📄 7.19.dguo.ps
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bpagebplot/dpi2point 12 defportraitMode 0216 7344 csm 1464 273 4274 4342 MR c np93 dict begin %Colortable dictionary/c0 { 0 0 0 sr} bdef/c1 { 1 1 1 sr} bdef/c2 { 1 0 0 sr} bdef/c3 { 0 1 0 sr} bdef/c4 { 0 0 1 sr} bdef/c5 { 1 1 0 sr} bdef/c6 { 1 0 1 sr} bdef/c7 { 0 1 1 sr} bdefc01 j1 sg 0 0 6913 5186 PR6 wgs 1464 389 4226 4226 MR c np0 sg4225 0 1464 2502 2 MP stroke0 -4225 3576 4614 2 MP stroke24 w1409 0 3576 2502 2 MP strokegr24 w0 sg/Helvetica /ISOLatin1Encoding 120 FMSR4985 2706 mt (s) s/Helvetica /ISOLatin1Encoding 96 FMSR5045 2766 mt (1) sgs 1464 389 4226 4226 MR c np470 -1328 3576 2502 2 MP strokegr/Helvetica /ISOLatin1Encoding 120 FMSR3835 1167 mt (s) s/Helvetica /ISOLatin1Encoding 96 FMSR3895 1227 mt (2) sgs 1464 389 4226 4226 MR c np36 w939 -663 3107 2833 2 MP stroke0 -1781 4046 2170 2 MP stroke0 1781 3107 2833 2 MP strokeDO6 w0 -332 4046 2502 2 MP stroke470 0 3576 2170 2 MP stroke3 0 3 -1 2 -1 3 -1 2 -1 3 -2 2 -2 1 -2 2 -2 2 -3 1 -2 1 -3 0 -2 1 -3 0 -3 0 -3 -1 -3 0 -2 -1 -3 -2 -3 -1 -2 -2 -2 -2 -2 -2 -2 -2 -2 -3 -1 -2 -1 -3 -1 -3 -1 -3 0 -2 0 -3 0 -3 1 -3 1 -2 1 -3 1 -2 2 -2 2 -2 2 -2 2 -2 2 -1 3 -1 2 -1 3 0 3 0 2 0 3 0 3 1 3 0 2 2 3 1 3 2 2 2 2 2 2 2 2 2 1 3 1 2 1 3 1 3 0 3 0 5454 1146 63 MPPPSO2 0 3 0 3 -1 2 -1 3 -1 2 -1 3 -2 2 -2 1 -2 2 -2 2 -3 1 -2 1 -3 0 -2 1 -3 0 -3 0 -3 -1 -3 0 -2 -1 -3 -2 -3 -1 -2 -2 -2 -2 -2 -2 -2 -2 -2 -3 -1 -2 -1 -3 -1 -3 -1 -3 0 -2 0 -3 0 -3 1 -3 1 -2 1 -3 1 -2 2 -2 2 -2 2 -2 2 -2 2 -1 3 -1 2 -1 3 0 3 0 2 0 3 0 3 1 3 0 2 2 3 1 3 2 2 2 2 2 2 2 2 2 1 3 1 2 1 3 1 3 0 3 0 5454 1146 64 MP stroke3 0 2 -1 3 -1 2 -1 3 -1 2 -2 2 -2 2 -2 2 -2 1 -3 1 -2 1 -3 1 -2 0 -3 1 -3 -1 -3 0 -3 -1 -2 -1 -3 -1 -3 -2 -2 -1 -2 -2 -2 -2 -2 -3 -2 -2 -1 -3 -1 -2 -1 -3 -1 -3 0 -3 0 -3 0 -2 1 -3 1 -3 1 -2 1 -2 2 -3 2 -2 2 -1 2 -2 2 -1 3 -1 2 -1 3 -1 3 0 2 0 3 1 3 0 3 1 2 1 3 2 3 1 2 2 2 2 2 2 2 3 1 2 1 3 1 3 1 3 0 2 0 2638 1146 63 MPPP3 0 3 0 2 -1 3 -1 2 -1 3 -1 2 -2 2 -2 2 -2 2 -2 1 -3 1 -2 1 -3 1 -2 0 -3 1 -3 -1 -3 0 -3 -1 -2 -1 -3 -1 -3 -2 -2 -1 -2 -2 -2 -2 -2 -3 -2 -2 -1 -3 -1 -2 -1 -3 -1 -3 0 -3 0 -3 0 -2 1 -3 1 -3 1 -2 1 -2 2 -3 2 -2 2 -1 2 -2 2 -1 3 -1 2 -1 3 -1 3 0 2 0 3 1 3 0 3 1 2 1 3 2 3 1 2 2 2 2 2 2 2 3 1 2 1 3 1 3 1 3 0 2 0 2638 1146 64 MP stroke2 -1 3 0 3 -1 2 -1 3 -2 2 -1 2 -2 2 -2 2 -3 1 -2 1 -3 1 -2 1 -3 0 -3 0 -3 0 -2 0 -3 -1 -3 -1 -3 -1 -2 -2 -2 -1 -3 -2 -2 -2 -2 -3 -1 -2 -2 -3 -1 -3 -1 -2 0 -3 0 -3 0 -3 0 -2 0 -3 1 -3 1 -2 2 -3 1 -2 2 -2 2 -1 2 -2 2 -1 3 -1 3 -1 2 -1 3 0 3 0 3 1 2 0 3 1 3 1 2 2 3 1 2 2 2 2 2 2 2 3 1 2 2 3 1 3 0 2 1 3 0 1699 3801 63 MPPP3 0 2 -1 3 0 3 -1 2 -1 3 -2 2 -1 2 -2 2 -2 2 -3 1 -2 1 -3 1 -2 1 -3 0 -3 0 -3 0 -2 0 -3 -1 -3 -1 -3 -1 -2 -2 -2 -1 -3 -2 -2 -2 -2 -3 -1 -2 -2 -3 -1 -3 -1 -2 0 -3 0 -3 0 -3 0 -2 0 -3 1 -3 1 -2 2 -3 1 -2 2 -2 2 -1 2 -2 2 -1 3 -1 3 -1 2 -1 3 0 3 0 3 1 2 0 3 1 3 1 2 2 3 1 2 2 2 2 2 2 2 3 1 2 2 3 1 3 0 2 1 3 0 1699 3801 64 MP stroke3 -1 2 0 3 -1 3 -1 2 -2 2 -1 2 -2 2 -2 2 -3 1 -2 2 -3 1 -2 0 -3 1 -3 0 -3 0 -2 -1 -3 -1 -3 -1 -3 -1 -2 -1 -2 -2 -3 -2 -2 -2 -2 -2 -1 -3 -2 -3 -1 -2 -1 -3 0 -3 0 -3 0 -2 0 -3 0 -3 1 -2 1 -3 2 -2 1 -2 2 -2 2 -2 2 -2 2 -1 3 -1 3 -1 2 0 3 -1 3 1 3 0 2 0 3 1 3 2 2 1 3 2 2 1 2 2 2 3 2 2 1 3 2 2 1 3 0 3 1 3 0 4515 3801 63 MPPP2 0 3 -1 2 0 3 -1 3 -1 2 -2 2 -1 2 -2 2 -2 2 -3 1 -2 2 -3 1 -2 0 -3 1 -3 0 -3 0 -2 -1 -3 -1 -3 -1 -3 -1 -2 -1 -2 -2 -3 -2 -2 -2 -2 -2 -1 -3 -2 -3 -1 -2 -1 -3 0 -3 0 -3 0 -2 0 -3 0 -3 1 -2 1 -3 2 -2 1 -2 2 -2 2 -2 2 -2 2 -1 3 -1 3 -1 2 0 3 -1 3 1 3 0 2 0 3 1 3 2 2 1 3 2 2 1 2 2 2 3 2 2 1 3 2 2 1 3 0 3 1 3 0 4515 3801 64 MP strokegr6 w/Helvetica /ISOLatin1Encoding 120 FMSR5539 1216 mt (++) s2440 1216 mt (-+) s4600 3871 mt (+-) s1502 3871 mt (--) s/Symbol /ISOLatin1Encoding 120 FMSR3976 2701 mt (r) s/Helvetica /ISOLatin1Encoding 120 FMSR4041 2701 mt ( A) s/Helvetica /ISOLatin1Encoding 96 FMSR4154 2761 mt (2) s/Symbol /ISOLatin1Encoding 120 FMSR3295 2158 mt (a) s/Helvetica /ISOLatin1Encoding 120 FMSR3370 2158 mt ( A) s/Helvetica /ISOLatin1Encoding 96 FMSR3483 2218 mt (2) sendeplotepageendshowpage%%EndDocument @endspecial 564 1372 a Fj(Figure)16 b(1:)j(Decision)e(region)e(of)g(the)g(detector.)0 1509 y Fa(\(1.b\))0 1595 y Fj(In)j(case)f(that)gFi(\015)i(>)d Fj(0,)i(i.e.,)f Fi(A)528 1602 y Fh(1)5641595 y Fi(>)g Fg(j)p Fi(\032)p