• Non ci sono risultati.

POLITECNICO DI TORINO Repository ISTITUZIONALE

N/A
N/A
Protected

Academic year: 2021

Condividi "POLITECNICO DI TORINO Repository ISTITUZIONALE"

Copied!
27
0
0

Testo completo

(1)

POLITECNICO DI TORINO Repository ISTITUZIONALE

VLSI Architectures for WIMAX Channel Decoders / MARTINA M.; MASERA G. - STAMPA. - (2009), pp. 107-132.

Original

VLSI Architectures for WIMAX Channel Decoders

Publisher:

Published DOI:

Terms of use:

openAccess

Publisher copyright

(Article begins on next page)

This article is made available under terms and conditions as specified in the corresponding bibliographic description in the repository

Availability:

This version is available at: 11583/2314089 since:

Upena, Dalal, Kosta

(2)

8.5+#TEJKVGEVWTGUHQT9+/#:%JCPPGN&GEQFGTU 

:



8.5+#TEJKVGEVWTGUHQT

9+/#:%JCPPGN&GEQFGTU

 0DXUL]LR0DUWLQDDQG*XLGR0DVHUD

3ROLWHFQLFRGL7RULQR

,WDO\



+PVTQFWEVKQP



:,0$; KDV JDLQHG D ZLGH SRSXODULW\ GXH WR WKH JURZLQJ LQWHUHVW DQG GLIIXVLRQ RI

EURDGEDQG ZLUHOHVV DFFHVV V\VWHPV ,Q RUGHU WR EH IOH[LEOH DQG UHOLDEOH :,0$; DGRSWV

VHYHUDO GLIIHUHQW FKDQQHO FRGHV QDPHO\ FRQYROXWLRQDOFRGHV &&  FRQYROXWLRQDOWXUER

FRGHV &7& EORFNWXUERFRGHV %7& DQGORZGHQVLW\SDULW\FKHFN /'3& FRGHVWKDWDUH

DEOHWRFRSHZLWKGLIIHUHQWFKDQQHOFRQGLWLRQVDQGDSSOLFDWLRQQHHGV

2Q WKH RWKHU KDQG KLJK SHUIRUPDQFH GLJLWDO &026 WHFKQRORJLHV KDYH UHDFKHG VXFK D

GHYHORSPHQW WKDW YHU\ FRPSOH[ DOJRULWKPV FDQ EH LPSOHPHQWHG LQ ORZ FRVW FKLSV

0RUHRYHU HPEHGGHG SURFHVVRUV GLJLWDO VLJQDO SURFHVVRUV SURJUDPPDEOH GHYLFHV DV

)3*$VDSSOLFDWLRQVSHFLILFLQVWUXFWLRQVHWSURFHVVRUVDQG9/6,WHFKQRORJLHVKDYHFRPHWR

WKHSRLQWZKHUHWKHFRPSXWLQJSRZHUDQGWKHPHPRU\UHTXLUHGWRH[HFXWHVHYHUDOUHDOWLPH

DSSOLFDWLRQVFDQEHLQFRUSRUDWHGHYHQLQFKHDSSRUWDEOHGHYLFHV

$PRQJWKHVHYHUDODSSOLFDWLRQILHOGVWKDWKDYHEHHQVWURQJO\UHLQIRUFHGE\WKLVWHFKQRORJ\

SURJUHVVFKDQQHOGHFRGLQJLVRQHRIWKHPRVWVLJQLILFDQWDQGLQWHUHVWLQJRQHV,QIDFWLWLV

NQRZQ WKDW WKH GHVLJQ RI HIILFLHQW DUFKLWHFWXUHV WR LPSOHPHQW VXFK FKDQQHO GHFRGHUV LV D

KDUGWDVNKDUGHQHGE\WKHKLJKWKURXJKSXWUHTXLUHGE\:,0$;V\VWHPVZKLFKLVXSWR

DERXW  0EV SHU FKDQQHO ,Q SDUWLFXODU &7& DQG /'3& FRGHV ZKRVH GHFRGLQJ

DOJRULWKPVDUHLWHUDWLYHDUHVWLOODPDMRUWRSLFRILQWHUHVWLQWKHVFLHQWLILFOLWHUDWXUHDQGWKH

GHVLJQRIHIILFLHQWDUFKLWHFWXUHVLVVWLOOIRVWHULQJVHYHUDOUHVHDUFKHIIRUWVERWKLQLQGXVWU\DQG

DFDGHP\

,Q WKLV &KDSWHU WKH GHVLJQ RI 9/6, DUFKLWHFWXUHV IRU :,0$; FKDQQHO GHFRGHUV ZLOO EH

DQDO\]HGZLWKHPSKDVLVRQWKUHHPDLQDVSHFWVSHUIRUPDQFHFRPSOH[LW\DQGIOH[LELOLW\7KH

FKDSWHU ZLOO EH GLYLGHG LQWR WZR PDLQ SDUWV WKH ILUVW SDUW ZLOO GHDO ZLWK WKH LPSDFW RI

V\VWHP UHTXLUHPHQWV RQ WKH GHFRGHU GHVLJQ ZLWK HPSKDVLV RQ PHPRU\ UHTXLUHPHQWV WKH

VWUXFWXUHRIWKHNH\FRPSRQHQWVRIWKHGHFRGHUVDQGWKHQHHGIRUSDUDOOHODUFKLWHFWXUHV7R

WKDWSXUSRVHDTXDQWLWDWLYHDSSURDFKZLOOEHDGRSWHGWRGHULYHIURPV\VWHPVSHFLILFDWLRQV

NH\DUFKLWHFWXUDOFKRLFHVPRVWLPSRUWDQWDUFKLWHFWXUHVDYDLODEOHLQWKHOLWHUDWXUHZLOOEHDOVR

GHVFULEHGDQGFRPSDUHG

7KHVHFRQGSDUWZLOOFRQFHQWUDWHRQDVLJQLILFDQWFDVHRIVWXG\WKHGHVLJQRIDFRPSOHWH&7&

GHFRGHU DUFKLWHFWXUH IRU :,0$; LQFOXGLQJ DOVR KDUGZDUH XQLWV IRU GHSXQFWXULQJ ELW

GHVHOHFWLRQ DQGH[WHUQDOGHLQWHUOHDYLQJ VXEEORFNGHLQWHUOHDYHU IXQFWLRQV



(3)

9+/#:0GY&GXGNQROGPVU



(TQOU[UVGOURGEKHKECVKQPUVQCTEJKVGEVWTCNEJQKEGU

7KHV\VWHPVSHFLILFDWLRQVDQGLQSDUWLFXODUWKHUHTXLUHPHQWRIDSHDNWKURXJKSXWRIDERXW

 0EV SHU FKDQQHO LPSRVHG E\ WKH :,0$; VWDQGDUG KDYH D VLJQLILFDQW LPSDFW RQ WKH

GHFRGHUDUFKLWHFWXUH,QWKHIROORZLQJVHFWLRQVZHDQDO\]HWKHPRVWVLJQLILFDQWDUFKLWHFWXUHV

SURSRVHG LQ WKH OLWHUDWXUH WR LPSOHPHQW && GHFRGHUV 9LWHUEL GHFRGHUV  %7& &7& DQG

/'3&GHFRGHUV



8KVGTDKFGEQFGTU

7KH PRVW ZLGHO\ XVHG DOJRULWKP WR GHFRGH &&V LV WKH 9LWHUEL DOJRULWKP >9LWHUEL @

ZKLFKLVEDVHGRQILQGLQJWKHVKRUWHVWSDWKDORQJDJUDSKWKDWUHSUHVHQWVWKH&&WUHOOLV$V

DQH[DPSOHLQ)LJDELQDU\VWDWHV&&LVVKRZQDVDIHHGEDFNVKLIWUHJLVWHU D WRJHWKHU

ZLWKWKHFRUUHVSRQGLQJVWDWHGLDJUDP E DQGWUHOOLV F UHSUHVHQWDWLRQV



F











 

 

 

 

















