SolutionsforMultiuserDetection.rar 2.15.oldowns.ps

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

%%EndSetup
%%Page: 1 1
1 0 bop 949 44 a Fk(ELE)35 b(533)g(-)g(Multiuser)g(Detection)g(-)g
(Chapter)f(2)1674 157 y Fj(Oliv)m(er)29 b(Do)m(wns)94
519 y Fi(2.15)112 b(Cross-correlations)37 b(in)f(Random)i(Signature)f
(Sequence)i(c)m(hannels)94 808 y Fj(The)30 b(source)h(sequence)g(in)e
(this)g(case)j(is)d Fh(s)1547 823 y Fg(k)1590 808 y Fj(\()p
Fh(t)p Fj(\))d(=)1868 773 y Ff(1)p 1825 788 122 4 v 1825
797 a Fe(p)p 1884 797 64 3 v 56 x Fg(N)1972 740 y Fd(P)2068
766 y Fg(N)2068 835 y(i)p Ff(=1)2201 808 y Fh(d)2248
823 y Fg(k)r(i)2315 808 y Fh(p)2361 822 y Fg(T)2402 830
y Fc(c)2438 808 y Fj(\()p Fh(t)21 b Fb(\000)f Fh(iT)2702
822 y Fg(c)2757 808 y Fj(+)g Fh(T)2901 822 y Fg(c)2936
808 y Fj(\),)31 b(and)f(with)f(the)i(cross-)94 932 y(correlations)f
(de\014ned)f(as)i(ab)s(o)m(v)m(e.)1127 1152 y Fh(\032)1174
1167 y Fg(k)r(l)1239 1152 y Fj(\()p Fh(\034)10 b Fj(\))26
b(=)1491 1090 y(1)p 1491 1131 46 4 v 1491 1214 a(2)1561
1065 y Fd(X)1615 1261 y Fg(i)1708 1065 y Fd(X)1757 1261
y Fg(j)1854 1152 y Fh(d)1901 1167 y Fg(k)r(i)1968 1152
y Fh(d)2015 1167 y Fg(l)q(j)2074 1152 y Fh(R)2143 1166
y Fg(p)2183 1152 y Fj(\()p Fh(\034)k Fb(\000)20 b Fj(\()p
Fh(j)26 b Fb(\000)20 b Fh(i)p Fj(\))p Fh(T)2687 1166
y Fg(c)2723 1152 y Fj(\))917 b(\(1\))94 1445 y(and)560
1713 y Fh(\032)607 1728 y Fg(l)q(k)671 1713 y Fj(\()p
Fh(\034)10 b Fj(\))26 b(=)942 1652 y(1)p 923 1692 83
4 v 923 1776 a Fh(N)1031 1589 y Fd(Z)1171 1600 y Fg(N)1137
1627 y Fd(X)1146 1822 y Fg(i)p Ff(=1)1284 1713 y Fh(d)1331
1728 y Fg(l)q(i)1381 1713 y Fh(p)1427 1727 y Fg(T)1468
1735 y Fc(c)1504 1713 y Fj(\()p Fh(t)20 b Fb(\000)g Fh(iT)1767
1727 y Fg(c)1823 1713 y Fj(+)g Fh(T)1967 1727 y Fg(c)2001
1713 y Fj(\))2086 1600 y Fg(N)2052 1627 y Fd(X)2056 1822
y Fg(j)t Ff(=1)2198 1713 y Fh(d)2245 1728 y Fg(k)r(j)2321
1713 y Fh(p)2367 1727 y Fg(T)2408 1735 y Fc(c)2444 1713
y Fj(\()p Fh(t)g Fb(\000)g Fh(j)5 b(T)2718 1727 y Fg(c)2774
1713 y Fj(+)20 b Fh(T)2918 1727 y Fg(c)2973 1713 y Fj(+)g
Fh(T)32 b Fb(\000)20 b Fh(\034)10 b Fj(\))350 b(\(2\))817
1998 y(=)942 1936 y(1)p 923 1977 V 923 2060 a Fh(N)1031
1911 y Fd(X)1085 2107 y Fg(i)1178 1911 y Fd(X)1227 2107
y Fg(j)1324 1998 y Fh(d)1371 2013 y Fg(l)q(i)1421 1998
y Fh(dk)s(j)7 b(R)1631 2012 y Fg(p)1670 1998 y Fj(\()p
Fh(\034)31 b Fb(\000)20 b Fj(\()p Fh(j)26 b Fb(\000)20
b Fh(i)p Fj(\))p Fh(T)2175 2012 y Fg(c)2231 1998 y Fb(\000)f
Fh(T)13 b Fj(\))1253 b(\(3\))3675 2241 y(\(4\))94 2461
y(with)29 b Fh(R)370 2475 y Fg(p)410 2461 y Fj(\()p Fh(\034)10
b Fj(\))26 b(=)652 2388 y Fd(R)712 2415 y Ff(+)p Fe(1)695
2493 y(\0001)857 2461 y Fh(p)903 2475 y Fg(T)944 2483
y Fc(c)980 2461 y Fj(\()p Fh(t)p Fj(\))p Fh(p)1129 2475
y Fg(T)1170 2483 y Fc(c)1207 2461 y Fj(\()p Fh(t)20 b
Fb(\000)g Fh(iT)1470 2475 y Fg(c)1525 2461 y Fj(+)g Fh(T)1669
2475 y Fg(c)1704 2461 y Fj(\))p Fh(dt)p Fj(.)41 b(Hence)1561
2679 y Fh(\032)1608 2694 y Fg(l)q(k)1673 2679 y Fj(\()p
Fh(\034)10 b Fj(\))26 b(=)f Fh(\032)1962 2694 y Fg(k)r(l)2026
2679 y Fj(\()p Fh(\034)31 b Fb(\000)20 b Fh(T)13 b Fj(\))1351
b(\(5\))94 2883 y(Clearly)29 b Fh(\032)457 2898 y Fg(k)r(l)521
2883 y Fj(\()p Fh(\034)10 b Fj(\))31 b(and)f Fh(\032)896
2898 y Fg(l)q(k)961 2883 y Fj(\()p Fh(\034)10 b Fj(\))31
b Fa(ar)-5 b(e)31 b Fj(dep)s(enden)m(t.)94 3114 y(The)f(correlation)g
(of)g(the)h(t)m(w)m(o)h(is)d(de\014ned)g(b)m(y)i Fh(E)5
b Fj([)p Fh(\032)1843 3129 y Fg(k)r(l)1908 3114 y Fh(\032)1955
3129 y Fg(l)q(k)2019 3114 y Fj(].)373 3379 y Fh(E)g Fj([)p
Fh(\032)517 3394 y Fg(k)r(l)582 3379 y Fh(\032)629 3394
y Fg(l)q(k)693 3379 y Fj(])26 b(=)860 3318 y(1)p 850
3358 66 4 v 850 3442 a Fh(T)941 3256 y Fd(Z)1031 3282
y Fg(T)991 3462 y Ff(0)1102 3379 y Fh(\032)1149 3394
y Fg(k)r(l)1213 3379 y Fj(\()p Fh(\034)10 b Fj(\))p Fh(\032)1380
3394 y Fg(k)r(l)1445 3379 y Fj(\()p Fh(\034)31 b Fb(\000)20
b Fh(T)13 b Fj(\))p Fh(d\034)1845 b Fj(\(6\))744 3638
y(=)921 3576 y(1)p 850 3617 189 4 v 850 3700 a Fh(T)13
b(N)999 3674 y Ff(2)1063 3552 y Fd(X)1117 3747 y Fg(i)1209
3552 y Fd(X)1259 3747 y Fg(j)1356 3552 y Fd(X)1390 3742
y Fg(m)1502 3552 y Fd(X)1547 3742 y Fg(n)1649 3514 y
Fd(Z)1740 3540 y Fg(T)1699 3720 y Ff(0)1810 3638 y Fh(R)1879
3652 y Fg(p)1919 3638 y Fj(\()p Fh(\034)30 b Fb(\000)20
b Fj(\()p Fh(j)26 b Fb(\000)20 b Fh(i)p Fj(\))p Fh(T)2423
3652 y Fg(c)2459 3638 y Fj(\))p Fh(R)2563 3652 y Fg(p)2603
3638 y Fj(\()p Fh(\034)30 b Fb(\000)20 b Fj(\()p Fh(m)h
Fb(\000)f Fh(n)p Fj(\))p Fh(T)3169 3652 y Fg(c)3223 3638
y Fb(\000)g Fh(T)13 b Fj(\))p Fh(d\034)173 b Fj(\(7\))3675
3881 y(\(8\))94 4083 y(for)39 b Fh(T)54 b Fb(6)p Fj(=)40
b Fh(T)513 4097 y Fg(c)548 4083 y Fj(,)i(and)c Fh(R)869
4097 y Fg(p)909 4083 y Fj(\()p Fh(\034)10 b Fj(\))41
b(=)g(0)f(when)e Fb(j)p Fh(\034)10 b Fb(j)41 b(\025)f
Fh(T)1818 4097 y Fg(c)1853 4083 y Fj(,)i(then)d Fh(E)5
b Fj([)p Fh(\032)2280 4098 y Fg(k)r(l)2346 4083 y Fh(\032)2393
4098 y Fg(l)q(k)2457 4083 y Fj(])41 b(=)f(0.)69 b(Therefore,)41
b(the)f(t)m(w)m(o)h(cross-)94 4196 y(correlations)30
b(are)h(uncorrelated.)1920 5635 y(1)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF