www.pudn.com > SolutionsforMultiuserDetection.rar > 2.8.kishore.ps

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y Fe(\000)k Fh(nT)16 b Fe(\000)9 b Fh(\034)c Fi(\)])184 
b(\(5\))257 1174 y(This)14 b(results)i(b)q(ecause)g(for)d 
Fh(k)g Fe(6)p Fi(=)g Fh(n)p Fi(,)g(E)q([)p Fh(b)p Fi([)p 
Fh(n)p Fi(])p Fh(b)p Fi([)p Fh(k)q Fi(]])8 b(=)13 b(0.)18 
b(Next,)d(w)o(e)f(note)h(that)f(since)h Fh(s)p Fi(\()p 
Fh(t)p Fi(\))g(is)257 1224 y(a)g(direct-sequence)i(spread-sp)q(ectrum)f 
(signal,)d(E[)p Fh(s)p Fi(\()p Fh(t)1117 1230 y Ff(1)1146 
1224 y Fe(\000)d Fh(nT)15 b Fe(\000)10 b Fh(\034)5 b 
Fi(\))p Fh(s)p Fi(\()p Fh(t)1383 1230 y Ff(2)1412 1224 
y Fe(\000)10 b Fh(nT)16 b Fe(\000)10 b Fh(\034)5 b Fi(\)])12 
b(=)h(0)257 1274 y(if)g Fh(t)310 1280 y Ff(1)338 1274 
y Fe(\000)d Fh(t)395 1280 y Ff(2)425 1274 y Fh(>)i(T)6 
b Fi(.)18 b(The)c(p)q(o)o(w)o(er)g(sp)q(ectral)h(densit)o(y)f(of)g 
Fh(z)r Fi(\()p Fh(t)p Fi(\))g(can)g(then)h(b)q(e)f(computed)g(as)661 
1377 y Fh(S)686 1383 y Fg(Z)713 1377 y Fi(\()p Fh(f)t 
Fi(\))43 b(=)886 1321 y Fd(Z)927 1331 y Fc(1)909 1415 
y(\0001)977 1377 y Fh(R)1009 1383 y Fg(Z)1035 1377 y 
Fi(\()p Fh(\033)q Fi(\))p Fh(e)1111 1360 y Fc(\000)p 
Ff(2)p Fg(\031)q(j)r(f)s(\033)1239 1377 y Fh(d\033)351 
b Fi(\(6\))812 1501 y(=)886 1445 y Fd(Z)927 1455 y Fg(T)909 
1539 y Ff(0)960 1501 y Fh(R)992 1507 y Fg(Z)1019 1501 
y Fi(\()p Fh(\033)q Fi(\))p Fh(e)1095 1484 y Fc(\000)p 
Ff(2)p Fg(\031)q(j)r(f)s(\033)1222 1501 y Fh(d\033)368 
b Fi(\(7\))257 1605 y(where)15 b Fh(\033)e Fi(=)f Fh(t)473 
1611 y Ff(1)500 1605 y Fe(\000)d Fh(t)556 1611 y Ff(2)574 
1605 y Fi(.)18 b(Replacing)13 b Fh(R)828 1611 y Fg(Z)854 
1605 y Fi(\()p Fh(\033)q Fi(\))h(as)g(p)q(er)g(\(6\))g(and)f(plugging)f 
(in)h(for)h Fh(s)p Fi(\()p Fh(t)p Fi(\),)f(w)o(e)h(can)257 
1655 y(simplify)d Fh(S)439 1661 y Fg(Z)467 1655 y Fi(\()p 
Fh(f)t Fi(\))k(in)e(the)h(follo)o(wing)e(manner)381 1768 
y Fh(S)406 1774 y Fg(Z)433 1768 y Fi(\()p Fh(f)t Fi(\))43 
b(=)642 1716 y Fc(1)628 1729 y Fd(X)606 1816 y Fg(n)p 
Ff(=)p Fc(\0001)718 1712 y Fd(Z)759 1722 y Fg(T)741 1806 
y Ff(0)792 1768 y Fi(E[)p Fh(s)p Fi(\()p Fh(t)882 1774 
y Ff(1)910 1768 y Fe(\000)10 b Fh(nT)15 b Fe(\000)10 
b Fh(\034)5 b Fi(\))p Fh(s)p Fi(\()p Fh(t)1147 1774 y 
Ff(2)1175 1768 y Fe(\000)k Fh(nT)16 b Fe(\000)9 b Fh(\034)c 
Fi(\)])p Fh(e)1392 1751 y Fc(\000)p Ff(2)p Fg(\031)q(j)r(f)s(\033)1519 
1768 y Fh(d\033)71 b Fi(\(8\))532 1916 y(=)642 1864 y 
Fc(1)628 1877 y Fd(X)606 1964 y Fg(n)p Ff(=)p Fc(\0001)718 
1860 y Fd(Z)759 1870 y Fg(T)741 1954 y Ff(0)807 1864 
y Fg(N)792 1877 y Fd(X)795 1965 y Fg(i)p Ff(=1)874 1864 
y Fg(N)859 1877 y Fd(X)863 1966 y Fg(l)p Ff(=1)919 1916 
y Fi(\()p Fe(\000)p Fi(1\))1004 1899 y Fg(c)1019 1903 
y Fb(i)1034 1916 y Fi(\()p Fe(\000)p Fi(1\))1119 1899 
y Fg(c)1134 1903 y Fb(l)1149 1916 y Fh(\026)p Fi(\()p 
Fh(t)1205 1922 y Ff(1)1223 1916 y Fh(;)7 b(i)p Fi(;)g 
Fh(t)1290 1922 y Ff(2)1308 1916 y Fh(;)g(l)q Fi(\))p 
Fh(e)1375 1899 y Fc(\000)p Ff(2)p Fg(\031)q(j)r(f)s(\033)1502 
1916 y Fh(d\033)88 b Fi(\(9\))532 2064 y(=)642 2012 y 
Fc(1)628 2025 y Fd(X)606 2112 y Fg(n)p Ff(=)p Fc(\0001)733 
2012 y Fg(N)718 2025 y Fd(X)721 2113 y Fg(i)p Ff(=1)800 
2012 y Fg(N)784 2025 y Fd(X)788 2114 y Fg(l)p Ff(=1)844 
2064 y Fi(\()p Fe(\000)p Fi(1\))929 2047 y Fg(c)944 2051 
y Fb(i)960 2064 y Fi(\()p Fe(\000)p Fi(1\))1045 2047 
y Fg(c)1060 2051 y Fb(l)1081 2008 y Fd(Z)1122 2018 y 
Fg(T)1104 2102 y Ff(0)1156 2064 y Fh(\026)p Fi(\()p Fh(t)1212 
2070 y Ff(1)1230 2064 y Fh(;)7 b(i)p Fi(;)g Fh(t)1297 
2070 y Ff(2)1315 2064 y Fh(;)g(l)q Fi(\))p Fh(e)1382 
2047 y Fc(\000)p Ff(2)p Fg(\031)q(j)r(f)s(\033)1509 2064 
y Fh(d\033)61 b Fi(\(10\))257 2183 y(where)300 2263 y 
Fh(\026)p Fi(\()p Fh(t)356 2269 y Ff(1)375 2263 y Fh(;)7 
b(i)p Fi(;)g Fh(t)442 2269 y Ff(2)460 2263 y Fh(;)g(l)q 
Fi(\))k(=)h(E)7 b([)p Fh(p)631 2269 y Fg(T)651 2273 y 
Fb(c)668 2263 y Fi(\()p Fh(t)699 2269 y Ff(1)727 2263 
y Fe(\000)i Fh(nT)15 b Fe(\000)10 b Fh(\034)k Fe(\000)c 
Fi(\()p Fh(i)f Fe(\000)h Fi(1\))p Fh(T)1090 2269 y Fg(c)1107 
2263 y Fi(\))p Fh(p)1144 2269 y Fg(T)1164 2273 y Fb(c)1181 
2263 y Fi(\()p Fh(t)1212 2269 y Ff(2)1240 2263 y Fe(\000)g 
Fh(nT)15 b Fe(\000)9 b Fh(\034)14 b Fe(\000)c Fi(\()p 
