Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise

doi:10.1364/OE.19.012781

Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise

Edouard Grellier and Alberto Bononi »View Author Affiliations

Optics Express, Vol. 19, Issue 13, pp. 12781-12788 (2011)
http://dx.doi.org/10.1364/OE.19.012781

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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 $10 Log (\frac{3}{2}) ≃ 1.76 dB,$ , 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.

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: February 28, 2011
Revised Manuscript: April 22, 2011
Manuscript Accepted: May 6, 2011
Published: June 17, 2011

Citation
Edouard Grellier and Alberto Bononi, "Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise," Opt. Express 19, 12781-12788 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-13-12781

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References

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, 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]
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]
J. Tang, “The Shannon channel capacity of dispersion-free nonlinear optical fiber transmission,” J. Lightwave Technol. 19, 1104–1109 (2001). [CrossRef]
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]
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.
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]
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.
E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightwave Technol. 27, 5115–5126 (2009). [CrossRef]
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]
A. Georgiadis “Gain, phase imbalance, and phase noise effects on error vector magnitude,” IEEE Trans. Veh. Technol. 53, 443–449 (2004). [CrossRef]

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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]

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Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise