Abstract

The probability density function and impact of equalization-enhanced phase noise (EEPN) is analytically investigated and simulated for 100 Gb/s coherent systems using electronic dispersion compensation. EEPN impairment induces both phase noise and amplitude noise with the former twice as much as the latter. The effects of transmitter phase noise on EEPN are negligible for links with residual dispersion in excess of 700 ps/nm. Optimal linear equalizer in the presence of EEPN is derived but show only marginal performance improvement, indicating that EEPN is difficult to mitigate using simple DSP techniques. In addition, the effects of EEPN on carrier recovery techniques and corresponding cycle slip probabilities are studied.

© 2010 Optical Society of America

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  1. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, "Coherent detection in optical fiber systems,’’Opt. Express 16(1), 753-791 (2008).
    [CrossRef] [PubMed]
  2. E. Ip and J. M. Kahn, "Digital equalization of Chromatic Dispersion and Polarization Mode Dispersion," IEEE/OSAJ. Lightwave Technol. 25(8), 2033-2043 (2007).
    [CrossRef]
  3. M. G. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments," IEEE Photon.Technol. Lett. 16(2), 674-676 (2004).
    [CrossRef]
  4. G. Goldfarb and G. Li, "Chromatic dispersion compensation using digital IIR filtering with coherent detection," IEEE Photon. Technol. Lett. 19(13), 969-971 (2007).
    [CrossRef]
  5. K. Roberts, C. Li, L. Strawczyski, M. O. Sullivan, and I. Hardcastle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18(13), 403-405 (2006).
    [CrossRef]
  6. F. Buchali and H. Bulow, "Adaptive PMD Compensation by Elecgtrical and Optical Techniques," IEEE/OSAJ. Lightwave Technol. 22(4), 1116-1126 (2004).
    [CrossRef]
  7. D. Schlump, B. Wedding, and H. Bulow, "Electronic equalization of PMD and chromatic dispersion induced distortion after 100 km standard fibre at 10Gb/s," in Proceedings ECOC, Madrid, Spain, 1998, pp. 535-536.
  8. J. M. Gené, P. J. Winzer, S. Chandrasekhar, and H. Kogelnik, "Simultaneous compensation of Polarization Mode Dispersion and chromatic dispersion using electronic signal processing," IEEE/OSAJ. Lightwave Technol. 26(7), 1735-1741 (2007).
    [CrossRef]
  9. H. Bulow, F. Buchali and A. Klekamp, "Electronic dispersion compensation," IEEE/OSAJ. Lightwave Technol. 26(1), 158-167 (2008).
    [CrossRef]
  10. E. Ip and J. M. Kahn, "Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation," IEEE/OSAJ. Lightwave Technol. 26(20), 3416-3425 (2008).
    [CrossRef]
  11. X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, "Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing," Opt. Express 16(2), 880-888 (2008).
    [CrossRef] [PubMed]
  12. K. Kikuchi, "Electronic post-compensation for nonlinear phase fluctuations in a 1000-km 20-Gbit/s optical quadrature phase-shift keying transmission system using the digital coherent receiver," Opt. Express 16(1), 889-896 (2008).
    [CrossRef] [PubMed]
  13. A.P.T. Lau and J. M. Kahn, "Signal design and detection in presence of nonlinear phase noise," J. Lightwave Technol. 25(10), 3008-3016 (2007).
    [CrossRef]
  14. E. Ip and J. M. Kahn, "Feedforward carrier recovery for coherent optical communications," J. Lightwave Technol. 25(9), 2675-2692 (2007).
    [CrossRef]
  15. D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, "Coherent Detection of Optical Quadrature Phase-Shift Keying Signals With Carrier Phase Estimation," J. Lightwave Technol. 24(1), 12-21 (2006).
    [CrossRef]
  16. R. Noe, "Phase noise-tolerant synchronous QPSK/BPSK baseband-type intradyne receiver concept with feedforward carrier recovery," J. Lightwave Technol. 23(2), 802-808 (2006).
    [CrossRef]
  17. S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, "Electronic compensation of chromatic dispersion using a digital coherent receiver," Opt. Express 15(5), 2120-2126 (2007).
    [CrossRef] [PubMed]
  18. G. Charlet, M. Salsi, P. Tran, M. Bertolini, H. Mardoyan, J. Renaudier, O. Bertran-Pardo, and S. Bigo, "72x100 Gb/s transmission over transoceanic distance, using large effective area fiber, hybrid Raman-Erbium amplification and coherent detection," in Proceedings OFC/NFOEC, San Diego, CA, 2009, Paper PDPB6.
  19. W. Shieh and K.P. Ho, "Equalization-enhanced phase noise for coherent detection systems using electronic digital signal processing," Opt. Express 16(20), 15718 - 15727 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2009 (1)

2008 (6)

2007 (6)

2006 (3)

2004 (2)

F. Buchali and H. Bulow, "Adaptive PMD Compensation by Elecgtrical and Optical Techniques," IEEE/OSAJ. Lightwave Technol. 22(4), 1116-1126 (2004).
[CrossRef]

M. G. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments," IEEE Photon.Technol. Lett. 16(2), 674-676 (2004).
[CrossRef]

Barros, D. J. F.

Bayvel, P.

Buchali, F.

Bulow, H.

Chandrasekhar, S.

Chen, X.

Gavioli, G.

Gené, J. M.

Goldfarb, G.

Hardcastle, I.

K. Roberts, C. Li, L. Strawczyski, M. O. Sullivan, and I. Hardcastle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18(13), 403-405 (2006).
[CrossRef]

Ho, K.P.

Ip, E.

Kahn, J. M.

Katoh, K.

Kikuchi, K.

Killey, R. I.

Kim, I.

Klekamp, A.

Kogelnik, H.

Lau, A. P. T.

Lau, A.P.T.

Li, C.

K. Roberts, C. Li, L. Strawczyski, M. O. Sullivan, and I. Hardcastle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18(13), 403-405 (2006).
[CrossRef]

Li, G.

Li, X.

Ly-Gagnon, D. S.

Mateo, E.

Noe, R.

Roberts, K.

K. Roberts, C. Li, L. Strawczyski, M. O. Sullivan, and I. Hardcastle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18(13), 403-405 (2006).
[CrossRef]

Savory, S. J.

Shieh, W.

Strawczyski, L.

K. Roberts, C. Li, L. Strawczyski, M. O. Sullivan, and I. Hardcastle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18(13), 403-405 (2006).
[CrossRef]

Sullivan, M. O.

K. Roberts, C. Li, L. Strawczyski, M. O. Sullivan, and I. Hardcastle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18(13), 403-405 (2006).
[CrossRef]

Taylor, M. G.

M. G. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments," IEEE Photon.Technol. Lett. 16(2), 674-676 (2004).
[CrossRef]

Tsukamoto, S.

Winzer, P. J.

Xie, C.

Yaman, F.

IEEE Photon. Technol. Lett. (2)

G. Goldfarb and G. Li, "Chromatic dispersion compensation using digital IIR filtering with coherent detection," IEEE Photon. Technol. Lett. 19(13), 969-971 (2007).
[CrossRef]

K. Roberts, C. Li, L. Strawczyski, M. O. Sullivan, and I. Hardcastle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18(13), 403-405 (2006).
[CrossRef]

IEEE Photon.Technol. Lett. (1)

M. G. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments," IEEE Photon.Technol. Lett. 16(2), 674-676 (2004).
[CrossRef]

J. Lightwave Technol. (9)

F. Buchali and H. Bulow, "Adaptive PMD Compensation by Elecgtrical and Optical Techniques," IEEE/OSAJ. Lightwave Technol. 22(4), 1116-1126 (2004).
[CrossRef]

J. M. Gené, P. J. Winzer, S. Chandrasekhar, and H. Kogelnik, "Simultaneous compensation of Polarization Mode Dispersion and chromatic dispersion using electronic signal processing," IEEE/OSAJ. Lightwave Technol. 26(7), 1735-1741 (2007).
[CrossRef]

H. Bulow, F. Buchali and A. Klekamp, "Electronic dispersion compensation," IEEE/OSAJ. Lightwave Technol. 26(1), 158-167 (2008).
[CrossRef]

E. Ip and J. M. Kahn, "Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation," IEEE/OSAJ. Lightwave Technol. 26(20), 3416-3425 (2008).
[CrossRef]

A.P.T. Lau and J. M. Kahn, "Signal design and detection in presence of nonlinear phase noise," J. Lightwave Technol. 25(10), 3008-3016 (2007).
[CrossRef]

E. Ip and J. M. Kahn, "Feedforward carrier recovery for coherent optical communications," J. Lightwave Technol. 25(9), 2675-2692 (2007).
[CrossRef]

D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, "Coherent Detection of Optical Quadrature Phase-Shift Keying Signals With Carrier Phase Estimation," J. Lightwave Technol. 24(1), 12-21 (2006).
[CrossRef]

R. Noe, "Phase noise-tolerant synchronous QPSK/BPSK baseband-type intradyne receiver concept with feedforward carrier recovery," J. Lightwave Technol. 23(2), 802-808 (2006).
[CrossRef]

E. Ip and J. M. Kahn, "Digital equalization of Chromatic Dispersion and Polarization Mode Dispersion," IEEE/OSAJ. Lightwave Technol. 25(8), 2033-2043 (2007).
[CrossRef]

Opt. Express (6)

Other (3)

D. Schlump, B. Wedding, and H. Bulow, "Electronic equalization of PMD and chromatic dispersion induced distortion after 100 km standard fibre at 10Gb/s," in Proceedings ECOC, Madrid, Spain, 1998, pp. 535-536.

G. Charlet, M. Salsi, P. Tran, M. Bertolini, H. Mardoyan, J. Renaudier, O. Bertran-Pardo, and S. Bigo, "72x100 Gb/s transmission over transoceanic distance, using large effective area fiber, hybrid Raman-Erbium amplification and coherent detection," in Proceedings OFC/NFOEC, San Diego, CA, 2009, Paper PDPB6.

C. Xie, "Local oscillator phase noise induced penalties in optical coherent detection systems using electronic chromatic dispersion compensation," in Proceedings OFC/NFOEC, San Diego, CA, 2009, Paper OMT4.

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Figures (12)

Fig 1.
Fig 1.

A coherent communication system in presence of both transmitter (Tx) phase noise e j ϕ t ( t ) and receiver (Rx) phase noise e j ϕ r ( t ) . The received signal is sampled and passed into a finite-impulse response (FIR) filter w followed by a carrier recovery (CR) unit to produce the symbol estimate n .

Fig. 2.
Fig. 2.

Pdf of EEPN for (a) Δυ = 5MHz, 6800 ps/nm uncompensated CD, no ASE noise; (b) Δυ = 5MHz, 13600 ps/nm uncompensated CD, no ASE noise; (c) Δυ = 10 MHz, 13600 ps/nm uncompensated CD, no ASE noise and (d) Δυ = 10 MHz, 13600 ps/nm uncompensated CD, OSNR = 13 dB. The modulation format is QPSK.

Fig. 3.
Fig. 3.

Phase noise variance vs. OSNR for a transmission distance of 1200 km using optical and electronic dispersion compensation. The LO linewidth is 3 MHz. In presence of Rx phase noise and electronic dispersion compensation, the overall phase noise variance increases significantly.

Fig.4.
Fig.4.

Phase noise variance vs. OSNR for a QPSK system with electronic dispersion compensation for various LO linewidths. The propagation distance is 3200 km.

Fig. 5.
Fig. 5.

Mean-squared error vs. OSNR for (a) 16-QAM and (b) 64-QAM systems with electronic dispersion compensation for various LO linewidths. The propagation distance is 1600 km.

Fig. 6.
Fig. 6.

Amplitude and phase noise variance vs. OSNR in presence of electronic CD compensation with a LO linewidth of 3MHz for a QPSK system. The length of propagation is 1200 km. Inset: corresponding received signal constellation diagram showing asymmetric noise distribution.

Fig. 7.
Fig. 7.

Phase noise variance using electronic CD compensation for various laser linewidths and propagation distance for a QPSK system. A laser linewidth of 1MHz corresponds to a 0 MHz Tx linewidth and 1 MHz Rx linewidth for the ‘Rx only’ case and 1 MHz linewidth for both lasers for the ‘Rx, Tx’ case.

Fig. 8.
Fig. 8.

Magnitude of MMSE filter tap coefficients for a QPSK system with electronic CD compensation and a LO linewidth of 3 MHz. The transmission distance is 1200 km; the over-sampling rate is 2;the OSNR is 21 dB; the length of the filter is 539 with tap index of 0 corresponding to the center tap.

Fig. 9.
Fig. 9.

Mean-squared error with various FIR filters for a QPSK system with electronic CD compensation. The length of propagation is 1200 km and the LO linewidth is 3MHz.

Fig. 10.
Fig. 10.

True carrier phase vs. tracked carrier phase for a QPSK system with a linewidth of 3 MHz for both the transmitter and receiver laser. The transmission distance is 1200 km. The tracking error is larger for systems with EEPN.

Fig. 11.
Fig. 11.

True carrier phase vs. tracked carrier phase for a QPSK system with a linewidth of 3 MHz for both the transmitter and receiver laser. The transmission distance is 1200 km. In presence of EEPN, the tracked carrier phase is more likely to have cycle slips.

Fig. 12.
Fig. 12.

Probability of cycle slips vs. OSNR for a QPSK system with 1200 km transmission. The linewidths of the transmitter and receiver laser are 3 MHz.

Equations (41)

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A ( t ) = n x n b ( t n T 0 )
y ( t ) = n x n q ( t n T 0 ) + ν ( t )
y = [ y S k + L y S k + L 1 y S k L + 1 y S k L ] T
x ̂ k = w T y .
w lin = ( E [ y * y T ] ) 1 E [ x k y * ] = A 1 α
A ( l , m ) = E [ y S k + L l * y S k + L m ] = n q * ( ( S k + L l ) T n T 0 ) q ( ( S k + L m ) T n T 0 )
+ N 0 p * ( t l T ) p ( t m T ) dt
α ( l ) = E [ x k y S k + L l * ] = q * ( ( S k + L l ) T k T 0 ) .
MSE 1 = E [ ε 2 ] = E [ x k α H A 1 y 2 ] = 1 α H A 1 α
σ θ 2 = E [ θ 2 ] 1 2 E [ ε 2 ]
E [ e j ( ϕ r ( t 1 ) ϕ r ( t 2 ) ) ] = exp ( π Δ υ t 1 t 2 ) .
y ( t ) = ( [ n x n g ( t n T 0 ) + n ( t ) ] e j ϕ r ( t ) ) * p ( t ) .
f ( ε x k ) = 1 C L · x C L 1 4 π 2 Δ υ T Λ ( X ) exp ( 1 4 π Δ υ T [ Re { ε }   Im { ε } ] Λ ( X ) 1 [ Re { ε } Im { ε } ] T )
y ( t ) = ( [ n x n g ( t n T 0 ) + n ( t ) ] · e j ϕ r ( t ) ) * p ( t ) = ( n x n g ( τ n T 0 ) ) e j ϕ r ( τ ) p ( t τ ) d τ + ( n ( t ) e j ϕ r ( t ) ) * p ( t ) .
A PN ( l , m ) = E [ y S k + L l * y S k + L m ]
= { n g * ( τ 1 n T 0 ) g ( τ 2 n T 0 ) p * ( ( S k + L l ) T τ 1 ) p ( ( S k + L m ) T τ 2 ) .
E [ e j ( ϕ r ( τ 2 ) ϕ r ( τ 1 ) ) ] d τ 1 d τ 2 } + N 0 p * ( t l T ) p ( t m T ) dt
= { n g * ( τ 1 n T 0 ) g ( τ 2 n T 0 ) p * ( ( S k + L l ) T τ 1 ) p ( ( S k + L m ) T τ 2 ) .
e π Δ υ τ 2 τ 1 d τ 1 d τ 2 } + N 0 p * ( t l T ) p ( t m T ) dt
α PN ( l ) = E [ x k y S k + L l * ] = g * ( τ k T 0 ) p * ( ( S k + L l ) T τ ) e π Δ υ τ k T 0 d τ .
( g ( t ) · e j ϕ r ( t ) ) * p ( t ) ( g ( t ) * p ( t ) ) · e j ϕ r ( t ) = q ( t ) e j ϕ r ( t )
y ( t ) = ( n x n q ( t n T 0 ) ) · e j ϕ r ( t ) + ( n ( t ) · e j ϕ r ( t ) ) * p ( t ) .
A PN ( l , m ) = E [ y S k + L l * y S k + L m ] = n q * ( ( S k + L l ) T n T 0 ) q ( ( S k + L m ) T n T 0 ) e π Δ υ l m T
+ N 0 p * ( t l T ) p ( t m T ) dt
α PN ( l ) = q * ( ( S k + L l ) T ) e π Δ υ L l T .
MSE 2 = E [ x k α T A 1 y 2 ] = 1 2 E [ x k y H ] A 1 α + α H A 1 E [ y * y T ] A 1 α
= 1 2 α PN H A 1 α + α H A 1 A PN A 1 α .
MSE 3 = E [ x k α PN T A PN 1 y 2 ] = 1 α PN H A PN 1 α PN .
y m = [ n x n q ( m T n T 0 ) ] e j ϕ r ( m T ) [ n x n q ( m T n T 0 ) ] [ 1 + j ϕ r ( m T ) ]
= n x n q ( m T n T 0 ) + j ϕ r ( m T ) n x n q ( m T n T 0 )
= Q m + Q m j ϕ r ( m T ) .
ε = x ̂ k x k = w lin T y · ( e j ϕ r ( k T 0 ) ) x k
= [ j Q S k + L Δ L J Q S k + L 1 Δ L 1 J Q S k L + 1 Δ L + 1 J Q S k L Δ L ] T w lin
= j w L Q S k + L Δ L + j w L 1 Q S k + L 1 Δ L 1 + jw L + 1 Q S k L + 1 Δ L + 1 + jw L Q S k L Δ L
= i = L 1 r i Δ i + 0 + i = 1 L r i Δ i
= i = L 1 [ ( Δ i Δ i + 1 ) m = L i r m ] + i = 1 L [ ( Δ i Δ i 1 ) m = i L r m ]
Λ ( X ) = [ i = L 1 ( m = L i Re { r m } ) 2 + i = 1 L ( m = i L Re { r m } ) 2 i = L 1 ( m = L i Re { r m } m = L i Im { r m } ) + i = 1 L ( m = i L Re { r m } m = i L Im { r m } ) i = L 1 ( m = L i Re { r m } m = L i Im { r m } ) + i = 1 L ( m = i L Re { r m } m = i L Im { r m } ) i = L 1 ( m = L i Im { r m } ) 2 + i = 1 L ( m = i L Im { r m } ) 2 ] .
P ( f ) P ( f f 1 ) for f 1 Δ υ 2 .
U ( f ) P ( f ) Δ υ 2 Δ υ 2 Φ ( f 1 ) G ( f f 1 ) df 1
Δ υ 2 Δ υ 2 Φ ( f 1 ) P ( f f 1 ) G ( f f 1 ) df 1
= Δ υ 2 Δ υ 2 Φ ( f 1 ) Q ( f f 1 ) df 1 = Q ( f ) * Φ ( f ) .

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