Multi-Eigenvalue Demodulation Using Complex Moment-Based Eigensolver and Neural Network

Optical eigenvalues originating in optical solitons are the potential for becoming information carriers not affected by chromatic dispersion and nonlinear effects in optical fibers. They are obtained by attributing the associated eigenvalue equations deduced by solving the nonlinear Schrödinger equation with inverse scattering transform (IST) to the matrix eigenvalue problem, and maintaining constant values regardless of the transmission distance. The eigenvalue communication systems require to solve the eigenvalues in soliton-by-soliton. While effective eigenvalue solution methods have not been studied well in telecommunication systems, one of the most well-known eigenvalue solution methods is the QZ decomposition-based method. However, the QZ algorithm requires a large complexity. To reduce the complexity, a method to demodulate the optical eigenvalues using a complex-moment eigenvalue solver (CME) was investigated. CME is a parallelizable eigenvalue solver that can extract any eigenvalue. This paper proposes a novel optical eigenvalue demodulation method that combines CME and an artificial neural network (ANN) based on employing an on-off encoded discrete eigenvalue modulation scheme. The ANN is sensitive to the input order of the units; therefore, the eigenvalues must be sorted. A lightweight sorting algorithm is hence required. In addition to the proposed scheme, this study proposes partial sorting using CME and ANN. Here, 2000 km fiber-transmission experiments for an on-off-encoded four-discrete-eigenvalue were conducted. The experimental results indicated that the proposed demodulation method obtained bit error rate (BER) characteristics comparable to conventional methods by devising an extraction range of eigenvalues in CME.