D E

H H

F

X

F

H H

XFF













)LJ  %LQDU\ VWDWH && H[DPSOH VKLIW UHJLVWHU D  VWDWH GLDJUDP E  DQG WUHOOLV F  UHSUHVHQWDWLRQV

,QWKHJLYHQH[DPSOHWKHIHHGEDFNVKLIWUHJLVWHULPSOHPHQWDWLRQRIWKHHQFRGHUJHQHUDWHV

WZRRXWSXWELWVFDQGFIRUHDFKUHFHLYHGLQIRUPDWLRQELWXFLVWKHV\VWHPDWLFELW7KH

VWDWHGLDJUDPEDVLFDOO\LVD0HDO\ILQLWHVWDWHPDFKLQHGHVFULELQJWKHHQFRGHUEHKDYLRXULQD

WLPH LQGHSHQGHQW ZD\ HDFK QRGH FRUUHVSRQGV WR D YDOLG HQFRGHU VWDWH UHSUHVHQWHG E\

PHDQVRIWKHIOLSIORSFRQWHQWHDQGHZKLOHHGJHVDUHODEHOOHGZLWKLQSXWDQGRXWSXWELWV

7KHWUHOOLVUHSUHVHQWDWLRQDOVRSURYLGHVWLPHLQIRUPDWLRQH[SOLFLWO\VKRZLQJWKHHYROXWLRQ

IURPRQHVWDWHWRDQRWKHULQGLIIHUHQWWLPHVWHSV RQHVLQJOHVWHSLVGUDZQLQWKHSLFWXUH 

$WHDFKWUHOOLVVWHSQWKH9LWHUELDOJRULWKPDVVRFLDWHVWRHDFKWUHOOLVVWDWH6DVWDWHPHWULFƥ6Q

WKDW LV FDOFXODWHG DORQJ WKH VKRUWHVW SDWK DQG VWRUHV D GHFLVLRQ G6Q ZKLFK LGHQWLILHV WKH

HQWHULQJWUDQVLWLRQRQWKHVKRUWHVWSDWK)LUVWWKHGHFRGHUFRPSXWHVWKHEUDQFKPHWULFV DŽQ 

WKDW DUH WKH GLVWDQFHV IURP WKH PHWULFV ODEHOOLQJ HDFK HGJH RQ WKH WUHOOLV DQG WKH DFWXDO

UHFHLYHGVRIWV\PEROV,QWKHFDVHRIDELQDU\&&ZLWKUDWHWKHVRIWV\PEROVDUHnjQDQG

njQ DQG WKH EUDQFK PHWULFV DŽQ FF  VHH )LJ  D  6WDUWLQJ IURP WKHVH YDOXHV WKH VWDWH

PHWULFV DUH XSGDWHG E\ VHOHFWLQJ WKH ODUJHU PHWULF DPRQJ WKH PHWULFV UHODWHG WR HDFK

LQFRPLQJHGJHRIDWUHOOLVVWDWHDQGVWRULQJWKHFRUUHVSRQGLQJGHFLVLRQG6Q)LQDOO\GHFRGHG

ELWV DUH REWDLQHG E\ PHDQV RI D UHFXUVLYH SURFHGXUH XVXDOO\ UHIHUUHG WR DV WUDFHEDFN ,Q

RUGHU WR HVWLPDWH WKH VHTXHQFH RI ELWV WKDW ZHUH HQFRGHG IRU WUDQVPLVVLRQ D VWDWH LV ILUVW

VHOHFWHG DW WKH HQG RI WKH WUHOOLV SRUWLRQ WR EH GHFRGHG WKHQ WKH GHFRGHU LWHUDWLYHO\ JRHV

EDFNZDUG WKURXJK WKH VWDWH KLVWRU\ PHPRU\ ZKHUH GHFLVLRQV G6Q KDYH EHHQ SUHYLRXVO\

VWRUHG WKLV DOORZV RQH WRVHOHFW IRU FXUUHQW VWDWH D QHZ VWDWH ZKLFKLV OLVWHG LQ WKH VWDWH

(4)

8.5+#TEJKVGEVWTGUHQT9+/#:%JCPPGN&GEQFGTU 

KLVWRU\WUDFHDVEHLQJWKHSUHGHFHVVRUWRWKDWVWDWH'LIIHUHQWLPSOHPHQWDWLRQPHWKRGVDUH

DYDLODEOH WR PDNH WKH LQLWLDO VWDWH FKRLFH DQG WR VL]H WKH SRUWLRQ RI WUHOOLV ZKHUH WKH WUDFH

EDFN RSHUDWLRQ LV SHUIRUPHG WKHVH PHWKRGV DIIHFW ERWK GHFRGHU FRPSOH[LW\ DQG HUURU

FRUUHFWLQJ FDSDELOLW\ )RU IXUWKHU GHWDLOV RQ WKH DOJRULWKP WKH UHDGHU FDQ UHIHU WR >9LWHUEL

@ >)RUQH\ @ /RRNLQJ DW WKH JOREDO DUFKLWHFWXUH WKH PDLQ EORFNV UHTXLUHG LQ D

9LWHUELGHFRGHUDUHWKHEUDQFKPHWULFXQLW %08 GHYRWHGWRFRPSXWHDŽQWKHVWDWHPHWULF

XQLW 608 WRFDOFXODWHƥ6QDQGWKHWUDFHEDFNXQLW 7%8 WRREWDLQWKHGHFRGHGVHTXHQFH

7KH%08LVPDGHRIDGGHUVDQGVXEWUDFWHUVWRSURSHUO\FRPELQHWKHLQSXWVRIWV\PEROV VHH

)LJ D 7KH608LVEDVHGRQWKHVRFDOOHGDGGFRPSDUHVHOHFWVWUXFWXUH $&6 DVVKRZQ

LQ)LJ E 6DLGLWKHLWKVWDUWLQJVWDWHWKDWLVFRQQHFWHGWRDQDUULYLQJVWDWH6E\DQHGJH

ZKRVHEUDQFKPHWULFLVDŽLQWKHQƥ6QLVFDOFXODWHGDVLQ  



`

^

PD[ *







*

LQ

LQ Q L

6

J

  



γ (01)Q γ (10)Q γ (11)Q G6Q Γ6Q ΓM

γQíM

γQíL

ΓQíL

í í í   í  

λ2 λ1

γ (00)Q

Q Q

D E

Qí

)LJ%08DQG$&6DUFKLWHFWXUHVIRUDUDWH&& 

$VLWFDQEHLQIHUUHGIURP  ƥ6QLVREWDLQHGE\DGGLQJEUDQFKPHWULFVZLWKVWDWHPHWULFV

FRPSDULQJDQGVHOHFWLQJWKHKLJKHUPHWULFWKDWUHSUHVHQWVWKHVKRUWHVWLQFRPLQJSDWK7KH

FRUUHVSRQGLQJGHFLVLRQG6QLVVWRUHGLQDPHPRU\WKDWLVODWHUUHDGE\WKH7%8WRUHFRQVWUXFW

WKHVXUYLYHGSDWK'XHWRWKHUHFXUVLYHIRUPRI  DVORQJDVQLQFUHDVHVWKHQXPEHURIELWV

WRUHSUHVHQWƥ6QWHQGVWREHFRPHODUJHU7KLVSUREOHPFDQEHVROYHGE\QRUPDOL]LQJWKHVWDWH

PHWULFVDWHDFKVWHS+RZHYHUWKLVVROXWLRQUHTXLUHVWRDGGDQRUPDOL]DWLRQVWDJHLQFUHDVLQJ

ERWK WKH 608 FRPSOH[LW\ DQG FULWLFDO SDWK $Q HIIHFWLYH WHFKQLTXH EDVHG RQ WZR

FRPSOHPHQW UHSUHVHQWDWLRQ KHOSV OLPLWLQJ WKH JURZWK RI VWDWH PHWULFV DV GHVFULEHG LQ

>+HNVWUD@



X

F

F 

)LJ:,0$;ELQDU\VWDWH&&ZLWKUDWHVKLIWUHJLVWHUUHSUHVHQWDWLRQ

(5)

9+/#:0GY&GXGNQROGPVU



7KH :,0$; VWDQGDUG VSHFLILHV D ELQDU\  VWDWHV && ZLWK UDWH  ZKRVH VKLIW UHJLVWHU

UHSUHVHQWDWLRQ LV VKRZQ LQ )LJ  8VXDOO\ 9LWHUEL GHFRGHU DUFKLWHFWXUHV H[SORLW WKH WUHOOLV

LQWULQVLF SDUDOOHOLVP WR VLPXOWDQHRXVO\ FRPSXWH DW HDFK WUHOOLV VWHS DOO WKH EUDQFK PHWULFV

DQG XSGDWH DOO WKH VWDWH PHWULFV 7KXV VDLG Q WKH QXPEHU RI VWDWHV RI D && D SDUDOOHO

DUFKLWHFWXUHHPSOR\VD%08DQGQ$&6PRGXOHV0RUHRYHUWRUHGXFHWKHGHFRGLQJODWHQF\

WKHWUDFHEDFNLVSHUIRUPHGDVDVOLGLQJZLQGRZSURFHVV>5DGDU@RQSRUWLRQVRIWUHOOLV

RI ZLGWK : 7KLV DSSURDFK QRW RQO\ UHGXFHV WKH ODWHQF\ EXW DOVR WKH VL]H RI WKH GHFLVLRQ

PHPRU\WKDWGHSHQGLQJRQWKH7%8UDGL[UHTXLUHVXVXDOO\:RU:FHOOV>%ODFN 0HQJ

@

7RLPSURYHWKHGHFRGHUWKURXJKSXWWZR>%ODFN 0HQJ@RUPRUH>)HWWZHLV 0H\U

@ >.RQJ  3DUKL @ >&KHQJ  3DUKL @ WUHOOLV VWHSV FDQ EH SURFHVVHG

FRQFXUUHQWO\ 7KHVH VROXWLRQV OHDG WR WKH VR FDOOHG KLJKHU UDGL[ RU 0ORRNDKHDG VWHS

DUFKLWHFWXUHV$FFRUGLQJWR>.RQJ 3DUKL@WKHWKURXJKSXWVXVWDLQHGE\DQ0ORRN

DKHDGVWHSDUFKLWHFWXUHGHILQHGDVWKHQXPEHURIGHFRGHGELWVRYHUWKHGHFRGLQJWLPHLV



N 0 : I

0 1

I 1

7 N

FON

7

FON

7

| ˜ ˜



˜

˜



  

ZKHUHIFONLVWKHFORFNIUHTXHQF\17LVWKHQXPEHURIWUHOOLVVWHSVN IRUDELQDU\&&N 

IRUDGRXEOHELQDU\&&DQGWKHULJKWPRVWH[SUHVVLRQLVREWDLQHGXQGHUWKHFRQGLWLRQ:

17WKDWLVDUHDVRQDEOHDVVXPSWLRQLQUHDOFDVHV

7KXVWRDFKLHYHWKHWKURXJKSXWUHTXLUHGE\WKH:,0$;VWDQGDUGZLWKDFORFNIUHTXHQF\

OLPLWHG WR WHQV WR IHZ WKRXVDQGV RI 0+] 0  UDGL[  RU 0  UDGL[  LV D UHDVRQDEOH

FKRLFH

+RZHYHUVLQFH&&VDUHZLGHO\XVHGLQPDQ\FRPPXQLFDWLRQV\VWHPVVRPHUHFHQWZRUNV

DV>%DWFKD 6KDPHUL@DQG>.DPXIHWDO@DGGUHVVWKHGHVLJQRIIOH[LEOH9LWHUEL

GHFRGHUV WKDW DUH DEOH WR VXSSRUW GLIIHUHQW &&V $V D IXUWKHU VWHS >9RJW  :KHQ @

SURSRVHGDPXOWLFRGHGHFRGHUDUFKLWHFWXUHDEOHWRVXSSRUWERWK&&VDQG&7&V



$6%FGEQFGTU

%ORFN7XUER&RGHVRUSURGXFWFRGHVDUHVHULDOO\FRQFDWHQDWHGEORFNFRGHV*LYHQWZREORFN

FRGHV& QN DQG& QN ZKHUHQLNLDQGDžLUHSUHVHQWWKHFRGHZRUGOHQJWKWKH

QXPEHU RI LQIRUPDWLRQ ELWV DQG WKH PLQLPXP +DPPLQJ GLVWDQFH UHVSHFWLYHO\ WKH

FRUUHVSRQGLQJ SURGXFW FRGH LV REWDLQHG DFFRUGLQJ WR >3\QGLDK @ DV DQ DUUD\ ZLWK N URZVDQG N FROXPQVFRQWDLQLQJWKHLQIRUPDWLRQ ELWV7KHQ FRGLQJ LV SHUIRUPHG RQWKHN URZVZLWK&DQGRQWKHQREWDLQHGFROXPQVZLWK&7KHGHFRGLQJRI%7&FRGHVFDQEH

SHUIRUPHG LWHUDWLYHO\ URZZLVH DQG FROXPQZLVH E\ XVLQJ WKH VXERSWLPDO DOJRULWKP

GHWDLOHGLQ>3\QGLDK@7KHEDVLFLGHDUHOLHVRQXVLQJWKH&KDVHVHDUFK>&KDVH@D

QHDUPD[LPXPOLNHOLKRRG QHDU0/ VHDUFKLQJVWUDWHJ\WRILQGDOLVWRIFRGHZRUGVDQGDQ

0/ GHFLGHG FRGHZRUG G ^G« GQ` ZLWK GM^` $FFRUGLQJ WR WKH QRWDWLRQ XVHG LQ

>9DQVWUDFHHOHHWDO@GHFLVLRQUHOLDELOLWLHVDUHFRPSXWHGDV





_ _

_ _

G

M

| U  F

 M 

 U  F

 M 

O

  

(6)

8.5+#TEJKVGEVWTGUHQT9+/#:%JCPPGN&GEQFGTU 

ZKHUH U ^U«UQ` LV WKH UHFHLYHG FRGHZRUG DQG F M  DQG F M  DUH WKH FRGHZRUGV LQ WKH

&KDVHOLVWDWPLQLPXP(XFOLGHDQGLVWDQFHIURPUVXFKWKDWWKHMWKELWRIWKHFRGHZRUGLV

DQGUHVSHFWLYHO\7KHQRQHGHFRGHUVHQGVWRWKHRWKHUWKHH[WULQVLFLQIRUPDWLRQ



M RXW M

M

G U

Z O 

  

,IWKH&KDVHVHDUFKIDLOVWKHH[WULQVLFLQIRUPDWLRQLVDSSUR[LPDWHGDV



RXW M

M

G

Z E ˜

  

ZKHUHǃLVDZHLJKWIDFWRULQFUHDVLQJZLWKWKHQXPEHURILWHUDWLRQV

7KHGHFRGHUWKDWUHFHLYHVWKHH[WULQVLFLQIRUPDWLRQXVHVDQXSGDWHGYHUVLRQRIUREWDLQHGDV



LQM MROG

MQHZ

U Z

U  D ˜

  



ZKHUHD LV D ZHLJKW IDFWRU LQFUHDVLQJ ZLWK WKH QXPEHU RI LWHUDWLRQV $ VFKHPH RI WKH

HOHPHQWDU\EORFNWXUERGHFRGHULVVKRZQLQ)LJZKHUHWKHEORFNQDPHG´GHFRGHUµLVD

6RIW,Q6RIWRXW 6,62 PRGXOHWKDWSHUIRUPVWKH&KDVHVHDUFKDQGLPSOHPHQWV    DQG

 $QHIIHFWLYHVROXWLRQWRLPSOHPHQWWKH6,62PRGXOHLVEDVHGRQDWKUHHSLSHOLQHGVWDJH

DUFKLWHFWXUHZKHUHWKHWKUHHVWDJHVDUHLGHQWLILHGDVUHFHSWLRQSURFHVVLQJDQGWUDQVPLVVLRQ

XQLWV>.HURXHGDQ $GGH@$VGHWDLOHGLQ>/H%LGDQHWDO@GXULQJHDFKVWDJHWKH

1 VRIW YDOXHV RI WKH UHFHLYHG ZRUG U DUH SURFHVVHG VHTXHQWLDOO\ LQ 1 FORFN SHULRGV 7KH

UHFHSWLRQ VWDJH LV GHYRWHG WR ILQG WKH OHDVW UHOLDEOH ELWV LQ WKH UHFHLYHG FRGHZRUG 7KH

SURFHVVLQJ VWDJH SHUIRUPV WKH &KDVH VHDUFK DQG WKH WUDQVPLVVLRQ VWDJHFDOFXODWHV nj GM  ZM DQG UMQHZ $QRWKHU VROXWLRQ LV SURSRVHG LQ >*RXELHU HW DO @ ZKHUH WKH HOHPHQWDU\

GHFRGHULVLPSOHPHQWHGDVDSLSHOLQHUHVRUWLQJWRWKHPLQLPD[LDOJRULWKPQDPHO\E\XVLQJ

PLQLPD[LDUUD\VWRVWRUHWKHEHVWPHWULFVRIDOOGHFRGHGFRGHZRUGVLQWKH&KDVHOLVW



Z

M

U

MQHZ

Z

MRXW

U U

MROG

α

GHOD\

GHOD\

LQ GHFRGHU

U

MQHZ

β U

)LJ(OHPHQWDU\EORFNWXUERGHFRGHUVFKHPH 

6HYHUDOZRUNVLQWKHOLWHUDWXUHGHDOZLWK%7&FRPSOH[LW\UHGXFWLRQ$VDQH[DPSOH>$GGH  3\QGLDK@VXJJHVWVWRFRPSXWHǃLQ  RQDSHUFRGHZRUGEDVLVZKHUHDVLQ>&KLHWDO

(7)

9+/#:0GY&GXGNQROGPVU



@WKHGHSHQGHQF\RQDLQ  LVVROYHGE\UHSODFLQJWKHWHUPDÃZMZLWKWDQK ZM ,Q>/H

HWDO@ERWKDLQ  DQGǃLQ  DUHDYRLGHGE\H[SORLWLQJ(XFOLGHDQGLVWDQFHSURSHUW\

'XH WR LWV URZFROXPQ VWUXFWXUH WKH EORFN WXUER GHFRGHU FDQ EH SDUDOOHOL]HG E\

LQVWDQWLDWLQJ VHYHUDO HOHPHQWDU\ GHFRGHUV WR FRQFXUUHQWO\ SURFHVV PRUH URZV RU FROXPQV

WKXVLQFUHDVLQJWKHWKURXJKSXW$VDVLJQLILFDQWH[DPSOHLQ>-HJRHWDO@DIXOO\SDUDOOHO

%7&GHFRGHULVSURSRVHG7KLVVROXWLRQLQVWDQWLDWHVQQGHFRGHUVWKDWZRUNFRQFXUUHQWO\

0RUHRYHUE\SURSHUO\PDQDJLQJWKHVFKHGXOLQJRIWKHGHFRGHUVDQGLQWHUFRQQHFWLQJWKHP

WKURXJK DQ 2PHJD QHWZRUN LQWHUPHGLDWH UHVXOWV URZ GHFRGHG GDWD RU FROXPQ GHFRGHG

GDWD DUHQRWVWRUHG

$ GHWDLOHG DQDO\VLV RI WKURXJKSXW DQG FRPSOH[LW\ RI %7& GHFRGHU DUFKLWHFWXUHV FDQ EH

IRXQGLQ>*RXELHUHWDO@DQG>/H%LGDQHWDO@,QSDUWLFXODUDFFRUGLQJWR>*RXELHU

HWDO@DVLPSOHRQHEORFNGHFRGHUDUFKLWHFWXUHWKDWSHUIRUPVWKHURZFROXPQGHFRGLQJ

VHTXHQWLDOO\ LQWHUOHDYHGDUFKLWHFWXUH UHTXLUHV QQ F\FOHVWRFRPSOHWHDQLWHUDWLRQDVD

FRQVHTXHQFHLWDFKLHYHVDWKURXJKSXW





 



Q Q ,

I N

7 N

FON



˜

˜

˜

  

ZKHUH , LV WKH QXPEHU RI LWHUDWLRQV DQG IFON LV WKH FORFN IUHTXHQF\ 7KH %7& VSHFLILHG IRU

:,0$;LVREWDLQHGXVLQJWZLFHDELQDU\H[WHQGHG+DPPLQJFRGHRXWRIWKHRQHVVKRZLQ

7DEOH

 1 N

 

 

 

7DEOH:,0$;ELQDU\H[WHQGHG+DPPLQJFRGHV + QN XVHGIRU%7&

&RQVLGHULQJ WKH LQWHUOHDYHG DUFKLWHFWXUH GHVFULEHG LQ >*RXELHU HW DO @ ZKHUH D IXOO\

GHFRGHGEORFNLVRXWSXWHYHU\KDOILWHUDWLRQVZHREWDLQWKDW0EVFDQEHREWDLQHG

ZLWKDFORFNIUHTXHQF\RI0+]0+]DQG0+]IRU+  +  DQG+   UHVSHFWLYHO\



%6%FGEQFGTU

&RQYROXWLRQDOWXUERFRGHVZHUHSURSRVHGLQE\%HUURX*ODYLHX[DQG7KLWLPDMVKLPD

>%HUURXHWDO@DVDFRGLQJVFKHPHEDVHGRQWKHSDUDOOHOFRQFDWHQDWLRQRIWZR&&VE\

WKHPHDQVRIDQLQWHUOHDYHU Ʋ DVVKRZQLQ)LJ D 7KHGHFRGLQJDOJRULWKPLVLWHUDWLYH

DQGLVEDVHGRQWKH%&-5DOJRULWKP>%DKOHWDO@DSSOLHGRQWKHWUHOOLVUHSUHVHQWDWLRQRI

HDFKFRQVWLWXHQW&& )LJ E 7KHNH\LGHDUHOLHVRQWKHIDFWWKDWWKHH[WULQVLFLQIRUPDWLRQ

RXWSXW E\ RQH && LV XVHG DV DQ XSGDWHG YHUVLRQ RI WKH LQSXW DSULRUL LQIRUPDWLRQ E\ WKH

RWKHU && $V D FRQVHTXHQFH HDFK LWHUDWLRQ LV PDGH RI WZR KDOI LWHUDWLRQV LQ RQH KDOI

LWHUDWLRQ WKH GDWD DUH SURFHVVHG DFFRUGLQJ WR WKH LQWHUOHDYHU Ʋ  DQG LQ WKH RWKHU KDOI

LWHUDWLRQ DFFRUGLQJ WR WKH GHLQWHUOHDYHU Ʋ  7KH VDPH UHVXOW FDQ EH REWDLQHG E\

LPSOHPHQWLQJ DQ LQRUGHU UHDGZULWH KDOI LWHUDWLRQ DQG D VFUDPEOHG LQWHUOHDYHG  UHDGZULWH KDOI LWHUDWLRQ 7KH EDVLF EORFN LQ D WXUER GHFRGHU LV D 6,62 PRGXOH WKDW

