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Traffic evolution of optical networks
According to the Cisco visual indexing report [1], the global Internet Protocol (IP) traffic will increase nearly threefold between 2015 and 2020, which corresponds to a compound annual growth rate (CAGR) of 22%. This exponential growth is mainly due to the expansion of the Internet, the huge amount of video streams and modern technologies such as cloud services, telepresence and social networks. By the year 2020, the number of devices connected to IP networks will be three times as high as the global population of the planet and the traffic generated by smartphones will exceed personal-computers (PC) traffic. The report indicates that the IP traffic is more important in Asia-Pacific region and North America then Europe. The IP traffic in Middle East and Africa is the lowest, however it is growing very fast with a CAGR of 41% between 2015 and 2020 (see Fig. 1.1).
To feed the traffic growing hunger, future optical networks also need to be developed to provide an infrastructure capable of welcoming all these requirements and avoid a capacity crunch.
Capacity evolution of optical fiber systems
The continuous capacity growth of optical systems since 1970 was possible thanks to the many physical dimensions that the optical fiber can afford. Five physical dimensions mostly known as degrees of freedom (DoF) allowed new multiplexing strategies and high spectral efficiency modulation formats which increased the throughput. These DoF are shown in Fig. 1.2:
1. Amplitude: In the first generation of optical systems, only the amplitude of the electromagnetic waves was used. The intensity modulation (IM) along with direct detection (DD) allowed to reach a capacity of 10 Gb/s. However, IM/DD systems operating at 40 Gb/s were not massively deployed because of a considerable sensitivity to propagation impairments mainly chromatic dispersion (CD) and polarization mode dispersion (PMD). Furthermore these systems also required high OSNR levels to reach the same distances as the 10 Gb/s systems.
2. Quadrature: The introduction of coherent detection allowed the access to the amplitude and also the phase of the electromagnetic wave. The latter was no longer a scalar but became a complex with real and imaginary parts. Consequently, the traditional On-Off keying (OOK) was replaced by more spectrally efficient modulation formats such as the quadrature-phase shift keying (QPSK) and the quadratureamplitude modulation (QAM). Later on, more sophisticated modulations such as probabilistic shaping of QAM [7] were proposed to increase the system throughput.
Propagation in multi-mode fibers
To cope with the exponential growth in the demand for more bandwidth and to afford an optical capacity that will support future data traffic, space division multiplexing (SDM) is being intensively investigated as the last physical dimension unused in optical fiber transmission systems. In fact, optical systems based single-mode fibers have already used time, phase, frequency and polarization in order to increase network capacity. Unfortunately these single-mode transmission systems have already reached their non-linear Shannon limit [33, 34]. Hence space is the last available degree of freedom to increase optical network bandwidth and avoid a capacity crunch.Space division multiplexing can be realized either by multi-core fibers (MCFs) which are fibers with many cores or few-mode fibers (FMFs) that support the propagation of a small number of modes. In the case of FMFs, space multiplexing is referred to as mode division multiplexing (MDM). Mode multiplexers/demultiplexers (MUX/DEMUX) are mandatory to inject and extract the set of spatial modes in and out of the FMF. Also fewmode optical amplifiers should enable the amplifications of modes simultaneously without separating them. After detection of modes by coherent receivers, digital signal processing is required in order to jointly or separately process modes according to the level of coupling. The number of propagating modes in FMFs depends on the characteristics of the fiber through the normalized frequency V given by equation 1.6. Each exact spatial mode represents a specific solution to the wave equation taking into account the boundary limits. However these modes can be combined to form a set of M linearly polarized (LP) modes where each mode has two polarizations. For step-index fibers, the spatial distributions of LP modes can be approximated by Bessel functions. For graded-index fibers a Laguerre- Gauss representation describes better the spatial distribution of modes. By using the linearly polarized representation, a spatial mode is denoted LPlq where l is the azimuthal order and q is the radial order of the mode. When l 6=0, a mode has two orthogonal spatial distributions known as degenerates and denoted as LPlq,a and LPlq,b. MDM consists in modulating each mode with independent data information, hence the capacity of the optical link is increased by the number of modes. In real systems, propagation through FMFs is also affected by impairments that require either optical or DSP compensation. In addition to physical impairments such as chromatic dispersion or polarization mode dispersion also present in single-mode fiber systems, propagating modes in FMFs suffer from additional effects caused by the simultaneous propagation of modes in the same fiber. First, modes travel at different velocities which causes a differential mode group delay (DMGD) that needs to be addressed in the design of the fiber line. Moreover, modes are also subject to unitary linear coupling that can be compensated by appropriate DSP at the receiver. Linear modal coupling can also be non-unitary known as mode dependent loss (MDL), in this case, it impacts directly the capacity and performance of MDM systems. In the next sections, we focus on these different effects and their impact on the performance.
Table of contents :
Glossary
List of Figures
List of Tables
General Introduction
1 Evolution of Optical Transmission Systems
1.1 The optical network: Traffic evolution and technologies to cope with it
1.1.1 Traffic evolution of optical networks
1.1.2 Capacity evolution of optical fiber systems
1.2 Principle of optical transmitter and receiver
1.2.1 Optical transmitter
1.2.2 Modulation formats
1.2.3 From Direct detection to coherent detection
1.3 Propagation in single mode fibers
1.3.1 Transmission loss
1.3.2 Chromatic dispersion
1.3.3 Polarization division multiplexing
1.3.4 Polarization mode dispersion
1.3.5 Polarization dependent loss
1.3.6 Non-linear effects
1.3.7 Optical amplification
1.4 Propagation in multi-mode fibers
1.4.1 Linear modal coupling
1.4.2 Differential mode group delay
1.4.3 Mode dependent loss
1.4.4 Mode multiplexers and demultiplexers
1.5 MIMO digital signal processing for MDM systems
1.5.1 Time-domain equalization
1.5.2 Frequency-domain equalization
2 Capacity of Mode Division Multiplexed Optical Systems Impaired by MDL
2.1 Capacity analysis of communication systems
2.1.1 Mutual information and Shannon capacity
2.1.2 Capacity of MIMO systems
2.2 Capacity of MDM systems in the presence of MDL
2.2.1 Spliced MDM channel model based FMF
2.2.2 Average and outage capacities of MDM optical channel impaired by MDL
2.3 Capacity enhancement of MDM optical systems using mode scrambling
2.3.1 MDM channel model including mode scramblers
2.3.2 Deterministic mode scrambling
2.4 Capacity enhancement of MDM systems using mode selection
2.4.1 Antenna selection for MIMO wireless communications
2.4.2 Mode selection for MDM optical systems
3 Space-Time Coding for MDL Mitigation in MDM Optical Systems
3.1 Space-Time coding for wireless MIMO channels
3.1.1 Error probability upper bound of space-time coded Rayleigh fading channels
3.1.2 Space-Time block codes
3.1.3 Decoding of MIMO systems
3.2 Space-Time coding for MDM optical systems impaired by MDL
3.2.1 Error probability upper bound of ST coded MDM optical systems
3.2.2 Design criterion and performance analysis
3.3 FEC and ST coding concatenation for MDM optical systems impaired by MDL
3.3.1 Preliminaries on FEC
3.3.2 Concatenation of ST codes and FEC for MDL mitigation in MDM systems
4 Realization of a ST coded MDM transmission in Experiment
4.1 OFDM for optical communications
4.1.1 Optical OFDM transmitter
4.1.2 Optical OFDM receiver
4.2 Mode division multiplexed system with both polarizations
4.2.1 Channel model
4.2.2 Performance analyses of combined effects of PDL and MDL
4.2.3 ST coding for MDM systems with both polarizations
4.3 Experimental demonstration of ST coding for MDL mitigation
4.3.1 Experimental setup
4.3.2 Transmitter overview
4.3.3 Optical link and receiver overview
4.3.4 Experimental results
Conclusions & Outlook
A Condensed French Version
A.1 Introduction g´en´erale
A.1.1 ´Evolution de la capacit´e des r´eseaux optiques
A.1.2 Motivations et contributions de la th`ese
A.2 Augmentation de la capacit´e des syst`emes de transmission optiques `a multiplexage modal
A.2.1 Mod`ele canal des syst`emes optiques `a multiplexage modal
A.2.2 Capacit´e des syst`emes MDM affect´es par la MDL
A.2.3 Augmentation de la Capacit´e des syst`emes MDM par les brouilleurs de modes
A.2.4 Augmentation de la Capacit´e des syst`emes MDM par la s´election de modes
A.3 Codage Espace-Temps pour les syst`emes optiques `a multiplexage modal
A.3.1 Canal optique MDM en pr´esence de la MDL
A.3.2 Crit`ere de construction de codes ST pour le canal optique MDM
A.3.3 Validation exp´erimentale du codage ST pour les syst`emes MDM
A.4 Conclusions
Bibliography
