MitigationofFiberLinearandNonlinear

EffectsinCoherentOpticalCommunication
Systems
XiaojunLiang*,ShivaKumar,andJingShao
DepartmentofElectricalandComputerEngineering,McMasterUniversity,HamiltonON,Canada
*
liangx5@mcmaster.ca

,QYLWHG3DSHU

Abstract­ Fiber dispersive and nonlinear effects GLVWRUWLRQV RFFXU DQG DFFXPXODWH DORQJ ILEHU GLVWDQFH
lead to signal distortions in a fiber optic link, which ZKLFKVHYHUHO\OLPLWVWUDQVPLVVLRQSHUIRUPDQFH
limits the transmission performance and system 'LJLWDO >@ DQG RSWLFDO WHFKQLTXHV >@ KDYH
capacity. Digital and optical techniques have been EHHQ SURSRVHG WR FRPSHQVDWH IRU OLQHDU DQG QRQOLQHDU
proposed to mitigate propagation impairments. In this GLVWRUWLRQV LQ ILEHU RSWLF FRPPXQLFDWLRQ V\VWHPV
paper, we give a brief review of digital and optical 'LJLWDO QRQOLQHDU FRPSHQVDWLRQ WHFKQLTXHV DUH EDVHG
nonlinear compensation techniques. Then, we present RQ GLJLWDO VLJQDO SURFHVVLQJ '63 3URSDJDWLRQ
our recent results on three techniques: GLVWRUWLRQV DUH FDOFXODWHG LQ WKH GLJLWDO GRPDLQ DW WKH
perturbation­based digital compensation, correlated WUDQVPLWWHU DQGRU UHFHLYHU DQG WKHQ UHPRYHG LQ RUGHU
digital back propagation (DBP), and optical back WR LPSURYH VLJQDO TXDOLW\ 'LJLWDO FRPSHQVDWLRQ
propagation (OBP). The OBP scheme using WHFKQLTXHV LQFOXGH GLJLWDO EDFN SURSDJDWLRQ >@
dispersion­decreasing fiber is successfully applied to a SHUWXUEDWLRQ EDVHG WHFKQLTXH >@ DQG D FRPELQDWLRQ
fiber optic system with mesh configuration and RI WKHVH WZR >@ 7KH GHWHUPLQLVWLF VLJQDO GLVWRUWLRQV
showed 9.8 dB Q­factor gains as compared with the GXHWRSURSDJDWLRQLQDQRSWLFDOILEHUDUHZHOOGHILQHG
conventional DBP scheme. E\ WKH QRQOLQHDU 6FKU|GLQJHU HTXDWLRQ 1/6( WKDW LV
 UHYHUVLEOH 7KHUHIRUH WKHRUHWLFDOO\ VSHDNLQJ
, ,1752'8&7,21 SURSDJDWLRQ GLVWRUWLRQV FDQ EH FRPSHQVDWHG IRU E\
7KH LQIRUPDWLRQ FDSDFLW\ RI ILEHU RSWLF VROYLQJ D UHYHUVH 1/6( LQ WKH GLJLWDO GRPDLQ XVLQJ
FRPPXQLFDWLRQ V\VWHPV KDV EHHQ DGYDQFHG RYHU WKH '%3 +RZHYHU DFFXUDWH FRPSHQVDWLRQ RI GLVWRUWLRQV
SDVW GHFDGHV E\ WHFKQRORJ\ GHYHORSPHQWV VXFK DV WKH XVLQJ '%3 UHTXLUHV YHU\ VPDOO QXPHULFDO VWHS VL]H
LQYHQWLRQ RI (UELXP GRSHG ILEHU DPSOLILHU (')$ ZKLFK PHDQV KXJH FRPSXWDWLRQDO FRPSOH[LW\ 7KH
ZDYHOHQJWK GLYLVLRQ PXOWLSOH[LQJ :'0 WHFKQLTXHV FRPSHQVDWLRQSHUIRUPDQFHRI'%3LQSUDFWLFDOV\VWHPV
FRKHUHQWWUDQVPLVVLRQWHFKQRORJLHVDQGVSDFHGLYLVLRQ LV OLPLWHG E\ '63 UHVRXUFHV DQG FXUUHQWO\ '%3 LV
PXOWLSOH[LQJ 6'0 &XUUHQWO\ WKH LQIRUPDWLRQ PRVWO\LPSOHPHQWHGIRURIIOLQHVLJQDOSURFHVVLQJRQO\
FDSDFLW\ RI ILEHU RSWLF V\VWHPV LV OLPLWHG E\ QRQOLQHDU 0DQ\ UHVHDUFK HIIRUWV KDYH EHHQ SXW LQ WKH
HIIHFWV RI WKH RSWLFDO ILEHU $Q RSWLFDO ILEHU LV D VLPSOLILFDWLRQ RI '%3 DOJRULWKP FRPSOH[LW\ DPRQJ
QRQOLQHDUPHGLXPZKRVHUHIUDFWLYHLQGH[ ZLOOFKDQJH ZKLFK SHUWXUEDWLYH VFKHPHV DQG FRUUHODWHG '%3
LQUHVSRQVHWRDQLQSXWRSWLFDOVLJQDO:KHQDQRSWLFDO SURYLGH VLJQLILFDQW FRPSOH[LW\ UHGXFWLRQ 3HUWXUEDWLRQ
VLJQDOSURSDJDWHVLQDQRSWLFDOILEHU.HUUQRQOLQHDULW\ EDVHG WHFKQLTXHV HPSOR\ WKH VHPLDQDO\WLFDO VROXWLRQ
LQWURGXFHVDSRZHUGHSHQGHQWSKDVHVKLIWWRWKHRSWLFDO RI WKH 1/6( DQG KHQFH LV SURPLVLQJ WR UHOD[ WKH
VLJQDO 'XH WR WKH LQWHUSOD\ EHWZHHQ FKURPDWLF QXPHULFDO FRPSXWDWLRQDO ORDG ,Q WKLV SDSHU ZH ZLOO
GLVSHUVLRQ DQG .HUU QRQOLQHDULW\ FRPSOLFDWHG VLJQDO GLVFXVVRXUUHVHDUFKZRUNRQDPXOWLVWDJHSHUWXUEDWLRQ

‹,(((  $VLORPDU

FRPSHQVDWLRQWHFKQLTXHDQGDFRUUHODWHG'%3VFKHPH FRVW GXH WRWKH UHGXFWLRQRI GLVSHUVLYH HIIHFWVDV ZHOO
$QRWKHU FKDOOHQJH RI GLJLWDO FRPSHQVDWLRQ WHFKQLTXHV DVQRQOLQHDUGLVWRUWLRQVZLWKLQHDFKVWDJH)LJVKRZV
LV WKDW WKH\ DUH LQFDSDEOH WR FRPSHQVDWH IRU WKDW WKH PXOWLVWDJH VFKHPH ZLWK  FRPSHQVDWLRQ
LQWHUFKDQQHO QRQOLQHDU GLVWRUWLRQV LQ ILEHU RSWLF PHVK VWDJHV SURYLGHV  G% 4IDFWRU LPSURYHPHQW DV
QHWZRUNV GXH WR WKH ODFN RI SDWK LQIRUPDWLRQ RI FRPSDUHG WR OLQHDU FRPSHQVDWLRQ DQG WKH
GLIIHUHQW ZDYHOHQJWK GLYLVLRQ PXOWLSOH[LQJ :'0 FRPSXWDWLRQDO FRVW LV UHGXFHG E\ D IDFWRU RI  DV
FKDQQHOV FRPSDUHGWRRQHVWDJHVFKHPH
2SWLFDOEDFNSURSDJDWLRQ2%3>@SURYLGHVDQ
DOWHUQDWLYH QRQOLQHDU FRPSHQVDWLRQ WHFKQLTXH WKDW
FRPSHQVDWHV GLVWRUWLRQ XVLQJ RSWLFDO VLJQDO SURFHVVLQJ
DQGLQKHUHQWO\DYRLGVWKHOLPLWDWLRQVRI'63UHVRXUFHV
,Q WKLV SDSHU ZH ZLOO GLVFXVV WKH UHVXOWV RI DQ 2%3
VFKHPH XVLQJ GLVSHUVLRQGHFUHDVLQJ ILEHU '') 7KH
2%3 VFKHPH XVLQJ '') LV VXFFHVVIXOO\ DSSOLHG WR D
ILEHU RSWLF PHVK QHWZRUN FRQILJXUDWLRQ DQG ZH ILQG
WKDWWKHLPSURYHPHQWLQ4IDFWRULVG%DVFRPSDUHG
ZLWKWKHFRQYHQWLRQDO'%3VFKHPH
7KHUHPDLQGHURIWKHSDSHULVRUJDQL]HGDVIROORZV
6HFWLRQ,,GLVFXVVHVDPXOWLVWDJHGLJLWDOFRPSHQVDWLRQ
WHFKQLTXH EDVHG RQ D UHFXUVLYH SHUWXUEDWLRQ WKHRU\ 
6HFWLRQ,,SUHVHQWVDFRUUHODWHG'%3VFKHPH EDVHGRQ )LJ&RPSHQVDWLRQSHUIRUPDQFHDQGFRPSXWDWLRQDO
FRPSOH[LW\RIPXOWLVWDJHSHUWXUEDWLRQVFKHPHV
SHUWXUEDWLRQ WKHRU\ 6HFWLRQ ,9 SUHVHQWV DQ 2%3
VLQJOHFKDQQHOV\VWHPV\PEROUDWH *EDXGPRGXODWLRQ 
VFKHPH EDVHG RQ '') $QG 6HFWLRQ 9 GUDZV WKH 4$0WUDQVPLVVLRQGLVWDQFH îNP)URP5HI>@
FRQFOXVLRQV 
 ,,, &255(/$7('',*,7$/%$&.
,, 08/7,67$*(',*,7$/&203(16$7,21 3523$*$7,21%$6('213(5785%$7,21
%$6('215(&856,9(3(5785%$7,21 ,Q VWDQGDUG '%3 WKH QRQOLQHDU SKDVH VKLIW GHSHQGV
7+(25< RQO\ RQ WKH LQVWDQWDQHRXV SRZHU RI WKH FXUUHQW SXOVH
3HUWXUEDWLRQEDVHG WHFKQLTXHV XVH VHPLDQDO\WLFDO ZKLOH WKH FRUUHODWLRQ EHWZHHQ DGMDFHQW SXOVHV LV QRW
VROXWLRQV RI WKH 1/6( WR FDOFXODWH WKH QRQOLQHDU LQFOXGHG $V DQ LPSURYHG YDULDQW FRUUHODWHG '%3
GLVWRUWLRQ LQ WKH GLJLWDO GRPDLQ &RQYHQWLRQDO VLJQLILFDQWO\ LQFUHDVHV WKH QXPHULFDO DFFXUDF\ E\
SHUWXUEDWLYH PHWKRGV XVH D RQHVWDJH FRPSHQVDWLRQ WDNLQJWKHFRUUHODWLRQEHWZHHQDGMDFHQWVLJQDOVDPSOHV
VFKHPH ZKHUH WKH ILUVW RUGHU GLVWRUWLRQ RI WKH HQWLUH LQWRDFFRXQW$FRUUHODWHG'%3VFKHPHLVGHYHORSHGLQ
ILEHURSWLFOLQNLVFDOFXODWHGLQRQHVWHSZKLFKUHVXOWV 5HI>@EDVHGRQSHUWXUEDWLRQWKHRU\DQGDQDQDO\WLFDO
LQ ORZ DFFXUDF\ DQG KLJK FRPSXWDWLRQDO FRVW ,Q 5HI H[SUHVVLRQIRUFRUUHODWLRQFRHIILFLHQWVKDVEHHQGHULYHG
>@DPXOWLVWDJHSHUWXUEDWLRQVFKHPHLVGHYHORSHGDQG )LJ  VKRZV WKDW FRUUHODWHG '%3 UHGXFHV WKH
UHDOL]HG FRPSHQVDWLRQ LQ PXOWLSOH VWDJHV DQG LQ D FRPSXWDWLRQDO FRVW E\ D IDFWRU RI  ZLWKRXW
UHFXUVLYH IDVKLRQ ZKLFK LV DFKLHYHG E\ UHSUHVHQWLQJ SHUIRUPDQFHSHQDOW\DVFRPSDUHGWRVWDQGDUG'%3
VLJQDOV XVLQJ RUWKRJRQDO VDPSOLQJ IXQFWLRQV 7KH
PXOWLVWDJHSHUWXUEDWLRQVFKHPHVXEVWDQWLDOO\LPSURYHV
ERWKWKHFRPSHQVDWLRQSHUIRUPDQFHDQGFRPSXWDWLRQDO


 QHWZRUNVZLWKFRPSOH[PHVKFRQILJXUDWLRQVGXHWRWKH
ODFN RI SDWK LQIRUPDWLRQ RI VLJQDO SURSDJDWLRQ ,Q
FRQWUDVW 2%3 LV DSSOLFDEOH WR QHWZRUN V\VWHPV E\
SODFLQJ DQ 2%3 PRGXOH DIWHU HDFK WUDQVPLVVLRQ ILEHU 
7KH SURSDJDWLRQ LPSDLUPHQWV RI HDFK WUDQVPLVVLRQ
ILEHUDUHFRPSHQVDWHGE\WKH2%3PRGXOHIROORZLQJLW
$OWHUQDWLYHO\ WKH 2%3 PRGXOH FDQ EH SODFHG DW HDFK
QRGH ZKLFK FRPSHQVDWHV IRU WKH LPSDLUPHQWV GXH WR
 SURSDJDWLRQ IURP WKH SUHYLRXV QRGH WR FXUUHQW QRGH
)LJ4IDFWRULPSURYHPHQWYHUVXVFRPSXWDWLRQDOFRVW :H VWXGLHG D ILEHU RSWLF V\VWHP ZLWK UHFRQILJXUDEOH
VLQJOHFKDQQHOV\VWHPV\PEROUDWH *EDXGPRGXODWLRQ 
RSWLFDO DGGGURS PXOWLSOH[HUV 52$'0V WR
4$0WUDQVPLVVLRQGLVWDQFH îNP)URP5HI>@
LQYHVWLJDWHWKHSHUIRUPDQFHRI2%3LQPHVKQHWZRUNV

DVVKRZQLQ)LJ
,9 237,&$/%$&.3523$*$7,2186,1*
',63(56,21'(&5($6,1*),%(5 transmission fiber OBP module
×N1

'LJLWDO PHWKRGV UHTXLUH HQRUPRXV FRPSXWDWLRQDO Tx OPC BPF G

UHVRXUFHVHVSHFLDOO\IRU:'0V\VWHPV:HSURSRVHGD ×N2 ROADM

Drop
Add
OBP module transmission fiber
FRPSHQVDWLRQ VFKHPH WR LPSOHPHQW EDFN SURSDJDWLRQ
G BPF OPC
LQ WKH RSWLFDO GRPDLQ >@ %DVHG RQ WKH 1/6( ZH
Drop
ROADM ×N3
GHULYHG DQDO\WLFDO H[SUHVVLRQV IRU WKH GHVLUHG Add
transmission fiber OBP module

GLVSHUVLRQ SURILOH DQG WKH UHTXLUHG ILEHU OHQJWK ZKLFK OPC BPF G Rx

FDQ IXOO\ FRPSHQVDWH IRU .HUU QRQOLQHDU HIIHFWV LQ WKH

 )LJ6FKHPDWLFRIDILEHURSWLFFRPPXQLFDWLRQV\VWHPZLWK
WUDQVPLVVLRQILEHU)LJFRPSDUHVWKHSHUIRUPDQFHRI
52$'0V7[WUDQVPLWWHU23&RSWLFDOSKDVHFRQMXJDWRU%3)
2%3ZLWKRWKHUFRPSHQVDWLRQVFKHPHV2%3HQKDQFHV
EDQGSDVVILOWHU52$'0UHFRQILJXUDEOHRSWLFDODGGGURS
WKH V\VWHP UHDFK RI D :'0 V\VWHP E\  DV
PXOWLSOH[HU5[UHFHLYHU
FRPSDUHG WR '%3 ZLWK  NP VWHS VL]H 2%3 FRXOG

