optimization of pulse and filter shape: matched filter

center frequency channel PM-16QAM PM-32QAM PM-64QAM PM-128QAM PM-256QAM. ECOC 2019 –Dublin www.optcom.polito.it 13 CUT ASE NLI OSNR P PP dB dB OSNR OS...

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accuracy ?? ECOC 2019 – Dublin

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The version with ISRS Nspan in [4] is about twice Rx (n) G NLI ( f CUT ) = GNLI ( f CUT ) as complex

 n =1

Nspan

  ( f )e (k )

(

)

k) −2 ( k ) f CUT  L(span

CUT

k = n +1

N ch n)  (n) 2 (n)  In( n )this paper 2 16 we( n ) 2 ( n ) −2 ( n ) ( f CUT ) L(span (n) ( n) (n) G NLI (on f CUTC-band  GCUT  ( GCUT ) I CUT + ) = (and)  f CUT  e  ( n ) 2 Gnch I nch  focus 27 nch =1, nch  nCUT   these formulas do not include ISRS ( n)     (n) (n) (n)

(

I n(chn )

(n)

)

 ( n)  2,nch Bnch   2,nch 2   − asinh   2 asinh  f − f + B   nch CUT   2  CUT  2 n f n(chn )  2 n f n(cnh )    = ( n) ( n) 4  2,nch  2 n f nch

(n) I CUT

( )

( )

  2  ( n)  2,CUT 2 asinh  BCUT   4  n f CUT    = ) 2 2,( nCUT  2 n f CUT

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(

(

)

)

( )

ch

 2,( n ) =  2( n ) + 3( n )  2 f CUT

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)

 ( n) Bnch   f nch − f CUT −  BCUT   2   

 2,( nn) =  2( n ) + 3( n )  f n( n ) + f ch

(

CUT

CUT

− 2 f c( n ) 

− 2 f c( n ) 

6

G NLI ( f CUT ) = Rx

Nspan

Nspan

 G ( f )   ( f )e (n)

NLI

n =1

(k )

CUT

(

)

k) −2 ( k ) f CUT  L(span

CUT

k = n +1

N ch n)  (n) 2 (n)  2 16 ( n ) 2 ( n ) −2 ( n ) ( f CUT ) L(span (n) (n) ( n) (n) G NLI ( f CUT ) = (  )  f CUT  e  GCUT  ( GCUT ) I CUT +  ( n ) 2 Gnch I nch  27 nch =1, nch  nCUT  

(

I n(chn )

 ( n)  2, nch 2 asinh    2 n f n(chn )  =

(n) I CUT

( )

)

  (n)  ( n) Bn(chn )   2, nch 2  f nch − f CUT +  BCUT  − asinh     2  2 n f n(cnh )   

( )

4  2,( nn)ch  2 n f n(cnh )

  2  ( n)  2,CUT 2 asinh  BCUT   4  n f CUT    = ) 2 2,( nCUT  2 n f CUT

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(

(n)

(

)

)

( )

ch

 2,( n ) =  2( n ) + 3( n )  2 f CUT

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)

  ( n) Bn(chn )   f nch − f CUT −  BCUT   2   

 2,( nn) =  2( n ) + 3( n )  f n( n ) + f ch

(

CUT

CUT

− 2 f c( n ) 

− 2 f c( n ) 

7

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* the full-fledged, numerically-integrated EGN-model ECOC 2019 – Dublin

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PM-16QAM PM-32QAM PM-64QAM PM-128QAM PM-256QAM

WDM COMB

THz

LINK

SMF TWC ELEAF

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PM-16QAM PM-32QAM PM-64QAM PM-128QAM PM-256QAM

WDM COMB

THz

lowest frequency channel

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center frequency channel

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highest frequency channel

12

OSNR =

PCUT PASE + PNLI

dB OSNR dB − OSNR CFM EGN

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PM-16QAM PM-32QAM PM-64QAM PM-128QAM PM-256QAM

WDM COMB

THz

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dB OSNR dB − OSNR CFM EGN

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dB OSNR dB − OSNR CFM EGN

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G NLI ( f CUT ) = Rx

Nspan

Nspan

 G ( f )   ( f )e (n)

(k )

CUT

NLI

n =1

(

)

k) −2 ( k ) f CUT  L(span

CUT

k = n +1

N ch n)  (n) 2 (n)  2 16 ( n ) 2 ( n ) −2 ( n ) ( f CUT ) L(span (n) (n) ( n) (n) G NLI ( f CUT ) = (  )  f CUT  e  GCUT  ( GCUT ) I CUT +  ( n ) 2 Gnch I nch  27 nch =1, nch  nCUT  

(

I n(chn )

 ( n)  2, nch 2 asinh    2 n f n(chn )  =

( )

)

  (n)  ( n) Bn(chn )   2, nch 2  f nch − f CUT +  BCUT  − asinh     2  2 n f n(cnh )   

 2,( nn) =  2( n ) + 3( n )  f n( n ) + f ECOC 2019 – Dublin

( )

( )

4  2,( nn)ch  2 n f n(cnh )

(n) I CUT

ch

(n)

ch

CUT

(

)

  ( n) Bn(chn )   f nch − f CUT −  BCUT   2   

  2  ( n)  2,CUT 2 asinh  BCUT   4  n f CUT    = ( n) 2 2,CUT  2 n f CUT

(

(

)

− 2 f c( n )  www.optcom.polito.it

)

 2,( n ) =  2( n ) + 3( n )  2 f CUT

CUT

− 2 f c( n )  18

“machine learning” factors G NLI ( f CUT ) = Rx

Nspan

Nspan

 G ( f )   ( f )e (n)

n =1

(k )

CUT

NLI

(

)

k) −2 ( k ) f CUT  L(span

CUT

k = n +1

N ch n)  (n)  2 16 ( n ) 2 ( n ) −2 ( n ) ( f CUT ) L(span (n) (n) ( n) 2 ( n) ( n) ( n) ( n) G NLI ( f CUT ) = (  )  f CUT  e  GCUT    CUT  ( GCUT ) I CUT +  ( n ) 2nch  Gnch I nch  27 nch =1 , nch  nCUT  

(

I n(chn )

(n)

)

 ( n)  2, nch 2 asinh    2 n f n(chn )  =

( )

  (n)  ( n) Bn(chn )   2, nch 2  f nch − f CUT +  BCUT  − asinh     2  2 n f n(cnh )   

( )

4  2,( nn)ch  2 n f n(cnh )

(n) I CUT

 2,( nn) =  2( n ) + 3( n )  f n( n ) + f ch

ECOC 2019 – Dublin

( )

ch

CUT

(

)

  ( n) Bn(chn )   f nch − f CUT −  BCUT   2   

  2  ( n)  2,CUT 2 asinh  BCUT   4  n f CUT    = ( n) 2 2,CUT  2 n f CUT

(

(

)

− 2 f c( n )  www.optcom.polito.it

)

 2,( n ) =  2( n ) + 3( n )  2 f CUT

CUT

− 2 f c( n )  19

(

 n( n ) = a1 + a2   na + 1 + a4  2,acc ( n, nch ) + a5 3

ch



(n) CUT

ch

= a9 + a10   CUT a11



(

)

a6

  a   a8  7 nch

 a13 + 1 + a12 RCUT + a14  2,acc n, nCUT + a15 

(

RCUT

)

)

a16

 a18  a17   CUT

 n −1

k)  2,acc ( n, nch ) =   2,( kn)  L(span k =1

ch

a1 ECOC 2019 – Dublin

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a18 20

dB OSNR dB − OSNR CFM EGN

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dB OSNR dB − OSNR CFM EGN

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dB OSNR dB − OSNR CFM EGN

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PM-16QAM PM-32QAM PM-64QAM PM-128QAM PM-256QAM

