Eigenvalue-based communication technologies using inverse scattering transform (IST) have gained attention as a new transmission strategy in optical fiber communications. In recent years, several studies on artificial neural network (ANN)based equalization and demodulation schemes for eigenvaluemodulated signal have been conducted to enhance the receiver sensitivity. However, in the case of a presence of a carrier frequency offset (CFO) at receiver, the effects of the CFO on ANN receiver of eigenvalue-modulated signal is yet to be reported. In this study, we numerically and experimentally investigated the generalization performances of eigenvalue domain ANN-based demodulator on CFO. Furthermore, we propose to combine an ANN-based demodulator with a CFO compensation method based on IST and a relation between frequency and eigenvalue shifts. The proposed method, based on an appropriate soliton pulse, achieves a high CFO estimation accuracy of submegahertz order even if the CFO reaches ± 2.5 GHz under the noiseless condition. In the presence of noise and a large CFO of 2.5 GHz, the method attains a CFO estimation accuracy below 60 MHz for OSNR=10 dB with a low pilot pulse rate, such as 0.064%. We show the simulation results obtained after applying the proposed CFO compensation to the ANN demodulator, which is valid for 2.5 GHz CFO and long-haul transmission over 5000 km. Experiments performed in this study demonstrate successful demodulation of an eigenvalue-modulated signal with OSNR penalty < 1 dB in the presence of CFO within 1 GHz at 2.5 Gb/s.

We experimentally demonstrate a CFO estimation method in the optical eigen-value domain. A fine CFO estimation of 5.3 MHz with only one soliton pilot pulse of 6.4 ns duration is achieved.

We investigate characteristics of a soliton-assisted CFO estimation method in the optical eigenvalue domain by numerical simulations. The soliton-assisted method demonstrates a high estimation accuracy below 10 MHz with only 64 pilot soliton pulses.

Optical eigenvalue transmission is a promising technique to overcome Kerr nonlinear limits in optical communication systems. The optical eigenvalue associated with the nonlinear Schrödinger equation is invariant during fiber-based nonlinear dispersive transmission. However, the effect of carrier frequency offset (CFO) induces an eigenvalue shift in the presence of the CFO for digitally coherent receivers. The CFO estimation method using eigenvalues capable of achieving highly accurate estimations and can be applied to an eigenvalue transmission system has been proposed. However, a detailed analysis of the eigenvalue-based CFO estimation method is yet to be examined. This study examines the estimation accuracy and limitations of the CFO estimation method through numerical simulations and experiments. The eigenvalue-based method achieves estimation accuracy of less than 10 kHz when the time window size W = 6.4 ns and sampling rate Rs = 20 GSa/s in numerical simulations. Moreover, the estimation error is proportional to energy loss when the time window size W and sampling rate Rs are limited. Through experiments, we achieve a fine estimation accuracy below 1 MHz when W = 12.8 ns and Rs = 5 GSa/s, although the accuracy is limited by the noise effect.