6.4.yingyao.ps

是multiuser detection 这本书的习题解答, 很有用的书.

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E end
%%EndProlog
%%BeginSetup
%%Feature: *Resolution 300
TeXDict begin @letter
%%EndSetup
%%Page: 1 1
bop 634 482 a Fl(Solution)21 b(to)h(Problem)f(6.4)843 602 y
Fk(Yingw)o(ei)15 b(Y)l(ao)827 700 y(April)g(16,)h(1999)262
846 y Fj(Without)c(loss)g(of)g(generalit)o(y)m(,)g(w)o(e)h(will)e(fo)q(cus)i
(on)g(the)g(detector)h(for)f(user)h(1.)j(When)c(using)262 896
y(di\013eren)o(tially-coheren)o(t)h(demo)q(dulation,)d(the)k(receiv)o(ed)g(w)
o(a)o(v)o(eform)d(is)358 1019 y Fi(y)q Fj(\()p Fi(t)p Fj(\))h(=)498
967 y Fh(K)483 980 y Fg(X)482 1069 y Fh(k)q Ff(=1)550 1019
y Fe(j)p Fi(A)593 1025 y Fh(k)613 1019 y Fe(j)p Fi(e)644 1002
y Fh(j)r(\022)676 1006 y Fd(k)695 1019 y Fj(\()p Fi(e)730 1025
y Fh(k)751 1019 y Fj([)p Fi(i)c Fe(\000)h Fj(1])p Fi(s)880
1025 y Fh(k)900 1019 y Fj(\()p Fi(t)f Fe(\000)h Fi(iT)15 b
Fj(+)10 b Fi(T)c Fj(\))j(+)h Fi(e)1193 1025 y Fh(k)1213 1019
y Fj([)p Fi(i)p Fj(])p Fi(s)1270 1025 y Fh(k)1291 1019 y Fj(\()p
Fi(t)f Fe(\000)g Fi(iT)d Fj(\)\))k(+)g Fi(\033)q(n)p Fj(\()p
Fi(t)p Fj(\))262 1143 y(Assume)f(the)i(linear)e(transformation)f(w)o(e)i(use)
g(is)g Fi(v)q Fj(\()p Fi(t)p Fj(\))i(=)1155 1112 y Fg(P)1199
1156 y Fh(k)1226 1143 y Fi(v)1246 1149 y Fh(k)1267 1143 y Fi(s)1286
1149 y Fh(k)1307 1143 y Fj(\()p Fi(t)p Fj(\),)e(then)h(the)f(decisions)262
1193 y(are)k(giv)o(en)f(b)o(y)707 1232 y(^)709 1243 y Fi(b)727
1249 y Fh(k)747 1243 y Fj([)p Fi(i)p Fj(])e(=)h Fi(sg)q(n)p
Fj(\()p Fe(<f)p Fi(y)993 1226 y Fc(\003)992 1253 y Ff(1)1013
1243 y Fj([)p Fi(i)d Fe(\000)h Fj(1])p Fi(y)1143 1249 y Ff(1)1161
1243 y Fj([)p Fi(i)p Fj(])p Fe(g)p Fj(\))p Fi(;)262 1314 y
Fj(where)699 1384 y Fi(y)719 1390 y Ff(1)738 1384 y Fj([)p
Fi(i)p Fj(])h(=)831 1327 y Fg(Z)873 1338 y Fh(iT)t Ff(+)p Fh(T)854
1422 y(iT)967 1384 y Fi(y)q Fj(\()p Fi(t)p Fj(\))p Fi(v)1056
1367 y Fc(\003)1077 1384 y Fj(\()p Fi(t)e Fe(\000)h Fi(iT)c
Fj(\))p Fi(dt)262 1476 y Fj(Denote)14 b Fi(\014)427 1482 y
Fh(k)459 1476 y Fj(=)p Fi(<)e(s)554 1482 y Fh(k)575 1476 y
Fi(;)7 b(v)13 b(>)p Fj(,)h(then)673 1599 y Fi(y)693 1605 y
Ff(1)712 1599 y Fj([)p Fi(i)p Fj(])d(=)820 1547 y Fh(K)805
1559 y Fg(X)805 1648 y Fh(k)q Ff(=1)872 1599 y Fe(j)p Fi(A)915
1605 y Fh(k)935 1599 y Fe(j)p Fi(e)966 1581 y Fh(j)r(\022)998
1585 y Fd(k)1018 1599 y Fi(\014)1041 1605 y Fh(k)1062 1599
y Fi(e)1081 1605 y Fh(k)1101 1599 y Fj([)p Fi(i)p Fj(])e(+)g
Fi(n)1214 1605 y Ff(1)1233 1599 y Fj([)p Fi(i)p Fj(])p Fi(:)262
1723 y(n)287 1729 y Ff(1)305 1723 y Fj([)p Fi(i)p Fj(])14 b(is)g(a)h(complex)
e(Gaussian)h(random)f(v)n(ariable)h(with)g(indep)q(enden)o(t)i(real)e(and)h
(imagi-)262 1772 y(nary)e(parts)i(eac)o(h)f(has)g(zero)h(mean)e(and)g(v)n
(ariance)802 1857 y Fi(\033)827 1840 y Ff(2)846 1857 y Fe(k)p
Fi(v)q Fe(k)909 1840 y Ff(2)939 1857 y Fj(=)f Fi(\033)1008
1840 y Ff(2)1027 1857 y Fb(v)1053 1840 y Ff(H)1080 1857 y Fb(Rv)p
Fi(;)262 1942 y Fj(where)k Fb(v)g Fj(=)f([v)505 1948 y Ff(1)523
1942 y Fi(;)7 b Fj(v)564 1948 y Ff(2)582 1942 y Fi(;)g Fe(\001)g(\001)g(\001)
t Fi(;)g Fj(v)696 1948 y Ff(K)723 1942 y Fj(])735 1927 y Ff(T)761
1942 y Fj(,)15 b Fb(R)h Fj(is)f(the)h(cross-correlation)h(matrix)d(of)h(the)h
(signature)262 1992 y(v)o(ectors.)j(F)m(ollo)o(w)12 b(the)i(deriv)n(ation)f
(of)g(Section)i(3.7,)d(let)763 2076 y Fb(e)p Fj([i])e(=)h([1)p
Fi(;)c Fj(e)944 2082 y Ff(2)962 2076 y Fj([i])p Fi(;)g Fe(\001)g(\001)g(\001)
t Fi(;)g Fj(e)1108 2082 y Ff(K)1135 2076 y Fj([i]])p Fi(:)262
2161 y Fj(and)454 2220 y Fb(a)12 b Fj(=)624 2192 y Fb(1)p 538
2210 197 2 v 538 2255 a(2)p Fi(\033)587 2218 y Fe(p)p 621 2218
114 2 v 621 2255 a Fb(v)647 2243 y Ff(T)673 2255 y Fb(Rv)740
2220 y Fj([)p Fb(A)788 2232 y(1)813 2220 y Fi(\014)836 2232
y Fb(1)863 2220 y(e)885 2199 y(j)p Fh(\022)916 2215 y Fb(1)943
2220 y Fi(;)7 b Fb(A)998 2232 y(2)1023 2220 y Fi(\014)1046
2232 y Fb(2)1073 2220 y(e)1095 2199 y(j)p Fh(\022)1126 2215
y Fb(2)1153 2220 y Fi(;)g Fe(\001)g(\001)g(\001)e Fi(;)i Fb(A)1282
2234 y(K)1321 2220 y Fi(\014)1344 2234 y Fb(K)1384 2220 y(e)1406
2197 y(j)p Fh(\022)1437 2215 y Fb(K)1478 2220 y Fj(])p Fi(;)262
2312 y Fj(then)14 b(the)h(error)f(probabilit)o(y)f(of)g(this)h(linear)f
(detector)j(for)d(user)i(1)f(is)349 2403 y Fi(P)382 2386 y
Fh(dcv)376 2413 y Ff(1)433 2403 y Fj(\()p Fi(\033)q Fj(\))e(=)g(4)567
2386 y Ff(1)p Fc(\000)p Fh(K)660 2363 y Fg(X)648 2454 y Fb(e)p
Ff([)p Fc(\000)p Ff(1])738 2363 y Fg(X)740 2454 y Fb(e)p Ff([0])805
2403 y Fi(T)6 b Fj(\()p Fe(j)p Fb(a)886 2386 y Ff(T)912 2403
y Fj(\()p Fb(e)p Fj([)p Fe(\000)p Fj(1])i Fe(\000)i Fb(e)p
Fj([0]\))p Fe(j)p Fi(;)d Fe(j)p Fb(a)1226 2386 y Ff(T)1249
2403 y Fj(\()p Fb(e)p Fj([)p Fe(\000)p Fj(1])h(+)i Fb(e)p Fj([0]\))p
Fe(j)p Fj(\))116 b(\(1\))967 2574 y(1)p eop
%%Page: 2 2
bop 262 307 a Fj(The)14 b(single)f(user)i(error)g(probabilit)o(y)d(of)i
(di\013eren)o(tially-coheren)o(t)g(demo)q(dulation)e(is)780
416 y Fi(P)813 399 y Fh(dc)807 426 y Ff(1)847 416 y Fj(\()p
Fi(\033)q Fj(\))g(=)965 388 y(1)p 965 406 21 2 v 965 444 a(2)990
416 y Fi(e)1009 399 y Fc(\000)p Fh(A)1060 386 y Fa(2)1060 407
y(1)1077 399 y Fh(=)p Ff(\(2)p Fh(\033)1144 386 y Fa(2)1160
399 y Ff(\))262 519 y Fj(so)h(the)i(asymptotic)e(m)o(ultiuser)f(e\016ciency)j
(is)596 615 y Fi(\021)617 621 y Ff(1)647 615 y Fj(=)d Fi(sup)p
Fe(f)p Fj(0)f Fe(\024)h Fi(r)g Fe(\024)g Fj(1)f(:)17 b(lim)982
641 y Fh(\033)q Fc(!)p Ff(0)1059 615 y Fi(P)1086 621 y Fh(k)1106
615 y Fj(\()p Fi(\033)q Fj(\))p Fi(e)1182 598 y Fh(r)q(A)1223
586 y Fa(2)1223 607 y(1)1240 598 y Fh(=)p Ff(\(2)p Fh(\033)1307
586 y Fa(2)1323 598 y Ff(\))1338 615 y Fe(g)262 720 y Fj(When)d
Fi(\033)h Fj(go)q(es)f(to)g(0,)336 828 y Fi(T)6 b Fj(\()p Fi(a;)h(b)p
Fj(\))k(=)h Fi(Q)p Fj(\()p Fi(a;)7 b(b)p Fj(\))i Fe(\000)691
800 y Fj(1)p 691 819 V 691 857 a(2)717 828 y Fi(I)735 834 y
Ff(0)754 828 y Fj(\()p Fi(ab)p Fj(\))e(exp\()p Fe(\000)p Fj([)p
Fi(a)978 811 y Ff(2)1006 828 y Fj(+)i Fi(b)1065 811 y Ff(2)1084
828 y Fj(])p Fi(=)p Fj(2\))i Fe(\030)g Fi(O)q Fj(\()p Fi(\033)e
Fj(exp[)p Fe(\000)p Fj(\()p Fi(b)g Fe(\000)g Fi(a)p Fj(\))1519
811 y Ff(2)1538 828 y Fj(])p Fi(=)p Fj(2\))p Fi(;)262 934 y
Fj(So)k(as)h Fi(\033)f Fe(!)e Fj(0,)j(ev)o(ery)g(term)g(in)f(equation)h
(\(1\))g(will)e(decrease)17 b(exp)q(onen)o(tially)c(and)g(one)i(or)262
983 y(sev)o(eral)f(terms)g(with)f(largest)h(v)n(alue)f(will)g(dominate.)j
(Denote)556 1089 y Fb(b)11 b Fj(=)h([)p Fb(A)686 1101 y(1)711
1089 y Fi(\014)734 1101 y Fb(1)761 1089 y(e)783 1068 y(j)p
Fh(\022)814 1084 y Fb(1)841 1089 y Fi(;)7 b Fb(A)896 1101 y(2)922
1089 y Fi(\014)945 1101 y Fb(2)971 1089 y(e)993 1068 y(j)p
Fh(\022)1024 1084 y Fb(2)1051 1089 y Fi(;)g Fe(\001)g(\001)g(\001)e
Fi(;)i Fb(A)1180 1103 y(K)1219 1089 y Fi(\014)1242 1103 y Fb(K)1282
1089 y(e)1304 1066 y(j)p Fh(\022)1335 1084 y Fb(K)1376 1089
y Fj(])p Fi(;)262 1180 y Fj(then)262 1281 y Fi(\021)283 1287
y Ff(1)342 1281 y Fj(=)503 1253 y(1)p 421 1271 185 2 v 421
1309 a(4)p Fi(A)473 1295 y Ff(2)473 1320 y(1)492 1309 y Fb(v)518
1297 y Ff(H)544 1309 y Fb(Rv)618 1281 y Fj(min)n Fe(f)p Fj(1)p
Fi(;)46 b Fj(min)748 1309 y Fb(e)p Ff([)p Fc(\000)p Ff(1])p
Fh(;)p Fb(e)p Ff([0])897 1281 y Fe(f)p Fj(\()p Fe(j)p Fb(b)973
1264 y Ff(T)998 1281 y Fj(\()p Fb(e)p Fj([)p Fe(\000)p Fj(1])8
b Fe(\000)i Fb(e)p Fj([0]\))p Fe(j)d(\000)j(j)p Fb(b)1346 1264
y Ff(T)1370 1281 y Fj(\()p Fb(e)p Fj([)p Fe(\000)p Fj(1])f(+)g
Fb(e)p Fj([0]\))p Fe(j)p Fj(\))1646 1264 y Ff(2)1663 1281 y
Fe(gg)342 1392 y Fj(=)503 1364 y(1)p 421 1383 V 421 1421 a(4)p
Fi(A)473 1406 y Ff(2)473 1432 y(1)492 1421 y Fb(v)518 1409
y Ff(H)544 1421 y Fb(Rv)618 1392 y Fj(min)n Fe(f)p Fj(1)p Fi(;)e
Fj(min)753 1421 y Fb(e)p Ff([0])816 1392 y Fe(f)p Fj(\()p Fe(j)p
Fb(b)892 1375 y Ff(T)917 1392 y Fj(\()p Fb(e)i Fe(\000)g Fb(e)p
Fj([0]\))p Fe(j)f(\000)h(j)p Fb(b)1188 1375 y Ff(T)1213 1392
y Fj(\()p Fb(e)h Fj(+)f Fb(e)p Fj([0]\))p Fe(j)p Fj(\))1413
1375 y Ff(2)1430 1392 y Fe(gg)262 1509 y Fj(where)15 b Fb(e)c
Fj(=)h([1)p Fi(;)7 b Fj(1)p Fi(;)g Fe(\001)g(\001)g(\001)s
Fi(;)g Fj(1].)967 2574 y(2)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF