6.25.kishore.ps

是multiuser detection 这本书的习题解答, 很有用的书.

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%%EndProlog
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1 0 bop 257 262 a Fi(Solution)13 b(to)i(6.25)h(b)o(y)f(Shalinee)e
(Kishore)i(4/16/99)40 b Fh(W)m(e)14 b(kno)o(w)f(that)h(the)h(linear)257
311 y(MMSE)e(detector)h(and)e(the)h(decorrelator)g(ac)o(hiev)o(e)g(the)
g(same)e(asymptotic)g(m)o(ultiuser)h(ef-)257 361 y(\014ciency)m(.)18
b(In)11 b(other)h(w)o(ords,)g Fg(\021)724 346 y Ff(M)723
371 y Fe(1)772 361 y Fh(=)g Fg(\021)838 346 y Ff(D)837
371 y Fe(1)868 361 y Fh(.)17 b(W)m(e)11 b(also)g(kno)o(w)g(that)g(the)h
(asymptotic)e(m)o(ultiuser)257 411 y(e\016ciency)15 b(of)e(the)i(MMSE)f
(detector)i(is:)560 556 y Fg(\021)582 538 y Ff(M)581
566 y Fe(1)631 556 y Fh(=)679 512 y(max)757 497 y Fe(2)782
466 y Fd(h)802 512 y Fh(0)p Fg(;)7 b Fh(1)h Fc(\000)912
481 y Fd(P)956 492 y Ff(K)956 525 y(k)q Fe(=2)1031 495
y Ff(A)1056 499 y Fb(k)p 1031 503 44 2 v 1032 527 a Ff(A)1057
531 y Fa(1)1079 512 y Fc(j)p Fg(\032)1112 518 y Fe(1)p
Ff(k)1158 512 y Fh(+)h Fc(h)p Fg(s)1234 518 y Ff(k)1255
512 y Fg(;)e(x)1298 497 y Ff(M)1298 523 y Fe(1)1334 512
y Fc(ij)1362 466 y Fd(i)p 679 546 703 2 v 932 585 a Fh(1)i(+)h
Fc(jj)p Fg(x)1052 571 y Ff(M)1052 596 y Fe(1)1087 585
y Fc(jj)1111 573 y Fe(2)1636 556 y Fh(\(1\))257 671 y(The)15
b(asymptotic)d(m)o(ultiuser)h(e\016ciency)i(for)e(the)i(decorrelator)g
(is)e(de\014ned)i(as:)820 779 y Fg(\021)842 762 y Ff(D)841
790 y Fe(1)883 779 y Fh(=)1017 751 y(1)p 932 770 191
2 v 932 809 a(1)9 b(+)h Fc(jj)p Fg(x)1052 795 y Ff(D)1052
820 y Fe(1)1081 809 y Fc(jj)1105 797 y Fe(2)1636 779
y Fh(\(2\))257 894 y(F)m(or)k(equal)f(asymptotic)g(m)o(ultiuser)g
(e\016ciency)m(,)g(it)h(is)g(required)h(that)579 1011
y(1)p 495 1030 V 495 1069 a(1)9 b(+)g Fc(jj)p Fg(x)614
1054 y Ff(D)614 1080 y Fe(1)643 1069 y Fc(jj)667 1057
y Fe(2)701 1039 y Fh(=)750 996 y(max)827 981 y Fe(2)853
950 y Fd(h)872 996 y Fh(0)p Fg(;)e Fh(1)i Fc(\000)983
965 y Fd(P)1027 975 y Ff(K)1027 1008 y(k)q Fe(=2)1101
979 y Ff(A)1126 983 y Fb(k)p 1101 986 44 2 v 1102 1010
a Ff(A)1127 1014 y Fa(1)1149 996 y Fc(j)p Fg(\032)1182
1002 y Fe(1)p Ff(k)1228 996 y Fh(+)h Fc(h)p Fg(s)1305
1002 y Ff(k)1326 996 y Fg(;)d(x)1369 981 y Ff(M)1369
1006 y Fe(1)1405 996 y Fc(ij)1433 950 y Fd(i)p 750 1030
703 2 v 1003 1069 a Fh(1)i(+)g Fc(jj)p Fg(x)1122 1054
y Ff(M)1122 1080 y Fe(1)1158 1069 y Fc(jj)1182 1057 y
Fe(2)1636 1039 y Fh(\(3\))257 1154 y(No)o(w)14 b(observ)o(e)h(that)598
1276 y(1)d Fc(\025)f Fh(max)752 1259 y Fe(2)777 1205
y Fd(")801 1276 y Fh(0)p Fg(;)c Fh(1)i Fc(\000)927 1224
y Ff(K)912 1236 y Fd(X)912 1326 y Ff(k)q Fe(=2)984 1248
y Fg(A)1015 1254 y Ff(k)p 984 1266 52 2 v 985 1304 a
Fg(A)1016 1310 y Fe(1)1041 1276 y Fc(j)p Fg(\032)1074
1282 y Fe(1)p Ff(k)1120 1276 y Fh(+)h Fc(h)p Fg(s)1197
1282 y Ff(k)1218 1276 y Fg(;)d(x)1261 1259 y Ff(M)1261
1286 y Fe(1)1297 1276 y Fc(ij)1325 1205 y Fd(#)1636 1276
y Fh(\(4\))257 1407 y(Th)o(us,)14 b(the)h(equalit)o(y)e(in)g(\(3\))h
(implies)e(that)752 1498 y(1)d(+)h Fc(jj)p Fg(x)872 1481
y Ff(D)872 1508 y Fe(1)901 1498 y Fc(jj)925 1481 y Fe(2)954
1498 y Fc(\025)i Fh(1)d(+)g Fc(jj)p Fg(x)1117 1481 y
Ff(M)1117 1508 y Fe(1)1153 1498 y Fc(jj)1177 1481 y Fe(2)1636
1498 y Fh(\(5\))257 1589 y(F)m(rom)15 b(this)h(w)o(e)h(see)h(that)e
Fc(jj)p Fg(x)726 1574 y Ff(D)726 1600 y Fe(1)755 1589
y Fc(jj)779 1574 y Fe(2)813 1589 y Fc(\025)g(jj)p Fg(x)909
1574 y Ff(M)909 1600 y Fe(1)944 1589 y Fc(jj)968 1574
y Fe(2)986 1589 y Fh(.)26 b(Therefore,)18 b(the)f(surplus)g(energy)g
(of)f(the)257 1639 y(decorrelator,)f Fc(jj)p Fg(x)548
1624 y Ff(D)548 1649 y Fe(1)577 1639 y Fc(jj)601 1624
y Fe(2)618 1639 y Fh(,)f(is)g(greater)g(than)g(that)g(of)g(the)g
(linear)f(MMSE)i(receiv)o(er,)g Fc(jj)p Fg(x)1601 1624
y Ff(M)1601 1649 y Fe(1)1636 1639 y Fc(jj)1660 1624 y
Fe(2)1678 1639 y Fh(.)963 2628 y(1)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF