� � � � � � �� �������� ������ �� �����
� � �����
��������� �� ������ !" # $ ��� %& ��� '�("���$ ���� &%�
��� )�*��� + ����� %& ,-���-� �� ���
.���"��� ,-�%% %& � �� /��% ,���� 0 ��1�����2
32
,�������� ) 4,� 1� 5 3 67 6
8 8 8 8 8
� �� /��% ,���� 0��1�����2
9::9
+ ����� 4� 7;�$ �����%� <%$ $ ����� =
>? @ ABCDCE FGBHCIJ? K LMNCOJ?>? @ POGQ? RQSJOBCIQ
� TT�%1�� U2
LMNCOJ?>JEQ?IV JHI WX YDJGI?CGQD
YHZCHJJ?CHZ
G� �WE�?CZBI ��
FCMMBQ?IB > �FCDNQ
����
��������
�I CO Q �JDD SHW�H XQGI IBQI W?IBWZWHQD X?J�JHG� MCNCOCWH V DICE DJ CHZ �P�> �
E?WNCMJO Q E?QGICGQD OWDICWH IW GWHIJ? IBJ CHIJ?O�V� WD CHIJ?XJ?JHGJ ��F�� E?W� DJV
CVEWOJM �� IBJ X?J�JHG��OJDJGICNJ XQMCHZ ��F�� GBQHHJD @ � BCDJ IBJ QEEDCGQICWH WX
P�> CH ODW���F� V DICEQIB GBQHHJDO CO �JDD HMJ?OIW WM K IBJ QEEDCGQICWH WX P�>
CH XQOI��F� V DICEQIB GBQHHJDO CO X?QZBI � CIB OJNJ?QD MC� G DICJO K V QH� WX �BCGBBQNJ HWI � JJH E?QGICGQDD� I?JQIJM CH IBJ DCIJ?QI?J @ �J E?JV COJ W? �W?S WH IBJ
GDQCV IBQI G??JHI I?JHMO CH �?WQM�QHM � C?JDJOO GWVVHCGQICWH O�OIJV O MCGIQIJ IBQI
GBQHHJD ICV J�NQ?CQICWH � CDD OW WH EDQ� QH CVEW?IQHI ?WDJ CH P�> O�OIJV O @ RBJ
E?CV Q?� QMNQHIQZJO WX G�GDCG E?J� P�> CH ICV J�CHNQ?CQHI �F� GBQHHJDO K C @J @K IBJ
Q�OJHGJ WX �F� QHM WX CHIJ?GQ??CJ? CHIJ?XJ?JHGJ ��� �� K MW HWI GQ??� WNJ? IW ICV J� QHM
X?J�JHG��OJDJGICNJ K C @J @K MW� D� �OJDJGICNJ GBQHHJDO @ L O Q ?JO DI K IBJ OIQHMQ?M �J?W�
XW?GCHZ ���� K DCHJQ? V CHCVV VJQH�O�Q?J J??W? �� FY � QHM V Q CVV DCSJDCBWWM� �� MJIJGICWH IJGBHC�JO � JGWV J E?WBC� CICNJD� GWV EDJ @
LH QHQD�ICG OIM� WX IBJ HQI?J WX �� � OBW� O IBQI CI CO VWOI E?WV CHJHI QV WHZ
HJQ?�� O� GQ??CJ?O @ �?IBJ? K CHGW?E W?QICHZ IBJ J�JGIO WX MCOIQHI�O� GQ??CJ?��� � VCZBI
CVE?WNJ IBJ MJIJGICWH E J?XW?V QHGJ �I �W DM E?JNJHI E?QGICGQD CV EDJV JHIQICWH @ L O
CC
Q E?QGICGQD O� WEICV QD QDIJ?HQICNJ K �J E?WEWOJ Q DW��GWVEDJ CI� DCHJQ? ?JGJCNJ? E?J�E?W GJOOCHZ OGBJV J IBQI ?JHMJ?O IBJ �� � ?JOE WHOJ OEQ?OJ K IBJ?J�� OCVEDCX� CHZ O�OJ�
�JHI O�V�WD MJIJGICWH @ RBJ �� � OI?GI?J OZZJOIO E?J�E?WGJOOCHZ IBQI OI?CNJO IW
DCV CI IBJ �� � IW ��� ���� � O� GQ??CJ?O @
� CHQDD� �J E?WE WOJ GWV EIQICWHQDD� �J� GCJHI O� WEICV QD MJGCOCWH�XJJM�QGS OI?QIJ�
ZCJO IW W�IQCH ?JDCQ� DJ OWXI�O�V�WD JOICV QIJO �BCGB GQH � J XJM IW Q MJGWMJ? @ FCV DQICWH
?JO DIO CHMCGQIJ ZWWM E J?XW?V QHGJ ?JDQICNJ IW IBJ OIQHMQ?M MJIJGIW?O �I � CIB OCZHC��
GQHI GWV EIQICWHQD OQNCHZO @
CCC
� � � � � � �� �������� ������ �� �����
32
,�������� ) 4,� 1� 5 + 6, 6
� �� /��% ,���� 0 ��1�����25 9::9
)� 6 ��� �T ,-������ 5 � �1 ����
�I CO Q �JDD SHW�H XQGI IBQI W?IBWZWHQD X?J�JHG� MCN COCWH V DICE DJ CHZ �P�> �
E?WNCMJO Q E?QGICGQD OWDICWH IW GWHIJ? IBJ CHIJ?O�V� WD CHIJ?XJ?JHGJ ��F�� E?W� DJVCVEWOJM �� IBJ X?J�JHG��OJDJGICNJ XQMCHZ ��F�� GBQHHJD @ � BCDJ IBJ QEEDCGQICWH WX
P�> CH ODW���F� V DICEQIB GBQHHJDO CO �JDD HMJ?OIW WM K IBJ QEEDCGQICWH WX P�>
CH XQOI��F� V DICEQIB GBQHHJDO CO X?QZBI � CIB OJNJ?QD MC� G DICJO K V QH� WX �BCGB
BQNJ HWI � JJH E?QGICGQDD� I?JQIJM CH IBJ DCIJ?QI?J @ �J E?JV COJ W? �W?S WH IBJ
GDQCV IBQI G??JHI I?JHMO CH �?WQM�QHM � C?JDJOO GWVVHCGQICWH O�OIJV O MCGIQIJ IBQI
GBQHHJD ICV J�NQ?CQICWH � CDD OW WH EDQ� QH CVEW?IQHI ?WDJ CH P�> O�OIJV O @ RBJ
E?CV Q?� QMNQHIQZJO WX G�GDCG E?J� P�> CH ICV J�CHNQ?CQHI �F� GBQHHJDO K C @J @K IBJQ�OJHGJ WX �F� QHM WX CHIJ?GQ??CJ? CHIJ?XJ?JHGJ ��� �� K MW HWI GQ??� WNJ? IW ICV J� QHM
X?J�JHG��OJDJGICNJ K C @J @K MW� D� �OJDJGICNJ GBQHHJDO @ L O Q ?JO DI K IBJ OIQHMQ?M �J?W�
XW?GCHZ ���� K DCHJQ? V CHCVV VJQH�O�Q?J J??W? �� FY � QHM V Q CVV DCSJDCBWWM
� �� MJIJGICWH IJGBHC�JO � JGWV J E?WBC� CICNJD� GWV EDJ @
�
LH QHQD�ICG OIM� WX IBJ HQI?J WX �� � OBW� O IBQI CI CO VWOI E?WV CHJHI QV WHZHJQ?�� O� GQ??CJ?O @ �?IBJ? K CHGW?E W?QICHZ IBJ J�JGIO WX MCOIQHI�O� GQ??CJ?��� � VCZBI
CVE?WNJ IBJ MJIJGICWH E J?XW?V QHGJ �I �W DM E?JNJHI E?QGICGQD CV EDJV JHIQICWH @ L O
Q E?QGICGQD O� WEICV QD QDIJ?HQICNJ K �J E?WEWOJ Q DW��GWVEDJ CI� DCHJQ? ?JGJCNJ? E?J�
E?W GJOOCHZ OGBJV J IBQI ?JHMJ?O IBJ �� � ?JOE WHOJ OEQ?OJ K IBJ?J�� OCVEDCX� CHZ O�OJ�
�JHI O�V�WD MJIJGICWH @ RBJ �� � OI?GI?J OZZJOIO E?J�E?WGJOOCHZ IBQI OI?CNJO IW
DCV CI IBJ �� � IW ��� ���� � O� GQ??CJ?O @
� CHQDD� �J E?WE WOJ GWV EIQICWHQDD� �J� GCJHI O� WEICV QD MJGCOCWH�XJJM�QGS OI?QIJ�ZCJO IW W�IQCH ?JDCQ� DJ OWXI�O�V�WD JOICV QIJO �BCGB GQH � J XJM IW Q MJGWMJ? @ FCV DQICWH
?JO DIO CHMCGQIJ ZWWM E J?XW?V QHGJ ?JDQICNJ IW IBJ OIQHMQ?M MJIJGIW?O �I � CIB OCZHC��
GQHI GWV EIQICWHQD OQNCHZO @
�
>JMCGQIJM IW V� EQ?JHIO ABCDW QHM � Q??� > �FCDNQ K V� OCOIJ? FBQDCHC QHM IBJ DWNJD� O @ LM?J� � ?QZQH�Q
CN
���������������
� I�W �JQ?O QI IBJ PBCW FIQIJ HCNJ?OCI� BQNJ � JJH Q Z?JQI DJQ?HCHZ JEJ?CJHGJ K�WIB QGQMJV CG QHM WIBJ?� COJ @ � IQSJ IBCO WEEW?IHCI� IW IBQHS IBJ CHOICIICWH QHM
QDD IBJ �WHMJ?X D E JWEDJ � �NJ GWVJ IW SHW� IB?WZB V� OIQ� QI PF @
� C?OI QHM XW?JVWOI K � �W DM DCSJ IW IBQHS V� Z?QMQIJ QMNCOW? K A?WX @ ABCDCE
FGBHCIJ? K XW? BCO EQICJHGJ QHM ICV JD� QMNCGJ @ � � CDD QD�Q�O GBJ?COB ABCD QO Q X?CJHM QHM
Z CMJ �BW ZQNJ V J ZWWM GWHOI?GICNJ XJJM�QGS QHM IQZBI V J IW �W?S OV Q?I QHM EDQ�
BQ?M @ � �W DM DCSJ IW IBQHS A?WX @ P OGQ? RQSJOBCIQ XW? � JCHZ Q EQ?I WX V� QOIJ? �O
JQV CHQICWH GWVV CIIJJ @ QH� IBQHSO QDOW ZW IW A?WXO @ � JOBQV YD� QV QD K �QHM� WOJO QHM �JJ AWIIJ? XW? IBJC? QMNCGJ K CHOCZBIX D GWVV JHIO QHM IJQGBCHZ @
� J I K � �W DM DCSJ IW IBQHS V� GWDDJQZJO QI IBJ �HXW?V QICWH A?WGJOOCHZ F�OIJV O
��AF� DQ�W?QIW?� XW? IBJC? X?CJHMOBCE QHM ZWWM OEC?CI @ � �QHI IW IBQHS �QNC XW? E?W�
NCMCHZ JGJDDJHI IJGBHCGQD OEEW?I IW IBJ �AF DQ� >JXHJ K YV ?J K �CHZ QHM � CQW CQ XW?
IBJC? BJDE QHM QMNCGJ WH ?JOJQ?GB QHM XW? � JCHZ CHOEC?CHZ OJHCW? DQ� V JV� J?O QHM IBJ
QV CGQ� DJ DS XW? BJ? QDQG?CI�@
� �W DM QDOW DCSJ IW IBQHS �QDEBQ� JICGQDD� � � JJIJOB K FQV ?QI K FQIBCOB K FBQDCHC KFSC?IC QHM RQIBQZQIBQ XW? � JCHZ Q EQ?I WX V� HVJ?WO JI?QG??CG DQ? QGICN CICJO @
FQNCHZ IBJ � JOI XW? DQOI K � �W DM DCSJ IW IBQHS LMQV QHM �IB XW? � JCHZ JJVEDQ?�
X?CJHMO �BW �J?J QD�Q�O IBJ?J XW? V J K QHM V� GDWOJOI X?CJHMO QI PF K � C� W� QHM LV WD K
XW? IBJ XH ICV JO �J BQM � CIB GDQOOJO K M COGOOCHZ ?JOJQ?GB K IBJ �Q? � GD� OGJHJO K IBJ
N
ECGHCGO K IBJ GQVECHZ I?CEO K IBJ ?WQM I?CEO K IBJ � CHMC �QHIJ? QHM QDD IBJ �HMCQH GWWSCHZIBQI V QMJ V� OIQ� CH IBJ F Q VJVW?Q� DJ WHJ @
N C
����
LE?CD �� K ���� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��W?H � QM?QO K �HMCQ
FVVJ? ���� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � @Y @ Y DJGI?WHCGO YHZCHJJ?CHZ KFQ?MQ? AQIJD �WDDJZJ WX YHZCHJJ?CHZ K�WV�Q�
�QDD ���� � FV VJ? ��� � � � � � � � � � � � � � � � � � � � � ?QMQIJ RJQGBCHZ L OOWGCQIJ KRBJ PBCW FIQIJ HCNJ?OCI�@
�QDD ��� �� �QDD ���� � � � � � � � � � � � � � � � � � � � � � � � � ?QMQIJ � JOJQ?GB L OOWGCQIJ KRBJ PBCW FIQIJ HCNJ?OCI�
���� ���� ��� �
ABCDCE FGBHCIJ? QHM FCMMBQ?IB > �FCDNQ K ��W���WVEDJ CI� >JIJGICWH WX P�> CH>W� D��>COE J?OCNJ �BQHHJDO� @ �� ���� � ����� � ���� ��� �� �� �������� ��������� ���! "��� K �AQGC�G ?WNJ K �L � K �WN @ ���� @
#���� � �# ����$
Q� W? � CJDM % YDJGI?CGQD YHZCHJJ?CHZ
FIMCJO CH %>JIJGICWH � YOICV QICWH RBJW?�K > CZCIQD A?WX @ ABCDCE FGBHCIJ?FCZHQD A?WGJOOCHZ K LMQEICNJ � CDIJ?CHZ
�WVVHCGQICWH RBJW?�K �WMCHZ RBJW?� A?WX @ � JOBQV YD� QV QD
N CC
����� �# ��������
����
L�OI?QGI @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ CC
>JMCGQICWH @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ CN
L GSHW� DJMZVJHIO @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ N
� CIQ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ N CC
� COI WX � CZ?JO @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
�BQEIJ?O %
� @ �HI?WMGICWH @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ �
� @� A?W� DJV O �HBJ?JHI IW � ?WQM�QHM � C?JDJOO �WVVHCGQICWH @ @ @ @ @ �
� @� P�> K Q A?QGICGQD L DIJ?HQICNJ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ �
� @� RBJOCO P?ZQHC�QICWH @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ �
� @ �QGSZ?WHM @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ �
� @� � C?JDJOO �BQHHJD WMJDO @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ �
� @� RBJ P�> O�OIJV VWMJD @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @� Y COICHZ FI?QIJZCJO XW? P�> CH >W� D��FJDJGICNJ �BQHHJDO @ @ @ @ ��
� @� P? A?WE WOQD @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @ RBJ Y� JGI WX Q >W� D��FJDJGICNJ �QMCHZ �BQHHJD WH P�> @ @ @ @ @ @ @ ��
� @� RCV J��QZ �BQHHJD FIQICOICGO @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��� @� >WEEDJ?��QZ �BQHHJD FIQICOICGO @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��� @� >WEEDJ?��?J�JHG� �BQHHJD FIQICOICGO @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
NCCC
� @ >WEEDJ?��BQHHJD FBW?IJHCHZ NCQ � CHJQ? � JGJCNJ? A?WGJOOCHZ @ @ @ @ @ @ @ ��
� @� WICNQICWH @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��� @� Y�JGI WX R CV J�>WV QCH � CHMW� CHZ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ � �
� @� Q�F��� � CHMW� >JOCZH @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @� Q�F��� � CHMW� % LEE?W CV QICWH CH �Q?ZJ��� �QOJ @ @ @ @ @ @ @ ��
� @ FGBJVJO XW? �WBJ?JHI YOICV QICWH K >JGWMCHZ � >JIJGICWH CH P�> @ @ @ ��
� @� >JIJGICWH FGBJV JO XW? HGWMJM P�> @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @� @� JHJ?QD ���� �� ?IJ��W?GJ �F> � @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @� @� >CQZWHQD ���� @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @� YOICV QICWH FGBJVJO XW? �WMJM P�> @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��� @� @� �JQOI�F�Q?JO YOICV QICWH @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��� @� @� � CHJQ? CH CVV JQH�F�Q?J Y??W? YOICV QICWH @ @ @ @ @ @ ��
� @� @� >CNJ?OCI� YEDWCICHZ �� �YOICV QICWH @ @ @ @ @ @ @ @ @ @ @ @ @ ��� @� @� FY ��QOJM >JGCOCWH�>C?JGIJM YOICV QICWH @ @ @ @ @ @ @ @ @ ��
� @ FCV DQICWH � JO DIO @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @ �WHGDOCWHO � �I?J �W?S @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
LEEJHMCGJO %
L @ P�> CH �R � �BQHHJDO @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� C� DCWZ?QEB� @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
C
� ��� �# #������
������ ����
� @� ����� �� � ���� ����� ��� �� ���� � � �������� ��� @ @ @ @ �
� @� ����� ��������� � ��� ��� �� ����� �� ���� � @ @ @ @ @ @ @ @ @ @ @ ��
� @� ���� �� �� ������� @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @� ���� � �� � �� � ! � �� �� " ����� ����� @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @� # ��� �� �� � �� " $ "% @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @� &����� � �� ���� @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @� '����� (�� �� ) ���� � ����*+,- . � ��. � � � ! � �� ��/ �� � ��� ����� " ��
� @� ����� �� �� (��� �� . � ��. � � @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @� 0����. � ��. � � *+,- 123 4256 7 ����� *��������,��� -���� 18 34) 9 7 @ @ ��
� @� 0����. � ��. � � *+,- 123 4256 7 ����� ,�����:� ����� *���� 1;� 7 @ @ � �
� @� �����. �� ������ ����� ��� ���� @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @� < �� �������� �� 1�7 �� ���� ����=� �� ��� ������ ���� . � ���. � � � � ���� � � > 1� 7 �� ��������=� �� ��� � ����� ���� . � ���. � � > � ���� � � � ���� ���� " @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @� ?-@<�� � ������ ������� �������� ���� ���� @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @� ��*������ ������ ������� ���� ���� @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @� � ���� ����� ���� ���� � �'+ ��� � @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @� &�������� �� ��(� � ������ ���� � ��� ���� ���� @ @ @ @ @ @ @ @ ��
� @� ?- �������� ������ ������ ����� ���� ������ ������ @ @ @ @ @ @ ��
� @� ?- �������� ������ ������ ����� �� *������ ������ ������ @ @ @ ��
� @� ��- ������� � �� �� ���*� ������ ����� ��� ��:� ����� �����;� @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @� ��- ������� � �� �� ��*������ ������ ������ ������ ����� �����:� ����� ����� ;� @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
� @� &�������� �� �� ���*� ������ � � �� �� *������ ������ ������������ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ��
C
������� �
��������� ���
� ?WQM�QHM � C?JDJOO GWVVHCGQICWH CO QH CVEW?IQHI GWVEWHJHI WX IBJ JNWDN CHZ
ZDW�QD CHXW?V QICWH CHX?QOI?GI?J @ �??JHI QHM XI?J ZJHJ?QICWH � C?JDJOO DCHSO Q?JJEJGIJM IW E?WN CMJ BCZB MQIQ ?QIJ I?QHOV COOCWH WX V DICV JMCQ OJ?NCGJO OGB QO � C?J�
DJOO N CMJW K � C?JDJOO �HIJ?HJI QGGJOO QHM VW� CDJ GWVEICHZ K QHM CH OWVJ GQOJO Q?J
JEJGIJM IW MW OW CH NJ?� BCZB VW� CDCI� OCIQICWHO ��� @ LI IBJ OQV J ICV J K W? DCV CIJM
?QMCW OE JGI?V BQO � JGWVJ QH CHG?JQOCHZD� E?JGCWO ?JOW?GJ K JHIQCDCHZ BCZB OE JGI?QD
J� GCJHG�K IBJ OJ WX BCZBJ? GQ??CJ? X?J�JHGCJO QHM CH OWVJ GQOJO OE JGI?V OBQ?CHZ
� JI�JJH MC�J?JHI � C?JDJOO OJ?O @ �H QMMCICWH K GWHOVJ? MJV QHMO MCGIQIJ IBQI IBJ GWOI
WX � C?JDJOO IJ?V CHQDO � J SJEI DW� QHM IBJC? OC�JO OV QDD @ RBO � C?JDJOO GWVVHCGQICWHIJGBHWDWZ� WX IBJ XI?J VOI WE J?QIJ QI BCZB MQIQ ?QIJO K QI BCZB GQ??CJ? X?J�JHGCJO K
CH BCZB VW� CDCI� OCIQICWHO QHM HMJ? BCZB DJNJDO WX OE JGI?QD CHIJ?XJ?JHGJ K QDD �BCDJ
V QCHIQCHCHZ ?JDCQ� DJ MQIQ I?QHOV COOCWH OCHZ OV QDD QHM CHJEJHOCNJ GWV EWHJHIO @
��� � ���� � �� ��� �� � �������� � ����� ��������� ���
�H � C?JDJOO GWVVHCGQICWH K QH CHXW?V QICWH OCZHQD � CIB Q EQ?ICG DQ? �QHM� CMIB COVWM DQIJM IW Q MJOCZHQIJM X?J�JHG� �QHM XW? I?QHOV COOCWH @ L MCZCIQD GWVVHCGQICWH
�
OCZHQD GQH � J NCJ�JM QO Q OJ�JHGJ WX E DOJO BQN CHZ E J?CWM � @ � CZB MQIQ ?QIJ QEEDC�GQICWHO HJGJOOCIQIJ IBJ OJ WX OBW?I E DOJO �J @Z @K � � �� O� QHM BJHGJ DQ?ZJ �QHM� CMIB
�� � ��� � � � �� K W? �?WQM�QHM OCZHQDO @
QH� VWMJ?H �?WQM�QHM � C?JDJOO O�OIJV O JV EDW� GQ??CJ? OCZHQDO QI X?J�JHGCJO
CH IBJ ?QHZJ WX OJNJ?QD � � K DJQMCHZ IW Q I?QHOV CIIJM�OCZHQD �QNJDJHZIB WH IBJ W?MJ?
WX V CDDCV JIJ?O @ FGB BCZB X?J�JHGCJO Q?J OJM � JGQOJ DW�J? X?J�JHGCJO BQNJ � JJH
?JOJ?NJM XW? E?J�J COICHZ GWVVHCGQICWH O�OIJV O @ L DOW K B CZBJ? X?J�JHGCJO QDDW� VW?J
OCZHC�GQHI X?J�JHG� ?J�OJ % � JGQOJ BCZB X?J�JHG� OCZHQDO Q?J JQOCD� QIIJHQIJM ��
� CDM CHZO K I?JJO QHM QIV WOEBJ?CG CVEJMCV JHIO QDDW� CHZ IBJ OQVJ X?J�JHG� ?QHZJ IW
� J OJM �� Q O� GCJHID� MCOIQHI K M C� J?JHI � C?JDJOO O� OIJV @ L BCZB�X?J�JHG� GQ??CJ?
GWEDJM � CIB Q �?WQM�QHM CHXW?V QICWH OCZHQD K E WOJO OCZHC�GQHI GBQDDJHZJO �BCGB GQH
� J HMJ?OIW WM �� GWHOCMJ?CHZ IBJ OCZHQD E?WEQZQICWH EQIB � JI�JJH IBJ I?QHOV CI QHM
?JGJCNJ QHIJHHQO @ LEQ?I X?WV Q MC?JGI �DCHJ�WX�OCZBI� OCZHQD GWVEWHJHI � JI�JJH QH�
IJHHQO ��BCGB Q?COJO CH GJ?IQCH OE JGCQD GC?GVOIQHGJO� K IBJ ?JGJCNJM OCZHQD GWHOCOIO
WX Q V DICIMJ WX I?QHOV CI�OCZHQD ?J�JGICWHO X?WV EB�OCGQD W�� JGIO �W? OGQIIJ?J?O� CHIBJ NCGCH CI� WX IBJ QHIJHHQO @ R�ECGQD OGQIIJ?J?O Q?J � CDM CHZO K I?JJO K GQ?O QHM IBJ
EQNJV JHI @ YQGB OGQIIJ?CHZ EQIB GQH � J GBQ?QGIJ?C�JM �� QH QIIJHQICWH K EBQOJ�OBCXI
QHM MJDQ�@ RBJOJ NQDJO Q?J Q XHGICWH WX IBJ ?J�JGICN CI� WX IBJ OGQIIJ?J? QHM IBJ
IWIQD DJHZIB WX IBJ ?J�JGIJM EQIB @ RBJ ?J�JGIJM OCZHQDO V Q� GWV� CHJ GWHOI?GICNJD�
W? MJOI?GICNJD� QI IBJ ?JGJCNJ QHIJHHQ K MJE JHMCHZ WH IBJC? ?JDQICNJ EBQOJ K ?JO DICHZ
CH QH QV EDC�GQICWH W? QHHCBCDQICWH WX IBJ I?QHOV CIIJM OCZHQD @ ����� EBQOJ MC�J?JHGJ
� CJDMO GWV EDJIJ GQHGJDDQICWH @��W? OCZHQDO CH IBJ � � X?J�JHG� ?QHZJ K EQIB�DJHZIB MC�J?JHGJO WH IBJ W?MJ? WX
V CDDCV JIJ?O GQH GQOJ OCZHC�GQHI EBQOJ MC� J?JHGJO QHM IBO V Q� W? �GIQICWHO CH IBJ
�
?JGJCNJM OCZHQD DJNJD @ RBCO CV EDCJO IBQI JNJH � CHM�CHMGJM QHIJHHQ QHM�W? I?JJ�DJQXVWNJVJHIO CH ��JM� � C?JDJOO QEEDCGQICWHO GQH E?WMGJ OJNJ?J OCZHQD XQMJO @ RBCO
�V DICEQIB�XQMCHZ� V QSJO CI MC� G DI IW ?JDCQ� D� ?JGWNJ? IBJ I?QHOV CIIJM CHXW?V Q�
ICWH �BJH IBJ ?JGJCNJM OCZHQD DJNJD XQDDO � JDW� IBJ HWCOJ�CHIJ?XJ?JHGJ DJNJD K QHM IBO
E?JOJHIO Q XHMQVJHIQD GBQDDJHZJ IW � C?JDJOO MQIQ GWVVHCGQICWH @
� BJH IBJ QHIJHHQO W? IBJ MWV CHQHI OGQIIJ?J?O Q?J VW� CDJ K IBJ ?JDQICNJ OGQIIJ?J?
DW GQICWHO V Q� GBQHZJ M?QOICGQDD� WNJ? OBW?I E J?CWMO WX ICV J K DJQMCHZ IW Q ?QECM GBQHZJ
CH OCZHQD DJNJD K W? ?QECM XQMCHZ @ RBJ �XQMCHZ�?QIJ� CO IBJH E?WEW?ICWHQD IW IBJ ?JDQICNJOE JJM � JI�JJH OGQIIJ?J?O QHM QHIJHHQO @
RBJ XQMCHZ VJGBQHCOV MJOG?C� JM Q�WNJ K GQDDJM ��QI�XQMCHZ� K QEEDCJO IW QH� OCZHQD
�HQ??W��QHM W? �?WQM�QHM � IBQI CO I?QHOV CIIJM QI BCZB X?J�JHGCJO @ LH QMMCICWHQD
XQMCHZ V JGBQHCOV CO CHBJ?JHI IW �?WQM�QHM OCZHQDO @ FQ� � CO OV QDD GWVEQ?JM IW IBJ
EQIB MJDQ� MC� J?JHGJO @ RBJH IBJ ?JGJCNJ QHIJHHQ V CZBI W�OJ?NJ WHJ E DOJ �W? MQIQ
O�V�WD� QG?WOO Q OBW?I�MJDQ� �J @Z @K DCHJ WX OCZBI� EQIB QHM OCV DIQHJWOD� W�OJ?NJ
E?JNCWOD��I?QHOV CIIJM E DOJO QG?WOO DWHZ�MJDQ� �J @Z @K M COIQHI OGQIIJ?J?� EQIBO @ RBOIBJ ?JGJCNJM OCZHQD CO HWI WHD� EDQZJM �� IBJ OCZHQD XQMCHZ MJOG?C� JM Q�WNJ �I QDOW
�� CHIJ?�O�V�WD CHIJ?XJ?JHGJ ��F�� % YQGB O�V�WD W�OJ?NQICWH CO GW??EIJM �� JGBWO WX
E?JNCWOD� I?QHOV CIIJM O�V�WDO @ �H XQGI K V QH� �?WQM�QHM � QEEDCGQICWHO BQNJ � ���
MC� J?JHI O�V� WDO CHIJ?XJ?CHZ QI QH� ZCNJH ICV J @ LZQCH K IBJOJ O�V� WDO V Q� GWV� CHJ
GWHOI?GICNJD� W? MJOI?GICNJD�K MJE JHMCHZ WH IBJ MQIQ NQDJO IBJ� ?JE?JOJHI K DJQMCHZ
IW E WIJHICQD OCZHQD GQHGJDDQICWH @ RBJ Q??CNQD WX V DICE DJ MJDQ�JM EQIBO QGIO DCSJ Q
� DIJ? WH IBJ I?QHOV CIIJM O�V�WD OJ�JHGJ K C @J @K �J JE JGI OWV J X?J�JHGCJO � CIB CH IBJ� �� ����� ��� ���� ��� ������������� � ��� � � �� ��� ������� ���� ��� ����� ��� ����� ��
��� ���� ����� �������� � ��� ������� ���������� �� �� � � �� ��� ��������
�
I?QHOV CIIJM�OCZHQD �QHM� CMIB IW � J QIIJHQIJM VW?J IBQH WIBJ?O @ �W? IBCO ?JQOWH KIBCO DQIIJ? XQMCHZ CO SHW�H QO �X?J�JHG��OJDJGICNJ XQMCHZ�� @
� BCDJ QI �?OI �F� VCZBI OJJV QO Q OJ?CWO CVEJMCV JHI IBQI � C?JDJOO O� OIJV MJOCZH�
J?O BQNJ IW GWHIJHM � CIB K IBJ E?JOJHGJ WX OJNJ?J �F� QGIQDD� W�J?O IBJ EWOOC� CDCI� WX
X?J�JHG��MCNJ?OCI� ZQCH Q�W?MJM �� IBJ OJJV CHZD� ?QHMWV HQI?J WX V DICEQIB XQM�
CHZ �� K�� @ RBJ WEICV QD OJ�JHGJ MJIJGIW? �IBJ V Q CVV � DCSJDCBWWM MJIJGIW?� ?J� C?JM
IW X DD� JEDWCI IBCO MCNJ?OCI� ZQCH CO E?WBC� CICNJD� GWV EDJ QO CIO GWVEDJ CI� CO QH
JEWHJHICQD XHGICWH WX IBJ GBQHHJD V JVW?� DJHZIB @ RBO K CH E?QGICGJ K �F��GBQDDJHZJMO�OIJV O JV EDW� ICV J�MWV QCH J�QDC�QICWH �� � �BCGB K �BCDJ O�WEICV QD X?WV Q MJIJG�
ICWH OIQHMEWCHI K ?JQOWHQ� D� JEDWCIO IBJ MCNJ?OCI� W� J?JM �� IBJ V DICEQIB GBQHHJD @
RBJ ICV J�MWV QCH J�QDC�J? �R>Y � QIIJVEIO IW QMQEICNJD� CHNJ?I IBJ � DIJ?CHZ QGICWH WX
IBJ GBQHHJD @ �I OBW DM � J HWIJM IBQI QO �F� CHG?JQOJO K GWV EICHZ IBJ R>Y GWJ� GCJHIO
� JGWV JO GWVEIQICWHQDD� CHIJHOCNJ V QSCHZ CI QH CHXJQOC� DJ QDIJ?HQICNJ @ � JQDC�CHZ IBQI
IBJ ICV J�MWV QCH � DIJ?CHZ �GWHNWDICWH � VJHICWHJM Q�WNJ CO J� CNQDJHI IW V DICE DCGQ�
ICWH WX IBJ OE JGI?Q WX IBJ OCZHQDO CHNWDNJM K X?J�JHG��MWV QCH J�QDC�QICWH ��>Y � �QOOZZJOIJM CH �� K�� @ � BCDJ �>Y GWVEDJ CI� CO CHMJE JHMJHI WX IBJ OC�J WX GBQHHJD V JV �
W?�K CI ?J� C?JO Q � DW GS I?QHOV COOCWH WX O�V� WDO � CIB Q O� GCJHID� DQ?ZJ ZQ?M CHIJ?NQD
QHM QDOW QOOVJO IBJ E?JOJHGJ WX Q GWHOIQHI GBQHHJD WNJ? IBJ � DW GS M?QICWH @
��� �#�� � � � ���� ���� � ��������
L VW?J E?QGICGQD OWDICWH IW IBJ OJNJ?J �F� E?W� DJV CO ZCNJH �� Q V DICGQ??CJ? V WM�
DQICWH OGBJV J SHW�H QO W?IBWZWHQD X?J�JHG� MCNCOCWH V DICE DJ CHZ �P�> � ����� @� � ����� � � ��� ����� ����� ��� ��� �������� ��� � ��� � ���� ��� ��� � ����� ���� ��
�������
�
������ �� � � �� �� � �� � ���� �� ���
����� � ��� � �� �� � � �� �
� � � � ��� � ���� �� ���
�� ��� �� � � �� � � � ������
��������� � � ���� � �� ��� �� ��� �� � ��
� CZ?J � @� % ����� �� � ���� ����� ��� �� ���� � � �������� ���
� J?J K �?WQM�QHM MQIQ CO I?QHOV CIIJM OCHZ Q DQ?ZJ HV� J? WX EQ?QDDJD DW��?QIJ �HQ?�
?W��QHM � OI?JQV O GQDDJM �O� GQ??CJ?O� �BWOJ O�V� WD E J?CWMO Q?J DQ?ZJ GWV EQ?JM IW
IBJ GBQHHJD MJDQ� OE?JQM @ RBO IBJ O� GQ??CJ?O JEJ?CJHGJ �QI �?QIBJ? IBQH X?J�JHG��OJDJGICNJ� XQMCHZ K QNWCMCHZ �F� QHM BJHGJ Z?JQID� OCV EDCX� CHZ ?JGJCNJ? MJOCZH @ WM�
DQICWH QHM MJV WM DQICWH WX IBJ O� GQ??CJ?O GQH � J QGGWVEDCOBJM CH Q � DW GS����� DW GS
XQOBCWH OCHZ IBJ GWVEIQICWHQDD��J� GCJHI XQOI �W?CJ? I?QHOXW?V ���R � QDZW?CIBV K
V QSCHZ P�> I?QHOGJCNJ? CV EDJV JHIQICWH E?QGICGQD @ LH CVEW?IQHI MJIQCD CO IBQI Q
ZQ?M CHIJ?NQD WX M?QICWH Z?JQIJ? IBQH IBJ GBQHHJD MJDQ� OE?JQM VOI � J CHOJ?IJM
� JI�JJH I?QHOV CIIJM � DW GSO IW V QSJ IBJV G�GDCG QHM JHO?J O� GQ??CJ? W?IBWZWHQDCI�
�BCGB CO IBJ SJ� IW ?JGJCNJ? OCV EDCGCI�@ RBJ P�> ZQ?M CHIJ?NQD DJQMO IW Q ODCZBIDWOO CH J� GCJHG�K QDIBWZB IBCO DWOO GQH � J V QMJ HJZDCZC� DJ �� CHG?JQOCHZ IBJ OC�J WX
�
IBJ P�> � DW GS @ RBO QI �?OI ZDQHGJ K P�> OJJV O IW W� J? QH J� GCJHI OWDICWH IWG??JHI �?WQM�QHM � C?JDJOO GWV VHCGQICWH E?W� DJV O @
RBJ WEJ?QICWH WX P�> MJOG?C� JM Q�WNJ ?J� C?JO IBQI IBJ XQMCHZ ?QIJ CO ODW�
JHWZB �ODW� ICV J NQ?CQICWH WNJ? IBJ P�> � DW GS � IW SJJE IBJ O� GQ??CJ?O W?IBWZW�
HQD @ L O IBJ XQMCHZ ?QIJ CHG?JQOJO K Q O� GQ??CJ? JEJ?CJHGJO Q XQMCHZ ZQCH IBQI NQ?CJO
OCZHC�GQHID� QDWHZ IBJ P�> � DW GS DJQMCHZ IW QH CHG?JQOJ CH IBJ O� GQ??CJ? �QHM�
� CMIB �BCGB CO E?WE W?ICWHQD IW IBJ XQMCHZ ?QIJ @ RBCO EBJHWVJHWH K SHW�H QO �>WEEDJ?�
OE?JQMCHZ� GQOJO P�> O� GQ??CJ?O IW CHIJ?XJ?J � CIB WHJ QHWIBJ? K Q EBJHWV JHWHGQDDJM CHIJ?GQ??CJ? CHIJ?XJ?JHGJ ��� �� �BCGB GQH OJNJ?JD� Q�JGI IBJ ?JGJCNJ? �O MJIJG�
ICWH EJ?XW?V QHGJ CX HJZDJGIJM @ �H FJGICWH � @� �J OBW� IBQI K XW? GBQHHJDO IBQI JBC� CI
XQOI ICV J�OJDJGICNJ XQMCHZ K IBJ DWOO WX O� GQ??CJ? W?IBWZWHQDCI� V QHCXJOIO QO OCZHC�GQHI
�� � @ RBO K IBJ E?CV Q?� QMNQHIQZJ WX P�> CH X?J�JHG��OJDJGICNJ GBQHHJDO K HQV JD�
IBJ Q�OJHGJ WX �F� QHM WX �� � K MW JO HWI GQ??� WNJ? IW ICV J� QHM X?J�JHG� �OJDJGICNJ
GBQHHJDO @
WOI G??JHI QEEDCGQICWHO WX P�> WEJ?QIJ HMJ? ODW��XQMCHZ GWHMCICWHO XW?�BCGB CHI?Q�O�V�WD GBQHHJD NQ?CQICWH GQH � J CZHW?JM K OW IBQI IBJ �� � E?W� DJV MWJO HWI
Q?COJ @ �W�JNJ? K ICV J�OJDJGICN CI� GQHHWI � J CZHW?JM CH IBJ MJOCZH WX XI?J �?WQM�QHM
� C?JDJOO O� OIJV O @ L O VJHICWHJM Q�WNJ K XI?J O�OIJV O Q?J DCSJD� IW WE J?QIJ QI NJ?�
BCZB GQ??CJ? X?J�JHGCJO �C @J @K � �� �� QHM >WEEDJ? OE?JQM K QH CHMCGQIW? WX XQMCHZ
?QIJ K CO DCHJQ?D� E?WE W?ICWHQD IW GQ??CJ? X?J�JHG� ���� @ �H WIBJ? �W?MO K J�JGICNJ ?QIJO
WX GBQHHJD NQ?CQICWH XW? Q �JM VW� CDJ OE JJM CHG?JQOJ @ FJGWHMD�K XI?J � C?JDJOO O� O�
IJV O Q?J �WHM IW WEJ?QIJ CH NJ?� BCZB VW� CDCI� OCIQICWHO �� � ��� SV �B � K OGB QO� JI�JJH BCZB�OE JJM GQ?O�I?QCHO IW �CHXW�OIQICWHO� EDQGJM QDWHZ IBJ NJBCGDJ �O EQIB ���� KQHM >WEEDJ? OE?JQM CO DCHJQ?D� E?WEW?ICWHQD IW NJBCGDJ OE JJM ���� @ RBC?M K IBJ?J CO
�
Q MJOC?J IW V CHCV C�J IBJ GQEQGCI� DWOI �� CHOJ?ICWH WX IBJ ?JMHMQHI P�> ZQ?MCHIJ?NQD @ L O I?QMCICWHQD P�> MJOCZH OE JGC�JO Q ZQ?M DJHZIB WX QI DJQOI IBJ GBQH�
HJD MJDQ� OE?JQM K ?JMHMQHG� GQH MCV CHCOBJM IB?WZB QH CHG?JQOJ CH P�> O�V� WD
M?QICWH @ �I K �� CHG?JQOCHZ IBJ P�> O�V�WD M?QICWH K IBJ O�OIJV � JGWV JO VW?J
OJHOCICNJ IW CHI?Q�� DW GS GBQHHJD NQ?CQICWH @ RBO �J GQH GWHGDMJ IBQI XI?J �?WQM�
�QHM � C?JDJOO QEEDCGQICWHO � CDD XQGJ GBQHHJDO IBQI Q?J OCZHC�GQHID� ICV J�OJDJGICNJ QO
�JDD QO X?J�JHG��OJDJGICNJ @
��� � ��� ������������
RBCO IBJOCO BQO � JJH W?ZQHC�JM CHIW OJNJH GBQEIJ?O @ �H �BQEIJ? � �J E?WNCMJ
QH WNJ?NCJ� WX � C?JDJOO GBQHHJD V WMJDO K MJOG?C� J IBJ �QOCG P�> O�OIJV K QHM ZCNJ
Q �?CJX MJOG?CEICWH WX IBJ J COICHZ �W?S WH P�> CH MW� D��OJDJGICNJ GBQHHJDO @ �H�BQEIJ? � �J QHQD��J QHM �QHICX� IBJ J�JGI WX Q MW� D� �OJDJGICNJ XQMCHZ GBQHHJD
WH P�> K HQV JD� �� � K QHM CH �BQEIJ? � �J E?WE WOJ DW��GWV EDJ CI� DCHJQ? ?JGJCNJ?
E?J�E?WGJOOCHZ IBQI ?JHMJ?O IBJ �� � ?JOEWHOJ OEQ?OJ� @ �H �BQEIJ? � �J ?JNCJ� EWOOC� DJ
OGBJV JO XW? O�V� WD MJIJGICWH QHM E?WEWOJ GWVEIQICWHQDD��J� GCJHI MJGCOCWH�XJJM�QGS
OWXI�O�V� WD JOICV QICWH OI?QIJZCJO IBQI JEDWCI IBJ OEQ?OJ �� � ?JOEWHOJ @ FCV DQICWH ?J�
O DIO CH �BQEIJ? � GDJQ?D� CHMCGQIJ ZWWM EJ?XW?V QHGJ WX IBJ E?WEWOJM O��WEICV QD
OGBJV JO ?JDQICNJ IW IBJ OIQHMQ?M MJIJGICWH IJGBHC�JO �I � CIB OCZHC�GQHI GWV EIQ�ICWHQD OQNCHZO @ � CHQDD� CH �BQEIJ? � �J GWHGDMJ W? �W?S QHM W�J? CHOCZBIO CHIW IBJ
QNJHJO XW? XI?J �W?S @
���� �� � �������� � ��� ����������� �� ���� �� �������� ����� �� ���� �� ������ � �� �� ������ ��� ��� ���� ��� �� � �� �� �� ��������� � ������ �������� � ���� ������� � ��� ��
�
������� �
����������
� �� � �� ��� � ���� � ����
RBJ � C?JDJOO GBQHHJD GQH � J NCJ�JM QO Q �� DQGS �W� EDQGJM � JI�JJH IBJ I?QHOV CI�
IJ? QHM ?JGJCNJ? WX Q GWV VHCGQICWH O�OIJV @ F�OIJV O JEJ?CJHGCHZ X?J�JHG� �OJDJGICNJ
XQMCHZ GBQHHJDO K V WMJD IBCO � DQGS �W QO Q ?QHMWV DCHJQ? ICV J� CHNQ?CQHI ��R �� � DIJ?QHM OV V Q?C�J CIO GBQ?QGIJ?COICGO �� Q MCOG?JIJ�ICV J �HCIJ CVE DOJ ?JOEWHOJ ���� �
� �� � � � � � � � � � ��� � � K �BJ?J �� MJHWIJO IBJ V Q CVV MJDQ� OE?JQM WX IBJ GBQH�
HJD CH �QM @ L O JEDQCHJM CH �BQEIJ? � K XI?J �?WQM�QHM � C?JDJOO QEEDCGQICWHO � CDD
XQGJ GBQHHJDO IBQI Q?J OCZHC�GQHID� ICV J� QHM X?J�JHG��OJDJGICNJ @ RBO K CH IBCO IBJOCO K
�J QMWEI Q VW?J ZJHJ?QD QEE?WQGB IW GBQHHJD VWMJDCHZ QHM NCJ� IBJ � C?JDJOO GBQHHJD
QO Q ?QHMWV DCHJQ? ICV J�NQ?CQHI ��R� � � DIJ? GBQ?QGIJ?C�JM �� WHJ WX IBJ XWDDW� CHZ
XW? O�OIJV V WMJDO @
� @ � �� ����� ��� �
RBJ ICV J�DQZ V WMJD K � JIIJ? SHW�H QO IBJ CVE DOJ ?JOEWHOJ WX Q �R� GBQHHJD K
GQH � J MJHWIJM �� � �� �� � � � � � � �� � � � � � � ��� � � @ � J?J � �� �� �� �
OE JGC�JO IBJ WIEI WX IBJ GBQHHJD QI ICV J CHMJ�� IW Q � ?WHJGSJ? MJDIQ QEEDCJM
�
QI ICV J CHMJ� �� �� � @ �H QH P�> O�OIJV �J CV EWOJ IBJ QMMCICWHQD GWHOI?QCHI� � � � � � � �� � � @ W?J JEDQHQICWH � CDD � J ZCNJH CH FJGICWH � @� @
� @ � �� ����������� ��� �
RBCO CO Q ICV J�NQ?� CHZ X?J�JHG� ?JOEWHOJ EQ?QVJIJ?C�QICWH WX IBJ �R� GBQHHJD @
�J MJHWIJ CI �HWH�OQVEDJM � �� � �� �� �� � � � � �� �� � �� � �BJ?J K
� �� �� �� � %� ��� � �� �� � � ��� � � �� @��
� J?J � CO IBJ DJHZIB WX IBJ W�OJ?NQICWH CHIJ?NQD CH ICV J �C @J @K � � � � � � � �� �
� � � � �� � @ �J GQH QDOW EQ?QV JIJ?C�J IBJ O�OIJV CH IJ?V O WX CIO OQVEDJM
ICV J�NQ?� CHZ X?J�JHG� ?JOEWHOJ � �� �� � � � � � � � � � � � �� � �
� �� �� � � � %� ��� � �� �� �� ��� ���� � �� @��
� @ ���� ������� ��� �
RBCO XW?V WX O�OIJV EQ?QV JIJ?C�QICWH CO WX EQ?ICG DQ? CHIJ?JOI XW? GBQHHJDO �BCGB
Q?J �WIB MJDQ� QHM >WEEDJ?�OE?JQM DCV CIJM QO CI JHQ� DJO Q OEQ?OJ �JI GWVEDJIJ
?JE?JOJHIQICWH WX IBJ GBQHHJD @ �J MJHWIJ IBJ HWH�OQV EDJM >WEEDJ?�DQZ ?JOEWHOJ
�� � � �� �� � � � � � �� � �� � � � � � � � � � ��� � �
� � �� �� � � � %� ��� 5 � �� �� � � ��� �5 �� @��
�BJ?J QZQCH �J BQNJ ?JOI?CGIJM � � � � � � � �� � � @ �J GQH QDOW EQ?QVJIJ?C�J IBJ
O� OIJV CH IJ?V O WX CIO OQVEDJM >WEEDJ?� DQZ ?JOEWHOJ �� �� �� � � � K � � � � � � � �� � �
�� �� �� � � � %� ��� 5 � �� �� �� ��� �� �� 5 �� @��
�
010
20
0
10
200
0.5
1
time [blks]
(a)
lag
|h|
010
20
0
0.5
1−30
−20
−10
0
time [blks]
(b)
freqdB
00.5
1
0
10
20−40
−20
0
20
doppler
(c)
lag
dB
00.5
1
0
0.5
1−40
−20
0
20
doppler
(d)
freq
dB
� CZ?J � @� % ����� ��������� � ��� ��� �� ����� �� ���� �
��
� @ ���� ������������� ��� �
RBCO VWMJD CO JIJHOCNJD� OJM CH IBCO IBJOCO IW GBQ?QGIJ?C�J IBJ GBQHHJD ?JOEWHOJ
QI IBJ P�> ?JGJCNJ? @ �I CO MJHWIJM �HWH�OQV EDJM � �� � � �� �� �� � � � ��
�� � �� � �BJ?J K OCHZ �� @�� QHM �� @��
� � �� �� �� � %� ��� � � �� �� � � ��� �
� �
� 5 � �� �� � � ��� �5 �� � �� @��
�?WV �� @�� QHM �� @� � �J GQH QDOW MJ�HJ IBJ OQV EDJM >WEEDJ?�X?J�JHG� ?JOEWHOJ�� �� �� � � � � � � � � � � � � � �� � �
�� �� �� � � � %� �
� 5 � �� �� � � ��� �� �� 5 �� �� �� �� @��
LDD IBJ OQVEDJM I?QHOV COOCWH XHGICWHO MJ�HJM Q�WNJ Q?J � �EJ?CWMCG CH IBJ >WEEDJ?
