6<//$%/(18&/(86'85$7,216(67,0$7,2186,1*/,1($55(*5(66,21%$6('
(16(0%/(02'(/
-LQJOL/X 5XLOL:DQJ /L\DQDJH&'H6LOYD <DQJ*DR
6FKRRORI(QJLQHHULQJDQG$GYDQFHG7HFKQRORJ\0DVVH\8QLYHUVLW\3DOPHUVWRQ1RUWK1HZ=HDODQG
6WDWH.H\/DERUDWRU\IRU1RYHO6RIWZDUH7HFKQRORJ\1DQMLQJ8QLYHUVLW\1DQMLQJ&KLQD
)DFXOW\RI6FLHQFH8QLYHUVLW\RI%UXQHL'DUXVVDODP%UXQHL'DUXVVDODP
'HSDUWPHQWRI&RPSXWHU6FLHQFH1DQMLQJ8QLYHUVLW\1DQMLQJ&KLQD
^-LQJOL/X5:DQJ`#PDVVH\DFQ]OL\DQDJHFG#\DKRRFRQ]JDR\#QMXHGXFQ
$%675$&7
8QOLNH FRQYHQWLRQDO DXWRPDWLF FRQWLQXRXV VSHHFK
VHJPHQWDWLRQPRGHOVWKDWGHDOZLWKHDFKERXQGDU\WLPH
PDUNLQGLYLGXDOO\LQWKLVSDSHUZHSURSRVHDQLQWHUYDO
GDWDEDVHG/LQHDU5HJUHVVLRQ0RGHOIRUV\OODEOHQXFOHXV
'XUDWLRQV (VWLPDWLRQ /50'( ZKLFK WUHDWV V\OODEOH
ERXQGDU\WLPHPDUNVLQSDLUV7KLVFKDUDFWHULVWLFRI/50
'( PDNHV LW PRUH VXLWDEOH IRU HVWLPDWLQJ V\OODEOH
GXUDWLRQVIRU(QJOLVKVHQWHQFHVZKLFKFDQEHXVHGIRU
VHQWHQFH VWUHVV GHWHFWLRQ /50'( FRPELQHV WKH
RXWFRPHVRIPXOWLSOHEDVHDXWRPDWLFVSHHFKVHJPHQWDWLRQ
PDFKLQHV$60VWRJHQHUDWHILQDOERXQGDU\WLPHPDUNV
WKDWPLQLPL]HWKHDYHUDJHGLVWDQFHRIWKHSUHGLFWHGDQG
UHIHUHQFHERXQGDU\ SDLUVRIV\OODEOHQXFOHL([SHULPHQWDO
UHVXOWVVKRZWKDWRQ7,0,7GDWDVHW/50'(UHGXFHVWKH
DYHUDJHGLIIHUHQFHEHWZHHQWKHSUHGLFWHGV\OODEOHQXFOHXV
GXUDWLRQVDQGWKHLUUHIHUHQFHRQHVIURPPVWKHEHVW
UHVXOW RI D VLQJOH $60 WR PV $OVR /50'(
LPSURYHVWKHV\OODEOHQXFOHXVVHJPHQWDWLRQDFFXUDF\IURP
WRZLWKLQDWROHUDQFHRIPV
,QGH[ 7HUPV² $XWRPDWLF VSHHFK VHJPHQWDWLRQ
PXOWLSOHOLQHDUUHJUHVVLRQHQVHPEOHPRGHO
,1752'8&7,21
5HVHDUFKVKRZVWKDWV\OODEOHQXFOHXVGXUDWLRQLHYRZHO
GXUDWLRQ LQ D V\OODEOH UHODWHG IHDWXUHV DUH FULWLFDO IRU
(QJOLVK VHQWHQFH VWUHVV GHWHFWLRQ >@ $ VWUDLJKWIRUZDUG
ZD\ WR HVWLPDWH WKH V\OODEOH QXFOHXV GXUDWLRQV LV XVLQJ
DXWRPDWLFVSHHFKVHJPHQWDWLRQWHFKQRORJ\$QDXWRPDWLF
VSHHFK VHJPHQWDWLRQ PDFKLQH $60 LV D V\VWHP
SURGXFLQJDVHTXHQFHRIERXQGDU\WLPHPDUNV JLYHQDQ
XWWHUDQFHDQGLWVSKRQHWLFWUDQVFULSWLRQ
+LGGHQ 0DUNRY 0RGHO +00 EDVHG IRUFHG
DOLJQPHQW LV WKH PRVW FRPPRQO\ XVHG DXWRPDWLF
VHJPHQWDWLRQDOJRULWKP+RZHYHUWKH+00VLQIRUFHG
DOLJQPHQWDUHEXLOWPDLQO\IRULGHQWLI\LQJSKRQHPHVQRW
,QWKLVSDSHUWKHUHIHUHQFHERXQGDULHVDUHPDQXDOO\VHJPHQWHG