(8)

8.5+#TEJKVGEVWTGUHQT9+/#:%JCPPGN&GEQFGTU 

LPSOHPHQWVWKH%&-5DOJRULWKPLQLWVORJDULWKPLFOLNHOLKRRGUDWLR //5 IRUP,IZHFRQVLGHU

D 5HFXUVLYH 6\VWHPDWLF && 56& FRGH  WKH H[WULQVLF LQIRUPDWLRQ njN X2  RI DQ XQFRGHG

V\PEROXDWWUHOOLVVWHSNRXWSXWE\D6,62LV





 `

^ PD[

`

^ PD[



a





E H E H X , F ,

2

X

N N X

X H X H X

H X

N H

O S

O   

  

ZKHUH Ɔ LV DQ XQFRGHG V\PERO WDNHQ DV D UHIHUHQFH XVXDOO\ Ɔ   H UHSUHVHQWV D FHUWDLQ

WUDQVLWLRQRQWKHWUHOOLVDQGX H LVWKHXQFRGHGV\PEROXDVVRFLDWHGWRH7KHPD[ IXQFWLRQLV

XVXDOO\LPSOHPHQWHGDVDPD[IROORZHGE\DFRUUHFWLRQWHUP>5REHUWVRQHWDO@>*URVV

 *XODN @ >&KHQJ  2WWRVVRQ @ >&ODVVRQ HW DO @ >:DQJ HW DO @

>7DODNRXEHWDO@$VFDOLQJIDFWRUFDQDOVREHDSSOLHGWRIXUWKHULPSURYHWKHPD[RU

PD[  DSSUR[LPDWLRQ >9RJW  )LQJHU @ 7KH FRUUHFWLRQ WHUP XVXDOO\ DGRSWHG ZKHQ

GHFRGLQJ ELQDU\ FRGHV FDQ EH RPLWWHG IRU GRXEOH ELQDU\ WXUER FRGHV >%HUURX HW DO @

ZLWKPLQRUHUURUUDWHSHUIRUPDQFHGHJUDGDWLRQ7KHWHUPE H LQ  LVGHILQHGDV



@

>

@

>

@

>

H



V H H V H

E D

N 6

 J

N

 E

N (   

@`

>

@

>

^ PD[

@

>





V H H

V

N 6 N

V H V

N H (

D J

D





  

@`

>

@

>

^ PD[

@

>





V H H

V

N ( N

V H V

N H 6

E J

E





  

@ 

>

@ 

>

@

> H

N

X H ,

N

F H ,

N

S S

J 

  



ZKHUHV6 H DQGV( H DUHWKHVWDUWLQJDQGWKHHQGLQJVWDWHVRIHDN>V6 H @DQGǃN>V( H @DUHWKH

IRUZDUGDQGEDFNZDUGVWDWHPHWULFVDVVRFLDWHGWRV6 H DQGV( H UHVSHFWLYHO\ VHH)LJ E  DQGDŽN>H@LVWKHEUDQFKPHWULFDVVRFLDWHGWRH7KHǑN>F H ,@WHUPLVFRPSXWHGDVDZHLJKWHG

VXPRIWKHnjN>F,@SURGXFHGE\WKHVRIWGHPRGXODWRUDV



¦

QLF L N L

N

> F H  , @ F H O > F H  , @

S

  

ZKHUHFL H LVRQHRIWKHFRGHGELWVDVVRFLDWHGWRH DQG QFLVWKHQXPEHURIELWV IRUPLQJD

FRGHGV\PEROFDQGǑN>FX H ,@LQ  LVREWDLQHGDVǑN>F H ,@FRQVLGHULQJRQO\WKHV\VWHPDWLF

ELWVFRUUHVSRQGLQJWRWKHXQFRGHGV\PEROXRXWRIWKHQFFRGHGELWV7KHǑN>X H ,@WHUPLV

REWDLQHGFRPELQLQJWKHLQSXWDSULRULLQIRUPDWLRQnjN X, DQGIRUDGRXEOHELQDU\FRGHFDQ

EHZULWWHQDVLQ  ZKHUH$DQG%UHSUHVHQWWKHWZRELWVIRUPLQJDQXQFRGHGV\PEROX

7KH&7&VSHFLILHGLQWKH:,0$;VWDQGDUGLVEDVHGRQDGRXEOHELQDU\VWDWHFRQVWLWXHQW

&&DVVKRZQLQ)LJZKHUHHDFK&&UHFHLYHVWZRXQFRGHGELWV $% DQGSURGXFHVIRXU

FRGHGELWVWZRV\VWHPDWLFELWV $% DQGWZRSDULW\ELWV <: $VDFRQVHTXHQFHDWHDFK

WUHOOLVVWHSIRXUWUDQVLWLRQVFRQQHFWDVWDUWLQJVWDWHWRIRXUSRVVLEOHHQGLQJVWDWHV'XHWRWKH

WUHOOLVV\PPHWU\RQO\EUDQFKPHWULFVRXWRIWKHSRVVLEOHEUDQFKPHWULFVDUHUHTXLUHGDW

HDFKWUHOOLVVWHS$VSRLQWHGRXWLQ>0XOOHUHWDO@KLJKWKURXJKSXWFDQEHDFKLHYHGE\

(9)

9+/#:0GY&GXGNQROGPVU



H[SORLWLQJ WKH WUHOOLV SDUDOOHOLVP QDPHO\ FRPSXWLQJ FRQFXUUHQWO\ DOO WKH EUDQFK DQG VWDWH

PHWULFV



° °

¯

°° ®

­





























%

$ H X LI

%

$ H X LI

%

$ H X LI

%

$ H X LI ,

X

N$%

%

$N

%

$N N

O O

S O

  



α N α

β β

Ní N

Ní N

H X H F H V H

V H

6

(

X &&

&&

F F

F

X

X

D E

λ>X2@ λ>X,@

>X,@ í

λ

>F,@

λ

λ>X2@

λ>F,@

6,62 6,62

Π

Π Π

)LJ&RQYROXWLRQDOWXUERFRGHFRGHUDQGLWHUDWLYH6,62EDVHGGHFRGHU D QRWDWLRQIRUD WUHOOLVVWHSLQWKH6,62 E 

7KHEUDQFKPHWULFVDUHFRPSXWHGE\D%08WKDWLPSOHPHQWV  DVVKRZQLQ)LJ7R

UHGXFHWKHODWHQF\RIWKH6,62XVXDOO\WKHGHFRGLQJLVEDVHGRQDVOLGLQJZLQGRZDSSURDFK

>%HQHGHWWRHWDO@$VDFRQVHTXHQFHDWOHDVWWZR%08VDUHUHTXLUHGWRFRPSXWHWKH

WZRUHFXUVLRQV IRUZDUGDQGEDFNZDUG DFFRUGLQJWRWKH%&-5DOJRULWKP+RZHYHUVLQFHǃ

PHWULFV UHTXLUH WR EH WUDLQHG EHWZHHQ VXFFHVVLYH ZLQGRZV XVXDOO\ D IXUWKHU %08 LV

UHTXLUHG $ VROXWLRQ EDVHG RQ WKH LQKHULWDQFH RI WKH ERUGHU PHWULFV RI HDFK ZLQGRZ

>$EEDVIDU <DR@UHTXLUHVRQO\WZR%08V)XUWKHUPRUHWKLVVWUDWHJ\UHGXFHVWKH6,62

ODWHQF\WRWKHVOLGLQJZLQGRZZLGWK:7KHVWDWHPHWULFVDUHXSGDWHGDFFRUGLQJWR  DQG

 E\WZRVWDWHPHWULFSURFHVVRUVHDFKRIZKLFKLVPDGHRIDSURSHUQXPEHURISURFHVVLQJ

HOHPHQWV 3(  $V VKRZQ LQ )LJ  IRU WKH :,0$; &7&  3(V DUH UHTXLUHG ,W LV ZRUWK

SRLQWLQJ RXW WKDW WKH FRQVWLWXHQW FRGHV RI WKH :,0$; &7& XVH WKH FLUFXODWLRQ VWDWH

WDLOELWLQJVWUDWHJ\SURSRVHGLQ>:HLVVHWDO@WKDWHQVXUHVWKDWWKHHQGLQJVWDWHRIWKH

ODVWWUHOOLVVWHSLVHTXDOWRWKHVWDUWLQJVWDWHRIWKHILVWWUHOOLVVWHS+RZHYHUWKLVWHFKQLTXH

UHTXLUHV HVWLPDWLQJ WKH FLUFXODWLRQ VWDWH DW WKH GHFRGHU VLGH 6LQFH WUDLQLQJ RSHUDWLRQV WR

HVWLPDWHWKHFLUFXODWLRQVWDWHZRXOGLQFUHDVHWKH6,62ODWHQF\DQHIIHFWLYHDOWHUQDWLYH>=KDQ

HWDO@LVWRLQKHULWWKHVHPHWULFVIURPWKHSUHYLRXVLWHUDWLRQ



(10)

8.5+#TEJKVGEVWTGUHQT9+/#:%JCPPGN&GEQFGTU 

&RGH &&

&RGH &&



&RQVWLWXHQW



&&

L <:

$

%

L L

L L

:





$

%

$

%

<



:

 LQWHUOHDYHU&7&

<

(Π)

