4.6.yingyao.ps

是multiuser detection 这本书的习题解答, 很有用的书.

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%%EndProlog
%%BeginSetup
%%Feature: *Resolution 300
TeXDict begin @letter
%%EndSetup
%%Page: 1 1
bop 812 307 a Fj(Solution)21 b(to)d(4.6)866 357 y Fi(Yingw)o(ei)13
b(Y)m(ao)262 457 y(4.6)f(\(a\))i(The)h(receiv)o(ed)g(signal)e(is)713
584 y Fh(y)q Fi(\()p Fh(t)p Fi(\))g(=)853 532 y Fg(K)838 545
y Ff(X)838 634 y Fg(k)q Fe(=1)905 584 y Fh(A)936 590 y Fg(k)957
584 y Fh(b)975 590 y Fg(k)995 584 y Fh(s)1014 590 y Fg(k)1035
584 y Fi(\()p Fh(t)p Fi(\))c(+)h Fh(\033)q(n)p Fi(\()p Fh(t)p
Fi(\))p Fh(;)262 708 y Fi(so)j(giv)o(en)h(the)g(transmitted)g(bits)g
Fd(b)p Fi(,)f(the)h(output)g(of)f(matc)o(hed)h(\014lter)g(1)f(is)757
833 y Fh(y)777 839 y Fe(1)808 833 y Fi(=)867 782 y Fg(K)852
794 y Ff(X)851 883 y Fg(k)q Fe(=1)919 833 y Fh(A)950 839 y
Fg(k)970 833 y Fh(b)988 839 y Fg(k)1009 833 y Fh(\032)1030
839 y Fg(k)q Fe(1)1076 833 y Fi(+)d Fh(\033)q(n)1168 839 y
Fe(1)1186 833 y Fh(;)262 958 y Fi(where)i Fh(n)404 964 y Fe(1)433
958 y Fi(is)f(a)g(zero-mean,)g(unit-v)n(ariance)f(Gaussian)h(random)e(v)n
(ariable.)16 b(Giv)o(en)11 b Fh(b)1591 964 y Fe(1)1620 958
y Fi(=)h Fh(b)p Fi(,)480 1083 y Fh(P)6 b Fi(\()p Fh(y)549 1089
y Fe(1)568 1083 y Fc(j)p Fh(b)598 1089 y Fe(1)627 1083 y Fi(=)12
b Fh(b)p Fi(\))g(=)f Fh(C)h Fc(\001)832 1043 y Ff(X)849 1141
y Fd(b)828 1165 y Fb(b)844 1171 y(1)860 1165 y(=b)909 1083
y Fi(exp)p Fc(f\000)1051 1055 y Fi(1)p 1030 1073 64 2 v 1030
1111 a(2)p Fh(\033)1075 1117 y Fe(2)1098 1083 y Fi(\()p Fh(y)1134
1089 y Fe(1)1162 1083 y Fc(\000)1219 1031 y Fg(K)1204 1043
y Ff(X)1204 1133 y Fg(k)q Fe(=1)1271 1083 y Fh(A)1302 1089
y Fg(k)1323 1083 y Fh(b)1341 1089 y Fg(k)1361 1083 y Fh(\032)1382
1089 y Fg(k)q Fe(1)1419 1083 y Fi(\))1435 1066 y Fe(2)1454
1083 y Fc(g)262 1252 y Fi(Since)17 b Fh(P)6 b Fi(\()p Fh(b)440
1258 y Fe(1)476 1252 y Fi(=)17 b(1\))g(=)h Fh(P)6 b Fi(\()p
Fh(b)696 1258 y Fe(1)731 1252 y Fi(=)17 b Fc(\000)p Fi(1\))h(=)921
1235 y Fe(1)p 921 1242 17 2 v 921 1266 a(2)943 1252 y Fi(,)f(the)h(minim)n
(um)o(-error-probabili)o(t)o(y)c(decision)262 1302 y(rule)g(is)f(just)h(the)h
(maxim)n(um)o(-l)o(ik)o(eli)o(ho)q(o)q(d)c(decision)j(rule,)g(that)f(is)712
1377 y(^)713 1388 y Fh(b)731 1394 y Fe(1)761 1388 y Fi(=)f(arg)39
b(max)870 1417 y Fg(b)p Fa(2f)p Fe(1)p Fg(;)p Fa(\000)p Fe(1)p
