www.pudn.com > SolutionsforMultiuserDetection.rar > 4.32.rickard.ps

%!PS (but not EPSF; comments have been disabled)
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%DVIPSParameters: dpi=600, compressed, comments removed
%DVIPSSource:  TeX output 1999.04.02:0929
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TeXDict begin

1 0 bop 1373 289 a Fk(Multiuser)45 b(Detection)1656 530
y Fj(Scott)33 b(Ric)m(k)-5 b(ard)1669 725 y(April)31
b(2,)h(1999)515 1083 y Fi(Solution)45 b(to)h(Problem)f(4.32)515
1264 y Fh(Find)28 b Fg(R)f Fh(suc)n(h)g(that,)1327 1447
y Ff(jj)p Fg(a)1420 1459 y Fe(1)1457 1447 y Ff(jj)1503
1413 y Fe(2)1563 1447 y Fd(<)c Fh(min)p Ff(f)p Fg(a)1877
1413 y Fc(T)1877 1468 y Fe(1)1930 1447 y Fg(R)2001 1459
y Fe(1)2038 1447 y Fg(a)2085 1459 y Fe(1)2122 1447 y
Fd(;)14 b Fg(a)2205 1413 y Fc(T)2205 1468 y Fe(1)2258
1447 y Fg(R)2329 1411 y Fb(\000)p Fe(1)2329 1468 y(1)2418
1447 y Fg(a)2465 1459 y Fe(1)2502 1447 y Ff(g)p Fd(:)706
b Fh(\(1\))515 1630 y(It)24 b(is)f(easy)g(to)g(sho)n(w)g(that)h
Fg(R)f Fh(m)n(ust)h(ha)n(v)n(e)e(at)i(least)f(3)g(o\013-diagonal)f
(non-zero)g(comp)r(onen)n(ts)515 1729 y(and)27 b(th)n(us)h
Fg(R)f Fh(m)n(ust)h(b)r(e)g(at)f(least)g(3-b)n(y-3.)35
b(Consider)27 b Fg(R)g Fh(of)h(the)g(form,)1288 2267
y Fg(R)23 b Fh(=)1470 1851 y Fa(0)1470 1997 y(B)1470
2047 y(B)1470 2097 y(B)1470 2147 y(B)1470 2196 y(B)1470
2246 y(B)1470 2296 y(B)1470 2346 y(B)1470 2396 y(B)1470
2445 y(B)1470 2499 y(@)1590 1907 y Fh(1)89 b Fd(:)14
b(:)g(:)104 b(\013)i(:)14 b(:)g(:)82 b(\014)88 b(:)14
b(:)g(:)1600 1995 y Fh(.)1600 2028 y(.)1600 2061 y(.)125
b(1)315 b Fd(\015)1584 2216 y(\013)1905 2158 y Fh(.)1938
2183 y(.)1970 2208 y(.)1600 2305 y(.)1600 2338 y(.)1600
2371 y(.)122 b Fd(\015)1585 2471 y(\014)1600 2559 y Fh(.)1600
2593 y(.)1600 2626 y(.)799 b(1)2533 1851 y Fa(1)2533
1997 y(C)2533 2047 y(C)2533 2097 y(C)2533 2147 y(C)2533
2196 y(C)2533 2246 y(C)2533 2296 y(C)2533 2346 y(C)2533
2396 y(C)2533 2445 y(C)2533 2499 y(A)3273 2267 y Fh(\(2\))515
2805 y(That)30 b(is,)g Fg(R)906 2817 y Fe(1)p Fc(i)993
2805 y Fh(=)d Fg(R)1157 2817 y Fc(i)p Fe(1)1244 2805
y Fh(=)g Fd(\013)p Fh(,)k Fg(R)1515 2817 y Fe(1)p Fc(j)1610
2805 y Fh(=)26 b Fg(R)1773 2817 y Fc(j)s Fe(1)1868 2805
y Fh(=)g Fd(\014)t Fh(,)31 b Fd(i)c Ff(6)p Fh(=)f Fd(j)5
b Fh(,)31 b Fg(R)2376 2817 y Fc(k)q(l)2465 2805 y Fh(=)26
b Fg(R)2628 2817 y Fc(lk)2717 2805 y Fh(=)h Fd(\015)5
b Fh(,)30 b Fd(k)g Ff(6)p Fh(=)c(1,)k Fd(l)f Ff(6)p Fh(=)d(1,)515
2904 y Fd(k)g Ff(6)p Fh(=)c Fd(l)r Fh(,)27 b(and)h Fg(R)981
2916 y Fc(mn)1109 2904 y Fh(=)22 b(0)27 b(otherwise.)36
b(F)-7 b(or)27 b(this)h Fg(R)p Fh(,)g(w)n(e)f(w)n(an)n(t)g(to)g(\014nd)
h(\()p Fd(\013;)14 b(\014)t(;)g(\015)5 b Fh(\))29 b(suc)n(h)e(that,)
1091 3087 y Ff(jj)p Fg(a)1183 3099 y Fe(1)1221 3087 y
Ff(jj)1267 3053 y Fe(2)1327 3087 y Fh(=)c Fd(\013)1468
3053 y Fe(2)1524 3087 y Fh(+)18 b Fd(\014)1658 3053 y
Fe(2)1719 3087 y Fd(<)k Fg(a)1853 3053 y Fc(T)1853 3107
y Fe(1)1905 3087 y Fg(R)1976 3099 y Fe(1)2014 3087 y
Fg(a)2060 3099 y Fe(1)2120 3087 y Fh(=)h Fd(\013)2261
3053 y Fe(2)2317 3087 y Fh(+)18 b(2)p Fd(\013\014)t(\015)24
b Fh(+)18 b Fd(\014)2743 3099 y Fe(2)2780 3087 y Fd(;)470
b Fh(\(3\))515 3270 y(and,)1217 3418 y Fd(\013)1270 3383
y Fe(2)1326 3418 y Fh(+)18 b Fd(\014)1460 3383 y Fe(2)1521
3418 y Fd(<)k Fg(a)1655 3383 y Fc(T)1655 3438 y Fe(1)1707
3418 y Fg(R)1779 3381 y Fb(\000)p Fe(1)1779 3439 y(1)1868
3418 y Fg(a)1914 3430 y Fe(1)1975 3418 y Fh(=)2072 3362
y Fd(\013)2125 3331 y Fe(2)2181 3362 y Ff(\000)c Fh(2)p
Fd(\013\014)t(\015)24 b Fh(+)18 b Fd(\014)2607 3374 y
Fe(2)p 2072 3399 572 4 v 2244 3475 a Fh(1)g Ff(\000)g
Fd(\015)2435 3451 y Fe(2)2654 3418 y Fd(:)596 b Fh(\(4\))515
3607 y(Equation)26 b(3)i(is)f(satis\014ed)g(if)h Fd(\013\014)t(\015)33
b Fh(is)28 b(p)r(ositiv)n(e.)36 b(Equation)27 b(4)g(is)h(satis\014ed)f
(if,)1657 3828 y Fd(\013)1710 3794 y Fe(2)1766 3828 y
Fh(+)18 b Fd(\014)1900 3794 y Fe(2)1960 3828 y Fd(<)2058
3772 y Fh(2)p Fd(\013\014)p 2058 3809 147 4 v 2107 3885
a(\015)2214 3828 y(:)1036 b Fh(\(5\))515 4055 y(Since)31
b(the)h(righ)n(t)f(hand)g(side)g(m)n(ust)h(b)r(e)f(p)r(ositiv)n(e)g
(\(from)h(Equation)e(3\))h(and)h Ff(j)p Fd(\015)5 b Ff(j)29
b(\024)f Fh(1,)k(w)n(e)515 4154 y(see)27 b(that)h Fd(\013)23
b Ff(6)p Fh(=)g Fd(\014)t Fh(.)37 b(So,)28 b(arbitrarily)d(setting)j
Fd(\013)23 b Fh(=)g(1)k(and)h Fd(\014)f Fh(=)c(1)p Fd(=)p
Fh(2,)j(from)h(Equation)g(5,)1794 4337 y Fd(\015)h(>)22
b Fh(4)p Fd(=)p Fh(5)p Fd(:)1172 b Fh(\(6\))515 4519
y(Setting)28 b Fd(\015)f Fh(=)c(9)p Fd(=)p Fh(10,)j(one)h
Fg(R)g Fh(satisfying)g(Equation)g(1)g(is,)1430 4802 y
Fg(R)c Fh(=)1613 4635 y Fa(0)1613 4784 y(@)1768 4701
y Fh(1)187 b(1)165 b(1)p Fd(=)p Fh(2)1768 4801 y(1)187
b(1)144 b(9)p Fd(=)p Fh(10)1727 4901 y(1)p Fd(=)p Fh(2)81
b(9)p Fd(=)p Fh(10)144 b(1)2391 4635 y Fa(1)2391 4784
y(A)3273 4802 y Fh(\(7\))1926 5506 y(1)p eop end
userdict /end-hook known{end-hook}if