www.pudn.com > SolutionsforMultiuserDetection.rar > 3.10.rickard.ps

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%%EndProlog
%%BeginSetup
%%Feature: *Resolution 600dpi
TeXDict begin
%%PaperSize: A4

%%EndSetup
%%Page: 1 1
1 0 bop 1373 872 a Fl(Multiuser)45 b(Detection)1656 1112
y Fk(Scott)33 b(Ric)m(k)-5 b(ard)1563 1308 y(F)d(ebruary)33
b(22,)f(1999)515 1665 y Fj(Solution)45 b(to)h(Problem)f(3.10)515
1847 y Fi(Note)32 b(that)g(w)n(e)g(can)f(represen)n(t)g(the)h(signal)g
Fh(Abs)p Fi(\()p Fh(t)p Fi(\))g(where)f Fg(j)p Fh(s)p
Fi(\()p Fh(t)p Fi(\))p Fg(j)g Fi(=)f(1)p Fh(=)2834 1777
y Fg(p)p 2903 1777 61 4 v 70 x Fh(T)43 b Fi(as)31 b Fh(A)3163
1817 y Ff(0)3187 1847 y Fh(bs)3262 1817 y Ff(0)3284 1847
y Fi(\()p Fh(t)p Fi(\))515 1947 y(where)k Fh(A)825 1917
y Ff(0)885 1947 y Fi(=)h Fh(A)1048 1876 y Fe(p)p 1131
1876 148 4 v 71 x Fh(\034)9 b(=T)47 b Fi(and)36 b Fg(j)p
Fh(s)1546 1917 y Ff(0)1569 1947 y Fi(\()p Fh(t)p Fi(\))p
Fg(j)h Fi(=)f(1)p Fh(=)1908 1887 y Fg(p)p 1976 1887 46
4 v 1976 1947 a Fh(\034)10 b Fi(.)61 b(Using)36 b(this)g(notation,)h
Fh(s)2922 1917 y Ff(0)2945 1947 y Fi(\()p Fh(t)p Fi(\))f(has)f(unit)515
2047 y(energy)g(o)n(v)n(er)f(\(0)p Fh(;)14 b(\034)9 b
Fi(\),)39 b(and)d(the)g(probabilit)n(y)f(of)h(error)e(using)i(the)g
(correlator)e(o)n(v)n(er)g(this)515 2188 y(in)n(terv)-5
b(al)27 b(is)g Fh(Q)p Fi(\()1006 2155 y Fd(A)1056 2130
y Fc(0)p 1006 2169 73 4 v 1022 2216 a Fd(\033)1088 2188
y Fi(\))d(=)e Fh(Q)p Fi(\()1339 2139 y Fd(A)1389 2082
y Fg(p)p 1458 2082 120 4 v 57 x Fd(\034)7 b(=T)p 1339
2169 239 4 v 1438 2216 a(\033)1588 2188 y Fi(\).)37 b(The)28
b(a)n(v)n(erage)d(probabilit)n(y)h(of)i(error)d(is)j(then,)1283
2327 y Fe(R)1338 2347 y Fd(T)1322 2423 y Fb(0)1404 2394
y Fh(Q)p Fi(\()1512 2361 y Fd(A)p 1512 2375 50 4 v 1517
2422 a(\033)1572 2323 y Fe(p)p 1655 2323 148 4 v 71 x
Fh(\034)9 b(=T)i Fi(\))p Fh(d\034)p 1283 2436 641 4 v
1573 2513 a(T)1956 2456 y Fi(=)2044 2343 y Fe(Z)2127
2363 y Fb(1)2090 2531 y(0)2178 2456 y Fh(Q)p Fi(\()2286
2399 y Fh(A)p 2286 2436 63 4 v 2292 2513 a(\033)2358
2392 y Fg(p)p 2428 2392 48 4 v 2428 2456 a Fh(x)p Fi(\))p
Fh(dx;)653 b Fi(\(1\))515 2685 y(where)27 b Fh(x)c Fi(=)g
Fh(\034)9 b(=T)j Fi(.)36 b(Using)28 b(the)g(follo)n(wing)e(prop)r(ert)n
(y)h(of)g(the)h(Q-function)f(\(Prop)r(ert)n(y)g(31\),)968
2814 y Fe(Z)1051 2834 y Fb(1)1014 3002 y(0)1102 2927
y Fh(Q)p Fi(\()p Fh(\025)1248 2863 y Fg(p)p 1317 2863
V 64 x Fh(x)q Fi(\))p Fh(dx)d Fi(=)e(\(1)d Fg(\000)1806
2871 y Fi(1)p 1784 2908 86 4 v 1784 2984 a Fh(\025)1832
2960 y Fb(2)1879 2927 y Fi(\))p Fh(Q)p Fi(\()p Fh(\025)p
Fi(\))h(+)2244 2871 y(1)p 2202 2908 128 4 v 2202 2984
a(2)p Fh(\025)2292 2960 y Fb(2)2357 2927 y Fg(\000)2534
2871 y Fi(1)p 2450 2908 210 4 v 2450 2993 a Fh(\025)2498
2924 y Fg(p)p 2568 2924 92 4 v 2568 2993 a Fi(2)p Fh(\031)2670
2927 y(e)2709 2893 y Ff(\000)p Fd(\025)2800 2868 y Fa(2)2832
2893 y Fd(=)p Fb(2)2903 2927 y Fh(;)347 b Fi(\(2\))515
3158 y(and)27 b(setting)h Fh(\025)23 b Fi(=)g Fh(A=\033)s
Fi(,)28 b(the)g(a)n(v)n(erage)d(probabilit)n(y)h(of)i(error)d(is,)1116
3393 y Fh(P)35 b Fi(=)22 b(\(1)d Fg(\000)1482 3337 y
Fh(\033)1532 3307 y Fb(2)p 1477 3374 100 4 v 1477 3450
a Fh(A)1539 3426 y Fb(2)1586 3393 y Fi(\))p Fh(Q)p Fi(\()1726
3337 y Fh(A)p 1726 3374 63 4 v 1732 3450 a(\033)1798
3393 y Fi(\))g(+)1969 3337 y Fh(\033)2019 3307 y Fb(2)p
1942 3374 142 4 v 1942 3450 a Fi(2)p Fh(A)2046 3426 y
Fb(2)2112 3393 y Fg(\000)2291 3337 y Fh(\033)p 2205 3374
224 4 v 2205 3460 a(A)2267 3391 y Fg(p)p 2336 3391 92
4 v 69 x Fi(2)p Fh(\031)2438 3393 y(e)2477 3359 y Ff(\000)p
Fd(A)2579 3334 y Fa(2)2611 3359 y Fd(=)p Fb(2)p Fd(\033)2718
3334 y Fa(2)2755 3393 y Fh(:)495 b Fi(\(3\))515 3620
y(The)27 b(increase)g(in)h(a)n(v)n(erage)c(error)i(probabilit)n(y)h(is)
g(th)n(us,)967 3851 y(\001)p Fh(P)35 b Fi(=)23 b Fh(P)30
b Fg(\000)18 b Fh(Q)p Fi(\()1486 3795 y Fh(A)p 1486 3832
63 4 v 1492 3908 a(\033)1558 3851 y Fi(\))23 b(=)1717
3795 y Fh(\033)1767 3765 y Fb(2)p 1711 3832 100 4 v 1711
3908 a Fh(A)1773 3884 y Fb(2)1821 3851 y Fi([)1854 3795
y(1)p 1854 3832 42 4 v 1854 3908 a(2)1923 3851 y Fg(\000)18
b Fh(Q)p Fi(\()2114 3795 y Fh(A)p 2114 3832 63 4 v 2120
3908 a(\033)2187 3851 y Fi(\)])g Fg(\000)2440 3795 y
Fh(\033)p 2353 3832 224 4 v 2353 3917 a(A)2415 3848 y
Fg(p)p 2485 3848 92 4 v 2485 3917 a Fi(2)p Fh(\031)2587
3851 y(e)2626 3817 y Ff(\000)p Fd(A)2728 3792 y Fa(2)2759
3817 y Fd(=)p Fb(2)p Fd(\033)2866 3792 y Fa(2)2904 3851
y Fh(:)346 b Fi(\(4\))1926 5255 y(1)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF