Johnson SU Distribution in Uncompensated QPSK Coherent Optical Transmission Systems

Abstract

In this paper, we investigate the statistical distribution of the received quadrature-phase shift keying (QPSK) signal components after propagation in a dispersion uncompensated coherent optical fiber link. The Gaussianity of the received QPSK signal is measured with two well-known Gaussian tests, the Anderson-Darling and the Jarque-Bera tests. Results of tests show that, when increasing the launch power, the received signal distribution starts to deviate from Gaussian. Recently, Johnson $\mathrm{S}_{U}$ distribution is proposed for performance evaluation of coherent optical orthogonal frequency-division multiplexing systems. We show that a good approximation is also provided by the Johnson $\mathrm{S}_{U}$ distribution in uncompensated QPSK coherent optical transmission systems. In particular, symbol error rate (SER) is derived based on the Johnson $\mathrm{S}_{U}$ distribution, obtaining performance estimations close to those achieved through accurate Monte-Carlo simulations based on the split-step Fourier method. It is also demonstrated that, in the nonlinear region, Johnson $\mathrm{S}_{U}$ distribution provides a more accurate power prediction than the one obtained using the Gaussian approximation.