Fg(j)p Fi(A)700 1602 yFh(2)719 1595 y Fj(,)g(the)h(decision)h(region)e(for)gFi(b)1234 1602 y Fh(1)1271 1595 y Fj(is)h(exactly)g(the)f(same)g(as)g(that)g(of)g(the)0 1651 y(optimal)f(detector,)f(so)h(the)f(optim)o(um)h(asymptotic)f(m)o(ultiuser)i(e\016ciency)g(is)f(alw)o(a)o(ys)f(ac)o(hiev)o(ed.)23 b(In)16 b(case)g(that)0 1708 y Fi(\015)j(<)fFj(0,)f(i.e.,)i Fi(A)273 1715 y Fh(1)309 1708 y Fg(\024)f(j)pFi(\032)p Fg(j)p Fi(A)446 1715 y Fh(2)464 1708 y Fj(,)g(the)g(decision)i(region)e(is)h(the)f(same)f(as)h(that)f(of)g(the)h(successiv)o(e)h(canceler)g(with)f(a)0 1764 y(decorrelating)e(\014rst)f(stage,)f(where)h(the)h(asymptotic)e(m)o(ultiuser)j(e\016ciency)f(is)1141883 y(min)197 1819 y Fc(\032)231 1883 y Fj(1)p Fi(;)2791853 y(A)313 1836 y Fh(2)313 1865 y(2)p 279 1873 54 2v 279 1915 a Fi(A)313 1900 y Fh(2)313 1928 y(1)338 1883y Fj(\(1)9 b Fg(\000)i Fi(\032)458 1865 y Fh(2)477 1883y Fj(\))495 1819 y Fc(\033)536 1883 y Fi(:)1343 b Fj(\(7\))02009 y(If)15 b Fg(j)p Fi(\032)p Fg(j)d(\024)174 1991y Fh(1)p 160 1998 48 2 v 160 2004 a Fd(p)p 189 2004 182 v 27 x Fh(2)212 2009 y Fj(,)114 2145 y(\(1)d Fg(\000)iFi(\032)234 2127 y Fh(2)253 2145 y Fj(\))276 2115 y Fi(A)3102098 y Fh(2)310 2127 y(2)p 276 2135 54 2 v 276 2178 aFi(A)310 2162 y Fh(2)310 2191 y(1)376 2145 y Fg(\025)4582115 y Fj(1)e Fg(\000)i Fi(\032)560 2098 y Fh(2)p 4582135 122 2 v 497 2177 a Fi(\032)521 2164 y Fh(2)18922145 y Fj(\(8\))376 2241 y Fg(\025)42 b Fj(1)p Fi(:)1403b Fj(\(9\))0 2335 y(Hence)24 b(the)e(optim)o(um)h(asymptotic)g(m)o(ultiuser)g(e\016ciency)i(is)e(ac)o(hiev)o(ed.)43 b(In)24b(all,)h(this)e(detector)f(ac)o(hiev)o(es)0 2392 y(optim)o(um)15b(asymptotic)g(m)o(ultiuser)h(e\016ciency)h(for)d(all)jFi(A)991 2399 y Fh(1)1010 2392 y Fi(=)m(A)1064 2399 yFh(2)1100 2392 y Fj(if)e Fg(j)p Fi(\032)p Fg(j)d(\024)12702374 y Fh(1)p 1256 2381 48 2 v 1256 2386 a Fd(p)p 12852386 18 2 v 27 x Fh(2)1308 2392 y Fj(.)964 2678 y(2)peop%%Page: 3 33 2 bop 0 49 a Fa(\(2.a\))0 135 y Fj(F)l(or)15 b(the)g(same)g(reason)g(as)f(in)i(\(1.a\))e(w)o(e)h(can)g(assume)g(that)g Fi(\032)dFg(\025)h Fj(0.)19 b(Let)d Fi(A)1294 142 y Fh(1)1326135 y Fj(=)d Fi(A)1408 142 y Fh(2)1441 135 y