SURYLGH FRPSHQVDWLRQ RI QRQOLQHDU LPSDLUPHQWV RI D  NKPGCTEQORGP
:'0V\VWHPLQUHDOWLPH &$2
 1$2
3HCEVQT
F$


            
.CWPEJRQYGTRGTEJCPPGN
F$O 
)LJ4IDFWRUYVODXQFKSRZHUSHUFKDQQHOQRRI:'0
 FKDQQHOV FKDQQHOVSDFLQJ *+]V\PEROUDWH 
)LJ%(5YVODXQFKSRZHUSHUFKDQQHOQRRI:'0 *EDXGPRGXODWLRQ 4$0WRWDOWUDQVPLVVLRQGLVWDQFH 
FKDQQHOV FKDQQHOVSDFLQJ *+]V\PEROUDWH  îNP
*EDXGPRGXODWLRQ 4$0WUDQVPLVVLRQGLVWDQFH î
NP)URP5HI>@ )LJFRPSDUHVWKHSHUIRUPDQFHRI2%3ZLWK'%3

0RUHRYHU LW LV KDUG WR XVH GLJLWDO WHFKQLTXHV WR 'XH WR WKH ORVV RI SDWK LQIRUPDWLRQ RQO\

FRPSHQVDWH IRU QRQOLQHDU LPSDLUPHQWV LQ ILEHU RSWLF VLQJOHFKDQQHO'%3LVSRVVLEOH ZKLFKRQO\EULQJV

G% 4IDFWRU JDLQ DV FRPSDUHG ZLWK OLQHDU


FRPSHQVDWLRQ +RZHYHU 2%3 EULQJV  4IDFWRU FRPSHQVDWLRQ LQ ORQJKDXO RSWLFDO FRPPXQLFDWLRQ V\VWHPV´
2SW([SUHVV
JDLQV )LJ  FRPSDUHV WKH RSWLPDO FRQVWHOODWLRQV RI
>@ ; /LDQJ DQG 6 .XPDU ³&RUUHODWHG GLJLWDO EDFN SURSDJDWLRQ
'%3DQG2%3UHVSHFWLYHO\ EDVHG RQ SHUWXUEDWLRQ WKHRU\´ 2SW ([SUHVV 
 

>@ - 6KDR 6 .XPDU DQG ; /LDQJ ³'LJLWDO EDFN SURSDJDWLRQ

 ZLWK RSWLPDO VWHS VL]H IRU SRODUL]DWLRQ PXOWLSOH[HG
3WCFTCVWTG


WUDQVPLVVLRQ´IEEE3KRWRQ7HFKQRO/HWW

 

>@ =7DR/'RX:<DQ//L7+RVKLGDDQG-&5DVPXVVHQ

 ³0XOWLSOLHUIUHH LQWUDFKDQQHO QRQOLQHDULW\ FRPSHQVDWLQJ

           DOJRULWKPRSHUDWLQJDWV\PEROUDWH´-/LJKWZ7HFKQRO
+PRJCUG

 >@ < *DR - & &DUWOHGJH $ 6 .DUDU DQG 6 6+ <DP
 ³5HGXFLQJ WKH FRPSOH[LW\ RI QRQOLQHDULW\ SUHFRPSHQVDWLRQ
 XVLQJ V\PPHWULF ('& DQG SXOVH VKDSLQJ´ LQ WK (XURSHDQ
3WCFTCVWTG


&RQIHUHQFHDQG([KLELWLRQRQ2SWLFDO&RPPXQLFDWLRQ(&2&



 >@ 7 2\DPD + 1DNDVKLPD 6 2GD 7 <DPDXFKL = 7DR 7
 +RVKLGD DQG - & 5DVPXVVHQ ³5REXVW DQG HIILFLHQW

         UHFHLYHUVLGH FRPSHQVDWLRQ PHWKRG IRU LQWUDFKDQQHOQRQOLQHDU
+PRJCUG  HIIHFWV´LQ2SWLFDO)LEHU&RPPXQLFDWLRQ&RQIHUHQFH2SWLFDO
)LJ6LJQDOFRQVWHOODWLRQVREWDLQHGDWRSWLPDOSRZHUVWRS 6RFLHW\RI$PHULFDSDSHU7X$
'%3ERWWRP2%3 >@ ; /LDQJ DQG 6 .XPDU ³0XOWLVWDJH SHUWXUEDWLRQ WKHRU\ IRU
 FRPSHQVDWLQJ LQWUDFKDQQHO QRQOLQHDU LPSDLUPHQWV LQ
ILEHURSWLFOLQNV´2SW([SUHVV
9 &21&/86,216 >@ ; /LDQJ 6 .XPDU - 6KDR 0 0DOHNLKD DQG ' 9 3ODQW
:H LQYHVWLJDWHG GLJLWDO DQG RSWLFDO QRQOLQHDU ³'LJLWDO FRPSHQVDWLRQ RI FURVVSKDVH PRGXODWLRQ GLVWRUWLRQV
FRPSHQVDWLRQ WHFKQLTXHV IRU ILEHU RSWLF XVLQJSHUWXUEDWLRQWHFKQLTXHIRUGLVSHUVLRQPDQDJHGILEHURSWLF
V\VWHPV´2SW([SUHVV
FRPPXQLFDWLRQ V\VWHPV :H GHYHORSHG D PXOWLVWDJH
>@ 6 .XPDU DQG ' <DQJ ³2SWLFDO EDFNSURSDJDWLRQ IRU
SHUWXUEDWLRQ WHFKQLTXH WKDW LPSURYHV WKH 4IDFWRU E\ ILEHURSWLFFRPPXQLFDWLRQVXVLQJKLJKO\QRQOLQHDUILEHUV´2SW
 G% DV FRPSDUHG ZLWK OLQHDU FRPSHQVDWLRQ :H /HWW
>@ -6KDRDQG6.XPDU³2SWLFDOEDFNSURSDJDWLRQIRUILEHURSWLF
VWXGLHG D FRUUHODWHG '%3 WKDW UHGXFHV WKH
FRPPXQLFDWLRQVXVLQJRSWLFDOSKDVHFRQMXJDWLRQDWWKHUHFHLYHU´
FRPSXWDWLRQDO FRPSOH[LW\ E\ D IDFWRU RI  $OVR ZH 2SW/HWW 
SUHVHQWHG DQ 2%3 WHFKQLTXH XVLQJ '') ZKLFK >@ 0'3HOXVL³:'0VLJQDODOORSWLFDOSUHFRPSHQVDWLRQRIWKH
LQFUHDVHV WKH WUDQVPLVVLRQ UHDFK E\ D IDFWRU RI  DV ILEHU QRQOLQHDULW\ LQ GLVSHUVLRQPDQDJHG OLQNV´ ,((( 3KRWRQ
7HFKQRO/HWW
FRPSDUHG WR OLQHDU FRPSHQVDWLRQ DQG SURYLGHV  G%
>@ 6.XPDUDQG-6KDR³2SWLFDOEDFNSURSDJDWLRQZLWKRSWLPDO
4IDFWRUJDLQVDVFRPSDUHGZLWKWKHFRQYHQWLRQDO'%3 VWHS VL]H IRU ILEHU RSWLF WUDQVPLVVLRQ V\VWHPV´ ,((( 3KRWRQ
VFKHPHLQDILEHURSWLFPHVKQHWZRUN 7HFKQRO/HWW
>@ ; /LDQJ 6 .XPDU DQG - 6KDR ³,GHDO RSWLFDO

EDFNSURSDJDWLRQ RI VFDODU 1/6( XVLQJ GLVSHUVLRQGHFUHDVLQJ
5()(5(1&(6 ILEHUV IRU :'0 WUDQVPLVVLRQ´ 2SW ([SUHVV 
>@ ;/L;&KHQ**ROGIDUE(0DWHR,.LP)<DPDQDQG 
* /L ³(OHFWURQLF SRVWFRPSHQVDWLRQ RI :'0 WUDQVPLVVLRQ 
LPSDLUPHQWV XVLQJ FRKHUHQW GHWHFWLRQ DQG GLJLWDO VLJQDO 
SURFHVVLQJ´2SW([SUHVV 
>@ ( ,S DQG - 0 .DKQ ³&RPSHQVDWLRQ RI GLVSHUVLRQ DQG 
QRQOLQHDU LPSDLUPHQWV XVLQJ GLJLWDO EDFNSURSDJDWLRQ´ - 
/LJKWZ7HFKQRO 
>@ / % 'X DQG $ - /RZHU\ ³,PSURYHG VLQJOH FKDQQHO 
EDFNSURSDJDWLRQ IRU LQWUDFKDQQHO ILEHU QRQOLQHDULW\