ZKLFKDUHFRQVLGHUHGDVWKHDFWXDOERXQGDULHV
IRU GHWHFWLQJ WKH SKRQHPH ERXQGDULHV 7KXV WKH\ FDQ
FDSWXUHDFHUWDLQDPRXQWRILQIRUPDWLRQWRLGHQWLI\ZKDW
WKH SKRQHPHV DUH EXW WKH\ FDQ RQO\ SURYLGH OLPLWHG
NQRZOHGJHDERXWWKHSKRQHPHWUDQVLWLRQ>@7KHUHIRUHWR
DFFXUDWHO\ PRGHO WKH SKRQHPH WUDQVLWLRQ YDULRXV
LPSURYHPHQWDOJRULWKPVKDYHEHHQGHYHORSHGZKLFKFDQ
EH URXJKO\ FDWHJRUL]HG LQWR WZR JURXSV UHILQHPHQW
PHWKRGVDQGHQVHPEOHPHWKRGV
,QWKHUHILQHPHQWPHWKRGVVRPHWXQLQJWHFKQLTXHVDUH
XVHGWRUHILQHWKHUDZVHJPHQWDWLRQVREWDLQHGE\DQ$60
VXFKDVVXSSRUWYHFWRUPDFKLQH>@PXOWLOD\HUSHUFHSWURQ
>@VWDWLVWLFDOFRUUHFWLRQWRFRPSHQVDWHIRUWKHV\VWHPDWLF
HUURU>@DQGWKHFRQWH[WGHSHQGHQWERXQGDU\PRGHO>@
,QVWHDGRIXVLQJWKHPD[LPXPOLNHOLKRRGFULWHULRQWKDWLV
XVHG LQ FRQYHQWLRQDO IRUFHG DOLJQPHQW WKH PLQLPXP
ERXQGDU\HUURUFULWHULRQLVXVHGLQ>@
,QWKHHQVHPEOHPHWKRGVVRPHWHFKQLTXHVDUHXVHGWR
SRVWSURFHVVWKHVHJPHQWDWLRQUHVXOWVRIPXOWLSOH$60VWR
JHW WKH ILQDO ERXQGDU\ WLPHPDUNV ,Q >@ WKH ILQDO
ERXQGDULHV DUH REWDLQHG E\ DYHUDJLQJ WKH RXWSXWV RI
PXOWLSOH$60V,Q>@WKHILQDOERXQGDULHVDUHDFKLHYHG
E\WKHZHLJKWHGVXPRIWKHELDVFRUUHFWHGERXQGDULHV
7KH FRQYHQWLRQDO DXWRPDWLF VHJPHQWDWLRQ DOJRULWKPV
WU\ WR PLQLPL]H WKH GLIIHUHQFHV EHWZHHQ WKH HVWLPDWHG
SKRQHPH ERXQGDULHV DQG WKHLU UHIHUHQFH FRXQWHUSDUWV
ZLWKRXW FRQVLGHULQJ WKH SKRQHPH GXUDWLRQ GLIIHUHQFHV
EHWZHHQ WKH HVWLPDWHG DQG WKH UHIHUHQFH RQHV 7KHVH
FRQYHQWLRQDO VHJPHQWDWLRQ DOJRULWKPV DUH VXLWDEOH WR
DXWRPDWLFDOO\JHQHUDWHWLPHDOLJQHGSKRQHPHDQQRWDWLRQ
RIVSHHFKFRUSRUDIRUXQLWVHOHFWLRQEDVHGFRQFDWHQDWLYH
VSHHFKV\QWKHVLVDQGLVRODWHGXQLWWUDLQLQJEDVHGVSHHFK
UHFRJQLWLRQ +RZHYHU WKLV LV SUREOHPDWLF WR REWDLQ WKH
V\OODEOH QXFOHXV GXUDWLRQV IRU VHQWHQFH VWUHVV GHWHFWLRQ
VLQFH DQ DFFHSWDEOH GLVFUHSDQF\ EHWZHHQ WKH HVWLPDWHG
DQGUHIHUHQFHV\OODEOHQXFOHXVERXQGDU\WLPHPDUNVGRHV
QRWDOZD\VOHDGWRDQDFFHSWDEOHGLIIHUHQFHEHWZHHQWKH
HVWLPDWHGDQGUHIHUHQFHV\OODEOHQXFOHXVGXUDWLRQV
7ZR H[DPSOHV DUH LOOXVWUDWHG LQ )LJXUH 7KH
KRUL]RQWDOOLQHLQGLFDWHVWKHWLPHD[LVRIDQXWWHUDQFH7KH
WZRVROLGGRWVDUHWKHUHIHUHQFHERXQGDU\WLPHPDUNVRID
V\OODEOHQXFOHXVEHWZHHQZKLFKLVUHIHUHQFHVHJPHQW W
4849 978-1-4244-2354-5/09/$25.00 ©2009 IEEE ICASSP 2009