5.17.huaidai.ps

是multiuser detection 这本书的习题解答, 很有用的书.

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D E end
TeXDict begin

1 0 bop 1146 569 a Fl(ELE533)52 b(Homew)l(ork)f(7)1586
951 y Fk(Huaiyu)40 b(Dai)1596 1269 y Fj(7)f(Apr)f(1999)-186
1730 y Fi(PR)m(OBLEM)33 b(5.17.)p Fh(Sho)m(w)e(that)e(in)g(the)h(t)m(w)
m(o-user)g(async)m(hronous)i(c)m(hannel,)f(the)f(necesssary)i(and)e
(su\016cien)m(t)-186 1850 y(condition)h(for)h(the)h(existence)h(of)e(a)
h(stable)f(realization)e(of)i(the)h(decorrelating)e(detector)j(is)1537
2070 y Fg(j)p Ff(\032)1615 2085 y Fe(12)1690 2070 y Fg(j)21
b Fh(+)h Fg(j)p Ff(\032)1915 2085 y Fe(21)1990 2070 y
Fg(j)28 b Ff(<)f Fh(1)p Ff(:)-186 2376 y Fi(Solution)p
Fh(:)-186 2582 y(A)47 b(stable)h(realization)c(for)j(decorrelating)f
(detector)j(for)d(the)i(async)m(hronous)i(c)m(hannel)e(exsits)g(as)f
(long)g(as)-186 2702 y(det)p Fi(S)p Fh(\()p Ff(z)t Fh(\))34
b(has)f(no)f(zeros)i(on)e(the)h(unit)f(circle.)43 b(F)-8
b(or)32 b(the)h(t)m(w)m(o-user)g(case,)h(this)e(b)s(ecomes)682
2922 y(\(1)22 b Fg(\000)h Ff(\032)941 2881 y Fe(2)941
2947 y(12)1038 2922 y Fg(\000)g Ff(\032)1188 2881 y Fe(2)1188
2947 y(21)1263 2922 y Fh(\))f Fg(\000)g Ff(\032)1472
2937 y Fe(12)1547 2922 y Ff(\032)1597 2937 y Fe(21)1672
2922 y Fh(\()p Ff(e)1755 2881 y Fd(j)t(!)1861 2922 y
Fh(+)g Ff(e)2004 2881 y Fc(\000)p Fd(j)t(!)2141 2922
y Fh(\))28 b Fg(6)p Fh(=)g(0)f(for)32 b(all)p Ff(!)d
Fg(2)f Fh([0)p Ff(;)17 b Fh(2)p Ff(\031)t Fh(])743 b(\(1\))-186
3142 y(where)1348 3287 y Ff(\032)1398 3302 y Fe(12)1501
3287 y Fh(=)1605 3170 y Fb(Z)1688 3196 y Fd(T)1651 3358
y(\034)1759 3287 y Ff(s)1805 3302 y Fe(1)1845 3287 y
Fh(\()p Ff(t)p Fh(\))p Ff(s)2002 3302 y Fe(2)2041 3287
y Fh(\()p Ff(t)22 b Fg(\000)h Ff(\034)11 b Fh(\))p Ff(dt)1259
3540 y(\032)1309 3555 y Fe(21)1412 3540 y Fh(=)1515 3423
y Fb(Z)1598 3449 y Fd(\034)1561 3612 y Fe(0)1658 3540
y Ff(s)1704 3555 y Fe(1)1743 3540 y Fh(\()p Ff(t)p Fh(\))p
Ff(s)1900 3555 y Fe(2)1940 3540 y Fh(\()p Ff(t)22 b Fh(+)g
Ff(T)36 b Fg(\000)23 b Ff(\034)11 b Fh(\))p Ff(dt)-186
3834 y Fh(W)-8 b(e)33 b(can)g(decomp)s(ose)g Ff(s)698
3849 y Fe(1)737 3834 y Fh(\()p Ff(t)p Fh(\))g(and)f Ff(s)1116
3849 y Fe(2)1156 3834 y Fh(\()p Ff(t)p Fh(\))g(as)h(follo)m(ws:)1423
4054 y Ff(s)1469 4069 y Fe(1)1508 4054 y Fh(\()p Ff(t)p
Fh(\))28 b(=)g Ff(f)1799 4069 y Fe(11)1874 4054 y Fh(\()p
Ff(t)p Fh(\))22 b(+)g Ff(f)2153 4069 y Fe(12)2228 4054
y Fh(\()p Ff(t)p Fh(\))1423 4274 y Ff(s)1469 4289 y Fe(2)1508
4274 y Fh(\()p Ff(t)p Fh(\))28 b(=)g Ff(f)1799 4289 y
Fe(21)1874 4274 y Fh(\()p Ff(t)p Fh(\))22 b(+)g Ff(f)2153
4289 y Fe(22)2228 4274 y Fh(\()p Ff(t)p Fh(\))-186 4449
y(where)h Ff(f)133 4464 y Fe(11)208 4449 y Fh(\()p Ff(t)p
Fh(\))f(is)g(the)h(part)f(of)g Ff(s)935 4464 y Fe(1)974
4449 y Fh(\()p Ff(t)p Fh(\))g(b)s(et)m(w)m(een)i([0)p
Ff(;)17 b(\034)11 b Fh(])23 b(and)f Ff(f)1923 4464 y
Fe(12)1998 4449 y Fh(\()p Ff(t)p Fh(\))g(is)g(the)h(part)e(of)h
Ff(s)2724 4464 y Fe(1)2764 4449 y Fh(\()p Ff(t)p Fh(\))g(b)s(et)m(w)m
(een)i([)p Ff(\034)6 b(;)17 b(T)d Fh(].)40 b(Similarly)-8
b(,)-186 4569 y Ff(f)-138 4584 y Fe(21)-63 4569 y Fh(\()p
Ff(t)p Fh(\))32 b(is)h(the)g(part)f(of)g Ff(s)715 4584
y Fe(2)754 4569 y Fh(\()p Ff(t)p Fh(\))h(b)s(et)m(w)m(een)i([0)p
Ff(;)17 b(T)35 b Fg(\000)23 b Ff(\034)11 b Fh(])33 b(and)f
Ff(f)1937 4584 y Fe(22)2012 4569 y Fh(\()p Ff(t)p Fh(\))h(is)f(the)h
(part)f(of)g Ff(s)2790 4584 y Fe(2)2830 4569 y Fh(\()p
Ff(t)p Fh(\))g(b)s(et)m(w)m(een)j([)p Ff(T)h Fg(\000)23
b Ff(\034)6 b(;)17 b(T)d Fh(].)-186 4775 y(No)m(w)33
b(w)m(e)h(construct)f(a)g(new)g(signal)1152 4995 y Ff(s)1198
4931 y Fa(0)1198 5020 y Fe(2)1238 4995 y Fh(\()p Ff(t)p
Fh(\))28 b(=)f Ff(f)1528 5010 y Fe(22)1603 4995 y Fh(\()p
Ff(t)22 b Fh(+)g Ff(T)36 b Fg(\000)23 b Ff(\034)11 b
Fh(\))22 b(+)g Ff(f)2248 5010 y Fe(21)2323 4995 y Fh(\()p
Ff(t)g Fg(\000)h Ff(\034)11 b Fh(\))-186 5215 y(It)33
b(can)f(b)s(e)h(v)m(eri\014ed)h(that)1113 5336 y Fg(k)p
Ff(s)1209 5271 y Fa(0)1209 5360 y Fe(2)1249 5336 y Fg(k)1299
5295 y Fe(2)1365 5336 y Fh(=)28 b Fg(k)p Ff(f)1567 5351
y Fe(21)1642 5336 y Fg(k)1692 5295 y Fe(2)1753 5336 y
Fh(+)22 b Fg(k)p Ff(f)1949 5351 y Fe(22)2024 5336 y Fg(k)2074
5295 y Fe(2)2141 5336 y Fh(=)27 b Fg(k)p Ff(s)2340 5351
y Fe(2)2379 5336 y Fg(k)2429 5295 y Fe(2)2496 5336 y
Fh(=)h(1)1857 5655 y(1)p eop
2 1 bop -186 167 a Fh(and)1087 287 y Fg(j)p Ff(\032)1165
302 y Fe(12)1262 287 y Fh(+)22 b Ff(\032)1410 302 y Fe(21)1485
287 y Fg(j)28 b Fh(=)f Fg(jh)p Ff(s)1757 302 y Fe(1)1796
287 y Ff(;)17 b(s)1886 223 y Fa(0)1886 312 y Fe(2)1925
287 y Fg(ij)27 b(\024)h(k)p Ff(s)2220 302 y Fe(1)2260
287 y Fg(kk)p Ff(s)2406 223 y Fa(0)2406 312 y Fe(2)2445
287 y Fg(k)f Fh(=)h(1)-186 547 y(By)33 b(c)m(hanging)f(the)h(p)s
(olarit)m(y)e(of)h Ff(f)1069 562 y Fe(21)1176 547 y Fh(and)h
Ff(f)1414 562 y Fe(22)1521 547 y Fh(separately)-8 b(,)33
b(w)m(e)h(can)f(reac)m(h)g(the)g(follo)m(wing)d(conclusion.)1550
767 y Fg(j)p Ff(\032)1628 782 y Fe(12)1702 767 y Fg(j)22
b Fh(+)g Fg(j)p Ff(\032)1928 782 y Fe(21)2003 767 y Fg(j)27
b(\024)h Fh(1)1611 b(\(2\))-186 987 y(Then)34 b(Let)e(us)i(examine)e
(the)h(condition)e(for)h(\(1\),)g(whic)m(h)h(can)g(b)s(e)g(rewrited)g
(as:)1399 1267 y(cos\()p Ff(!)t Fh(\))27 b Fg(6)p Fh(=)1811
1199 y(1)22 b Fg(\000)g Ff(\032)2031 1163 y Fe(2)2031
1224 y(12)2128 1199 y Fg(\000)h Ff(\032)2278 1163 y Fe(2)2278
1224 y(21)p 1811 1243 543 4 v 1933 1335 a Fh(2)p Ff(\032)2032
1350 y Fe(12)2106 1335 y Ff(\032)2156 1350 y Fe(21)3823
1267 y Fh(\(3\))-186 1537 y(F)-8 b(rom)31 b(\(2\))h(w)m(e)i(kno)m(w)
1481 1716 y Fg(j)1519 1649 y Fh(1)22 b Fg(\000)g Ff(\032)1739
1613 y Fe(2)1739 1674 y(12)1837 1649 y Fg(\000)g Ff(\032)1986
1613 y Fe(2)1986 1674 y(21)p 1519 1693 V 1641 1785 a
Fh(2)p Ff(\032)1740 1800 y Fe(12)1815 1785 y Ff(\032)1865
1800 y Fe(21)2071 1716 y Fg(j)28 b(\025)g Fh(1)1542 b(\(4\))-186
1941 y(with)32 b(eqalit)m(y)g(holds)g(if)g(and)h(only)f(if)f
Fg(j)p Ff(\032)1269 1956 y Fe(12)1344 1941 y Fg(j)22
b Fh(+)g Fg(j)p Ff(\032)1570 1956 y Fe(21)1644 1941 y
Fg(j)28 b Fh(=)f(1.)43 b(F)-8 b(urthermore,)32 b Fg(j)p
Ff(cos)p Fh(\()p Ff(!)t Fh(\))p Fg(j)27 b(\024)h Fh(1)k(for)g(all)p
Ff(!)d Fg(2)f Fh([0)p Ff(;)17 b Fh(2)p Ff(\031)t Fh(].)-186
2147 y(So)32 b(the)h(necessary)i(and)e(su\016cien)m(t)h(condition)d
(for)h(\(1\))g(to)g(hold)g(is)1550 2367 y Fg(j)p Ff(\032)1628
2382 y Fe(12)1703 2367 y Fg(j)22 b Fh(+)g Fg(j)p Ff(\032)1929
2382 y Fe(21)2004 2367 y Fg(j)27 b Ff(<)h Fh(1)1611 b(\(5\))1857
5655 y(2)p eop end
userdict /end-hook known{end-hook}if