Experimental demonstration of a NFDM based optical transmission system 

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Traffic evolution of optical networks

The data traffic demand is expected to sky-rocket over the next few years The latest global Internet Protocol (IP) traffic forecast by Cisco Visual Network Index (VNI) shown in Fig.(1:2) reported a global network traffic of 1.2 zettabytes (ZB), i.e. 1021 bytes, per year, or 96 ExaBytes (EB), i.e. 1018 bytes, per month [32]. The IP traffic is expected to grow with compounded growth rate of 24% per year, resulting in roughly a three-fold increase in traffic over five years. In contrast, web-based applications, video streaming, and cloud computing have forced the short-reach optical link within data centers to grow even larger. The data center IP traffic is already exceeding 10 ZB, and it is expected to grow at 25% per year as shown in Fig.(1:3(a)). The forecasts also projects that by the year 2021, that 71% of the global IP traffic distribution is expected to reside within data centers, while only 14% accounts for user-destined traffic. The remaining 15% will be traffic between data centers, as indicated in Fig.(1:3(b)). This trend will be further stretched by machine-learning applications, whereby significant traffic is dedicated to answer simple queries.

The Optical Fiber Channel

Current high-speed long-haul data transmissions are carried out by optical fiber due to their low loss and large bandwidth when compared with other available waveguides [[1];Ch:2]. In a data communication scenario, optical fibers made of silica (SiO2) glass are the workhorse of the industry. A typical fiber is composed by a cylindrical symmetric waveguide with three main layers, i.e. core, cladding, and external jacket. This structure allows light to mainly propagate inside the core in a guided mode, while a very small evanescent field propagates through the cladding. In order to guide light inside the core, the refractive index of the core is kept slightly higher than that of the cladding. As a result, it becomes possible to propagate light inside a fiber thanks to total internal reflection (TIR). Depending on the index profile, a typical fiber can be classified as either a step-index or a graded-index fiber. Most data transmission networks rely on step-index fibers, that show an abrupt change in the refractive index at the core and cladding interface. The light gathering capability of such fiber, also known as the numerical aperture (N.A.), is defined as where n1 and n2 represent the refractive index of the core and the cladding, respectively. In order to launch the maximum amount of light through the fiber, the value of the N.A. should be made as large as possible. However, as the N.A. increases, the light rays launched into the fiber take different path lengths to arrive at the output end of the fiber. As a result, the pulse at the fiber output exhibits a spreading in the temporal domain, which limits the achievable information rate (AIR) of the optical fiber. Such dispersive pulse spread is minimized by reducing the core radius and the refractive index difference between the core and cladding, so that few rays travel inside the core. Such fibers are called single mode fibers (SMFs) since they only support one spatial mode, also called the fundamental mode. As for today, the vast majority of deployed optical fibers are SMFs. In SMFs, the electric field of light, E, that propagates at a carrier frequency, !0, can be expressed as.

Fiber capacity increment

Communicating through a nonlinear channel, such as an optical fiber, poses many practical and theoretical challenges. Capacity increases were mostly facilitated by improving the fiber quality and the electronics for transmitters and receivers. Coherent detection techniques in combination with a preexisting technologies such as EDFAs and WDM, led to a dramatic increase of the capacity of the fiber channel though accessing every degree of freedom (DoF) available for modulation and multiplexing of optical signals [45]. Fig.1:9 summarizes the five DoF for an electromagnetic wave that propagates in an optical fiber, as proposed in [45]: Time: The time dimension is exploited in the optical time-domain multiplexing (OTDM) technique. OTDM generates a high-speed serial data stream and sends it in temporal succession. Pulse shaping can be used to compress the spectrum of signal pulses subject to fundamental time/frequency constraints. The OTDM technique is fundamentally compatible with modern multi-level quadrature amplitude modulation (QAM) formats and digital coherent detection to increase the achievable information rate.

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Table of contents :

List of Symbols
1 State of the Art of Optical Communication Systems 
1.1 Fiber optic network
1.1.1 Traffic evolution of optical networks
1.2 The Optical Fiber Channel
1.3 Fiber impairments
1.3.1 Fiber loss
1.3.2 Chromatic dispersion
1.3.3 Polarization mode dispersion
1.3.4 Kerr nonlinearity
1.3.5 Optical amplification and noise
1.4 Scalar nonlinear Schrödinger equation
1.5 Coupled nonlinear Schrödinger equation
1.6 Capacity of optical fiber channels
1.6.1 Fiber capacity increment
1.6.2 The nonlinear Shannon limit
1.7 Fiber nonlinearity mitigation
1.7.1 Digital back-propagation
1.7.2 VSTF based nonlinear equalizer
1.8 Summary
2 Optical Transmission Systems based on the Nonlinear Fourier Transform 
2.1 Introduction
2.2 Principle of the nonlinear Fourier transform
2.3 Theory of the nonlinear Fourier transform
2.4 Numerical method for computing the NFT
2.4.1 Numerical Forward NFT using the AL-discretization method
2.4.2 Numerical Inverse NFT using the LP method
2.5 Nonlinear Frequency Division Multiplexed Systems
2.6 NFT of polarization division multiplexed signal
2.7 Summary
3 Experimental demonstration of a NFDM based optical transmission system 
3.1 Introduction
3.2 Brief review of the coherent optical OFDM transmissions
3.3 Experimental generation, transmission and detection of NFDM signal
3.3.1 NFDM signal generation
3.3.2 Optical modulator
3.3.3 Amplified Optical fiber transmission link
3.3.4 Coherent receiver
3.3.5 NFDM signal detection
3.4 NFDM digital transmitter design
3.4.1 Modulation and symbol mapping
3.4.2 Baseband signal generation
3.4.3 Guard interval insertion
3.4.4 Forward mapping
3.4.5 Signal denormalization
3.5 NFDM digital receiver design
3.5.1 Time synchronization
3.5.2 Carrier frequency offset compensation
3.5.3 Signal normalization
3.5.4 NFT computation and channel inversion
3.5.5 Spectral demapping and guard interval removal
3.5.6 Residual channel equalization
3.5.7 Laser phase noise compensation
3.5.8 Data decoding and performance measurement
3.6 Experimental Validation
3.6.1 Experimental demonstration of a single-polarization NFDM transmission
3.6.2 Experimental demonstration of a dual-polarization NFDM transmission
3.6.3 NFDM comparison in the normal and anomalous dispersion regime
3.7 Conclusions
4 Practical challenges in NFDM implementation 
4.1 Simulation setup
4.1.1 Physical constraints
4.1.2 NFDM signal dimensioning
4.2 Intrinsic physical challenges
4.2.1 Noisy channel
4.2.2 Gaussian pulse propagation in a noisy fiber channel .
4.2.3 Transmission of a 16QAM NFDM signal
4.2.4 Lossy channel
4.3 Optical challenges
4.3.1 Frequency Offset and Laser Phase Noise
4.3.2 Transmission analysis of laser phase noise penalty
4.4 DSP implementation and transmission device issues
4.4.1 Guard interval and spectral efficiency
4.4.2 Oversampling and numerical accuracy
4.5 Transmitter and receiver limitations
4.5.1 TX and RX limitation in B2B performance
4.5.2 TX and RX limitation in transmission performance
4.6 Summary
5 Conclusions and Future Work 
5.1 Conclusion
5.2 Future Work


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