&RQVWLWXHQW

)LJ:,0$;&7&HQFRGHUDQGFRQVWLWXHQW&&VWUXFWXUHV 

$VLQ9LWHUELGHFRGHUDUFKLWHFWXUHVRIWHQLQ&7&GHFRGHUVWKHVWDWHPHWULFVDUHFRPSXWHGE\

PHDQV RI WKH ´ZUDSSLQJµ UHSUHVHQWDWLRQ WHFKQLTXH SURSRVHG LQ >+HNVWUD @ 7KLV

VROXWLRQ UHTXLUHV D QRUPDOL]DWLRQ VWDJH GHSLFWHG LQ )LJ  ZKHQ FRPELQLQJD ǃ DQG DŽ

PHWULFVWRFRPSXWHWKHH[WULQVLFLQIRUPDWLRQDVLQ  7KHODVWVWDJHRIWKHRXWSXWSURFHVVRU

WKDWFRPSXWHVWKHRXWSXWH[WULQVLFLQIRUPDWLRQLVDWUHHRIPD[EORFNVIRUHDFKFRPSRQHQW

RIWKHH[WULQVLFLQIRUPDWLRQDQGIHZDGGHUVWRLPSOHPHQW  $VKLJKOLJKWHGLQ)LJWKLV

VFKHGXOLQJ UHTXLUHV D EXIIHU WR VWRUH LQSXW //5V WKDW DUH XVHG WR FRPSXWH WKH EDFNZDUG

UHFXUVLRQ %080(0  6LQFH WKH RXWSXW H[WULQVLF LQIRUPDWLRQ LV FRPSXWHG GXULQJ WKH

EDFNZDUG UHFXUVLRQ IRUZDUG UHFXUVLRQ PHWULFV DUH VWRUHG LQ D EXIIHU D0(0  )XUWKHU

PHPRU\LVUHTXLUHGWRLPSOHPHQWWKHERUGHUPHWULFLQKHULWDQFHD(;70(0ǃ(;70(0

DQGǃ/2&0(0

7KHWKURXJKSXWVXVWDLQHGE\WKH&7&GHFRGHUGHILQHGDVWKHQXPEHURIGHFRGHGELWVRYHU

WKHWLPHUHTXLUHGIRUWKHLUFRPSXWDWLRQLV



F\FGHF FON 7 F\F,'

F\F6,62 FON 7

1 ,

I 1 N 1

1 ,

I 1 7 N

˜

˜

˜



˜

˜

˜





  

ZKHUHIFONLVWKHFORFNIUHTXHQF\17LVWKHQXPEHURIWUHOOLVVWHSVN IRUDELQDU\&7&N 

IRUDGRXEOHELQDU\&7&,LVWKHQXPEHURIKDOILWHUDWLRQV1F\F6,62DQG1F\F,'UHSUHVHQWWKH

QXPEHU RI FORFN F\FOHV UHTXLUHG E\ RQH 6,62 DQG E\ WKH LQWHUOHDYLQJGHLQWHUOHDYLQJ

VWUXFWXUH 6LQFH ERWK 1F\F6,62 DQG 1F\F,' DUH D IXQFWLRQ RI 17 WKH\ FDQ EH UHZULWWHQ DV

1F\F6,62 17Ã636,62F\FODWDQG1F\F,' 17Ã63,'F\FRKZKHUH63LVWKHVHQGLQJSHULRGQDPHO\

WKHUDWHVXVWDLQHGE\WKHGHFRGHUWRRXWSXWWZRFRQVHFXWLYHYDOLGRXWSXWGDWD 63 PHDQV

DW HDFK FORFN F\FOH QHZ YDOLG RXWSXW GDWD DUH UHDG\  6,62F\FODW LV WKH GHFRGHU ODWHQF\

QDPHO\WKHQXPEHURIFORFNF\FOHVVSHQWWRSURGXFHWKHILUVWYDOLGRXWSXWGDWDDQG,'F\FRKLV

WKH LQWHUOHDYHUGHLQWHUOHDYHU DUFKLWHFWXUH RYHUKHDG H[SUHVVHG LQ FORFN F\FOHV 8VXDOO\

UHVRUWLQJWRSLSHOLQLQJ1F\F6,62DQG1F\F,'FDQEHSDUWLDOO\RYHUODSSHGWKXVWKHQXPEHURI

F\FOHV UHTXLUHG E\ RQH 6,62 GHFRGHU LV 1F\FGHF 17Ã636,62F\FODW,'F\FRK 8VLQJ WKH VOLGLQJ

ZLQGRZWHFKQLTXHZLWKWKHERUGHUPHWULFLQKHULWDQFHVWUDWHJ\>$EEDVIDU <DR@>=KDQ

HW DO @ ZH REWDLQ 6,62F\FODW§63Ã: DQG VR   FDQ EH UHZULWWHQ DV   ZKHUH WKH

ULJKWPRVWH[SUHVVLRQLVREWDLQHGFRQVLGHULQJ:17DQG,'F\FRK63Ã17WKDWLVDUHDVRQDEOH

DVVXPSWLRQLQUHDOFDVHV

(11)

9+/#:0GY&GXGNQROGPVU



63 ,

I N ,'

: 1 63 ,

I 1

7 N

RK FON

F\F 7

FON 7

˜

| ˜





˜

˜

˜

˜



@

>



  



γN

βNí

αN

α/βN α/βN

βNí

αN

γN

β γN

α Ní

γN

N

α/βN α/βN

λ%N>F,@ λ:N>F,@

λ >X,@$%N λ >X,@$%N

λ<N>F,@

λ >X,@$%

   







γ γ γ γN N N Nγ γ γ γ γ γ γ γN N N N N N N Nγ γ γ γ   N N N N

>H@

 L

>H@

 L

>H@

 L

PD[

PD[



>V@L  >V@L  >V@L  >V@L

>V@L

>V@L

>H@

 L

3(

α í%08 γN SURFHVVRUα αLQ

αNí

αN

í%08 β SURFHVVRUβ

γN

βN

β í/2&í0(0 βLQ

βNí βSUY β í(;7í0(0

βRXW í2

λ

λN>X2@

XN SURFHVVRU í0(0

α í(;7í0(0 α

αRXW

αNí

βN γN

λ$%N>X2@

λ$%N>X2@

λ$%N>X2@

XN

λ$%N>X,@

λ$%N>X,@

λ$%N>X,@

í2 λ SURFHVVRU

>@

>@ >@ >@

λ$N>F,@

3(

(α/β,γ)N (α/β,γ)N

SURFHVVRU α/β



%08 N

PD[

λN>X,@

λN>F,@ %08í0(0 6,62

QRUPQRUP 

PD[





λN>7@

3(

PD[WUHH PD[WUHH PD[WUHH PD[WUHH

)LJ:,0$;6,62EORFNVFKHPH 

8VXDOO\RSWLPL]HGDUFKLWHFWXUHV>0DVHUDHWDO@>%LFNHUVWDIIHWDO@>.LP 3DUN

@DUHREWDLQHGZLWK63 ZKHUHDVIOH[LEOHDUFKLWHFWXUHVKDYHKLJKHU63YDOXHV>9RJW  :HKQ@>0XOOHUHWDO@+RZHYHUHYHQZLWK63 DGRXEOHELQDU\WXUERGHFRGHU

DUFKLWHFWXUH WKDW DFKLHYHV WKH WKURXJKSXW LPSRVHG E\ :,0$; ZLWK HLJKW LWHUDWLRQV ,  

ZRXOGUHTXLUHIFON 0+]$SRVVLEOHVROXWLRQWRLPSURYHWKHWKURXJKSXWE\DIDFWRUWKDW

UDQJHV LQ > @ LV WKH EDVHG RQ GHFRGHU OHYHO SDUDOOHOLVP >0XOOHU HW DO @ DQG LV

XVXDOO\UHIHUUHGWRDV´VKXIIOLQJµ>=KDQJ )RVVRULHU@+RZHYHUWRIXUWKHULPSURYH

WKHWKURXJKSXWDSDUDOOHOGHFRGHUPDGHRI36,62VZRUNLQJFRQFXUUHQWO\LVUHTXLUHG$VD

FRQVHTXHQFHDSDUDOOHODUFKLWHFWXUHDFKLHYHVDWKURXJKSXW



63 ,

I 3 N ,'

3 : 63 1

,

I 1

7 N

FON

F\FRK 7

FON 7

˜

˜

| ˜





˜

˜

˜

˜

@ 

>



  

7KXVVHWWLQJ3 , DQG63 WKH:,0$;WKURXJKSXWLVREWDLQHGZLWKI FON 0+],WLV

ZRUWK SRLQWLQJ RXW WKDW D 3SDUDOOHO &7& GHFRGHU LV PDGH RI 3 6,62V FRQQHFWHG WR 3

PHPRULHVGHYRWHGWRVWRUHWKHH[WULQVLFLQIRUPDWLRQ+RZHYHULQDSDUDOOHOGHFRGHUGXULQJ

WKHVFUDPEOHGKDOILWHUDWLRQFROOLVLRQVFDQRFFXUQDPHO\PRUH6,62VFRXOGQHHGWRDFFHVV

(12)