Fj(=)g Fi(A)pFj(.)20 b(Then)114 225 y Fi(\015)14 b Fj(=)f Fi(\032:)1632b Fj(\(10\))0 314 y(The)15 b(decision)i(b)q(oundary)f(is)g(determined)g(b)o(y)f(the)h(solution)g(to)114 412 y Fi(y)136 419 yFh(1)166 412 y Fg(\000)10 b Fi(\032Af)291 419 y Ff(\015)321362 y Fc(\020)353 382 y Fi(y)375 389 y Fh(2)p 353 40243 2 v 357 444 a Fi(A)400 362 y Fc(\021)440 412 y Fj(=)j(0)pFi(;)1345 b Fj(\(11\))0 511 y(i.e.,)114 670 y Fi(y)136677 y Fh(1)168 670 y Fj(=)216 563 y Fc(8)216 604 y(>)216618 y(<)216 700 y(>)216 713 y(:)257 605 y Fi(\032A)95b Fj(if)16 b Fi(y)474 612 y Fh(2)506 605 y Fi(>)d(\032A;)257672 y(y)279 679 y Fh(2)410 672 y Fj(if)j Fg(j)p Fi(y)487679 y Fh(2)506 672 y Fg(j)d(\024)g Fi(\032A;)257 740y Fg(\000)p Fi(\032A)60 b Fj(if)16 b Fi(y)474 747 y Fh(2)506740 y Fi(<)d Fg(\000)p Fi(\032A:)1869 670 y Fj(\(12\))0829 y(This)h(curv)o(e)g(divides)h(the)e(2)g(dimensional)j(plane)e(in)o(to)g(t)o(w)o(o)e(regions)h(that)g(corresp)q(ond)h(to)e(the)i(t)o(w)o(o)e(h)o(yp)q(otheses.)0 886 y(It)j(is)h(the)g(same)f(as)g(sho)o(wn)g(in)h(Figure)g(1)f(for)g(\(1.a\).)k(It)c(is)h(in)o(teresting)g(that)f(the)h(cen)o(tral)f(section)h(of)f(the)h(curv)o(e)0 942y(divides)h(the)e(angle)h(in)g(b)q(et)o(w)o(een)g Fb(s)600949 y Fh(1)634 942 y Fj(and)f Fb(s)743 949 y Fh(2)778942 y Fj(in)o(to)g(t)o(w)o(o)f(equal)i(halv)o(es.)0 1063y Fa(\(2.b\))0 1149 y Fj(In)21 b(case)g(that)f Fi(\015)k(>)eFj(0,)g(i.e.,)f Fi(A)557 1156 y Fh(1)599 1149 y Fi(>)hFg(j)p Fi(\032)p Fg(j)p Fi(A)740 1156 y Fh(2)759 1149y Fj(,)f(the)g(decision)i(region)e(for)f Fi(b)1292 1156y Fh(1)1332 1149 y Fj(is)h(exactly)g(the)g(same)f(as)g(that)g(of)01205 y(the)d(optimal)h(detector,)e(so)h(the)g(optim)o(um)g(asymptotic)g(m)o(ultiuser)h(e\016ciency)g(is)g(alw)o(a)o(ys)e(ac)o(hiev)o(ed.)26b(In)18 b(case)0 1262 y(that)h Fi(\015)j(<)e Fj(0,)g(i.e.,)gFi(A)385 1269 y Fh(1)424 1262 y Fg(\024)h(j)p Fi(\032)pFg(j)p Fi(A)564 1269 y Fh(2)582 1262 y Fj(,)f(the)g(detector)f(b)q(ecomes)h(the)g(successiv)o(e)g(in)o(terference)h(canceler.)34b(F)l(or)19 b(its)0 1318 y(asymptotic)h(m)o(ultiuser)h(e\016ciency)g(to)f(b)q(e)h(alw)o(a)o(ys)e(optimal,)i(it)g(is)f(required)i(that)d(when)i Fi(A)1654 1325 y Fh(1)1694 1318 y Fg(\024)g(j)pFi(\032)p Fg(j)p Fi(A)1834 1325 y Fh(2)1853 1318 y Fj(,)g(the)01375 y(successiv)o(e)16 b(in)o(terference)h(canceler)f(w)o(orks)e(at)h(an)g(optimal)g(p)q(oin)o(t.)21 b(If)15 b Fg(j)p Fi(\032)pFg(j)d(\025)1341 1357 y Fh(1)p 1341 1364 18 2 v 13411390 a(2)1378 1375 y Fj(this)k(requires)g(that)119 1459y Fi(A)153 1466 y Fh(1)p 119 1479 54 2 v 119 1521 a Fi(A)1531528 y Fh(2)190 1490 y Fg(\024)d(j)p Fi(\032)p Fg(j)e(\))3621459 y Fi(A)396 1466 y Fh(2)p 362 1479 V 362 1521 a Fi(A)3961528 y Fh(1)434 1490 y Fg(\025)i Fj(1)d(+)g Fg(j)p Fi(\032)pFg(j)p Fi(;)1246 b Fj(\(13\))0 1595 y(i.e.,)132 1670y(1)p 119 1691 49 2 v 119 1732 a Fg(j)p Fi(\032)p Fg(j)1851701 y(\025)13 b Fj(1)d(+)g Fg(j)p Fi(\032)p Fg(j)p Fi(;)1495b Fj(\(14\))0 1813 y(or,)14 b(equiv)m(alen)o(tly)l(,)1141931 y Fg(j)p Fi(\032)p Fg(j)d(\024)228 1862 y(p)p 2661862 23 2 v 38 x Fj(5)f Fg(\000)g Fj(1)p 228 1920 1392 v 286 1962 a(2)372 1931 y Fi(:)1484 b Fj(\(15\))0 2038y(If)15 b Fg(j)p Fi(\032)p Fg(j)d Fi(<)160 2020 y Fh(1)p160 2027 18 2 v 160 2054 a(2)198 2038 y Fj(this)j(requires)h(that)1192122 y Fi(A)153 2129 y Fh(1)p 119 2143 54 2 v 119 2184a Fi(A)153 2191 y Fh(2)190 2153 y Fg(\024)d(j)p Fi(\032)pFg(j)e(\))362 2122 y Fi(A)396 2129 y Fh(2)p 362 2143V 362 2184 a Fi(A)396 2191 y Fh(1)434 2153 y Fg(\025)iFj(4)p Fg(j)p Fi(\032)p Fg(j)p Fj(\(1)8 b Fg(\000)i Fi(\032)6732134 y Fh(2)693 2153 y Fj(\))p Fi(;)1145 b Fj(\(16\))02259 y(i.e.,)132 2334 y(1)p 119 2354 49 2 v 119 2396a Fg(j)p Fi(\032)p Fg(j)185 2365 y(\025)13 b Fj(4)p Fg(j)pFi(\032)p Fg(j)p Fj(\(1)8 b Fg(\000)i Fi(\032)424 2346y Fh(2)444 2365 y Fj(\))p Fi(;)1394 b Fj(\(17\))0 2476y(whic)o(h)16 b(is)g(alw)o(a)o(ys)e(true.)20 b(In)c(all,)f(this)h(detector)f(ac)o(hiev)o(es)h(optim)o(um)f(asymptotic)g(m)o(ultiuser)h(e\016ciency)g(for)f(all)0 2538 y Fi(A)34 2545 y Fh(1)542538 y Fi(=)m(A)108 2545 y Fh(2)143 2538 y Fj(if)h Fg(j)pFi(\032)p Fg(j)11 b(\024)299 2492 y Fd(p)p 328 2492 182 v 28 x Fh(5)p Fd(\000)p Fh(1)p 299 2527 93 2 v 3362554 a(2)396 2538 y Fj(.)964 2678 y(3)p eop%%Trailerenduserdict /end-hook known{end-hook}if%%EOF
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