A New Non-Gaussian Performance Evaluation Method in Uncompensated Coherent Optical Transmission SystemsUniversity of Birjand
: Optical Communication
Seyed Sadra Kashef
Coherent optical fiber link,
Johnson s_U distribution,
nonlinear transmission performance,
In this paper, the statistical distribution of the received quadrature amplitude modulation (QAM) signal components is analyzed after propagation in a dispersion uncompensated coherent optical fiber link. Two Gaussian tests, the Anderson-Darling and the Jarque-Bera have been used to measure the distance from the Gaussian distribution. By increasing the launch power, the received signal distribution starts to deviate from Gaussian. This deviation can have significant effects in system performance evaluation. The use of the Johnson s_U distribution is proposed for the performance evaluation of orthogonal frequency division multiplexing in an uncompensated coherent optical system. Here, the Johnson s_U is extended to predict the performance of multi-subcarrier and also single carrier systems with M-QAM signals. In particular, symbol error rate is derived based on the Johnson s_U distribution and performance estimations are verified through accurate Monte-Carlo simulations based on the split-step Fourier method. In addition, a new formulation for the calculation of signal to noise ratio is presented, which is more accurate than those proposed in the literature. In the linear region, the Johnson based estimations are the same as Gaussian; however, in the nonlinear region, Johnson s_U distribution power prediction is more accurate than the one obtained using the Gaussian approximation, which is verified by the numerical results.
 P. Poggiolini and Y. Jiang, "Recent advances in the modeling of the impact of nonlinear fiber propagation effects on uncompensated coherent transmission systems," Journal of Lightwave Technology, Vol. 35, No 3, 2017, pp. 458-480.
 P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, F. Forghieri, "The GN model of fiber non-linear propagation and its applications," Journal of Lightwave Technology, Vol. 32, No. 4, 2014, pp. 694-721.
 P. Poggiolini, Y. Jiang, A. Carena, F. Forghieri, Analytical Modeling of the Impact of fber Non-Linear Propagation on Coherent Systems and Networks, in Enabling Technologies for High Spectral-effciency Coherent Optical Communication Networks, Xiang Zhou, Chongjin Xie editors, chapter 7, pp. 247-310, ISBN: 978-1-118-71476-8, Wiley, Hoboken (NewJersey), 2016.
 R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, "Capacity limits of optical fiber networks," Journal of Lightwave Technology, Vol. 28, No 4, 2010, pp. 662–701.
 G. P. Agrawal, Nonlinear fiber optics, Academic Press, 2007.
 L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Transaction on Communication, Vol. 60, No 11, 2012, pp. 3440-3450.
 R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Properties of nonlinear noise in long, dispersion-uncompensated fiber links,” Optics Express, Vol. 21, No 22, 2013, pp. 25685-25699.
 A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” Journal of Lightwave Technology, Vol. 30, No 10, 2012, pp.1524-1539.
 P. Serena, A. Bononi, and N. Rossi, “The impact of the modulation dependent nonlinear interference missed by the gaussian noise model,” ECOC 2014.
 S. T. Le, K. J. Blow, V. K. Mezentsev, and S. K. Turitsyn, “Bit error rate estimation methods for QPSK CO-OFDM transmission,” Journal of Lightwave Technology, Vol. 32, No 17, 2014, pp. 2951-2959.
 S. S. Kashef, P. Azmi, G. Bosco, M.D. Matinfar, and D. Pilori, “NonGaussian Statistics of CO-OFDM Signals after Non-Linear Optical Fiber Transmission,” IET optoelectronics, Vol. 12, No 3, 2017, pp. 150 – 155.
 A. Carena, G. Bosco, V. Curri,Y. Jiang, P. Poggiolini, and F. Forghieri, “On the accuracy of the GN-model and on analytical correction terms to improve it,” arXiv preprint arXiv:1401.6946, 2014.
 G. Gao, X. Chen, and W. Shieh, “Analytical expressions for nonlinear transmission performance of coherent optical OFDM systems with frequency guard band,” IEEE Photonics Technology Letters, Vol. 30, No 15, 2012, pp. 2447-2454.
 D. Uzunidis, C. Matrakidis, and A. Stavdas,“An improved model for estimating the impact of FWM in coherent optical systems,” Optics Communications, Vol. 378, 2016, pp. 22-27.#3
 A. Carena, G. Bosco, V. Curri, Y. Jiang, P. Poggiolini, and F, Forghieri, “EGN model of non-linear fiber propagation,” Optics Express, Vol. 22, No 13, 2014, pp. 16335-16362.
 S. S. Kashef and P. Azmi, “Performance Analysis of Nonlinear Fiber Optic in CO-OFDM Systems with High Order Modulations,” IEEE Photonics Technology Letters, Vol. 30, No 8, 2018, pp. 696-699.
 S. S. Kashef, G. Bosco, and P. Azmi, “Johnson S U Distribution in Uncompensated QPSK Coherent Optical Transmission Systems.” ICEE, 2019, pp. 1284-1288.
 D. Uzunidis, C. Matrakidis, and A. Stavdas, “Analytical FWM expressions for coherent optical transmission systems,” Journal of Lightwave Technology, Vol. 35, No13, 2017, pp. 2734-2740.
 D. Uzunidis, C. Matrakidis, and A. Stavdas, “Closed-form FWM expressions accounting for the impact of modulation format,” Optics Communications, Vol. 440, 2019, pp.132-138.
 F. P. Guiomar, A. Carena, G. Bosco, L. Bertignono, A. Nespola, and P. Poggiolini, “Nonlinear mitigation on subcarrier-multiplexed PM-16QAM optical systems,” Optics Express, Vol. 25, No 4, 2017, pp. 4298-4311.
 F. Buchali, W. Idler, K. Schuh, L. Schmalen, T. Eriksson, G. Bcherer, P. Schulte, and F. Steiner, “Study of electrical subband multiplexing at 54 GHz modulation bandwidth for 16QAM and probabilistically shaped 64QAM,” ECOC, 2016, pp. 4951.
 R. D'Agostino, Goodness-of-fit-techniques, Routledge, 2017.
 C.M. Jarque, and A. K. Bera, “A test for normality of observations and regression residuals,” International Statistical Review/Revue Internationale de Statistique, 1987, pp. 163-172.
 A. Carena, V. Curri, G. Bosco, P. Poggiolini, F. Forghieri, “Modeling of the Impact of Non-Linear Propagation Effects in Uncompensated Optical Coherent Transmission Links,” Journal of Lightwave Technology, Vol. 30, No 10, 2012, pp. 1524-1539.
 P. Jenneve, P. Ramantanis, J.C. Antona, G. de Valicourt, M. Mestre, H. Mardoyan, and S. Bigo, “Pitfalls of error estimation from measured nongaussian nonlinear noise statistics over dispersion-unmanaged systems,” ECOC 2014.
 W. P. Elderton and N. L. Johnson, Systems of frequency curves, Cambridge University Press London, 1969.
 I. D. Hill, R. Hill, R. L. Holder,“Algorithm AS 99: Fitting Johnson curves by moments,” J. the royal statistical society. Series C (Applied statistics), vol. 25, no. 2, 1976, pp 180-189.