8.5+#TEJKVGEVWTGUHQT9+/#:%JCPPGN&GEQFGTU 

WKHVDPHPHPRU\GXULQJWKHVDPHF\FOH6LQFHWKHFROOLVLRQSKHQRPHQRQLQFUHDVHV,'F\FRK

VHYHUDO DOJRULWKPLF DSSURDFKHV WR GHVLJQ FROOLVLRQ IUHH LQWHUOHDYHUV >*LXOLHWWL HW DO @

>.ZDN /HH@>*QDHGLJHWDO@>7DUDEOHHWDO@KDYHEHHQSURSRVHG2QWKH

RWKHU KDQG DUFKLWHFWXUHV WR PDQDJH FROOLVLRQV LQ D SDUDOOHO WXUER GHFRGHU KDYH DOVR EHHQ

SURSRVHGLQWKHOLWHUDWXUH>7KXOHWDO@>*LOEHUWHWDO@>7KXOHWDO@>6SH]LDOL

 =RU\@>0DUWLQDHWDOD@>0DUWLQD HW DOE@LQSDUWLFXODU>0DUWLQDHWDO

E@GHDOVZLWKWKHSDUDOOHOL]DWLRQRIWKH:,0$;&7&LQWHUOHDYHUDQGDYRLGVFROOLVLRQE\

WKHPHDQVRIDWKURXJKSXWSDUDOOHOLVPVFDODEOHDUFKLWHFWXUHWKDWIHDWXUHV,'F\FRK 

,WLVZRUWKSRLQWLQJRXWWKDWSDUDOOHODUFKLWHFWXUHVLQFUHDVHQRWRQO\WKHWKURXJKSXWEXWDOVR

WKH FRPSOH[LW\ RI WKH GHFRGHU VR WKDW VRPH UHFHQW ZRUNV DLP DW UHGXFLQJ WKH DPRXQW RI

PHPRU\ UHTXLUHG WR LPSOHPHQW 6,62 ORFDO EXIIHUV ,Q >/LX HW DO @ DQG >.LP  3DUN

@VDWXUDWLRQRIIRUZDUGVWDWHPHWULFVDQGTXDQWL]DWLRQRIERUGHUEDFNZDUGVWDWHPHWULFV

LV SURSRVHG )XUWKHU VWXGLHV KDYH EHHQ SHUIRUPHG WR UHGXFH WKH H[WULQVLF LQIRUPDWLRQ ELW

ZLGWK E\ XVLQJ DGDSWLYH TXDQWL]DWLRQ >6LQJK HW DO @ SVHXGRIORDWLQJ SRLQW

UHSUHVHQWDWLRQ>3DUNHWDO@DQGELWOHYHOUHSUHVHQWDWLRQ>.LP 3DUN@



.&2%EQFGFGEQFGTU

/'3& FRGHV ZHUH RULJLQDOO\ LQWURGXFHG LQ  E\ *DOODJHU >*DOODJHU @ DQG

UHGLVFRYHUHG LQ  E\ 0DF.D\ DQG 1HDO >0DF.D\ @ $V WXUER FRGHV WKH\ DFKLHYH

QHDURSWLPXPHUURUFRUUHFWLRQSHUIRUPDQFHDQGDUHGHFRGHGE\PHDQVRIKLJKFRPSOH[LW\

LWHUDWLYHDOJRULWKPV

$Q/'3&FRGHLVDOLQHDUEORFNFRGHGHILQHGE\D&u%SDULW\FKHFNPDWUL[+FKDUDFWHUL]HG

E\DORZGHQVLW\RIRQHV%LVWKHQXPEHURIELWVLQWKHFRGH EORFNOHQJWK ZKLOH&LVWKH

QXPEHU RI SDULW\ FKHFNV $ RQH LQ D JLYHQ FHOO RI WKH + PDWUL[ LQGLFDWHV WKDW WKH ELW

FRUUHVSRQGLQJWRWKHFHOOFROXPQLVXVHGIRUWKHFDOFXODWLRQRIWKHSDULW\FKHFNDVVRFLDWHGWR

WKHURZ$SRSXODUGHVFULSWLRQRIDQ/'3&FRGHLVWKHELSDUWLWH RU7DQQHU JUDSKVKRZQLQ

)LJXUHIRUDVPDOOH[DPSOHZKHUH%YDULDEOHQRGHV 91 DUHFRQQHFWHGWR&FKHFNQRGHV

&1 WKURXJKHGJHVFRUUHVSRQGLQJWRWKHSRVLWLRQVRIWKHRQHVLQ+

/'3& FRGHV DUH XVXDOO\ GHFRGHG E\ PHDQV RI DQ LWHUDWLYH DOJRULWKP YDULRXVO\ NQRZQ DV

VXPSURGXFW EHOLHI SURSDJDWLRQ RU PHVVDJH SDVVLQJ DQG UHIRUPXODWHG LQ D YHUVLRQ WKDW

SURFHVVHV ORJDULWKPLF OLNHOLKRRG UDWLRV LQVWHDG RI SUREDELOLWLHV ,Q WKH ILUVW LWHUDWLRQ KDOI

YDULDEOHQRGHVUHFHLYHGDWDIURPDGMDFHQWFKHFNQRGHVDQGIURPWKHFKDQQHODQGXVHWKHP

WRREWDLQXSGDWHGLQIRUPDWLRQVHQWWRWKHFKHFNQRGHVLQWKHVHFRQGKDOIFKHFNQRGHVWDNH

WKHXSGDWHGLQIRUPDWLRQUHFHLYHGIURPFRQQHFWHGELWQRGHVDQGJHQHUDWHQHZPHVVDJHVWR

EHVHQWEDFNWRYDULDEOHQRGHV

,QPHVVDJHSDVVLQJGHFRGHUVPHVVDJHVDUHH[FKDQJHGDORQJWKHHGJHVRIWKH7DQQHUJUDSK

DQGFRPSXWDWLRQVDUHSHUIRUPHGDWWKHQRGHV7RDYRLGPXOWLSOLFDWLRQVDQGGLYLVLRQVWKH

GHFRGHUXVXDOO\ZRUNVLQWKHORJDULWKPLFGRPDLQ

 

(13)

9+/#:0GY&GXGNQROGPVU



&







 



% % %

& &

)LJ([DPSOH7DQQHUJUDSK 

7KHPHVVDJHSDVVLQJDOJRULWKPLVGHVFULEHGLQWKHIROORZLQJHTXDWLRQVZKHUHNUHSUHVHQWV

WKHFXUUHQWLWHUDWLRQ4MLLVWKHPHVVDJHJHQHUDWHGE\91MDQGGLUHFWHGWR&1L5LMLVWKH

PHVVDJHFRPSXWHGE\&1LDQGVHQWWR91M&>M@LVWKHZKROHVHWRILQFRPLQJPHVVDJHVIRU

91MDQG5>L@LVWKHZKROHVHWRIWKHLQFRPLQJPHVVDJHVIRU&1L

(DFK YDULDEOH QRGH LV LQLWLDOL]HG ZLWK WKH ORJOLNHOLKRRG UDWLR //5 OM DVVRFLDWHG WR WKH

UHFHLYHG ELW 1H[W PHVVDJHV DUH SURSDJDWHG IURP WKH YDULDEOH QRGHV WR WKH FKHFN QRGHV

DORQJ WKH HGJHV RI WKH 7DQQHU JUDSK $W WKH ILUVW LWHUDWLRQ RQO\OM DUH GHOLYHUHG ZKLOH

VWDUWLQJIURPWKHVHFRQGLWHUDWLRQ91VVXPXSDOOWKHPHVVDJHV5LMFRPLQJIURP&1VDQG

FRPELQHWKHPZLWKOMDFFRUGLQJWR



> @



¦



 L M

&

NM N M

ML

5

4





D D

O

  

7KHFKHFNQRGHFRPSXWHVQHZFKHFNWRYDULDEOHPHVVDJHVDV



> @

> @L M LM 5

NL

LMN

4

5 G

E E

» ˜

¼

« º

¬ ª <

< ¦







 ZLWK



> @

–

M ML

L 5

LM

 VJQ 4

G

  

ZKHUH_5>M@_LVWKHFDUGLQDOLW\RIWKH&1DQG< [ LVDQRQOLQHDUIXQFWLRQGHILQHGDV



> @  ¨¨© § ¸¸¹ ·

< [ OQ WDQK  [

  

$IWHUDQXPEHURILWHUDWLRQVWKDWVWURQJO\GHSHQGVRQWKHDGGUHVVHGDSSOLFDWLRQDQGFRGH

UDWH W\SLFDOO\WR YDULDEOHQRGHVFRPSXWHDQRYHUDOOHVWLPDWLRQRIWKHGHFRGHGELWLQ

WKHIRUP



> @

¦







/

M

&

NM N M

M

5

D D

O

  



ZKHUHWKHVLJQRI/MFDQEHXQGHUVWRRGDVWKHKDUGGHFLVLRQRQWKHGHFRGHGELW

(14)

8.5+#TEJKVGEVWTGUHQT9+/#:%JCPPGN&GEQFGTU 

$ ODUJH LPSOHPHQWDWLRQ FRPSOH[LW\ LV DVVRFLDWHG WR   ZKLFK LV VLPSOLILHG LQ GLIIHUHQW

ZD\V)LUVWRIDOOIXQFWLRQ< [ FDQEHREWDLQHGE\PHDQVRIUHGXFHGFRPSOH[LW\HVWLPDWLRQV

>0DVHUD HW DO @ 0RUHRYHU VXERSWLPDO ORZ FRPSOH[LW\ DOJRULWKPV KDYH EHHQ

VXFFHVVIXOO\ SURSRVHG WR VLPSOLI\   VXFK DV IRU H[DPSOH WKH QRUPDOL]HG 0LQ6XP

DOJRULWKP>&KHQHWDO@ZKHUHRQO\WKHWZRVPDOOHVWPDJQLWXGHVDUHXVHG

$IXUWKHUFKDQJHLVXVXDOO\DSSOLHGWRWKHVFKHGXOLQJRIYDULDEOHDQGFKHFNQRGHVLQRUGHUWR

LPSURYH FRPPXQLFDWLRQV SHUIRUPDQFH ,Q WKH WZRSKDVH VFKHGXOLQJ WKH XSGDWLQJ RI

YDULDEOHDQGFKHFNQRGHVLVDFFRPSOLVKHGLQWZRVHSDUDWHSKDVHV2QWKHFRQWUDU\WKHWXUER

GHFRGLQJPHVVDJHSDVVLQJ 7'03 >0DQVRXU 6KDQEKDJ@DOVRNQRZQDVOD\HUHGRU

VKXIIOHG GHFRGLQJ DOORZV IRU RYHUODSSHG XSGDWH RSHUDWLRQV PHVVDJHV FDOFXODWHG E\ D

VXEVHWRIFKHFNQRGHVDUHLPPHGLDWHO\XVHGWRXSGDWHYDULDEOHQRGHV7KLVVFKHGXOLQJKDV

EHHQ SURYHG WR EH DEOH WR UHGXFH WKH QXPEHU RI LWHUDWLRQV E\ XS WR  DW D IL[HG

FRPPXQLFDWLRQVSHUIRUPDQFH

7KHUHTXLUHGQXPEHURIIXQFWLRQDOXQLWVLQDGHFRGHUFDQEHHVWLPDWHGEDVHGRQWKHFRQFHSW

RISURFHVVLQJSRZHU3F>*RXLOORGHWDO@ZKLFKFDQEHHYDOXDWHGRQWKHEDVLVRIWKHUDWH

5FRIWKHFRGHWKHQXPEHU.RILQIRUPDWLRQELWVWUDQVPLWWHGSHUFRGHZRUGWKHEORFNVL]H

1 .5F WKH UHTXLUHG LQIRUPDWLRQ WKURXJKSXW ' WKH RSHUDWLQJ FORFN IUHTXHQF\ IFON WKH

PD[LPXP QXPEHU RI LWHUDWLRQV L0$; DQG WKH WRWDO QXPEHU RI HGJHV WR EH SURFHVVHG SHU

LWHUDWLRQH7KLVUHODWLRQLVH[SUHVVHGDV



FON

F

. I

0$;

L 3 '

˜

˜

H ˜



 

$VWZRPHVVDJHVDUHDVVRFLDWHGZLWKHDFKHGJH WREHVHQWIURPWKH&1WRWKH91DQGYLFH

YHUVD  3F JLYHV WKH QXPEHU RI PHVVDJHV WKDW PXVW EH FRQFXUUHQWO\ SURFHVVHG DW HDFK

GHFRGLQJ LWHUDWLRQ LQ RUGHU WR DFKLHYH WKH WDUJHW WKURXJKSXW ' (TXDWLRQ   GRHV QRW

FRQVLGHU WKH PHVVDJH H[FKDQJH RYHUKHDG \HW LW DVVXPHV WKDW DOO PHVVDJHV GLVSDWFKHG

GXULQJDF\FOHDUHGHOLYHUHGVLPXOWDQHRXVO\GXULQJWKHVDPHF\FOH7KH3FYDOXHPXVWWKHQ

EHDVVXPHGDVDORZHUERXQGDQGWKHDFWXDOGHJUHHRISDUDOOHOLVPVWURQJO\GHSHQGVRQERWK

WKHVWUXFWXUHRIWKH+PDWUL[>'LQRLHWDO@DQGWKHDGRSWHGLQWHUFRQQHFWDUFKLWHFWXUH

DPRQJSURFHVVLQJXQLWV>4XDJOLRHWDO@>0DVHUDHWDO@

$FWXDOO\PRVWRIWKHLPSOHPHQWDWLRQFRQFHUQVFRPHIURPWKHFRPPXQLFDWLRQVWUXFWXUHWKDW

PXVW EH DOORFDWHG WR VXSSRUW PHVVDJH SDVVLQJ IURP ELW WR FKHFN QRGHV DQG YLFH YHUVD

6HYHUDOKDUGZDUHUHDOL]DWLRQVWKDWKDYHEHHQSURSRVHGLQWKHOLWHUDWXUHDUHIRFXVHGRQKRZ

HIILFLHQWO\SDVVLQJPHVVDJHVEHWZHHQWKHWZRW\SHVRISURFHVVLQJXQLWV

7KUHHDSSURDFKHVFDQEHIROORZHGLQWKHKLJKOHYHORUJDQL]DWLRQRIWKHGHFRGHUFRPLQJWR

WKUHHNLQGVRIDUFKLWHFWXUHV

 6HULDO DUFKLWHFWXUHV ELW DQG FKHFN SURFHVVRUV DUH DOORFDWHG DV VLQJOH LQVWDQFHV HDFK

VHUYLQJPXOWLSOHQRGHVVHTXHQWLDOO\PHVVDJHVDUHH[FKDQJHGE\PHDQVRIDPHPRU\

 )XOO\SDUDOOHODUFKLWHFWXUHVSURFHVVLQJXQLWVDUHDOORFDWHGIRUHDFKVLQJOHELWDQGFKHFN

QRGHDQGDOOPHVVDJHVDUHSDVVHGLQSDUDOOHORQGHGLFDWHGURXWHV

 3DUWLDOO\ SDUDOOHO DUFKLWHFWXUHV PRUH SURFHVVLQJ XQLWV ZRUN LQ SDUDOOHO VHUYLQJ DOO ELW

DQG FKHFN QRGHV ZLWKLQ D QXPEHU RI F\FOHV VXLWDEOH RUJDQL]DWLRQ DQG KDUGZDUH

VXSSRUWLVUHTXLUHGWRH[FKDQJHPHVVDJHV

(15)

9+/#:0GY&GXGNQROGPVU



)RUPRVWFRGHVDQGDSSOLFDWLRQVWKHILUVWDSSURDFKUHVXOWVLQVORZLPSOHPHQWDWLRQVZKLOH

WKHVHFRQGRQHKDVDQH[FHVVLYHFRVW$VDUHVXOWWKHRQO\JHQHUDOYLDEOHVROXWLRQLVWKHWKLUG

SDUWLDOO\ SDUDOOHO DSSURDFK ZKLFK RQ WKH RWKHU KDQG LQWURGXFHV WKH FROOLVLRQ SUREOHP

DOUHDG\ NQRZQ LQ WKH LPSOHPHQWDWLRQ RI SDUDOOHO WXUER GHFRGHUV 7ZR PDLQ DSSURDFKHV

KDYHEHHQSURSRVHGWRGHDOZLWKFROOLVLRQV

 7RGHVLJQFROOLVLRQIUHHFRGHV>0DQVRXU 6KDQEKDJ@>+RFHYDU@

 7RGHVLJQGHFRGHUDUFKLWHFWXUHDEOHWRDYRLGRUDWOHDVWPLWLJDWHFROOLVLRQHIIHFWV>.LHQOH

HWDO@>7DUDEOHHWDO@

(YHQ LI WKH ILUVW DSSURDFK KDV SURYHQ WR EH HIIHFWLYH LW VLJQLILFDQWO\ OLPLWV WKH VXSSRUWHG

FRGHFODVVHV7KHVHFRQGDSSURDFKRQWKHRWKHUKDQGLVZHOOVXLWHGIRUIOH[LEOHDQGJHQHUDO

DUFKLWHFWXUHV $Q HYHQ PRUH FKDOOHQJLQJ WDVN LV WKH GHVLJQ RI /'3& GHFRGHUV WKDW DUH

IOH[LEOHLQWHUPVRIVXSSRUWHGEORFNVL]HVDQGFRGHUDWHV>0DVHUDHWDO@

,Q SDUWLDOO\ SDUDOOHO VWUXFWXUHV SHUPXWDWLRQ QHWZRUNV DUH XVHG WR HVWDEOLVK WKH FRUUHFW

FRQQHFWLRQV EHWZHHQ IXQFWLRQDO XQLWV +RZHYHU VWUXFWXUHG /'3& FRGHV VXFK DV WKRVH

VSHFLILHG LQ :,0$; DOORZ IRU UHSODFLQJ SHUPXWDWLRQ QHWZRUNV E\ ORZ FRPSOH[LW\ EDUUHO

VKLIWHUV>%RXWLOORQHWDO@>0DQVRXU 6KDQEKDJ@

(DUO\WHUPLQDOVFKHPHVFDQEHDGRSWHGWRLPSURYHWKHGHFRGLQJHIILFLHQF\E\G\QDPLFDOO\

DGMXVWLQJWKHLWHUDWLRQQXPEHUDFFRUGLQJWRWKH615YDOXHV7KHVLPSOHVWDSSURDFKUHTXLUHV

WKDW GHFRGLQJ GHFLVLRQV DUH VWRUHG DQG FRPSDUHG DFURVV WZR FRQVHFXWLYH LWHUDWLRQV LI QR

FKDQJHV DUH GHWHFWHG WKH GHFRGLQJ LV WHUPLQDWHG RWKHUZLVH LW LV FRQWLQXHG XS WR D

PD[LPXP QXPEHU RI LWHUDWLRQV 0RUH VRSKLVWLFDWHG LWHUDWLRQ FRQWURO VFKHPHV DUH DEOH WR

UHGXFHWKHPHDQQXPEHURILWHUDWLRQVVRVDYLQJERWKODWHQF\DQGHQHUJ\>.LHQOH :KHQ

@>6KLQHWDO@



%CUGQHUVWF[EQORNGVG9+/#:%6%FGEQFGTFGUKIP

7KH:,0$;&7&GHFRGHULVPDGHRIWKUHHPDLQEORFNVV\PEROGHVHOHFWLRQ 6' VXEEORFN

GHLQWHUOHDYHUDQG&7&GHFRGHUDVKLJKOLJKWHGLQ)LJZKHUH1UHSUHVHQWVWKHQXPEHURI

FRXSOHVLQFOXGHGLQDGDWDIUDPH6'VXEEORFNGHLQWHUOHDYHUDQG&7&GHFRGHUEORFNVDUH

FRQQHFWHGWRJHWKHUE\PHDQVRIPHPRU\EXIIHUVLQRUGHUWRJXDUDQWHHWKDWWKHQRQLWHUDWLYH

SDUW RI WKH GHFRGHU QDPHO\ 6' DQG VXEEORFNGHLQWHUOHDYHU  DQG WKHGHFRGLQJ ORRS ZRUN

VLPXOWDQHRXVO\ RQ FRQVHFXWLYH GDWD IUDPHV 6LQFH WKH PD[LPXP GHFRGHU WKURXJKSXW LV

DERXW0EVDQGWKHQDWLYH&7&UDWHLV WZRXQFRGHGELWVSURGXFHVL[FRGHGELWV DW

WKHLQSXWRIWKHGHFRGLQJORRSWKHPD[LPXPWKURXJKSXWFDQULVHXSWRPLOOLRQVRI//5V

SHU VHFRQG 7KH VDPH WKURXJKSXW RXJKW WR EH VXVWDLQHG E\ WKH VXEEORFN GHLQWHUOHDYHU

ZKHUHDVHYHQKLJKHUWKURXJKSXWKDVWREHVXVWDLQHGDWWKH6'XQLWLQFDVHRIUHSHWLWLRQ



5[ODQNFGUGNGEVKQP

'HSHQGLQJ RQ DPRXQW RI GDWD VHQW E\ WKH HQFRGHU SXQFWXULQJ RU UHSHWLWLRQ  WKH

WKURXJKSXWVXVWDLQHGE\WKHV\PEROGHVHOHFWLRQ 6' FDQULVHXSWRPLOOLRQVRI//5VSHU

VHFRQG UHSHWLWLRQu :KHQWKHHQFRGHUSHUIRUPVUHSHWLWLRQWKHVDPHV\PEROLVVHQWPRUH

WKDQRQFH7KXVWKHGHFRGHUFRPELQHVWKH//5VUHIHUUHGWRWKHVDPHV\PEROWRLPSURYHWKH

UHOLDELOLW\RIWKDWV\PERO$VVKRZQLQ)LJWKLVFDQEHDFKLHYHGSDUWLWLRQLQJWKHV\PERO

GHVHOHFWLRQLQSXWEXIIHULQWRIRXUPHPRULHVHDFKRIZKLFKFRQWDLQLQJXSWR1//5V

6LQFHWKHV\PEROGHVHOHFWLRQDUFKLWHFWXUHFDQUHDGXSWRIRXU//5VSHUFORFNF\FOHLWUHGXFHV

WKH LQFRPLQJ WKURXJKSXW WR  PLOOLRQV RI //5V SHU VHFRQG +RZHYHU WKH V\PERO

(16)

8.5+#TEJKVGEVWTGUHQT9+/#:%JCPPGN&GEQFGTU 

GHVHOHFWLRQKDVWRFRPSXWHWKHVWDUWLQJORFDWLRQDQGWKHQXPEHURI//5VWREHZULWWHQLQWR

WKHRXWSXWEXIIHU7KHQXPEHURI//5VDQGWKHVWDUWLQJORFDWLRQDUHREWDLQHGDVLQ  DQG

  UHVSHFWLYHO\ ZKHUH 16&+N PN DQG 63,'N DUH SDUDPHWHUV VSHFLILHG E\ WKH :,0$;

VWDQGDUGIRUWKHNLQGH[VXESDFNHWZKHQ+$54LVHQDEOHGQDPHO\16&+NLVWKHQXPEHURI

FRQFDWHQDWHGVORWVPNLVWKHPRGXODWLRQRUGHUDQG63,'NLVWKHVXESDFNHW,'



6&+N N

N

P 1

/  ˜ ˜

  

1 /

63,'

)

N

N

˜

N

PRG 

  



6LQFH16&+N>@DQGPN^`ZHFDQUHZULWH  DV



° ¯

° ®

­

˜



˜



˜



























N 6&+N

6&+N

N 6&+N

6&+N

N 6&+N

6&+N N

P ZKHQ 1

1

P ZKHQ 1

1

P ZKHQ 1

1

/

  

7KHHIILFLHQWLPSOHPHQWDWLRQRI  LVREWDLQHGZLWKDQDGGHUZKRVHLQSXWVDUH16&+NDQG

WKHVHOHFWLRQEHWZHHQWZRKDUGZLUHGOHIWVKLIWHGYHUVLRQVRI 16&+N RQHSRVLWLRQDQGWKUHH

SRVLWLRQV  IROORZHG E\ D SURJUDPPDEOH OHIW VKLIWHU ILYHVL[ SRVLWLRQV  6LPLODUO\ VLQFH

63,'N^`WKHPXOWLSOLFDWLRQLQ  LVDYRLGHGDV



° °

¯

°° ®

­

 PRG  





 PRG





 PRG





N N

N

N N

N N

N

N

63,' ZKHQ

1 /

/

63,' ZKHQ

1 /

63,' ZKHQ

1 /

63,' ZKHQ

)

  





λN

LQíRUGHU DGGUHVV

VFUDPEOHG LQíRUGHU

DGGUHVV VFUDPEOHG

>X,@

λN λΑΒ λΑΒ λΑΒ λN>X2@

$ % < : < :   

)N /N

XSíFRXQWHU

//5V

1

1

1

1

&8

6,62

XNSDFNHWL]HU GHFLVLRQKDUG PHPRU\

DGGUHVV JHQHUDWRU

$

%

<

:

6XEEORFNGHLQWHUOHDYHU &7&GHFRGHU

6\PEROGHVHOHFWLRQ





>F,@

)LJ&RPSOHWH&7&GHFRGHUEORFNVFKHPH 

$EORFNVFKHPHRIWKHDUFKLWHFWXUHHPSOR\HGWRFRPSXWH) NDQG/NLVGHSLFWHGLQ)LJ D 

)XUWKHUPRUH LQ RUGHU WR VXSSRUW WKH SXQFWXULQJ PRGH WKH RXWSXW PHPRU\ ORFDWLRQV

FRUUHVSRQGLQJ WR XQVHQW ELWV PXVW EH VHW WR ]HUR 7R HDVH WKH 6' DUFKLWHFWXUH

LPSOHPHQWDWLRQ DOO WKH RXWSXW PHPRU\ ORFDWLRQV DUH VHW WR ]HUR ZKLOH /N DQG )N DUH

(17)

9+/#:0GY&GXGNQROGPVU



FRPSXWHG$VDFRQVHTXHQFHDERXWWZRFORFNF\FOHVSHUVDPSOHDUHUHTXLUHGWRFRPSOHWH

WKHV\PEROGHVHOHFWLRQQDPHO\1//5VDUHRXWSXWLQ1FORFNF\FOHV6RWKDWWKHV\PERO

GHVHOHFWLRQWKURXJKSXWFDQEHHVWLPDWHGDV









FON

FON

6'

I I

1

7 1

  

$VLWFDQEHREVHUYHGWRVXVWDLQPLOOLRQVRI//5VSHUVHFRQGDFORFNIUHTXHQF\RI

0+]LVUHTXLUHG7RRYHUFRPHWKLVSUREOHPZHLPSRVHQRWRQO\WRSDUWLWLRQWKHLQSXWEXIIHU

LQWR IRXU PHPRULHV EXW DOVR WR LQFUHDVH WKH PHPRU\ SDUDOOHOLVP VR WKDW HDFK PHPRU\

ORFDWLRQFRQWDLQVS//5V7KXVZHFDQUHZULWH  DV  DQGE\VHWWLQJSWRDFRQVHUYDWLYH

YDOXHDVS WKH6'DUFKLWHFWXUHSURFHVVHVVLPXOWDQHRXVO\XSWRVL[WHHQ//5VZLWKIFON 

0+]



  

FON

FON

6'

I S I

1 1 S

7 ˜

  



5WDDNQEMFGKPVGTNGCXGT

7KHUHFHLYHG//5VEHORQJWRVL[SRVVLEOHVXEEORFNVGHSHQGLQJRQWKHFRGHGELWVWKH\DUH

UHIHUUHG WR $ % < : < :  DQG HDFK VXEEORFN LV PDGH RI 1 //5V 7KH VXEEORFN

GHLQWHUOHDYHUWUHDWVHDFKVXEEORFNVHSDUDWHO\DQGVFUDPEOHVLWV//5VDFFRUGLQJWR$OJRULWKP

JLYHQEHORZZKHUHPDQG-DUHFRQVWDQWVVSHFLILHGE\WKH:,0$;VWDQGDUGDQG%52P \  LVWKHELWUHYHUVHGPELWYDOXHRI\



Nł

Lł

ZKLOHL1GR

7NłP NPRG- %52P ¬N-¼ 

LI7N1WKHQ

LłL

HOVH

GLVFDUG7N

HQGLI

NłN

HQGZKLOH

$OJRULWKP6XEEORFNGHLQWHUOHDYHUDGGUHVVJHQHUDWRU

$VDFRQVHTXHQFHWKHQXPEHURIWHQWDWLYHDGGUHVVHVJHQHUDWHG10FDQEHJUHDWHUWKDQ1

([KDXVWLYHVLPXODWLRQVSHUIRUPHGRQWKHSRVVLEOH1VSHFLILHGE\WKHVWDQGDUGVKRZWKDW

WKH ZRUVW FDVH LV 10  WKDW RFFXUV ZLWK 1  6LQFH   D FRQVHUYDWLYH

DSSUR[LPDWLRQLV10 17KHZKROHVXEEORFNGHLQWHUOHDYHUDUFKLWHFWXUHLVREWDLQHGZLWK

RQHVLQJOHDGGUHVVJHQHUDWRULPSOHPHQWLQJ$OJRULWKPWRVLPXOWDQHRXVO\ZULWHRQH//5

IURPHDFKRIWKHVL[VXEEORFNPHPRULHV,QSDUWLFXODUDVLPSRVHGE\WKH:L0D[VWDQGDUG

WKHLQWHUOHDYHG//5VEHORQJLQJWRWKH$DQG%VXEEORFNVDUHVWRUHGVHSDUDWHO\ZKHUHDVWKH

Riferimenti

Documenti correlati

Lo studio dei frammenti di sovra-dipinta è stato strutturato, principalmente, sull’analisi della categoria ceramica della Dott.ssa Emma Vitale, pubblicata nel quinto volume

Un indizio archeologico ancora più significativo stante la pressoché totale mancanza nelle stratificazioni fin qui indagate di strati di vita e di accumuli di rifiuti riferibili

A partire da L’ermeneutica del soggetto, viene analizzato il campo semantico e pratico relativo alla direzione di coscienza stoica ed epicurea, in cui Foucault oppone la

The existence of a volumetrically large magma source beneath the central rift segment can also explain the volume deficit of magma sourced from the DVC [Wright et al., 2006; Ayele

10 – Example extracted from one of the best ESS allocations for network investment reduction (storage device of 2.1 MW – 8 h, installed on node 62): a) stored energy profile,

Tanto Leonardo si sofferma nella descrizione delle sue circonvoluzioni, da porre egli stesso all’origine di tale interesse un ricor- do personale risultato poi degno dell’analisi

albopictusDEXQGDQFHRQWKHEDVLVRIGDWDIURPVHDVRQDO URXQGPRQLWRULQJFDUULHGRXWRYHUPXOWLSOH\HDUVDFURVVDQGEH\RQGWKHXUEDQDUHDRI5RPHDQG %DUL$ILQHVFDOH