SolutionsforMultiuserDetection.rar 3.14.oldowns.ps

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E01FE000332A7CA83A>I E end
%%EndProlog
%%BeginSetup
%%Feature: *Resolution 600dpi
TeXDict begin
%%PaperSize: Letter

%%EndSetup
%%Page: 1 1
1 0 bop 949 44 a Fh(ELE)35 b(533)g(-)g(Multiuser)g(Detection)g(-)g
(Chapter)f(3)1674 157 y Fg(Oliv)m(er)29 b(Do)m(wns)94
519 y Ff(3.14)112 b(Optimal)54 b(Detectors)g(in)h(non-Equiprobable,)60
b(single-user)55 b(Gaussian-noise)405 635 y(c)m(hannels)94
925 y Fg(W)-8 b(e)32 b(ha)m(v)m(e)f(the)g(binary)-8 b(,)29
b(equiprobable,)f(an)m(tip)s(o)s(dal,)h(single)g(user,)h(white)g
(Gaussian)f(noise)h(c)m(hannel)1361 1129 y Fe(y)s Fg(\()p
Fe(t)p Fg(\))c(=)f Fe(Abs)p Fg(\()p Fe(t)p Fg(\))c(+)e
Fe(\033)s(n)p Fg(\()p Fe(t)p Fg(\))p Fe(;)c(t\017)p Fg([0)p
Fe(;)g(T)e Fg(])1153 b(\(1\))94 1333 y(where)41 b Fe(\031)420
1347 y Fd(0)503 1333 y Fg(=)i Fe(P)13 b Fg([)p Fe(b)44
b Fg(=)f(0])i Fc(6)p Fg(=)e Fe(P)13 b Fg([)p Fe(b)44
b Fg(=)f(1])i(=)e Fe(\031)1713 1347 y Fd(1)1752 1333
y Fg(.)74 b(W)-8 b(e)43 b(are)f(lo)s(oking)e(for)h(the)h(detector)h
(that)f(minimises)94 1446 y(the)j(error)g(probabilit)m(y)-8
b(.)83 b(W)-8 b(e)47 b(kno)m(w)e(that)h(in)e(the)h(case)h(of)g(a)f
(linear)f(detector,)50 b(if)44 b(w)m(e)i(consider)e(the)94
1559 y(linear)c(transformation)g(of)i Fe(y)s Fg(\()p
Fe(t)p Fg(\))g(under)d Fe(h)p Fg(\()p Fe(t)p Fg(\),)46
b(then)41 b(the)g Fe(h)p Fg(\()p Fe(t)p Fg(\))h(whic)m(h)f(minimises)d
(the)j(probabilit)m(y)e(of)94 1672 y(error)f(is)f(giv)m(en)i(b)m(y)f
Fe(h)p Fg(\()p Fe(t)p Fg(\))i(=)e Fe(\013s)p Fg(\()p
Fe(t)p Fg(\))h(with)e Fe(\013)i Fg(some)g(p)s(ositiv)m(e)e(constan)m
(t.)66 b(If)38 b(w)m(e)h(c)m(ho)s(ose)g(the)g(same)g(form)94
1785 y(of)c(linear)e(detector)814 1761 y(^)817 1785 y
Fe(b)g Fc(/)993 1711 y Fb(R)1068 1785 y Fe(y)s Fg(\()p
Fe(t)p Fg(\))p Fe(s)p Fg(\()p Fe(t)p Fg(\))p Fe(dt)p
Fg(,)k(but)d(adjust)h(the)g(detector,)i(suc)m(h)e(that)2912
1761 y(^)2915 1785 y Fe(b\017)p Fg([0)p Fe(;)15 b Fg(1],)38
b(and)c(suc)m(h)h(that)94 1908 y Fe(P)13 b Fg(\()197
1884 y(^)200 1908 y Fe(b)26 b Fg(=)f(0\))h(=)f Fe(\031)615
1922 y Fd(0)654 1908 y Fg(,)30 b(and)g Fe(P)13 b Fg(\()989
1884 y(^)992 1908 y Fe(b)26 b Fg(=)f(1\))h(=)f Fe(\031)1407
1922 y Fd(1)1446 1908 y Fg(,)31 b(in)e(the)h(form)1003
2138 y(^)1006 2162 y Fe(b)c Fg(=)1177 2126 y Fd(1)p 1177
2141 36 4 v 1177 2193 a(2)1237 2034 y Fb(\022\022)1371
2162 y Fg(sgn)1518 2038 y Fb(Z)1624 2162 y Fe(y)s Fg(\()p
Fe(t)p Fg(\))p Fe(s)p Fg(\()p Fe(t)p Fg(\))p Fe(dt)21
b Fg(+)f Fe(\014)5 b Fg(\()p Fe(\031)2256 2176 y Fd(1)2316
2162 y Fc(\000)20 b Fe(\031)2459 2176 y Fd(0)2498 2162
y Fg(\))2533 2034 y Fb(\023)2620 2162 y Fg(+)g(1)2756
2034 y Fb(\023)2839 2162 y Fe(;)811 b Fg(\(2\))94 2425
y(with)37 b Fe(\014)44 b Fg(c)m(hosen)c(suc)m(h)e(that)h
Fe(P)1209 2352 y Fb(\000)o(R)1326 2425 y Fe(y)s Fg(\()p
Fe(t)p Fg(\))p Fe(s)p Fg(\()p Fe(t)p Fg(\))p Fe(dt)26
b(<)f(\013)p Fg(\()p Fe(\031)1970 2439 y Fd(1)2030 2425
y Fc(\000)20 b Fe(\031)2173 2439 y Fd(0)2212 2425 y Fg(\))2247
2352 y Fb(\001)2329 2425 y Fg(=)38 b Fe(\031)2490 2439
y Fd(0)2530 2425 y Fg(.)66 b(This)37 b(lea)m(v)m(es)i(the)g(optimalit)m
(y)f(of)94 2538 y Fe(h)p Fg(\()p Fe(t)p Fg(\))26 b(=)f
Fe(s)p Fg(\()p Fe(t)p Fg(\))31 b(una\013ected.)94 2769
y(This)e(implies)e(that)1492 3018 y Fe(Q)1579 2890 y
Fb(\022)1656 2957 y Fe(\013)p Fg(\()p Fe(\031)1801 2971
y Fd(1)1861 2957 y Fc(\000)20 b Fe(\031)2004 2971 y Fd(0)2043
2957 y Fg(\))p 1656 2997 423 4 v 1840 3081 a Fe(\033)2089
2890 y Fb(\023)2181 3018 y Fg(=)25 b Fe(\031)2329 3032
y Fd(0)2368 3018 y Fe(:)1282 b Fg(\(3\))94 3268 y(Th)m(us)29
b(the)i(optimal)e(detector)j(for)e(the)h(non-equiprobable)d
(Gaussian-noise)h(c)m(hannel)h(is)f(giv)m(en)h(b)m(y)1003
3493 y(^)1006 3517 y Fe(b)c Fg(=)1177 3481 y Fd(1)p 1177
3496 36 4 v 1177 3548 a(2)1237 3388 y Fb(\022\022)1371
3517 y Fg(sgn)1518 3393 y Fb(Z)1624 3517 y Fe(y)s Fg(\()p
Fe(t)p Fg(\))p Fe(s)p Fg(\()p Fe(t)p Fg(\))p Fe(dt)21
b Fg(+)f Fe(\014)5 b Fg(\()p Fe(\031)2256 3531 y Fd(1)2316
3517 y Fc(\000)20 b Fe(\031)2459 3531 y Fd(0)2498 3517
y Fg(\))2533 3388 y Fb(\023)2620 3517 y Fg(+)g(1)2756
3388 y Fb(\023)2839 3517 y Fe(;)811 b Fg(\(4\))94 3766
y(with)1484 3970 y Fe(\013)26 b Fg(=)1828 3908 y Fe(\033)p
1674 3949 365 4 v 1674 4032 a Fg(\()p Fe(\031)1761 4046
y Fd(1)1821 4032 y Fc(\000)19 b Fe(\031)1963 4046 y Fd(0)2003
4032 y Fg(\))2048 3970 y Fe(Q)2120 3932 y Fa(\000)p Fd(1)2214
3970 y Fg(\()p Fe(\031)2301 3984 y Fd(0)2341 3970 y Fg(\))p
Fe(:)1274 b Fg(\(5\))1920 5635 y(1)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF