i)1359 1847 y Fd(j)p Fg(Z)s Fh(]\))j(to)h Fb(a)h(p)n
(osteriori)257 1897 y Fh(probabilit)o(y)i(of)h(another)h(h)o(yp)q
(othesis)g Fg(H)911 1903 y Fe(j)942 1897 y Fh(to)g(a)f(kno)o(wn)g
(threshold)h Fg(\034)1362 1903 y Fe(ij)1391 1897 y Fh(.)20
b(W)m(e)14 b(then)h(select)257 1947 y(the)h(h)o(yp)q(othesis)g
Fg(H)571 1953 y Fe(i)600 1947 y Fh(for)f(whic)o(h)g(the)h(condition)e
(in)h(\(4\))h(is)f(met)f(for)h(all)f Fg(j)i Fd(6)p Fh(=)f
Fg(i)p Fh(.)22 b(W)m(e)15 b(th)o(us)257 1997 y(see)21
b(that)e(the)h(probablities)e Fg(P)6 b Fh([)p Fg(H)813
2003 y Ff(1)830 1997 y Fd(j)p Fg(Z)s Fh(])p Fg(;)h(P)f
Fh([)p Fg(H)984 2003 y Ff(2)1000 1997 y Fd(j)p Fg(Z)s
Fh(])p Fg(;)h(:)g(:)g(:)t(P)f Fh([)p Fg(H)1208 2004 y
Ff(\()p Fe(M)s Fa(\000)p Ff(1\))1312 1997 y Fd(j)p Fg(Z)s
Fh(])19 b(form)e(a)i(su\016cien)o(t)257 2047 y(statistic)h(since)f(w)o
(e)g(can)g(\014rst)h(compute)e Fg(P)6 b Fh([)p Fg(H)1017
2053 y Fe(M)1053 2047 y Fd(j)p Fg(Z)s Fh(])18 b(from)f(it)h(and)h(then)
h(compare)e(the)257 2097 y(ab)q(o)o(v)o(e)g(indicated)f(ratios)h(of)f
Fg(P)6 b Fh([)p Fg(H)813 2103 y Ff(1)830 2097 y Fd(j)p
Fg(Z)s Fh(])p Fg(;)h(P)f Fh([)p Fg(H)984 2103 y Ff(2)1000
2097 y Fd(j)p Fg(Z)s Fh(])p Fg(;)h(:)g(:)g(:)t(P)f Fh([)p
Fg(H)1208 2103 y Fe(M)1243 2097 y Fd(j)p Fg(Z)s Fh(])17
b(to)g(kno)o(wn)g(thresholds)257 2146 y(to)d(c)o(ho)q(ose)h(an)e
(appropriate)h(h)o(yp)q(othesis)h(that)f(equates)h(to)f(the)g
(condition)f(in)h(\(1\).)320 2196 y(Note)g(that)g(one)h(could)e(also)h
(select)h(h)o(yp)q(otheses)h(based)f(on)e(the)i(maxim)n(um)10
b(a)k(p)q(oste-)257 2246 y(riori)f(\(MAP\))g(rule.)18
b(Here)c(the)f(decision)h(rule)f(selects)h(the)g(h)o(yp)q(otehsis)f
(with)g(the)g(highest)257 2296 y Fg(P)6 b Fh([)p Fg(H)337
2302 y Fe(i)350 2296 y Fd(j)p Fg(Z)s Fh(].)17 b(Once)d(again,)e(since)i
(w)o(e)g(can)f(obtain)g Fg(P)6 b Fh([)p Fg(H)1107 2302
y Ff(1)1124 2296 y Fd(j)p Fg(Z)s Fh(])p Fg(;)h(P)f Fh([)p
Fg(H)1278 2302 y Ff(2)1294 2296 y Fd(j)p Fg(Z)s Fh(])p
Fg(;)h(:)g(:)g(:)t(P)f Fh([)p Fg(H)1502 2302 y Fe(M)1538
2296 y Fd(j)p Fg(Z)s Fh(])12 b(from)257 2346 y Fg(P)6
b Fh([)p Fg(H)337 2352 y Ff(1)354 2346 y Fd(j)p Fg(Z)s
Fh(])p Fg(;)h(P)f Fh([)p Fg(H)508 2352 y Ff(2)524 2346
y Fd(j)p Fg(Z)s Fh(])p Fg(;)h(:)g(:)g(:)e(P)h Fh([)p
Fg(H)733 2353 y Ff(\()p Fe(M)s Fa(\000)p Ff(1\))836 2346
y Fd(j)p Fg(Z)s Fh(],)15 b(these)i(\()p Fg(M)f Fd(\000)11
b Fh(1\))k(probablities)g(are)i(a)e(su\016cien)o(t)257
2395 y(statistic)g(under)h(MAP)f(decision)g(rule)g(as)f(w)o(ell.)20
b(Su\016ciency)15 b(results)h(b)q(ecause)h(with)d(the)257
2445 y(observ)o(ed)i Fg(Z)g Fh(=)d Fg(z)r Fh(,)i(one)g(merely)e(has)i
(to)g(determine)f(the)i(maxim)n(um)10 b(of)k(these)i
Fg(M)k Fb(a)15 b(p)n(os-)257 2495 y(teriori)e Fh(probabilities.)963
2628 y(1)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF