www.pudn.com > SolutionsforMultiuserDetection.rar > 3.17.rickard.ps


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%DVIPSSource:  TeX output 1999.03.03:1302
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TeXDict begin

1 0 bop 1373 289 a Fj(Multiuser)45 b(Detection)1656 530
y Fi(Scott)33 b(Ric)m(k)-5 b(ard)1643 725 y(Marc)m(h)34
b(3,)e(1999)515 1083 y Fh(Solution)45 b(to)h(Problem)f(3.17)515
1264 y Fg(The)32 b(signal)e(p)r(ortion)i(of)g Ff(y)s
Fg(\()p Ff(t)p Fg(\))e(=)f Ff(Abs)p Fg(\()p Ff(t)p Fg(\))22
b(+)f Ff(\033)s(n)p Fg(\()p Ff(t)p Fg(\))33 b(passes)d(through)h(the)h
(ideal)g(lo)n(w-pass)515 1364 y(\014lter)g(\()p Ff(B)j
Fg(=)953 1331 y Fe(1+)p Fd(\013)p 953 1345 128 4 v 1000
1393 a Fe(2)1090 1364 y Fg(\)\))e(undisturb)r(ed)g(b)r(ecause)e(it)i
(is)f(lo)n(wpass.)49 b(After)32 b(\014ltering,)h(the)g(noise)515
1464 y(has)21 b(p)r(o)n(w)n(er)g Ff(\033)944 1434 y Fe(2)982
1464 y Fg(\(1)7 b(+)g Ff(\013)p Fg(\),)23 b(and)f(b)r(ecause)g(it)g(is)
g(still)g(has)g(zero)f(mean,)27 b(~)-46 b Ff(n)o Fg(\()p
Ff(t)p Fg(\))24 b Fc(\030)f Ff(\021)s Fg(\(0)p Ff(;)14
b(\033)3048 1434 y Fe(2)3085 1464 y Fg(\(1)7 b(+)g Ff(\013)p
Fg(\)\).)515 1563 y(Th)n(us,)27 b(a)h(sample)f(tak)n(en)g(at)h(time)g
Ff(t)c Fg(=)f(0,)k(has)h(distribution)g Ff(\021)s Fg(\()p
Ff(Abs)p Fg(\(0\))p Ff(;)14 b(\033)2854 1533 y Fe(2)2892
1563 y Fg(\(1)k(+)g Ff(\013)p Fg(\)\))p Ff(:)29 b Fg(The)515
1663 y(probabilit)n(y)d(of)i(error)d(is)j(then,)1660
1891 y Ff(Q)1740 1774 y Fb(\022)1937 1835 y Ff(A)p 1810
1872 317 4 v 1810 1954 a(\033)1860 1888 y Fc(p)p 1930
1888 197 4 v 1930 1954 a Fg(1)18 b(+)g Ff(\013)2136 1774
y Fb(\023)2211 1891 y Ff(:)1039 b Fg(\(1\))515 2119 y(The)27
b(optim)n(um)h(detector)f(w)n(ould)g(ha)n(v)n(e)g(probabilit)n(y)f(of)i
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y Ff(A)p 1937 2327 63 4 v 1943 2403 a(\033)2009 2229
y Fb(\023)2084 2347 y Ff(:)1166 b Fg(\(2\))515 2574 y(Note)23
b(that)h(optimal)g(detection)g(is)f(obtained)g(when)h
Ff(\013)g Fg(=)e(0.)35 b(W)-7 b(e)24 b(can)g(see)f(wh)n(y)g(this)h(is)g
(the)515 2674 y(case)29 b(b)n(y)h(noting)g(that)h(the)g(impulse)f(resp)
r(onse)g(of)g(the)h(lo)n(wpass)e(\014lter)h(is)g Ff(h)p
Fg(\()p Ff(t)p Fg(\))e(=)g(sinc)o(\()p Ff(t)p Fg(\))515
2774 y(whic)n(h)g(is)g(also)f(the)i(signal)e(itself.)40
b(Th)n(us,)28 b(the)h(op)r(eration)e(of)h(lo)n(wpass)f(\014ltering)h
Ff(y)s Fg(\()p Ff(t)p Fg(\))g(and)515 2873 y(sampling)f(at)g
Ff(t)c Fg(=)g(0)k(is)h(equiv)-5 b(alen)n(t)27 b(to)g(matc)n(hed)h
(\014ltering.)992 3098 y(\()p Ff(y)s Fg(\()p Ff(t)p Fg(\))19
b Fc(\003)f Ff(h)p Fg(\()p Ff(t)p Fg(\)\))1415 3110 y
Fd(t)p Fe(=0)1552 3098 y Fg(=)1640 2985 y Fb(Z)1723 3006
y Fa(1)1686 3174 y(\0001)1822 3098 y Ff(y)s Fg(\()p Ff(t)p
Fg(\))p Ff(h)p Fg(\()p Fc(\000)p Ff(t)p Fg(\))p Ff(dt)24
b Fg(=)2351 2985 y Fb(Z)2434 3006 y Fa(1)2397 3174 y(\0001)2533
3098 y Ff(y)s Fg(\()p Ff(t)p Fg(\))p Ff(s)p Fg(\()p Ff(t)p
Fg(\))p Ff(dt:)373 b Fg(\(3\))1926 5506 y(1)p eop end
userdict /end-hook known{end-hook}if