Fa(g)1017 1388 y Fh(P)6 b Fi(\()p Fh(y)1086 1394 y Fe(1)1105
1388 y Fc(j)p Fh(b)1135 1394 y Fe(1)1164 1388 y Fi(=)12 b Fh(b)p
Fi(\))262 1499 y(If)h(the)i(op)q(en-ey)o(e)f(condition)g(is)f(satis\014ed)i
(then,)720 1624 y Fh(sg)q(n)p Fi(\()p Fh(b)819 1630 y Fe(1)838
1624 y Fi(\))d(=)g Fh(sg)q(n)p Fi(\()1007 1572 y Fg(K)991 1584
y Ff(X)991 1674 y Fg(k)q Fe(=1)1059 1624 y Fh(A)1090 1630 y
Fg(k)1111 1624 y Fh(b)1129 1630 y Fg(k)1149 1624 y Fh(\032)1170
1630 y Fg(k)q Fe(1)1207 1624 y Fi(\))p Fh(;)262 1748 y Fi(so)h(the)i(minim)n
(um)o(-error-probabil)o(it)o(y)c(decision)j(rule)g(is)862 1824
y(^)863 1835 y Fh(b)881 1841 y Fe(1)911 1835 y Fi(=)e Fh(sg)q(n)p
Fi(\()p Fh(y)1056 1841 y Fe(1)1076 1835 y Fi(\))262 1922 y(\(b\))i(Giv)o(en)f
Fd(b)p Fi(,)665 1972 y Fh(y)685 1978 y Fe(1)716 1972 y Fi(=)f
Fh(A)791 1978 y Fe(1)810 1972 y Fi(\()p Fh(b)844 1978 y Fe(1)871
1972 y Fc(\000)e Fi(0)p Fh(:)p Fi(8)p Fh(b)985 1978 y Fe(2)1012
1972 y Fi(+)f(0)p Fh(:)p Fi(3)p Fh(b)1125 1978 y Fe(3)1143
1972 y Fi(\))g(+)g Fh(\033)q(n)1259 1978 y Fe(1)1278 1972 y
Fh(;)262 2044 y Fi(If)16 b(there)i(is)f(no)g(noise,)g(then)h(when)f
Fh(b)867 2050 y Fe(1)902 2044 y Fi(=)g(1,)g Fh(y)1021 2050
y Fe(1)1057 2044 y Fi(can)g(only)f(tak)o(e)h(four)g(p)q(ossible)g(v)n(alues:)
262 2093 y(0)p Fh(:)p Fi(5)p Fh(;)7 b Fc(\000)p Fi(0)p Fh(:)p
Fi(1)p Fh(;)g Fi(2)p Fh(:)o Fi(1)p Fh(;)f Fi(1)p Fh(:)p Fi(5)o(;)19
b(similarly)d(when)k Fh(b)902 2099 y Fe(1)941 2093 y Fi(=)h
Fc(\000)p Fi(1,)f Fh(y)1099 2099 y Fe(1)1138 2093 y Fi(can)f(tak)o(e)h(the)g
(follo)o(wing)c(v)n(alues:)262 2143 y Fc(\000)p Fi(0)p Fh(:)p
Fi(5)p Fh(;)7 b Fi(0)p Fh(:)p Fi(1)p Fh(;)g Fc(\000)p Fi(2)p
Fh(:)o Fi(1)p Fh(;)g Fc(\000)p Fi(1)p Fh(:)o Fi(5.)16 b(When)784
2126 y Fg(A)809 2130 y Fb(1)p 784 2133 42 2 v 794 2158 a Fg(\033)842
2143 y Fc(!)c(1)p Fi(,)i(the)h(minim)n(um)o(-)o(error)e(-probabilit)o(y)f
(decision)262 2193 y(region)h(for)h Fh(b)468 2199 y Fe(1)498
2193 y Fi(=)d(1)j(is)755 2243 y(\012)785 2249 y Fe(1)815 2243
y Fi(=)e([)p Fc(\000)p Fi(0)p Fh(:)p Fi(3)p Fh(;)7 b Fi(0])g
Fc([)i Fi([0)p Fh(:)p Fi(3)p Fh(;)e Fc(1)p Fi(])p Fh(;)262
2315 y Fi(and)13 b(the)i(decision)f(region)f(for)h Fh(b)777
2321 y Fe(1)807 2315 y Fi(=)e Fc(\000)p Fi(1)i(is)901 2402
y(\012)931 2408 y Fe(2)961 2402 y Fi(=)e(\012)1035 2385 y Fg(c)1035
2412 y Fe(1)967 2574 y Fi(1)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF