5.9.rickard.ps

是multiuser detection 这本书的习题解答, 很有用的书.

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TeXDict begin

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Fg(k)s Fh(th)g(user)f(transmits,)1552 2042 y Fg(A)1614
2054 y Ff(k)1669 1963 y Fe(X)1717 2140 y Ff(i)1803 2042
y Fg(s)1842 2054 y Ff(k)1883 2042 y Fh(\()p Fg(t)18 b
Fd(\000)g Fg(iT)12 b Fh(\))p Fg(b)2204 2054 y Ff(k)2244
2042 y Fh([)p Fg(i)p Fh(])p Fg(;)931 b Fh(\(1\))515 2297
y(a)27 b(decorrelating)f(detector)h(has)g(probabilit)n(y)f(of)i(error,)
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2575 y Fh(\()p Fg(\033)s Fh(\))c(=)f Fg(Q)1416 2458 y
Fe(\022)1487 2519 y Fg(A)1549 2531 y Ff(k)p 1487 2556
104 4 v 1513 2632 a Fg(\033)1600 2472 y Fe(q)p 1683 2472
477 4 v 103 x Fh(1)18 b Fd(\000)g Fg(a)1870 2546 y Ff(T)1870
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275 4 v 2493 2671 a Fg(\033)2543 2572 y Fe(q)p 2627 2572
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3675 y(k)1590 3654 y Fh(\()p Fg(\033)s Fh(\))d(=)f Fg(Q)1896
3537 y Fe(\022)1966 3598 y Fg(\013A)2081 3610 y Ff(k)2123
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4418 y Fh(\()p Fg(t)p Fh(\))p Fd(jj)1924 4384 y Fb(2)1985
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(e)h(written)g(equiv)-5 b(alen)n(tly)e(,)1297 4845 y
Fg(Q)1377 4678 y Fe(0)1377 4828 y(@)1543 4789 y Fg(A)1605
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4843 y Fe(q)p 1593 4843 134 4 v 1593 4942 a Fg(R)1657
4907 y Fb(+)1656 4965 y(11)1736 4678 y Fe(1)1736 4828
y(A)1892 4845 y Fg(<)83 b(Q)2120 4728 y Fe(\022)2190
4789 y Fg(\013A)2305 4801 y Fb(1)2343 4789 y Fd(jj)s
Fh(~)-45 b Fg(s)2428 4801 y Fb(1)2465 4789 y Fd(jj)p
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4845 y Fh(\(7\))1926 5255 y(1)p eop
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550 y Fh(\(8\))1712 750 y(1)p 1666 787 V 1666 868 a Fg(R)1730
833 y Fb(+)1729 891 y(11)1892 806 y Fg(>)2049 749 y(R)2113
713 y Fb(+)2112 771 y(11)2197 687 y Fe(P)2284 707 y Ff(K)2284
774 y(k)q Fb(=1)2423 749 y Fg(A)2485 719 y Fb(2)2485
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y Ff(K)2140 903 y(k)q Fb(=1)2279 878 y Fg(A)2341 850
y Fb(2)2341 903 y Ff(k)2382 878 y Fg(R)2446 843 y Fb(+)2445
903 y Ff(k)q(k)3273 806 y Fh(\(9\))1461 985 y Ff(K)1431
1010 y Fe(X)1431 1188 y Ff(k)q Fb(=1)1565 1088 y Fg(A)1627
1054 y Fb(2)1627 1109 y Ff(k)1668 1088 y Fg(R)1732 1053
y Fb(+)1731 1114 y Ff(k)q(k)1892 1088 y Fg(>)83 b Fh(\()p
Fg(R)2136 1053 y Fb(+)2135 1111 y(11)2205 1088 y Fh(\))2237
1054 y Fb(2)2319 985 y Ff(K)2289 1010 y Fe(X)2289 1188
y Ff(k)q Fb(=1)2423 1088 y Fg(A)2485 1054 y Fb(2)2485
1109 y Ff(k)2526 1088 y Fg(:)682 b Fh(\(10\))515 1359
y(Note)21 b(the)g(last)f(inequalit)n(y)h(cannot)f(b)r(e)h(satis\014ed)g
(with)g(K=2.)33 b(In)21 b(this)h(case,)f Fg(R)2978 1324
y Fb(+)2977 1382 y(11)3070 1359 y Fh(=)i Fg(R)3222 1324
y Fb(+)3221 1382 y(22)3314 1359 y Fh(=)584 1426 y Fb(1)p
525 1440 152 4 v 525 1488 a(1)p Fc(\000)p Ff(\032)644
1471 y Fa(2)708 1459 y Fh(and)e(the)g Fg(A)h Fh(terms)f(cancel,)h
(resulting)e(in)i(the)f(inequalit)n(y)g(0)i Fg(>)f(\032)2711
1429 y Fb(2)2748 1459 y Fh(,)h(an)e(imp)r(ossibilit)n(y)-7
b(.)639 1559 y(In)36 b(order)d(to)i(\014nd)h(a)e(set)i(of)f(parameters)
e(that)i(satisfy)g(Equation)f(10,)i(w)n(e)f(need)g(to)515
1658 y(mak)n(e)i(\()p Fg(R)838 1623 y Fb(+)837 1680 y(11)908
1658 y Fh(\))940 1628 y Fb(2)1016 1658 y Fh(small)h(\(close)g(to)g(1\))
h(without)f(making)g Fg(R)2398 1623 y Fb(+)2397 1683
y Ff(k)q(k)2513 1658 y Fh(\()p Fg(k)44 b Fd(6)p Fh(=)d(1\))d(small.)69
b(Noting)515 1758 y(that)34 b Fg(R)765 1722 y Fb(+)764
1783 y Ff(k)q(k)874 1758 y Fh(=)f(1)22 b Fd(\000)g Fg(a)1167
1728 y Ff(T)1167 1781 y(k)1219 1758 y Fg(R)1283 1722
y Fc(\000)p Fb(1)1282 1783 y Ff(k)1372 1758 y Fg(a)1416
1770 y Ff(k)1457 1758 y Fh(,)35 b(w)n(e)e(see)g(that)h(w)n(e)f(w)n(an)n
(t)g(parameters)f(whic)n(h)i(mak)n(e)e Fg(s)3247 1770
y Fb(1)3284 1758 y Fh(\()p Fg(t)p Fh(\))515 1858 y(nearly)g(orthogonal)
g(to)i(the)g(other)f(signature)g(w)n(a)n(v)n(eforms)e(while)j(the)g
(other)f(signature)515 1957 y(w)n(a)n(v)n(eforms)25 b(can)i(b)r(e)h
(highly)g(correlated.)35 b(F)-7 b(or)27 b(example,)g(consider)g(the)h
(case)e(where,)1423 2235 y Fg(R)d Fh(=)1597 2068 y Fe(0)1597
2217 y(@)1764 2134 y Fh(1)136 b Fg(:)p Fh(001)81 b Fg(:)p
Fh(001)1711 2234 y Fg(:)p Fh(001)135 b(1)g Fg(:)p Fh(999)1711
2334 y Fg(:)p Fh(001)82 b Fg(:)p Fh(999)134 b(1)2362
2068 y Fe(1)2362 2217 y(A)2448 2235 y Fg(;)760 b Fh(\(11\))515
2513 y(whic)n(h)27 b(results)g(in,)1157 2790 y Fg(R)1221
2756 y Fc(\000)p Fb(1)1333 2790 y Fd(\031)1420 2623 y
Fe(0)1420 2773 y(@)1567 2690 y Fh(1)p Fg(:)p Fh(0000)113
b Fd(\000)p Fh(0)p Fg(:)p Fh(0005)80 b Fd(\000)p Fh(0)p
Fg(:)p Fh(0005)1534 2789 y Fd(\000)p Fh(0)p Fg(:)p Fh(0005)166
b(500)220 b Fd(\000)p Fh(500)1534 2889 y Fd(\000)p Fh(0)p
Fg(:)p Fh(0005)134 b Fd(\000)p Fh(500)219 b(500)2627
2623 y Fe(1)2627 2773 y(A)2714 2790 y Fg(:)494 b Fh(\(12\))515
3068 y(F)-7 b(or)24 b(all)g(reasonably)e(balanced)i(c)n(hoices)g(of)g
Fg(A)1956 3080 y Ff(i)1984 3068 y Fh(,)h(this)g(c)n(hoice)f(of)g
Fg(R)i Fh(satis\014es)d(Equation)h(10.)639 3168 y(Alternativ)n(ely)-7
b(,)23 b(w)n(e)e(could)g(satisfy)g(the)h(inequalit)n(y)g(b)n(y)f
(\014nding)h(\(in)g(the)g(same)f(w)n(a)n(y\))f(an)515
3267 y Fg(R)k Fh(whic)n(h)g(barely)f(satis\014es)g(\()p
Fg(R)1482 3232 y Fb(+)1481 3289 y(11)1551 3267 y Fh(\))1583
3237 y Fb(2)1644 3267 y Fg(<)f(R)1795 3232 y Fb(+)1794
3292 y Ff(k)q(k)1896 3267 y Fh(for)h(some)g Fg(k)s Fh(,)i(and)e(then)h
(mak)n(e)f(the)h(asso)r(ciated)515 3367 y Fg(A)577 3379
y Ff(k)646 3367 y Fh(term)j(extremely)g(large)f(to)i(w)n(ash)e(out)i
(the)g(other)f(terms.)1926 5255 y(2)p eop end
userdict /end-hook known{end-hook}if