Abstract

By assuming the nonlinear noise as a signal-independent circular Gaussian noise, a typical case in non-dispersion managed links with coherent multilevel modulation formats, we provide several analytical properties of a new quality parameter – playing the role of the signal to noise ratio (SNR) at the sampling gate in the coherent receiver – which carry over to the Q-factor versus power (or “bell”) curves. We show that the maximum Q is reached at an optimal power, the nonlinear threshold, at which the amplified spontaneous emission (ASE) noise power is twice the nonlinear noise power, and the SNR penalty with respect to linear propagation is 10Log(32)1.76dB,, although the Q-penalty is somewhat larger and increases at lower Q-factors, as we verify for the polarization-division multiplexing quadrature phase shift keying (PDM-QPSK) format. As we vary the ASE power, the maxima of the SNR vs. power curves are shown to slide along a straight-line with slope ≃−2 dB/dB. A similar behavior is followed by the Q-factor maxima, although for PDM-QPSK the local slope is around −2.7 dB/dB for Q-values of practical interest.

© 2011 OSA

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  1. In the following, we will call noise both the nonlinear perturbations coming from the same channel, which should more properly be called distortions, and cross-channel nonlinear perturbations.
  2. A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. Tapia Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” Proc. ECOC’10, paper P4.07.
  3. P. Ramanatanis and Y. Frignac, “Pattern-dependent nonlinear impairments on QPSK signals in dispersion-managed optical transmission systems,” Proc. ECOC’10 , paper Mo.1.C.4.
  4. G. Bosco, V. Curri, A. Carena, P. Poggiolini, and F. Forghieri, “On the performance of Nyquist-WDM terabit superchannels based on PM-BPSK, PM-QPSK, PM-8QAM or PM-16QAM subcarriers,” J. Lightwave Technol. 29, 53–61 (2011).
    [CrossRef]
  5. H. Louchet, A. Hodzic, K. Petermann, A. Robinson, and R. Epworth, “Analytical model for the design of multi-span DWDM transmission systems,” IEEE Photon. Technol. Lett. 17, 247–249 (2005).
    [CrossRef]
  6. J. Tang, “The Shannon channel capacity of dispersion-free nonlinear optical fiber transmission,” J. Lightwave Technol. 19, 1104–1109 (2001).
    [CrossRef]
  7. E. Narimanov and P. P. Mitra, “The channel capacity of a fiber optics communication system: perturbation theory,” J. Lightwave Technol. 20, 530–537 (2002).
    [CrossRef]
  8. G. Bosco, A. Carena, R. Cigliutti, V. Curri, P. Poggiolini, and F. Forghieri, “Performance prediction for WDM PM-QPSK transmission over uncompensated links,” in Proc. OFC’11 , paper OThO7.
  9. A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. 16, 73–85 (2010).
    [CrossRef]
  10. A. Bononi, P. Serena, N. Rossi, and D. Sperti, “Which is the dominant nonlinearity in long-haul PDM-QPSK coherent transmissions?,” Proc. ECOC’10 , paper Th.10.E.1.
  11. E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightwave Technol. 27, 5115–5126 (2009).
    [CrossRef]
  12. G. Charlet, J. Renaudier, H. Mardoyan, P. Tran, O. Bertran Pardo, F. Verluise, M. Achouche, A. Boutin, F. Blache, J. Dupuy, and S. Bigo, “Transmission of 16.4-bit/s capacity over 2550 km using PDM QPSK modulation format and coherent receiver,” J. Lightwave Technol. 27, 153–157 (2009).
    [CrossRef]
  13. A. Georgiadis “Gain, phase imbalance, and phase noise effects on error vector magnitude,” IEEE Trans. Veh. Technol. 53, 443–449 (2004).
    [CrossRef]

2011 (1)

2010 (1)

A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. 16, 73–85 (2010).
[CrossRef]

2009 (2)

2005 (1)

H. Louchet, A. Hodzic, K. Petermann, A. Robinson, and R. Epworth, “Analytical model for the design of multi-span DWDM transmission systems,” IEEE Photon. Technol. Lett. 17, 247–249 (2005).
[CrossRef]

2004 (1)

A. Georgiadis “Gain, phase imbalance, and phase noise effects on error vector magnitude,” IEEE Trans. Veh. Technol. 53, 443–449 (2004).
[CrossRef]

2002 (1)

2001 (1)

Achouche, M.

Agrell, E.

Bertran Pardo, O.

Bigo, S.

Blache, F.

Bononi, A.

A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. 16, 73–85 (2010).
[CrossRef]

Bosco, G.

Boutin, A.

Carena, A.

Charlet, G.

Curri, V.

Dupuy, J.

Epworth, R.

H. Louchet, A. Hodzic, K. Petermann, A. Robinson, and R. Epworth, “Analytical model for the design of multi-span DWDM transmission systems,” IEEE Photon. Technol. Lett. 17, 247–249 (2005).
[CrossRef]

Forghieri, F.

Georgiadis, A.

A. Georgiadis “Gain, phase imbalance, and phase noise effects on error vector magnitude,” IEEE Trans. Veh. Technol. 53, 443–449 (2004).
[CrossRef]

Hodzic, A.

