3 research outputs found
Advanced optical fibre communication via nonlinear Fourier transform
Optical fibre communication using the Nonlinear Fourier transform (NFT) is one of the
potential solutions to tackle the so-called capacity crunch problem in long-haul optical fibre
networks. The NFT transforms the nonlinear propagation of temporal signal, governed by
the nonlinear Schr¨odinger equation (NLSE), into simple linear evolutions of continuous and
discrete spectra in the so-called nonlinear spectral domain. These spectra and the corresponding
nonlinear spectral domain, defined by the NFT, are the generalized counterparts of the linear
spectrum and frequency domain defined by the ordinary Fourier transform. Using the NFT,
the optical fibre channel is effectively linearised, and the basic idea is to utilize degrees of
freedom in the nonlinear spectral domain for data transmission. However, many aspects of this
concept require rigorous investigation due to complexity and infancy of the approach. In this
thesis, the aim is to provide a comprehensive investigation of data transmission over mainly
the continues spectrum (CS) and partly over of the discrete spectrum (DS) of nonlinear optical
fibres. First, an optical fibre communication system is defined, in which solely the CS carries
the information. A noise model in the nonlinear spectral domain is derived for such a system by
asymptotic analysis as well as extensive simulations for different scenarios of practical interest.
It is demonstrated that the noise added to the signal in CS is severely signal-dependent such
that the effective signalling space is limited. The variance normalizing transform (VNT) is used
to mathematically verify the limits of signalling spaces and also estimate the channel capacity.
The numerical results predict a remarkable capacity for signalling only on the CS (e.g., 6
bits/symbol for a 2000-km link), yet it is demonstrated that the capacity saturates at high power.
Next, the broadening effect of chromatic dispersion is analysed, and it is confirmed that some
system parameters, such as symbol rate in the nonlinear spectral domain, can be optimized so
that the required temporal guard interval between the subsequently transmitted data packets
is minimized, and thus the effective data rate is significantly enhanced. Furthermore, three
modified signalling techniques are proposed and analysed based on the particular statistics
of the noise added to the CS. All proposed methods display improved performance in terms of
error rate and reach distance. For instance, using one of the proposed techniques and optimized
parameters, a 7100-km distance can be reached by signalling on the CS at a rate of 9.6 Gbps.
Furthermore, the impact of polarization mode dispersion (PMD) is examined for the first time,
as an inevitable impairment in long-haul optical fibre links. By semi-analytical and numerical
investigation, it is demonstrated that the PMD affects the CS by causing signal-dependent
phase shift and noise-like errors. It is also verified that the noise is still the dominant cause
of performance degradation, yet the effect of PMD should not be neglected in the analysis of
NFT-based systems. Finally, the capacity of soliton communication with amplitude modulation
(part of the degrees of freedom of DS) is also estimated using VNT. For the first time,
the practical constraints, such as the restricted signalling space due to limited bandwidth,
are included in this capacity analysis. Furthermore, the achievable data rates are estimated
by considering an appropriately defined guard time between soliton pulses. Moreover, the
possibility of transmitting data on DS accompanied by an independent CS signalling is also
validated, which confirms the potentials of the NFT approach for combating the capacity
crunch
Investigation into Information Capacity of Nonlinear Optical Fibre Communication Systems
The optical fibre is a ubiquitous transmission medium since it is able to provide both high speed and low loss. Optical fibre transmission systems carry 99% of the world’s telecommunication traffic. The emergence of new services and Internet applications gives rise to the exponentially increasing demand for higher transmission data rates, motivating the search for new methods to enhance the capacity of optical fibre systems. However, due to the presence of power-dependent signal degradation effects (the optical Kerr effects) together with bandwidth limitations constrained by the low-loss region of the fibre, the current optical fibre communication infrastructure is unable to cope with the ever-growing demand for data rates. The capacity of an optical fibre channel remains unknown and is an open research question. The PhD research described in this thesis aimed to theoretically investigate the capacity of the nonlinear optical fibre channel using information-theoretic tools with the view to improving information data rates of optical fibre networks. The first part of the thesis is concerned with a comprehensive study of Kerr nonlinearity-compensated dispersion unmanaged ultra-wide bandwidth optical fibre communication systems. The bounds on information rate, based on the proposed model, which takes into account the fundamental limitations due to nonlinear interactions between optical signal and amplifier noise, were accurately estimated. The second part deals with the application of the so-called integrability property (the general ideas based around nonlinear Fourier transform (NFT)) of a lossless and noiseless nonlinear Schrödinger equation (NLSE). A new non-Gaussian channel model for soliton-based transmission, in which data is assumed to be embedded into the imaginary part of the nonlinear discrete spectrum was proposed for the first time. New asymptotic semi-analytic approximations for non-decaying capacity bounds have been derived. The theoretical results of this research can be considered as an important first step towards the ultimate capacity limits of nonlinear optical communication links
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 Schrdinger 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