The effects of UWB interference on GSM systems

(1)

Int. Zurich Seminar on Communications (IZS), Feb. 18–20, 2004

0-7803-8329-X/04/$20.00 c2004 IEEE. 86

!"# #$$#%&' ($ )*+ ,-&#.$#.#-%# (- /01 '2'&#3'

4,5,#. 67-5,^† 8-'&,&9&# :9.#%(3

;;;<= .(9&# 5#' >.#&#'

?@<?A 0(B",7CD-&,B(E,'= F.7-%#

:37,EG 4,5,#.H67-5,I#9.#%(3H$.

>".,'&,7- F,'%"#.

0J,''%(3 8--(K7&,(-'= 8LMCLD>

M'&#.39-5,-N#-'&.H <O O??@ +#.-= 0J,&P#.E7-5

:37,EG >".,'&,7-HF,'%"#.QI'J,''%(3H%(3

!"#$%&'$! "#$ $%%$&'( )% *+, -.'$/%$/$.&$ ). 012 344 5.6 012 7844 (9('$:( 5/$ &).(-6$/$6 %)/ &;//$.' <== /$>;?5'-).(

5( @$?? 5( A/)A)($6 B"1C $:-((-). ?-:-'( %)/ '#$ &/-'$/-5 )% $-'#$/

5 7 6, ?)(( -. '#$ 1CDE )/ 5 ?)(( ?$56-.> ') '#$ :-.-:;:

/$F;-/$6 1CDE 5' '#$ &$?? $6>$G *+, 6$.(-'-$( 5/$ &):A;'$6

%)/ 6-%%$/$.' 012 /$;($ %5&')/( 5.6 '#$ /$(;?'( (#)@ '#5' .)

#5/:%;? -.'$/%$/$.&$ -( ') H$ $IA$&'$6 %)/ 012 344 (9('$:(G C. '#$ &5($ )% 012 7844 (9('$:(J '#$ A/)A)($6 B"1C $:-((-).

?-:-'( 5/$ %);.6 ') H$ )%%$/-.> (;%!&-$.' A/)'$&'-). @#$/$5( '#$

&;//$.' <== /$>;?5'-).( @);?6 /$(;?' -. (->.-!&5.' -.'$/%$/$.&$G

8H 8L!RM4)>!8ML

!"# )E&.7C*,5#S7-5 T)*+U .#N9E7&(.2 B.(%#'' ,- &"#

)-,&#5 0&7&#' J7' 7%%(3B7-,#5 S2 '&.(-N (BB(',&,(- 7N7,-'&

&"# #3,'',(- E,3,&'= 37,-E2 S2 9'#.' ($ E,%#-'#5 S7-5'= J(..,#5 7S(9& &"# ,3B7%& (- &"#,. #V,'&,-N '#.K,%#'H 8- &",' B7B#.= J#

%(-',5#. &"# #$$#%&' (- /01 -#&J(.W' &"7& 372 7.,'# $.(3 7 37'' 5#BE(23#-& ($ )*+ 5#K,%#'= 9',-N S(&" %9..#-& F>>

.#N9E7&,(-' XQY= X;Y 7' J#EE 7' B.(B('#5 :!08 .#N9E7&,(-' XOYH

!"# -#N7&,K# #$$#%&' ($ #V&.7 ,-&#.$#.#-%# (- 7 /01 '2'&#3

%7- 3('& %(-K#-,#-&E2 S# 7''#''#5 S2 E((W,-N 7& &"# 08LR 7& &"# %#EE #5N#= ,H#H 7& &"# %(K#.7N# E,3,&H 4#B#-5,-N (- &"#

E#K#E ($ ,-&#.$#.#-%#= &"# E('' ,- 08LR J,EE #$$#%&,K#E2 .#'9E&

,- 7 .#59%#5 %#EE %(K#.7N# .75,9'H

*# '"(J 7 3(5#E &( %(3B9&# &"# 7NN.#N7&# ,-&#.$#.#-%#

$.(3 )*+ 5#K,%#' $(. ,-5((. 7-5 (9&5((. '%#-7.,(' J,&"

K7.2,-N )*+ 5#K,%# 5#-',&,#'H *# %(-',5#. &J( 5,$$#.#-&

3#&"(5' &( ,-K#'&,N7&# &"# #$$#%& ($ &"# ,-&#.$#.#-%# $.(3 )*+

5#K,%#' 7& &"# %#EE #5N#G 7 .#E7&,K# E('' ,- 08LR 7-5 5#N.7C 57&,(- &( 7 &7.N#& 08LRH +7'#5 (- &"#'# %(-',5#.7&,(-' J#

#K7E97&# &"# 37V,393 B#.3,'',SE# )*+ &.7-'3,&&#. 5#-',&,#'H

88H )*+ 8L!:RF:R:L>:1M4:6

1('& )*+ 5#K,%#' 7.# #VB#%&#5 &( $7EE ,-&( &"# N#-#.7E

%7&#N(.2 ($ T3(S,E#U %(339-,%7&,(- 5#K,%#'H !",' &2B# ($

7BBE,%7&,(- ,' .#'&.,%&#5 S2 &"# F>> &( "7K# ,&' 37,- &.7-'C 3,'',(- S7-5' ,- &"# .7-N# ($ OHQ &( Q?H@ /ZP XQY= X;YH D&

&"('# $.#[9#-%,#'= &"# 7&&#-97&,(- J,&" 5,'&7-%# ,' ',N-,!%7-&

7-5 &"#.#$(.#= 7 K,%&,3 .#%#,K#. J,EE S# 3('& 7$$#%&#5 S2 &"#

$#J -#7.#'& )*+ &.7-'%#,K#.'H /,K#- &"7& S7'# '&7&,(-' 7.#

N#-#.7EE2 ,- #E#K7&#5 E(%7&,(-' (. (&"#.J,'# ,-7%%#'',SE#= &"#

,-&#.$#.#-%# #$$#%&' J,EE S# $#E& 37,-E2 7& &"# 3(S,E# &#.3,-7EH

†!"# 79&"(. J7' J(.W,-N 7& 0J,''%(3 8--(K7&,(-' ,- &"# %(-&#V& ($ ",' 5,BE(37 J(.W J",E# 7 '&95#-& 7& 8-'&H :9.#%(3H

Z#-%#= J# J,EE %(-',5#. &"# #$$#%&' (- &"# 5(J-E,-WH 8- &"#

7S'#-%# ($ $9-%&,(-7E ,-59'&.2 '&7-57.5' $(. )*+= J# 7''93#

&"# )*+ ',N-7E &( S# 'B#%&.7EE2"7& ,- &"# ,-&#.$#.#5 S7-5H

*# '"7EE %(-',5#. 7 ',&97&,(- J"#.# (9. K,%&,3 .#%#,K#.= &"#

3(S,E# &#.3,-7E= ,' E(%7&#5 ,- 7 BE7-# 73(-N'& )*+ 5#K,%#' 9-,$(.3E2 5,'&.,S9&#5 B#. 9-,& 7.#7= ',3,E7. &( XAYH >(-',5#.

&"# K,%&,3 .#%#,K#. BE7%#5 7& &"# %#-&.# ($ &J( %(-%#-&.,%

%,.%E#' J,&" .75,9'rmin 7-5rmax= .#'B#%&,K#E2= J,&"rmin<

rmaxH *# 7''93# &"7& &"#.# ,' 7 3,-,393 '#B7.7&,(- 5,'&7-%#

S#&J##- &"# K,%&,3 7-5 &"# -#7.#'& )*+ 5#K,%#H 8- &"# %7'#

($ 7- ($!%#= $(. #V73BE#= ,& ,' .#7'(-7SE# &( 7''93# &"7& -(

(&"#. .75,( 5#K,%# J,EE S# BE7%#5 %E('#. &"7- 7 3#&#. $.(3 &"#

K,%&,3H *# %7- J.,&# &"# B.(S7S,E,&2 5#-',&2 $9-%&,(- TB5$U ($

&"# )*+ &.7-'3,&&#.' 7' 7 $9-%&,(- ($ &"# .75,9'θ7'G pdf(θ) =

0 θ < rmin 7-5θ > rmax r_max² 2θ−r²_min θ∈[rmin, rmax]

!"# 3#7- ,-&#.$#.#-%# E#K#E ,' N,K#- S2 &"# 3#7- .#%#,K#5 B(J#. $.(3 7EE &"# ,-&#.$#.,-N )*+ &.7-'3,&&#.'= ,H#H

E{P}=PR = N _r_max

θ=rmin

P(θ) 2θ

r²_max−r²_mindθ

= 2πρ _r_max

θ=rmin

P(θ)θdθ TQU

J"#.# P(.) 5#!-#' &"# .#%#,K#5 ',N-7E B(J#. ($ (-# )*+

&.7-'3,&&#. 7& &"# K,%&,3 .#%#,K#. 7' 7 $9-%&,(- ($ &"# 5,'&7-%#

S#&J##- &"#3 7-5ρ=N/[π(r²_min−r_max² )],' &"# 5#-',&2 ($

)*+ &.7-'3,&&#.' B#. 9-,& 7.#7=N,' &"# &(&7E -93S#. ($ )*+

&.7-'3,&&#.'H !"# .#%#,K#5 B(J#. 7' 7 $9-%&,(- ($ 5,'&7-%# %7- S# 7BB.(V,37&#5 S2 X\Y

P(d) =PT

λ

4πd

₂

d0

d0+d ₂

T;U J"#.# λ ,' &"# J7K#E#-N&" ($ &"# ',N-7E 7-5 7''93#5 &(

%(..#'B(-5 &( &"# $.#[9#-%2 ($ &"# 7$$#%&#5 /01 '#.K,%#=PT

,' &"# &.7-'3,& B(J#. ($ &"# )*+ &.7-'3,&&#.=d,' &"# 5,'&7-%#

S#&J##- &"# K,%&,3 7-5 &"# &.7-'3,&&#. 7-5d0,' &"# S.#7WB(,-&

5,'&7-%#H F(. ',3BE,%,&2= J# 7''93# &"7& 7EE ,-&#.$#.,-N )*+

5#K,%#' &.7-'3,& 7& #[97E B(J#.PTH !"# S.#7WB(,-& 5,'&7-%#

%7- S# $(9-5 7BB.(V,37&#E2 $.(3 X\Y d0= 12hThR

λ TOU

(2)