QHM X?J�JHG� CHMCGJO � QHM � @ �WIJ IBQI IBJ O�OG?CEIO WH JQGB WX IBJ I?QHOV COOCWH
XHGICWH Q?J OJM IW MJHWIJ IBJ ICV J�DQZ QHM >WEEDJ?�X?J�JHG� CHIJ?E?JIQICWH WX CIOI�W Q?ZVJHIO @ � CZ @ � @� ZCNJO QH JQV EDJ WX Q ICV J�NQ?� CHZ GBQHHJD ?JE?JOJHIJM ��
IBJ XW? I?QHOV COOCWH XHGICWHO MJ�HJM Q� WNJ @
� �� � �#�� ���� ���
���� � � �
�� ���� ����
��� ������� �
���� � � � ��������
��� � ��������
�� �������
� �� � �� � � � � � ��� �
� CZ?J � @� % ���� �� �� �������
��
RW QCM W? MCOGOOCWH WX P�> � JBQNCW? CH XQMCHZ � C?JDJOO GBQHHJDO K �J WIDCHJ QO�OIJV VWMJD IW GWHNJ� IBJ V QCH GWHGJEIO @ FJJ � CZ @ � @� XW? QH CDDOI?QICWH @
�H QH P�> O�OIJV K JQGB � DW GS WX MQIQ GWHIQCHO CHXW?V QICWH X?WV � �X?J�JHG��
MWV QCH O�V� WDO ���6�� �� � ���� M?Q�H X?WV Q ��L QDEBQ� JI @ � J?J MJHWIJO IBJ
P�> � DW GS CHMJ QHM MJHWIJO IBJ OC�J WX IBJ �L QDEBQ� JI @ RBJ � � X?J�JHG��
MWV QCH O�V�WD CO OJM IW VWM DQIJ Q G�GDCGQDD��E?JE JHMJM CHNJ?OJ �W?CJ? I?QHOXW?V
��>�R � �QOCO NJGIW? K OW IBQI Q OQV EDJM NJ?OCWH WX IBJ ICV J�MWV QCH I?QHOV CIIJM OCZHQD
�� �6� �� ��� � �5���� XW? IBJ � � DW GS CO ZCNJH ��
� �6� �� � � ���� � ����
� �6�� � �� � � �� @��
�BJ?J �� ��� � � � MJHWIJO IBJ DJHZIB WX IBJ G�GDCG�E?J� �ZQ?M CHIJ?NQD� @ RW
E?JNJHI CHIJ?�� DW GS CHIJ?XJ?JHGJ QI IBJ ?JGJCNJ? QHM IW JHO?J Q GC?G DQ? �?QIBJ? IBQH
DCHJQ?� GWHNWDICWH � CIB IBJ GBQHHJD ?JOEWHOJ K IBJ ICV J�MWV QCH � DW GSO Q?J G�GDCGQDD�E?JE JHMJM � CIB Q E?J� DJHZIB �� WX QI DJQOI IBJ GBQHHJD CV E DOJ ?JOE WHOJ DJHZIB @
RBJ ICV J�MWV QCH � DW GSO Q?J IBJH OJ?CQDD� I?QHOV CIIJM IB?WZB Q V DICEQIB XQMCHZ
GBQHHJD @
L OOVJ IBQI IBJ ICV J�MWV QCH ?JGJCNJM OCZHQD � �6� �� � CO Q HWCOJ GW??EIJM QHM
DCHJQ?D� MCOIW?IJM NJ?OCWH WX � �6� �� � QO Q GWHOJ�JHGJ WX Q �R� GBQHHJD � CIB CV E DOJ
?JOEWHOJ � �6� �� �� � � � @ � J?J � �6� �� �� � � � OE JGC�JO IBJ WIEI WX IBJ O� OIJV QI ICV J CHMJ �
� CIB CH IBJ � � DW GS IW Q � ?WHJGSJ? MJDIQ QEEDCJM QI ICV J CHMJ �� � � � @ RBJ GBQHHJDCO QOOVJM IW GBQHZJ GWHICHWOD� � CIB CH Q � DW GS �C @J @K WNJ? � � QO �JDD QO � JI�JJH
� DW GSO �C @J @K WNJ? � @ RBCO ICV J� DQZ � DW GS�CHMJJM GBQHHJD ?JOE WHOJ GQH � J ?JDQIJM IW
��
IBJ ZJHJ?QD ICV J� DQZ GBQHHJD ?JOE WHOJ � �� ��� � � � MJ�HJM CH FJGICWH � @� QO
� �� ��� � � � � ��� � ���� ��� �� �� ���� ��
� ��� � �� � � � � � �� �
� �6� �� �� � � � � � �� � �� �� � � � � � � � � � ���� � � � � �� � ���X IBJ GBQHHJD CO GQOQD � CIB Q V Q CVV CV E DOJ ?JOEWHOJ M?QICWH �� K �BJ?J �� �
�� � � K IBJH
� �6� �� � � � � ���
� �6� �� �� � � �� �6� �� � � � �� �6�5 � � �� � � � � �� � �� �� @��
RBJ QMJ�QIJ DJHZIB WX IBJ G�GDCG E?J� JHQ� DJO IBJ NQDJO WX � �6� �� �� � CH �� @�� IW � J
�JDD MJ�HJM @ �J QOOV J IBQI �� �6�5 Q?J �J?W�V JQH �BCIJ QHM QOOCQH � CIB NQ?CQHGJ
� �� @ LI JQGB � DW GS K IBJ ?JGJCNJ? M?WEO IBJ OQVEDJO GW??JOE WHMCHZ IW IBJ G�GDCG�E?J�
QHM QEEDCJO �� �6� �� ��� � �5�� IW Q MCOG?JIJ �W?CJ? I?QHOXW?V �>�R � K � CJDM CHZ �� �6�� �� � ����� �6�� � ���
� � �5��
� �6� �� ��� �� �� 5 �� @��
�I CO GWHNJHCJHI IW J IJHM IBJ MJ�HCICWH WX � �6�� WNJ? QDD � � OCHZ IBJ E?WE J?I�� �6��� �� � � �6�� @ �J GQH ?JDQIJ � �6�� IW � �6�� OCHZ IBJ O�OIJV J�QICWHO �� @�� K �� @�� � �� @��
QHM IBJ OQVEDJM I?QHOV COOCWH XHGICWHO MJ�HJM CH FJGICWH � @�
� �6�� � ���� � �5��
�� � ���
� �6� �� �� � � � ���� � ����
� �6�� � �� � �� �� � �� �6�5 � �� �� �� 5
� ���� � �5��
�� �6�5 �� �� �� 5
� � ����
����
� � ���
����
� � �5��
� �6� �� �� � � ��� �� ���� �� 5� �� ���� � � �6��
� � �6�� � � ����
����
� � ���
� �6�� �� �� � � � � ��� ���� � � �6��
� � �6�� � � ����
� �6�� �� �� � � � � �� �6�� �� @���
��
>J IW IBJ W?IBWHW?V QDCI� WX IBJ >�R �QOCO NJGIW?O K IBJ X?J�JHG��MWV QCH HWCOJOQV EDJO � �6�� Q?J OIQICOICGQDD� J� CNQDJHI IW IBJC? ICV J�MWV QCH GWHIJ?EQ?IO HQV JD�
�J?W�V JQH K �BCIJ QHM QOOCQH � CIB NQ?CQHGJ � �� @ �?WV �� @��� CI CO JN CMJHI IBQI JQGB� �6�� GWHIQCHO GWHI?C�ICWHO X?WV QDD IBJ � �6�� I?QHOV CIIJM CH IBJ � P�> � DW GS @ RBCO
EBJHWVJHWH CO SHW�H QO �� � @ RBJ J IJHI WX �� � CO Q XHGICWH WX IBJ ?QIJ WX GBQHHJD
ICV J�NQ?CQICWH � CIB CH IBJ P�> � DW GS @ W?J JEDQHQICWH Q� WI CI � CDD � J ZCNJH
CH �BQEIJ? � @ �W�JNJ? K JNJH CX �� � OEQHO �OI Q XJ� O�V�WDO K �J GDJQ?D� OJJ IBQI
HJZDJGICHZ CI GW DM OJNJ?JD� Q� JGI IBJ E J?XW?V QHGJ WX O�V�WD MJIJGICWH @ � JHGJ IBCO�� � HJJMO IW � J JEDCGCID� QMM?JOOJM @
�X IBJ GBQHHJD CO �R � K �� � CO Q�OJHI �FJJ LEEJHMC L � QHM IBO JQGB � �6�� GQH
� J W�IQCHJM �� OCVED� OGQDCHZ IBJ GW??JOE WHMCHZ � �6�� XWDDW�JM �� IB?JOBWDMCHZ @ RBCO
OCV EDJ MJIJGICWH CO IBJ W?CZCHQD V WICNQICWH XW? OCHZ G�GDCG�E?J� P�> CH X?J�JHG��
OJDJGICNJ XQMCHZ GBQHHJDO @
Y�QICWH �� @��� GQH � J � ?CIIJH CH NJGIW? XW?V QO
�����
� �6��� �6��@@@� �6�� � �
�����
� �� ����
������
� �6�� �� �� � �� � �6�� �� �� � � �� � � � � �6�� �� �� � � �� � ��� �6�� �� �� � �� � �6�� �� �� � �� � � � � �6�� �� �� � � �� � ��
@@@ @@@ @ @ @ @@@� �6�� �� �� � � � �� � �6�� �� �� � � � �� � � � � �6�� �� �� �� � ��
������
� �� � ��� ��
�����
� �6��� �6��@@@� �6�� � �
�����
� �� � ��������
� �6��� �6��@@@� �6�� � �
�����
� �� � ����� @���
�?WV Q MJIJGICWH OIQHMEWCHI K �� @��� GDJQ?D� OZZJOIO IBQI IBJ �QOCG �J?W XW?GCHZ ����
MJIJGIW? W? IBJ DCHJQ? V CHCVV V JQH O�Q?J J??W? �� FY � MJIJGIW? � CDD ?J� C?J
Q V QI?C CHNJ?OCWH WX IBJ >WEEDJ?�X?J�JHG� GBQHHJD I?QHOXJ? XHGICWH V QI?C � �6�� �� @� DJQ?D� � �6�� �� CO Q HWH�MCQZWHQD � �� V QI?C QHM CHNJ?ICHZ OGB Q V QI?C BQO � �� � �
GWV EDJ CI�@
��
WMJ?H GWVVHCGQICWH O�OIJV O JVEDW� CHZ P�> E?JXJ? DQ?ZJ � DW GS DJHZIBO V W�ICNQIJM �� IBJ MJOC?J IW ?JMGJ GQEQGCI� DWOO MJ IW CHOJ?ICWH WX ?JMHMQHI ZQ?M
CHIJ?NQD QHM IW V QCHIQCH HQ??W� O� GQ??CJ? OEQGCHZ �IW JHO?J �QI XQMCHZ E J? GQ??CJ?�
QO IBJ O�OIJV �QHM� CMIB CHG?JQOJO @ RBCO V JQHO IBQI IBJ �QOCG �� QHM � FY MJ�
IJGIW?O � CDD BQNJ E?WBC� CICNJ GWVEDJ CI� QHM Q HJ� QEE?WQGB HJJMO IW � J QMWEIJM IW
JHO?J CV EDJV JHIQ� DJ O�V�WD MJIJGICWH XW? P�> CH MW� D��OJDJGICNJ GBQHHJDO @
FCHGJ MJIJGICWH OI?QIJZCJO WXIJH ?JD� WH SHW� DJMZJ WX IBJ GBQHHJD GWJ� GCJHIO K
GWV EIQICWHQDD��J� GCJHI GBQHHJD JOICV QICWH QDZW?CIBV O Q?J QDOW JOOJHICQD @ A?JOJHGJWX OCZHC�GQHI ICV J�NQ?CQICWH CHG?JQOJO � WIB IBJ HV� J? WX GBQHHJD EQ?QVJIJ?O IBQI
VOI � J JOICV QIJM QO �JDD QO IBJ MC� G DI� WX JOICV QICHZ IBJOJ EQ?QVJIJ?O @
RBO K GDJQ?D�K P�> CH MW� D��OJDJGICNJ JHNC?WHVJHIO EWOJO HJ� GBQDDJHZJO X?WV
QH CVEDJV JHIQICWH OIQHMEWCHI @
� �� �� ��� ��� ������ �� ��� �#�� �� ����������� �� � ������
� CIB NJ?� XJ� JGJEICWHO K IBJ P�> DCIJ?QI?J QOOV JO GBQHHJDO IBQI Q?J GWH�
OIQHI WNJ? IBJ � DW GS CHIJ?NQD K GW??JOEWHMCHZ IW IBJ GQOJ CH �BCGB IBJ O� GQ??CJ?O
V QCHIQCH W?IBWZWHQDCI� QHM �� � CO QNWCMJM @ RBWZB CHI?Q�� DW GS GBQHHJD�NQ?CQICWH CO
SHW�H IW MJZ?QMJ E J?XW?V QHGJ �BJH CZHW?JM �J @Z @K ���� ���� WHD� Q XJ� IJGBHC�JO
BQNJ � JJH E?WEWOJM IW GWEJ � CIB CI @ W?JWNJ? K HWHJ WX IBJOJ IJGBHC�JO QEE JQ? IW � J
E?QGICGQD X?WV Q CV EDJV JHIQICWH OIQHMEWCHI @�W? JQV EDJ K �� ��VCICZQICHZ VJIBWMO BQNJ � JJH E?WE WOJM XW? �QI�XQMCHZ ��� K ��� K
�BJ?JQO K P�> �O E?CV Q?� QMNQHIQZJ GWHGJ?HO X?J�JHG��OJDJGICNJ GBQHHJDO @ �OOJDD
QHM FI� J? ���� BQNJ E?WEWOJM J??W?�GWHI?WD GWMCHZ QHM QHIJHHQ MCNJ?OCI� IW CVE?WNJ
E J?XW?V QHGJ @ �W�JNJ? K IBJOJ IJGBHC�JO Q?J CHIJHMJM IW GWV�QI HOI?GI?JM HWCOJ
��
?QIBJ? IBQH OI?GI?JM �� � K QHM BJHGJ OBW DM � J OJM CH QMMCICWH IW JEDCGCI �� �
?JMGICWH @ L ?V OI?WHZ JI QD @ ���� BQNJ OZZJOIJM E WD�HWV CQD GQHGJDDQICWH GWMCHZ �A�� �
���� IW OEE?JOO >WEEDJ?�CHMGJM �� � �QOJM WH IBJ XQGI IBQI A�� CO SHW�H IW OEE?JOO
�� � ?JO DICHZ X?WV GQ??CJ? X?J�JHG� W� OJI @ �Q??CJ?�W� OJI�CHMGJM �� � K BW�JNJ? K BQO Q
OE JGCQD OI?GI?J HWI OBQ?JM �� >WEEDJ?� CHMGJM �� � K V QSCHZ A�� CHJ�JGICNJ @ �H XQGI K
���� MJVWHOI?QIJM QMNQHIQZJO WHD� � CIB XQMJO OW �QI QHM ODW� QO IW � J QEE?W CV QIJM
�� Q �JM MJDQ�@ �JWH JI QD @ ���� QIIQGSJM IBJ E?W� DJV WX CHI?Q�� DW GS GBQHHJD NQ?CQICWH
QOOVCHZ IBQI IBJ DQ?ZJ�NQ?CQHGJ IQEO CH ���� W GG? E?CV Q?CD� QDWHZ IBJ V QCH MCQZWHQD @�H �BQEIJ? � �J � CDD OBW� IBQI BCO QOOVEICWH �QO XQ? X?WV QGG?QIJ @
� CHHQ?I� QHM W?WSBWN ���� OJM Q I�W�IJ?V RQ� DW? OJ?CJO JEQHOCWH IW DCHJQ?D�
QEE?W CV QIJ ICV J�MWV QCH GBQHHJD NQ?CQICWHO QHM X?WV IBCO MJOCZHJM Q FY MJ�
IJGIW? @ �BWC JI QD @ ���� K E?WEWOJM Q VW?J ZJHJ?QD VWMJD XW? IBJ ICV J�NQ?CQICWH QHM
MJ?CNJM V QIGBJM�� DIJ? K �F QHM FY MJIJGIW?O IBQI CHGW?EW?QIJ MJGCOCWH�XJJM�QGS
E?CHGCE DJO @ RBWZB ��� K�� � Q?J CHIJ?JOICHZ QHM �JDD XW?V DQIJM K IBJ� ?J� C?J IBJ CHNJ?�
OCWH WX V QI?CGJO � CIB MCV JHOCWH J�QD IW IBJ P�> � DW GS DJHZIB � �BCGB CO CHXJQOC� DJXW? DQ?ZJ � DW GS DJHZIBO @
�H ���� K CQHHQSCO JI QD @ MJ?CNJM Q V QIGBJM � DIJ? � WHM � �� � XW? P�> CH
MW� D��OJDJGICNJ XQMCHZ GBQHHJDO K QHM OBW�JM IBQI GBQHHJD NQ?CQICWHO CHI?WMGJ IJV �
EW?QD MCNJ?OCI�K �BCGB BQO IBJ E WIJHICQD IW CVE?WNJ IBJ � CI J??W? ?QIJ ��Y� � EJ?XW?�
V QHGJ CX E?WE J?D� JEDWCIJM @ RBJ� QDOW OIMCJM IBJ �� � QHM JHJ?Z� DJQSQZJ IBQI Q?J
GQOJM �� IBJ ICV J�NQ?� CHZ GBQHHJD @ � JI K �QOJM WH IBJ XQGI IBQI K �� � EW�J? CO OCZ�
HC�GQHI WNJ? HJQ?�� O� GQ??CJ?O IBJ� MJNJDWE JM � �� � � GWV EDJ CI� FY QHM >�Y?JGJCNJ?O @ � BCDJ IBJ FY ?JGJCNJ? JBC� CIO QH J??W? �WW? K IBJ >�Y ?JGJCNJ? MW JO
JEDWCI IBJ IJV EW?QD MCNJ?OCI� W� J?JM �� IBJ GBQHHJD K QHM CIO �Y� EJ?XW?V QHGJ GWV JO
��
GDWOJ IW IBJ �� XW? ODW��XQMCHZ GBQHHJDO @ YNJH IBJH K XW? DQ?ZJ � DW GS DJHZIB IBJC?QDZW?CIBV O �W DM � J CVE?QGICGQD IW CV EDJV JHI @
� BCDJ GBQHHJD JOICV QICWH BQO � JJH JIJHOCNJD� I?JQIJM CH ODW� D��XQMCHZ V DICGQ?�
?CJ? O�OIJV O �� CIB HW CHI?Q�� DW GS GBQHHJD NQ?CQICWH � NJ?� DCIIDJ BQO � JJH E?WE WOJM XW?
MW� D��OJDJGICNJ GBQHHJDO @ �JWH JI QD @ ���� E?WEWOJM Q OCV EDJ IJGBHC�J �BJ?J�� Q
ICV J�MWV QCH � ?WHJGSJ? MJDIQ ECDWI OJ�JHGJ CO CHOJ?IJM JNJ?� � P�> � DW GSO XW?
JQO� JOICV QICWH K QHM IBJ GBQHHJD CO QOOV JM IW GBQHZJ DCHJQ?D� WNJ? IBJ � � DW GSO @� DJQ?D� IBCO �W?SO WHD� XW? NJ?� ODW� D� NQ?� CHZ GBQHHJDO @ � JGJHID� �BWC JI QD @ ��� �E?WE WOJM FY DCHJQ? E?JMCGICWH WX IBJ �R� CVE DOJ ?JOE WHOJ OCHZ E J?CWMCG ECDWI
X?QV JO @ FE JGC�GQDD�K �� ECDWI W�OJ?NQICWHO K GWDDJGIJM WNJ? Q E J?CWM WX � �� OQVEDJO K
Q?J DCHJQ?D� E?W GJOOJM IW � CJDM � WCHI JOICV QIJO WX � � NQDJO WX � �� �� � � � K � CIB � GJH�
IJ?JM CH IBJ W�OJ?NQICWH EJ?CWM @ � J� C?CHZ � �� � V DICE DCJO QHM Q DWHZ E?WGJOOCHZ
MJDQ�K IB CO CO HWI E?QGICGQD XW? DQ?ZJ � @
� �� ��� � �������
P? GDQCV CO IBQI IBJ E?QGICGQD QEEDCGQICWH WX V DICGQ??CJ? VWM DQICWH CH MW� D� �
OJDJGICNJ JHNC?WHVJHIO ?J� C?JO Q XHMQV JHIQDD� HJ� QEE?WQGB IW O� OIJV MJOCZH QHM
QHQD�OCO @ R?QMCICWHQD G�GDCG�E?J� P�> BQO � JJH MJOCZHJM JEDCGCID� XW? IBJ GQOJ WX
HWH�ICV J�OJDJGICNJ XQMCHZ K QHM HW E?QGICGQD V JIBWMO BQNJ � JJH E?WEWOJM IW BQHMDJ IBJGBQDDJHZCHZ GWV� CHQICWH WX ICV J�OJDJGICN CI� QHM DQ?ZJ � DW GS DJHZIB IBQI CO JEJGIJM CH
XI?J �?WQM�QHM � C?JDJOO QEEDCGQICWHO @ �X �J QGGJEI IBJ XQGI IBQI CHIJ?XJ?JHGJ CH IBJ
XW?V WX �� � QHM�W? �F� CO QH HQNWCMQ� DJ GWHOJ�JHGJ WX �QHM� CMIB�J� GCJHI GWVV�
HCGQICWH WNJ? MW� D��OJDJGICNJ GBQHHJDO K IBJH �J OBW DM MJOCZH V DICGQ??CJ? O�OIJV O
GQEQ� DJ WX BQHMDCHZ IBCO CHIJ?XJ?JHGJ CH QH J� GCJHI V QHHJ? @ � BCDJ �� � CHG?JQOJO IBJ
��
GWV EDJ CI� WX IBJ OIQHMQ?M �� QHM � FY MJIJGIW?O K CI QDOW Q�W?MO MCNJ?OCI� �BCGBGQH � J DJNJ?QZJM IW CHG?JQOJ E J?XW?V QHGJ CH XQMCHZ GBQHHJDO @ �HI CICNJD� OE JQSCHZ K IBJ
W��MCQZWHQD JDJV JHIO WX ���� V Q� E?WNCMJ CV EW?IQHI CHXW?V QICWH Q�WI IBJ HSHW�H
O�V�WDO K �BJH IBJ V QCH MCQZWHQD GWHIQCHO OV QDD NQDJO @
�H IBCO IBJOCO K �J WIDCHJ Q OJI WX OCZHQD E?W GJOOCHZ OI?QIJZCJO IBQI GWHOICIIJ Q
HJ� X?QV J�W?S XW? GWV VHCGQICWH WNJ? OCZHC�GQHID� MW� D��OJDJGICNJ GBQHHJDO @ �J
XW GO WH E?QGICGQDD� CV EDJV JHIQ� DJ OWDICWHO IBQI W� J? ZWWM E J?XW?V QHGJ @ L VW?J
IBW?WZB MJOG?CEICWH WX IBJ E?WEWOJM �W?S � CDD � J ZCNJH CH �BQEIJ? � QHM �BQEIJ? � @�H �BQEIJ? � �J OZZJOI DW��GWVEDJ CI� DCHJQ? E?J�E?WGJOOCHZ �BCGB I?HGQIJO IBJ �� �
?JOEWHOJ � CJDM CHZ Q OEQ?OJ � �6�� �� QHM CH �BQEIJ? � �J E?WEWOJ GWV EIQICWHQDD� �J� GCJHI
O� WEICV QD MJGCOCWH�XJJM�QGS JOICV QICWH OGBJV JO �JEDWCICHZ IBJ OEQ?OJ OI?GI?J WX
� �6�� �� � �BCGB W� J? ZWWM E J?XW?V QHGJ ?JDQICNJ IW IBJ OIQHMQ?M MJIJGIW?O �I � CIB OCZ�
HC�GQHI GWV EIQICWHQD OQNCHZO @
��
������� �
��� �##��� �# � �����$ ������� ��� #�� ���
������� �� �#��
�H �BQEIJ? � �J OI?JOOJM IBJ XQGI IBQI XI?J � C?JDJOO QEEDCGQICWHO � CDD XQGJ GBQH�
HJDO IBQI Q?J XQC?D� ICV J� QHM X?J�JHG� OJDJGICNJ @ �H FJGICWH � @� �J OBW�JM BW�
P�> CH ICV J�OJDJGICNJ GBQHHJDO XQDDO E?J� IW �� � @ RBCO GBQEIJ? QIIJV EIO IW �QHICX�
IBCO >WEEDJ? CHMGJM �� � QO Q XHGICWH WX NQ?CWO O� OIJV EQ?QVJIJ?O HQV JD�K �� IBJ
HW?V QDC�JM >WEEDJ? X?J�JHG�K �� IBJ NQ?CQHGJO WX IBJ �� DQZ GBQHHJD GW J� GCJHIOQHM �� IBJ P�> � DW GS DJHZIB � @ �H FJGICWH � @� �J MJOG?C� J IBJ �QOCG ICV J�DQZ
GBQHHJD VWMJD IBQI �J OJ CH W? QHQD�OCO QHM OCV DQICWHO @ �H FJGICWH � @� �J MJ�
?CNJ IBJ �5� W?MJ? OIQICOICGO XW? IBJ HWH�OQV EDJM >WEEDJ?�DQZ GBQHHJD IQEO � �6�� �� �� � � � @� CHQDD� CH FJGICWH � @� �J OJ IBJ ?JO DIO X?WV FJGICWH � @� IW MJ?CNJ IBJ �5� W?MJ?
