Fiber-Optic Communication via the Nonlinear Fourier Transform

In future optical communication systems more and more data has to be transmitted, e.g. due to the increasing popularity of on-demand streaming of high-resolution audio and video formats or an increasing amount of machine-to-machine (M2M) communication. As the achievable rates of modern transmission systems seem to saturate, it is necessary to consider alternative approaches for fiber optic data transmission. In recent years, many publications have explored possibilities to overcome this phenomenon, commonly known as 'capacity crunch', by using the nonlinear Fourier transform (NFT).

By means of the nonlinear Fourier transform, signals propagating according to an intricate interplay between dispersion and nonlinear effects, captured by the nonlinear Schrödinger equation can be described by their respective nonlinear Fourier spectra in the nonlinear Fourier domain (or generalized frequency domain). As a result, the channel affects the nonlinear frequency components only by a multiplicative term. In an ideal case, this decouples the nonlinear spectral components during propagation and makes compensation at the receiver trivial.

However, the NFT relies on the integrability of the underlying channel model, which does not include loss or noise terms. This impairments are not negligible in real systems, thus strategies to deal with these realistic system impairments have to be studied if NFT-aided optical transmission systems are to be considered as a successor for the existing wave division multiplexing (WDM) approach.

These considerations regarding realistic transmission systems are of central interest for my research. I study realistic models for coherent detection optical transmission systems using the nonlinear Fourier transform for design and detection of the transmitted waveforms. This includes considerations regarding hardware impairments, the influence of realistic optical amplification schemes and the search for optimized transmission and detection schemes, also utilizing methods from other research areas such as clustering and coding.