H. Louchet, A. Hodzic, K. Petermann, A. Robinson, and R. Epworth, “Analytical model for the design of multi-span DWDM transmission systems,” IEEE Photon. Technol. Lett. 17, 247–249 (2005).
[CrossRef]

Karlsson, M.

Louchet, H.

H. Louchet, A. Hodzic, K. Petermann, A. Robinson, and R. Epworth, “Analytical model for the design of multi-span DWDM transmission systems,” IEEE Photon. Technol. Lett. 17, 247–249 (2005).
[CrossRef]

Mardoyan, H.

Mitra, P. P.

Narimanov, E.

Petermann, K.

H. Louchet, A. Hodzic, K. Petermann, A. Robinson, and R. Epworth, “Analytical model for the design of multi-span DWDM transmission systems,” IEEE Photon. Technol. Lett. 17, 247–249 (2005).
[CrossRef]

Poggiolini, P.

Renaudier, J.

Robinson, A.

H. Louchet, A. Hodzic, K. Petermann, A. Robinson, and R. Epworth, “Analytical model for the design of multi-span DWDM transmission systems,” IEEE Photon. Technol. Lett. 17, 247–249 (2005).
[CrossRef]

Rossi, N.

A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. 16, 73–85 (2010).
[CrossRef]

Serena, P.

A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. 16, 73–85 (2010).
[CrossRef]

Tang, J.

Tran, P.

Verluise, F.

IEEE Photon. Technol. Lett. (1)

H. Louchet, A. Hodzic, K. Petermann, A. Robinson, and R. Epworth, “Analytical model for the design of multi-span DWDM transmission systems,” IEEE Photon. Technol. Lett. 17, 247–249 (2005).
[CrossRef]

IEEE Trans. Veh. Technol. (1)

A. Georgiadis “Gain, phase imbalance, and phase noise effects on error vector magnitude,” IEEE Trans. Veh. Technol. 53, 443–449 (2004).
[CrossRef]

J. Lightwave Technol. (5)

Opt. Fiber Technol. (1)

A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. 16, 73–85 (2010).
[CrossRef]

Other (5)

A. Bononi, P. Serena, N. Rossi, and D. Sperti, “Which is the dominant nonlinearity in long-haul PDM-QPSK coherent transmissions?,” Proc. ECOC’10 , paper Th.10.E.1.

In the following, we will call noise both the nonlinear perturbations coming from the same channel, which should more properly be called distortions, and cross-channel nonlinear perturbations.

A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. Tapia Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” Proc. ECOC’10, paper P4.07.

P. Ramanatanis and Y. Frignac, “Pattern-dependent nonlinear impairments on QPSK signals in dispersion-managed optical transmission systems,” Proc. ECOC’10 , paper Mo.1.C.4.

G. Bosco, A. Carena, R. Cigliutti, V. Curri, P. Poggiolini, and F. Forghieri, “Performance prediction for WDM PM-QPSK transmission over uncompensated links,” in Proc. OFC’11 , paper OThO7.

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Figures (4)

Fig. 1
Fig. 1

New quality parameter S versus power P, for two values of ASE power NA differing by 3 dB (solid lines). Dashed lines indicate the left and right asymptotes [Eqs. (3), (4)]. Breakpoints are marked with squares. Maxima are marked with circles, and their vertical and horizontal distance from the linear left asymptote is 1.76 dB. As NA is changed, the maxima slide along the shown dash-dotted line with slope −2 dB/dB.

Fig. 2
Fig. 2

Q-factor versus SNR for a 28 Gbaud PDM-QPSK signal and DSP-based coherent receiver. Symbols: Monte-Carlo simulations. Solid line: parablic fit Eq. (11).

Fig. 3
Fig. 3

Q 2 (left) and SNR S (right) vs. channel power P for an SMF NDM 12x100 km link and 7 channels with 112Gb/s PDM-QPSK modulation on a 50 GHz grid, for NA = [−10, −9.2, −8.4] dBm. Symbols: simulations. Solid lines: Analytical best fit. Left and right asymptotes and locus of maxima are also shown for reference.

Fig. 4
Fig. 4

Q-penalty at NLT vs. Q-factor at NLT for 28 Gbaud PDM-QPSK signal and DSP coherent receiver. Symbols: Monte-Carlo simulations. Solid line: Eq. (12). aNL = 0.0066 (mW)−2.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

r = s P + n L + n NL
N NL = Var [ n NL ] = a NL P 3 [ W ]
S = P N A + a NL P 3 .
S L , dB P dB N A , dB if P P B
S R , dB 2 P d B a NL , dB if P P B
S = S L 1 + a NL P 3 N A
SP = 1 + a NL P 3 N A
N A = 2 ( a NL P 3 )
P NLT = ( N A 2 a NL ) 1 3
S NLT = P NLT 3 2 N A = ( 3 3 a NL ( N A 2 ) 2 ) 1 3 .
Q = 2 erfc 1 ( 2 BER ( S ) )
Q dB 2 = A OSN R dB 2 + B OSN R dB C
Q P dB = S P dB [ B A ( S P dB + 2 ( S dB + b ) ]

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