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📄 1.6.yyao.ps

📁 是multiuser detection 这本书的习题解答, 很有用的书.
💻 PS
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13127F9115>97 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Ff(1)732 1475 y Fh(\()p Fg(t)p Fh(\),)h(w)o(e)g(can)f(treat)hFg(x)1078 1481 y Ff(2)1097 1475 y Fh(\()p Fg(t)p Fh(\))g(as)f(noise.)26b(Since)17 b Fg(x)1477 1481 y Ff(2)1496 1475 y Fh(\()p Fg(t)pFh(\))f(is)h(inde-)262 1525 y(p)q(enden)o(t)d(of)f Fg(n)p Fh(\()pFg(t)p Fh(\),)h(the)g(total)f(noise)h(p)q(o)o(w)o(er)g(is)fFg(P)1028 1531 y Ff(2)1055 1525 y Fh(+)c Fg(N)c Fh(,)13 b(so)h(the)g(highest)g(rate)g(user)h(1)e(can)262 1575 y(attain)g(is)g Fg(C)s Fh(\()5071558 y Fc(P)528 1562 y Fb(1)p 479 1565 93 2 v 479 1589 a Fc(P)5001593 y Fb(2)517 1589 y Ff(+)p Fc(N)576 1575 y Fh(\).)262 1635y(Since)i(when)g Fg(R)512 1641 y Ff(1)543 1635 y Fh(=)e Fg(C)sFh(\()669 1618 y Fc(P)690 1622 y Fb(1)p 641 1625 V 641 1649a Fc(P)662 1653 y Fb(2)679 1649 y Ff(+)p Fc(N)738 1635 y Fh(\),)i(the)g(data)f(of)g(user)i(1)e(can)h(b)q(e)g(deco)q(ded)h(reliably)m(,)d(the)i(in-)2621684 y(teference)h(brough)o(t)f(b)o(y)f Fg(x)675 1690 y Ff(1)6941684 y Fh(\()p Fg(t)p Fh(\))h(is)f(completely)g(suppressed)j(in)d(our)h(successiv)o(e)h(deco)q(ding)262 1734 y(sc)o(heme)f(and)g(user)h(2)f(can)h(transmit)e(at)h(the)h(rate)f Fg(C)s Fh(\()1125 1717 y Fc(P)11461721 y Fb(2)p 1125 1724 38 2 v 1129 1749 a Fc(N)1168 1734 yFh(\))g(reliably)m(.)21 b(Hence)16 b(the)g(reliable)262 1784y(comm)o(uni)o(cation)11 b(is)j(p)q(ossible)g(at)g(\()p Fg(R)8481769 y Fc(b)848 1794 y Ff(1)866 1784 y Fg(;)7 b(R)917 1769y Fc(b)917 1794 y Ff(2)934 1784 y Fh(\).)262 1834 y(Using)13b(similar)e(argumen)o(t,)h(w)o(e)h(can)h(sho)o(w)f(that)h(the)g(rate)g(pair)e(\()p Fg(R)1327 1819 y Fc(a)1327 1844 y Ff(1)1348 1834 y Fg(;)7b(R)1399 1819 y Fc(a)1399 1844 y Ff(2)1418 1834 y Fh(\))13b(is)h(also)e(attain-)262 1884 y(able.)262 1933 y(\(c\))i(If)g(\()p384 1900 32 2 v Fg(R)416 1939 y Ff(1)434 1933 y Fg(;)p 4531900 V 7 w(R)484 1939 y Ff(2)503 1933 y Fh(\))g(is)g(a)f(con)o(v)o(ex)h(com)o(bination)e(of)h(\()p Fg(R)1077 1918 y Fc(a)1077 1944 y Ff(1)10971933 y Fg(;)7 b(R)1148 1918 y Fc(a)1148 1944 y Ff(2)1168 1933y Fh(\))14 b(and)f(\()p Fg(R)1326 1918 y Fc(b)1326 1944 y Ff(1)13451933 y Fg(;)7 b(R)1396 1918 y Fc(b)1396 1944 y Ff(2)1413 1933y Fh(\),)14 b(that)g(is)p 656 2006 V 656 2039 a Fg(R)688 2045y Ff(1)718 2039 y Fh(=)e Fg(\013C)s Fh(\()843 2011 y Fg(P)8702017 y Ff(1)p 843 2030 46 2 v 847 2068 a Fg(N)893 2039 y Fh(\))d(+)h(\(1)fFe(\000)g Fg(\013)p Fh(\))p Fg(C)s Fh(\()1188 2011 y Fg(P)12152017 y Ff(1)p 1144 2030 134 2 v 1144 2068 a Fg(P)1171 2074y Ff(2)1198 2068 y Fh(+)h Fg(N)1283 2039 y Fh(\))p 656 213632 2 v 656 2170 a Fg(R)688 2176 y Ff(2)718 2170 y Fh(=)i Fg(\013C)sFh(\()887 2142 y Fg(P)914 2148 y Ff(2)p 843 2160 134 2 v 8432198 a Fg(P)870 2204 y Ff(1)897 2198 y Fh(+)e Fg(N)981 2170y Fh(\))g(+)f(\(1)g Fe(\000)h Fg(\013)p Fh(\))p Fg(C)s Fh(\()12332142 y Fg(P)1260 2148 y Ff(2)p 1233 2160 46 2 v 1237 2198 aFg(N)1283 2170 y Fh(\))262 2266 y(where)15 b(0)c Fe(\024)hFg(\013)f Fe(\024)h Fh(1,)h(then)p 680 2233 32 2 v 14 w Fg(R)7122272 y Ff(1)740 2266 y Fh(+)p 782 2233 V 10 w Fg(R)813 2272y Ff(2)844 2266 y Fh(=)e Fg(\013C)s Fh(\()968 2249 y Fc(P)9892253 y Fb(1)1005 2249 y Ff(+)p Fc(P)1051 2253 y Fb(2)p 9682256 101 2 v 1003 2281 a Fc(N)1073 2266 y Fh(\))e(+)h(\(1)fFe(\000)h Fg(\013)p Fh(\))p Fg(C)s Fh(\()1325 2249 y Fc(P)13462253 y Fb(1)1361 2249 y Ff(+)p Fc(P)1407 2253 y Fb(2)p 13242256 V 1360 2281 a Fc(N)1429 2266 y Fh(\))i(=)g Fg(C)s Fh(\()15552249 y Fc(P)1576 2253 y Fb(1)1592 2249 y Ff(+)p Fc(P)1638 2253

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