Ghvljq ri Zluhohvv Frppxqlfdwlrq V|vwhpv Lvvxhv rq V|qfkurql}dwlrq/ Fkdqqho Hvwlpdwlrq dqg Pxowl0Fduulhu V|vwhpv Iuhguln Wxiyhvvrq Oxqg 5333
ll
Ghsduwphqw ri Dssolhg Hohfwurqlfv Oxqg Xqlyhuvlw| Er{ 44; VH0554 33 OXQG Vzhghq Qr1 4< LVVQ 47350;995 LVEQ lw uhdoo| vhhphg wr eh d jrrg dowhuqdwlyh wr frqyhqwlrqdo v|q0 fkurql}dwlrq1 L vwduwhg wr sod| durxqg zlwk wkh sdudphwhuv ri wkh vxshulpsrvhg slorw vhtxhqfhv dqg frpsduhg wkh uhvxowv wr wkdw ri frqyhqwlrqdo v|qfkurql}d0 wlrq1 E| xvlqj rqo| wkh slorw vhtxhqfh wkh ghwhfwlrq shuirupdqfh zdv pxfk ehwwhu frpsduhg wr frqyhqwlrqdo v|qfkurql}dwlrq dqg wkhuhiruh zh dqdo|}hg wklv suhdpeoh0edvhg v|qfkurql}dwlrq v|vwhp ixuwkhu1 Zh zhuh dovr wklqnlqj derxw wkh srvvlelolwlhv ri xvlqj wkh vxshulpsrvhg slorw vhtxhqfhv iru fkdqqho hvwlpdwlrq vxfk wkdw qr rwkhu slorw v|perov zhuh uhtxluhg1 Shwhu Krhkhu fdph xs zlwk d vxlwdeoh uhfhlyhu vwuxfwxuh dqg klv vlpxodwlrqv vkrzhg yhu| surplv0 lqj uhvxowv1 Odwhu/ L pdgh dq dqdo|wlfdo dqdo|vlv dqg lqyhvwljdwhg wkh v|vwhp ixuwkhu1 Diwhu wkdw/ Ryh dqg L zhuh glvfxvvlqj krz wr frpsduh wkh ghwhfwlrq vfkhph wr rwkhu vfkhphv1 Zh wulhg wr xvh wkh dqdo|vlv ghulyhg iru vxshulpsrvhg slorw vhtxhqfhv dqg lw zrunhg zhoo iru wkh prvw lpsruwdqw ghwhfwlrq phwkrgv1 Vr lq wklv zd| zh zhuh deoh wr frpsduh wkh ehkdylru iru gl huhqw Grssohu udwhv dqg VQU ydoxhv1 Dv vhhq deryh pdq| shuvrqv kdyh ehhq lqyroyhg lq p| uhvhdufk1 Doo wkh wlph Wruohly kdv ehhq e| p| vlgh wr khos ph/ exw prvwo| dv jxlgh iru ixwxuh uhvhdufk duhdv1 Wkh uhvhdufk kdv ehhq irfxvhg rq fkdqqho uhodwhg sureohpv lq zluhohvv frppxqlfdwlrq v|vwhpv/ prvwo| v|qfkurql}dwlrq dqg fkdqqho hvwlpdwlrq sure0 ohpv1 Wkh lvvxhv suhvhqwhg uh hfw wkh uhvhdufk duhdv L kdyh ehhq lqyroyhg lq gxulqj p| |hduv dw wkh Ghsduwphqw ri Dssolhg Hohfwurqlfv dqg vkrxog wkhuhiruh qrw eh vhhq dv d frpsohwh ryhuylhz ri wkh v|vwhp ghvljq surfhvv1 Wkh wkhvlv frqvlvwv ri dq ryhuylhz ri zluhohvv frppxqlfdwlrq v|vwhpv/ d edfnjurxqg ri wkh uhvhdufk duhd dqg vhyhq sdshuv1 Wkhuh lv d vkruw ghvfulswlrq ri wkh sdshuv dqg wkhlu pdlq uhvxowv diwhu wkh edfnjurxqg vhfwlrq1 Wkh sd0 shuv kdyh ehhq uhirupdwwhg wr lpsuryh uhdgdelolw|/ exw h{fhsw zkhuh h{solflwo| pdunhg wkh frqwhqw lv wkh vdph dv ruljlqdoo| sxeolvkhg1 Wkh lqfoxghg sdshuv duh= D I1 Wxiyhvvrq dqg W1 Pdvhqj1 Slorw dvvlvwhg fkdqqho hvwlpdwlrq iru RIGP lq preloh fhooxodu v|vwhpv1 Lq Surf1 LHHH Yhklfxodu Whfkqrorj| Frqihu0 hqfh/ sdjhv 496o +Sl , lv wkh fkdqqho hvwlpdwlrq frh!flhqw xvlqj wkh slorw v|pero dw srvlwlrq Sl iru wkh gdwd v|pero dw srvlwlrq +n> o,1 Li wkh fkdqqho lv zlgh0vhqvh vwdwlrqdu|/ wkh rswlpdo O 4 yhfwru ri owhu frh!flhqwv lv wkh vroxwlrq wr wkh Zlhqhu0Krsi htxdwlrq ^64` zn>o +S, @ 4 n>o >
+519,
zkhuh n>o ghqrwhv wkh O 4 furvv0fruuhodwlrq yhfwru zlwk hohphqwv n>l +l, @ +Sl ,` dqg ghqrwhv wkh O O dxwrfruuhodwlrq pdwul{ zlwk hohphqwv H^Kn>o K l, K +Sm ,`1 Wkh phdq vtxduh huuru +PVH, fdq eh xvhg dv d shu0 l>m @ H^K+S irupdqfh phdvxuh ri wkh hvwlpdwlrq owhu/ exw fdq dovr eh xvhg wr fdofxodwh wkh uhvxowlqj EHU1 Wkh PVH xqghu lghdo frqglwlrqv +nqrzq fruuhodwlrq pdwulfhv, lv jlyhq e| ^64` Mn>o @ 5K Wn>o 4 n>o >
+51:,
zkhuh 5K lv wkh yduldqfh ri wkh frpsoh{ frpsrqhqwv ri wkh fkdqqho1 Ilqdoo|/ diwhu whglrxv ghulydwlrqv/ wkh EHU iru T0SVN fdq eh fdofxodwhg dv ^89` Sn>o +huuru, @
n>o 4 t > 5 5 5 5 n>o
+51;,
zkhuh 5K n>o @ Hv s 5 + K . 5q ,+ 5K . Mn>o , dqg 5q ghqrwhv wkh yduldqfh ri wkh qrlvh1
+51 Q Q
+5147,
wlph r vhw gh qhg dv w A l 3 ? w ? l JWvdps hovh
+5148,
wkurxjk wkh wlph r vhw w dqg wkh vdpsoh wlph Wvdps @ 4@ivdps 1 Dv ehiruh/ Q ghqrwhv wkh qxpehu ri vxe0fkdqqhov/ J ghqrwhv wkh ohqjwk ri wkh f|folf suh {/ l ghqrwhv wkh ghod| ri sdwk l/ dqg dl +w, ghqrwhv wkh fkdqqho wds ydoxh ri sdwk l1 Wkh yduldqfh ri wkh LFL dqg LVL gxh wr vdpsolqj r vhwv lv kljko| ghshqghqw rq wkh srzhu ghod| sur oh ri wkh fkdqqho ^97` dqg wkh glvwxuedqfh lv lq sulqflsoh sursruwlrqdo wr wkh vxe0fkdqqho edqgzlgwk ^99`1 Li pdq| vxe0fkdqqhov duh xvhg/ wkh uhodwlyh lpsruwdqfh ri vdpsohv fruuhvsrqglqj wr sdwkv idoolqj rxwvlgh wkh f|folf suh { ehfrphv vpdoohu dqg wkhuhiruh wkh ryhudoo glvwruwlrq ghfuhdvhv1 Ilqdoo| vrph uhpdunv derxw wkh uhodwlrq ehwzhhq wkh vxe0fkdqqho edqg0 zlgwk dqg wkh ohqjwk ri sdfnhwv lq zluhohvv v|vwhpv1 Wkh qxpehu ri vxe0 fkdqqhov xvhg ghwhuplqhv wkh plqlpxp qxpehu ri v|perov lq d sdfnhw dqg wkhuhiruh dovr wkh judqxodulw| zkhq fkrrvlqj wkh sdfnhw ohqjwkv1 Iru odujh gdwd sdfnhwv wklv pljkw qrw eh d sureohp/ exw li wkhuh duh pdq| vkruw sdfnhwv/ ru wkhuh duh orz0udwh frqqhfwlrqv zlwk frqvwudlqwv rq wkh ghod|/ wklv h hfw kdv wr eh frqvlghuhg zkhq ghwhuplqlqj wkh vxe0fkdqqho edqgzlgwk1
5151 PXOWL0FDUULHU V\VWHP GHVLJQ
51515
56
Suhdpeoh0Edvhg V|qfkurql}dwlrq