87

!"#$# hT %&' hR %$# ("# "#)*"(+ %,-.# *$-/&' -0 ("#

($%&+1)((#$ %&' ("# $#2#).#$3 $#+4#2().#567 864)2%5563 !# !-/5'

%++/1#hT =hR = 1.5 17 8"# ,$#%94-)&( )+ %5+- % 0/&2()-&

-0 ("# 4$-4%*%()-& #&.)$-&1#&( %&' 2%& ,# +#( 5-!#$ (-

#7*7d0 = 101 (- %22-1-'%(# 0-$ )&'--$ #&.)$-&1#&(+ !)("

+($-&*#$ %((#&/%()-& 4#$ /&)( ')+(%&2#7 8- 2-14/(# ("# (-(%5 )&(#$0#$#&2# $#2#).#' ,6 ("# .)2()13 !# 2-1,)&# #:/%()-&+ ;<=

%&' ;>= (- -,(%)&

PR(r) = 2πρPTd²₀ λ

4π

₂ r_max r=r_min

1 r(r+d0)²dr IU W B =PR(r)|r_max→∞

= 2πρPT

λ 4π

₂ ln

1 + d0

rmin

− 1 1 + ^r^min_d₀

;?=

!"#$# !# "%.# )&(#*$%(#' ,6 4%$()%5 0$%2()-& %&' 5#( ("# -/(#$

$%')/+3rmax3 (#&' (- )&!&)(67

@@@7 ABC DEFDGHIIJK@I8JLMJLJIDJCENJK

E&# -0 ("# )14-$(%&( 5)1)()&* 0%2(-$+ )& ABC +6+(#1+ )+

("# 5#.#5 -0 )&(#$0#$#&2# $#2#).#' 0$-1 -("#$ ,%+# +(%()-&+

("%( ($%&+1)( -& ("# +%1# 0$#:/#&263 ("# +-F2%55#' 2-F2"%&&#5 )&(#$0#$#&2#7 O+)&* ("# 4%(" 5-++ 1-'#5 )&($-'/2#' )& ;>=3 !#

2%& !$)(# ("# B@IL %( ("# 1-,)5# (#$1)&%5 %+

SIN R(r) = PT

_λ

4πr

₂

d₀ d₀+r

2

_M

i=1P_T,i λ

4πd_i 2

d₀ d₀+d_i

2+IU W B+n

;P=

!"#$#PT %&'PT,i %$# ("# ($%&+1)++)-& 4-!#$ -0 ("# 4$)1%$6 2#55 ;!"#$# ("# .)2()1 1-,)5# )+ 5-2%(#'= %&' ("# )&(#$0#$)&*

2#55+ i = {1,2, . . . , M}3 $#+4#2().#567 r %&' di %$# ("# ')+F (%&2#+ 0$-1 ("# 4$)1%$6 %&' ("# )&(#$0#$)&* 2#55+ (- ("# 1-,)5#3

%&'n)+ ("# ("#$1%5 &-)+#7 @& -$'#$ (- 0%2)5)(%(# 2-14/(%()-&3

!# %++/1# % +(%&'%$' "#Q%*-&%5 2#55 25/+(#$ 1-'#5 RST !)("

(64)2%556K ∈ {3,4,7,9,12,21}7 M-$ 2-F2"%&&#5 )&(#$0#$#&2#

4/$4-+#+3 )( )+ *#&#$%556 +/0!2)#&( (- 2-&+)'#$ ("# !$+( ()#$ -0

&#)*",-/$)&* ,%+# +(%()-&+ ("%( ($%&+1)( -& ("# +%1# 0$#:/#&26

%+ ("# 4$)1%$6 ,%+# +(%()-&7 U)("-/( 2#55 +#2(-$)V%()-&3 !#

-,(%)& M = 6 )&(#$0#$)&* 2#55+ 0-$ ("# %,-.# .%5/#+ -0 K7 8"# !-$+( 2%+# %$)+#+ !"#& ("# 1-,)5# )+ 5-2%(#' %( ("# #'*#

-0 )(+ +#$.)&* 2#55 +)&2# ("# $#2#).#' +)*&%5 4-!#$ )+ %( % 1)&)1/1 ("#$#7 H++/1)&* #:/%5 $%')) %&' "#&2# ($%&+1)(

4-!#$ PT = PT,i 0-$ %55 ,%+#+(%()-&+3 ("# 2#55 $%')/+3 R3 )+ (64)2%556 1/2" +1%55#$ ("%& ("# ')+(%&2# (- ("# )&(#$0#$)&*

,%+# +(%()-&+ %&' !# 2%& !$)(# di ≈ D : D >> R3 !"#$#

D=√

3KR)+ ("# ')+(%&2# ,#(!##& ,%+#+(%()-&+7 M/$("#$3 )0 ("# 2#55 $%')/+ )+ 1/2" 5%$*#$ ("%& ("# ,$#%94-)&( ')+(%&2#d0

;d0 )+ %$-/&' WX1 0-$ ABC YXX=3 !# 2%& %44$-Q)1%(# ("#

4%(" 5-++ )& ;>= ,6Z

P(d) ^d>>d≈ ⁰ PT

λ 4πd₀

₂ d0

d ₄

;S=

@& ("# %,+#&2# -0 &-)+# %&' OU[ )&(#$0#$#&2#3 #:/%()-& ;P= %(

("# 2#55 #'*#3r=R3 +)145)!#+ (- ("#!"##$%#&'(&$)'%#*%#%)!%&

#"'$(RSTZ

C/I= 1

M(3K)² ;\=

@& % &-)+#F0$##3 #:/%5 4-!#$ #&.)$-&1#&(3 ("#C/I )+ ("#$#0-$#

2-145#(#56 '#(#$1)&#' ,6 ("# 2#55 25/+(#$ +($/2(/$#7 +, -%.. #"/$01 "1 " *0)!'$() (* '2% 3456

B)&2# ("# &-)+#F0$## 2-&+)'#$%()-&+ %,-.# +"-! ("%( ("#C/I )+ )&'#4#&'#&( -0 ("# ($%&+1)( 4-!#$3 ("# #00#2().# 2-.#$%*#

$%')/+ R3 0-$ % $#:/)$#' B@IL3 '#4#&'+ -&56 -& ("# )&(#$F 0#$#&2# 45/+ &-)+# 2-14-&#&( )& ("# B@IL7 U# 9&-! ("%(

%& SIN Rmin = 9'[ +/0!2#+ (- 1%)&(%)& % +)145# .-)2#

2-&&#2()-&7 O+)&*D=√

3KR3 ;S=3 ;\= %&' ("# #:/%5 ($%&+1)(

4-!#$ %++/14()-&3 !# 2%& &-! !$)(# ("# B@IL )& ;P= %+

SIN R = C/I 1

1 +C/I ^R_γ⁴(IU W B+n) ;W=

!"#$# γ = PTd⁴₀ λ

4πd₀

27 8"# ("#$1%5 &-)+# "--$ )+ *).#&

0$-1 n =kT Brx %&' k )+ ("# [-5(V1%&]+ 2-&+(%&( ;1.38× 10⁻²³U^GV^_#5.)&=3Brx)+ ("# $#2#).#$ ,%&'!)'(" %( %1,)#&(

(#14#$%(/$#K3 )& '#*$##+ _#5.)&7 M-$ ABC3Brx= 200kHz

%&' (#14#$%(/$# K = 290 !# !&' % &-)+# "--$ -0 n =

−120'[17

7, -%.. #"/$01 "1 " *0)!'$() (* '2% 1$8)". .%9%.

H+ )( (/$&+ -/(3 ("# +)*&%5 5#.#5 )+ $%("#$ 5-! %( ("#

SIN Rmin = 9 '[ 5)1)( %&' ("# 2#55 $%')/+ )+ %2(/%556 5)1)(#' ,6 ("# $#2#).#$ +#&+)().)(67 U# 0-/&' ("%( %& %22#4(%,5#

1)&)1/1 +)*&%5 5#.#5 %( ("# 1-,)5# )+ &-$1%556 FYX '[17 B)&2# ("# 1-,)5# $#2#).#$ 2%&&-( ')+()&*/)+" ,#(!##& ("#

/+#0/5 +)*&%53 &-)+# %&' )&(#$0#$#&2#3 !# 2%& +)1456 '#!&#

("# $%')/+ -0 ("# 2#553 R3 +/2" ("%( ("# $#2#).#' +)*&%5 4-!#$

)+ FYX '[17 8"# (-(%5 $#2#).# 4-!#$3 %&' ("#$#0-$# ("# $%')/+3 )+ *).#& ,6

Ptot = γ R⁴

1 + 1

C/I

+IU W B+n

R = ⁴ γ

1 +_C/I¹

Ptot−IU W B−n

D%52/5%()&* ("# 2-.#$%*# $%')/+ ,%+#' -& $#2#).#$ +#&+)().)(6

$#+/5(+ )& %& B@IL ("%( )+ +($)2(56 *$#%(#$ ("%& ("# 1)&)1/1 Y '[ $#:/)$#'7 G#&2#3 !# 2%& 2-14/(# ("# 1%Q)1/1 4#$1)++)F ,5# OU[ @&(#$0#$#&2# ("%( !)55 5#%' (- % '"#8%' 3456 %( ("#

2#55 #'*#3 )7#7

IU W B = γ R⁴

C/I−SIN Rtrgt

SIN Rtrgt C/I

−n

8-*#("#$ !)(" #:/%()-& ;?= !# 2%& ("#$#0-$# -,(%)& ("# '#&+)(6 -0 OU[ ($%&+1)((#$+3 ρ3 ("%( 2%& ,# (-5#$%(#' ,6 ("# +6+(#1 0-$ % *).#&SIN Rtrgt7

(3)

88

!"# $%& !'()*+)*)',) (-./0 122

%3 4566 784 987:5;3< =>3 ?@@659?=587 8A =>3 <3:B6=: 8A

=>3 @<3C58B: :39=587: =8 ./0 122 :D:=3E:F B:57G =>3 +,, 3E5::587 65E5=: ?7; ? @<8@8:3; )(/! 3E5::587 E?:H IJK# /5793

$%& 57;B:=<D :=?7;?<;: ?<3 D3= =8 L3 ;3!73;F 43 ?::BE3

=>3 $%& :5G7?6 =8 L3 :@39=<?66D "?= ?7; =<?7:E5==57G ?= =>3 E?M5EBE @843< @3<E5==3; 57 =>3 L?7; 8A =>3 C59=5E <3935C3<F

?998<;57G =8 =>3 +,,N)(/! 3E5::587 E?:H:#

%3 987:5;3< =48 ;5AA3<37= :937?<58:O ? <36?=5C3 ;3G<?;?=587 57 /!'* 8A P ;& ?7; =>3 ;3G<?;?=587 =8 ?7 ?L:86B=3F E575EBE

=?<G3= /!'*# Q <36?=5C3 /!'* ;39<3?:3 5: 876D <363C?7= 4>37

=>3 <3B:3 A?9=8< 5: :E?66 8<F E8<3 G373<?66DF =>3 63C36 8A 57=3<A3<3793 5: >5G>F 5#3# 57 =>3 684 /!'* <3G5E3# !7 =>5: 9?:3F

=>3 68:: 8A P ;& 5: :5G75!9?7= :5793 65==63 ?;;5=587?6 68:: 57 /!'* 9?7 L3 =863<?=3;# -7 =>3 8=>3< >?7;F A8< ? 6?<G3 <3B:3 A?9=8<F =>3 575=5?6 /!'* 4566 L3 4366 ?L8C3 =>3 E575EBE :8

=>?= ? 68:: 8A P ;& 9?7 L3 987:5;3<3; 57:5G75!9?7=# !7 =>3:3 9?:3:F 5= 5: E8<3 E3?757GAB6 =8 987:5;3< =>3 E?M5EBE $%&

=<?7:E5==3< ;37:5=D =>?= 4566 ?9>53C3 ? E575EBE :5G7?6 RB?65=DF 5#3# /!'*# (8 ?::3:: =>3 8L=?573; ;37:5=53:F 43 987:5;3< =>?= ? E575EBE 8A ρ = 0.2 ?64?D:S87 T5#3# 45=> ? B75=D ?9=5C5=D A?9=8<U $%& =<?7:E5==3<: @3< E² 733; =8 L3 =863<?L63 LD

=>3 :D:=3E 57 8<;3< =8 98796B;3 =>?= =>3 57=3<A3<3793 5: 78=

>?<EAB6# %3 3E@>?:5V3 =>?= ?9=B?6 ?9=5C5=D A?9=8<: ?<3 65H36D

=8 L3 :BL:=?7=5?66D 6843<F E3?757G =>?= ? @8=37=5?66D EB9>

6?<G3< 7BEL3< 8A @>D:59?6 ;3C593: 4566 9?B:3 =>3 :?E3 63C36 8A 57=3<A3<3793 ?: =>3 B75=D ?9=5C5=D A?9=8< ;3C593: 987:5;3<3;

57 =>5: :=B;D#

!" #$% &'()*+)*)',) -.&'/ (0) 122 34.5

(>3 +,, ;3!73: ;5AA3<37= 96?::3: 8A $%& ;3C593: IPKF IWK# X3<3F 43 4566 876D 987:5;3< =>3 96?:: 8A 98EEB759?=587

?7; E3?:B<3E37= :D:=3E: ?: =>3D ?<3 A8<39?:= =8 <3@<3:37=

9?# 1YZ 8A =>3 E?<H3=# (>3:3 $%& ;3C593: EB:= >?C3 =>35<

=<?7:E5::587 L?7; 57 =>3 <?7G3 A<8E J#P .XV =8 P2#[ .XV#

X3793F =>3 ./0 122 L?7; 5: 963?<6D 8B=:5;3 =>3 E?57 L?7;

?7; 4566 =>3<3A8<3 876D <3935C3 8B=S8ASL?7; 57=3<A3<3793# +8<

L8=> 57;88< ?7; 8B=;88< ?@@659?=587:F =>3 E?M5EBE 3E5::587

@843< :@39=<?6 ;37:5=D 5: 65E5=3; =8 S\] ;&EN0XV 57 =>3 122 0XV L?7;: 8A ./0# !7 ? ./0 122 9>?7736 8A W22 HXVF =>5:

98<<3:@87;: =8 ? E?M5EBE $%& =<?7:E5= @843< 8A SYW ;&E#

(>3 <?;5B: 8A =>3 5773< 95<963 ;3!757G =>3 E575EBE ;5:=?793

=8 =>3 968:3:= 57=3<A3<3< 5: :3= =8 rmin= 1E#

!7 +5GB<3 PF =>3 $%& =<?7:E5==3< ;37:5=53: 63?;57G =8 ? P

;& ;3G<?;?=587 8A =>3 /!'* ?7; ? <3;B9=587 =8 ?7 ?L:86B=3 /!'* 8A 1;& ?= =>3 9366 3;G3 ?<3 :>847 4>37 B:57G =>3 +,, 3E5::587 E?:H# (>3 ;5AA3<3793 L3=4337 =>3 8B=;88< ?7;

57;88< 37C5<87E37=: 5: =>3 :3==57G 8A =>3 L<3?H@857=O +8< =>3 57;88< 37C5<87E37=F =>3 L<3?H@857= >?: L337 :3= =8d0= 10EF 4>3<3?: A8< =>3 8B=;88< 37C5<87E37=F =>3 L<3?H@857= 5: :3=

?998<;57G =8 TJU# +<8E +5GB<3 P 43 9?7 :33 =>?= =>3 57;88<

37C5<87E37= 9?7 :B@@8<= >5G>3< ;37:5=53: =>?7 =>3 8B=;88<

37C5<87E37=# (>5: 5: ;B3 =8 =>3 :=<87G3< ?==37B?=587 8A =>3 57=3<A3<57G $%& =<?7:E5==3<: 45=> ;5:=?793# %3 ?6:8 <3E?<H

=>?= =>3 ;37:5=D 63C36 ;39<3?:3: 45=> =>3 <3B:3 A?9=8< A8< P;&

<36?=5C3 68::F 4>59> E?D G5C3 =>3 E5:=?H37 5E@<3::587 =>?=

!"

!"#$

!%

!%#$

!&

!&#$

!'

!' !( !$ !) !* !+ !, !%" !%% !%&

-./!01234560071!8734609

:;<4071!46=7>?7<47!@2A0B1 -./!01234560071!873460674!CB1!DEF!,""G!@::

638BB1G!%8/!;B44 B<08BB1G!%8/!;B44 B<08BB1G!EHI?!,8/

638BB1G!EHI?!,8/

172;6406A2;;9!17J<6178!8734609

+5G# P# (>3 ;37:5=53: 8A $%& =<?7:E5==3<: 9?B:57G ? P ;& ;<8@ 57 /!'*?=

=>3 9366 3;G3 T./0 122F +,,U

=>3 :D:=3E 45=> ? >5G>3< <3B:3 A?9=8< 5: E8<3 :B:93@=5L63 =8 3M=<? 57=3<A3<3793# Q6=>8BG> =>5: ?@@3?<: :8E34>?= 98B7=3<S 57=B5=5C3F =>5: 5: ;B3 =8 =>3 A?9= =>?= =>3 <3935C3;-.)+-6:5G7?6

<3E?57: ?L8B= 987:=?7= A8< C?<58B: <3B:3 A?9=8<: 4>563 =>3 785:3 ?7; 57=3<A3<3793 =3<E ;39<3?:3:# X3793F A8< 6?<G3< <3B:3 A?9=8<:F ? P ;& ;39<3?:3 899B<: ?= ? EB9> >5G>3< /!'* =><8BG>

? EB9> :E?663< 47.86-() 579<3?:3 57 =>3 57=3<A3<3793 =3<E#

*39?66 A<8E 3RB?=587 T\U =>?= ?UC/I∝K² ?7; LU =>3 /!'*

57 3RB?=587 TYU 5: 65E5=3; 876D LD =>3 57=3<A3<3793 @6B: 785:3

=3<E :B9> =>?=

SIN R∝ 1 1/K²+c

K→∞= 1 c

4>3<3 c = ^R_γ⁴(IUW B +n)# !A 43 987:5;3< =>3 9?:3 8A ?

;3G<?;?=587 =8 =>3 E575EBEFSIN Rtrgt = 9 ;&F43 :33 =>?=

=>3 :B@@8<=3; ;37:5=53: ?<3 6?<G36D ?L8C3 =>3 <3RB5<3; 2#W

=<?7:E5==3<:NE²F 3M93@= A8< *3B:3 A?9=8<K= 3# !7 =>5: 9?:3F

=>3 /!'* 45=>8B= $%& 57=3<A3<3793 4?: ?6<3?;D 63:: =>?7 P

;& ?L8C3SIN Rtrgt#

/5793 =>3 :B@@8<=3; ;37:5=53: ?<3 G<3?=3< =>?7 2#W

=<?7:E5==3<:Nm²57 =>3 684 /!'* <3G5E3 TK= 3,4U A8< ? P ;&

;<8@ 57 =>3 /!'* ?7; 6?<G36D ?L8C3 57 =>3 >5G> /!'* <3G5E3 TK >4UF 43 98796B;3 =>?= 5= 5: B765H36D =>?= =>3 ?@@659?=587 8A =>3 +,, :@39=<?6 E?:H 48B6; 63?; =8 >?<EAB6 57=3<A3<3793

=8 =>3 ./0 122 :D:=3E ?= =>3 9366 L8<;3<#

%" #$% &'()*+)*)',) -.&'/ (0) 9*898.): ;<=> 34.5

(>3 E?57 ;5AA3<3793 57 =>3 )(/! @<8@8:?6 A<8E =>3 +,,

<3GB6?=587: 5: =>3 E8<3 :=<57G37= 8B=S8ASL?7; 65E5=: =>?= ?@@6D#

(>3 ?@@<8?9> B:3; =8 3C?6B?=3 =>3 :B@@8<=3; ;37:5=53: 5:

3RB5C?637= =8 =>3 873 G5C37 ?L8C3 A8< =>3 +,, <3GB6?=587:#

+<8E IJKF 43!7; =>?= =>3 $%& 57=3<A3<3793 @843< 57 ? ./0 9>?7736 8A W22 HXV 5: 65E5=3; =8 ? E?M5EBE 8A SP2] ;&E#

$:57G =>3 :?E3 @?<?E3=3<: ?: 57 =>3 6?:= :39=587F 43 !7;

=>3 <3:B6=: 57 +5GB<3 W A8< ? P ;& ;3G<?;?=587 57 /!'* ?7;

A8< ? ;3G<?;?=587 ;847 =8 SIN Rtrgt = 9;&F <3:@39=5C36D#

+<8E =>8:3 <3:B6=: 5= 5: 5EE3;5?=36D 963?< =>?= =>3 ;37:5=53:

:B@@8<=3; LD =>3 @<8@8:3; )(/! 65E5=: ?<3 378<E8B: ?7;F

=>3<3A8<3F =>3 3AA39= 8A $%& 57=3<A3<3793 87 ./0 122 :D:=3E:

5: 98E@63=36D 73G65G5L63 A8< <3?65:=59 ;37:5=53: 8A≤2#W $%&

=<?7:E5==3<:NE²#

(4)

89

!"

!#""

!$""

!%""

!&""

!'""

!(""

!% !& !' !( !) !* !+ !#" !## !#$

,-.!/012345//60!76235/8

9:;3/60!35<6=>6;36!?1@/A0 ,-.!/012345//60!76235/563!BA0!CDE!+""F!GHDI

527AA0F!#7.!:A33 A;/7AA0F!#7.!:A33 A;/7AA0F!DIJ>!+7.

527AA0F!DIJ>!+7.

061:53/5@1::8!06K;5067!76235/8

!"#$ %$ &'( )(*+","(+ -. /01 ,23*+4",,(2+ 536+"*# 3 7 )1 )2-8 "* 9:;< 3, ,'( 5(== ()#( >?9@ ABBC D&9:E

!"

!"L"'

!"L#

!"L#'

!"L$

!"L$'

!"L%

!"L%'

!"L&

!% !& !' !( !) !* !+ !#" !## !#$

,-.!/012345//60!76235/8

9:;3/60!35<6=>6;36!?1@/A0 ,-.!/012345//60!76235/563!BA0!CDE!#*""F!?99

527AA0F!DIJ>!+7.

061:53/5@1::8!06K;5067!76235/8

!"#$ F$ &'( )(*+","(+ -. /01 ,23*+4",,(2+ 536+"*# 3 7 )1 )2-8 "* 9:;< 3, ,'( 5(== ()#( >?9@ 7GBBC !HHE

I$ /01 :;&D<!D<D;HD &J?9@ 7GBB

&'( -*=K )"..(2(*5( L(,M((* ?9@ 7GBB 3*) ?9@ ABB "+

,'( 5'3*#( -. ,'( ,23*+4"++"-* .2(N6(*5KC =(3)"*# 82"432"=K ,- 3 #2(3,(2 3,,(*63,"-* M",' )"+,3*5($ 0'"=( ?9@ 7GBB "+ +,"==

-6, -. ,'( 43"* /01 ,23*+4"++"-* L3*)C ,'( .35, ,'3, ", "+

+6L+,3*,"3==K 5=-+(2 4(3*+ ,'3, ,'( /01 "*,(2.(2(*5( 8-M(2

"+ "*52(3+()$ &'( -,'(2 83234(,(2+ 32( ,'( +34( 3+ .-2 ,'(

?9@ ABB 53=56=3,"-*+ 3L-O($

!" #$% &'()*+)*)',) -./'0 (1) 233 45.6 7 89: ;<==

;-,( ,'3, "* ,'( 53+( -. ,'( !HH ="4",+C ,M- )"..(2(*, ="4",+

(P"+, .-2 -6,)--2 3*) "*)--2 388="53,"-*+ Q7RC Q%R$ &'(+( 2(+6=,

"* STB)14 3*) SUB)14 /01 "*,(2.(2(*5( 8-M(2 .-2 "*)--2 3*) -6,)--2 388="53,"-*+C 2(+8(5,"O(=KC "* 3 %BB VWX ?9@

5'3**(=$ :* !"#62( FC ,'( 2(+6=,+ .-2 3 7 )1 =-++ "* 9:;<

3*) .-2SINRtrgt = 9)1 32( +'-M*$ 0( 53* +(( ,'3, (O(*

.-2 =-M 2(6+( .35,-2+CK = 3,4C ,'( 8(24"++"L=( )(*+","(+ 32(

5=(32=K L(=-M ,'( )(+"2() B$% /01 ,23*+4",,(2+Y4² .-2 ,'(

7 )1 =-++ "* 9:;<$ :* ,'( 53+( M'(2( ,'( ,32#(, 9:;< "+

5-*+")(2() ,'( +688-2,() ,23*+4",,(2 )(*+","(+ 32( +-4(M'3, '"#'(2 L6, +,"== 23,'(2 =-MC (O(* .-2 '"#' 2(6+( .35,-2+ 3*) 9:;<$ :* 832,"56=32C ,'( (P,23 ,23*+4"++"-* 8-M(2 "*)--2+ "+

2(+8-*+"L=( .-2 O(2K =-M 355(8,3L=( ,23*+4",,(2 )(*+","(+ "*

,'"+ (*O"2-*4(*,$ W(*5(C ,'( !HH (4"++"-* ="4",+ 32( ="V(=K

!"

!#

!$

!%

!&

!'

!(

!% !& !' !( !) !* !+ !#" !## !#$

,-.!/012345//60!76235/8

9:;3/60!35<6=>6;36!?1@/A0 ,-.!/012345//60!76235/563!BA0!CDE!#*""F!GHDI

527AA0F!DIJ>!+7.

061:53/5@1::8!06K;5067!76235/8

!"#$ Z$ &'( )(*+","(+ -. /01 ,23*+4",,(2+ 536+"*# 3 7 )1 )2-8 "* 9:;< 3, ,'( 5(== ()#( >?9@ 7GBBC D&9:E

,- 2(+6=, "* '324.6= "*,(2.(2(*5( .-2 ?9@ 7GBB 3, ,'( 5(==

L-6*)32K$ &'( -6,)--2 53+( +((4+ L-2)(2="*( +6.!5"(*, M'"=(

,'( "*)--2 53+( "+ 5=(32=K "*+6.!5"(*,$

%" #$% &'()*+)*)',) -./'0 (1) >*?>?.)@ AB9& 45.6 7 89:

;<==

&'( D&9: 43+V )-(+ *-, )"+,"*#6"+' L(,M((* "*)--2 3*) -6,)--2 388="53,"-*+ QFR$ :* ,'( 7GBB @WX L3*)C ,'( 2(+6=,"*#

/01 "*,(2.(2(*5( 8-M(2 .-2 3 %BB VWX ?9@ 5'3**(= "+

="4",() ,- SUA )14$ &'( 43P"464 /01 )(O"5( )(*+","(+

.-2 3 7 )1 )(#23)3,"-* "* 9:;< 3*) 3 )(#23)3,"-* ,- ,'(

,32#(, 9:;< -. A )1 32( +'-M* "* !"#62( Z$ [+ 53* L( +((*C ,'( 2(+6=,"*# )(*+","(+ .-2 ,'( 7 )1 =-++ "* 9:;< 32( 5=(32=K +6.!5"(*, ,- 355-44-)3,( 2(3="+,"5 )(O"5( )(*+","(+C "$($ \B$%

,23*+4",,(2+Y4²$ DN63==KC ,'( )(*+","(+ .-2 ,'( '"#'(2 2(6+(

.35,-2+ 3*) '(*5( ,'( '"#' 9:;< 53+(+C 32( M(== 3L-O( ,'(

2(N6"2() 4"*"464 )(*+",K$ :* +64432KC ", 53* L( +,3,() ,'3,

*- +"#*"!53*, "*,(2.(2(*5( "+ ="V(=K ,- ?9@ 7GBB +K+,(4+ .2-4 /01 +K+,(4+ (48=-K"*# ,'( D&9: +8(5,23= 43+V$

I:$ HJ;H]/9:J;9

&'"+ 838(2 5-*+")(2+ ,'( (..(5,+ -* ?9@ .2-4 /01 +K+S ,(4+C 6+"*# (",'(2 ,'( !HH -2 82-8-+() D&9: (4"++"-* ="4",+$

:, M3+ +'-M* ,'3, *- '324.6= "*,(2.(2(*5( "+ ,- L( (P8(5,() .-2 ?9@ ABB +K+,(4+$ :* ,'( 53+( -. ?9@ 7GBB +K+,(4+C ,'(

82-,(5,"-* 3..-2)() LK ,'( !HH 2(#6=3,"-*+ 388(32+ "*+6.!5"(*, 3, ,'( 5(== L-2)(2 M'(2(3+ ,'( 82-8-+() D&9: ="4",+ 3O-") 3*K +"#*"!53*, "*,(2.(2(*5($

<D!D<D;HD9

Q7R !()(23= H-446*"53,"-* H-44"++"-*C233 =C7D< 2/*.( E*@)* 5'@ F)>?*(C MMM$.55$#-OC [82"= %%C %BB%$

Q%R !()(23= H-446*"53,"-* H-44"++"-*C 233 =G7G :)4?*5'@-4 E>/'/?' 5'@ E*@)* 5'@ 2-*(1)* H?(/,) ?+ I*?>?.)@ F-J) :56/'0C MMM$.55$#-OC

@325' 7%C %BBF$

QFR D&9:CAF: 91?*( F5'0) @)K/,). -./'0 #$% (),1'?J?0L +?* ,?44-'/,57 (/?' >-*>?.). /' (1) +*)M-)',L *5'0) G"; 8NO (? ;="P 8NO QRF!2BSTAH G=C =PU K;"="= T I5*( ; 5'@ I5*( CC MMM$(,+"$-2#C %BB%$

QZR ],)$ @6=,"8=( [55(++ H-446*"53,"-*+C!' &'K).(/05(/?' /'(? (1) I?()'(/5J

&4>5,( ?+ #J(*57$/@)V5'@ B*5'.4/../?' 9L.()4.C MMM$23)"-$#-O$6V$

Q^R &$9$ <38838-2,C $/*)J).. 3?44-'/,5(/?'. 7 I*/',/>J). 5'@ I*5,(/,)C _2(*,"5( W3==C 7AAT$

QTR <3K4-*) 9,((=(C:?V/J) F5@/? 3?44-'/,5(/?'.C _(*,(5' _2(++ ]"4",()C 7AA%$