Nonlinear Fourier transform using multistage perturbation technique for fiber-optic systems

Abstract

In nonlinear frequency division multiplexed systems, inverse nonlinear Fourier transform (INFT) and nonlinear Fourier transform (NFT) are applied at the transmitter and receiver, respectively, so as to minimize the impact of fiber nonlinear effects. Typically, the INFT is applied at the digital signal processing of the transmitter to the individual channels of a wavelength division multiplexed (WDM) system, and these channels are linearly multiplexed using the wavelength-division multiplexer. Hence, currently, NFT-based systems suffer from nonlinear impairments due to other channels of a WDM system. This problem can be alleviated if the signals are nonlinearly multiplexed/demultiplexed using INFT and NFT in the optical domain, which is hard to achieve. In this paper, we develop a novel multistage perturbation technique to realize the NFT as the cascade of linear discrete Fourier transforms. Since all-optical discrete Fourier transforms have been implemented in silicon photonics, the proposed approach provides a promising way to implement the NFT in the optical domain. The other challenge in real time implementation of the NFT-based system is the computational complexity of the NFT. In this paper, we develop a novel nonlinear discrete Fourier transform algorithm to realize NFT. When the signal energy is small, the NFT can be evaluated by the single stage second- or third-order perturbation methods. However, as the signal energy increases, we show that the single stage technique is not accurate and the multistage perturbation technique provides reasonably accurate results for high energy signals. The number of stages required depends on the signal energy and desired accuracy. Modifying the fast Fourier transform (FFT) algorithm, the computational cost of the NFT based on the multistage perturbation technique is found to be O(KN log2 N/K), where N is the number of signal samples and K is the number of stages. An advantage of the proposed approach is that the computation can be split into FFTs of smaller lengths, which can be processed on K parallel processors. The computational cost per processor is O(N log2 N/K).