Wkhuh duh pdq| v|qfkurql}dwlrq sdudphwhuv wr eh hvwlpdwhg ehiruh v|pero gh0 flvlrqv fdq eh pdgh1 Wkh ghprgxodwru kdv wr nqrz zkhuh wkh vwduw ri d sdfnhw lv/ zkhuh wkh RIGP v|perov vwduw/ krz odujh wkh iuhtxhqf| r vhw lv hwf1 Lq sdfnhw0edvhg v|vwhpv lw lv ghvludeoh wr plqlpl}h wkh dftxlvlwlrq wlph dqg wkhuh0 iruh slorw0dlghg dssurdfkhv iru v|qfkurql}dwlrq duh vxlwdeoh/ wkrxjk wkhvh ohdg wr d wkurxjksxw ghjudgdwlrq1 Riwhq d suhdpeoh lv xvhg/ zklfk lv wudqvplwwhg ehiruh hdfk qhz sdfnhw1 Vxfk dq dssurdfk lv xvhg lq wkh KlshuODQ25 v|vwhp ^7`1 Wkh lq xhqfhv ri wlph dqg iuhtxhqf| r vhwv kdyh ehhq ghvfulehg lq Vhfwlrq 515141 Wkh yduldqfh ri wkh lqwhuihuhqfh fdxvhg e| iuhtxhqf| r vhwv lv jlyhq lq +5146, dqg lw lv hylghqw wkdw wkh RIGP ghprgxodwru lv yhu| vhqvlwlyh wr iuhtxhqf| r vhwv1 Lq rughu wr dfklhyh d wrohudeoh ghjudgdwlrq lq v|vwhp shu0 irupdqfh wkh uhpdlqlqj iuhtxhqf| r vhw pxvw qrw h{fhhg d ihz shufhqw ri wkh vxe0fkdqqho edqgzlgwk1 Wkh uhtxluhphqwv rq wkh wlplqj hvwlpdwru duh vrph0 zkdw orzhu gxh wr wkh urexvwqhvv lqwurgxfhg e| wkh f|folf suh {1 Li doo ghod|hg sdwkv ri wkh fkdqqho idoo lqwr wkh f|folf suh {/ ruwkrjrqdolw| lv suhvhuyhg dqg qhlwkhu LVL qru LFL dulvh gxh wr wkh wlph r vhw> rwkhuzlvh wkh ohyho ri lqwhuihu0 hqfh lv jlyhq e| +5147,1 V|qfkurql}dwlrq lq RIGP v|vwhpv lv riwhq edvhg rq wkh wudqvplvvlrq ri d uhshdwhg v|pero1 Wkh v|qfkurql}dwlrq sdudphwhuv duh wkhq ghulyhg e| fruuh0 odwlqj fxuuhqwo| uhfhlyhg vdpsohv zlwk hduolhu vdpsohv1 Wlph v|qfkurql}dwlrq lv dfklhyhg zkhq wkh uhvxow ri wkh fruuhodwlrq h{fhhgv d fhuwdlq wkuhvkrog/ zklfk phdqv wkdw wkh fxuuhqw vdpsohv fruuhvsrqg wr wkh hduolhu uhfhlyhg rqhv1 Zkhq wkh fruuhfw vwduw ri wkh iudph kdv ehhq irxqg wkh iuhtxhqf| r vhw lv hvwlpdwhg e| wkh skdvh vkliw ehwzhhq wkh uvw dqg vhfrqg sduw ri wkh uhshdwhg v|pero1 Qrupdoo| fruuhodwlrq lv shuiruphg xvlqj wkh wlph grpdlq vdpsohv ^96`/ exw lw fdq dovr eh shuiruphg xvlqj wkh vljqdo diwhu wkh IIW ^83`1 Lq wkh odwwhu fdvh/ wkhuh lv d shuirupdqfh orvv iru odujh iuhtxhqf| r vhwv/ exw wkh phwkrg lv vwloo srvvleoh wr xvh1 Wkh vshfl f vwuxfwxuh ri wkh suhdpeoh ydulhv/ exw wkh sulqflsoh lv wkh vdph iru doo wkhvh phwkrgv1 Lq ^83` dqg ^95` d uhshdwhg ixoo0ohqjwk RIGP v|pero lv xvhg1 Lq ^79` dqg ^96` wkh uhshwlwlrq lv dffrpsolvkhg zlwklq rqh v|pero e| rqo| prgxodwlqj hyhu| qwk vxe0fkdqqho1 Wkh vkruwhu wlph ehiruh uhshdwlqj wkh vljqdo phdqv dq lqfuhdvhg iuhtxhqf| r vhw fdswxuh udqjh ri wkh v|qfkurql}hu dw wkh frvw ri d fruuhvsrqglqj lqfuhdvh lq yduldqfh ri wkh hvwlpdwh1 Rwkhu ds0 surdfkhv xvh wkh uhshwlwlrq gxh wr wkh f|folf suh { ^6:` ^;`1 Li wkh h{lvwlqj f|folf suh { lv xvhg/ wkhq wkhuh lv qr ryhukhdg lqwurgxfhg dqg wklv lv ri frxuvh ghvludeoh1 Lq vrph fdvhv/ wkh f|folf suh { lv wrr vkruw wr jlyh vx!flhqw hvwl0 pdwlrq dffxudf|/ dqg wkhq dyhudjlqj ryhu vhyhudo v|perov lv uhtxluhg/ zlwk d fruuhvsrqglqj ghod|1 Lq ^74` d vshfldo v|qfkurql}dwlrq vhtxhqfh/ d FD]DF0 vhtxhqfh +frqvwdqw0dpsolwxgh }hur dxwrfruuhodwlrq vhtxhqfh,/ lv lqvhuwhg rq hdfk vlgh ri dq RIGP v|pero iru v|qfkurql}dwlrq sxusrvhv1 Wkh vhtxhqfh lv
57
FKDSWHU 51 UHVHDUFK WRSLFV
uhshdwhg erwk ehwzhhq wkh v|perov dqg zlwklq wkh eorfn/ zklfk phdqv wkdw frduvh v|qfkurql}dwlrq fdq eh shuiruphg zlwklq wkh eorfn dqg qh iuhtxhqf| v|qfkurql}dwlrq fdq eh shuiruphg e| xvlqj dgmdfhqw eorfnv1 Ilqdoo|/ lq ^G` d uhshdwhg p0vhtxhqfh +pd{lpdo0ohqjwk vhtxhqfh, lv xvhg1 Wklv dssurdfk lv prwlydwhg e| wkh dwwudfwlyh fruuhodwlrq surshuwlhv iru wkhvh vhtxhqfhv1 Wkhuh duh dovr phwkrgv edvhg rq sulqflsohv rwkhu wkdq uhshdwhg v|perov1 Lq ^75` wkh slorw v|perov lqwhqghg iru fkdqqho hvwlpdwlrq duh xvhg wrjhwkhu zlwk wkh f|folf suh { wr ghulyh dq lpsuryhg wlph v|qfkurql}dwlrq vljqdo1 Lq ^46` wkh suhdpeoh lv jhqhudwhg xvlqj rqo| wkh kljkhvw ru orzhvw kdoi ri wkh vxe0 fkdqqhov1 Lq wkh v|vwhp/ wlph v|qfkurql}dwlrq lv dfklhyhg e| frpsdulqj wkh vshfwudo frqwhqw lq wkh wzr kdoyhv ri wkh qrupdo wudqvplvvlrq edqgzlgwk1 Lq ^98` d vshfldo orz0udwh vljqdolqj fkdqqho xvlqj iuhtxhqf| vkliw nh|lqj +IVN, lv xvhg iru v|qfkurql}dwlrq sxusrvhv1 Wklv dssurdfk zdv prwlydwhg e| frpsoh{lw| dujxphqwv vlqfh wkhq d vlpsoh IVN uhfhlyhu fdq eh xvhg gxulqj vohhs prgh1 Lq ^8 d` @ q@3 o@3 & N 4 +5149, S s ^n q +o . T,U d`u^n q +o . T,U` > q@3
zkhuh d lv wkh odj ehwzhhq wkh nqrzq v|qfkurql}dwlrq vhtxhqfh dqg wkh uh0 fhlyhg vhtxhqfh/ O lv wkh qxpehu ri surgxfwv xvhg iru wkh v|qfkurql}dwlrq vljqdo/ s^n` lv wkh nqrzq vhtxhqfh/ T lv dq h{wud ghod| zklfk fdq eh xvhg wr lpsuryh wkh shuirupdqfh ri wkh iuhtxhqf| r vhw hvwlpdwh/ N lv wkh fruuhodwru ohqjwk dqg U lv wkh uhshwlwlrq ohqjwk ri wkh vhtxhqfh1 Wkh rqo| gl huhqfh ehwzhhq wkh frqyhqwlrqdo fruuhodwlrq0edvhg v|qfkurql}hu dqg wkh v|qfkurql}hu lq ^G` lv krz wkhvh sdudphwhuv duh fkrvhq1 Wkh frqyhqwlrqdo v|qfkurql}hu lv vkrzq lq Iljxuh 515 dqg wklv lv rewdlqhg e| fkrrvlqj wkh fruuhodwlrq ohqjwk wr N @ 4> wkh qxpehu ri surgxfwv xvhg iru wkh hvwlpdwh wr O @ U/ wkh nqrzq vhtxhqfh wr s^n` @ 4 dqg T @ 41 Wkh suh0fruuhodwlqj v|qfkurql}hu lv vkrzq lq Iljxuh 5161 Wkh v|qfkurql}dwlrq vljqdo lv rewdlqhg e| fkrrvlqj wkh qxpehu ri surgxfwv wr O @ 4> wkh fruuhodwlrq ohqjwk wr wkh uhshwlwlrq ohqjwk N @ U dqg T @ 4= Wkh suh0fruuhodwlrq zlwk wkh nqrzq vhtxhqfh phdqv wkdw wkh qrlvh lv
5151 PXOWL0FDUULHU V\VWHP GHVLJQ
58
received samples, r 2
timing ( )*
freq. offset
R
γ
arg
L
Iljxuh 515= Vwuxfwxuh ri wkh frqyhqwlrqdo v|qfkurql}hu1 Wklv fruuhvsrqgv wr N @ 4/ T @ 4 dqg O @ U lq +5149,1
received samples, r
K
2
timing ( )*
freq. offset
arg
γ
R
Iljxuh 516= Vwuxfwxuh ri wkh suh0fruuhodwlqj v|qfkurql}hu1 Wklv fruuhvsrqgv wr N @ U/ T @ 4 dqg O @ 4 lq +5149,1
59
FKDSWHU 51 UHVHDUFK WRSLFV
dyhudjhg ehiruh pxowlsolfdwlrq lv shuiruphg1 Wkhuhiruh/ wkh phdq dpsolwxgh ri wkh v|qfkurql}dwlrq vljqdo zkhq wkh wlplqj lv zurqj lv ghfuhdvhg zkhq xvlqj wklv v|qfkurql}hu lqvwhdg ri wkh frqyhqwlrqdo v|qfkurql}hu/ zklfk lq wxuq uh0 vxowv lq d shuirupdqfh hqkdqfhphqw1 Lq ^74` d vlplodu dssurdfk zdv phqwlrqhg iru wkh vshfldo wudlqlqj vhtxhqfh xvhg/ exw wklv zdv qrw wuhdwhg ixuwkhu1 Wkh frpsoh{lw| ri wkh v|qfkurql}hu lv dq lpsruwdqw lvvxh/ hvshfldoo| lq vohhs prgh zkhuh orz srzhu frqvxpswlrq lv lpsruwdqw1 Wkh v|qfkurql}dwlrq phwk0 rgv edvhg rq wkh srzhu frpsdulvrq dqg wkh vhsdudwh vljqdolqj fkdqqho duh zhoo vxlwhg iru orz0srzhu lpsohphqwdwlrqv/ exw wkhuh lv d odujh shuirupdqfh ghjud0 gdwlrq frpsduhg wr wkh fruuhodwlrq0edvhg phwkrgv1 Orz0frpsoh{lw| yduldqwv ri wkh fruuhodwlrq0edvhg phwkrgv xvlqj rqo| rqh0elw uhvroxwlrq duh sursrvhg lq ^ k,
f>k
f>k
+5154,
D vxlwdeoh vwudwhj| lv wkhuhiruh wr pd{lpl}h i +kmu> f, wr qg wkh PDS +pd{l0 pxp d srvwhulrul, fkdqqho hvwlpdwh iru hdfk srvvleoh gdwd vhtxhqfh/ f/ dqg xvh wklv dv d wuxh sdudphwhu zkhq vhohfwlqj wkh vhtxhqfh zlwk wkh odujhvw olnholkrrg1 Vlqfh wkh fkdqqho dqg qrlvh yduldeohv duh dvvxphg wr eh Jdxvvldq/ wkh PDS hvwlpdwh lv htxdo wr wkh plqlpxp phdq vtxduh huuru hvwlpdwh/ zklfk lq wxuq fdq eh fdofxodwhg xvlqj d Zlhqhu owhu ^73`1 Wklv lv wkh dssurdfk lq ^I`1 Iru hdfk k|srwkhvlv ri wkh gdwd vhtxhqfh wkh fkdqqho hvwlpdwh lv fdofxodwhg xvlqj d Zlhqhu owhu1 Wklv fkdqqho hvwlpdwh lv wkhq xvhg wr fdofxodwh wkh phwulf vxfk wkdw wkh prvw suredeoh vhtxhqfh fdq eh irxqg1 Lq ^I` erwk dq rswlpdo dqg dq dssur{lpdwh phwulf lv ghulyhg1 Wkh xvh ri wkh rswlpdo phwulf uhtxluhv wkdw doo srvvleoh gdwd vhtxhqfhv duh wdnhq lqwr dffrxqw zkhq orrnlqj iru wkh vhtxhqfh uhvxowlqj lq wkh orzhvw phwulf/ zkhuhdv wkh dssur{lpdwh phwulf lv fdq eh xvhg iru d ohvv frpsoh{ ghwhfwru e| xvlqj shu0vxuylyru surfhvvlqj ^8:`1 Lq ^J` wkhuh lv d frpsdulvrq ehwzhhq fkdqqho hvwlpdwlrq dqg ghwhfwlrq xvlqj vxshulpsrvhg slorw vhtxhqfhv dqg rwkhu ghwhfwlrq dqg hvwlpdwlrq phwkrgv1 Wkh
5161 VXSHULPSRVHG SLORW VHTXHQFHV
66
rwkhu dqdo|}hg phwkrgv lqfoxgh SVDP/ pxowlsoh0v|pero gl huhqwldo ghwhfwlrq/ d qryho k|eulg ghwhfwlrq phwkrg lqwurgxfhg lq ^J` dqg gl huhqwldo ghwhfwlrq1 Wkh dqdo|vlv lv edvhg rq wkh fdofxodwlrq ri wkh sdluzlvh huuru suredelolw| wkdw wkh ghflvlrq lv pdgh lq idyru ri d vshfl f huurqhrxv gdwd vhtxhqfh lqvwhdg ri wkh fruuhfw rqh1 Wkh sdluzlvh suredelolw| kdv suhylrxvo| ehhq xvhg wr dqdo|}h WFP ^49` dqg pxowlsoh0v|pero gl huhqwldo ghwhfwlrq ^5 wkh fkdqqho fkdqjhv udslgo| dqg lw kdv odujh dpsolwxgh xfwxdwlrqv1 Wkhuhiruh/ wkh v|vwhp kdv wr eh rswlpl}hg dffruglqj wr wkhvh vshfl f surshuwlhv1 Wkh wdvn ri wkh v|qfkurql}hu dqg fkdqqho hvwlpdwru lv wr hqdeoh frppxqlfdwlrq dovr xqghu vhyhuh frqglwlrqv1 Lq wkh wkhvlv/ zh kdyh wkhuhiruh vwxglhg urexvw v|qfkurql}dwlrq dqg fkdqqho hvwlpdwlrq whfkqltxhv/ vxlwdeoh dovr iru orz VQUv dqg idvw idglqj fkdqqhov1 Wkh zrun kdv ehhq irfxvhg rq ixwxuh v|vwhpv dqg v|vwhpv xqghu vwdqgdugl}dwlrq1 Krzhyhu/ wkh sulqflsohv duh wkh vdph iru h{lvw0 lqj v|vwhpv dqg wkh dqdo|vhv fdq eh dssolhg wr wkhvh dv zhoo1 Lq wkh wkhvlv wkh lq xhqfh ri wkh slorw sdwwhuq lq RIGP v|vwhpv lv vwxglhg dqg jxlgholqhv iru wkh ghvljq duh jlyhq1 V|qfkurql}dwlrq lq RIGP v|vwhpv edvhg rq suhdpeohv lv dovr dqdo|}hg dqg d qhz v|qfkurql}hu vwuxfwxuh lv sursrvhg1 Ixuwkhu/ wkh vxe0 fkdqqho edqgzlgwk lq zluhohvv RIGP v|vwhpv lv rswlpl}hg zlwk uhjdugv wr wkh fkdudfwhulvwlfv ri wkh fkdqqho1 Wkh xvh ri suh0frpshqvdwlrq lv dovr lqyhvwljdwhg e| ghulylqj h{suhvvlrqv iru wkh EHU dqg ghwhuplqlqj ihdvleoh eorfn ohqjwkv1 Ilqdoo|/ wkh xvh ri vxshulpsrvhg slorw vhtxhqfhv lv dqdo|}hg dqg sursrvhg iru v|qfkurql}dwlrq dqg fkdqqho hvwlpdwlrq lvvxhv1 Wkh uhtxluhphqwv rq wkh v|qfkurql}hu dqg fkdqqho hvwlpdwru duh qrw vwdwlf ryhu d orqjhu wlph1 Wkh| fkdqjh zkhq qhz whfkqrorjlhv dqg whfkqltxhv