• Aucun résultat trouvé

Egalisation Autodidacte Adaptative : Application aux Systèmes d'Accès à Répartition dans le temps

N/A
N/A
Protected

Academic year: 2022

Partager "Egalisation Autodidacte Adaptative : Application aux Systèmes d'Accès à Répartition dans le temps"

Copied!
6
0
0

Texte intégral

(1)

HAL Id: hal-02147870

https://hal.archives-ouvertes.fr/hal-02147870

Submitted on 11 Jun 2021

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Egalisation Autodidacte Adaptative : Application aux Systèmes d’Accès à Répartition dans le temps

Joël Labat, Christophe Laot

To cite this version:

Joël Labat, Christophe Laot. Egalisation Autodidacte Adaptative : Application aux Systèmes d’Accès à Répartition dans le temps. GRETSI’99 Symposium, Sep 1999, Vannes, France. pp.1081 - 1084. �hal- 02147870�

(2)

(JDOLVDWLRQ$XWRGLGDFWH$GDSWDWLYH$SSOLFDWLRQDX[6\VWqPHV G$FFqV0XOWLSOHVj5pSDUWLWLRQGDQVOH7HPSV

-RsO/$%$7HW&KULVWRSKH/$27

*(7(167%UHWDJQH%3%UHVW&pGH[)UDQFH (PDLOMRHOODEDW#HQVWEUHWDJQHIUFKULVWRSKHODRW#HQVWEUHWDJQHIU

5pVXPp/pJDOLVDWLRQDGDSWDWLYHDXWRGLGDFWHRXHQWUDvQpHQpFHVVLWHHQJpQpUDOXQWHPSVGHFRQYHUJHQFHTXLVDFFRPRGHPDOGHVV\VWqPHV GDFFqVPXOWLSOHVjUpSDUWLWLRQGDQVOHWHPSV$057V\VWqPHVGDQVOHVTXHOVODWUDQVPLVVLRQVHIIHFWXHHQPRGHSDTXHWV3DUDLOOHXUVOH QRPEUH GDSSOLFDWLRQV XWLOLVDQW FH W\SH GDFFqV QH FHVVH GH FURvWUH 'H FH SRLQW GH YXH LO SDUDvW RSSRUWXQ GH UpIOpFKLU j GHV VROXWLRQV SHUPHWWDQWjXQpJDOLVHXUGHFRQYHUJHUVXUGHVSDTXHWVRXEORFVFRXUWVFRPSRUWDQWTXHOTXHVGL]DLQHVGHV\PEROHV3DUPLOHVDSSOLFDWLRQV YLVpHVRQSHXWFLWHUGHPDQLqUHQRQH[KDXVWLYHOH*60OH'(&7HWF'DQVFKDFXQGHFHVV\VWqPHVOHEORFFRPSRUWHXQHVpTXHQFHFRQQXH GRQWODORQJXHXUVDYqUHJpQpUDOHPHQWLQVXIILVDQWHSRXUSHUPHWWUHODFRQYHUJHQFHGXQpJDOLVHXUDGDSWDWLIHQWUDvQp$XWUDYHUVGHFHWDUWLFOH QRXVDOORQVPRQWUHUTXHOpJDOLVHXUDXWRGLGDFWHDGDSWDWLIUpFHPPHQWLQWURGXLWSDU/DEDWHWDOSHXWVDFFRPRGHUGHFHWWHFRQWUDLQWHDYHFXQH FRPSOH[LWpUDLVRQQDEOH

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

SURSRVHGE\/DEDWHWDOFDQWDNHXSWKLVFKDOOHQJHDWWKHSULFHRIDUHDVRQDEOHFRPSOH[LW\

,QWURGXFWLRQ

/pJDOLVHXUUHWHQXGDQVFHWDUWLFOHDpWpUpFHPPHQWSURSRVp GDQV >@ >@ HW GpYHORSSp GDQV >@ 6D FDUDFWpULVWLTXH IRQGDPHQWDOH HVW VRQ DGDSWDWLYLWp VWUXFWXUHOOH HW DOJRULWKPLTXH &HWWH SURSULpWp PqQH j GHV SHUIRUPDQFHV UHPDUTXDEOHV j OD IRLV VXU OH SODQ GH OD YLWHVVH GH FRQYHUJHQFH HW VXU FHOXL GH OHUUHXU TXDGUDWLTXH PR\HQQH (40 (Q SpULRGH GH SRXUVXLWH VHV SHUIRUPDQFHV VRQW SUpFLVpPHQWFHOOHVGHOpJDOLVHXUjUHWRXUGHGpFLVLRQ(5' FRQYHQWLRQQHO 'DQV VRQ PRGH GH FRQYHUJHQFH OH QRXYHO pJDOLVHXUjUHWRXUGHGpFLVLRQVDXWRGLGDFWH(5'$pOpPHQW GHEDVHGHQRWUHFRQWULEXWLRQHVWOLQpDLUHHWUpFXUVLIHWSHXW rWUH YX SRXU OHVVHQWLHO FRPPH OD FDVFDGH GXQ ILOWUH EODQFKLVVDQWSXUHPHQWUpFXUVLIGXQILOWUHWUDQVYHUVHHWGXQ JDLQ FRPSOH[H DVVXUDQW OD GRXEOH IRQFWLRQ GH FRQWU{OH GH JDLQ HW GH FRUUHFWLRQ GH SKDVH >@ (Q PRGH GH SRXUVXLWH O(5'$ VH FRQILJXUH HQ XQ pJDOLVHXU j UHWRXU GH GpFLVLRQ FRQYHQWLRQQHO/DWUDQVLWLRQDXWRPDWLTXHGHOXQHjODXWUHGH FHVGHX[FRQILJXUDWLRQVVHIDLWVXUODFRPSDUDLVRQjXQVHXLO DSSURSULp GXQ VLJQDO pODERUp HQ OLJQH WHO TXH OHUUHXU TXDGUDWLTXHPR\HQQHHVWLPpHOHNXUWRVLVGXVLJQDOGHVRUWLH RXHQFRUHOHUUHXUDXVHQVGH*RGDUG>@GH6KWURPHW)DQ

>@HWF$LQVLjFKDTXHIRLVTXHFHODHVWSRVVLEOHFHVWjGLUH W\SLTXHPHQWGDQVOHFDVGXQUDSSRUWVLJQDOjEUXLWVXIILVDQW OpJDOLVHXUVHFRQILJXUHHQPRGH(5'(QUHYDQFKHGqVTXH OH FDQDO VXELW XQH PRGLILFDWLRQ EUXWDOH GpVDGDSWDQW VpYqUHPHQW OpJDOLVHXU O(5'$ GpWHFWH FH FKDQJHPHQW HW PRGLILH DORUV VD FRQILJXUDWLRQ FHVWjGLUH j OD IRLV VD VWUXFWXUH HW VHV FULWqUHV GRSWLPDOLWp 4XDQW j OpJDOLVHXU HQWUDvQp (5'( LO HVW FODLU TXH VXU GHV FDQDX[ QRQ VWDWLRQQDLUHVHWSRXUGHVV\VWqPHVjIORWFRQWLQXGHGRQQpHV

VRQXWLOLVDWLRQSUpVHQWHGHVULVTXHVPDMHXUVGpYROXWLRQYHUV GHVSRLQWVGpTXLOLEUHVSDWKRORJLTXHV

1RXVDYRQVHQHIIHWH[DPLQpHWWHVWpDYHFVXFFqVO(5'$VXU GHVILFKLHUVGHVLJQDX[UpHOVGHFRPPXQLFDWLRQVDFRXVWLTXHV VRXVPDULQHV$60HQUHJLVWUpVSDUOH*(60$'*$DORUV TXH OH VRQGHXU GX QDYLUH pWDLW HQ URXWH VRQGHXU GRQW OH VSHFWUHpWDLWSUpFLVpPHQWLQFOXVGDQVFHOXLGXVLJQDOpPLV,O HVWIUDSSDQWGHFRQVWDWHUTXHO(5'(GLYHUJHUpJXOLqUHPHQW GH IDoRQ LUUpPpGLDEOH WDQGLV TXH O(5'$ DX SUL[ GXQH PRGLILFDWLRQ GH FRQILJXUDWLRQ VHQ VRUW GH IDoRQ UHPDUTXDEOH/HVH[HPSOHVGRQWQRXVGLVSRVRQVVRQWOpJLRQ HWOHVFDQDX[H[DPLQpVWUqVVpYqUHVOpWDOHPHQWWHPSRUHOGH OD UpSRQVH LPSXOVLRQQHOOH SRXYDQW DWWHLQGUH OD FHQWDLQH GH GXUpHVV\PEROHV'HSOXVFHWpJDOLVHXUDpWpLPSODQWpVXUXQ '630RWRURODHWVRQFRPSRUWHPHQWDSXrWUHREVHUYp VXU GHV KHXUHV GHQUHJLVWUHPHQW 6HV SURSULpWpV VRQW UHPDUTXDEOHVODRXQ(5'(pFKRXHGHPDQLqUHUpJXOLqUH O(5'$VXUPRQWHODGLIILFXOWpGHIDoRQFODLUYR\DQWHFHTXL OpJLWLPH DX SDVVDJH OD UpWLFHQFH GHV DXWHXUV >@ SRXU OD WHUPLQRORJLH KDELWXHOOHPHQW HPSOR\pH GpJDOLVHXU DYHXJOH EOLQG

'DQV FHWWH FRQWULEXWLRQ QRXV DOORQV QRXV LQWpUHVVHU j

OXWLOLVDWLRQGHO(5'$GDQVOHFRQWH[WHGHVV\VWqPHVGDFFqV PXOWLSOH j UpSDUWLWLRQ GDQV OH WHPSV 3RXU FHOD QRXV SURSRVRQV XQH VROXWLRQ TXL FRQVLVWH SRXU OHVVHQWLHO j UpLWpUHU OH SURFHVVXV GpJDOLVDWLRQ DXWDQW GH IRLV TXH QpFHVVDLUH W\SLTXHPHQW j IRLV VXU OH EORF FRQVLGpUp

&RQFHSWXHOOHPHQW RQ pFKDQJH XQH WDLOOH GH EORF

(3)

VXIILVDPPHQW LPSRUWDQWH SRXU DVVXUHU OD FRQYHUJHQFH GH OpJDOLVHXU FRQWUH XQH WDLOOH UpGXLWH GXQ EORF TXH ORQ UHMRXHSOXVLHXUVIRLV1DWXUHOOHPHQWODWDLOOHPLQLPDOHGX EORF GpSHQG GX W\SH GH PRGXODWLRQ XWLOLVpH 'H IDoRQ JURVVLqUHRQSHXWFRQVLGpUHUTXHFHWWHWDLOOHPLQLPDOHHVWGH ORUGUHGHIRLVODGLPHQVLRQGHODOSKDEHW$XIRQGGDQV FHWWH DSSURFKH OLGpH VRXVMDFHQWH HVW TXj OLVVXH GXQH LWpUDWLRQ GH UDQJ Q OHV SDUDPqWUHV GH OpJDOLVHXU VRQW YUDLVHPEODEOHPHQWSOXVSURFKHVGHOHXUYDOHXURSWLPDOH'qV ORUVLOVXIILWGHGpPDUUHUOLWpUDWLRQGHUDQJQDYHFSRXU SDUDPqWUHVLQLWLDX[FHX[HVWLPpVjODILQGHOLWpUDWLRQGHUDQJ Q

/DVHFRQGHSDUWLHGHFHWDUWLFOHUDSSHOOHVRPPDLUHPHQWOH SULQFLSH GH O(5'$ WDQGLV TXH OD WURLVLqPH SDUWLH GpFULW OD PpWKRGH XWLOLVpH DLQVL TXH OHV GLYHUV VLJQDX[ pODERUpV HQ OLJQH SHUPHWWDQW GHVWLPHU OH GHJUp GH SHUIRUPDQFHV DWWHLQW SDU OpJDOLVHXU DILQ GHQ FRQWU{OHU OD FRQILJXUDWLRQ /D TXDWULqPH SDUWLH DSSRUWH XQ FHUWDLQ QRPEUH GH UpVXOWDWV GH VLPXODWLRQVjODIRLVVXUGHVVLJQDX[GHV\QWKqVHHWVXUGHV VLJQDX[UpHOVGHFRPPXQLFDWLRQV$60/DGHUQLqUHSDUWLHHVW FRQVDFUpH j OD FRQFOXVLRQ HW DX[ SHUVSHFWLYHV GXQH WHOOH DSSURFKH

(JDOLVHXUjVWUXFWXUHDGDSWDWLYH

(JDOLVHXUOLQpDLUHRSWLPDOHQ04

6RLW +] OD IRQFWLRQ GH WUDQVIHUW GX FDQDO 6L ORQ FRQVLGqUH GHV GRQQpHVGQ EODQFKHV FHQWUpHV GH YDULDQFH σG HW XQ EUXLW GREVHUYDWLRQ DGGLWLIEQ VWDWLRQQDLUH DX VHFRQGRUGUHFHQWUpEODQFHWGHYDULDQFHσERQUDSSHOOHTXH OpJDOLVHXUOLQpDLUHRSWLPDOHQ04DSRXUIRQFWLRQGHWUDQVIHUW

&]= σG+ ]

σG+]+ ]E

/HGpQRPLQDWHXUGHFHWWHH[SUHVVLRQSHXWVHIDFWRULVHUVRXVOD

IRUPH

']=6*]* ]6>

6GpVLJQDQW XQH FRQVWDQWH UpHOOH SRVLWLYH GpSHQGDQW GHσG σEHWGXFDQDO+&HWWHIDFWRULVDWLRQHVWXQLTXHGqVORUVTXH ORQ LPSRVH j *] UHVS* ]GrWUH FDXVDO HW j SKDVH PLQLPDOH UHVS DQWLFDXVDO HW j SKDVH PD[LPDOH HW GRQF GLQYHUVH FDXVDO UHVS DQWLFDXVDO 3DU FRQVpTXHQW VL ORQ GpVLJQH SDU ],LL=1 OHV1 UDFLQHV VLWXpHV j OLQWpULHXUGXGLVTXHXQLWp8RQREWLHQW

*]=

[

−],L]

]

L=

1 =+$]DYHF],L <

'DSUqVHWOpJDOLVHXUOLQpDLUHRSWLPDOHQ04SHXWrWUH YX FRPPH OD FDVFDGH GXQ ILOWUH5 SXUHPHQW UpFXUVLI HW VWDEOHGHIRQFWLRQGHWUDQVIHUW *]HWGXQILOWUHOLQpDLUH WUDQVYHUVH3GHIRQFWLRQGHWUDQVIHUW

3]=]/'/

[ ]

σG 6 + ]

[

* ]

]

R'/LQGLTXHXQGpYHORSSHPHQWOLPLWpWURQTXpjORUGUH/ HQIRQFWLRQGHVSXLVVDQFHVSRVLWLYHVHQ],OHQUpVXOWHTXXQ pJDOLVHXU OLQpDLUH RSWLPDO DX VHQV GH OD PLQLPLVDWLRQ GH OHUUHXUTXDGUDWLTXHPR\HQQHSHXWrWUHYXHFRPPHODFDVFDGH GXQ ILOWUH EODQFKLVVDQW UpFXUVLI HW GXQ ILOWUH WUDQVYHUVH GH GLPHQVLRQ VXIILVDQWH 3RXU GHV UDLVRQV GRUGUH SUDWLTXH XQ GLVSRVLWLIVXSSOpPHQWDLUHGHJDLQFRPSOH[H*&HVWUDMRXWp

