The achievable information rates of optical communication systems using ultra-wide bandwidth 100-nm distributed Raman amplification have been investigated for each individual subchannels, based on the first-order perturbative analysis of nonlinear distortions

Alvarado, A

Bayvel, P

Galdino, L

Killey, RI

Liga, G

Paskov, M

Saavedra Mondaca, GA

Semrau, D

Shevchenko, M

Xu, T

Shevchenko, Nikita A.

Xu, Tianhua

Semrau, Daniel

Saavedra, Gabriele Liga

Paskov, Milen

Galdino, Lidia

Alvarado, Alex

Killey, Robert I.

Bayvel, Polina

Warwick Research Archives Portal Repository

     warwick.ac.uk/lib-publications      Original citation: Shevchenko, Nikita A., Xu, Tianhua, Semrau, Daniel, Saavedra, Gabriele Liga, Paskov, Milen, Galdino, Lidia, Alvarado, Alex, Killey, Robert I. and Bayvel, Polina (2016) Achievable information rates estimation for 100-nm ramana amplified optical transmission system. In: 42nd European Conference on Optical Communication (ECOC 2016), Dusseldorf, Germany, 18-22 Sep 2016. Published in: Proceedings of ECOC 2016 ; 42nd European Conference on Optical Communication.  Permanent WRAP URL: http://wrap.warwick.ac.uk/94787   Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available.  Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way.  Publisher’s statement: © VDE Verlag 2016. Reproduced with permission. A note on versions: The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher’s version. Please see the ‘permanent WRAP URL’ above for details on accessing the published version and note that access may require a subscription.  For more information, please contact the WRAP Team at: wrap@warwick.ac.uk  Achievable Information Rates Estimation for 100-nm Raman-Amplified Optical Transmission System Nikita A. Shevchenko, Tianhua Xu*, Daniel Semrau, Gabriel Saavedra, Gabriele Liga, Milen Paskov, Lidia Galdino, Alex Alvarado, Robert I. Killey, Polina Bayvel Optical Networks Group, University College London (UCL), WC1E 7JE, London, United Kingdom, *tianhua.xu@ucl.ac.uk  Abstract The achievable information rates of optical communication systems using ultra-wide bandwidth 100-nm distributed Raman amplification have been investigated for each individual sub-channels, based on the first-order perturbative analysis of nonlinear distortions. Introduction To date, optical fibre communications have achieved unprecedented growth and success over the past three decades and now stand alone as the enabling technology that underpins the global information infrastructure. The data rates of optical communication systems have been raised from 100-Mbit/s per fibre in the 1970s to 10-Tbit/s in current commercial systems, an astonishing 100,000-fold increase. The key technologies that fueled this surge in capacity were wavelength division multiplexing (WDM), improved fibre design and fabrication, optical amplification and coherent detection. The use of Erbium-doped and Raman fibre amplifiers negated the need for electronic regenerators and enabled dense WDM transmission, although the success and performance of these amplifier technologies is seen as limiting the usable fibre bandwidth to approximately 10-15 THz, ultimately limiting the maximum throughput of optical systems. Within the usable optical bandwidth, the increase of the spectral efficiency in Nyquist-spaced WDM systems is determined by the densest constellation that can be used. Denser constellations, however, typically operate well only at high signal-to-noise ratios (SNRs), where high optical launch power is required1. In such schemes, the achievable information rate (AIR) of optical fibre communication systems is essentially limited by nonlinear (NL) distortions due to the optical Kerr effect manifesting itself as self-phase modulation, cross-phase modulation and four-wave mixing (FWM). The AIRs have been evaluated for the total bandwidth of approximately the optical C-band (~4.3-THz) under the key assumption of ideally distributed Raman amplification schemes, while the Raman pump power and the distribution of the optical field-gain along the amplifier span have not been taken into account2. In this paper, for the first time to our knowledge, the AIR of optical communication system using ultra-wideband optical Raman amplification extended to ~100-nm (12.51-THz) optical bandwidth in a standard single mode fiber (SSMF) has been numerically estimated by using a large-bandwidth first-order perturbative analysis of NL distortions. These estimations have been carried out separately for each sub-channel in Nyquist-spaced WDM transmission system. The AIR of the Raman-amplified transmission system with 1251-Channel× 10-GHz using linear electronic dispersion compensation (EDC) and full-field (FF) nonlinear compensation (NLC) has been analysed. A first-order perturbative analysis was implemented to numerically evaluate the NL distortions for each individual sub-channel in Nyquist-spaced WDM transmission system, by removing the assumption of the "whiteness" of the NL distortion spectra. Raman amplified optical system  We examine the backward-pumped geometry of optical Raman amplification. In this model, the Raman power gain is independent of the laser wavelength, and the pump depletion effect is neglected. The AIRs are evaluated in the optical communication system with distributed Raman amplification over ~100-nm (12.51-THz). We consider the transmission consisting of 1251 sub-channels with a symbol rate of 10-Gbaud and a channel spacing of 10-GHz. The detailed Tab. 1: System parameter values  Parameters Values Num. of Channels () 1251 Symbol Rate () 10-Gbaud Channel spacing (∆) 10-GHz Roll-off factor  0% Total Raman pump power (	) 5×680 mW Span length () 80 km Fiber loss () 0.20 dB/km Fiber loss for Raman pump (	) 0.25 dB/km Dispersion () 17.0 ps/nm/km Dispersion slope () 0.067 ps/nm2/km NL coefficient () 1.20 1/W/km  parameters of the optical communication system are indicated in Tab. 1. Analysis of nonlinear distortions for Raman amplified system In optical communications, the performance of the WDM transmission system can be described by an effective SNR including both amplified spontaneous emission (ASE) and nonlinear interference noise contributions. This SNR can be approximated as                      SNR 				                   (1) where   denotes the average launched power per channel,   is the total ASE noise of the transmission system,  is the total noise due to the nonlinear signal-signal interactions, and   is the total noise due to NL signal-ASE noise interaction.  For multi-span Nyquist-spaced WDM transmission systems, the total power of the ASE noise due to optical counter-pumped fibre Raman amplification can be calculated as                      ∙ "# ⋅                 (2) where   is the total number of spans in the optical link, 	  is the number of polarisation states,   1.13 is the temperature dependent phonon occupancy factor1, "#  is the average photon energy at the optical carrier frequency,  is the symbol rate of the signal,  represents the spontaneous emission noise photon number3. For dual polarization (DP) Raman-amplified Nyquist-spaced WDM transmission system, the signal-signal NL interference power is defined as4                           () ⋅ *+                      (3) where , is the coherent factor which is between 0 and 1 depending on the decorrelation of NL distortions between each amplifier span4. The NL distortion coefficient *  -W/0  can be effectively modelled as follows            *123 )∆4 	5 13	613789:;8 <⋅∆4789;8 <⋅∆4=         (4) 13  )>?8/@A8	∬ Π 74;484D < E1), /, 3	=)=/G8G8 (5) where H   ⋅ ∆  represents the total WDM transmission bandwidth, ∆  is the channel spacing,  is the fibre NL coefficient, and Π1I3 denotes the rectangular function. Eq. (4) implies the filtering of the PSD 13  in the coherent receiver by a matched filter with a baseband transfer function 613. The WDM channel index is given by the following set 2  JK 1LM)3/ , … ,1LM)3/ O, where  is the total number of WDM channels. E1), /, 3  is the appropriate FWM efficiency factor, taking into account the Raman amplification5. Finally, the signal-ASE noise interference term is given by6   3P ⋅ *	/                   (6) where the factor P  depends on the number of spans and can be approximated as follows              P  QR:;/ SQR:8(/ 	.                       (7) Results and discussions Due to the large bandwidth of the investigated signal, the Raman effect amplifies lower frequencies at the cost of higher frequencies during propagation. In order to prevent a large asymmetric power profile over the individual sub-channels, gain flattening filters will be employed at each span in practical applications. However, here we neglect the power redistribution and cross-talk resulting from intrapulse Raman scattering. The NL distortion coefficient has been numerically computed for the central channel of WDM transmission system and its edges considering the slope of chromatic dispersion.  It can be seen according to the results of numerical calculations in Tab. 2 that the dispersion slope does not have a considerable impact on the NL distortions, e.g., setting T+ to zero gives almost the same results, especially for the center channel. However, taking the slope into consideration substantially reduces the rate of convergence in the numerical integrations. Thus, we can fairly assume the negligibility of the dispersion slope throughout the paper without any significant loss in accuracy.  According to the above assumptions, the NL Tab. 2: NL distortions coefficient (*)  Nonlinear distortion coefficient 1/(mW)2 Ch. Index, 2 -625 0 625 w/ T+ 0.0149 0.0275 0.0149 w/o T+ 0.0125 0.0276 0.0187   Fig. 1: Nonlinear distortion coefficient and SNR in Raman- amplified optical communication system distortion coefficients in the ~100-nm Raman- amplified system have been numerically calculated for individual sub-channels. It can be seen in Fig. 1 that the nonlinear distortion coefficients in the outer channels are lower than those in the central sub-channels, physically due to less inter-channel NL distortion from neighboring channels. The differences become considerable when the channel index is outside the range -500 to +500. The SNR in each individual sub-channel has also been estimated based on the nonlinear distortion coefficients at 25×80 km using EDC, as shown in Fig. 1. In this case, the SNR difference between the central channel and the side channel is ~1 dB. To obtain an indication of the AIR of the system, we compute soft-decision mutual information (MI) based on the Gaussian assumption on the channel. As detailed in7, this MI is an important figure of merit as it is a transmission rate that can be achieved by a receiver based on this Gaussian assumption.  The MI for each individual sub-channel was numerically calculated using Gauss-Hermite quadrature. We considered dual-polarization 64-QAM and 256-QAM, and both EDC and FF-NLC (the latter using ideal full-field digital back-propagation or optical phase conjugation). The obtained results for a transmission distance of 25×80 km are shown in Fig. 2. These results show that FF-NLC gives a significant improvement over EDC for 256-QAM. For 64-QAM the gains are smaller since the MIs for EDC are already close to their maximum value of 12 [bit/symbol].  Finally, to estimate the AIR over the entire bandwidth, the sub-channels were assumed to be independent, and thus, the total AIR was calculated as the sum of the MIs of each channel. Results were obtained for DP-64QAM and DP-256QAM under different transmission distances. These results are presented in Fig. 3 and show a significant improvement of FF-NLC over EDC for both modulation formats. The AIR for DP-256QAM exceeds 150-Tbit/s with linear EDC and 200-Tbit/s with FF-NLC for transmission distances of up to 1600 km. Conclusions The achievable information rates of optical fibre communication systems based on standard SMF and using ~100-nm ultra-wideband optical Raman amplification has been numerically investigated using the first-order perturbative analysis of large-bandwidth NL distortions. The numerical estimations has been carried out for each individual sub-channel in Nyquist-spaced WDM transmission systems. It is estimated that ~100-nm distributed Raman amplification gives the possibility of achieving AIRs of 150-Tbit/s using linear EDC, and 200-Tbit/s using FF-NLC over a transmission distance of 1600 km using DP-256QAM. Acknowledgements This work is supported by UK EPSRC project UNLOC (EP/J017582/1). References [1] R. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol., Vol. 28, no. 4, p. 662 (2010). [2] G. Bosco et al., “Analytical Results on Channel Capacity in Uncompensated Optical Links with Coherent Detection,” Opt. Express, Vol. 19, no. 26, p. B438 (2011). [3] S. R. Chinn, “Analysis of Counter-Pumped Small-Signal Fibre Raman Amplifiers,” Electron. Lett., Vol. 28, no. 7, p. 607 (1997). [4] P. Poggiolini et al., “The GN-Model of Fiber Non-Linear Propagation and its Applications,” J. Lightwave Technol., Vol. 32, no. 4, p. 694 (2014). [5] P. Poggiolini et al., “A Detailed Analytical Derivation of the GN model of Non-Linear Interference in Coherent Optical Transmission Systems,” (2014). Available: http://arxiv.org/abs/1209.0394 [6] D. Rafique, A. D. Ellis, “Impact of Signal-ASE Four-Wave Mixing on the Effectiveness of Digital Back-Propagation in 112 Gb/s PM-QPSK Systems,” Opt. Express, Vol. 19, no. 4, p. 3449 (2011). [7] T. Fehenberger, A. Alvarado, P. Bayvel, N. Hanik, “On Achievable Rates for Long-haul Fiber-Optic Communications,” Opt. Express, Vol. 23, no. 7., p. 9183 (2015).   Fig. 2: Mutual information of individual sub-channels at 25x80 km transmission distance  Fig. 3: Achievable information rates of 100-nm Raman amplified optical transmission system 

Achievable information rates estimation for 100-nm ramana amplified optical transmission system

UCL Discovery

Achievable Information Rates Estimation for 100-nm Raman-Amplified Optical Transmission System Nikita A. Shevchenko, Tianhua Xu*, Daniel Semrau, Gabriel Saavedra, Gabriele Liga, Milen Paskov, Lidia Galdino, Alex Alvarado, Robert I. Killey, Polina Bayvel Optical Networks Group, University College London (UCL), WC1E 7JE, London, United Kingdom, *tianhua.xu@ucl.ac.uk  Abstract The achievable information rates of optical communication systems using ultra-wide bandwidth 100-nm distributed Raman amplification have been investigated for each individual sub-channels, based on the first-order perturbative analysis of nonlinear distortions. Introduction To date, optical fibre communications have achieved unprecedented growth and success over the past three decades and now stand alone as the enabling technology that underpins the global information infrastructure. The data rates of optical communication systems have been raised from 100-Mbit/s per fibre in the 1970s to 10-Tbit/s in current commercial systems, an astonishing 100,000-fold increase. The key technologies that fueled this surge in capacity were wavelength division multiplexing (WDM), improved fibre design and fabrication, optical amplification and coherent detection. The use of Erbium-doped and Raman fibre amplifiers negated the need for electronic regenerators and enabled dense WDM transmission, although the success and performance of these amplifier technologies is seen as limiting the usable fibre bandwidth to approximately 10-15 THz, ultimately limiting the maximum throughput of optical systems. Within the usable optical bandwidth, the increase of the spectral efficiency in Nyquist-spaced WDM systems is determined by the densest constellation that can be used. Denser constellations, however, typically operate well only at high signal-to-noise ratios (SNRs), where high optical launch power is required1. In such schemes, the achievable information rate (AIR) of optical fibre communication systems is essentially limited by nonlinear (NL) distortions due to the optical Kerr effect manifesting itself as self-phase modulation, cross-phase modulation and four-wave mixing (FWM). The AIRs have been evaluated for the total bandwidth of approximately the optical C-band (~4.3-THz) under the key assumption of ideally distributed Raman amplification schemes, while the Raman pump power and the distribution of the optical field-gain along the amplifier span have not been taken into account2. In this paper, for the first time to our knowledge, the AIR of optical communication system using ultra-wideband optical Raman amplification extended to ~100-nm (12.51-THz) optical bandwidth in a standard single mode fiber (SSMF) has been numerically estimated by using a large-bandwidth first-order perturbative analysis of NL distortions. These estimations have been carried out separately for each sub-channel in Nyquist-spaced WDM transmission system. The AIR of the Raman-amplified transmission system with 1251-Channel× 10-GHz using linear electronic dispersion compensation (EDC) and full-field (FF) nonlinear compensation (NLC) has been analysed. A first-order perturbative analysis was implemented to numerically evaluate the NL distortions for each individual sub-channel in Nyquist-spaced WDM transmission system, by removing the assumption of the "whiteness" of the NL distortion spectra. Raman amplified optical system  We examine the backward-pumped geometry of optical Raman amplification. In this model, the Raman power gain is independent of the laser wavelength, and the pump depletion effect is neglected. The AIRs are evaluated in the optical communication system with distributed Raman amplification over ~100-nm (12.51-THz). We consider the transmission consisting of 1251 sub-channels with a symbol rate of 10-Gbaud and a channel spacing of 10-GHz. The detailed Tab. 1: System parameter values  Parameters Values Num. of Channels () 1251 Symbol Rate () 10-Gbaud Channel spacing (∆) 10-GHz Roll-off factor  0% Total Raman pump power (	) 5×680 mW Span length () 80 km Fiber loss () 0.20 dB/km Fiber loss for Raman pump (	) 0.25 dB/km Dispersion () 17.0 ps/nm/km Dispersion slope () 0.067 ps/nm2/km NL coefficient () 1.20 1/W/km  parameters of the optical communication system are indicated in Tab. 1. Analysis of nonlinear distortions for Raman amplified system In optical communications, the performance of the WDM transmission system can be described by an effective SNR including both amplified spontaneous emission (ASE) and nonlinear interference noise contributions. This SNR can be approximated as                      SNR 				                   (1) where   denotes the average launched power per channel,   is the total ASE noise of the transmission system,  is the total noise due to the nonlinear signal-signal interactions, and   is the total noise due to NL signal-ASE noise interaction.  For multi-span Nyquist-spaced WDM transmission systems, the total power of the ASE noise due to optical counter-pumped fibre Raman amplification can be calculated as                      ∙ "# ⋅                 (2) where   is the total number of spans in the optical link, 	  is the number of polarisation states,   1.13 is the temperature dependent phonon occupancy factor1, "#  is the average photon energy at the optical carrier frequency,  is the symbol rate of the signal,  represents the spontaneous emission noise photon number3. For dual polarization (DP) Raman-amplified Nyquist-spaced WDM transmission system, the signal-signal NL interference power is defined as4                           () ⋅ *+                      (3) where , is the coherent factor which is between 0 and 1 depending on the decorrelation of NL distortions between each amplifier span4. The NL distortion coefficient *  -W/0  can be effectively modelled as follows            *123 )∆4 	5 13	613789:;8 <⋅∆4789;8 <⋅∆4=         (4) 13  )>?8/@A8	∬ Π 74;484D < E1), /, 3	=)=/G8G8 (5) where H   ⋅ ∆  represents the total WDM transmission bandwidth, ∆  is the channel spacing,  is the fibre NL coefficient, and Π1I3 denotes the rectangular function. Eq. (4) implies the filtering of the PSD 13  in the coherent receiver by a matched filter with a baseband transfer function 613. The WDM channel index is given by the following set 2  JK 1LM)3/ , … ,1LM)3/ O, where  is the total number of WDM channels. E1), /, 3  is the appropriate FWM efficiency factor, taking into account the Raman amplification5. Finally, the signal-ASE noise interference term is given by6   3P ⋅ *	/                   (6) where the factor P  depends on the number of spans and can be approximated as follows              P  QR:;/ SQR:8(/ 	.                       (7) Results and discussions Due to the large bandwidth of the investigated signal, the Raman effect amplifies lower frequencies at the cost of higher frequencies during propagation. In order to prevent a large asymmetric power profile over the individual sub-channels, gain flattening filters will be employed at each span in practical applications. However, here we neglect the power redistribution and cross-talk resulting from intrapulse Raman scattering. The NL distortion coefficient has been numerically computed for the central channel of WDM transmission system and its edges considering the slope of chromatic dispersion.  It can be seen according to the results of numerical calculations in Tab. 2 that the dispersion slope does not have a considerable impact on the NL distortions, e.g., setting T+ to zero gives almost the same results, especially for the center channel. However, taking the slope into consideration substantially reduces the rate of convergence in the numerical integrations. Thus, we can fairly assume the negligibility of the dispersion slope throughout the paper without any significant loss in accuracy.  According to the above assumptions, the NL Tab. 2: NL distortions coefficient (*)  Nonlinear distortion coefficient 1/(mW)2 Ch. Index, 2 -625 0 625 w/ T+ 0.0149 0.0275 0.0149 w/o T+ 0.0125 0.0276 0.0187   Fig. 1: Nonlinear distortion coefficient and SNR in Raman- amplified optical communication system distortion coefficients in the ~100-nm Raman- amplified system have been numerically calculated for individual sub-channels. It can be seen in Fig. 1 that the nonlinear distortion coefficients in the outer channels are lower than those in the central sub-channels, physically due to less inter-channel NL distortion from neighboring channels. The differences become considerable when the channel index is outside the range -500 to +500. The SNR in each individual sub-channel has also been estimated based on the nonlinear distortion coefficients at 25×80 km using EDC, as shown in Fig. 1. In this case, the SNR difference between the central channel and the side channel is ~1 dB. To obtain an indication of the AIR of the system, we compute soft-decision mutual information (MI) based on the Gaussian assumption on the channel. As detailed in7, this MI is an important figure of merit as it is a transmission rate that can be achieved by a receiver based on this Gaussian assumption.  The MI for each individual sub-channel was numerically calculated using Gauss-Hermite quadrature. We considered dual-polarization 64-QAM and 256-QAM, and both EDC and FF-NLC (the latter using ideal full-field digital back-propagation or optical phase conjugation). The obtained results for a transmission distance of 25×80 km are shown in Fig. 2. These results show that FF-NLC gives a significant improvement over EDC for 256-QAM. For 64-QAM the gains are smaller since the MIs for EDC are already close to their maximum value of 12 [bit/symbol].  Finally, to estimate the AIR over the entire bandwidth, the sub-channels were assumed to be independent, and thus, the total AIR was calculated as the sum of the MIs of each channel. Results were obtained for DP-64QAM and DP-256QAM under different transmission distances. These results are presented in Fig. 3 and show a significant improvement of FF-NLC over EDC for both modulation formats. The AIR for DP-256QAM exceeds 150-Tbit/s with linear EDC and 200-Tbit/s with FF-NLC for transmission distances of up to 1600 km. Conclusions The achievable information rates of optical fibre communication systems based on standard SMF and using ~100-nm ultra-wideband optical Raman amplification has been numerically investigated using the first-order perturbative analysis of large-bandwidth NL distortions. The numerical estimations has been carried out for each individual sub-channel in Nyquist-spaced WDM transmission systems. It is estimated that ~100-nm distributed Raman amplification gives the possibility of achieving AIRs of 150-Tbit/s using linear EDC, and 200-Tbit/s using FF-NLC over a transmission distance of 1600 km using DP-256QAM. Acknowledgements This work is supported by UK EPSRC project UNLOC (EP/J017582/1). References [1] R. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol., Vol. 28, no. 4, p. 662 (2010). [2] G. Bosco et al., “Analytical Results on Channel Capacity in Uncompensated Optical Links with Coherent Detection,” Opt. Express, Vol. 19, no. 26, p. B438 (2011). [3] S. R. Chinn, “Analysis of Counter-Pumped Small-Signal Fibre Raman Amplifiers,” Electron. Lett., Vol. 28, no. 7, p. 607 (1997). [4] P. Poggiolini et al., “The GN-Model of Fiber Non-Linear Propagation and its Applications,” J. Lightwave Technol., Vol. 32, no. 4, p. 694 (2014). [5] P. Poggiolini et al., “A Detailed Analytical Derivation of the GN model of Non-Linear Interference in Coherent Optical Transmission Systems,” (2014). Available: http://arxiv.org/abs/1209.0394 [6] D. Rafique, A. D. Ellis, “Impact of Signal-ASE Four-Wave Mixing on the Effectiveness of Digital Back-Propagation in 112 Gb/s PM-QPSK Systems,” Opt. Express, Vol. 19, no. 4, p. 3449 (2011). [7] T. Fehenberger, A. Alvarado, P. Bayvel, N. Hanik, “On Achievable Rates for Long-haul Fiber-Optic Communications,” Opt. Express, Vol. 23, no. 7., p. 9183 (2015).   Fig. 2: Mutual information of individual sub-channels at 25x80 km transmission distance  Fig. 3: Achievable information rates of 100-nm Raman amplified optical transmission system 

Achievable Information Rates Estimation for 100-nm Raman-Amplified Optical Transmission System

http://discovery.ucl.ac.uk/1539054/1/Xu_Manuscript_Raman_AIR_Final.pdf

Achievable information rates estimation for 100-nm ramana amplified optical transmission system

Abstract

Similar works

Full text

Available Versions

Warwick Research Archives Portal Repository

UCL Discovery