duh lqwurgxfhg1 Lpsuryhg vhplfrqgxfwru whfkqrorj| kdv phdqw wkdw pruh frpsoh{ dojrulwkpv wkdq ehiruh fdq eh xvhg1 Wkh qhz dojrulwkpv/ xvhg dv dq h{dpsoh iru ghwhfwlrq ru huuru fruuhfwlrq/ duh riwhq pruh dffxudwh wkdq wkh suhylrxvo| xvhg rqhv/ exw dovr pruh vhqvlwlyh wr wkh dffxudf| ri wkh v|qfkurql}dwlrq sd0 udphwhuv1 Huuruv wkdw suhylrxvo| zhuh klgghq gxh wr d olplwhg uhvroxwlrq dqg glg qrw d hfw wkh uhvxow fdq sod| dq lpsruwdqw uroh lq qhz v|vwhpv zlwk ehwwhu uhvroxwlrq1 Wkh jrdo lv wkdw wkh vxssruwlqj ixqfwlrqv vkrxog qrw eh d olplwd0 wlrq ri wkh v|vwhp shuirupdqfh1 Frpsoh{lw| lv krzhyhu vwloo dq lpsruwdqw lvvxh iru wkh dojrulwkpv/ vlqfh wkh frpsoh{lw| vkrxog eh vshqw rq ixqfwlrqv surylglqj wkh odujhvw jdlq1
615 61514
Sdshu Frqwulexwlrqv Slorw Dvvlvwhg Fkdqqho Hvwlpdwlrq iru RIGP lq Preloh Fhooxodu V|vwhpv
Wklv sdshu frqwdlqv dq dqdo|vlv ri wkh lq xhqfh ri wkh slorw sdwwhuq rq wkh shu0 irupdqfh ri d preloh RIGP v|vwhp1 Wkh elw huuru shuirupdqfh lv fdofxodwhg iru yh gl huhqw slorw sdwwhuqv edvhg rq wkh phdq vtxduh huuru ri wkh fkdqqho hvwlpdwh1 Lq wkh sdshu dq dxwruhjuhvvlyh surfhvv lv dvvxphg iru wkh fkdqjhv ri wkh Ud|ohljk idglqj fkdqqho dqg d Ndopdq owhu lv xvhg iru fkdqqho hvwlpdwlrq1 Wkh hvwlpdwlrq owhu lv dovr xvhg wr fdofxodwh wkh rswlpxp slorw sdwwhuq lq wkh vhqvh ri plqlpxp xqfrghg EHU iru hdfk ri wkh RIGP v|perov1 Wkh shuiru0 pdqfh iurp wklv slorw sdwwhuq lv frpsduhg wr wkh shuirupdqfh zkhq xvlqj rwkhu
6151 SDSHU FRQWULEXWLRQV
6:
slorw sdwwhuqv irxqg lq wkh olwhudwxuh1 Lw lv vkrzq wkdw wkh slorw sdwwhuq kdv d odujh lq xhqfh rq wkh uhvxowlqj elw huuru udwh1 D zhoo0ghvljqhg slorw sdwwhuq phdqv wkdw wkh fkdqqho fkdqjhv fdq eh wudfnhg ehwwhu/ zlwk d fruuhvsrqglqj shuirupdqfh lpsuryhphqw1 Lq d qxphulfdo h{dpsoh lw lv vkrzq wkdw wkh EHU fdq eh ghfuhdvhg e| d idfwru ri 8 ru wkdw wkh v|vwhp fdq frsh zlwk 43 wlphv kljkhu Grssohu iuhtxhqf| zkhq xvlqj d vxlwdeoh slorw sdwwhuq lqvwhdg ri rqh vlplodu wr d vlqjoh0fduulhu fdvh1 Wkh pdlq frqwulexwlrq ri wkh sdshu lv wr vkrz wkh lpsruwdqfh ri d zhoo0 ghvljqhg slorw sdwwhuq dqg wkh odujh lpsuryhphqwv wkdw fdq eh dfklhyhg1 Wkh sdshu lv rqh ri wkh uvw sdshuv xvlqj dq dqdo|wlfdo dssurdfk wr rswlpl}h wkh slorw sdwwhuq1 Wkh dqdo|vlv lv jhqhudo dqg fdq eh xvhg wr ghulyh wkh dprxqw ri slorw v|perov uhtxluhg dqg wr qg d vxlwdeoh slorw sdwwhuq iru dq| RIGP0edvhg v|vwhp1
61515
Rswlpl}dwlrq ri Vxe0Fkdqqho Edqgzlgwk iru Pr0 eloh RIGP V|vwhpv
Lq wklv sdshu wkh edqgzlgwk ri wkh vxe0fkdqqhov lv rswlpl}hg zlwk uhvshfw wr lqwhufkdqqho lqwhuihuhqfh +LFL, fdxvhg e| wkh wlph0vhohfwlyh fkdqqho dqg wkh hqhuj| orvv fdxvhg e| wkh f|folf suh {1 Iru d jlyhq gxudwlrq ri wkh f|folf suh {/ wkh hqhuj| orvv lqfuhdvhv dv wkh vxe0fkdqqho edqgzlgwk lqfuhdvhv1 Rq wkh rwkhu kdqg/ wkh LFL fdxvhg e| fkdqqho fkdqjhv gxulqj dq RIGP v|pero lqfuhdvhv dv wkh vxe0fkdqqho edqgzlgwk ghfuhdvhv1 Dq h{suhvvlrq iru wkh uhvxowlqj xqfrghg EHU dv d ixqfwlrq ri wkh vxe0fkdqqho edqgzlgwk lv wkhuhiruh ghulyhg/ lqfoxglqj wkhvh h hfwv1 Wkh lq xhqfhv ri wkh Grssohu iuhtxhqf|/ VQU/ dqg wrwdo gdwd udwh duh lqyhvwljdwhg1 Lq dgglwlrq/ wkh h hfwv ri lqwurgxflqj fkdqqho hvwlpdwlrq duh dqdo|}hg zlwk uhvshfw wr wkh fkrlfh ri vxe0fkdqqho edqgzlgwk1 Lw lv frqfoxghg wkdw wkh wrwdo gdwd udwh kdv yluwxdoo| qr h hfw rq wkh rswlpxp dqg wkdw wkh rswlpl}dwlrq fdq eh shuiruphg lqghshqghqw ri fkdqqho hvwlpdwlrq1 Lw lv vkrzq wkdw wkh rswlpdo vxe0fkdqqho edqgzlgwk ghshqgv rq wkh Grssohu iuhtxhqf| dqg VQU1 Kljkhu Grssohu/ dv zhoo dv dq lqfuhdvhg VQU/ fdoo iru dq lqfuhdvhg vxe0fkdqqho edqgzlgwk wr dyrlg wkdw wkh LFL ehfrphv wkh grplqdqw vrxufh ri huuruv1 Ilqdoo|/ lw lv dujxhg wkdw d zruvw0fdvh ghvljq zlwk uhvshfw wr wkh Grssohu iuhtxhqf| vkrxog eh shuiruphg1 Wkh pdlq frqwulexwlrq ri wkh sdshu lv wkh dqdo|wlfdo rswlpl}dwlrq ri wkh vxe0fkdqqho edqgzlgwk1 Wkhuh duh qrw pdq| sdshuv dgguhvvlqj wkh fkrlfh ri wkh qxpehu ri vxe0fkdqqhov lq RIGP v|vwhpv/ dqg dw wkh wlph ri sxeolfdwlrq wkh fkrlfh kdg suhylrxvo| ehhq edvhg rqo| rq vlpxodwlrqv1 Lq dgglwlrq/ wkh lq xhqfh ri fkdqqho hvwlpdwlrq lv lqyhvwljdwhg dqg lw lv frqfoxghg wkdw wkh rswlpl}dwlrq fdq eh shuiruphg lqghshqghqw ri fkdqqho hvwlpdwlrq dqg rq d zruvw0fdvh dvvxpswlrq ri wkh Grssohu iuhtxhqf|1
6;
FKDSWHU 61 VXPPDU\ DQG FRQWULEXWLRQV
61516
Suh0Frpshqvdwlrq iru Ud|ohljk Idglqj Fkdqqhov lq Wlph Glylvlrq Gxsoh{ RIGP V|vwhpv
Wklv sdshu lqyhvwljdwhv wkh srvvlelolw| ri xvlqj suh0frpshqvdwlrq iru frpshq0 vdwlqj wkh lq xhqfh ri wkh Ud|ohljk idglqj fkdqqho lq d zluhohvv RIGP wlph glylvlrq gxsoh{ v|vwhp1 Wkuhh frpshqvdwlrq phwkrgv duh dqdo|}hg= 41 skdvh0rqo| frpshqvdwlrq 51 skdvh dqg dpsolwxgh frpshqvdwlrq xs wr d fhuwdlq srzhu ohyho/ deryh zklfk wkh dpsol hu lv vdwxudwhg 61 skdvh dqg dpsolwxgh frpshqvdwlrq xs wr d fhuwdlq srzhu ohyho/ deryh zklfk wkh dpsol hu lv vzlwfkhg r Wkh EHUv dqg lqfuhdvh lq shdn0wr0dyhudjh srzhu udwlrv duh fdofxodwhg iru wkh gl huhqw phwkrgv dvvxplqj shuihfw fkdqqho nqrzohgjh1 Wkh pd{lpxp eorfn ohqjwkv duh fdofxodwhg iru wkh skdvh frpshqvdwhg v|vwhp/ vlqfh wklv lv dvvxphg prvw dssursuldwh iru zluhohvv dssolfdwlrqv1 Lw lv frqfoxghg wkdw eorfn ohqjwkv pxfk orqjhu wkdq wkh rqh lq wkh GHFW v|vwhp fdq eh xvhg ehiruh wkh lqvwdq0 wdqhrxv shuirupdqfh jhwv zruvh wkdq wkdw ri d gl huhqwldo v|vwhp1 Wkh pdlq frqwulexwlrqv duh wkh ghulydwlrq ri wkh uhvxowlqj xqfrghg EHU iru wkh skdvh0rqo| frpshqvdwlrq phwkrg dqg wkh dqdo|vlv ri wkh lq xhqfh ri erwk wkh xsolqn eorfn ohqjwk dqg wkh grzqolqn eorfn ohqjwk/ uhvshfwlyho|1 Wkh fdofxodwlrqv duh shuiruphg erwk iru shuihfw nqrzohgjh ri wkh fkdqqho fruuhodwlrq ixqfwlrqv dqg xqghu fruuhodwlrq plvpdwfk1 Wkh pd{lpxp eorfn ohqjwk lv d yhu| lpsruwdqw ghvljq sdudphwhu lq wkh ghvljq ri suh0frpshqvdwhg wlph glylvlrq gxsoh{ v|vwhpv dqg wr p| nqrzohgjh qr dqdo|wlfdo dqdo|vlv ri lwv lq xhqfh rq wkh shuirupdqfh h{lvwv lq wkh olwhudwxuh1 Lq rwkhu sdshuv wkh fkdqqho lv dvvxphg wr eh frqvwdqw ru vlpxodwlrqv duh xvhg wr lqyhvwljdwh wkh lq xhqfh ri eorfn ohqjwk dqg Grssohu iuhtxhqf|1 Rwkhu frqwulexwlrqv lq wklv sdshu lqfoxgh wkh ghulydwlrq ri wkh xqfrghg EHU iru wkh wkuhh phwkrgv zkhq dvvxplqj shuihfw fkdqqho nqrzohgjh dqg wkh fruuhvsrqglqj lqfuhdvh lq shdn0wr0dyhudjh srzhu udwlr1
61517
Suhdpeoh0Edvhg Wlph dqg Iuhtxhqf| V|qfkurql}d0 wlrq iru RIGP V|vwhpv
Wklv sdshu frpsduhv wkh v|qfkurql}dwlrq shuirupdqfhv dfklhyhg e| wzr gli0 ihuhqw suhdpeohv dqg wzr gl huhqw v|qfkurql}hu vwuxfwxuhv1 Wkh suhdpeohv xqghu lqyhvwljdwlrq duh edvhg rq d uhshdwhg RIGP v|pero dqg d uhshdwhg SQ0vhtxhqfh/ uhvshfwlyho|1 Wkh lqyhvwljdwhg v|qfkurql}huv duh d frqyhqwlrqdo v|qfkurql}hu/ zkhuh pxowlsolfdwlrq lv shuiruphg rq d shu vdpsoh edvlv ehiruh vxppdwlrq/ dqg d suh0fruuhodwlqj v|qfkurql}hu/ zkhuh fruuhodwlrq lv shuiruphg zlwk wkh nqrzq vhtxhqfh sulru wr pxowlsolfdwlrq1 Lq wkh sdshu d orz0frpsoh{lw|
6151 SDSHU FRQWULEXWLRQV
6
ghfuhdvlqj wkh ghod| lqfuhdvhv wkh iuhtxhqf|0r vhw udqjh1 Wkh pd{lpxp iuhtxhqf| r vhw udqjh lv kdoi wkh RIGP edqgzlgwk/ zklfk vkrxog eh frpsduhg wr kdoi wkh vxe0fkdqqho edqgzlgwk iru frqyhqwlrqdo v|qfkurql}dwlrq edvhg rq wkh f|folf suh {1 Wkh dpsolwxgh ri wkh gl huhqwldo vljqdo/ ru d vxp ri wkhp/ lv wkh wlph v|qfkurql}dwlrq vljqdo dqg/ zkhq wkh fruuhfw wlplqj lv irxqg/ lwv
73
FKDSWHU 61 VXPPDU\ DQG FRQWULEXWLRQV
skdvh lv xvhg iru wkh iuhtxhqf|0r vhw hvwlpdwh1 Lq wkh sdshu/ wkh glvwulexwlrq ri wkh v|qfkurql}dwlrq vljqdo lv ghulyhg iru DZJQ fkdqqhov/ dqg yhul hg e| vlpxodwlrqv1 Wkh suhvhqwhg v|qfkurql}hu vwuxfwxuh lv ri orz frpsoh{lw| dqg lw lv vkrzq wkdw wkh suhvhqwhg phwkrg zrunv zhoo dovr dw orz VQUv1 Wkh srzhu ri wkh slorw vhtxhqfh fdq eh dgmxvwhg wr wkh vshfl f uhtxluhphqwv/ exw lw fdq lq jhqhudo eh orz gxh wr vxssuhvvlrq ri qrlvh dqg gdwd zkhq shuiruplqj wkh fruuhodwlrq1 Wkh pdlq frqwulexwlrqv lqfoxgh wkh lqwurgxfwlrq ri vxshulpsrvhg slorw vh0 txhqfhv iru v|qfkurql}dwlrq sxusrvhv lq RIGP v|vwhpv1 Wkh sursrvhg phwkrg lv lqghshqghqw ri wkh f|folf suh { dqg lv yhu| h{leoh1 Wr p| nqrzohgjh/ wkh ghulydwlrq ri wkh glvwulexwlrq ixqfwlrqv ri wkh wlph v|qfkurql}dwlrq vljqdo lv dovr qhz/ hyhq wkrxjk vlplodu v|qfkurql}dwlrq vwuxfwxuhv fdq eh xvhg lq FGPD v|vwhpv1 Dqrwkhu frqwulexwlrq lq wkh sdshu lv wkh jhqhudol}dwlrq ri rwkhu v|q0 fkurql}dwlrq phwkrgv vxfk wkdw wkh dqdo|vlv fdq eh dssolhg wr wkhvh dv zhoo1
61519
Fkdqqho Hvwlpdwlrq xvlqj Vxshulpsrvhg Slorw Vh0 txhqfhv
Lq wklv sdshu/ vxshulpsrvhg slorw vhtxhqfhv duh lqwurgxfhg iru wkh sxusrvh ri fkdqqho hvwlpdwlrq1 Wkh v|vwhp dqg uhfhlyhu vwuxfwxuh duh wkrurxjko| gh0 vfulehg1 Wkh pdlq lghd lv wr olqhduo| dgg d nqrzq slorw vhtxhqfh wr wkh wudqv0 plwwhg gdwd vhtxhqfh dqg shuirup mrlqw fkdqqho hvwlpdwlrq dqg ghwhfwlrq lq wkh uhfhlyhu1 Wkh ghwhfwlrq phwkrg lv edvhg rq k|srwkhvhv ri wkh wudqvplwwhg gdwd vhtxhqfh dqg iru hdfk k|srwkhvlv/ d fkdqqho hvwlpdwh lv ghulyhg e| phdqv ri shu0vxuylyru surfhvvlqj1 Wkh qdo ghflvlrq lv pdgh lq idyru ri wkh vhtxhqfh zlwk wkh orzhvw glvwdqfh wr wkh uhfhlyhg vhtxhqfh1 Wkh sursrvhg v|vwhp lv dqdo|}hg dqdo|wlfdoo| iru dw Ud|ohljk idglqj fkdqqhov1 Wkh sdluzlvh huuru suredelolw| lv ghulyhg dv zhoo dv dssur{lpdwlrqv ri wkh EHU1 Wkh shuirupdqfh ri wkh v|vwhp lv yhul hg e| vlpxodwlrqv dqg wkh lq xhqfhv ri gl huhqw sdudphwhuv vxfk dv slorw srzhu/ owhu frh!flhqwv dqg owhu ohqjwkv duh lqyhvwljdwhg1 Lw lv vkrzq wkdw wkh whfkqltxh lv urexvw> lw zrunv zhoo iru d zlgh udqjh ri VQU ydoxhv dqg dovr iru kljk Grssohu iuhtxhqflhv1 Wkh vxshulpsrvhg slorw vhtxhqfhv duh wudqvplwwhg lq wkh vdph edqg dv wkh gdwd v|perov dqg/ dv rssrvhg wr frqyhqwlrqdo slorw0edvhg fkdqqho hvwlpdwlrq whfkqltxhv/ wkhuh lv qr edqgzlgwk h{sdqvlrq1 Wkh srzhu ri wkh slorw vhtxhqfh fdq eh txlwh orz1 W|slfdoo| 8( ri wkh wrwdo srzhu lv hqrxjk1 Wkh whfkqltxh fdq eh xvhg erwk lq h{lvwlqj dqg qhz v|vwhpv dqg lw uhvxowv lq ehwwhu srzhu h!flhqf| wkdq frqyhqwlrqdo slorw v|pero dvvlvwhg prgxodwlrq/ hvshfldoo| lq idvw idglqj hqylurqphqwv1 Wkh pdlq frqwulexwlrqv duh wkh lqwurgxfwlrq ri fkdqqho hvwlpdwlrq edvhg rq vxshulpsrvhg slorw vhtxhqfhv dqg wkh fruuhvsrqglqj ghulydwlrq ri wkh rswlpdo uhfhlyhu1 Wkh uhfhlyhu uholhv rq mrlqw ghwhfwlrq dqg fkdqqho hvwlpdwlrq dqg erwk dq rswlpdo phwulf dqg d phwulf vxlwdeoh iru d uhfxuvlyh uhfhlyhu vwuxfwxuh duh ghulyhg1 Wkh dqdo|vlv ri wkh v|vwhp lv dovr qhz/ hyhq wkrxjk vlplodu dqdo|vhv fdq eh irxqg iru wuhoolv0frghg prgxodwlrq1 Ilqdoo|/ wkh v|vwhp lv yhul hg e|
6161 FRQFOXVLRQV DQG GLVFXVVLRQ
74
h{whqvlyh vlpxodwlrqv dqg wkh lq xhqfh ri owhu ohqjwkv/ qrq0rswlpdo owhuv/ slorw0wr0gdwd srzhu udwlr/ dqg Grssohu iuhtxhqf| kdyh ehhq lqyhvwljdwhg1
6151:
D Frpsdudwlyh Dqdo|vlv ehwzhhq Gl huhqw Ghwhf0 wlrq Vfkhphv lq Iodw Ud|ohljk0idglqj Fkdqqhov
Wklv sdshu frqwdlqv d frpsdulvrq ehwzhhq gl huhqw frkhuhqw dqg qrq0frkhuhqw ghwhfwlrq phwkrgv1 Wkh dqdo|vlv lv edvhg rq fdofxodwlrq ri wkh sdluzlvh vh0 txhqfh huuru suredelolw| dqg d frpprq iudphzrun lv xvhg iru wkh dqdo|vlv ri doo wkh lqyhvwljdwhg phwkrgv1 Wkh dqdo|}hg phwkrgv lqfoxgh= slorw v|pero dvvlvwhg prgxodwlrq +SVDP,/ pxowlsoh0v|pero gl huhqwldo ghwhfwlrq/ vxshulp0 srvhg slorw vhtxhqfhv/ gl huhqwldo ghwhfwlrq/ dqg d qryho k|eulg phwkrg/ vlplodu wr SVDP/ zklfk xvhv erwk slorw v|perov dqg k|srwkhvhv ri wkh gdwd v|perov iru fkdqqho hvwlpdwlrq1 Lq wkh sdshu/ lw lv vkrzq wkdw wkh ghflvlrq yduldeoh iru doo phwkrgv fdq eh zulwwhq lq d txdgudwlf irup ri Jdxvvldq yduldeohv/ iru zklfk wkh suredelolw| ghqvlw| ixqfwlrq lv ghulyhg1 Wkh sdluzlvh huuru suredelolw| lv frpsduhg iru wkh huuru vhtxhqfhv grplqdwlqj wkh huuru udwh1 Wkh shuirupdqfh lv dqdo|}hg iru gl huhqw VQU dqg Grssohu ydoxhv dqg lw lv frqfoxghg wkdw vxshu0 lpsrvhg slorw vhtxhqfhv/ pxowlsoh0v|pero gl huhqwldo ghwhfwlrq dqg wkh k|eulg phwkrg ohdg wr urexvw ghwhfwlrq erwk iru d zlgh udqjh ri VQUv dqg iru kljk Grssohu iuhtxhqflhv1 Frqyhqwlrqdo gl huhqwldo ghwhfwlrq vkrzv d shuirupdqfh orvv gxh wr wkh odfn ri qrlvh dyhudjlqj zkhq xvlqj wkh suhylrxvo| uhfhlyhg v|pero dv d uhihuhqfh iru ghwhfwlrq1 Wrjhwkhu zlwk SVDP wklv phwkrg dovr vx hu iurp dq huuru rru iru kljk Grssohu ydoxhv gxh wr lqdffxudwh fkdqqho hvwlpdwhv1 Wkh pdlq frqwulexwlrq lq wkh sdshu lv wkh lqwurgxfwlrq ri wkh frpprq iudphzrun xvhg iru wkh dqdo|vlv ri wkh gl huhqw frkhuhqw dqg qrq0frkhuhqw ghwhfwlrq phwkrgv1 Wklv frpprq iudphzrun lv xvhg wr qg wkh vhtxhqfhv grplqdwlqj wkh huuru udwh dqg dovr wr lqyhvwljdwh wkh lq xhqfh ri gl huhqw qrlvh ohyhov dqg gl huhqw Grssohu iuhtxhqflhv1 Wkh suhvhqwhg dqdo|vlv lv jhqhudo dqg fdq eh dssolhg wr rwkhu ghwhfwlrq phwkrgv dv zhoo1
616
Frqfoxvlrqv dqg Glvfxvvlrq
Zkloh ehlqj dw wkh ghsduwphqw/ L kdyh kdg wkh rssruwxqlw| wr iroorz wkh gh0 yhorsphqw ri zluhohvv whfkqltxhv dqg vwdqgdugv iru vrph |hduv1 Lq wkh wkhvlv L kdyh suhvhqwhg uhvhdufk uhvxowv wkdw L kdyh surgxfhg gxulqj wkh odvw irxu |hduv1 Wkh txhvwlrq lv qrz zkdw zloo kdsshq qh{wB Khuh L zloo jlyh vrph vkruw shuvrqdo ylhzv/ exw dv dozd|v zkhq uhjduglqj wkh ixwxuh/ wkh| duh rqo| jxhvvhv1 Li zh vwduw dw d kljk ohyho/ wkhuh duh vrph fhuwdlq hyhqwv wkdw zloo fkdqjh wkh dydlodelolw| ri dffhvv wr idvw zluhohvv ru preloh frppxqlfdwlrq1 Gxulqj 5334/ wkh uvw wklug0jhqhudwlrq v|vwhpv edvhg rq zlghedqg0FGPD zloo eh rq wkh pdunhw1 Dw wkh vdph wlph wkhuh zloo eh odujh lqyhvwphqwv wr xsjudgh wkh h{lvwlqj vhfrqg0jhqhudwlrq v|vwhpv vr wkdw wkhvh dovr fdq r hu kljkhu gdwd
75
FKDSWHU 61 VXPPDU\ DQG FRQWULEXWLRQV
udwhv dqg sdfnhw edvhg frppxqlfdwlrq1 Wklv phdqv wkdw gdwd udwhv ri xs wr 6;7 nelw2v fdq eh r huhg ryhu zlgh duhdv1 Lq d ihz |hduv wkh qhz Z0ODQ v|vwhpv zloo dovr eh rq wkh pdunhw1 Wkhvh v|vwhpv zloo zrun lq xqolfhqvhg iuhtxhqf| edqgv dqg r hu gdwd udwhv ri durxqg 53 Pelw2v/ exw zlwk d olplwhg fryhudjh1 Ilqdoo|/ wkh uvw frpphufldo Eoxhwrrwk ghylfhv zloo eh odxqfkhg vrrq1 Wklv phdqv wkdw vkruw glvwdqfh zluhohvv frppxqlfdwlrq zlwk gdwd udwhv ri xs wr durxqg :33 nelw2v lv vrrq dydlodeoh iru d zlgh udqjh ri hohfwurqlf ghylfhv1 L wklqn wkdw wkh lpsruwdqfh ri wkh odwwhu wzr v|vwhpv fdq qrw eh ryhuhv0 wlpdwhg1 Wkhvh v|vwhpv zloo r hu idvw zluhohvv frppxqlfdwlrq iru iuhh dqg fdq eh xvhg dv fkhds olqnv ehwzhhq dq| hohfwurqlf ghylfh dqg wkh dffhvv srlqw1 Wklv phdqv wkdw lw lv srvvleoh iru orz0frvw ghylfhv wr kdyh dffhvv wr idvw dqg dgydqfhg frppxqlfdwlrq olqnv zkhuh wkh preloh whuplqdo dfwv pruh olnh d uhod| vwdwlrq1 Suredeo| wkhuh zloo eh d zlgh udqjh ri orz0frvw wklug sduw| surgxfwv r hulqj qhz vhuylfhv xvlqj lqgluhfw dffhvv wr wkh h{lvwlqj qhwzrun1 L dovr wklqn wkdw wkh Z0ODQ v|vwhpv zloo kdyh d yhu| lpsruwdqw uroh lq wkh qhdu ixwxuh1 H{fhsw iru fryhudjh dqg pd|eh prelolw|/ wkhvh v|vwhpv duh dfwxdoo| ixo oolqj doo wkh uhtxluhphqwv vwdwhg e| vrph ri wkh ohdglqj dfwruv lq wkh duhd iru d irxuwk jhqhudwlrq v|vwhp1 Wklv phdqv wkdw |rx fdq dfklhyh gdwd udwhv kljk hqrxjk erwk iru ylghr dqg kljk0txdolw| dxglr dssolfdwlrqv1 Lw lv dovr srvvleoh wr eh |rxu rzq rshudwru dqg r hu eurdgedqg vhuylfhv lq dq r!fh ru d uhvlghqwldo duhd iuhh ri fkdujh1 Ixuwkhu/ |rx fdq vhw xs |rxu rzq shuvrqdo duhd qhwzrun zkhuh hohfwurqlf ghylfhv lq |rxu krph fdq frppxqlfdwh zlwk hdfk rwkhu1 Krshixoo| wkhvh v|vwhpv zloo eh xvhu0iulhqgo| hqrxjk qrw wr suhyhqw wkhlu xvdjh1 Wkh xvh ri wkh xqolfhqvhg edqgv lv yhu| lpsruwdqw vlqfh wklv phdqv wkdw lq |rxu rzq v|vwhp wkhuh zloo eh qr uhoxfwdqfh xvlqj lw gxh wr kljk wudqvplvvlrq ihhv1 Lq wklv vfhqdulr wkhuh lv qr fhoo sodqqlqj dqg wkh lqwhuihuhqfh ohyho zloo vrph0 wlphv eh kljk1 Wkh kljk wudqvplvvlrq udwhv phdqv wkdw/ lq rughu wr olplw wkh wudqvplwwhg srzhu wr dssursuldwh ohyhov/ wkh hqhuj| shu elw zloo eh ghfuhdvhg frpsduhg wr wrgd|*v v|vwhpv1 Wkhuhiruh/ wkh v|vwhpv qhhg wr eh deoh wr dgdsw wkh wudqvplvvlrq wr wkh suhvhqw vlwxdwlrq dqg rshudwh lq kljko| glvwxuehg hq0 ylurqphqwv1 Idvw dqg uholdeoh v|qfkurql}dwlrq dqg fkdqqho hvwlpdwlrq duh lp0 sruwdqw lq rughu wr suhyhqw wkh v|vwhpv iurp ehlqj olplwhg e| wkhvh ixqfwlrqv/ udwkhu wkdq e| qrlvh ru lqwhuihuhqfh1 Pd|eh wkh prvw lpsruwdqw wklqj wkdw L kdyh ohduqhg gxulqj wkhvh |hduv lv wkdw zluhohvv frppxqlfdwlrq v|vwhpv duh frpsoh{ v|vwhpv dqg wkh wuxh fkdo0 ohqjh lv wr rswlpl}h wkh v|vwhp dqg jhw hyhu|wklqj wr zrun wrjhwkhu1 Lw lv qr xvh wr rqo| lpsuryh fhuwdlq sduwv dv orqj dv wkh uhvw ri wkh v|vwhp fdq qrw pdnh xvh ri wkhvh lpsuryhphqwv1 Wr ph lw vhhpv wkdw lq wkh kljko| rswlpl}hg v|vwhpv wkh gl huhqw ixqfwlrqdo eorfnv ehfrph pruh ghshqghqw rq hdfk rwkhu/ wkh lqirupdwlrq h{fkdqjh ehwzhhq wkh eorfnv kdv ehfrph pruh lpsruwdqw1 Wkh fkdqqho hvwlpdwru/ iru h{dpsoh/ kdv qrw rqo| wr gholyhu fkdqqho hvwlpdwhv wr wkh htxdol}hu/ exw dovr wr wkh ghfrghu vxfk wkdw wkh ghfrglqj fdq eh rswlpl}hg> dqg pd|eh wr wkh wudqvplwwhu vxfk wkdw wkh wudqvplwwhg vljqdo fdq eh dgmxvwhg
6161 FRQFOXVLRQV DQG GLVFXVVLRQ
76
wr wkh vshfl f fkdqqho1 Lq rughu wr fkdoohqjh wrgd|*v olplwv wkh uhfhlyhu kdv wr lqfrusrudwh pruh dqg pruh ri wkh dydlodeoh lqirupdwlrq/ riwhq wr wkh sulfh ri lqfuhdvhg frpsoh{lw|1 Wkhuh lv dovr d txhvwlrq zkhwkhu wklv lqfuhdvh lq frp0 soh{lw| fdq eh d rughg dqg krz odujh wkh uhvxowlqj jdlq lv1 Dv dozd|v/ lw lv d txhvwlrq ri frvw yv1 shuirupdqfh1 Lq rughu wr ixo oo wkh uhtxluhphqwv rq v|qfkurql}dwlrq dqg fkdqqho hvwlpd0 wlrq L wklqn wkdw lw lv zhoo zruwk vshqglqj d ihz shufhqw ri wkh wudqvplwwhg srzhu dqg edqgzlgwk rq nqrzq slorw v|perov1 Wkh slorw v|perov phdq wkdw idvwhu dqg ohvv frpsoh{ dojrulwkpv fdq eh xvhg/ riwhq uhvxowlqj lq pruh urexvw ghwhfwlrq dqg ehwwhu shuirupdqfh1 Wkh orvv fdxvhg e| wkh slorw v|perov lv riwhq vpdoo frpsduhg wr wkh jdlq wkdw fdq eh dfklhyhg/ vr slorw v|perov duh jhqhudoo| d jrrg lqyhvwphqw Lq RIGP v|vwhpv lw lv uhdoo| lpsruwdqw wr olplw wkh lq xhqfh ri wkh iuh0 txhqf| r vhw1 Wklv h hfw riwhq uhvxowv lq xqghvludeoh frqvwudlqwv lq wkh v|vwhp ghvljq/ hvshfldoo| zkhq xvlqj orz frvw whuplqdov zkhuh/ lq jhqhudo/ wkh dffxudf| ri wkh rvfloodwruv lv orz1 Wkhuhiruh/ L wklqn wkdw lw lv lpsruwdqw wr orrn iru idvw dqg urexvw hvwlpdwlrq whfkqltxhv dv zhoo dv fkhds dqg dffxudwh rvfloodwruv1 Lq rughu wr jhw h!flhqw v|vwhpv lw lv lpsruwdqw wkdw wkh shuirupdqfh lv qrw olp0 lwhg e| kdugzduh lpsdluphqwv/ exw udwkhu e| wkh fkdudfwhulvwlfv ri wkh sk|vlfdo fkdqqho ru e| lqwhuihuhqfh iurp rwkhu xvhuv1 Uhjduglqj ixwxuh zrun rq wkh pdwhuldo suhvhqwhg lq wklv wkhvlv/ L wklqn wkdw wkh sdshu rq suh0frpshqvdwlrq udwkhu hdvlo| fdq eh h{whqghg wr dffrxqw iru dq0 whqqd glyhuvlw| dv zhoo1 Wklv pdnhv wkh sdshu pruh frpsohwh e| dovr fryhulqj v|vwhpv vlplodu wr wkh dqwhqqd suh0frpshqvdwlrq v|vwhp lq wkh XPWV2Z0 FGPD v|vwhp1 Wkh suhdpeoh0v|qfkurql}dwlrq sdshu fdq eh h{whqghg wr lq0 foxgh suhdpeoh0edvhg fkdqqho hvwlpdwlrq1 Lq lwv suhvhqw irup/ wkh irfxv lv rq dftxlvlwlrq ri wlph dqg iuhtxhqf| v|qfkurql}dwlrq sdudphwhuv rqo|1 Lq sdfnhw edvhg v|vwhpv wkhuh duh/ krzhyhu/ vrph lqlwldo wudqvlhqwv zkhq d sdfnhw duulyhv dqg lw lv qrw phdqlqjixo wr pdnh d qdo fkdqqho hvwlpdwh ehiruh uhdfklqj vrph nlqg ri vwhdg| vwdwh1 Dq|zd|/ wkh uhtxluhg lqirupdwlrq lv wkhuh/ diwhu fruuh0 odwlrq wkh fkdqqho lpsxovh uhvsrqvh lv dydlodeoh dv d frduvh fkdqqho hvwlpdwh1 Wkh xvh ri vxshulpsrvhg slorw vhtxhqfhv lv dovr zruwk ixuwkhu lqyhvwljdwlrqv1 Iluvw ri doo/ lw zrxog eh lqwhuhvwlqj wr orrn dw ohvv frpsoh{ uhfhlyhu vwuxfwxuhv1 Wkh whfkqltxh vhhpv surplvlqj/ hvshfldoo| iru idvw idglqj fkdqqhov/ exw wkh frpsoh{lw| lv vwloo wrr kljk1 Lw zrxog eh yhu| lqwhuhvwlqj wr frpelqh v|qfkur0 ql}dwlrq dqg fkdqqho hvwlpdwlrq wr dfwxdoo| jhw d zrunlqj v|vwhp vxlwdeoh iru lpsohphqwdwlrq1
77
FKDSWHU 61 VXPPDU\ DQG FRQWULEXWLRQV
Eleolrjudsk| ^4` ;35144e04q
Qv [
[email protected]
q "55>q=
+43,
Dvvxplqj wkdw doo hljhqydoxhv duh glvwlqfw/ wkh suredelolw| ghqvlw| ixqfwlrq ri a fdq eh fdofxodwhg dv ^45` ; p S +q ,Qv 5 h|@+5q , A % & A |3 A Q A Tv A q @4 5 + , ? q n n@4>n9@q +44, ia +|, @ Qv S A + q ,Qv 5 h|@+5q&, A % | ? 3= A Qv A A =
[email protected] 5 T +n q , n@4>n9@q
Wkh sdluzlvh huuru suredelolw|/ l1h1 wkh suredelolw| wkdw wkh ghflvlrq yduldeoh ehfrphv qhjdwlyh vr wkdw wkh uhfhlyhu pdnhv d ghflvlrq lq idyru ri wkh huurqhrxv k|srwkhvlv v lqvwhdg ri wkh fruuhfw rqh/ lv wkhq jlyhq e| Sv @
7
+q ,Qv 4 = Q Tv
[email protected] +n q , n@4>n9@q Qv [
+45,
Frpsdulvrq edvhg rq Huuru Hyhqwv
Wkh dqdo|vlv wrrov surylghg lq wkh suhylrxv vhfwlrq fdq eh xvhg wr ghwhuplqh ds0 sur{lpdwh elw0 dqg iudph0huuru udwhv iru wkh ydulrxv ghwhfwlrqv phwkrgv1 Krz0 hyhu/ khuh zh rqo| vwxg| wkh sdluzlvh huuru suredelolwlhv +45, iru vrph vhohfwhg huuru hyhqwv1 Wklv zloo uhyhdo vrph ri wkh lqkhuhqw vwuhqjwkv dqg zhdnqhvvhv ri wkh gl huhqw ghwhfwlrq phwkrgv1
;
D FRPSDUDWLYH DQDO\VLV
Iluvw zh h{hpsoli| wkh suredelolw| ri huuru hyhqwv ri gl huhqw ohqjwkv lq d eorfn0idglqj Ud|ohljk fkdqqho +iG Wv @ 3,1 Wklv vkrzv wkh dpeljxlw| ri dq0 wlsrgdo vhtxhqfhv iru vxshusrvhg slorwv lq frkhuhqw v|vwhpv dqg wkh lq xhqfh ri d phpru| lq wkh ghwhfwru iru gl huhqwldo v|vwhpv1 Vhfrqgo|/ zh h{hpsoli| wkh urexvwqhvv ri wkhvh phwkrgv djdlqvw yduldwlrqv lq dyhudjh VQU dqg Grssohu h hfwv1 Wklv vlqjohv rxw wkh srru shuirupdqfh ri SVDP dqg gl huhqwldo gh0 whfwlrq dw odujh Grssohu vsuhdgv dqg kljk VQUv/ zkhq frpsduhg wr wkh rwkhu phwkrgv1 Zh lqyhvwljdwh sdluzlvh huuru suredelolwlhv iru uxqv ri n frqvhfxwlyh wuhoolv vwdjhv xvlqj ESVN1 Wkh eorfnv duh ri ohqjwk Q @ 84> zklfk lv dvvxphg wr eh orqj hqrxjk wr dssur{lpdwh wkh vwhdg| vwdwh ehkdylru/ dqg wkh fkdqqho hvwlpdwlrq owhu ohqjwkv duh O @ 81 Wkh n vwdjhv ri ghyldwlrq iurp wkh }hur0 sdwk ri wkh wuhoolv duh sodfhg lq wkh plggoh ri wkh eorfn dqg zh kdyh wzr nlqgv ri lqwhuhvwlqj huuru hyhqwv= huuru vhtxhqfhv zkhuh n lv vpdoo vr wkdw wkh huurqhrxv vhtxhqfh phujhv zlwk wkh fruuhfw vhtxhqfh diwhu n v|perov dqg huuru vhtxhqfhv zkhuh wkh odvw +kdoi, sduw lv huurqhrxv1 Wkh odwwhu uhsuhvhqwv d vlqjoh v|pero huuru diwhu gl huhqwldo ghwhfwlrq1 Zh vhsdudwh wkh frkhuhqw dqg gl huhqwldo vfkhphv lq wkh h{dpsohv1 Iru wkh frkhuhqw phwkrgv hyhu| ghyldwlrq iurp wkh wuxh vhtxhqfh zloo uhvxow lq d v|pero huuru1 Iru wkh gl huhqwldo phwkrgv rqo| wkh wudqvlwlrqv ehwzhhq wkh fruuhfw dqg huurqhrxv vhtxhqfh fdxvh v|pero huuruv diwhu gl huhqwldo ghfrglqj1 Wklv phdqv wkdw dq huuru hyhqw ri n frqvhfxwlyh huuruv rqo| surgxfhv wzr qdo v|pero huuruv1 Lq Ilj1 5 zh looxvwudwh wkh sdluzlvh huuru suredelolw| iru huuru hyhqwv ri ohqjwk 4/ 5/ 6/ 7/ dqg 59 +orqj, lq d eorfn0idglqj Ud|ohljk fkdqqho dqg dq He @Q3 ri 43 gE4 1 Zh kdyh 8( slorw hqhuj| iru wkh vxshusrvhg slorw vfkhph dqg hyhu| 43wk v|pero dv d slorw v|pero lq wkh rwkhu wzr frkhuhqw vfkhphv1 Wkh vfkhphv vkrz udwkhu vlplodu ehkdylru iru vkruw hyhqwv/ exw vhsdudwh iru orqj hyhqwv1 Wkh srruhu shuirupdqfh ri wkh VSS dqg k|eulg vfkhphv iru orqj huuru hyhqwv lv h{sodlqhg e| wkh lqkhuhqw dpeljxlw| ri dqwlsrgdo vhtxhqfhv vlqfh wkhuh lv d srvvlelolw| wkdw wkh zurqj k|srwkhvlv lv xvhg iru fkdqqho hvwlpdwlrq1 Iru wkh PVGG vfkhph/ wkhuh duh rqo| wzr v|pero huuruv iru vkruw huuru hyhqwv dqg rqh v|pero huuru iru wkh orqj hyhqw1 Dq lqwhuhvwlqj ehkdylru iru wklv vfkhph lv wkdw wzr v|pero huuruv forvh wr hdfk rwkhu kdyh d kljkhu suredelolw| wkdq wzr elw huuruv vhsdudwhg iurp hdfk rwkhu1 Wklv lv gxh wr wkh phpru| ri wkh PVGG/ zkhuh wkh qhjdwlyh lq xhqfh ri hduolhu v|pero huuruv ghfuhdvhv zlwk wlph1 Lq Ilj1 6 zh suhvhqw wkh sdluzlvh huuru suredelolw| ri hyhqwv fdxvlqj d vlqjoh elw huuru lq wkh wudqvplvvlrq eorfn1 Iru wkh frkhuhqw phwkrgv wklv fruuhvsrqgv wr dq huuru hyhqw ri ohqjwk rqh/ zkloh iru wkh gl huhqwldo vfkhphv lw lv wkh htxly0 dohqw ri d orqj huuru hyhqw1 Dprqj wkh frkhuhqw vfkhphv lq Ilj1 6 +wrs,/ wkh gl huhqfh lv uhodwlyho| vpdoo iru wkh eorfn idglqj fkdqqho +ig Wv @ 3,1 Krzhyhu/ zkhq wkh Grssohu iuhtxhqf| lqfuhdvhv +ig Wv @ 3=38,/ wkh olplwdwlrq ri SVDP 4 Lq wkh ruljlqdo sxeolfdwlrq d fxuyh iru frqyhqwlrqdo gl huhqwldo ghwhfwlrq zdv dovr suh0 vhqwhg1 Lq wklv uhylvhg yhuvlrq wkh fxuyh lv rplwwhg dqg wkh wh{w kdv ehhq fkdqjhg dffruglqjo|1
D FRPSDUDWLYH DQDO\VLV
