www.pudn.com > SolutionsforMultiuserDetection.rar > 1.3.xinwang.ps

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672 y Fm(By)35 b(Xin)g(Wang)1462 868 y Fl(F)-8 b(ebruary)33
b(4,)f(1999)-61 1167 y Fk(Problem)27 b(1.3)d Fj(Let)h(us)g(sa)n(y)e
(that)j(t)n(w)n(o)e(orthogonal)f(signals)g(are)h Fi(str)l(ongly)k
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1349 y(strongly)f(orthogonal)g(is)h(that)h(there)f(exists)h(a)f(time)h
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Fh(t)p Fj(,)1305 1524 y Fh(s)1344 1536 y Fg(1)1381 1524
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Fh(s)2597 1826 y Fg(1)2662 1814 y Fj(and)g Fh(s)2863
1826 y Fg(2)2928 1814 y Fj(ha)n(v)n(e)f(\014nite)h(energy)-7
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Fj(\()p Fh(!)s Fj(\))h(and)f Fh(S)2634 1918 y Fg(2)2671
1906 y Fj(\()p Fh(!)s Fj(\))h(resp)r(ectiv)n(ely)-7 b(.)-61
1997 y(No)n(w)20 b(de\014ne)g(signals)j(^)-45 b Fh(s)654
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Fh(s)935 2009 y Fg(1)972 1997 y Fj(\()p Fh(t)t Fj(+)t
Fh(T)1156 2009 y Fg(0)1194 1997 y Fj(\))f(and)j(^)-46
b Fh(s)1440 2009 y Fg(1)1478 1997 y Fj(\()p Fh(t)p Fj(\))23
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2105 y Fj(\()p Fh(t)p Fj(\).)48 b(Denote)31 b(the)g(F)-7
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b Fh(s)2286 2117 y Fg(2)2323 2105 y Fj(\()p Fh(t)p Fj(\))32
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2105 y Fh(S)3008 2117 y Fg(2)3045 2105 y Fj(\()p Fh(!)s
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2332 y Fg(1)983 2320 y Fj(\()p Fh(!)s Fj(\))p Fh(e)1141
2290 y Fe(\000)p Fd(i!)r(T)1299 2298 y Fc(0)1336 2320
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Fh(!)s Fj(\))c(=)1880 2299 y(^)1866 2320 y Fh(S)1917
2332 y Fg(2)1954 2320 y Fj(\()p Fh(!)s Fj(\))p Fh(e)2112
2290 y Fe(\000)p Fd(i!)r(T)2270 2298 y Fc(0)2307 2320
y Fj(.)-61 2411 y(Let)e Fh(h)p Fj(\()p Fh(t)p Fj(\))h(and)f
Fh(H)7 b Fj(\()p Fh(!)s Fj(\))21 b(b)r(e)h(the)g(impulse)f(resp)r(onse)
g(and)g(frequency)g(resp)r(onse)f(of)h(an)g(arbitrary)e(L)-7
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2503 y(Theorem,)27 b(w)n(e)g(ha)n(v)n(e)619 2720 y Ff(h)p
Fh(s)690 2732 y Fg(1)745 2720 y Ff(\003)18 b Fh(h;)c(s)929
2732 y Fg(2)985 2720 y Ff(\003)k Fh(h)p Ff(i)83 b Fj(=)1391
2664 y(1)p 1365 2701 92 4 v 1365 2777 a(2)p Fh(\031)1467
2720 y Ff(h)p Fh(S)1550 2732 y Fg(1)1588 2720 y Fh(H)r(;)14
b(S)1747 2732 y Fg(2)1784 2720 y Fh(H)7 b Ff(i)1208 2920
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2920 y Ff(h)1513 2899 y Fj(^)1499 2920 y Fh(S)1550 2932
y Fg(1)1588 2920 y Fh(e)1627 2885 y Fe(\000)p Fd(i!)r(T)1785
2893 y Fc(0)1821 2920 y Fh(H)r(;)1943 2899 y Fj(^)1929
2920 y Fh(S)1980 2932 y Fg(2)2018 2920 y Fh(e)2057 2885
y Fe(\000)p Fd(i!)r(T)2215 2893 y Fc(0)2251 2920 y Fh(H)g
Ff(i)1208 3127 y Fj(=)1391 3071 y(1)p 1365 3108 V 1365
3184 a(2)p Fh(\031)1481 3014 y Fb(Z)1564 3035 y Fe(1)1527
3203 y(\0001)1677 3106 y Fj(^)1663 3127 y Fh(S)1714 3139
y Fg(1)1751 3127 y Fj(\()p Fh(!)s Fj(\))p Fh(e)1909 3093
y Fe(\000)p Fd(i!)r(T)2067 3101 y Fc(0)2104 3127 y Fh(H)g
Fj(\()p Fh(!)s Fj(\))2313 3106 y(^)2299 3127 y Fh(S)2355
3093 y Fe(\003)2350 3148 y Fg(2)2393 3127 y Fj(\()p Fh(!)s
Fj(\))p Fh(e)2551 3093 y Fd(i!)r(T)2657 3101 y Fc(0)2694
3127 y Fh(H)2770 3093 y Fe(\003)2808 3127 y Fj(\()p Fh(!)s
Fj(\))p Fh(d!)1208 3361 y Fj(=)1391 3304 y(1)p 1365 3341
V 1365 3418 a(2)p Fh(\031)1481 3248 y Fb(Z)1564 3268
y Fe(1)1527 3436 y(\0001)1677 3340 y Fj(^)1663 3361 y
Fh(S)1714 3373 y Fg(1)1751 3361 y Fj(\()p Fh(!)s Fj(\))1885
3340 y(^)1870 3361 y Fh(S)1926 3326 y Fe(\003)1921 3381
y Fg(2)1964 3361 y Fj(\()p Fh(!)s Fj(\))p Fh(H)g Fj(\()p
Fh(!)s Fj(\))p Fh(H)g Fj(\()p Ff(\000)p Fh(!)s Fj(\))p
Fh(d!)s(;)-186 3597 y Fj(where)27 b(the)h(last)f(equalit)n(y)g(is)h
(from)f(the)h(fact)g(that)g Fh(h)p Fj(\()p Fh(t)p Fj(\))g(is)f(real.)
-61 3704 y(Since)i(b)r(oth)369 3683 y(^)355 3704 y Fh(S)406
3716 y Fg(1)444 3704 y Fj(\()p Fh(!)s Fj(\))h(and)f Fh(H)7
b Fj(\()p Fh(!)s Fj(\))p Fh(H)g Fj(\()p Ff(\000)p Fh(!)s
Fj(\))29 b(are)g(ev)n(en)g(symmetric,)h(and)2180 3683
y(^)2165 3704 y Fh(S)2221 3674 y Fe(\003)2216 3725 y
Fg(2)2259 3704 y Fj(\()p Fh(!)s Fj(\))g(is)g(o)r(dd)g(symmetric,)g(the)
g(in)n(tegrand)e(is)i(o)r(dd)-186 3796 y(symmetric.)37
b(Therefore,)26 b(the)i(in)n(tegral)e(is)i(0.)-61 3887
y(Hence,)h Fh(s)249 3899 y Fg(1)306 3887 y Ff(\003)19
b Fh(h)29 b Fj(and)g Fh(s)646 3899 y Fg(2)702 3887 y
Ff(\003)19 b Fh(h)29 b Fj(are)f(orthogonal)f(for)i(an)n(y)f(impulse)h
(resp)r(onse)f Fh(h)p Fj(\()p Fh(t)p Fj(\).)42 b(Therefore,)28
b(b)n(y)h(the)h(de\014nition,)g Fh(s)3630 3899 y Fg(1)3696
3887 y Fj(and)-186 3978 y Fh(s)-147 3990 y Fg(2)-82 3978
y Fj(are)c(strongly)h(orthogonal.)-61 4070 y(Note:)36
b(the)28 b(orthogonalit)n(y)e(of)h Fh(s)960 4082 y Fg(1)1025
4070 y Fj(and)g Fh(s)1225 4082 y Fg(2)1290 4070 y Fj(is)h(a)f(sp)r
(ecial)g(case)g(of)h(the)g(result)f(when)h Fh(h)p Fj(\()p
Fh(t)p Fj(\))23 b(=)g Fh(\016)s Fj(\()p Fh(t)p Fj(\))p
Fh(:)-61 4161 y Fa(2)1801 5392 y Fj(1)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF

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