OIQICOICGO XW? IBJ OQVEDJM >WEEDJ?�X?J�JHG� GBQHHJD IQEO � �6�� �� �� � � � @ �?WV �� @��� K �J
SHW� IBQI � �6�� �� �� � � � CO IBJ JDJV JHI CH IBJ � � GWDV H QHM � � MCQZWHQD �� � � MJHWIJO
IBJ V QCH MCQZWHQD� WX IBJ >WEEDJ?�X?J�JHG� GBQHHJD I?QHOXJ? XHGICWH V QI?C � �6�� �� @RBO IBJ ?JO DIO X?WV FJGICWH � @� � CDD BJDE O � JIIJ? HMJ?OIQHM IBJ ZJHJ?QD OI?GI?J
WX ���� �BCGB CO QH CHMCGQIW? WX IBJ JIJHI WX �� � CH IBJ P�> O�OIJV @
��
� �� � � ���� � ���� ���� ������
�J QOOV J Q � CMJ�OJHOJ OIQICWHQ?� HGW??JDQIJM OGQIIJ?CHZ �� FFF� GBQHHJD
�BJ?J IBJ ICV J� DQZ GBQHHJD GW J� GCJHIO � �6� �� �� � � � Q?J GW??JDQIJM WNJ? ICV J�� QHM Q?J
CHMJE JHMJHI WNJ? DQZ�� OW IBQI K
Y �� �6� �� �� � � �� �6� �� � �� � � � � � ��� � � �� � �� ��� ��� � � �� �� � ��� @��
�BJ?J �� ��� CO �J?W�W?MJ? � JOOJD XHGICWH WX �?OI SCHM K QHM �� CO IBJ �V Q CVV � HW?�
V QDC�JM >WEEDJ? X?J�JHG�� MJ�HJM ��
�� � � � � 3�BJ?J � CO IBJ GQ??CJ? X?J�JHG�K � IBJ V W� CDJ NJDW GCI�K � 3 IBJ OQVEDCHZ CHIJ?NQD QHM
IBJ OE JJM WX DCZBI @ � JHGJXW?IB �J MJ�HJ IBJ QIW GW??JDQICWH XW? IBJ �� DQZ QO
� �� �� � � � � Y �� �6� �� �� �� �� �6�� �� �� � � � � ��LO V JHICWHJM CH FJGICWH � @� IBJ GBQHHJD CO QOOVJM IW GBQHZJ GWHICHWOD� WNJ? � QO
�JDD QO WNJ? @
� �� � ��� ������ � ���� ������� ���
�?WV �� @�� �J SHW� IBQI IBJ HWH�OQVEDJM >WEEDJ?�DQZ ?JOE WHOJ CO ZCNJH ��
� � �� �� � � � � ���� � �5��
� �� �� � � ��� �5�BJ?J IBJ DCV CIO WH � Q?J MJ IW IBJ �HCIJ P�> � DW GS DJHZIB � @ �J BQNJ
Y �� �6�� �� �� � � �� �6��� �� �� � � � � ��� Y ���
� � �5��
� �6� �� �� � � ��� �5 ���� � ����
� �6� �� � �� � � �� ���� ����� ���� �� � �����
��
� �
�� � �5��
� � ����
Y �� �6� �� �� � � �� �6�� �� �� � � ���� �5 � ���� ��
� �
�� � �5��
� � ����
� �� �� � � � � ��� � �5� ���� � � �� @��
� �
�� � �� ��
� � ������
� �� �� � � ��� �� �� � � �
��� � �� �� �
� � �����
� �� �� � � ��� �� �� � �� �
�� � �� ��
� �� �� � � ��� �� � � ������
�� � � �
��� � �� �� �
� �� �� � � ��� ���� �� � � �������� � �
OCHZ IBJ > C?CGBDJI OCHG XHGICWH�� ����
�� � � � OCH ������OCH �� ��� �� �� ��� �� �� @��
�J BQNJ
Y �� �6�� �� �� � � �� �6��� �� �� � � � � ��� �
�� � �� ��
� �� �� � � ��� �� OCH �� �� � � ����OCH �� ��� �� �� �� �� � ��
�
��� � �� �� �
� �� �� � � ��� ���� �� OCH �� �� � ����OCH �� ��� �� �� �� �� � ��
� �
�� � �� ��
� �� �� � � ��� ��� �� �� OCH �� �� � � ����OCH �� ��� �� �� �� � ��
�� � �� �� �
� �� �� � � ��� ��� �� �� OCH �� �� � ����OCH �� ��� �� �� �� � ��
� �
�� � �� ��� � �
� �� �� � � ��� ��� �� �� OCH �� �� � �� �����OCH �� ��� �� �� �� � ��
�J GQH CHIJ?E?JI IBJ E?JNCWO JE?JOOCWH OCHZ Q � �EQ?QV JIJ?C�JM DQZ�MWV QCH
� CHMW�
� �� � � � � OCH �� �� � �� �����OCH �� ��� �� �� �� �� � �� � �� �� � �� � �� ��
��
NCQ IBJ CHMCGQIW? XHGICWH
� �� �� � �� � �� �� � � �
��� � �� �� � ��JDOJ
OW IBQI
Y �� �6�� �� �� � � �� �6��� �� �� � � � � �� � �� ���� �� �� � � �� �� �� ��� �� �� @��
R�W CHIJ?JOICHZ E?WE J?ICJO WX IBJ � CHMW� XHGICWH Q?J
� �� �� � ���� ��� � �� �
� � � �� �� � �� � �� ��
DCV��� � �� �� � � �� � � �
� � �� � �� �
CVED� CHZ IBQI
DCV��� Y �� �6�� �� �� � � �� �6��� �� �� � � � � �� � � �� �� �� � � �
�� � �� �� �
�BJ?J �� �� �� � � � MJHWIJO IBJ >WEEDJ? OE JGI?V WX IBJ DQZ�� GBQHHJD GWJ� GCJHI %
�� �� �� � � � � �� ���� �� �� � � ��� ��
� � ��� ��� � �� ����
�� � � �� ��JDOJ
RBJ � CHMW� XHGICWH GQH � J JE?JOOJM CH IBJ X?J�JHG� MWV QCH QO
� �� � �� � �� ���� �� �� ��� ��
� Y �� �6�� �� �� � � �� �6��� �� �� � � � � �� � �� �� � �� � �� �
�� � �5��
�� �5 � � ����
� ���� �� �� @��
� �
�OCH ��� ���OCH ����� �� �� �� � �� OCH ��� � � �� ���
OCH ��� � � ���� � ���� �� �� � �� �� @��
� �
�OCH ��� ���OCH �����
OCH ��� � � �� ���OCH ��� � � ���� �� �� �� � ��
��
�BJ?J �� @�� QHM �� @�� XWDDW� X?WV �� @�� QHM �� @�� ?JOE JGICNJD�@ FWV J E?WE J?ICJO WX IBJX?J�JHG��MWV QCH NJ?OCWH WX IBJ � CHMW� XHGICWH Q?J
� �� � � � ���� � �
��OCH ��� ���
OCH ����� � �
DCV���
�
� � �� � � � � � �
�� � � � �JDOJ
RBCO X?J�JHG��MWV QCH MJOG?CEICWH CO OJX D CH IBQI �� @� � GQH � J ?J� ?CIIJH QO
Y �� �6�� �� �� � � �� �6��� �� �� � � � � �� � � ��� �� �� �� � � �� �� � � � � ���
� �� �� �� � � � � � �� � ���BJ?J ��� MJHWIJO GWHNWDICWH QO MJ�HJM Q� WNJ @ � CHQDD�K �J HWIJ IBQI
Y �� �6�� �� �� � � �� �6��� �� �� � � � � � � �� � � � �� �� �
� �� � ��� ���#������ � ���� ������� ���
�?WV �� @�� �J SHW� IBQI IBJ HWH�OQVEDJM >WEEDJ?�X?J�JHG� ?JOE WHOJ CO MJHWIJM
��
� � �� �� �� � � ���� � ���
� � �� �� � � ��� �
� ���� � ���
� � �� �� � � ��� ��J BQNJ
Y �� �6�� �� �� �� �� �6��� �� �� � � �� � � ��� Y ���
� � ���
� �6�� �� �� � � ��� � ���� � ���� � �6�� �� � �� � � � � �� �� � �� �
� �
�� � ���
� � ���� Y �� �6�� �� �� � � �� �6��� �� �� � � � � ���� � � �� � ��
��
� �
�� � ���
Y �� �6�� �� �� � � �� �6��� �� �� � � � � ���� �
�� � ��� �� �� �� � � ��� � � �
� � �� � � �� �� �� �� � � � � �
� � �� � � ��BJ?J �� �� �� � � � MJHWIJO IBJ >WEEDJ?�X?J�JHG� OE JGI?V %
�� �� �� � � � � �� � ���� � �� ��� ��� ��� � �� ���
�
�� � � �� ��JDOJ
RBJ OQVEDJM >WEEDJ?�X?J�JHG� OIQICOICGO Q?J IBJH
Y �� �6�� �� �� � � �� �6��� �� �� � � � � � ��� � �
� �� �� �� � �� �� � � � �� � �� �� � �� �� ��� JHGJ IBJ NQ?CQHGJ J�QDO
Y � �� �6�� �� �� � � � �� � �� � � � ��� � �� ��� �� �� � ��
� �� ��� � � � �� ��� � � OCH ��� ���� OCH ������ � �� �� ��
�� @��
LO V JHICWHJM � JXW?J K �� �� �� � � � ?JE?JOJHIO IBJ JDJV JHI CH IBJ � � GWDVH QHM� � MCQZWHQD ��� � � � � WX � ��� @ Y�QICWH �� @�� OZZJOIO IBQI ��� �� �� � � � � � CDD BQNJ
?JQOWHQ� D� DQ?ZJ NQDJO XW? OV QDD NQDJO WX � K �BCGB GW??JOEWHM IW IBJ IJ?V O IBQI
OCZHC�GQHID� GWHI?C�IJ IW�Q?MO IBJ O�OIJV �� � EW�J? @ PH IBJ WIBJ? BQHM ��� �� �� � � � �� CDD BQNJ ?JDQICNJD� OV QDD NQDJO XW? DQ?ZJ NQDJO WX � K �BCGB GW??JOEWHM IW IBJ IJ?V O
IBQI BQNJ Q NJ?� OV QDD GWHI?C�ICWH IW�Q?MO IBJ O� OIJV �� � EW�J? @� DJQ?D� IBJ JIJHI WX �� � CO E?WEW?ICWHQD IW IBJ XQMCHZ ?QIJ �GBQ?QGIJ?C�JM �� �� �
JBC� CIJM �� IBJ GBQHHJD @ �W? GBQHHJDO IBQI MW HWI JBC� CI ICV J�OJDJGICN CI� ��� � �� K��� �� �� � � � � � � XW? � �� � @ �H � CZ @ � @� �J JNQDQIJ �� @�� XW? � DW GS DJHZIB � � �� K HCI
NQ?CQHGJ DQZ GW J� GCJHIO QHM NQ?CWO �� @
��
−80 −60 −40 −20 0 20 40 60 80−50
−40
−30
−20
−10
0
10
dB
diagonal index
N=64
fd=0.05 fd=0.02 fd=0.01 fd=0.005fd=0.002fd=0.001
� CZ?J � @� % ���� � �� � �� � ! � �� �� " ����� �����
−4 −3 −2 −1 0 1 2 3 4
−25
−20
−15
−10
−5
0
5
dB
diagonal index
N=64
fd=0.05 fd=0.02 fd=0.01 fd=0.005fd=0.002fd=0.001
� CZ?J � @� % # ��� �� �� � �� " $ "%
��
P�OJ?NJ IBQI JNJH ?JDQICNJD� ODW� GBQHHJDO % GBQHHJDO XW? �BCGB IBJ >WEEDJ? OE?JQMCO VGB DJOO IBQH IBJ CHIJ?GQ??CJ? OEQGCHZ �C @J @K �� � ��� � JBC� CI OCZHC�GQHI �� �
EW�J? @
��
������� �
������� �������� ������� ��� ��� � ��������� ���� ����������
� �� � ���������
RBJ P�> ?JGJCNJ? W�OJ?NJO IBJ WIEI WX IBJ HWCO� DCHJQ? GBQHHJD QHM MCOGQ?MO
IBJ OQV EDJO GW??JOEWHMCHZ IW IBJ E?J� K QXIJ? �BCGB IBJ ICV J�MWV QCH W�OJ?NQICWH
OJ�JHGJ XW? IBJ � P�> � DW GS GQH � J � ?CIIJH CH NJGIW? XW?V QO �FJJ �� @���
� �6� � � �6� �� �� � �6� �� �6� �� @��
�H �� @�� K � �6� MJHWIJO Q NJGIW? WX X?J�JHG��MWV QCH �L O�V�WDO I?QHOV CIIJM CH IBJ
� P�> � DW GS K �� Q HCIQ?� V QI?C ?JE?JOJHICHZ IBJ CHNJ?OJ � ���R WEJ?QICWH
MJ�HJM JDJV JHI� COJ QO
��� �6 �� � ��� � ��� 6� �� �6� �� CO IBJ ICV J�DQZ GBQHHJD I?QHOXJ? XHGICWH V QI?C ?JE?JOJHICHZ IBJ ICV J�MWV QCH
J�JGI WX IBJ GBQHHJD QHM �� �6� Q NJGIW? WX �J?W�VJQH �BCIJ QHM QOOCQH HWCOJ OQVEDJO� CIB NQ?CQHGJ � �� @ AJ?XW?V CHZ QH � �EWCHI ��R QI IBJ ?JGJCNJ? �MJHWIJM �� � � K �J
��
W�IQCH IBJ X?J�JHG� �MWV QCH W�OJ?NQICWH NJGIW? �FJJ �� @���
� �6� � �� �6�
� �� �6� �� �� � �6� � �� �6�
� � �6�� �� � �6� � �6� �� @��
�BJ?J � �6�� �� CO IBJ >WEEDJ?�X?J�JHG� I?QHOXJ? XHGICWH V QI?C IBQI ?JE?JOJHIO IBJ
X?J�JHG��MWV QCH J�JGI WX IBJ GBQHHJD QHM � �6� CO Q NJGIW? GWHIQCHCHZ X?J�JHG��
MWV QCH HWCOJ OQVEDJO @
�W? �R � GBQHHJDO �HW >WEEDJ? OE?JQM � K � �� CO Q GC?G DQHI V QI?C QHM ���� CO
M CQZWHQD @ � J?J K WEICV QD MJIJGICWH WX IBJ � � JDJV JHI CH � GQH � J QGGWVEDCOBJM OCHZWHD� IBJ � � JDJV JHI WX � QHM IBJ � � MCQZWHQD JDJV JHI WX � ��� @ � BJH IBJ >WEEDJ?
OE?JQM CO HWH�I?CN CQD ��R� GBQHHJDO� K � �� DWOJO CIO GC?G DQHI OI?GI?J K E?JNJHICHZ ����
X?WV � JCHZ MCQZWHQD �FJJ �� @���� �BCGB GQOJO �� � QHM GWVEDCGQIJO IBJ MJIJGICWH WX � @
� BCDJ OIQHMQ?M MJIJGICWH OI?QIJZCJO �J @Z @K �� K � FY QHM �F> ����� Q?J JQO� IW
XW?V DQIJ K IBJ� Q?J CVE?QGICGQD IW CVEDJV JHI �BJH IBJ MCV JHOCWH WX � ��� �ZCNJH ��
IBJ P�> � DW GS DJHZIB K �BCGB V Q� � J � ����� CO DQ?ZJ @ �H �BQEIJ? � �J MJ?CNJM QH
JE?JOOCWH XW? IBJ NQ?CQHGJ WX IBJ JDJV JHIO CH � ��� �BCGB OZZJOIO IBQI K WH QNJ?QZJ K IBJV QZHCIMJO WX IBJ W��MCQZWHQD JDJV JHIO MJGQ� ODW� D� � CIB CHG?JQOCHZ MCOIQHGJ X?WV
IBJ V QCH�MCQZWHQD �FJJ � CZ @ � @�� K C @J @K �� � CO �W?OI QVWHZ �HJQ?��� O� GQ??CJ?O @ RBO K
CHGW?E W?QICHZ IBJ J�JGIO WX MCOIQHI��� � VCZBI CV E?WNJ IBJ MJIJGICWH EJ?XW?V QHGJ �I
E?JNJHIO E?QGICGQD CV EDJV JHIQICWH @
�H IBCO GBQEIJ? K �J E?WEWOJ DW��GWV EDJ CI� DCHJQ? ?JGJCNJ? E?J�E?WGJOOCHZ IW I?H�
GQIJ IBJ W��MCQZWHQD �C @J @K �� �� ?JOE WHOJ WX � ��� @ � BCDJ ���� GW DM W�NCWOD� � J MC�
QZWHQDC�JM IB?WZB IBJ ��J?W�XW?GCHZ� DCHJQ? I?QHOXW?V QICWH � � �� �� K IB CO BQO I�W V Q� W?
��
MCOQMNQHIQZJO % �� IBJ � �� � � GWVEDJ CI� WX V QI?C CHNJ?OCWH K QHM �� IBJ E WIJHICQDXW? HWCOJ ZQCH % � � �� �� � � � � � �� ��� �BJ?J � � �� ��� V Q� � J DQ?ZJ @ �HOIJQM K �J E?WEWOJ
IW �OBW?IJH IBJ �� � ?JOEWHOJ� K ?JO DICHZ CH OW�GQDDJM �GWHI?WDDJM �� �� IBQI GQH � J J��
GCJHID� BQHMDJM � CIB QEE?WE?CQIJ MJIJGICWH QDZW?CIBV O �MCOGOOJM CH �BQEIJ? �� @ RBCO
CO QHQDWZWO IW �F��GBQHHJD OBW?IJHCHZ JVEDW�JM CH OCHZDJ�GQ??CJ? O�OIJV O IW ?JMGJ
IBJ GWVEDJ CI� WX V Q CVV DCSJDCBWWM OJ�JHGJ MJIJGICWH � �F> � ��� K ��� @� BCDJ OCHZDJ�GQ??CJ? O�OIJV O I�ECGQDD� QGGWVEDCOB �F��OBW?IJHCHZ OCHZ GWHNWDICNJ
� DIJ?CHZ K �J E?WE WOJ �� ��OBW?IJHCHZ OCHZ �XQOI GWHNWDICWH� ���� CH W?MJ? IW DJNJ?QZJIBJ ��R WEJ?QICWH QD?JQM� � JCHZ EJ?XW?V JM �� IBJ P�> ?JGJCNJ? @ RBJ OCVEDJOI
QEE?WQGB �W DM CHNWDNJ �� CHMW� CHZ� IBJ � �EWCHI ICV J�MWV QCH ?JGJCNJM OCZHQD � �6�E?CW? IW IBJ ��R @ � CHMW� CHZ BQO � JJH E?WEWOJM QO Q GWVEIQICWHQDD��J� GCJHI V JQHO
WX CHG?JQOCHZ IBJ MJGQ� ?QIJ WX IBJ ?JO DICHZ �� � IJ?V O �J @Z @K �������� @ �H IBWOJ EQE J?O K
IBJ ICV J�MWV QCH I?QHOV CIIJM QHM�W? ?JGJCNJM OCZHQDO �J?J V DICE DCJM �� Q OJ�JHGJ WX
� CHMW� GWJ� GCJHIO I�ECGQDD� GBWOJH X?WV IBJ �JDD�SHW�H � QHH K � QCOJ? K W? � DQGSV QH
OBQE JO ��� � @ � BCDJ IBJOJ EQ?ICG DQ? � CHMW� O BQNJ � JJH OBW�H IW ?JMGJ �� � K IBJ� Q?JHWI WEICV QD XW? IBCO QEEDCGQICWH K DJQNCHZ ?WWV XW? OCZHC�GQHI CVE?WNJV JHI @
�H IBCO GBQEIJ? �J E?WEWOJ IBJ MJOCZH WX OIQICOICGQDD� �WEICV QD � CHMW� O �QOJM WH
QEE?WE?CQIJ OIQICOICGQD XQMCHZ V WMJDO ���� @ � BCDJ CI �W DM � J EWOOC� DJ IW MJOCZH IBJOJ
� CHMW� O IW V CHCV C�J IBJ NQ?CQHGJ WX QDD �� � K IB CO V Q� � J XW WDCOB X?WV Q �MCNJ?OCI��
OIQHMEWCHI % �H IBJ JNJHI IBQI IBJ MCQZWHQD JDJV JHIO �J?J NJ?� OV QDD �C @J @ XQMJM � K
W��MCQZWHQD JDJV JHIO V Q� GWHIQCH G?CICGQD CHXW?V QICWH XW? O�V�WD MJIJGICWH @ �W? IBCO
?JQOWH K �J E?WEWOJ � CHMW� O �BCGB QDDW� GWHI?WDDJM �� � QHM �BJ?J IBJ �IQ?ZJI �� ��CO WEICV C�JM � WCHID� � CIB IBJ � CHMW� @
��
�MJQDD�K IBJ �� ��OBW?IJHCHZ � CHMW� OBW DM � J WEICV C�JM IW V Q CV C�J O�V�WD MJIJG�ICWH EJ?XW?V QHGJ @ �X �J QOOVJ QH P�> O�OIJV JV EDW� CHZ EW�J?X D J??W?�GWHI?WD
GWMCHZ K IBJH IBJ �HQD MJIJGICWH E J?XW?V QHGJ CO E?WE W?ICWHQD IW IBJ QNJ?QZJ OCZHQD
IW CHIJ?XJ?JHGJ�EDO�HWCOJ ?QICW �F��� � QG?WOO GQ??CJ?O ���� K QHM �F��� WEICV C�QICWH�
� JGWV JO IBJ WEICV QD G?CIJ?CWH @ � J?J K CHIJ?XJ?JHGJ ?JXJ?O IW IBJ GWHI?C�ICWHO X?WV IBJ
HWH�GWHI?WDDJM �� � @
�H XQGI K WHJ GW DM IQSJ IBJ � CHMW� CHZ GWHGJEI X?IBJ? % ?JGQDD K IBQI � �6� BQO � JJH
?JGIQHZ DQ?D� � CHMW�JM CH IBJ ZQ?M ?JV WNQD OIJE IW E?JNJHI CHIJ?�� DW GS CHIJ?XJ?JHGJ��� �� @ CNJH IBQI V DICEQIB GBQHHJDO I�ECGQDD� JBC� CI QH JEWHJHICQDD� MJGQ� CHZ MJDQ�
E?W� DJ ���� K CI CO DCSJD� IBQI Q OV QDD QVWHI WX �� � GQH � J I?QMJM XW? Q DQ?ZJ? ?JMGICWH
CH �� � @ RBO K QH CV E?WNJM OI?QIJZ� �W DM CHNWDNJ � CHMW� CHZ QH � �� �� �EWCHI
OJZV JHI WX IBJ ?JGJCNJM OCZHQD K �BJ?J �� MJHWIJO IBJ G�GDCG E?J� DJHZIB QHM ��
IBJ V Q CVV GBQHHJD MJDQ� OE?JQM CH �QM @ �H QMMCICWH K N CJ� CHZ IBJOJ � CHMW� CHZ
WEJ?QICWHO QO MCQZWHQD V QI?C V DICE DCGQICWHO K Q �QHMJM V QI?C V DICE DCGQICWH K W?
�OE J?�� CHMW� CHZ� V Q� W�J? �JI CVE?WNJM EJ?XW?V QHGJ QI Q ?JDQICNJD� OV QDD GWV �
EDJ CI� CHG?JQOJ @
�H IBCO IBJOCO K �J XW GO WH IBJ �QOCG � �EWCHI � CHMW� MJOCZHJM IW V Q CV C�J F��� @
FJGICWH � @� JEDQCHO IBJ J�JGI WX ICV J�MWV QCH � CHMW� CHZ WH P�> QHM E?WNCMJO
IBJ OJI E ?J� C?JM XW? IBJ WEICV QD�� CHMW� MJOCZH @ �H FJGICWH � @� �J MJ?CNJ QH
JE?JOOCWH XW? IBJ GWJ� GCJHIO WX IBJ � CHMW� IBQI V Q CV C�JO IBJ F��� CH IJ?V O WX
IBJ GBQHHJD ?JOE WHOJ � �� �� � � � K L�� NQ?CQHGJ � �� QHM IBJ MJOC?JM �� ��OE?JQM � @
� CHQDD�K XW? GBQHHJDO � CIB OCZHC�GQHI MJDQ� OE?JQM K �J GQH OBW� IBQI IBJ F��� �WEICV QD� CHMW� CO �JDD QEE?W CV QIJM �� Q XHGICWH WX WHD� GBQHHJD QHM HWCOJ OIQICOICGO �C @J @K
��
HWI ?JQDC�QICWHO� K �BCGB CO NJ?� QMNQHIQZJWO X?WV QH CV EDJV JHIQICWH OIQHMEWCHI @FE JGC�GO Q?J E?WNCMJM CH FJGICWH � @� @
� �� ���� � � � � ������ � ����� ���
L �� CHMW� CHZ� ?JGJCNJ? QEEDCJO Q ICV J�MWV QCH � CHMW� � CIB GWJ� GCJHIO � �� � � JXW?JIQSCHZ IBJ >�R K � CJDM CHZ IBJ WIEI �� �6�� �� � ����
� �6�� � ���� � �5��
� �� � � �6� �� ��� �� �� 5 �� @��
RBJOJ � CHMW�JM X?J�JHG��MWV QCH ?JGJCNJM OQV EDJO GQH � J ?JDQIJM IW IBJC? HWH�
� CHMW�JM GWHIJ?EQ?IO X?WV �� @�� QO
� �6�� � ���� � �5��
� � ����
� ��� � �6� �� ��5� ��� �� �� 5
�BJ?J �� CO Q > C?QG�MJDIQ XHGICWH XHGICWH MJ�HJM QO
�� � � �
�� � �JDOJ
FW K
� �6�� � ���� � �5��
� � ����
� ��� � �6� �� � ��
�� � �� ��
�� �� ��� �� �� �� �� �� 5
� ���� � �� ��
����
� � ����
� ����� ���� �� ����
� � �5��
� �6� �� ��� �� ���� �� 5�� ���
� � �� ��
�� � �6���� �� @��
RBCO GQH � J MJ?CNJM OCHZ IBJ � �� >�R V QI?C � K MJ�HJM JDJV JHI� COJ QO
�� �6 �� ���� �� ��� 6� �
� �
IBJ NJGIW?�IW�MCQZWHQD V QI?C WE J?QIW? � ��� K IBJ NJGIW?�IW�GC?G DQHI V QI?C WEJ?QIW?� ��� K QHM IBJ >�R E?WE J?I� ����
�� �� ��� � ��� � � ������� �� @��
QO XWDDW� O
� �6� � �� �� �� �6�
� �� �� ��� �� �6�
� ���� �� �� �6�
� ��� � �� � �� �6�� �� � �6� � �6�� �� @��
RBJ QCV WX � CHMW� CHZ CO IW V QSJ IBJ V QI?C � �� �� �6�� �� OEQ?OJ K �BCGB ?JMGJO IBJ HV �
� J? WX OCZHC�GQHI GBQHHJD GW J� GCJHIO IW � J BQHMDJM �� IBJ ?JGJCNJ? K IBJ?J�� ?JMGCHZ
IBJ GWVEDJ CI� WX IBJ O�V� WD MJIJGICWH @
�H XQGI K QO MJIJGICWH GWHGJ?HO K IBJ ?JGJCNJ? QOOVJO IBQI IBJ � CHMW�JM GBQHHJD
V QI?C � �� �� �6�� �� BQO V QH� �J?W�NQDJM JDJV JHIO K QHM QH� JDJV JHIO � ?WHZX DD� QO�
OV JM IW � J �J?W � CDD GWHI?C�IJ IW IBJ WNJ?QDD DJNJD WX CHIJ?XJ?JHGJ @ RBJ CHIJ?XJ?JHGJ
DJNJD GQH � J �QHIC�JM � CIB IBJ QCM WX Q V QOS WE J?QIW? � ��� �BCGB H DDO QH� V QI?CJDJV JHIO QOOVJM �J?W �� IBJ ?JGJCNJ? QHM IBJ GWV EDJV JHIQ?� V QOSCHZ WE J?QIW? � ����BCGB H DDO IBJ JDJV JHIO QOOV JM HWH��J?W �� IBJ ?JGJCNJ? @ RBJ J� JGICNJ �OCZHQD� QHM
�HWCOJ CHIJ?XJ?JHGJ� GWVEWHJHIO Q?J IBJH
�OCZHQD� � ��� � �� �� �� �6�� �� � � �6�
�HWCOJ CHIJ?XJ?JHGJ� � ��� � �� �� �� �6�� �� � � �6� ���� �� �� �6�
��
� CJDM CHZ IBJ XWDDW� CHZ �OCZHQD� QHM �HWCOJ CHIJ?XJ?JHGJ� JHJ?ZCJO �QOOV CHZ Y �� �6�� �6�� � �
� � Y �� �6�� �6�� � � � �� � QHM Y �� �6�� �6�� � � � �
� 3 � �
� �� �� �� �� �6�� �� � ����56 � �
� �� �� �� �� �6�� �� � ��� � ��� �� �� � ����BJ?J � � � MJHWIJO IBJ �?W� JHCO HW?V @
� �� � ������� � ����� � ����
�?WV J�QICWH �� @�� QHM � CZ @ � @� K �J Q?J V WICNQIJM IW GBWWOJ QH �QM� QGJHI�GQ??CJ?�
MJOC?JM �� � ?JZCWH K C @J @K � �� �� �6�� �� � CIB Q �QHMJM OI?GI?J �CHGDMCHZ IBJ IWE�?CZBIQHM � WIIWV �DJXI GW?HJ?O� @ Y� CNQDJHID�K IBJ V QOS WEJ?QIW? � ��� H DDO IBJ � � MCQZWHQD
XW? JQGB � CH IBJ ?QHZJ � � � �� � � � � � � � K �BJ?J � � � GW??JOEWHMO IW
IBJ V QCH MCQZWHQD @ RBJ EQ?QVJIJ? � GWHI?WDO IBJ IQ?ZJI DJNJD WX �� � OBW?IJHCHZ %
1
D
D
D
D+
+1
� CZ?J � @� % &����� � �� ����
OV QDDJ? � GW??JOEWHMO IW Q OBW?IJ? �� � OEQH QHM IBO ?JMGJM MJIJGICWH GWVEDJ CI�@
��
� BCDJ IJGBHCGQDD� �J ?J� C?J � � � � �� � � K �J BQNJ W�OJ?NJM IBQI K XW? ZWWM � CHMW�EJ?XW?V QHGJ K � VOI � J GBWOJH CH QGGW?MQHGJ � CIB IBJ >WEEDJ? OE?JQM @
P? MJ�HCICWH WX � ��� QDDW� O IBJ OCV EDC�GQICWH
�� �� �� �� �6�� �� � ��� � �� � �� �� �6�� �� ���
�BJ?J
� ������ � � �� � �� � ��
��
QHM � �6�� �� CO Q ?J�Q??QHZJVJHI WX � �6�� �� MJ�HJM JDJV JHI� COJ ��
�� �6�� �� �� �� � � �6�� �� �� � � � �FCV CDQ?D� �J BQNJ
�� �� �� �� �6�� �� � ��� � �� �� �� �� �6�� �� ���
�BJ?J � � � ��� � @ �WICHZ IBQI
�� �� � ��� � � �� ��
�� �� �� �6�� �� ��� � � ��� �� ���� �6�� ��� ���� � �� �� �� �6� �� ���� � �� MCQZ �� �6� ��� �6� �� � ��
�� � �� �� �6�� �� ��� � � �� �� �� �� �6� �� ���
�BJ?J
�� �6� �� �5 � � � �6� �� �� � � �
��
QHM IBQI
�� �� �� �6�� �� ��� � ��� � � �� �� �� �6�� �� ���� �� � �� �� �6�� �� ��� �� �� �� �� �6�� �� ���
OW IBQI
�� �� �� �� �6�� �� ��� � �� �� �� �6�� �� ��� � �� � �� �� �6�� �� ���� � �� MCQZ �� �6� ��� �6� �� � �� � � �� �� �� �� �6� �� ���
Q CV C�CHZ F��� � 3��56 CO QGGWV EDCOBJM ��
�� � Q?Z V Q�
�� � �� �� �6�� �� ����� �� �� �� �6�� �� ��� � �� �� �� � ���
� Q?Z V Q�
�� �� �� �� �6� �� ����� MCQZ �� �� � � �6� ��� �6� �� � �� � �� �� �� �� �6� �� ���
RBCO GQH � J OWDNJM CH GDWOJM XW?V IB?WZB
�� � MCQZ �� �� � � �6� ��� �6� �� � � �� ���� � Q?Z V Q��
�� �� ��� � �� �6� �� ������ �� � �� �� ��� � �� �6� �� ���
OCHZ
�� �6� �� � MCQZ �� �� � � �6� ��� �6� �� � �� ��� �6� �� �� @��
�WICHZ IBQI IBJ F��� CO CHNQ?CQHI IW IBJ OGQDCHZ WX �� K �J GQH QOOVJ � CIBWI QH�
DWOO WX ZJHJ?QDCI� IBQI ��� � � � K CH �BCGB GQOJ
��� � Q?Z V Q� �� �� � �� �� ��� � �� �6� �� ���
��
�I BJDEO IW � ?CIJ IBJ Q� WNJ HW?V QO
�� �� ��� � �� �6� �� ��� � � � ��� �� ���
���
� � �5��
��5 �� �� �� 5 �� �6� �� �� � � � �
� �
� 5 �� ��5 ���� �� ����� �� � ���� � � � �
���� �6� �� �� � � ��� �6�� �� �� � � �
� ���� ���BJ?J � CO MJ�HJM � JDW� �OCHZ � IW MJHWIJ JDJV JHI� COJ V DICE DCGQICWH � %
� � �
� �� ����� �� � ���� � � � � �
���� �6� �� �� � � ��� �6�� �� �� � � � �� @��
� � � � � � XW?����� �� � �5 � �
� �� � �� ���� �� �5� ���
�� � �� �5� ���� � � � �� �6� �� �� �6�� �� � � �� @��
OCHGJ X?WV �� @�� �J SHW� IBQI
�� ����� � � � OCH �� ��� �� ���
OCH �� ��� �
RBO ��� CO IBJ E?CHGCE DJ JCZJHNJGIW? WX � QHM
�� � MCQZ �� �� � � �6� ��� �6� �� � �� �� ��� �� @���
� CZ @ � @� CDDOI?QIJO IBJ J� JGI WX � �EWCHI V Q�F��� � CHMW� CHZ WH Q ?JE?JOJHIQICNJ
?JQDC�QICWH WX ���� �BJ?J IBJ MWI OC�J CO E?WEW?ICWHQD IW IBJ GWJ� GCJHI DWZ�V QZHCIMJ @
� �� � ������� � ����� � ������ � ����� �� ����� ���
RBJ WEICV QD � CHMW� GW J� GCJHIO �� X?WV �� @��� K ?J� C?J IBJ SHW� DJMZJ WX IBJ G?�
?JHI GBQHHJD GWJ� GCJHIO �FJJ �� @��� @ RBJ GWVEIQICWHQD �?MJH JOOJHICQDD� DCJO CH
GQDG DQICHZ IBJ JDJV JHIO WX V QI?C � � @ �J HW� OJJS Q GBQHHJD� CHMJE JHMJHI QEE?W C�
V QICWH IW �� @��� @ �?WV �� @�� QHM �� @�� K �J OJJ IBQI � � GQH � J JEQHMJM CHIW
� � � MCQZ �� �� � � �6� ��� �6�� �� �� �� �� �6� ��� �6�� �� � � MCQZ �� �� � � �6� ��� �6�� �� �� ����
pre−window post−window
� CZ?J � @� % '����� (�� �� ) �� �� � ����*+,- . � ��. � � � ! � �� �� / �� � ��� ����� "
�W? GBQHHJDO IBQI JBC� CI Q DQ?ZJ MJDQ��OE?JQM �C @J @K DQ?ZJ �� � K �J GQH QEE?W CV QIJIBJ OVV QICWH CH � �6� ��� �6�� �� OCHZ QH JEJGIQICWHO %
�� �6� ��� �6�� �� �5 �� � Y � � ���
� �6� �� �� � � �� �6�� �� �� � � ��� � � �
��� � �� ��� �� �� � ���
�BJ?J �J OJM IBJ E?WE J?I� WX Y �� �6� �� �� � � �� �6�� �� �� � � �� ZCNJH �� �� @�� @ RBJ V Q�F���� CHMW� �QHICICJO IBJH � JGWVJ
�� ��� �� � ��
� �� � �� ���
�� � �� �5 �� � �� � �� �� � � �� � � �� ��� �� �� � ���
LO MJOC?JM K QH QEE?W CV QIJ V Q�F��� � CHMW� GQH � J GWHOI?GIJM OCHZ GBQHHJD QHMHWCOJ � �� ��� ���� ?QIBJ? IBQH GBQHHJD ������� ����� @ �?IBJ?VW?J K � �� QHM � � WHD� QGI
IW OGQDJ IBJ � CHMW� �QHM BJHGJ MW HWI Q� JGI IBJ ?JO DICHZ F��� � @ RBO IBJ � CHMW�
GWJ� GCJHIO JOOJHICQDD� MJEJHM WHD� WH �� K � QHM � @ RBCO E?WNJO NJ?� � JHJ�GCQD X?WV
QH CVEDJV JHIQICWH OIQHMEWCHI @
��
0 20 40 600
0.5
1
1.5
(a) Hd,f
none, SINR=14dB
0 20 40 600
0.5
1
1.5
(c) Hd,f
opt, SINR=28.1dB
0 20 40 600
0.5
1
1.5
(d) Hd,f
approx, SINR=28dB
0 20 40 600
0.5
1
1.5
(b) Hd,f
hamming, SINR=26.4dB
� CZ?J � @� % ����� �� �� (��� �� . � ��. � �
��
� CZ @ � @� E?WN CMJO QH JQVEDJ IW W�OJ?NJ IBJ J�JGIO WX � CHMW� CHZ @ �J GWHOCMJ? QHP�> O� OIJV � CIB � � �� K �� � �� QHM �� � � ���� @ �J MJOCZH IBJ V Q�F���
� CHMW� QHM IBJ QEE?W CV QIJ V Q�F��� � CHMW� XW? � � � QI F�� � �� M� QHM
QOOVJ IBJ V QOS WE J?QIW? E?JOJ?NJO MCQZWHQDO ��� � � � � �� � @ �J OJ MWIIJM DCHJO
IW CHMCGQIJ IBJ GW J� GCJHIO IBQI Q?J � ?WHZX DD� QOOV JM IW � J �J?W �� IBJ ?JGJCNJ?
�MJ IW IBJ V QOSCHZ WEJ?QICWH � @ �WIJ K IBJOJ GWJ� GCJHIO � CDD GWHI?C�IJ IW IBJ WNJ?QDD
DJNJD WX CHIJ?XJ?JHGJ CH IBJ O�OIJV @ �H � CZ @ � @� ��� �J GWHOCMJ? QH P�> O� OIJV
IBQI MWJO HWI CHGW?EW?QIJ � CHMW� CHZ @ P�OJ?NJ K IBJ V QZHCIMJO WX IBJ CHIJ?XJ?JHGJGWJ� GCJHIO Q?J OCZHC�GQHI QHM DJQMO IW Q NJ?� DW� F��� NQDJ @ �H � CZ @ � @� ��� �J
CHGW?E W?QIJ Q � QVV CHZ � CHMW� QHM W�OJ?NJ IBQI � CHMW� CHZ V QHQZJO IW OCZHC�GQHID�
?JMGJ IBJ JIJHI WX IBJ �� � ?JOE WHOJ @ �W�JNJ? K CIO HWI IBJ � JOI �J GQH MW QO XQ?
QO V Q CV C� CHZ IBJ F��� @ �H � CZ @ � @� �� � ��� �J CHGW?E W?QIJ V Q�F��� � CHMW� CHZ
QHM CIO ?JQDC�QICWH�CHMJE JHMJHI QEE?W CV QICWH ?JOE JGICNJD�@ RBJ V Q�F��� � CHMW�
E?WNCMJO IBJ BCZBJOI NQDJ WX F��� QHM CIO JHGW?QZCHZ IW W�OJ?NJ Q HJQ?�WEICV QD
E J?XW?V QHGJ �� IBJ QEE?W CV QIJ V Q�F��� � CHMW� @�H � CZ @ � @� K �J EDWI F��� �� 3��56 � NJ?OO O�V� WD�IW�HWCOJ EW�J? ?QICW XW? QH P�>
O�OIJV � CIB � � ��� ��� � �� � QHM NQ?CWO NQDJO WX �� @ RBJ � JHJ�IO WX � CHMW��
CHZ Q?J GDJQ? @ P�OJ?NJ IBQI IBJ V Q�F��� � CHMW� QHM CIO ?JQDC�QICWH� CHMJE JHMJHI
QEE?W CV QICWH BQNJ HJQ?D� CMJHICGQD E J?XW?V QHGJ @
�H � CZ @ � @� K �J EDWI F��� �� 3��56 � NJ?OO IBJ HW?V QDC�JM >WEEDJ? OE?JQM XW? QH
P�> O�OIJV � CIB � � ��� ��� � �� � QHM NQ?CWO NQDJO WX F�� @ �W? Q ZCNJH OCZHQD
IW HWCOJ ?QICW K IBJ QNJ?QZJ F��� WX IBJ P�> O�OIJV MJG?JQOJO � CIB CHG?JQOJ CHGBQHHJD ICV J NQ?CQICWH �GBQ?QGIJ?C�JM �� �� � @ P�OJ?NJ IBQI K IBJ V Q�F��� � CHMW�JM
O�OIJV BQO IBJ BCZBJOI F��� @
��
−10 0 10 20 30−10
−5
0
5
10
fd = 0.01
SNR, Es/No
SIN
R, d
B
W/O WindowHammingMax−SINR~SINR
−10 0 10 20 30−10
−5
0
5
10
15
20
25
fd = 0.005
SNR, Es/NoS
INR
, dB
−10 0 10 20 30−10
0
10
20
30
fd = 0.001
SNR, Es/No
SIN
R, d
B
−10 0 10 20 30−10
0
10
20
30
fd = 0.0005
SNR, Es/No
SIN
R, d
B
� CZ?J � @� % 0����. � ��. � � *+,- 123 4256 7 ����� *��������,��� -���� 18 3 4) 9 7
��
2 4 6 8 10
x 10−3
8
9
10
11
12
13
14
15SNR=10dB
fdTs
SIN
R, d
B
W/O WindowHamming Max−SINR ~SINR
2 4 6 8 10
x 10−3
8
9
10
11
12
13
14
15SNR=15dB
fdTsS
INR
, dB
2 4 6 8 10
x 10−3
10
12
14
16
18
SNR=20dB
fdTs
SIN
R, d
B
2 4 6 8 10
x 10−3
10
12
14
16
18
20
22
24
SNR=25dB
fdTs
SIN
R, d
B
� CZ?J � @� % 0����. � ��. � � *+,- 123 4256 7 ����� ,�����:� ����� *���� 1;� 7
� �
������� �
������� #�� �������� ��� ���� ��� � ����� ���
� ������ ��� �� �#��
RBJ E?W GJOO WX MJIJGICHZ IBJ I?QHOV CIIJM O�V� WDO QOOV CHZ EJ?XJGI GBQHHJD SHW� D�
JMZJ CO GQDDJM ��� ���� � MJIJGICWH @ FCHGJ IBJ JHM ?JO DI �J �QHI IW QGBCJNJ CO ?JDCQ� DJ
MQIQ I?QHOV COOCWH K � CI J??W? ?QIJ ��Y� � V CHCV C�QICWH � JGWVJO IBJ G?CIJ?CWH XW? WEIC�
V QDCI� WX MJIJGICWH @ �H HGWMJM P�> O�OIJV O � CIB C @C @M @ O�V�WDO QHM HWCOJ K �Y�
GQH � J WEICV QDD� VCHCV C�JM �� V Q CVV DCSJDCBWWM OJ�JHGJ MJIJGICWH � �F> � @ RBJV QCH M?Q��QGS WX �F> CO CIO JEWHJHICQD GWVEDJ CI�@ F�WEICV QD DCHJQ? MJIJGICWH
OGBJVJO CHNWDNJ ZJHJ?QICWH WX DJQOI�O�Q?JO ��F� W? DCHJQ? V CHCVV VJQH O�Q?J J??W?
�� FY � OWXI�JOICV QIJO XW? CHMCN CMQD O�V�WDO XWDDW�JM �� IB?JOBWDMCHZ IW E?WMGJ
BQ?M O�V�WD JOICV QIJO @ RBWZB O� WEICV QD K IBJOJ IJGBHC�JO GQH � J CVEDJV JHIJM
� CIB EWD�HWV CQD GWV EDJ CI�@ L V Q� W? M?Q��QGS WX HGWMJM P�> O�OIJV O CO IBJC?
CHQ� CDCI� IW JEDWCI IBJ ������� �� W� J?JM �� IBJ XQMCHZ V DICEQIB GBQHHJD OCHGJ IBJ� � CDD
HWI ?JDCQ� D� MJIJGI O�V�WDO I?QHOV CIIJM WH O� GQ??CJ?O IBQI JEJ?CJHGJ OJNJ?J XQMCHZ @FCHGJ P�> CO E?CV Q?CD� OJM � CIB GBQHHJDO IBQI Q?J XQC?D� X?J�JHG��OJDJGICNJ K �J
JEJGI IW JHGWHIJ? MJJE OE JGI?QD H DDO � CIJ WXIJH @ RBO E?QGICGQD P�> O�OIJV O
VOI CHGW?EW?QIJ J??W? GWHI?WD GWMCHZ IW JEDWCI V DICEQIB MCNJ?OCI� QHM WNJ?GWVJ
IBJOJ M?Q��QGSO @
��
� � � � ��� � � � �� � � ������
� �� �� ������
���� � �� �� ��
� � � �� � � � � � � � �� ���
����
��� �� �� ����
�� �� ��� ������
� � �� ���� � � ��
��� �� ����
��� ��� �� ����
�� ����� �� ����
�� �� ����� �� ����
�� ���� � ����� �� �� � �� �� � � ��
���� � ����
��������� ��
����� � � ���� ����� ����
�� �� � ��� ��
�� � ���� � �� �� ��� � �
������� � �� �� ��� � �
� CZ?J � @� % �����. �� ������ ����� ��� ����
��
�H GWMJM P�> O�OIJV O K OQDD�K QH JOICV QICWH IJGBHC�J CO OJM IW W�IQCH OWXI�JOICV QIJO WX IBJ CHMCN CMQD I?QHOV CIIJM O�V� WDO @ RBJOJ OWXI�JOICV QIJO Q?J IBJH XJM IW
Q MJGWMJ? �BCGB WIEIO IBJ BQ?M O�V�WD MJGCOCWHO @ �X �J QOOVJ QH P�> O� OIJV
JVEDW� CHZ E W�J?X D J??W?�GWHI?WD GWMCHZ K IBJH IBJ �HQD �Y� EJ?XW?V QHGJ CO E?WEW?�
ICWHQD IW IBJ QNJ?QZJ F��� QG?WOO GQ??CJ?O ���� @ �H FJGICWH � @� �J ?JNCJ� MJIJGICWH
OGBJVJO XW? HGWMJM P�> O� OIJV O �BCDJ CH FJGICWH � @� �J E?WE WOJ IJGBHC�JO IW
W�IQCH OWXI�O�V�WD�JOICV QIJO XW? P�> O� OIJV O JVEDW� CHZ � ����� �� GWMCHZ @
� �� � ������ �� � ��� ������ �#��
�?WV �� @��� �J SHW� IBQI JQGB � DW GS WX QH P�> O� OIJV GQH � J JE?JOOJM ��
IBJ NJGIW? J�QICWH
� � � ��� � � �� @��
� BJH IBJ I?QHOV CIIJM O�V�WDO ��� QHM IBJ HWCOJ �� � Q?J C @C @M @ �C @J @K IBJ HGWMJM
L�� GQOJ� K WEICV QD MJIJGICWH WX � X?WV IBJ W�OJ?NQICWH NJGIW? � GQH � J QGGWV �
EDCOBJM �� V Q CVV DCSJDCBWWM OJ�JHGJ MJIJGICWH � �F> � �FJJ FJGICWH � @� @�� @ �X
� CHMW� CHZ CH JVEDW�JM IW ZCNJ ���� Q OEQ?OJ ��QHMJM � OI?GI?J K IBJH �F> GQH � J
J� GCJHID� QGGWVEDCOBJM �� IBJ � CIJ?� C QDZW?CIBV ���� OCHZ EQIB V JI?CGO MJIJ?V CHJM
�� IBJ HWH �J?W JHI?CJO WX ���� @ �W�JNJ? K CH ZJHJ?QD K CX OWV J OW?I WX GWMCHZ CO JV �
EDW�JM �C @J @K � CO HW DWHZJ? C @C @M @� QHM�W? � CHMW� CHZ CO JVEDW�JM �C @J @K � CO HW DWHZJ?
C @C @M @� K IBJ � CIJ?� C QDZW?CIBV CO HW DWHZJ? �F> @ YNJH OW K IBJ � CIJ?� C QDZW?CIBV V Q�
E?WNCMJ ?JDQICNJD� ZWWM E J?XW?V QHGJ� K JOE JGCQDD� CX IBJ GWVEDJ CI� WX Q GWV� CHJM GBQH�HJD�GWMJ I?JDDCO GQH � J IWDJ?QIJM @ � BJH IBJ GBQHHJD CO �R � K � ��� � JGWVJO MCQZWHQD
� � ����������� � ��� � ��� ���� ��� � �� � ���������� ������ � ��� ������� ��� ���������� ��� ���������� �� ��� � ����� ��������� ��
��
QHM �F> ?JMGJO IW Q OCVEDJ � �� � GWVEDJ CI� �J?W�XW?GCHZ J�QDC�QICWH XWDDW�JM�� IB?JOBWDMCHZ �FJJ FJGICWH � @� @��
� ���� ����� ���� �� ����#��� ���� ��?WV �� @�� K CX ���� CO SHW�H K IBJ GWHMCICWHQD E?W�Q� CDCI� MJHOCI� XHGICWH WX �
ZCNJH � CO
� �� ��� � �
���� �� � �� JE �� �
�� �� �� � ���� � ��� �� @��
� J?J �J BQNJ QOOVJM IBQI � QHM � Q?J HGW??JDQIJM QHM K CH QMMCICWH K � � � �� � � �� �� @RBJ �F> ? DJ CO ZCNJH ��K
�� � Q?Z V Q�� � �� ���
� Q?Z V CH�� �� � ���� � �� �� @��
�BJ?J MJHWIJO IBJ OJI WX QDD E WOOC� DJ NQDCM O�V�WD NJGIW?O QHM �� @�� XWDDW� O X?WV
�� @�� @ RBO �F> CHNWDNJO Q �?IJ�XW?GJ OJQ?GB WNJ? QDD E WOOC� DJ � QHM IBJ WHJ
IBQI OQICO�JO �� @�� CO IBJ OWDICWH @ � DJQ?D� IBJ GWVEDJ CI� WX MJIJGICWH CO JEWHJHICQD
CH IBJ DJHZIB WX � �C @J @K � � V QSCHZ IBCO IJGBHC�J BCZBD� CV E?QGICGQD @
� ���� � ������� �����W? �R � GBQHHJDO K ���� CO M CQZWHQD QHM IBJ �� @�� GQH � J JE?JOOJM QO Q OJI WX
MJGWEDJM J�QICWHO
� 6 � � 6�6 � 6 � � � � � � � �� � �
� JI �J GQH ?J� ?CIJ �� @�� QO
� �� ��� � �
��� � �� � �� JE��
�
�� �� � � �6��
�� 6 � � 6�6 ���� �� � �6�� � �� 6 ��6 �
��
OCHGJ
� �� 6 ��6 � � �
��� � �� JE �� �
�� �� �� 6 � � 6 �6 ��� �
P�OJ?NJ K IBJ � WCHI DCSJDCBWWM XHGICWH CO Q E?WMGI WX V Q?ZCHQD DCSJDCBWWM XHGICWHO KIBO �HMCHZ IBJ � OWDICWH XW? � CO J� CNQDJHI IW �HMCHZ IBJ � OWDICWH XW? JQGB
�6 CHMCN CMQDD�@ � DJQ?D�K
��6 � Q?Z V Q3���� �� 6 ��6 �
� Q?Z V CH3����� 6 � � 6�6 ��
�BJ?J � CO IBJ OJI WX �L O�V�WDO @ � DJQ?D� IBJ � OWDICWH XW? �6 CO W�IQCHJM
�� IB?JOBWDMCHZ � 6�� 6 @ � CIB MCQZWHQD � ��� K IBJ � OWDICWH ?JMGJO IW QH JDJV JHI�
���JDJV JHI IB?JOBWDMCHZ WX � � �� �� � @ RBO XW? IBJ �R � GBQHHJD GQOJ K � MJIJGICWH CO
J� CNQDJHI IW Q � �� � GWVEDJ CI� �J?W�XW?GCHZ J�QDC�QICWH XWDDW�JM �� IB?JOBWDMCHZ @
� �� � �� � ����� �� � ��� ���� �#��
�H GWMJM OCHZDJ�GQ??CJ? O�OIJV O IBQI XQGJ �F� K CI CO I�ECGQD IW JVEDW� ICV J�MWV QCH
J�QDC�QICWH �BWOJ OWXI O�V�WD JOICV QIJO Q?J IBJH OJM XW? O�OJ�JHI MJGWMCHZ @R�ECGQDD�K IBJ �F� GBQHHJDO CH OCHZDJ�GQ??CJ? O�OIJV O Q?J ODW� D��NQ?� CHZ X?WV O�V� WD
IW O�V�WD K OW IBQI Q �JM W? I?QGSCHZ DCHJQ? � DIJ? CO J� JGICNJ XW? J�QDC�QICWH @ �H
W? OGJHQ?CW K �J W�IQCH IBJ OWXI O�V�WD JOICV QIJO IB?WZB X?J�JHG��MWV QCH >WEEDJ?
J�QDC�QICWH WX IBJ �� � ?JOEWHOJ @ FCHGJ IBJ �� � ?JOE WHOJO NQ?� OCZHC�GQHID� X?WV
O� GQ??CJ? IW O� GQ??CJ? �QO CH � CZ @ � @�� K �J GQHHWI ?JD� WH Q OCV CDQ? � DIJ?CHZ QEE?WQGB @
�H FJGICWH � @� @� QHM FJGICWH � @� @� �J XW?V DQIJ OGBJV JO IW W�IQCH OWXI O�V� WD JO�
ICV QIJO �BCGB Q?J WEICV QD CH IBJ DJQOI�O�Q?JO QHM V CHCVV VJQH O�Q?J J??W? OJHOJ
��
?JOE JGICNJD�@ RBWZB JQO� IW XW?V DQIJ IBJOJ Q?J BCZBD� CV E?QGICGQD IW CVEDJV JHI MJIW IBJC? � �� � � GWVEDJ CI�@
L O QDIJ?HQICNJO K �J E?WE WOJ I�W GWV EIQICWHQDD� J� GCJHI OGBJVJO XW? OWXI O�V� WD
JOICV QICWH �BCGB JEDWCI IBJ OI?GI?J WX IBJ OEQ?OJ EWOI�� CHMW�JM GBQHHJD V QI?C @
�H FJGICWH � @� @� �J WIDCHJ Q OCV EDJ MCNJ?OCI� JEDWCICHZ �� ��QOJM MJGCOCWH�MC?JGIJM
JOICV QICWH OGBJVJ BQNCHZ � �� �� � GWVEDJ CI� �� � � � QHM CH FJGICWH � @� @� �J
WIDCHJ Q FY ��QOJM MJGCOCWH�MC?JGIJM JOICV QICWH OGBJVJ BQNCHZ Q VGB � JIIJ?
E J?XW?V QHGJ IBWZB QI QH CHG?JQOJM � �� �� � GWV EDJ CI�@
� �� �� ����������� � ��������
� JGQDD X?WV �� @��� K JQGB � DW GS WX QH P�> O�OIJV GQH � J JE?JOOJM �� IBJ NJGIW?
J�QICWH � � ���� � � @ RBJ DJQOI�O�Q?JO ��F� JOICV QIJ XW? IBJ HSHW�H O�V�WDO
CH � CO ZCNJH ��
�� �3 � Q?Z V CH� ��� � � ��� ��� �� � ���� ���
�JI � � �� � ���� ��� �� � ���� �� K V CHCV C�CHZ � CIB ?JOE JGI IW �
��
� �� �� �� �� �� � � ��� �� � �
QHM IBJ �F JOICV QIJ �QOOVCHZ CHNJ?IC� DJ � ��� � CO
�� �3 � � � �� �� �RBO K IBJ �F JOICV QIW? CO J� CNQDJHI IW Q �J?W�XW?GCHZ ���� J�QDC�J? @ RBJOJ OWXIJOICV QIJO Q?J IBJH XJM IW IBJ MJGWMJ? XW? O�OJ�JHI MJGWMCHZ QXIJ? �BCGB IBJ BQ?M
O�V�WD JOICV QIJO Q?J W�IQCHJM @ � DJQ?D� IBJ V QCH M?Q��QGS WX IBCO JOICV QICWH IJGB�
HC�J CO IBJ � �� � � GWVEDJ CI� WX CHNJ?ICHZ IBJ HWH�MCQZWHQD � � � GBQHHJD V QI?C
���� @
��
� �� �� � ���� � �� �� � �������� � ���� � ��������
RBJ DCHJQ? V CHCVV V JQH�O�Q?J J??W? �� FY � JOICV QIJ XW? IBJ HSHW�H O�V �
�WDO CH � CO ZCNJH �� ����
�� � 3� � � �� � � ��BJ?J � CO HGW??JDQIJM � CIB HWCOJ � � Y ��� � � � � � QHM � ��� CO SHW�H @ � � MJHWIJO
IBJ G?WOO�GWNQ?CQHGJ V QI?C � JI�JJH � QHM � QHM � MJHWIJO IBJ QIW�GWNQ?CQHGJV QI?C WX � @ RBO K
� � � Y ���� �� � �� ��
�BJ?J �J QOOVJ Y ���� � � � QHM
� � Y ���� �� � ��� � �� �� � �� �
�BJ?J � �� MJHWIJO IBJ NQ?CQHGJ WX IBJ JDJV JHIO CH � @ RBO IBJ � FY JOICV QIJ CO
ZCNJH ��
�� � 3� � � �� �� �� ���� �� �� � �� ��� �� �� @��
QHM IBJOJ OWXI JOICV QIJO Q?J OJM XW? O�OJ�JHI MJGWMCHZ @ RBJ JOICV QIJO W�IQCHJM
X?WV IBJ � FY JOICV QIW? Q?J V W?J ?JDCQ� DJ IBQH IBJ �F JOICV QIW? MJ IW Q�OJHGJWX HWCOJ JHBQHGJV JHI CHBJ?JHI IW �� J�QDC�J?O @ �W�JNJ? QZQCH K IBJ V QCH M?Q��QGS
WX IBCO JOICV QICWH OGBJVJ CO IBJ � �� � � GWVEDJ CI� WX V QI?C CHNJ?OCWH CH �� @� � @
��
� �� �� � ������� ��� �� �� ��� �������������� ��������� ��� �� � � �����
����� � ! "#$�%& '� ( !) * +#, - � �&.��//�0 #/ $1� .�203+$ 24 #, � �
3,%$#�� " #$�%& 5 #,0 #, � ! 3..�� $�%#,637#� " #$�%& �
8* 9:;< = 859:;: 8� 9:;<>1%/ .�%,+%.7� %/ ?,2@, #/ $1� ABC0�+2".2/%$%2, 24 # " #$�%& D E2�� /. �+%F+#77�GHIJ J JK L KM N N N K<O O O
PQ
R ST UV=
HIJ J JWX L WXM N N N WX:O O O
PQ
R ST UY
HZZZZZZZI
[X L [ \ WX L � KM ] \ WX L � K^ ] N N N \ WX L � K< ][XM [ \ WXM � K^ ] N N N \ WXM � K< ]D D D N N N DDD[X< [N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N_: `<;<
PaaaaaaaQ
R ST Ub@1��� \� � c] = cV � G [ d [ 0�,2$�/ $1� ��+$2� ,2�" G Ke f g : #,0
X L = K L �Xh = Kh � h`Liej L \ WXe � Kh ] WXe � k = l � N N N � �WXe = Xe[Xe [
m� no ��p q np�c���� rXs�����tu /�/$�" 24 7%,�#� �v3#$%2,/ +#, -� @ �%$$�, %, ��+$2� 42�" #/
8w 9:;L = 8* 9:;< 8� 9<;Lx/%,6 $1� ABC0�+2".2/%$%2, $�+1,%v3� �&.7#%,�0 #-2�� @� 1#��
8w 9:;L = 859:;: 8y 9:;< 8� 9<;Lzw = 5V w = y � '{ D{)
|}
�� ,2@ .�2+��0 $2 /27�� 42� $1� �7�" �,$/ %, � 4�2" zw �y D >1� /$�3+$3�� 24 y "#?�/%$ .2//%- 7� $2 /27�� 42� $1� ! �� �7�" �,$ %, � 3/%,6 2,7� $1� ! �� �7�" �,$ %, zw #,08y 9< �< D �,2@ %,6 $1� ! �� �7�" �,$ 24 � #,0 $1� �7�" �,$/ 8y 9<`L �< #,0 8y 9<`L �<`L @�+#, $1�, /27�� 42� $1� '! � �)�� �7�" �,$ 24 � D � �2 +��0%,6 %, $1%/ 4#/1%2, @� +#,/27�� 42� #77 $1� �7�" �,$/ %, � D >1%/ .�2+�03�� %/ +2".3$#$%2,#77�C�� +%�,$ - �+#3/�%$ 0%0 ,2$ ��v3%�� #, � '!^ ) +2".7�& %$� " #$�%& %,���/%2, $2 /27�� 42� �7�" �,$/ %,� '� = * w � * = '* V * )`L* V ) D 2@���� G @� ,��0 $2 4��0-#+? $1� �#73� 24�#+1 0�$�+$�0 �7�" �,$ %, � %, 2�0�� $2 /27�� 42� /3-/�v3�,$ �7�" �,$/ D u,� @ �2,60�+%/%2,/ 4�0 -#+? @2370 � �2.#�0%�� 43$3�� 0�+%/%2,/ 7�#0%,6 $2 $1� .2//%- %7%$� 24 ���2�C.�2.#6#$%2, $1%/ %/ $1� " #%, 0�#@-#+? 24 $1� 0�+%/%2,C0%��+$�0 4��0-#+? $�+1,%v3� D�� �� �o��t ���t���� ������� rt��������
�, # ,3$/1�77 G $1� 62#7 24 $1� /%6,#7 .�2 +�//%,6 0�/+�%- �0 %, �1#.$�� | @#/ $2��,0�� #, #++3�#$� �.#�/%" 2,%23/� ��.��/�,$#$%2, 24 $1� 023-7�C/�7�+$%�� +1#,,�7 Du ++3�#+� %/ �,/3��0 -� "#&C���B ��+�%��� .��C.�2+�//%,6 $1#$ �%�70/ #, ���+$%��7�/.#�/� �2..7��C4��v3�,+� +1#,,�7 $�#,/4�� 43,+$%2, "#$�%& ���� D �4 @� @ %,02@ $1�$%" �C02" #%, ��+�%��0 /%6,#7 .�%2� $2 $#?%,6 $1� ��> G $1� �v3%�#7�,$ /�/$�" +#, -��&.��//�0 #/ '��� '| D�))
w = �� ! '" ) '� ��� t # $ )
x/%,6 $1� " #&C���B $�+1,%v3� /366�/$�0 %, ��+$%2, | D% @� +#, 0�/%6, $1� $%" �C02"#%, @ %,02@ +2 �� +%�,$/ c /3+1 $1#$ $1� " #$�%& ! '" )� ��� %/ /.#�/� D �. �+%F+#77�@� 0�/%6, $1� @ %,02@ $2 /v3���� #77 $1� �,��6� %, $1� 0%#62,#7/ &�' � N N N �' ( D � �&$@� #..7� $1� " #/? 2.��#$2� 0�F,�0 %, ��+$%2, | Dl 2, ! '" )���� $2 .��/���� 2,7� $1�0%#62,#7/ &�' � N N N �' ( D �� +#77 $1%/ ,�@ "#$�%& � ��� #,0 %$/ 6�,��#7 /$�3+$3�� %/
{)
/��, %, � %6 D { Dl '#) @1��� $1� /1#0�0 .2�$%2, %,0%+#$�/ $1� �7�" �,$/ .��/����0 -� $1�" #/? 2.��#$2� � 'd) D >13/ $1� @ %,02@�0 ���E /�/$�" +#, -� @ �%$$�, %, $��" / 24
� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �
� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �
� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �
� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �
� L
� L L
M�L
� � �� �
� %63�� { Dl � ������� ��������� �� ��� ��� �� ���!���"����# ������� $����% ����� & ��'�& ��(��' $��) ��( * �+ � ��� �� ���!���"����# ������� $ ����% ����� & ��'�& ��( * $ ��) ��( ��'����$� '���� ��� ,
/%6,#7 #,0 ,2%/�C.73/C%,$��4���,+� +2".2,�,$/ #/w = � ��� t # $ '{ D�)
@1���� ��� = �
� � '! '" )� ��� )$ = �
� -� '! '" )� ��� )t # $ . N�4 $1� F�/$ ' #,0 $1� 7#/$ ' �7�" �,$/ 24 t #�� ?,2@, 2� /3..��//�0 .%72$/ G $1�
��7#$%2,/1%. - �$@��, $1� 3,?,2@, /�"-27/ t/ #,0 $1� @ %,02@�0 4��v3�,+�C02" #%,2-/���#$%2, ��+$2� w �L� '#4$�� .%72$ ��"2�#7) +#, -� @ �%$$�,
w �L� = � �L�� �� t/ # $ �L� '{ D0){�
@1��� � �L�� �� 1#/ $1� -#,0�0 /$�3+$3�� #/ /��, %, � %6 D { Dl '- ) D>1� 6�,��#7 /$�3+$3�� 24 � �L�� �� "#?�/ %$ . 2//%- 7� $2 2-$#%, # /24$C�/$%" #$� 24 $1�7#/$ �7�" �,$ %, t/ 3/%,6 2,7� $1� 7#/$ �7�" �,$ %, w �L� D u 4$�� $1��/1270%,6 G $1� ��/37$%,61#�0 /�"-27 �/$%" #$� +2370 - � 4�0 -#+? #,0 3/�0 $2 0�$�+$ $1� /�+2,0C$2C7#/$ �7�" �,$%, t/ G #,0 /2 2, D
2@���� G %4 $1� 72@�� 0%#62,#7 �,$�%�/ %, � �L�� �� #�� /" #77 G $1� 0�+%/%2,/ " #0� @1%7�0�$�+$%,6 $1� 7#/$ 4�@ �7�" �,$/ %, t/ @2370 -� 3,��7%#-7� D u,� @ �2,6 0�+%/%2,/ 4�0-#+? +2370 +#3/� ���2�/ @1%7� 0�$�+$%,6 /3-/�v3�,$ /�"-27/ D �����#6%,6 0%���/%$�G @�.�2. 2/� # ABC0�+2".2/%$%2, $1#$ #,,%1%7#$�/ $1� 72@�/$ 0%#62,#7 %, � �L�� �� G .�203+%,6# ,�@ /�/$�" 24 �v3#$%2,/ 6%��, -�
w �M� = � �M�� �� t/ # $ �M� �@1��� G
� �M�� �� = 5 �L��� �L�� ��w �M� = 5 �L�� w �L�
�2,$%,3%,6 %, $1%/ " #,,�� G @� +#, ��"2�� $1� 0%#62,#7/ 2,� #$ # $%" � 4�2" $1�-2$$2" G �%�70 %,6 # /�$ 24 +#3/#7 0%���/%$� " 20�7/
w �e� = � �e�� �� t/ # $ �e� � � = � � N N N � l' # �
� �e� L�� �� = 5 �e��� �e�� �� � � = � � N N N � l'w �e� L� = 5 �e�� w �e� � � = � � N N N � l'
>1� /$�3+$3�� 24 &� �e�� �� (Mej L #+$3#77� �,#-7�/ 3/ $2 . ��42�" �#+1 ABC0�+2".2/%$%2, �%#� ' � l' ) �� %��,/ �2$#$%2,/� @ %$1 # $2$#7 24 � | ' "37$%. 7%�/ D
{l
(a) remove pilots (b) after first QR (c) after second QR
� %63�� { D% � ���� ����� '�� �����!' ������' ' �������# ��� �$�� ���
� %6 D { D% %773/$�#$�/ $1� AB �� %��,/ 0�+%/%2,C0%��+$�0 0%���/%$� �/$%" #$%2, /$�#$�6�42� ' = � D � %6 D { D% '#) /12@ / $1� 6�,��#7 /$�3+$3�� 24 � �L�� �� D � %6 D { D% '- ) G '+) /12@$1� 6�,��#7 /$�3+$3�� 24 � �M�� �� #,0 � �^�� �� 2-$#%,�0 #4$�� $1� AB �� %��,/ 0�+2".2/%$%2,24 � �L�� �� #,0 � �M�� �� ��/. �+$%��7�D>1�/� 'l' # �) 0%���/%$� "20�7/ +#, -� +21���,$7� +2"-%,�0 $2 2-$#%, $1� /24$�/$%" #$� 24 $1� 7#/$ /�"-27 %, t/ D >1%/ '$�,$#$%��) 0�+%/%2, +#, $1�, -� 4�0 -#+? /2$1#$ $1� /�+2,0C$2C7#/$ /�"-27 +#, - � +21���,$7� �/$%" #$�0 G #,0 /2 2, D � %,#77�G #77/24$ �/$%" #$�/ @2370 - � /�,$ $2 $1� 0�+20�� $2 2-$#%, $1� 1#�0 /�"-27 �/$%" #$�/ D
>13/ @� 2-/���� $1#$ �#+1 /�"-27 %, t/ %/ �/$%" #$�0 4�2" # +21���,$ +2"-%,#$%2,24 'l' # �) +1#,,�7 +2�� +%�,$/ $1���-� �&.72%$%,6 0%���/%$� � D� �� � ������ � � � ����� �� �� � ����� ���
u//3" %,6 $1� /#"� /�$3. #/ %, ��+$%2, { Dl D% G 4�2" '{ D0) @� 1#��w = � ��� t/ # $
���� � ����� ��� �������� �� !"#��� ��!�" $� ! ����$� %&' ( )* +,+ -�".��"� /{%
@1��� $1� /3. ��/+�%.$ 1#/ - ��, 0�2.. �0 42� +2,��,%�,+� #,0 $ %/ # ��+$2� +2,$#%,%,6+2���7#$�0 �#3//%#, ,2%/� /#".7�/ '$ � � '_ � � M� ��V ) G � = ! '" )) D>1� /$�3+$3�� 24 � ��� '��� � %6 D { Dl '-)) /366�/$/ $1#$ #77 %,42�" #$%2, #-23$ $1�7#/$ �7�" �,$ %, t/ %/ +2,$#%,�0 %, $1� 'l' # �) 7#/$ �7�" �,$/ 24 w D >13/ @� +#, /�$3. $1� ��7#$%2,
w �L� = � �L�� �� t �L�/ # $ �L�@1��� ,2@ w �L� � t �L�/ �$ �L� #�� $1� 'l' # �) 7#/$ �,$�%�/ 24 w � t/ �$ ��/. �+$%��7� #,0 � �L�� ��%/ $1� 'l' # �) 'l' # �) 3.. �� $�%#,637#� " #$�%& 42�" �0 -� $1� 7#/$ 'l' # �) �2@ /#,0 +273",/ 24 � ��� D
(a) (b) (c) (d)
� %63�� { D| � ���� !+���' '�� �����!' ������' ��� �$�� ���
� %6 D { D| '#) /12@ / $1� -#/%+ /$�3+$3�� 24 � ��� 42� ' = � @ %$1 $1� 0#/1�0 ��6%2, %0�,C$%4� %,6 $1� 3..�� $�%#,637#� " #$�%& � �L�� �� D � %$1 +1#,,�7 ?,2@ 7�06� G @� +#, .��42�"7%,�#�CEE �� �/$%" #$%2, 24 $1� 7#/$ �7�" �,$ %, t �L�/ 3/%,6 #, � '' ^ ) " #$�%& %,���/� �
8Wt/ 9M� L = �VM� L � �L��� �� '� �L�� �� � �L��� �� # � M� � �L���L�� )`Lw �L�
{|
u-2�� @� 3/�0 $1� 4#+$ $1#$ $ �L� � � '_ � � M� � �L�� �L�� ) G @1��� � �L� %/ # " #$�%& +2,C$#%, %,6 $1� 'l' # �) 7#/$ �2@ / 24 � #,0 �M� L %/ # 7�,6$1 'l' # �) 3,%$ ��+$2� 6%��,-� �M� L = 8) � N N N � ) � �9V D
#�%,6 �/$%" #$�0 $1� 7#/$ �7�" �,$ %, t/ G # $�,$#$%�� 0�+%/%2, +#, - � 4�0 -#+? $2 ��C"2�� $1� %,�3�,+� 24 $1%/ /�"-27 D >1%/ %,�27��/ +#,+�7%,6 $1� /�"-27 �/ +2,$�%-3$%2,/$2 w 3/%,6 $1� 7#/$ +273", 24 � ��� #/ /12@, %, � %6 D { D| '-) D �2@ $1� /�+2,0C$2C7#/$�7�" �,$ 24 t/ +#, -� EE �� �/$%" #$�0 3/%,6 $1� /#" � .�2+�03�� D >1%/ .�2+�// +#, -���. �#$�0 3,$%7 2,7� $1� F�/$ 'l' # �) �7�" �,$/ 24 t/ ��" #%, #/ /12@, %, � %6 D { D| '0 ) D>1�/� /�"-27/ +#, - � � 2%,$7� �/$%" #$�0 3/%,6 # 7%,�#� EE �� /+1�"� #/ 42772@ / � � %�/$@� /�$ 3. $1� ��7#$%2,
w = � ��� t/ # $@1��� w %/ # ��+$2� +2,$#%,%,6 $1� '|' # �) F�/$ �7�" �,$/ 24 w #4$�� +#,+�7%,6 $1�+2,$�%-3$%2,/ 24 $1� #7��#0� 0�$�+$�0 /�"-27/ G � ��� $1� '|' # �) 'l' # �) " #$�%&%,0%+#$�0 -� $1� 0#/1�0 ��6%2, %, � %6 D { D| '0) #,0 $ # ��+$2� +2,$#%,%,6 +2���7#$�0,2%/� /#".7�/ @ %$1 $ � � '_ � � M� � �
V )G @1��� � %/ # " #$�%& +2,$#%,%,6 $1� '|' # �)F�/$ �2@ / 24 � D >1� � 2%,$ EE �� �/$%" #$� 24 $1� 3,?,2@, /�"-27/ %/
Wt/ = � V� �� '� ���� V� �� # � M� � �V )`L w
D ��� #6#%, G $1� EE �� �/$%" #$�/ '/24$C0�+%/%2,/) #�� /#��0 #$ �#+1 /$�. 42� /3-/�C
v3�,$ 0�+20%,6 D >1%/ 0�+%/%2,C0%��+$�0 EE �� /+1�" � %/ �&. �+$�0 $2 23$. ��42�" $1�0�+%/%2, 0%��+$�0 AB /+1�"� 4�2" ��+$%2, { Dl D% G $12361 @ %$1 #, %,+��#/�0 +2".7�& %$�24 � '' ^ ) ��7#$%�� $2 � '' M ) "37$%. 7%�/ D >1��� #�� /����#7 @#�/ $2 6�,��#7%�� $1%//+1�" � D �2� �&#".7� G %,+2�.2�#$%,6 "2�� 2-/���#$%2,/ #$ �#+1 EE �� /$�. @2370
{{
6�,��#$� - �$$�� �/$%" #$�/ -3$ ��v3%�� 7#�6�� " #$�%& %,���/�/ D �, #00%$%2, %$��#$%2,"#� .�2�� @2�$1@1%7� G 42� �&#".7� G %$ %/ . 2//%- 7� $2 ��C+2".3$� $1� /�"-27 �/$%" #$�/#/ /22, #/ $1� F�/$ 0�+20�0 ���/%2, %/ #�#%7#-7� 7�#0%,6 $2 # /%6,%F+#,$ %".�2��" �,$%, $1� �/$%" #$�/ 24 $1� %,%$%#7 �7�" �,$/ %, t/ D
{�
������� �������� �������
�, � %6 D � D� @� .72$ $1� #..�2& %" #$� ��B .��42�" #,+� 42� +20�0 #,0 3,+20�0���E %, #, �> � +1#,,�7 D �� ?,2@ $1#$ �#+1 ���E -72+? +#, -� ��.��/�,$�0 -�$1� /�/$�" 24 �v3#$%2,/ � e = � e e # � e @1��� � = &) � N N N ( #,0 � e � � ') � � M� ) D >13/42� #, 3,+20�0 ���E /�/$�" �".72�%,6 A��� @� 1#��
� '� �� e ) = �l ��4+ � �� e �M
l� M� � '� D�)#,0 @� +#, #..�2& %" #$� $1� ��B 42� # -72 +? � '� �* )
� '� �* ) = � � `Liej� � '� �� e ) '� Dl)
@1��� * = 0%#6 '� e ) D � �&$ $1%/ ��B +#, -� #���#6�0 2��� # 7#�6� ,3"-�� 24 -72 +?/$2 �%�70 $1� #���#6� ��B 24 $1� /�/$�"
� '�) = � 8� '� �* )9 = � � � � `Liej� � '� �� e )� '� D%)
�-/���� $1#$ $1� ��B 42� #, ���E /�/$�" %/ # 43,+$%2, 24 $1� %,0%� %03#7 /3- +#��%�����B/ D u,� ,377/ %, $1� +1#,,�7 /. �+$�3" @2370 +2���/. 2,0 $2 # 72@ /3- +#��%�����B D ��2" '� D�) @� /�� $1#$ # 72@ /3-+#��%�� ���B @2370 $�#,/7#$� $2 # 1%61 � '� �� e ) D>1�/� $��" / @2370 02" %,#$� $1� /3" %, '� Dl) #,0 7�#0 $2 #, 2���#77 1 %61 /�/$�" ��B D
{0
>13/ 42� 3,+20�0 ���E /�/$�" / G $1� ��B .��42�" #,+� %/ 0%+$#$�0 -� $1� 72@�/$/3- +#��%�� ���B D �, 6�,��#7 G 42� +1#,,�7/ $1#$ #�� 4#%�7� 4��v3�,+�C/�7�+$%�� G 3,+20�0���E 2���/ # .22� ��B .��42�" #,+� D
�2� #, ���E /�/$�" �".72�%,6 . 2@��437 +20%,6 G @� +#, #//3" � $1#$ $1� ��B%/ # 43,+$%2, 24 $1� #���#6� ���B #+�2// /3- +#��%��/ 8%�9 #,0 /2 '� Dl) - �+2" �/
0 2 4 6 8 10 12 14 1610
−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
SNR, Eb/No
Bit
erro
r pr
obab
ility
UncodedCoded, N
h = 8
Coded, Nh = 16
Coded, Nh = 32
� %63�� � D� � ����'�' ������ ��'�' ���� �� ��� ��������
� '� �* ) � �l ��4+
�� � `Lej� �� e �M
l � M�� '� D|)
{�
#,0 $1� #���#6� ��B +#, -� +#7+37#$�0 #/ %, '� D%) D �-/���� $1#$ $1� ��B G $12361/$%77 # 43,+$%2, 24 $1� %,0%� %03#7 /3- +#��%�� ���B/ G %/ ,2 72,6�� 02" %,#$�0 -� $1�@2�/$ /3- +#��%�� ���B D >1%/ +#, - � 3,0��/$220 -� $1� 4#+$ $1#$ G ���, $12361 G /2" �/3- +#��%��/ 1#�� # 72@ ���B G $1� #���#6� ���B 2��� #77 $1� /3-+#��%��/ %/ 1 %61 �,2361 G7�#0%,6 $2 # 6220 ��B .��42�" #,+� D �3�$1�� G /%,+� G
� 8��4+ 'd)9 ( ��4+ '� 8d9)@� +#, - � /3�� $1#$ $1� ��B 2-$#%,�0 4�2" '� D|) @ %77 #7@#�/ - � 7�// $1#, 2� �v3#7$2 $1#$ 2-$#%,�0 4�2" '� Dl) D � %$1 %,+��#/� %, +1#,,�7 0�7#� /.��#0 � G $1��� %/0 %���/%$� 2� ���0 -� $1� "37$%.#$1 +1#,,�7 D �%"37#$%2, ��/37$/ /12@ $1#$ ��B 42� $1�+20�0 ���E /�/$�" %".�2��/ @ %$1 $1� %,+��#/� %, +1#,,�7 0�7#� /.��#0 � G $13/�&.72%$%,6 0%���/%$�D >1%/ %/ $1� .�%" #�� "2$%�#$%2, 42� $1� 3/� 24 +1#,,�7 +20%,6 %,���E /�/$�" / D
�, � %6 D � Dl @� .72$ $1� #..�2& %" #$� ��B .��42�" #,+� 24 $1� 0�$�+$%2, /+1�"�/0�/+�%- �0 %, ��+$%2, { Dl D >1� ���E /�/$�" �".72��0 A��� #,0 -72 +? 7�,6$1 =�l� D >1� +1#,,�7 @#/ ���x� B#�7�%61 @ %$1 0�7#� /.��#0 � = %l #,0 ,2�" #7%��0�2..7�� �� = ) N) � %, '�) #,0 �� = ) N)) � %, '�) D � %$ ���2� .�2-#-%7%$� @#/ +#7+37#$�0 #/42772@ / D � %�/$ �#?�/ � "�$120 @#/ 3/�0 $2 6�,��#$� 4#0%,6 +1#,,�7 ��#7%�#$%2,/ 2��� #/.#, 24 " #,� -72+?/ D �2� ���� -72 +? G $1� ���B/ 24 /�"-27 �/$%" #$�/ @��� +2".3$�0#$ �#+1 /3- +#��%�� 3/%,6 $1� 0%� ���,$ �/$%" #$%2, $�+1,%v3�/ 0%/+3//�0 %, ��+$%2, { Dl D� �&$ $1� ���B/ @��� #���#6�0 2��� $1� /3- +#��%��/ G #,0 $1�, +2,���$�0 $2 ��B#//3" %,6 �#3//%#, %,$��4���,+� #,0 # A��� 0�+%/%2, "�+1#,%/"
� '� �� ��� ) � �l ��4+ �� � 8���B9
l � N
{}
0 5 10 15 2010
−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
100
SNR, Eb/No
Bit
erro
r pr
obab
ility
(a)
0 5 10 1510
−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
100
SNR, Eb/No
Bit
erro
r pr
obab
ility
(b)
Simple−DDQR−DDMMSE−DDLMMSELTI channel
� %63�� � Dl � ��$ �� ���� �� ' ������� '����� ��� ����$ �� ��� ��'�' ����
�)
� %,#77�G $1�/� ��B/ @��� #���#6�0 2��� # 7#�6� ,3"-�� 24 -72 +?/ D u / 0%/+3//�0.���%23/7�G +#��%��C#���#6%,6 24 ���B @#/ �".72��0 $2 " %" %+ $1� 3/� 24 . 2@��437+20%,6 D >1� ��> � +1#,,�7� $�#+�/ %, � %6 D � Dl @��� %,+730�0 #/ # ��4���,+� $1������+$ $1� +#/� @1��� $1� +1#,,�7 ��" #%,/ F&�0 $1�236123$ �#+1 -72 +? -3$ +1#,6�/- �$@��, -72+?/ D >1� �> � +1#,,�7 $�#+� %,0%+#$�/ $1� - �/$ ��B .��42�" #,+� $1#$+#, - � �&. �+$�0 4�2" $1� +20�0 ���E /�/$�" %, # �> � "37$%.#$1 +1#,,�7 @ %$10�7#� /.��#0 � = %l D �$ %/ �,+23�#6%,6 $2 2-/���� $1#$ $1� 72@C+2".7�& %$� /+1�"�/0�/+�%- �0 %, ��+$%2, { Dl D% #,0 ��+$%2, { Dl D| 2��� 6220 . ��42�" #,+� ��7#$%�� $2 $1�2.$%" #7 �> � +1#,,�7 $�#+� D
� �&$ G @� .�2+��0 $2 $#?� # +72/�� 72 2? #$ /2" � 24 $1� $�#+�/ 4�2" � %6 D � Dl $2/3..2�$ $1� +7#%" / @� "#0� %, �1#.$�� { D �, ��+$%2, { Dl D% @� #�63�0 $1#$ $1� /24$C/�"-27 �/$%" #$�/ 2-$#%,�0 -� $1� AB 0%���/%$� �&.72%$%,6 $�+1,%v3� @��� " 2�� ��7%#-7�$1#, $1� /%" .7� 0�+%/%2, 4��0-#+? $�+1,%v3� D �, � %6 D � D% @� .72$ $1� #..�2& %" #$���B .��42�" #,+� 24 $1� $@2 42� #, ���E /�/$�" �".72�%,6 A��� @ %$1 -72 +?7�,6$1 = �l� D >1� +1#,,�7 @#/ ���x� B#�7�%61 @ %$1 0�7#� /.��#0 � = %l #,0,2�" #7%��0 �2..7�� �� = ) N) � %, '� ) #,0 �� = ) N))� %, '�) D E #&C���B @ %,02@ %,6@#/ �".72��0 @ %$1 ' = l %, '�) #,0 ' = � %, '�) D � %6 D � D% 0�"2,/$�#$�/ $1#$ $1�� '' M ) +2".7�& %$� AB $�+1,%v3� 23$. ��42�" / $1� � ' ) /%".7� 0�+%/%2, $�+1,%v3�@1�, �� = ) N)) � @1%7� $1�� -2$1 .�2� %0� $1� /#" � .��42�" #,+� #$ �� = ) N) � D
�, � %6 D � D| @� .72$ $1� ��B .��42�" #,+� 24 $1� ABC-#/�0 0�+%/%2, 4��0-#+? �/$%C" #$2� #,0 $1� EE ��C-#/�0 0�+%/%2, 4��0-#+? �/$%" #$2� 42� #, ���E /�/$�" �"C.72�%,6 A��� @ %$1 -72 +? 7�,6$1 = �l� D >1� +1#,,�7 @#/ ���x� B#�7�%61 @ %$10�7#� /.��#0 � = %l #,0 ,2�" #7%��0 �2..7�� �� = ) N) � %, '�) #,0 �� = ) N)) � %, '�) DE #&C���B @ %,02@ %,6 @#/ �".72��0 $2 /12�$�, $1� ��� ��/. 2,/�/ $2 ' = l %, '� ) #,0
� �
0 5 10 15 20
10−4
10−3
10−2
10−1
100
SNR, Eb/No
Bit
erro
r pr
obab
ility
(a)
0 5 10 15 2010
−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
100
SNR, Eb/No
Bit
erro
r pr
obab
ility
(b)
Simple decision−directionQR decision direction
� %63�� � D% � �� ' �������# '�� ����� ���'+��) ������ ��$ �� '�� ����� ���'+��)
�l
0 5 10 15 2010
−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
100
SNR, Eb/No
Bit
erro
r pr
obab
ility
(a)
0 5 10 15 2010
−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
100
SNR, Eb/No
Bit
erro
r pr
obab
ility
(b)
QR decision directionMMSE decision direction
� %63�� � D| � �� ' �������# '�� ����� ���'+��) ������ ���� !+���' '�� ����� ���'+��)
�%
' = � %, '�) D � %6 D � D| 0�"2,/$�#$�/ $1#$ $1� EE ��C-#/�0 /+1�"� 4#� 23$. ��42�" /$1� ABC-#/�0 /+1�"� #$ # "20�/$ %,+��#/� %, +2".7�& %$� 24 � '' ^ ) #/ 2..2/�0 $2� '' M ) "37$%. 7%�/ D
0 2 4 6 8 10 12 14 1610
−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
SNR, Eb/No
Bit
erro
r pr
obab
ility
fd = 0.01fd = 0.005fd = 0.001LTI channel
� %63�� � D{ � ��� �����$���� �� ��� ����� '������� ������ ���$�����' �� ��� � ���'��
�, � %6 D � D{ #,0 � %6 D � D� @� .72$ $1� . ��42�" #,+� 24 $1� � ' ^ ) 7%,�#� EE ��0�$�+$2� '��+$%2, { Dl Dl) #,0 $1� � '' ^ ) EE ��C-#/�0 0�+%/%2,C4��0-#+? 0�$�+$2�
�|
0 2 4 6 8 10 12 14 1610
−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
SNR, Eb/No
Bit
erro
r pr
obab
ility
fd = 0.01fd = 0.005fd = 0.001LTI channel
� %63�� � D� � ��� �����$���� �� ��� ���� !+���' '�� ����� ���'+��) '������� ������ ���!$ �����' �� ��� � ���' ��
�{
'��+$%2, { Dl D|) ��/. �+$%��7� 42� �#�%23/ �2..7�� /.��#0 �� D >1� $��,0 /366�/$/ #. ��42�" #,+� 0�6�#0#$%2, @ %$1 %,+��#/� %, +1#,,�7 $%" �C�#�%#$%2, D
0 5 1010
−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
SNR, Eb/No
Bit
erro
r pr
obab
ility
(a)
0 5 10 1510
−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
SNR, Eb/No
(b)
LTI channelO(N3) Linear−MMSEO(D3N) DD−MMSE
� %63�� � D0 � ��$ �� ���� �� ��� ����� '������� ��' ��� ���� !+���' '�� ����� ���'+��)'�������
� %6 D � D0 0�"2,/$�#$�/ $1#$ $1� EE ��C-#/�0 0�+%/%2,C4��0-#+? /+1�"� 2���/ 6220.��42�" #,+� ��7#$%�� $2 $1� 7%,�#� EE �� 0�$�+$2� D � 1�, �� = ) N)) � G #/ /��, %, '�) G$1� � ' ^ ) 7%,�#� 0�$�+$2� 23$. ��42�" / $1� � '' ^ ) 0�+%/%2,C4��0-#+? 0�$�+$2� #$$1� +2/$ 24 # "3+1 6��#$�� +2".7�& %$�D � 1�, �� = ) N) � G #/ /��, %, '�) G 12@���� G $1�
��
0�+%/%2,C4��0-#+? 0�$�+$2� 23$. ��42�" / $1� 7%,�#� 0�$�+$2� ���, $12361 $1� 42�" �� %//%" .7�� $2 %".7�" �,$ � >1%/ +#, -� 3,0��/$2 20 -� $1� 4#+$ $1#$ $1� 0�+%/%2,C4��0-#+?0�$�+$2� �".72�/ ,2,C7%,�#� .�2 +�//%,6 $2 7����#6� ��+�%��� ?,2@ 7�06� 24 $1� F,%$�C#7.1#-�$ +2,/$�77#$%2, D
�0
������� �
���� �� � � ������ ���
�, $1%/ $1�/%/ G @� 1#�� #00��//�0 .�2-7�" / 4#+�0 -� ���E /�/$�" / %, +1#,,�7/$1#$ #�� $%" �C #,0 4��v3�,+�C/�7�+$%�� D ���1#./ $1� /%,67� 7#�6�/$ %" .�0%" �,$ $2��7%#-7� +2""3,%+#$%2, %, # 023-7�C/�7�+$%�� +1#,,�7 %/ %,$��4���,+� %, $1� 42�" 24��� #,0�2� ��� D �, �1#.$�� % @� 0��%��0 �&.��//%2,/ $2 v3#,$%4� $1� �&$�,$ 24 ���.2@�� #/ # 43,+$%2, 24 2$1�� /�/$�" .#�#" �$��/ D >1�/� ��/37$/ /366�/$�0 $1#$ G ���.2@�� @#/ .�2" %,�,$ 2��� ,�#�-� /3-+#��%��/ #,0 ,2$ /2 /%6,%F+#,$ #/ @� "2��0 $20%/$#,$ /3-+#��%��/ D ���, $1�, G ,�67�+$%,6 0%/$#,$C/3- +#��%�� ��� @#/ 0�$�%" �,$#7 $2/�/$�" .��42�" #,+� @1%7� %,+2�.2�#$%,6 %$/ �� �+$/ 7�#0 $2 .�2-7�" / @ %$1 %".7�" �,$#C$%2, D u / #, #7$��,#$%�� G @� /366�/$�0 # 72@C+2".7�& %$� 7%,�#� ��+�%��� .��C.�2+�//%,6/$�#$�6� '% D� DG " #&C���B @ %,02@ %,6) $1#$ 2.$%" #77� ��03+�0 $1� �&$�,$ 24 ��� %,$1� /�/$�" D � %,#77� @� .�2. 2/�0 72@C+2".7�& %$� �/$%" #$%2, /+1�" �/ $1#$ �&.72%$ $1�.2/$C@ %,02@�0 /.#�/� ��� ��/.2,/� $2 2-$#%, ��7%#-7� /24$C/�"-27 �/$%" #$�/ D �%"37#C$%2, ��/37$/ +7�#�7� %,0%+#$� 6220 .��42�" #,+� ��7#$%�� $2 /$#,0#�0 0�$�+$%2, /+1�"�/-3$ @ %$1 /%6,%F+#,$ +2".3$#$%2,#7 /#� %,6/ D u / $1%/ $1�/%/ /3""#�%��/ .��7%" %,#����/�#�+1 %, $1%/ #��# $1��� #�� # ,3"-�� 24 #��,3�/ 42� 43$3�� @2�? D
��
r�K����� �����o�� � ������ ��tt��p�, �1#.$�� | @� .�2.2/�0 $1� 0�/%6, 24 # -#/%+ C. 2%,$ " #&C���B @ %,02@ $2
2.$%" #77� ��03+� $1� �&$�,$ 24 ��� .2@�� D � %��, $1#$ "37$%.#$1 +1#,,�7/ $�.%+#77��&1%-%$ #, �&.2,�,$%#77� 0�+#� %,6 0�7#� .�2F7� 8%{9 G %$ %/ 7%?�7� $1#$ # /" #77 #"23,$ 24%,$��-72 +? %,$��4���,+� '�� �) +#, - � $�#0�0 42� # 7#�6�� ��03+$%2, %, ��� D >13/ G #, %" C.�2��0 /$�#$�6� @2370 %,�27�� @ %,02@ %,6 # # � # � C. 2%,$ /�6" �,$ 24 $1� ��+�%��0/%6,#7 G @1��� � 0�,2$�/ $1� +�+7%+C.��F& 7�,6$1 #,0 � $1� +1#,,�7 0�7#� /.��#0 D�3�$1��" 2�� G � %�@ %,6 $1�/� @ %,02@ %,6 2.��#$%2,/ #/ 0%#62,#7 " #$�%& "37$%. 7%+#$%2, G@� .��/3"� $1#$ -#,0�0 " #$�%& "37$%. 7%+#$%2, G 2� � �� ��������� G " #� 2� �� ��$%".�2��0 .��42�" #,+� #$ # ��7#$%��7� /" #77 %,+��#/� %, +2".7�& %$�D u / 43$3�� @2�? G@� +2370 0��%�� �&.��//%2,/ 42� C. 2%,$ " #&C���B @ %,02@ / G /3. ��C@ %,02@ / G #,0$1�%� ��#7%�#$%2,C%,0�. �,0�,$ #..�2& %" #$%2,/ D >1� �&$�,/%2, $2 "37$%. 7� $�#,/" %$#,0�2� ��+�%�� #,$�,,#/ +2370 - � #7/2 +2,/%0���0 D
�, .�#+$%+� G " #&C���B @ %,02@ +2�� +%�,$/ " #� - � %,+2,��,%�,$ $2 +2".3$� - �C+#3/� G � D6 DG $1� +1#,,�7 +2�� +%�,$/ � � �� "%61$ - � 3,#�#%7#-7� 2� $1� +2".3$#$%2,24 $1� .�%,+%. 7� �%6�,��+$2� '��� ��+$%2, | D%) " #� - � $22 �&. �,/%�� D �3�$1��" 2�� G%4 $1� +1#,,�7 02 �/ ,2$ /#$%/4� $1� B#�7�%61 #//3".$%2, 2� $1� ,2%/� �#�%#,+� #,0�2..7�� /.��#0 #�� 3,?,2@, G $1�, 0%��+$ +2".3$#$%2, 24 $1� ��#7%�#$%2,C%,0�. �,0�,$#..�2& %" #$%2, @ %77 ,2$ - � .2//%-7� �%$1�� D �, $1�/� +#/�/ G %$ /12370 /$%77 - � 4�#/%- 7� $20�$��" %,� $1� " #&C���B @ %,02@ +2�� +%�,$/ ����� � ������� 3/%,6 0�+%/%2,C0%��+$�02� ���, -7%,0 #0#.$%�� $�+1,%v3�/ D >13/ #/ 43$3�� @2�? %$ @2370 -� %,$���/$%,6 $2%,��/$%6#$� #0#.$%�� #762�%$1" / $2 0�/%6, /+1�"�/ 42� " #&C���B @ %,02@ +2�� +%�,$#0#.$#$%2, D
�}
��$ �����n�� ��w �K����n rt�������� q np����K� t� %,+� 0�$�+$%2, /$�#$�6%�/ 24$�, ��7� 2, ?,2@ 7�06� 24 $1� +1#,,�7 +2�� +%�,$/ G
+2".3$#$%2,#77�C�� +%�,$ +1#,,�7 �/$%" #$%2, #762�%$1" / /12370 -� %,��/$%6#$�0 D �2����E %, 023-7�C0%/. ��/%�� +1#,,�7/ G /%6,%F+#,$ $%" �C�#�%#$%2, %,+��#/�/ -2$1 $1�,3"-�� 24 +1#,,�7 .#�#" �$��/ $1#$ "3/$ - � �/$%" #$�0 #/ @�77 #/ $1� 0%� +37$� 24�/$%" #$%,6 $1�/� .#�#"�$��/ D u / "�,$%2,�0 -�42�� G $1��� �& %/$/ ��7#$%��7� 7%$$7� @2�?2, 023-7�C/�7�+$%�� +1#,,�7 �/$%" #$%2, %, # "37$%+#��%�� +2,$�&$ G #,0 $1� �& %/$%,6 #.C.�2#+1�/ #�� ,2$ ,2$ .�#+$%+#7 42� $�.%+#7 - 72 +? 7�,6$1/ D u / 43$3�� @2�? G %$ @2370 -�%,$���/$%,6 $2 %,��/$%6#$� .%72$C-#/�0�-7%,0 �>� +1#,,�7 �/$%" #$%2, G %,+730%,6 .��C42�" #,+� #,#7�/%/ #,0 �&$�,/%2,/ $2 "37$%. 7�C#,$�,,# /�/$�" / 42� $1� .#�/%"2,%23/+1#,,�7 ��.��/�,$#$%2,/ 3/�0 %, $1%/ $1�/%/ D �2$� $1#$ -7%,0 "37$%+#��%�� #762�%$1" /1#�� ��+�,$7� - ��, 0��%��0 42� $1� �> � +#/� -#/�0 2, F,%$�C#7.1#-�$ 8|)9 G /3-/.#+� 8| �9#,0 +�+72/$#$%2,#�%$� 8|l9 %0�#/ D��� ��p ��� �o��t��w ����
��2" � %6 D � D� %$ %/ �� %0�,$ $1#$ ���E /�/$�" / "3/$ �".72� /2"� /2�$ 24 +1#,,�7+20%,6 $�+1,%v3�/ %, 2�0�� $2 �&.72%$ $1� 0%���/%$� 2����0 -� $1� "37$%.#$1 4#0%,6+1#,,�7 D �, $1%/ $1�/%/ @� 6�,��#$�0 ��B .72$/ 3,0�� $1� #//3".$%2, $1#$ 42� +20�0���E /�/$�" / $1� ��B %/ # 43,+$%2, 24 $1� #���#6� ���B #+�2// /3- +#��%��/ D u /43$3�� @2�? G $1� ���+$ 24 .�#+$%+#7 +20%,6 /+1�" �/ $1#$ 62 1#,0C%,C1#,0 @ %$1 "2��/2.1%/$%+#$�0 0�$�+$%2, #762�%$1" / '� D6 DG �$3�- 2� "�$120/) +2370 - � /$30%�0 D �, /%,67�+#��%�� /�/$�" / +20%,6 $�+1,%v3�/ #�� ?,2@, $2 �&.72%$ $1� 4��v3�,+�C0%���/%$� 2����0-� $1� ��� +1#,,�7 $2 %".�2�� ��B .��42�" #,+� D >13/ +20%,6 /+1�" �/ /12370 -�
0)
0��%��0 $1#$ +#, �&.72%$ -2$1 $1� 4��v3�,+�C #,0 $�".2�#7C0 %���/%$� 0%���/%$� $1#$$1� 023-7�C/�7�+$%�� +1#,,�7 1#/ $2 2��� D ��������� n ��������
� %����,$%#7 0�$�+$%2, '�� ) 8�)9 %/ 3/�43 7 @1�, +21���,$ 0�$�+$%2, G @ %$1 %$/ ��C7%#,+� 2, +1#,,�7 ?,2@ 7�06� G - �+2"�/ %".�#+$%+#7 D �� 1#/ - ��, #..7%�0 $2 ���E3,0�� $%" �C02"#%, 0%� ���,$%#7 " 2037#$%2, '>��E)G @1��� %,42�" #$%2, %/ +20�0 %,$2�#+1 /3-+#��%�� �/ %,$��C- 72 +? 0%� ���,+�/ G 2� 4��v3�,+�C02" #%, 0%� ���,$%#7 "2037#$%2,'���E)G @1��� %,42�" #$%2, %/ +20�0 %,$2 �#+1 -72+? �/ %,$��C+#��%�� 0%����,+�/ 8|%9 D>2 23� ?,2@ 7�06� G �� C���E 1#/ - ��, .�2.2/�0 2,7� 42� $1� /72@ 7�C4#0%,6 +#/� G% D� DG @1��� %,$�#C-72 +? +1#,,�7 �#�%#$%2, %/ ,�67%6%- 7� D >1��� %$/ 1#/ - ��, /12@, $1#$>��E .��42�" / - �$$�� $1#, ���E @1�, +1#,,�7 �#�%#$%2, #+�2// -72 +?/ %/ 7�// $1#,+1#,,�7 �#�%#$%2, #+�2// +#��%��/ G #,0 � %+�C���/# 8||9 D
�, 023-7�C/�7�+$%�� +1#,,�7/ G �� C���E %/ +2".7%+#$�0 -� $1� .��/�,+� 24 ��� Du / 43$3�� @2�? %$ @2370 -� %,$���/$%,6 $2 %,��/$%6#$� �� C���E #762�%$1" / 42� $1%/+#/� $1#$ 7����#6� @2�? 2, �� 42� /%,67�C+#��%�� ��� +1#,,�7/ '� D6 DG 8|{ G|�9) D >1� 12.�%/ $1#$ $1� %,+��#/�0 0�$�+$%2, +2".7�& %$� '��7#$%�� $2 +21���,$) @2370 -� 2� /�$ -�#�2%0#,+� 24 +1#,,�7 �/$%" #$%2, D
0�
����� �� ��� � ��� ������
u//3"� $1#$ $1� $%" �C02" #%, ��+�%��0 /%6,#7 � �e� '! ) %/ # ,2%/� +2��3.$�0 #,07%,�#�7� 0%/$2�$�0 ���/%2, 24 � �e� '! ) #/ # +2,/�v3�,+� 24 # �> � +1#,,�7 @ %$1 %".37/���/.2,/� � �e� '� ) D >1� +1#,,�7 %/ #//3"�0 +2,/$#,$ 2��� $1� ��� -72+? D �4 $1� +1#,,�7%/ +#3/#7 @ %$1 # " #&%"3" %".37/� ��/.2,/� 03�#$%2, � G @1��� � � � � G $1�,
� �e� '! ) = � �`Li:j� � �e� '� )� �e� '! � � ) # z� �e�< � ! f &) � N N N � � �( 'u D�)>1� #0�v3#$� 7�,6$1 24 $1� +�+7%+ .��F& �,#-7�/ $1� �#73�/ 24 � �e� '! � � ) %, 'u D�) $2- � @�77 0�F,�0 D �� #//3"� $1#$ z� �e�< #�� ���2C" �#, @1%$� #,0 �#3//%#, @ %$1 �#�%#,+�� M� D u$ �#+1 -72 +? � G $1� ��+�%��� 0�2./ $1� /#".7�/ +2���/. 2,0%,6 $2 $1� +�+7%+C.��F&#,0 #..7%�/ &� �e� '! )(� `L<j� $2 # 0%/+��$� �23�%�� $�#,/42�" '��>)G � %�70 %,6 &� �e�� (� `L�j�� �e�� = �
� � `Li<j� � �e� '! )�`� �� <
�� +#, ��7#$� �e�h $2 � �e�� 3/%,6 $1� /�/$�" �v3#$%2,/ 'l D0) G 'u D�)� �e�� = �� � `Li
<j� �� �`Li:j� � �e� '� ) � �
� � `Lihj� �e�h �� �� � �� � h� # z� �e�< � �`� �� <= �
� � `Li<j� z� �e�< �`� �� < # � `Lihj� �e�h � �
� � �`Li:j� � �e� '� )�`� �� � :� � �� � `Li
<j� �`� �� � ��� <�= � �e�� # � `Lihj� �e�h ' z* �e�h ) '� ��`h )= � �e�� # �e�� * �e�� 'u Dl)
0l
>1� � �e�� #�� /$#$%/$%+#77� �v3%�#7�,$ $2 $1�%� $%" �C02" #%, +23,$��.#�$/ D �#+1 � �e�� %,$1� ��� -72+? +2,$#%,/ %,42�" #$%2, #-23$ 2,7� $1� +2���/. 2,0%,6 �e�� G % D� DG ��� %/ #-/�,$ D�, ��+$2� 42�" 'u Dl) +#, - � @ �%$$�, #/
w �e� = � �e�t �e� # $ �e�@1��� � �e� %/ # 0%#62,#7 " #$�%& $1#$ ��.��/�,$/ $1� 4��v3�,+�C02"#%, �� �+$ 24 $1�+1#,,�7 #,0 1#/ * �e�� #/ %$/ %,0%� %03#7 �,$�%�/ D �,2@ %,6 w �e� #,0 � �e� G EE �� 0�$�+$%2,24 $1� 3,%$ �#�%#,+� AuE /�"-27/ %, t �e� %/ #++2".7%/1�0 -� �7�" �,$C-�C�7�" �,$$1��/1270%,6 24 $1� ��+$2�
Wt �e�� � �� = � �e�V '� �e�� �e�V # � M� �)`Lw �e�
� %,+� � �e� %/ 0%#62,#7 G $1� " #$�%& %,���/%2, ��v3%��0 %, $1� EE �� 0�$�+$%2, %/ $�%� %#7 D>1%/ %/ $1� +7#//%+#7 "2$%�#$%2, 42� +�+7%+C.��F& ���E D
0%
� ����������
8�9 �.�+%#7 �//3� 2, G �� %��7�// -�2#0-#,0 +2""3,%+#$%2,/ /�/$�" /� G ���� �2" C"3,%+#$%2,/ E#6#� %,� G �#, �}}0 D8l9 u DE D �#���0 #,0 � D u #�1#,6 G ��2%,$ "37$%.#$1C02..7�� 0%���/%$� %, "2-%7�@ %��7�// +2""3,%+#$%2,/� G ���� ���� �� �� ��������� G �27 D |0 G .. D �l%��%l G �#, D �}}} D8%9 � D� D �##/ #,0 � D� D >#� 72� G �E#$+1�0 F7$�� -23,0/ 42� @ %��7�// +2""3,%+#$%2,2��� �#�7�%61 4#0%,6 0%/. ��/%�� +1#,,�7/� G ���� ���� �� �� ��������� G �27 D|} G .. D �{l{� �{l� G ��.$ D l)) � D8|9 � Dx D D A3��/1% G �u0#.$%�� �v3#7%�#$%2,� G ���������� �� �� � ���� G �27 D 0% G .. D
�%|}� �%�0 G ��.$ D �}�{ D8{9 D �#�% G � D � #�#" G #,0 � D ��#,+7#30� G ����v3�,+�C02"#%, �v3#7%�#$%2, 24 "2-%7��#0%2 #,0 $����/$�%#7 -�2#0+#/$ +1#,,�7/� G ���� ���� ������ ������ ������
���� ���� G �27 D � G .. D �� { G �}}| D8�9 � D �#7+2,�� G � D� D u �%�#�%/%$#?37 G u D � �,�#" %,C����#� G #,0 � D � %0/2, G ����Cv3�,+� 02"#%, �v3#7%�#$%2, 42� /%,67�C+#��%�� -�2#0-#,0 @ %��7�// /�/$�" /� G ����
�� ��������� � ���� �� �G �27 D |) G .. D {���� G u.�%7 l))l D809 � D� D ��%,/$�%, #,0 � DE D �- ��$ G �� #$# $�#,/" %//%2, -� 4��v3�,+� 0%�%/%2, "37$%C. 7�& %,6 3/%,6 $1� 0%/+��$� 423�%�� $�#,/42�" � G ���� ���� �� �� ��������� G�27 D �} G .. D �l���%| G � +$ D �}0� D8�9 � D� D � %" %,% �� DG �u,#7�/%/ #,0 /%"37#$%2, 24 # 0%6%$#7 "2-%7� �#0%2 +1#,,�7 3/%,62�$1262,#7 4��v3�,+� 0%� %/%2, "37$%.7�& %,6� G ���� ���� �� �� ��������� G�27 D %% G .. D ��{� 0�{ G �37� �}�{ D8}9 � Du D� D � %,61#" G �E37$%+#��%�� "2037#$%2, 42� 0#$# $�#,/" %//%2, � u, %0�# @12/�$%" � 1#/ +2"�� G ���� �� ��������� � ���� �� �G �27 D l� G .. D {� �| G E #� �}}) D8�)9 � D� D � �2#?%/ G � �� ���� �� ��������� G E +� �#@C %77 G � �@ 2�? G � G %�0 �0%$%2, G
�}}{ D0|
8��9 B D� D #$�/ #,0 � D� D E #,0#�#" G ��1#77�,6�/ %, 72@C+2/$ @ %��7�// $�#,/" %//%2,� G���� � ����� � ������� � ���� �� �G �27 D �0 G .. D }%� �)l G E#� l))) D8�l9 � D� D �#7+2,�� #,0 � DB D E #6�� G �u0#.$%�� +1#,,�7 " �"2�� $�3,+#$%2, 42� " #&C%"3" 7%?�7%1220 /�v3�,+� �/$%" #$%2,� G � �� � ���� ��������� � ������G �27 D {l G.. D �{| �� �{�l G �2� D �}0% D8�%9 � D� D � %66#�% G �u,#7�/%/ 24 "37$%+#��%�� $�#,/" %//%2, %, $%" �C�#��%,6 +1#,,�7/� G���� ���� ������ ���� �� �� ��������� G �27 D % G .. D ��} �� ��}{ G �}}0 D
8�|9 � D B2- ��$/2, #,0 � D � #%/�� G �>1� ���+$/ 24 02..7�� /.��#0/ 2, ���E 'u ) "2-%7��#0%2 /�/$�" /� G ���� ���� ��� ��� ��� ���������� ���� ���� ��G �27 D � G .. D %l}�%%% G �}}} D8�{9 D D � %" G � D �2,6 G D� D � %" G > D �1#,6 G #,0 DE D � %" G ����42�" #,+� #,#7�/%/24 # +20�0 ���E /�/$�" %, $%" �C�#�%#,$ "37$%.#$1 �#�7�%61 4#0%,6 +1#,,�7/� G
���� ���� �� ��� ������ ���������� G �27 D |� G ,2 D { G .. D ���)� ���{ G �}}} D8��9 � D �$#,$+1�� #,0 � D ��$$@�%/ G �>%"�C�#�%#,$ 0%/$2�$%2,/ %, ���E � G ����
�� ��������� ������ G �27 D | G .. D % �l�% �| G � +$ D l))) D8�09 � D u1, #,0 D� D ��� G ����v3�,+� 02" #%, �v3#7%�#$%2, 24 ���E /%6,#7/ 2���4��v3�,+� ,2,/�7�+$%�� B#�7�%61 4#0%,6 +1#,,�7/� G � ��������� ������ G �27 D l} G.. D �|0�� �|00 G u36 D �}}% D8��9 � D �#, #,0 � D� D �3-��G �u,#7�/%/ 24 $1� 0�"2037#$%2, $�+1,%v3�/ 42� ���E/%6,#7/ 3,0�� +2���7#$�0 B#�7�%61 4#0%,6� G ���� ���� ��� ��� ��� ����������
���� ���� ��G �27 D � G .. D 00l� 0l� G l)) � D8�}9 E D B3//�77 #,0 � D� D �$3- �� G ��,$��+1#,,�7 %,$��4���,+� #,#7�/%/ 24 ���E %, #"2-%7� �,�%�2,"�,$� G ���� ���� ��� ������ ���������� ���� ���� ��G �27 D l G .. D�l)��l| G �}}{ D8l)9 � D u �" /$�2,6 G � DE D � �#,$ G #,0 � D �2���G ��27�,2" %#7 +#,+�77#$%2, +20%,6 24���E $2 ��03+� %,$��+#��%�� %,$��4���,+� 03� $2 02..7�� /.��#0� G ���� ���������� ������ ��������� ���� G �27 D { G .. D l00�� l00� G �}}� D8l�9 D �1#2 #,0 � DC� D #66" #, G ��,$��+#��%�� %,$��4���,+� /�74C+#,+�77#$%2, /+1�"�42� ���E "2-%7� +2""3,%+#$%2, /�/$�" /� G ���� ���� �� �� ��������� G�27 D |} G .. D ���{� ��}� G �37� l)) � D8ll9 � D� D ��2, G � D D �1#,6 G #,0 D� D �12 G �u, �v3#7%�#$%2, $�+1,%v3� 42� 2�$1262C,#7 4��v3�,+�C0%� %/%2, "37$%. 7�& %,6 /�/$�" / %, $%" �C�#�%#,$ "37$%.#$1 +1#,,�7/� G���� ���� �� �� ��������� G �27 D |0 G .. D l0�%l G �#, D �}}} D
0{
8l%9 � DC� DE D� D � %,,#�$� #,0 u D �2�2?12� G �� �@ �v3#7%�#$%2, #..�2#+1 42� ���E2��� 0%/. ��/%�� #,0 �#.%07� $%" � �#��%,6 +1#,,�7/� G ���� ���� �������� �� � ���� �� � ������� ������ ��� � ����� ����� �� ��������� G �27 D l G .. D �%0{��%0} G l))) D8l|9 DC� D �12% G �D� D �27$� G #,0 � Du D �#//#�# G ��, +1#,,�7 �/$%" #$%2, #,0 0�$�+$%2,42� "37$%+#��%�� /%6,#7/ %, 4#/$ #,0 /�7�+$%�� �#� 7�%61 4#0%,6 +1#,,�7/� G �������� �� �� ��������� G �27 D |} G .. D �%0{� �%�0 G u36 D l)) � D8l{9 � D �#% #,0 � D� D � %#,,#?%/ G ��2@C+2".7�& %$� ��� /3..��//%2, 42� 240" 2���$%" �C #,0 4��v3�,+�C/�7�+$%�� B#�7�%61 4#0%,6 +1#,,�7/� G ���� � ��� �� ���� �� � ������ ���� ��� �� � ���� G �2� D l))l D8l�9 � D ���03 G ������ �� � �������� G �#"-�%06� G � �@ 2�? G �}}� D
8l09 � D u 7C�1#1%� G ���B +1#,,�7C/12�$�,%,6 F7$��/ 42� E �E� ��� +1#,,�7/� G �������� �� �� ��������� G �27 D |} G .. D l�%� l�� G ��- D l)) � D8l�9 � D� D E %$�# G � �� ���� � ����� � ������� G E +� �#@C %77 G � �@ 2�? G � G l,0 �0%$%2, G%)) � D
8l}9 B D � % #,0 � D �$�$$� G �>%" �C7%" %$�0 2�$1262,#7 "37$%+#��%�� " 2037#$%2, /+1�"�/� G���� ���� �� �� ��������� G �27 D |% G ,2 D l�%�| G .. D �l�}� �l0l G �}}{ D8%)9 E D �30"3,0/2, #,0 � DC� D u,0��/2, G �u0� #+�,$ +1#,,�7 %,$��4���,+� %, #,���E /�/$�" � G ���� ���� ��� ������ ���������� ���� ���� ��G .. D } ���}ll Gu.� D �}}� D
8% �9 � D E #$1�3/ #,0 � DC� D � #""���� G ��.$%" #7 0�/%6, 24 # "37$%+#��%�� /�/$�"@ %$1 /24$ %".37/� /1#.%,6 %,+730%,6 �v3#7%�#$%2, %, $%" � 2� 4��v3�,+� 0%��+$%2,� G���� ���� ������ ������ ��������� ���� G �27 D � G .. D % �)�% �| G �}}0 D
8%l9 B D� D �2@0��" %7? #,0 4 D1#��%/ G �� �/%6, #,0 .��42�" #,+� 24 4#0%,6 %,/�,/%$%��2�$1262,#7 4��v3�,+� 0%�%/%2, "37$%. 7�& %,6 '���E) 3/%,6 .27�.1#/� F 7$��%,6$�+1,%v3�/� G ���� � ��� �� ���� �� � ������ ���� ��� �� � ���� G .. D�0|��0� G �}}0 D
8%%9 � D E3/+1#77%? G ��".�2�%,6 ���E ��+�.$%2, 3/%,6 #0#.$%�� ��v3%/$ @ %,02@ %,6� G���� ���� �� ���� �� � ��������� G �27 D |l G .. D l{}� l�} G u36 D �}}� D8%|9 u D� D �.. �,1�%" #,0 B D� D �+1#4�� G � � ������ �� � � ����� � ������� G � ��,$%+�C #77 G �,67�@220 � 7%� / G �� G �}�} D
8%{9 � D� D �#?�/ G � �������� � ����� �� ��������� G � %7��G � �@ 2�? G � G �}0| D
0�
8%�9 D �#�% G � D � #�#" G #,0 � D ��#,+7#30� G �>�#,/" %//%2, $�+1,%v3�/ 42� 0%6%$#7$����/$�%#7 >� -�2#0+#/$%,6� G ���� �� ��������� � ���� �� �G .. D �))� �)} G��- D �}}{ D
8%09 � D � #�%/ G ��������� � ������ G � %7��G � �@ 2�? G �}0} D8%�9 � D �2�,��G �E#&%"3"C7%?�7%1220 /�v3�,+� �/$%" #$%2, 24 0%6%$#7 /�v3�,+�/ %, $1�.��/�,+� 24 %,$�� /�"-27 %,$��4���,+�� G ���� ���� �� ��� �� ����� �� ���� G �27 D
�� G ,2 D % G E #� �}0l D8%}9 � D� D �+1#�4 G � ��������� � ����� � ������� �� ��������� ��� ������ ��� �� � � ��
��� �������G �27 D � G u00%/%2,C��/7��G � G �}} � D8|)9 D �123 #,0 � D� D � %#,,#?%/ G �� %, %$�C#7.1#- �$ -#/�0 +1#,,�7 �/$%" #$%2, 42����E #,0 ��7#$�0 "37$%+#��%�� /�/$�" /� G ���� ���� �� �� ��������� G�27 D |} G .. D �|)l� �| �| G u36 D l)) � D8| �9 � D E3v3�$ G E D � � �23��%77� G #,0 �D �31#" �7 G ��3-/.#+�C-#/�0 -7%,0 #,0 /�" %C-7%,0 +1#,,�7 �/$%" #$%2, 42� ���E /�/$�" /� G ���� ���� �� � ����� � ������� G�27 D {) G .. D ��}}� �0�l G �37� l))l D8|l9 D �27+/?�% G B D� D �#$1 G #,0 u D� D �#37�#� G �� 7%,0 +1#,,�7 %0�,$%F+#$%2, #,0�v3#7%�#$%2, %, ���EC-#/�0 "37$%#,$�,,# /�/$�" /� G ���� ���� �� � �����
� ������� G �27 D {) G .. D }�� �)} G �#, D l))l D8|%9 D B217%,6 G > D E#�G � D � �3,%,61#3/ G #,0 B D � �3,1�%0 G �� �2#0C-#,0 ���E�#0%2 $�#,/" %//%2, 42� "37$%" �0%# #..7%+#$%2,/� G ���������� �� �� � ���� G �27 D�0 G .. D �00�� �0�} G � +$ D �}}} D8||9 E D �2$$ G ��2".#�%/2, 24 4��v3�,+� #,0 $%" � 02"#%, 0%����,$%#7 " 2037#$%2, %,#, ���E /�/$�" 42� @ %��7�// u>E � G ���� ���� ��� ��� ��� ���������� ���� ���
�� ��G �27 D l G .. D �00���% G �}}} D8|{9 B D �+12- �� #,0 � D D � ��/$#+?�� G �u0#.$%�� ,2,+21���,$ 7%,�#� " %,%"3" ����v3#7%�#$%2, 42� E���� #,0 E�u��� /%6,#7/� G ���� ���� �� � ����� � �������� G �27 D |} G .. D l) ��� l)% � G ��.$ D l)) � D8|�9 B D �+12-�� #,0 � D D � ��/$#+?�� G ��2,+21���,$ #0#.$%�� +1#,,�7 %0�,$%F+#$%2,#762�%$1" / 42� ,2,+21���,$ /�v3�,+� �/$%" #$%2,� G ���� ���� �� �� ���������� G �27 D |} G .. D ll}�l%| G ��- D l))� D
00