$ FKDUJH SRXU OXL GDVVXUHU OD GRXEOH IRQFWLRQ GH FRQWU{OH DXWRPDWLTXH GH JDLQ HW GH FRUUHFWLRQ GH SKDVH SKDVH URWDWRU $LQVL XQH IRUPH SRVVLEOH GH UpDOLVDWLRQ GH OpJDOLVHXUOLQpDLUHFRUUHVSRQGjODFDVFDGHGHOD)LJ

+

-

X

A(z)

P(z)

s(n) w(n)

g t(n)

exp(-jθ)

+

R T CP

u(n) v(n) d (n )ˆ

CG

),*(JDOLVHXUOLQpDLUHUpFXUVLI

&RPSWHWHQXGHODOLQpDULWpGHODVWUXFWXUHLOHVWpYLGHQW TXHOHFRQWU{OHGHJDLQ&*SHXWrWUHVLWXpHQGLYHUVSRLQWV GH OD FKDvQH HW QRWDPPHQW MXVWH DSUqV OH ILOWUH EODQFKLVVDQW UpFXUVLI&HGHUQLHUPLQLPLVHODSXLVVDQFHGHVDVRUWLHWDQGLV TXHOHILOWUHWUDQVYHUVHXWLOLVHSRXUVRQDGDSWDWLRQXQFULWqUH GHW\SH*RGDUG>@6KWURP )DQ>@6KDOYL :HLQVWHLQ

>@HWF/HFRUUHFWHXUGHSKDVHSHXWSDUH[HPSOHXWLOLVHUXQ FULWqUHGHUUHXUTXDGUDWLTXHPR\HQQHHVWLPpH'qVORUVTXLO HVWSLORWpSDUGpFLVLRQVLOHVWSUpIpUDEOHGHOHVLWXHUHQDYDOGH OD FKDvQH /H FRQWU{OH GH JDLQ D SRXU IRQFWLRQ GDGDSWHU OD SXLVVDQFH GX VLJQDOXQ j FHOOH GHV V\PEROHV pPLV SDU OD VRXUFH /HV pTXDWLRQV GH IRQFWLRQHPHQW GH O(5'$ VRQW GpFULWHVHQGpWDLOGDQV>@

0RGHGHIRQFWLRQQHPHQWQRUPDO(5'

/RUVTXH OD FRQYHUJHQFH YHUV XQH VROXWLRQ SURFKH GH

ORSWLPXP D pWp UHQGXH SRVVLEOH SDU ODSSURFKH DXWRGLGDFWH SUpFpGHPPHQW GpFULWH RQ PRGLILH GH IDoRQ UpYHUVLEOH j OD IRLV OD VWUXFWXUH HW OHV FULWqUHV GRSWLPDOLWp SRXUREWHQLUO(5'FRQYHQWLRQQHOFRQIRUPpPHQWDXVFKpPD GHOD)LJ&HFLHVWSDUIDLWHPHQWOpJLWLPpSDUOHIDLWTXH SRXUXQ(5'RSWLPDOHQ04OHILOWUHDUULqUHDSRXUIRQFWLRQ GHWUDQVIHUWVWULFWHPHQWFDXVDOH$]=*]−(QFODLU OD SDUWLH UpFXUVLYH GX ILOWUH EODQFKLVVDQW5GX PRGH GH IRQFWLRQQHPHQW LQLWLDO FRUUHVSRQG H[DFWHPHQW DX ILOWUH DUULqUHGHO(5'FRQYHQWLRQQHORSWLPDOHQ04&HUpVXOWDW SDUWLFXOLqUHPHQWLQWpUHVVDQWFRQVWLWXHODFOHIGHYR€WHGHQRWUH pJDOLVHXU'HSOXVOHILOWUHWUDQVYHUVHGHO(5'RSWLPDOHQ 04 D SRXU IRQFWLRQ GH WUDQVIHUW 3] &H UpVXOWDW UHPDUTXDEOH OpJLWLPH GH IDFWR OD PRGLILFDWLRQ DOJRULWKPLTXH HW VWUXFWXUHOOH GH QRWUH DSSURFKH (Q HIIHW PrPHVLOHFULWqUHGH*RGDUGQHPqQHSDVULJRXUHXVHPHQWj OD VROXWLRQ 3]RQ FRQVWDWH HQ SUDWLTXH TXH FHV GHX[

VROXWLRQV VRQW VXIILVDPPHQW SURFKHV &HVW OD UDLVRQ HVVHQWLHOOH TXL MXVWLILH OD FRPPXWDWLRQ VWUXFWXUHOOH HW DOJRULWKPLTXHRSpUpHGDQVO(5'$/D)LJGpFULWO(5'$

GDQV VRQ PRGH GH SRXUVXLWH /H &* HVW DORUV LQKLEp OpJDOLVHXU OLQpDLUH WUDQVYHUVH SUHQDQW HQ FKDUJH FHWWH IRQFWLRQ

(4)

+ + -

A(z) w(n)

X

P(z) s(n)

g

t(n) x(n)

exp(-jθ)

T CP

d (n)ˆ

R CG

),*(JDOLVHXUORUVGHVLWXDWLRQVIDFLOHV(5' 'qV ORUV OXQLTXH FULWqUH GH FH PRGH GH IRQFWLRQQHPHQW

FRUUHVSRQGjODIRQFWLRQFR€W

(G =(   ZQ−GÖQ  

TXL QHVW DXWUH TXH O(40 HVWLPpH /DGDSWDWLRQ GHV SDUDPqWUHV GH OpJDOLVHXU SHXW DORUV VH IDLUH FODVVLTXHPHQW VHORQODOJRULWKPHGXJUDGLHQWVWRFKDVWLTXHRXGHVPRLQGUHV FDUUpV UpFXUVLIV 0&5 ,O UHVWH GpVRUPDLV j GpWHUPLQHU OD UqJOHGHFRPPXWDWLRQUpYHUVLEOHTXLSHUPHWGHPRGLILHUjOD IRLVOHVFULWqUHVHWODVWUXFWXUHGHOpJDOLVHXU(QFODLULOQRXV IDXW GpWHUPLQHU XQ LQGLFH GH SHUIRUPDQFH DSSURSULp QH QpFHVVLWDQWDXFXQHFRQQDLVVDQFHDSULRULGHVGRQQpHVpPLVHV GQ

5qJOHGHFRPPXWDWLRQ

/DFRQYHUJHQFHGHOpJDOLVHXUSHXWrWUHFDUDFWpULVpHSDUOD YDOHXU GH O(40 0DLV SXLVTXH OHVGQ VRQW LQFRQQXHV LO QHVWJXqUHSRVVLEOHGHODPHVXUHU(QUHYDQFKHHOOHSHXWrWUH HVWLPpH VXU OD EDVH GHV GpFLVLRQVGQÖ SDU ODOJRULWKPH UpFXUVLI

(GQ= λ (G Q−+−λ ZQ−GÖQ

Rλ ∈]]HVWXQIDFWHXUGRXEOL&HWHVWLPDWHXUSLORWpSDU GpFLVLRQVHVWSHUWLQHQWDXVHQVRjSDUWLUGXQFHUWDLQVHXLOLO UHQG HIIHFWLYHPHQW FRPSWH GH O(40 YUDLH 8QH DXWUH DSSURFKHSRVVLEOHFRQVLVWHjHVWLPHUOHNXUWRVLVGHZQVHORQ XQDOJRULWKPHDGDSWDWLIVLPLODLUHjRXQHIRQFWLRQFR€W WHOOHTXHFHOOHGH*RGDUG(*>@RX6KWURPHW)DQ(6)>@

DYHFS T HWζ GpILQLHVFLGHVVRXV

(* =(

[

ZQ −5

]

DYHF5 =

(6) =(

[

ZQ−(

{

ZQ

} ]

.Z = (

{

ZQ

}

(

{

ZQ

}

'DQV VD YHUVLRQ OD SOXV VLPSOH OD UqJOH GH FRPPXWDWLRQ VpQRQFH GH OD IDoRQ VXLYDQWH /RUVTXH O(40 HVWLPpH (GQRXWRXWDXWUHVLJQDODSSURSULpIUDQFKLWGDQVXQVHQV RX GDQV ODXWUH XQ VHXLO QRWp - DGDSWp DX W\SH GH PRGXODWLRQ XWLOLVpH O(5'$ RSqUH XQH PRGLILFDWLRQ VWUXFWXUHOOHHWDOJRULWKPLTXH

$GDSWDWLRQGHO(5'$jXQHVWUDWpJLH7'0$

,O HVW FODLU TXH SRXU XQH WHOOH DSSOLFDWLRQ OD YLWHVVH GH FRQYHUJHQFH HVW GH SUHPLqUH LPSRUWDQFH (Q OpWDW O(5'$

HVW LQDSSURSULp FDU PrPH VL VD YLWHVVH GH FRQYHUJHQFH HVW pOHYpH HOOH GHPHXUH HQ WRXW pWDW GH FDXVH ODUJHPHQW LQVXIILVDQWH3RXUUHQGUHO(5'$SOXVDWWUDFWLIGDQVFHPRGH GH WUDQVPLVVLRQ QRXV SURSRVRQV XQH VWUDWpJLH LWpUDWLYH DXWRGLGDFWH HW DGDSWDWLYH /LGpH IRUFH TXL DSSDUDvW HQ ILOLJUDQHHVWTXHQVWUDWpJLHDXWRGLGDFWHODWRWDOLWpGXEORFHVW H[SORLWDEOH SDU OpJDOLVHXU WDQGLV TXD FRQWUDULR VDJLVVDQW GXQH DSSURFKH HQWUDvQpH VHXOH OD VpTXHQFH GDSSUHQWLVVDJH SHXW rWUH H[SORLWpH 0DOKHXUHXVHPHQW GDQV OHV DSSOLFDWLRQV SUDWLTXHV OD ORQJXHXU GH FHWWH VpTXHQFH HVW LQFRPSDWLEOH DYHF XQHDSSURFKHDGDSWDWLYH1RXVDOORQVPRQWUHUTXLOHQ YD WRXW DXWUHPHQW GH ODSSURFKH DXWRGLGDFWH TXL XWLOLVH XQLTXHPHQWODFRQQDLVVDQFHDSULRULGHODVWDWLVWLTXHGXVLJQDO pPLV HW TXL SHXW DLQVL WLUHU SURILW GH OD WRWDOLWp GX EORF FRQVLGpUp 1DWXUHOOHPHQW SRXU TXH O(5'$ FRQYHUJH YHUV XQHVROXWLRQYRLVLQHGHORSWLPDOLOHVWQpFHVVDLUHTXHODWDLOOH GXEORFVRLWVXIILVDPPHQWFRQVpTXHQWHSRXUQHSDVELDLVHUOD VROXWLRQ 'DQV FHW DUWLFOH OD PpWKRGH TXH QRXV SURSRVRQV FRQVLVWH j UHMRXHU OH EORF XQ FHUWDLQ QRPEUH GH IRLV W\SLTXHPHQWjIRLV'DQVFHVFRQGLWLRQVjOLWpUDWLRQGH UDQJQO(5'$HVWLQLWLDOLVpDYHFOHVSDUDPqWUHV$3HWθ HVWLPpVjODILQGHOLWpUDWLRQGHUDQJQ/K\SRWKqVHIRUWH PDLVUDLVRQQDEOHHVWTXHVXUOKRUL]RQGXQEORFGHGRQQpHV OHFDQDOSXLVVHrWUHFRQVLGpUpFRPPHVWDWLRQQDLUHFHVWGX UHVWH OK\SRWKqVH VXU ODTXHOOH UHSRVHQW OHV UpFHSWHXUV *60 DFWXHOV

5pVXOWDWV

'DQVFHTXLVXLWQRXVDOORQVLOOXVWUHUOHVSHUIRUPDQFHVGX QRXYHO pJDOLVHXU j OD IRLV GDQV XQ FRQWH[WH VWDWLRQQDLUH HW GDQVXQFRQWH[WHQRQVWDWLRQQDLUHGHFRPPXQLFDWLRQV$60

&DQDOVWDWLRQQDLUH

/HFDQDOTXHQRXVSURSRVRQVHVWWUqVVpOHFWLIHQIUpTXHQFH

>@ ,O D SRXU UpSRQVHLPSXOVLRQQHOOHK >

@/(5'$FRPSRUWHFRHIILFLHQWV GDQVVDSDUWLHDYDQWHWFRHIILFLHQWVGDQVVDSDUWLHDUULqUH2Q SURFqGH DX WLUDJH DOpDWRLUH GH ILFKLHUV FRPSRUWDQW V\PEROHVFHQWUpVHWGHYDULDQFHXQLWDLUH/HUUHXUGHSKDVH SRXUFKDTXHILFKLHUHVWHTXLUpSDUWLHVXU>π@/HVHXLOGH FRPPXWDWLRQ HQ WHUPHV G(40 HVW GH G% /D ILJXUH LQGLTXHOpYROXWLRQDXILOGHVLWpUDWLRQVHWSRXUXQVQUGH G% GXQ FHUWDLQ QRPEUH GH IRQFWLRQV LQGLFDWULFHV SRXYDQW HIIHFWLYHPHQW FRPPDQGHU OD FRPPXWDWLRQ VWUXFWXUHOOH GH O(5'$jVDYRLU(GQ(*Q(6)QRX.ZQ

(5)

100 200 300 400 500 -15

-10 -5 0

EQM estimée en dB

Itération 1

Itération 10

100 200 300 400 500

-15 -10 -5 0

Erreur de Godard en dB

Itération 1

Itération 10

100 200 300 400 500

-15 -10 -5 0

Erreur de Shtrom & Fan en dB

Itération 1

Itération 10

100 200 300 400 500

-1 -0.5 0 0.5

Kurtosis

Itération 1

Itération 10

),*6LJQDX[GHUUHXUVpODERUpVHQOLJQH(40HVWLPpH

*RGDUG6WURP )DQHWNXUWRVLVVQU G%

8QFHUWDLQQRPEUHGHUHPDUTXHVSHXYHQWrWUHIRUPXOpHVVXU OD EDVH GH FHWWH ILJXUH /D SUHPLqUH HVW TXH OH QRPEUH GLWpUDWLRQVQpFHVVDLUHVQHGpSDVVHJXqUHRX/DVHFRQGH LQIRUPDWLRQHVWTXHOHUUHXUDXVHQVGH*RGDUGpYROXHGHOD PrPHPDQLqUHTXHO(40jXQGpFDODJHSUqVGHORUGUHGH G%&HVLJQDOGRQWOpODERUDWLRQHQOLJQHUHVWHGHFRPSOH[LWp PRGHVWHSHXWHQFRQVpTXHQFHrWUHXWLOLVpSRXUFRPPDQGHU OD PRGLILFDWLRQ VWUXFWXUHOOH GH O(5'$ 2Q UHPDUTXH SDU DLOOHXUVTXHOHNXUWRVLVHVWLPpDWWHLQWXQPLQLPXPGHORUGUH GH SRXU XQ NXUWRVLV QRPLQDO GH VRXUFH LLG GH YDULDQFH XQLWDLUH /D ILJXUH GRQQH OpYROXWLRQ GX WDX[

GHUUHXUV ELQDLUHV 7(% DX ILO GHV LWpUDWLRQV SRXU XQVQU YDULDQWGHjG%FHTXLFRUUHVSRQGjXQUDWLR(E1 FRPSULVHQWUHHWG%/HVSUHPLqUHVGpFLVLRQVQRQW SDV pWp SULVHV HQ FRPSWH GDQV OpYDOXDWLRQ GX 7(% ,O HVW PDQLIHVWH TXH OHVVHQWLHO GH ODSSRUW OLp j QRWUH VWUDWpJLH HVW REWHQXDXERXWGHLWpUDWLRQVFHTXLFRUURERUHWRWDOHPHQWOHV REVHUYDWLRQVGHODILJXUH

1 2 3 4 5 6 7 8 9 10

10-4 10-3 10-2 10-1 100

Taux d'erreurs binaires

Nombre d'itérations

snr= 10 dB (Eb/No=7 dB)

snr= 15 dB (Eb/No=12 dB)

)LJ7DX[GHUUHXUVELQDLUHVDXILOGHVLWpUDWLRQV

&DQDO$60

'DQV FHW H[HPSOH QRXV DYRQV FKRLVL XQ VLJQDO UpHO GH FRPPXQLFDWLRQV $60 GH W\SH 0'3 436. HQUHJLVWUp ORUVGXQHFDPSDJQHGHPHVXUHVHIIHFWXpHVSDUOH*(60$

DX ODUJH GH %UHVW )UDQFH /D VpTXHQFH pPLVH HVW XQH VpTXHQFHSpULRGLTXHEODQFKHGHORQJXHXUPD[LPDOH6%/0 GHORQJXHXU/DIUpTXHQFHSRUWHXVHHVWGHN+]HWOH GpELW QXPpULTXH GH NEV /D UpSRQVH LPSXOVLRQQHOOH VpWHQG VXU GXUpHV V\PEROH /H EORF FRQVLGpUp ILFKLHU FRPSRUWH pFKDQWLOORQV SUpOHYpV j XQH FDGHQFH7GH

VRUWH TXH VXU FHW KRUL]RQ OH FDQDO SXLVVH rWUH FRQVLGpUp FRPPHVWDWLRQQDLUH/DILJXUHLQGLTXHOpYROXWLRQDXILOGHV LWpUDWLRQV GXQ FHUWDLQ QRPEUH GH IRQFWLRQV LQGLFDWULFHV SRXYDQW HIIHFWLYHPHQW FRPPDQGHU OD FRPPXWDWLRQ VWUXFWXUHOOH GH O(5'$ j VDYRLU O(40 HVWLPpH OHUUHXU DX VHQVGH*RGDUGGH6KWURP )DQRXHQFRUHOHNXUWRVLV

0 200 400 600 800 1000

-12 -10 -8 -6 -4 -2

EQM estimée en dB

Itération 1

Itération 5

0 200 400 600 800 1000

-12 -10 -8 -6 -4 -2

Erreur de Godard en dB

Itération 1

Itération 5

0 200 400 600 800 1000

-12 -10 -8 -6 -4 -2

Erreur de Shtrom & Fan en dB

Itération 1

Itération 5

0 200 400 600 800 1000

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

Kurtosis

Itération 1

Itération 5

),*6LJQDX[GHUUHXUVpODERUpVHQOLJQH(40HVWLPpH

*RGDUG6WURP )DQHWNXUWRVLV

/H WDEOHDX QRXV LQGLTXH OH QRPEUH GHUUHXUV FRPPLVHV j

FKDTXHLWpUDWLRQ7URLVFDVGHILJXUHVVRQWHQYLVDJpVVRLWRQ GpWHUPLQH OH QRPEUH WRWDO GHUUHXUV PRGH VRLW RQ IDLW DEVWUDFWLRQGHVPRGHRXGHVPRGHSUHPLqUHV GpFLVLRQV SRXU WHQLU FRPSWH GH OH[LVWHQFH GXQ pYHQWXHO SUpDPEXOH,OHVWFODLUTXHJOREDOHPHQWQRWUHVWUDWpJLHVDYqUH SDUWLFXOLqUHPHQW HIILFDFH FRPSWH WHQX GH OpWDOHPHQW WHPSRUHOGHODUpSRQVHLPSXOVLRQQHOOHHWSDUWDQWGXQRPEUH GH FRHIILFLHQWV GH OpJDOLVHXU FRHIILFLHQWV SRXU OD SDUWLH DYDQWHWSRXUODSDUWLHDUULqUH/HVSDVGDGDSWDWLRQVRQW GH HW OH VHXLO GH G% $LQVL ORUV GH OD GHUQLqUH LWpUDWLRQ VHXOHV HUUHXUV ELQDLUHV VXU RQW pWp GpQRPEUpHV PDLV VHXOHPHQW VVXUYLHQQHQW DSUqV OHV SUHPLHUV V\PEROHV $X GHPHXUDQW OH UDWLR RX QHVW HQ ULHQ GpUDLVRQQDEOH DX UHJDUG GH ODFWXHO

*60

7$%1RPEUHGHUUHXUVVXUELWVWUDQVPLV

,WpUDWLRQ PRGH PRGH PRGH

&H WDEOHDX UHQG FRPSWH GX IDLW TXH OHV HUUHXUV VXUYLHQQHQW

PDMRULWDLUHPHQWHQGpEXWGXILFKLHU,OHVWSDUDLOOHXUVXWLOHGH UDSSHOHUTXXQHVWUDWpJLHGHUpFHSWLRQRSWLPDOHHVWWRWDOHPHQW LQDSSURSULpH HQ UDLVRQ GH OD ORQJXHXU GH OD UpSRQVH LPSXOVLRQQHOOH7

&RQFOXVLRQ

1RXV YHQRQV GH GpPRQWUHU ORULJLQDOLWp HW OLQWpUrW GH O(5'$ >@ GDQV OH FRQWH[WH GHV V\VWqPHV GH FRPPXQLFDWLRQVXWLOLVDQWODFFqVPXOWLSOHjUpSDUWLWLRQGDQVOH

(6)

WHPSV $057 /HV UpVXOWDWV REWHQXV VRQW H[WUrPHPHQW HQFRXUDJHDQWV HW PRQWUHQW OLQWpUrW GXQH WHOOH DSSURFKH FRPSWHWHQXGHODIDLEOHFRPSOH[LWpFDOFXODWRLUHDVVRFLpH3DU DLOOHXUV FHWWH SURSULpWp SHXW pJDOHPHQW rWUH H[SORLWpH SRXU DPpOLRUHU DX SUL[ GXQ UHWDUG GH UHVWLWXWLRQ OD YLWHVVH GH FRQYHUJHQFHGHO(5'$GDQVOHVDSSOLFDWLRQVjIORWFRQWLQX GHGRQQpHV(QILQLOHVWFODLUTXHOHFKRL[GXQHPRGXODWLRQ ELQDLUH0'3*06.VHUDLWHQFRUHGHQDWXUHjDFFpOpUHUOD FRQYHUJHQFH HW j UpGXLUH FH IDLVDQW OD ORQJXHXU GH EORF QpFHVVDLUHjQRWUHVWUDWpJLH5DLVRQQDEOHPHQWRQSHXWSHQVHU TXHFHWWHGHUQLqUHHVWGRUHVHWGpMjFRPSDWLEOHDYHFODFWXHO VWDQGDUG*60

5HPHUFLHPHQWV

1RXVWHQRQVjUHPHUFLHUOH*(60$'*$O,)5(0(5 HW2UFD,QVWUXPHQWDWLRQSRXUOHXUVFRQWULEXWLRQVUHVSHFWLYHV ORUVGHVFDPSDJQHVGHPHVXUHVPHQpHVDXODUJHGH%UHVW

5pIpUHQFHV

>@ - /DEDW & /DRW 2 0DFFKL'LVSRVLWLI GpJDOLVDWLRQ DGDSWDWLI SRXU V\VWqPHV GH FRPPXQLFDWLRQV QXPpULTXHV )UHQFK 3DWHQWVHSWHPEHU

>@ - /DEDW 2 0DFFKL & /DRW 1 /H 6TXLQ,V WUDLQLQJ RI DGDSWLYH HTXDOL]HUV VWLOO XVHIXOO " 3URF *OREHFRP /RQGRQ 8.1RYHPEHUYROSS

>@ - /DEDW 2 0DFFKL & /DRW$GDSWLYH GHFLVLRQ IHHGEDFN HTXDOL]DWLRQFDQ\RXVNLSWKHWUDLQLQJSHULRG",(((7UDQVRQ

&RP9RO1RSS-XO\

>@ ' 1 *RGDUG6HOIUHFRYHULQJ HTXDOL]DWLRQ DQG FDUULHU WUDFNLQJ LQ WZR GLPHQVLRQDO GDWD FRPPXQLFDWLRQ V\VWHP ,(((

7UDQVRQ&RPYROSS

>@ 9 6KWURP + )DQ1HZ &ODVV RI =HUR)RUFLQJ &RVW )XQFWLRQVLQ%OLQG(TXDOL]DWLRQ,(((7UDQVRQ63YRO1R 2FWREHUSS

>@6KDOYL (:HLQVWHLQ1HZFULWHULDIRUEOLQGGHFRQYROXWLRQ RIQRQPLQLPXPSKDVHV\VWHPVFKDQQHOV,(((7UDQVRQ,7YRO 1R0DUFKSS

Références

Documents relatifs

Ils se caractérisent tous par leur grande robustesse, leur simplicité d'utilisation et leur maintenance facile, ainsi que par leur manœuvrabilité, étant très utiles dans

[r]

3 Dans chaque cas, complète les phrases par les mots côté ou diagonale puis construis le quadrilatère demandé à partir du segment déjà tracé

3 Dans chaque cas, complète les phrases par les mots côté ou diagonale puis construis le quadrilatère demandé à partir du segment déjà tracé

La modification de la liste des méthodes d'analyses pour l'adoption de méthodes équivalentes, tout comme la modification du type de spécimen ou de la nature des analyses

1  Dans chaque cas, complète les phrases par les mots côté ou diagonale, puis construis le quadrilatère demandé à partir du segment déjà tracéa. le

[r]

/¶RSpUDWHXU DSUqV DYRLU DFFURFKp OHV SLqFHV j WUDLWHU VXU OH FDGUH VLWXp DX SRLQW GH FKDUJHPHQW HQ SRVLWLRQ EDVVH GRQQH O¶LQIRUPDWLRQ GpSDUW F\FOH GF\ /H FKDULRW DXWRPRWHXU &amp;0