Achievable information rates for nonlinear frequency division multiplexed fibre optic systems

Fibre optic infrastructure is critical to meet the high data rate and long-distance communication requirements of modern networks. Recent developments in wireless communication technologies, such as 5G and 6G, offer the potential for ultra-high data rates and low-latency communication within a single cell. However, to extend this high performance to the backbone network, the data rate of the fibre optics connection between wireless base stations may become a bottleneck due to the capacity crunch phenomena induced by the signal dependent Kerr nonlinear effect. To address this, the nonlinear Fourier transform (NFT) is proposed as a solution to resolve the Kerr nonlinearity and linearise the nonlinear evolution of time domain pulses in the nonlinear frequency domain (NFD) for a lossless and noiseless fibre. Nonlinear frequency division multiplexing (NFDM), which encodes information on NFD using the discrete and continuous spectra revealed by NFT, is also proposed. However, implementing such signalling in an optical amplifier noise-perturbed fibre results in complicated, signal-dependent noise in NFD, the signal-dependent statistics and unknown model of which make estimating the capacity of such a system an open problem. In this thesis, the solitonic part of the NFD, the discrete spectrum is first studied. Modulating the information in the amplitude of soliton pulse, the maximum time-scaled mutual information is estimated. Such a definition allows us to directly incorporate the dependence of soliton pulse width to its amplitude into capacity formulation. The commonly used memoryless channel model based on noncentral chi-squared distribution is initially considered. Applying a variance normalising transform, this channel is approximated by a unit-variance additive white Gaussian noise (AWGN) model. Based on a numerical capacity analysis of the approximated AWGN channel, a general form of capacity-approaching input distributions is determined. These optimal distributions are discrete comprising a mass point at zero (off symbol) and a finite number of mass points almost uniformly distributed away from zero. Using this general form of input distributions, a novel closed-form approximation of the capacity is determined showing a good match to numerical results. A mismatch capacity bounds are developed based on split-step simulations of the nonlinear Schr$\rm \ddot{o}$dinger equation considering both single soliton and soliton sequence transmissions. This relaxes the initial assumption of memoryless channel to show the impact of both inter-soliton interaction and Gordon-Haus effects. Our results show that the inter-soliton interaction effect becomes increasingly significant at higher soliton amplitudes and would be the dominant impairment compared to the timing jitter induced by the Gordon-Haus effect. Next, the intrinsic soliton interaction, Gordon Haus effect and their coupled perturbation on the soliton system are visualised. The feasibility of employing an artificial neural network to resolve the inter-soliton interaction, which is the dominant impairment in higher power regimes, is investigated. A method is suggested to improve the achievable information rate of an amplitude modulated soliton communication system using a classification neural network against the inter-soliton interaction. Significant gain is demonstrated not only over the eigenvalue estimation of nonlinear Fourier transform, but also the continuous spectrum and eigenvalue correlation assisted detection scheme in the literature. Lastly, for the nonsolitonic radiation of the NFT, the continuous spectrum is exploited. An approximate channel model is proposed for direct signalling on the continuous spectrum of a NFDM communication system, describing the effect of noise and nonlinearity at the receiver. The optimal input distribution that maximises the mutual information of the proposed approximated channel under peak amplitude constraint is then studied. We present that, considering the input-dependency of the noise, the conventional amplitude-constrained constellation designs can be shaped geometrically to provide significant mutual information gains. However, it is observed that further probabilistic shaping and constellation size optimisation can only provide limited additional gains beyond the best geometrically shaped counterparts, the 64 amplitude phase shift keying. Then, an approximated channel model that neglects the correlation between subcarriers is proposed for the matched filtered signalling system, based on which the input constellation is shaped geometrically. We demonstrate that, although the inter-subcarrier interference in the filtered system is not included in the channel model, shaping of the matched filtered system can provide promising gains in mismatch capacity over the unfiltered scenario