Fh(l)g Fe(\000)g Fi(1\))p Fh(T)1602 2269 y Fg(c)1619 
2263 y Fi(\)])1616 2313 y(\(11\))257 2371 y(Let)15 b(us)f(no)o(w)f 
(denote)i Fh(g)q Fi(\()p Fh(f)t Fi(\))e(=)739 2337 y 
Fd(R)767 2347 y Fg(T)759 2385 y Ff(0)800 2371 y Fh(\026)p 
Fi(\()p Fh(t)856 2377 y Ff(1)874 2371 y Fh(;)7 b(i)p 
Fi(;)g Fh(t)941 2377 y Ff(2)959 2371 y Fh(;)g(l)q Fi(\))p 
Fh(e)1026 2355 y Fc(\000)p Ff(2)p Fg(\031)q(j)r(f)s(\033)1153 
2371 y Fh(d\033)q Fi(.)18 b(Th)o(us)345 2486 y Fh(g)q 
Fi(\()p Fh(f)t Fi(\))43 b(=)548 2458 y(1)p 544 2476 31 
2 v 544 2515 a Fh(T)586 2430 y Fd(Z)627 2440 y Fg(T)609 
2524 y Ff(0)660 2430 y Fd(Z)702 2440 y Fg(T)683 2524 
y Ff(0)735 2486 y Fh(p)756 2492 y Fg(T)776 2496 y Fb(c)793 
2486 y Fi(\()p Fh(t)824 2492 y Ff(1)852 2486 y Fe(\000)9 
b Fh(nT)16 b Fe(\000)9 b Fh(\034)14 b Fe(\000)c Fi(\()p 
Fh(i)f Fe(\000)h Fi(1\))p Fh(T)1215 2492 y Fg(c)1232 
2486 y Fi(\))f Fe(\001)347 b Fi(\(12\))963 2628 y(1)p 
eop 
%%Page: 2 2 
2 1 bop 622 262 a Fh(p)643 268 y Fg(T)663 272 y Fb(c)680 
262 y Fi(\()p Fh(t)711 268 y Ff(2)739 262 y Fe(\000)9 
b Fh(nT)16 b Fe(\000)9 b Fh(\034)14 b Fe(\000)c Fi(\()p 
Fh(l)g Fe(\000)g Fi(1\))p Fh(T)1101 268 y Fg(c)1118 262 
y Fi(\))p Fh(e)1153 244 y Fc(\000)p Ff(2)p Fg(\031)q(j)r(f)s(\033)1280 
262 y Fh(d\034)i(d\033)238 b Fi(\(13\))465 355 y(=)548 
327 y(1)p 544 345 31 2 v 544 383 a Fh(T)586 298 y Fd(Z)627 
308 y Fg(T)609 392 y Ff(0)660 298 y Fd(Z)702 308 y Fg(T)683 
392 y Ff(0)735 355 y Fh(p)756 361 y Fg(T)776 365 y Fb(c)793 
355 y Fi(\()p Fh(t)824 361 y Ff(1)852 355 y Fe(\000)9 
b Fh(nT)16 b Fe(\000)9 b Fh(\034)14 b Fe(\000)c Fi(\()p 
Fh(i)f Fe(\000)h Fi(1\))p Fh(T)1215 361 y Fg(c)1232 355 
y Fi(\))f Fe(\001)347 b Fi(\(14\))622 446 y Fh(p)643 
452 y Fg(T)663 456 y Fb(c)680 446 y Fi(\()p Fh(t)711 
452 y Ff(1)739 446 y Fe(\000)9 b Fh(\033)i Fe(\000)e 
Fh(nT)16 b Fe(\000)9 b Fh(\034)14 b Fe(\000)c Fi(\()p 
Fh(l)g Fe(\000)g Fi(1\))p Fh(T)1177 452 y Fg(c)1194 446 
y Fi(\))p Fh(e)1229 429 y Fc(\000)p Ff(2)p Fg(\031)q(j)r(f)s(\033)1356 
446 y Fh(d\034)i(d\033)162 b Fi(\(15\))465 539 y(=)548 
511 y(1)p 544 530 V 544 568 a Fh(T)586 483 y Fd(Z)627 
493 y Fg(T)609 577 y Ff(0)660 539 y Fh(p)681 545 y Fg(T)701 
549 y Fb(c)718 539 y Fi(\()p Fh(t)749 545 y Ff(1)777 
539 y Fe(\000)10 b Fh(nT)15 b Fe(\000)10 b Fh(\034)k 
Fe(\000)9 b Fi(\()p Fh(i)h Fe(\000)f Fi(1\))p Fh(T)1140 
545 y Fg(c)1157 539 y Fi(\))h Fe(\001)421 b Fi(\(16\))622 
596 y Fd( )655 610 y(Z)696 620 y Fg(T)678 704 y Ff(0)729 
666 y Fh(p)750 672 y Fg(T)770 676 y Fb(c)787 666 y Fi(\()p 
Fh(t)818 672 y Ff(1)846 666 y Fe(\000)10 b Fh(\033)g 
Fe(\000)g Fh(nT)15 b Fe(\000)9 b Fh(\034)15 b Fe(\000)9 
b Fi(\()p Fh(l)i Fe(\000)e Fi(1\))p Fh(T)1284 672 y Fg(c)1301 
666 y Fi(\))p Fh(e)1336 649 y Fc(\000)p Ff(2)p Fg(\031)q(j)r(f)s(\033) 
1464 666 y Fh(d\033)1511 596 y Fd(!)1557 666 y Fh(d\034)19 
b Fi(\(17\))257 793 y(In)14 b(the)g(\014rst)h(line)e(ab)q(o)o(v)o(e,)g 
(w)o(e)g(used)i(the)f(fact)g(that)f Fh(\034)19 b Fi(is)13 
b(a)h(uniform)d(random)h(v)n(ariable)h(on)257 843 y(the)18 
b(in)o(terv)n(al)d([0)p Fh(;)7 b(T)f Fi(])15 b(to)i(explicitly)e 
(compute)h(the)h(exp)q(ectation)h(in)e Fh(\026)p Fi(\()p 
Fh(t)1408 849 y Ff(1)1427 843 y Fh(;)7 b(i)p Fi(;)g Fh(t)1494 
849 y Ff(2)1511 843 y Fh(;)g(l)q Fi(\).)26 b(No)o(w,)257 
892 y(observ)o(e)15 b(that,)257 956 y Fd(Z)299 966 y 
Fg(T)280 1050 y Ff(0)332 1012 y Fh(p)353 1018 y Fg(T)373 
1022 y Fb(c)390 1012 y Fi(\()p Fh(t)421 1018 y Ff(1)448 
1012 y Fe(\000)8 b Fh(\033)h Fe(\000)g Fh(nT)k Fe(\000)c 
Fh(\034)k Fe(\000)8 b Fi(\()p Fh(l)h Fe(\000)f Fi(1\))p 
Fh(T)874 1018 y Fg(c)892 1012 y Fi(\))p Fh(e)927 995 
y Fc(\000)p Ff(2)p Fg(\031)q(j)r(f)s(\033)1054 1012 y 
Fh(d\033)k Fi(=)g Fh(S)1183 995 y Fc(\003)1181 1023 y 
Fg(p)1203 1012 y Fi(\()p Fh(f)t Fi(\))p Fh(e)1278 995 
y Fc(\000)p Ff(2)p Fg(\031)q(j)r(f)s Ff(\()p Fg(t)1402 
999 y Fa(1)1419 995 y Fc(\000)p Fg(nT)t Fc(\000)p Fg(\034)s 
Fc(\000)p Ff(\()p Fg(l)p Fc(\000)p Ff(1\))p Fg(T)1659 
999 y Fb(c)1674 995 y Ff(\))1616 1085 y Fi(\(18\))257 
1135 y(where)j Fh(S)402 1141 y Fg(p)422 1135 y Fi(\()p 
Fh(f)t Fi(\))g(is)f(the)g(p)q(o)o(w)o(er)h(sp)q(ectral)g(densit)o(y)f 
(of)f(the)i(c)o(hip)e(w)o(a)o(v)o(eform)f Fh(p)1441 1141 
y Fg(T)1461 1145 y Fb(c)1478 1135 y Fi(\()p Fh(t)p Fi(\).)19 
b(W)m(e)13 b(can)257 1185 y(further)i(simplify)c Fh(g)q 
Fi(\()p Fh(f)t Fi(\):)356 1304 y Fh(g)q Fi(\()p Fh(f)t 
Fi(\))43 b(=)555 1272 y Fh(S)582 1257 y Fc(\003)580 1282 
y Fg(p)602 1272 y Fi(\()p Fh(f)t Fi(\))p 555 1295 105 
2 v 592 1333 a Fh(T)664 1304 y(e)683 1287 y Fc(\000)p 
Ff(2)p Fg(\031)q(j)r(f)s Ff(\()p Fg(t)807 1291 y Fa(1)823 
1287 y Fc(\000)p Fg(nT)t Fc(\000)p Ff(\()p Fg(l)p Fc(\000)p 
Ff(1\))p Fg(T)1019 1291 y Fb(c)1033 1287 y Ff(\))1058 
1304 y Fe(\001)546 b Fi(\(19\))550 1359 y Fd(Z)591 1369 
y Fg(T)573 1453 y Ff(0)624 1416 y Fh(p)645 1422 y Fg(T)665 
1426 y Fb(c)682 1416 y Fi(\()p Fh(t)713 1422 y Ff(1)741 
1416 y Fe(\000)10 b Fh(nT)15 b Fe(\000)10 b Fh(\034)k 
Fe(\000)9 b Fi(\()p Fh(i)h Fe(\000)f Fi(1\))p Fh(T)1104 
1422 y Fg(c)1121 1416 y Fi(\))p Fh(e)1156 1398 y Ff(2)p 
Fg(\031)q(j)r(f)s(\034)1256 1416 y Fh(d\034)320 b Fi(\(20\))476 
1533 y(=)555 1501 y Fh(S)582 1486 y Fc(\003)580 1511 
y Fg(p)602 1501 y Fi(\()p Fh(f)t Fi(\))p 555 1524 V 592 
1562 a Fh(T)664 1533 y(e)683 1516 y Fc(\000)p Ff(2)p 
Fg(\031)q(j)r(f)s Ff(\()p Fg(t)807 1520 y Fa(1)823 1516 
y Fc(\000)p Fg(nT)t Fc(\000)p Ff(\()p Fg(l)p Fc(\000)p 
Ff(1\))p Fg(T)1019 1520 y Fb(c)1033 1516 y Ff(\))1058 
1533 y Fe(\001)8 b Fh(S)1103 1539 y Fg(p)1123 1533 y 
Fi(\()p Fh(f)t Fi(\))p Fh(e)1198 1516 y Fc(\000)p Ff(2)p 
Fg(\031)q(j)r(f)s Ff(\()p Fc(\000)p Fg(t)1348 1520 y 
Fa(1)1365 1516 y Ff(+)p Fg(nT)t Ff(+\()p Fg(i)p Fc(\000)p 
Ff(1\))p Fg(T)1561 1520 y Fb(c)1576 1516 y Ff(\))1616 
1533 y Fi(\(21\))476 1640 y(=)555 1612 y Fe(j)p Fh(S)592 
1618 y Fg(p)611 1612 y Fi(\()p Fh(f)t Fi(\))p Fe(j)679 
1597 y Ff(2)p 555 1631 144 2 v 611 1669 a Fh(T)703 1640 
y(e)722 1623 y Fc(\000)p Ff(2)p Fg(\031)q(j)r(f)s Ff(\()p 
Fg(i)p Fc(\000)p Fg(l)p Ff(\))p Fg(T)914 1627 y Fb(c)1616 
1640 y Fi(\(22\))257 1745 y(W)m(e)18 b(can)h(then)g(plug)f(this)h 
(result)g(in)o(to)f(\(11\))g(to)g(obtain)g(the)h(\014nal)f(expression)i 
(for)e(the)257 1795 y(p)q(o)o(w)o(er)d(sp)q(ectral)g(densit)o(y)f(of)f 
Fh(z)r Fi(\()p Fh(t)p Fi(\).)963 2628 y(2)p eop 
%%Trailer 
end 
userdict /end-hook known{end-hook}if 
%%EOF