Design and Analysis for Multilevel-Modulated Signal Using the Scattering Coefficient $b$ in Inverse Scattering Transform

Multilevel modulation schemes based on the inverse scattering transform (IST) are some of the promising technologies for achieving a significant advancement in transmission capacity within optical fiber communication systems overcoming the nonlinear Shannon limit. Despite the recognized potential of multilevel modulation using the scattering coefficient$b$to enhance the transmission capacity, previous studies assumed that the distributions of eigenvalues and$b$follow a Gaussian distribution for the signal point assignment. Because the distributions of eigenvalues and$b$do not exactly follow a Gaussian distribution, signal design considering these distributions is to be studied. In this paper, we propose a novel signal point arrangement method for the$b$-modulation considering the distribution to maximize transmission capacity. The amplitude and argument of$b$correspond to the temporal center position$T_{c}$and phase$\theta$of the soliton component, respectively. Therefore, we arrange the signal points of the$b$-modulation after converting the coefficient$b$from the$b$-plane to the$T_{c}$-$\theta$-plane in this paper. Through numerical simulations in the back-to-back configuration, we demonstrate that the proposed method improves the bit error rate (BER) performance by approximately 10–12 dB compared with a conventional signal point assignment method such as QAM. Moreover, the result of the transmission simulation demonstrates that the proposed method can extend the achievable transmission distance by 1000–3000 km. Furthermore, by performing the analysis of the noise characteristics of$b$on the$T_{c}$-$\theta$-plane, the estimation accuracy of the generalized mutual information can be improved in the$b$modulation scheme. The proposed scheme is expected to be applied to high-capacity and long-haul optical fiber transmission systems overcoming the nonlinear Shannon limit.