WDM COMB COMB WDM

THz

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PM-16QAM PM-32QAM PM-64QAM PM-128QAM PM-256QAM

WDM COMB COMB WDM

D>1 ps/(nm km)

high-freq channel

D ps/(nm km)

D=0.58 THz

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dB OSNR dB − OSNR CFM EGN

there are “outliers”

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dB OSNR dB − OSNR CFM EGN

“outermost” outlier at +0.62 dB

turns out NLI «coherence» is the problem ECOC 2019 – Dublin

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“machine learning” factors G NLI ( f CUT ) = Rx

Nspan

Nspan

 G ( f )   ( f )e (n)

n =1

(k )

CUT

NLI

(

)

k) −2 ( k ) f CUT  L(span

CUT

k = n +1

N ch n)  (n)  2 16 ( n ) 2 ( n ) −2 ( n ) ( f CUT ) L(span (n) (n) ( n) 2 ( n) ( n) ( n) ( n) G NLI ( f CUT ) = (  )  f CUT  e  GCUT    CUT  ( GCUT ) I CUT +  ( n ) 2nch  Gnch I nch  27 nch =1 , nch  nCUT  

(

I n(chn )

(n)

)

 ( n)  2, nch 2 asinh    2 n f n(chn )  =

( )

  (n)  ( n) Bn(chn )   2, nch 2  f nch − f CUT +  BCUT  − asinh     2  2 n f n(cnh )   

( )

4  2,( nn)ch  2 n f n(cnh )

(n) I CUT

 2,( nn) =  2( n ) + 3( n )  f n( n ) + f ch

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( )

ch

CUT

(

)

  ( n) Bn(chn )   f nch − f CUT −  BCUT   2   

  2  ( n)  2,CUT 2 asinh  BCUT   4  n f CUT    = ( n) 2 2,CUT  2 n f CUT

(

(

)

− 2 f c( n )  www.optcom.polito.it

)

 2,( n ) =  2( n ) + 3( n )  2 f CUT

CUT

− 2 f c( n )  28

“machine learning” factors

“NLI coherence correction” term G NLI ( f CUT ) = Rx

Nspan

Nspan

 G ( f )   ( f )e (n)

n =1

(k )

CUT

NLI

(

)

k) −2 ( k ) f CUT  L(span

CUT

k = n +1

N ch n)  (n)  2 16 ( n ) 2 ( n ) −2 ( n ) ( f CUT ) L(span (n) (n) ( n) 2 ( n) ( n) ( n) ( n) G NLI ( f CUT ) = (  )  f CUT  e  GCUT    CUT  ( GCUT ) I CUT +  ( n ) 2nch  Gnch I nch  27 nch =1 , nch  nCUT  

(

I n(chn )

)

 ( n)  2, nch 2 asinh    2 n f n(chn )  =

( )

(n)

I CUT

(n)

  (n)  ( n) Bn(chn )   2, nch 2  f nch − f CUT +  BCUT  − asinh     2  2 n f n(cnh )   

( )

( )

4  2,( nn)ch  2 n f n(cnh )

(

) (n) 2   2  ( n)  Si  2  2,( nCUT Lspan BCUT 2,CUT 2   asinh BCUT + 2  4  n f CUT    n f CUT L(spna)n   = 2 2(,nCU) T  2 n f CUT

(

)

(

) (

) HN ( N

)

 

(

)

  ( n) Bn(chn )   f nch − f CUT −  BCUT   2   

span − 1) +

1 − N span   N span 

[7] P. Poggiolini, “A Closed-Form GN-Model Non-Linear Interference Coherence Term,” arXiv:1906.03883, June 10th 2019. ( n) (n) (n) (n) ( n) (n) (n) (n) (n)  

 2,n =  2 + 3  f n + f ch

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ch

CUT

− 2 f c 

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 2,

CUT

=  2 + 3  2 f CUT − 2 f c 

29

no coher. term

with coher. term

clean !

clean !

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dB OSNR dB − OSNR CFM SIM

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