Optimal Nonlinear Spectral Back Rotation for Discrete Eigenvalue Transmission Systems

Nonlinear frequency division multiplexing (NFDM) provides interference-free transmission in lossless and noiseless fiber up to a phase rotation in the nonlinear spectrum and hence signal recovery using a simple phase back rotation will suffice. However, amplified spontaneous emission (ASE) noise distorts both the discrete eigenvalues and nonlinear spectrum of the signal, reducing the effectiveness of this simple back rotation method. We propose back rotating the nonlinear spectral phase by only half of the transmission distance as a computationally simple impairment compensation algorithm for discrete eigenvalue transmission systems. We analytically prove its optimality and show that it is equivalent to the linear minimum mean square error (LMMSE) algorithm in terms of its ability to eliminate the correlations between the discrete eigenvalues and b-coefficient and hence its performance but with lower complexity and no need to use training data to determine the filter coefficients in the LMMSE algorithm. Analytical, numerical, and experimental results are presented to verify the proposed algorithm. We also discussed the influence of possible non-ideal factors in practical systems affecting the proposed scheme.